TSTP Solution File: SWW275+1 by Bliksem---1.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWW275+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n022.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 300.05s 300.53s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWW275+1 : TPTP v8.1.0. Released v5.2.0.
% 0.03/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n022.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % DateTime : Sat Jun 4 15:32:21 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.96/1.57 *** allocated 10000 integers for termspace/termends
% 0.96/1.57 *** allocated 10000 integers for clauses
% 0.96/1.57 *** allocated 10000 integers for justifications
% 0.96/1.57 *** allocated 15000 integers for termspace/termends
% 0.96/1.57 *** allocated 22500 integers for termspace/termends
% 0.96/1.57 *** allocated 33750 integers for termspace/termends
% 0.96/1.57 Bliksem 1.12
% 0.96/1.57
% 0.96/1.57
% 0.96/1.57 Automatic Strategy Selection
% 0.96/1.57
% 0.96/1.57 *** allocated 50625 integers for termspace/termends
% 0.96/1.57 *** allocated 75937 integers for termspace/termends
% 0.96/1.57 *** allocated 113905 integers for termspace/termends
% 0.96/1.57
% 0.96/1.57 Clauses:
% 0.96/1.57
% 0.96/1.57 { ! hAPP( Y, skol1( X, Y ) ) = hAPP( X, skol1( X, Y ) ), Y = X }.
% 0.96/1.57 { ! v_n = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.57 { ! v_na____ = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.57 { ! v_qa____ = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.96/1.57 tc_Complex_Ocomplex ) ) }.
% 0.96/1.57 { ! c_Polynomial_Oorder( tc_Complex_Ocomplex, v_a____, v_pa____ ) =
% 0.96/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.57 { ! v_pa____ = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.96/1.57 tc_Complex_Ocomplex ) ) }.
% 0.96/1.57 { ! v_k____ = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.96/1.57 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Oorder(
% 0.96/1.57 tc_Complex_Ocomplex, X, v_pa____ ), v_na____ ) }.
% 0.96/1.57 { v_s____ = c_Polynomial_OpCons( tc_Complex_Ocomplex, v_k____,
% 0.96/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) )
% 0.96/1.57 ) }.
% 0.96/1.57 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Oorder(
% 0.96/1.57 tc_Complex_Ocomplex, v_a____, v_pa____ ), v_na____ ) }.
% 0.96/1.57 { v_pa____ = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly
% 0.96/1.57 ( tc_Complex_Ocomplex ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.96/1.57 tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ), c_Polynomial_OpCons(
% 0.96/1.57 tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex
% 0.96/1.57 , v_a____ ), c_Polynomial_OpCons( tc_Complex_Ocomplex,
% 0.96/1.57 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ),
% 0.96/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) )
% 0.96/1.57 ) ) ), c_Polynomial_Oorder( tc_Complex_Ocomplex, v_a____, v_pa____ ) ) )
% 0.96/1.57 , v_s____ ) }.
% 0.96/1.57 { v_qa____ = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly
% 0.96/1.57 ( tc_Complex_Ocomplex ) ), c_Polynomial_OpCons( tc_Complex_Ocomplex,
% 0.96/1.57 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, v_a____ ),
% 0.96/1.57 c_Polynomial_OpCons( tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(
% 0.96/1.57 tc_Complex_Ocomplex ), c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.96/1.57 tc_Complex_Ocomplex ) ) ) ) ), v_r____ ) }.
% 0.96/1.57 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), v_a____ ) =
% 0.96/1.57 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.96/1.57 { c_Polynomial_Odegree( tc_Complex_Ocomplex, v_pa____ ) = v_na____ }.
% 0.96/1.57 { v_pa____ = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly
% 0.96/1.57 ( tc_Complex_Ocomplex ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.96/1.57 tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ), c_Polynomial_OpCons(
% 0.96/1.57 tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex
% 0.96/1.57 , v_a____ ), c_Polynomial_OpCons( tc_Complex_Ocomplex,
% 0.96/1.57 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ),
% 0.96/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) )
% 0.96/1.57 ) ) ), c_Polynomial_Oorder( tc_Complex_Ocomplex, v_a____, v_pa____ ) ) )
% 0.96/1.57 , skol2 ) }.
% 0.96/1.57 { ! v_s____ = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.96/1.57 tc_Complex_Ocomplex ) ) }.
% 0.96/1.57 { c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( tc_Complex_Ocomplex ),
% 0.96/1.57 hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly(
% 0.96/1.57 tc_Complex_Ocomplex ) ), c_Polynomial_OpCons( tc_Complex_Ocomplex,
% 0.96/1.57 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, v_a____ ),
% 0.96/1.57 c_Polynomial_OpCons( tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(
% 0.96/1.57 tc_Complex_Ocomplex ), c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.96/1.57 tc_Complex_Ocomplex ) ) ) ) ), c_Polynomial_Oorder( tc_Complex_Ocomplex,
% 0.96/1.57 v_a____, v_pa____ ) ), v_pa____ ) }.
% 0.96/1.57 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.57 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.57 c_Groups_Ozero__class_Ozero( X ), Z ), ! c_Orderings_Oord__class_Oless(
% 0.96/1.57 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), T ),
% 0.96/1.57 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.57 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.96/1.57 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.96/1.57 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.96/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.96/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.96/1.57 { ! class_Power_Opower( X ), ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 0.96/1.57 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) =
% 0.96/1.57 c_Groups_Oone__class_Oone( X ) }.
% 0.96/1.57 { ! class_Power_Opower( X ), Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.96/1.57 , hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) = hAPP( hAPP(
% 0.96/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.96/1.57 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ominus__class_Ominus(
% 0.96/1.57 tc_Nat_Onat, Z, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 0.96/1.57 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.57 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.96/1.57 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 0.96/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), hAPP(
% 0.96/1.57 hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.96/1.57 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.57 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.96/1.57 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.57 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.96/1.57 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.96/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 0.96/1.57 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.57 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.96/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.96/1.57 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.57 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.96/1.57 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.96/1.57 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.57 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.96/1.57 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.57 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.96/1.57 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.96/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 0.96/1.57 { ! class_Rings_Olinordered__semidom( X ), !
% 0.96/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 0.96/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.96/1.57 ), ! c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oone__class_Oone
% 0.96/1.57 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.57 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.96/1.57 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 0.96/1.57 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 0.96/1.57 c_Power_Opower__class_Opower( X ), T ), Z ) = hAPP( hAPP(
% 0.96/1.57 c_Power_Opower__class_Opower( X ), Y ), Z ), !
% 0.96/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.96/1.57 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.96/1.57 X ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ), T = Y }.
% 0.96/1.57 { c_Polynomial_Odegree( tc_Complex_Ocomplex, v_s____ ) =
% 0.96/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.57 { ! hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_p ), X ) =
% 0.96/1.57 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), hAPP(
% 0.96/1.57 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q ), X ) =
% 0.96/1.57 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.96/1.57 { ! hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), X ) =
% 0.96/1.57 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), hAPP(
% 0.96/1.57 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_qa____ ), X ) =
% 0.96/1.57 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.96/1.57 { c_Polynomial_Odegree( tc_Complex_Ocomplex, v_p ) = v_n }.
% 0.96/1.57 { c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( tc_Complex_Ocomplex ),
% 0.96/1.57 c_Polynomial_OpCons( tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus
% 0.96/1.57 ( tc_Complex_Ocomplex, v_a____ ), c_Polynomial_OpCons(
% 0.96/1.57 tc_Complex_Ocomplex, c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ),
% 0.96/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) )
% 0.96/1.57 ) ), v_qa____ ) }.
% 0.96/1.57 { ! v_qa____ = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.96/1.57 tc_Complex_Ocomplex ) ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly(
% 0.96/1.57 tc_Complex_Ocomplex ), v_pa____, hAPP( hAPP( c_Power_Opower__class_Opower
% 0.96/1.57 ( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ), v_qa____ ), v_na____ ) )
% 0.96/1.57 }.
% 0.96/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, v_na____ ), ! hAPP(
% 0.96/1.57 c_Polynomial_Opoly( tc_Complex_Ocomplex, Z ), skol3( T, Z ) ) =
% 0.96/1.57 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), !
% 0.96/1.57 c_Polynomial_Odegree( tc_Complex_Ocomplex, Y ) = X, X =
% 0.96/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 0.96/1.57 tc_Polynomial_Opoly( tc_Complex_Ocomplex ), Y, hAPP( hAPP(
% 0.96/1.57 c_Power_Opower__class_Opower( tc_Polynomial_Opoly( tc_Complex_Ocomplex )
% 0.96/1.57 ), Z ), X ) ) }.
% 0.96/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, v_na____ ), hAPP(
% 0.96/1.57 c_Polynomial_Opoly( tc_Complex_Ocomplex, Y ), skol3( Y, Z ) ) =
% 0.96/1.57 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), !
% 0.96/1.57 c_Polynomial_Odegree( tc_Complex_Ocomplex, Y ) = X, X =
% 0.96/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 0.96/1.57 tc_Polynomial_Opoly( tc_Complex_Ocomplex ), Y, hAPP( hAPP(
% 0.96/1.57 c_Power_Opower__class_Opower( tc_Polynomial_Opoly( tc_Complex_Ocomplex )
% 0.96/1.57 ), Z ), X ) ) }.
% 0.96/1.57 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.57 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) = X }.
% 0.96/1.57 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 0.96/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), Y =
% 0.96/1.57 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.96/1.57 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 0.96/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X =
% 0.96/1.57 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.96/1.57 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.96/1.57 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Groups_Oone__class_Oone(
% 0.96/1.57 tc_Nat_Onat ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.96/1.57 , Y ), X ) }.
% 0.96/1.57 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.96/1.57 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 0.96/1.57 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.96/1.57 c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y = c_Groups_Oone__class_Oone(
% 0.96/1.57 tc_Nat_Onat ) }.
% 0.96/1.57 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.96/1.57 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X = c_Groups_Oone__class_Oone(
% 0.96/1.57 tc_Nat_Onat ) }.
% 0.96/1.57 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.96/1.57 c_Groups_Oone__class_Oone( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.96/1.57 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.96/1.57 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X )
% 0.96/1.57 , X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y =
% 0.96/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.57 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.96/1.57 Y ), c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 0.96/1.57 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.96/1.57 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.96/1.57 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.96/1.57 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z = X
% 0.96/1.57 , Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.57 { ! Z = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.96/1.57 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }
% 0.96/1.57 .
% 0.96/1.57 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.96/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.96/1.57 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.96/1.57 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Y = X
% 0.96/1.57 , Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.57 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.96/1.57 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.96/1.57 .
% 0.96/1.57 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.96/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.96/1.57 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.96/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.96/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.96/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.57 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.96/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.57 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.96/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.57 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.96/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.96/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.57 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) =
% 0.96/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.57 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.96/1.57 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.96/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 0.96/1.57 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.96/1.57 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) }.
% 0.96/1.57 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.96/1.57 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.96/1.57 tc_Nat_Onat ) ) = Y }.
% 0.96/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.96/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.96/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), T ), hAPP( hAPP(
% 0.96/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.96/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.96/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.96/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP(
% 0.96/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.96/1.57 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 0.96/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 0.96/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) ) }.
% 0.96/1.57 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 0.96/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) }.
% 0.96/1.57 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.96/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.96/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.96/1.57 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.96/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) =
% 0.96/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.96/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.96/1.57 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.96/1.57 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), Y ), !
% 0.96/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, U, Z ),
% 0.96/1.57 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.96/1.57 ), T ), U ), Y ) }.
% 0.96/1.57 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.96/1.57 Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, U, T ),
% 0.96/1.57 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.96/1.57 ), Z ), U ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ) ) }
% 0.96/1.57 .
% 0.96/1.57 { ! class_Rings_Ocomm__semiring__1( X ), !
% 0.96/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ),
% 0.96/1.57 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.96/1.57 ), T ), Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ) ) }
% 0.96/1.57 .
% 0.96/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.57 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 0.96/1.57 ( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Z ), hAPP( hAPP
% 0.96/1.57 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ),
% 0.96/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.96/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.57 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.96/1.57 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), X =
% 0.96/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.57 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.57 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.96/1.57 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.96/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.57 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 0.96/1.57 ), X ) ) }.
% 0.96/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.96/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.57 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.96/1.57 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP
% 0.96/1.57 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.96/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.96/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.57 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.96/1.57 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP
% 0.96/1.57 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.96/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.96/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.96/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.57 tc_Nat_Onat ), Y ) }.
% 0.96/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.96/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.96/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X ) }.
% 0.96/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.57 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.96/1.57 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.96/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.96/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.96/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 0.96/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.57 tc_Nat_Onat ), Z ) }.
% 0.96/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.96/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 0.96/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.96/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.57 ( tc_Nat_Onat ), Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 0.96/1.57 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.96/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.96/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.57 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.96/1.57 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 0.96/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.57 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.96/1.57 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.96/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.57 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 0.96/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.57 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.57 Y ), X ) ) }.
% 0.96/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.96/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), !
% 0.96/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.57 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X
% 0.96/1.57 ) }.
% 0.96/1.57 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.57 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 0.96/1.57 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 0.96/1.57 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.96/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ),
% 0.96/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.96/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.96/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.96/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 0.96/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.57 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 0.96/1.57 ) }.
% 0.96/1.57 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.57 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 0.96/1.57 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 0.96/1.57 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.96/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.96/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.96/1.57 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Orderings_Oord__class_Oless(
% 0.96/1.57 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 0.96/1.57 c_Rings_Odvd__class_Odvd( X, Y, hAPP( hAPP( c_Power_Opower__class_Opower
% 0.96/1.57 ( X ), Y ), Z ) ) }.
% 0.96/1.57 { ! class_Rings_Ocomm__semiring__1( X ), ! Y = c_Groups_Oone__class_Oone( X
% 0.96/1.57 ), c_Rings_Odvd__class_Odvd( X, Y, hAPP( hAPP(
% 0.96/1.57 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.96/1.57 { alpha38( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 0.96/1.57 hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.96/1.57 { alpha38( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP
% 0.96/1.57 ( X, Y ), Z ) ) }.
% 0.96/1.57 { ! alpha38( X, Y, Z ), alpha40( X, Y, Z ), Z = Y }.
% 0.96/1.57 { ! alpha38( X, Y, Z ), alpha40( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z
% 0.96/1.57 ) ) }.
% 0.96/1.57 { ! alpha40( X, Y, Z ), alpha38( X, Y, Z ) }.
% 0.96/1.57 { ! Z = Y, hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha38( X, Y, Z ) }.
% 0.96/1.57 { ! alpha40( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y )
% 0.96/1.57 }.
% 0.96/1.57 { ! alpha40( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.96/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ), hBOOL( hAPP( hAPP(
% 0.96/1.57 X, Y ), Z ) ), alpha40( X, Y, Z ) }.
% 0.96/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.96/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X = Y }.
% 0.96/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.96/1.57 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.96/1.57 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.96/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.96/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.96/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.96/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.96/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ), Y = X }.
% 0.96/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.96/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 0.96/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ) }.
% 0.96/1.57 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.96/1.57 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ) }.
% 0.96/1.57 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, X ) }.
% 0.96/1.57 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.96/1.57 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.96/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ), Y ) }.
% 0.96/1.57 { ! class_Rings_Oring__1__no__zero__divisors( X ), Y =
% 0.96/1.57 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.96/1.57 c_Power_Opower__class_Opower( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 0.96/1.57 ( X ) }.
% 0.96/1.57 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.96/1.57 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.96/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.96/1.57 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.57 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.96/1.57 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.96/1.57 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.96/1.57 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.57 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 0.96/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.96/1.57 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.96/1.57 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.96/1.57 c_Power_Opower__class_Opower( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.96/1.57 = c_Groups_Oone__class_Oone( X ) }.
% 0.96/1.57 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.96/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.57 tc_Nat_Onat ), X ) }.
% 0.96/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X =
% 0.96/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.96/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.96/1.57 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.96/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.57 tc_Nat_Onat ), X ) }.
% 0.96/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.57 ( tc_Nat_Onat ), X ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 0.96/1.57 .
% 0.96/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.96/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.96/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.96/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 0.96/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.57 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.96/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.96/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.96/1.57 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.96/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.96/1.57 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.96/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 0.96/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.96/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.96/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.96/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.96/1.57 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.96/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.96/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.96/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 0.96/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.96/1.57 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.96/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.96/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.96/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.96/1.57 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, X ) =
% 0.96/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.57 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 0.96/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = X }.
% 0.96/1.57 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.57 tc_Nat_Onat ), X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.96/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 0.96/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.96/1.57 ( tc_Nat_Onat, Z, X ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.96/1.57 ) }.
% 0.96/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.96/1.57 ( tc_Nat_Onat, Y, Z ), X ) }.
% 0.96/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.96/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.96/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 0.96/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ),
% 0.96/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ) }.
% 0.96/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.96/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.96/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 0.96/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 0.96/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 0.96/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.96/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ),
% 0.96/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.96/1.57 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.96/1.57 ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) }.
% 0.96/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.96/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.96/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.96/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X = Z }.
% 0.96/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.96/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), ! X = Z,
% 0.96/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.96/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) }.
% 0.96/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 0.96/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = Y }.
% 0.96/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, Z ),
% 0.96/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) }.
% 0.96/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ),
% 0.96/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 0.96/1.57 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ), Y ) }.
% 0.96/1.57 { ! class_Rings_Olinordered__semidom( X ), !
% 0.96/1.57 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.96/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.96/1.57 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.57 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.96/1.57 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.96/1.57 { ! class_Rings_Olinordered__semidom( X ), !
% 0.96/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.96/1.57 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.96/1.57 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.96/1.57 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.57 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless
% 0.96/1.57 ( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.96/1.57 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.96/1.57 { ! class_Rings_Olinordered__semidom( X ), !
% 0.96/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), Y )
% 0.96/1.57 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.96/1.57 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.96/1.57 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.96/1.57 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.96/1.57 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.96/1.57 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.96/1.57 .
% 0.96/1.57 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.96/1.57 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.96/1.57 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.96/1.57 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.57 tc_Nat_Onat ) }.
% 0.96/1.57 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.96/1.57 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.96/1.57 , ! Z = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 0.96/1.57 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y )
% 0.96/1.57 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.57 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.57 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! hAPP( hAPP(
% 0.96/1.57 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 0.96/1.57 c_Power_Opower__class_Opower( X ), Y ), Z ), T = Z }.
% 0.96/1.57 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.57 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! T = Z, hAPP( hAPP(
% 0.96/1.57 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 0.96/1.57 c_Power_Opower__class_Opower( X ), Y ), Z ) }.
% 0.96/1.57 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.96/1.57 , Y ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.96/1.57 c_Groups_Oone__class_Oone( X ) }.
% 0.96/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.57 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 0.96/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.96/1.57 ( tc_Nat_Onat, Y, X ), Y ) }.
% 0.96/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.57 ( tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 0.96/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.96/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ),
% 0.96/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.57 tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 0.96/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.96/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.57 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.96/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.96/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.96/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.96/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.96/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.96/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.96/1.57 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.96/1.57 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ) }.
% 0.96/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.96/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.96/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 0.96/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.96/1.57 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.96/1.57 ) }.
% 0.96/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.96/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ),
% 0.96/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.96/1.57 ( tc_Nat_Onat, Y, Z ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z )
% 0.96/1.57 ) }.
% 0.96/1.57 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.57 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP
% 0.96/1.57 ( c_Power_Opower__class_Opower( X ), Y ), T ) ), !
% 0.96/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.96/1.57 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.96/1.57 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.57 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.96/1.57 X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ), hAPP( hAPP(
% 0.96/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.96/1.57 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.96/1.57 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.57 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.96/1.57 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.96/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.96/1.57 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.96/1.57 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), ! Y =
% 0.96/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.57 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.96/1.57 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.96/1.57 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), Y =
% 0.96/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.57 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.96/1.57 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.57 { ! class_Rings_Oring__1( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.96/1.57 ), c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 0.96/1.57 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.57 c_Power_Opower__class_Opower( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.96/1.57 c_Groups_Oone__class_Oone( X ) ) ), Y ) ), hAPP( hAPP(
% 0.96/1.57 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.96/1.57 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.57 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.96/1.57 c_Groups_Oone__class_Oone( X ), T ), c_Orderings_Oord__class_Oless( X,
% 0.96/1.57 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.57 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.96/1.57 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.57 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.96/1.57 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.96/1.57 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.96/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.96/1.57 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.57 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.96/1.57 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.96/1.57 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.96/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.96/1.57 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.57 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.96/1.57 ( tc_Nat_Onat, T, Z ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.57 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.96/1.57 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.96/1.57 { ! class_Rings_Olinordered__semidom( X ), !
% 0.96/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 0.96/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), T )
% 0.96/1.57 , c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.57 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.57 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.96/1.57 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.57 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.96/1.57 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.96/1.57 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.96/1.57 c_Power_Opower__class_Opower( X ), Y ), Z ) ), hAPP( hAPP(
% 0.96/1.57 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.96/1.57 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.57 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.96/1.57 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 0.96/1.57 , T, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.96/1.57 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.96/1.57 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 0.96/1.57 { v_qa____ = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly
% 0.96/1.57 ( tc_Complex_Ocomplex ) ), c_Polynomial_OpCons( tc_Complex_Ocomplex,
% 0.96/1.57 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, v_a____ ),
% 0.96/1.57 c_Polynomial_OpCons( tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(
% 0.96/1.57 tc_Complex_Ocomplex ), c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.96/1.57 tc_Complex_Ocomplex ) ) ) ) ), skol4 ) }.
% 0.96/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( tc_Complex_Ocomplex ),
% 0.96/1.57 hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly(
% 0.96/1.57 tc_Complex_Ocomplex ) ), c_Polynomial_OpCons( tc_Complex_Ocomplex,
% 0.96/1.57 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, v_a____ ),
% 0.96/1.57 c_Polynomial_OpCons( tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(
% 0.96/1.57 tc_Complex_Ocomplex ), c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.96/1.57 tc_Complex_Ocomplex ) ) ) ) ), c_Nat_OSuc( c_Polynomial_Oorder(
% 0.96/1.57 tc_Complex_Ocomplex, v_a____, v_pa____ ) ) ), v_pa____ ) }.
% 0.96/1.57 { ! class_Rings_Oidom( X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly(
% 0.96/1.57 X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) )
% 0.96/1.57 , c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.96/1.57 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 0.96/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ),
% 0.96/1.57 c_Polynomial_Oorder( X, Z, Y ) ), Y ) }.
% 0.96/1.57 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.96/1.57 ( X ), c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 0.96/1.57 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.96/1.57 tc_Polynomial_Opoly( X ) ) ) ), Y ), hAPP( c_Polynomial_Opoly( X, Y ),
% 0.96/1.57 c_Groups_Ouminus__class_Ouminus( X, Z ) ) = c_Groups_Ozero__class_Ozero(
% 0.96/1.57 X ) }.
% 0.96/1.57 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Y ),
% 0.96/1.57 c_Groups_Ouminus__class_Ouminus( X, Z ) ) = c_Groups_Ozero__class_Ozero(
% 0.96/1.57 X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ),
% 0.96/1.57 c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 0.96/1.57 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.96/1.57 tc_Polynomial_Opoly( X ) ) ) ), Y ) }.
% 0.96/1.57 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.96/1.57 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd(
% 0.96/1.57 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X,
% 0.96/1.57 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Polynomial_OpCons( X,
% 0.96/1.57 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.96/1.57 tc_Polynomial_Opoly( X ) ) ) ), Z ) }.
% 0.96/1.57 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.96/1.57 ( X ), c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.96/1.57 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 0.96/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ), Z ), hAPP(
% 0.96/1.57 c_Polynomial_Opoly( X, Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.57 { v_s____ = c_Polynomial_OpCons( tc_Complex_Ocomplex, skol5,
% 0.96/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) )
% 0.96/1.57 ) }.
% 0.96/1.57 { v_s____ = c_Polynomial_OpCons( tc_Complex_Ocomplex, skol6,
% 0.96/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) )
% 0.96/1.57 ) }.
% 0.96/1.57 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless(
% 0.96/1.57 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), hAPP( hAPP
% 0.96/1.57 ( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.57 c_Power_Opower__class_Opower( X ), Z ), c_Groups_Ominus__class_Ominus(
% 0.96/1.57 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ), Z ) =
% 0.96/1.57 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) }.
% 0.96/1.57 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Odegree( X, hAPP(
% 0.96/1.57 hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ),
% 0.96/1.57 c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 0.96/1.57 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.96/1.57 tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ) = Y }.
% 0.96/1.57 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.96/1.57 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 0.96/1.57 tc_Polynomial_Opoly( X ) ), ! c_Polynomial_Oorder( X, Y, Z ) =
% 0.96/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.57 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.96/1.57 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.96/1.57 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.57 { ! class_Rings_Oidom( X ), c_Polynomial_Oorder( X, Y, Z ) =
% 0.96/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( c_Polynomial_Opoly( X,
% 0.96/1.57 Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.57 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Y,
% 0.96/1.57 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.57 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, c_Nat_OSuc(
% 0.96/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) }.
% 0.96/1.57 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( X ) ) }.
% 0.96/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.96/1.57 X ) ) }.
% 0.96/1.57 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.57 tc_Nat_Onat ), c_Nat_OSuc( X ) ) }.
% 0.96/1.57 { ! X = c_Nat_OSuc( X ) }.
% 0.96/1.57 { ! c_Nat_OSuc( X ) = X }.
% 0.96/1.57 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP
% 0.96/1.57 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.96/1.57 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 0.96/1.57 { ! Y = X, c_Nat_OSuc( Y ) = c_Nat_OSuc( X ) }.
% 0.96/1.57 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 0.96/1.57 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 0.96/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.96/1.57 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z
% 0.96/1.57 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.57 c_Nat_OSuc( Z ) ), X ), Y = X }.
% 0.96/1.57 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.57 c_Nat_OSuc( Z ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.96/1.57 tc_Nat_Onat ), c_Nat_OSuc( Z ) ), X ) }.
% 0.96/1.57 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 0.96/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.96/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X = c_Nat_OSuc(
% 0.96/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.96/1.57 { ! X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 0.96/1.57 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.96/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.96/1.57 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.96/1.57 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.96/1.57 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 0.96/1.57 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.57 { ! class_Groups_Oab__group__add( X ), c_Polynomial_Odegree( X,
% 0.96/1.57 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) =
% 0.96/1.57 c_Polynomial_Odegree( X, Y ) }.
% 0.96/1.57 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.96/1.57 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.96/1.57 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.57 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.57 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.96/1.57 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.57 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.96/1.57 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y = c_Nat_OSuc
% 0.96/1.57 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.96/1.57 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.96/1.57 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X = c_Nat_OSuc
% 0.96/1.57 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.96/1.57 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.96/1.57 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.96/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 0.96/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.96/1.57 { ! hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) =
% 0.96/1.57 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 0.96/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = c_Nat_OSuc(
% 0.96/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.96/1.57 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.57 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 0.96/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.96/1.57 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP(
% 0.96/1.57 hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc
% 0.96/1.57 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.96/1.57 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), c_Nat_OSuc(
% 0.96/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) = c_Nat_OSuc(
% 0.96/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.96/1.57 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 0.96/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), !
% 0.96/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.96/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.96/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.96/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.96/1.57 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) )
% 0.96/1.57 }.
% 0.96/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 0.96/1.57 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.96/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.96/1.57 X ) ) }.
% 0.96/1.57 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.96/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y = X }
% 0.96/1.57 .
% 0.96/1.57 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X,
% 0.96/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.96/1.57 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.96/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), X = Y }
% 0.96/1.57 .
% 0.96/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.96/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) = X
% 0.96/1.57 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.96/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.96/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 0.96/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) }.
% 0.96/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.96/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.96/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.96/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.96/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 0.96/1.57 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.96/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.96/1.57 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.96/1.57 ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.96/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.96/1.57 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.96/1.57 ), X ) ) }.
% 0.96/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), X ) }
% 0.96/1.57 .
% 0.96/1.57 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) }.
% 0.96/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ), !
% 0.96/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.96/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.96/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 0.96/1.57 ) }.
% 0.96/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.96/1.57 { ! Y = c_Nat_OSuc( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 0.96/1.57 , c_Nat_OSuc( X ) ) }.
% 0.96/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 0.96/1.57 c_Nat_OSuc( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X )
% 0.96/1.57 }.
% 0.96/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 0.96/1.58 c_Nat_OSuc( X ) ) }.
% 0.96/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.96/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 0.96/1.58 ) }.
% 0.96/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.96/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.96/1.58 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.96/1.58 ), X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.96/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.96/1.58 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.96/1.58 ), X ) ) }.
% 0.96/1.58 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.96/1.58 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ), c_Rings_Odvd__class_Odvd(
% 0.96/1.58 tc_Nat_Onat, Y, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) }.
% 0.96/1.58 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Groups_Oone__class_Oone(
% 0.96/1.58 tc_Nat_Onat ) ), X = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.96/1.58 { ! X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd
% 0.96/1.58 ( tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.96/1.58 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.96/1.58 X ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 0.96/1.58 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.96/1.58 ( tc_Nat_Onat, c_Nat_OSuc( Z ), Y ), c_Nat_OSuc( X ) ) =
% 0.96/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.96/1.58 ( tc_Nat_Onat, Z, Y ), X ) }.
% 0.96/1.58 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), hAPP( hAPP(
% 0.96/1.58 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.96/1.58 c_Nat_OSuc( Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.58 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.96/1.58 , Z ), c_Nat_OSuc( c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.96/1.58 ) ) ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc(
% 0.96/1.58 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), Z = Y, Z =
% 0.96/1.58 c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.96/1.58 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 0.96/1.58 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 0.96/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP(
% 0.96/1.58 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 0.96/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.96/1.58 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.96/1.58 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc(
% 0.96/1.58 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP
% 0.96/1.58 ( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 0.96/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.96/1.58 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.96/1.58 , Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.96/1.58 , Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.96/1.58 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.96/1.58 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.58 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) }.
% 0.96/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.58 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y
% 0.96/1.58 ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.96/1.58 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.58 tc_Nat_Onat ), Z ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.96/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.58 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( skol7( X ) ) }.
% 0.96/1.58 { ! X = c_Nat_OSuc( Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.96/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.96/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X =
% 0.96/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.58 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.96/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.96/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.96/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y =
% 0.96/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha1( X, Y ) }.
% 0.96/1.58 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.96/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.96/1.58 { ! alpha1( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.96/1.58 c_Nat_OSuc( X ) ) }.
% 0.96/1.58 { ! alpha1( X, Y ), Y = c_Nat_OSuc( skol8( Z, Y ) ) }.
% 0.96/1.58 { ! alpha1( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol8( X, Y
% 0.96/1.58 ), X ) }.
% 0.96/1.58 { ! Y = c_Nat_OSuc( Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.96/1.58 ), alpha1( X, Y ) }.
% 0.96/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.96/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.96/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.96/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.96/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.96/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.96/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.96/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.96/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.96/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.96/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.96/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.96/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.96/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.96/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.96/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) }.
% 0.96/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.96/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.96/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) }.
% 0.96/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.96/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.96/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.96/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.96/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.96/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.96/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.96/1.58 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ) }.
% 0.96/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.96/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.96/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.96/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.96/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.96/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.96/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.96/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.96/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.96/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.96/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X = Y }
% 0.96/1.58 .
% 0.96/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X = Y,
% 0.96/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 0.96/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.96/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.96/1.58 { c_Groups_Oone__class_Oone( tc_Nat_Onat ) = c_Nat_OSuc(
% 0.96/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.96/1.58 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, c_Groups_Ominus__class_Ominus
% 0.96/1.58 ( tc_Nat_Onat, Y, X ) ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y )
% 0.96/1.58 , ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ),
% 0.96/1.58 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ) }.
% 0.96/1.58 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, c_Groups_Ominus__class_Ominus
% 0.96/1.58 ( tc_Nat_Onat, Y, X ) ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X )
% 0.96/1.58 , ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ),
% 0.96/1.58 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.96/1.58 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.96/1.58 ( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) ) }.
% 0.96/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) =
% 0.96/1.58 c_Nat_OSuc( c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.96/1.58 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 0.96/1.58 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 0.96/1.58 { ! class_Groups_Ozero( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat
% 0.96/1.58 , c_Polynomial_Odegree( X, c_Polynomial_OpCons( X, Z, Y ) ), c_Nat_OSuc(
% 0.96/1.58 c_Polynomial_Odegree( X, Y ) ) ) }.
% 0.96/1.58 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.58 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, c_Polynomial_OpCons
% 0.96/1.58 ( X, Z, Y ) ) = c_Nat_OSuc( c_Polynomial_Odegree( X, Y ) ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__semidom( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.96/1.58 ), ! c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone
% 0.96/1.58 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.58 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ), Y ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__semidom( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.58 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ), hAPP( hAPP(
% 0.96/1.58 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ) ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.96/1.58 ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 0.96/1.58 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ) = hAPP( hAPP(
% 0.96/1.58 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.96/1.58 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.96/1.58 X ), Y ), Z = Y }.
% 0.96/1.58 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.58 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.96/1.58 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.96/1.58 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ) ) }.
% 0.96/1.58 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.96/1.58 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, c_Polynomial_OpCons
% 0.96/1.58 ( X, Y, Z ) ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.58 { ! class_Groups_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 0.96/1.58 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, c_Polynomial_OpCons
% 0.96/1.58 ( X, Y, Z ) ) = c_Nat_OSuc( c_Polynomial_Odegree( X, Z ) ) }.
% 0.96/1.58 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.58 tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 0.96/1.58 ) }.
% 0.96/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.58 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 0.96/1.58 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ), Y =
% 0.96/1.58 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.96/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.58 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 0.96/1.58 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ) }.
% 0.96/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.58 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 0.96/1.58 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ), Y =
% 0.96/1.58 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.96/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.58 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 0.96/1.58 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ) }.
% 0.96/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.58 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.96/1.58 tc_Nat_Onat, X, c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) )
% 0.96/1.58 ) ) = X }.
% 0.96/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.58 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X ) }.
% 0.96/1.58 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.58 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.96/1.58 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ) ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 0.96/1.58 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 0.96/1.58 ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__idom( X ), Z = Y,
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.96/1.58 X, Y, Z ) }.
% 0.96/1.58 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.96/1.58 Y ), ! c_Rings_Odvd__class_Odvd( X, Y, T ), c_Rings_Odvd__class_Odvd( X,
% 0.96/1.58 Z, T ) }.
% 0.96/1.58 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Y, Y
% 0.96/1.58 ) }.
% 0.96/1.58 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 0.96/1.58 c_Polynomial_OpCons( X, Z, Y ), U = Z }.
% 0.96/1.58 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 0.96/1.58 c_Polynomial_OpCons( X, Z, Y ), T = Y }.
% 0.96/1.58 { ! class_Groups_Ozero( X ), ! U = Z, ! T = Y, c_Polynomial_OpCons( X, U, T
% 0.96/1.58 ) = c_Polynomial_OpCons( X, Z, Y ) }.
% 0.96/1.58 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 0.96/1.58 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ), Z = Y }.
% 0.96/1.58 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Z = Y,
% 0.96/1.58 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.58 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.58 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ),
% 0.96/1.58 c_Groups_Oone__class_Oone( X ) ) }.
% 0.96/1.58 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.96/1.58 tc_Nat_Onat, Z, Y ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ),
% 0.96/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) ) = hAPP
% 0.96/1.58 ( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.58 c_Power_Opower__class_Opower( X ), T ), c_Groups_Ominus__class_Ominus(
% 0.96/1.58 tc_Nat_Onat, Y, Z ) ) ), T ) }.
% 0.96/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.58 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.96/1.58 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) = X }.
% 0.96/1.58 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.58 tc_Polynomial_Opoly( X ) ), ! c_Rings_Odvd__class_Odvd(
% 0.96/1.58 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.96/1.58 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.96/1.58 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 0.96/1.58 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.96/1.58 tc_Polynomial_Opoly( X ) ) ) ) ), c_Nat_OSuc( c_Polynomial_Oorder( X, Z,
% 0.96/1.58 Y ) ) ), Y ) }.
% 0.96/1.58 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.58 tc_Polynomial_Opoly( X ) ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.96/1.58 ( X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X )
% 0.96/1.58 ), c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.96/1.58 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 0.96/1.58 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ),
% 0.96/1.58 c_Polynomial_Oorder( X, Z, Y ) ), Y ) }.
% 0.96/1.58 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.58 tc_Polynomial_Opoly( X ) ), ! c_Rings_Odvd__class_Odvd(
% 0.96/1.58 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.96/1.58 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.96/1.58 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 0.96/1.58 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.96/1.58 tc_Polynomial_Opoly( X ) ) ) ) ), c_Nat_OSuc( c_Polynomial_Oorder( X, Z,
% 0.96/1.58 Y ) ) ), Y ) }.
% 0.96/1.58 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.58 ( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) =
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.58 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.58 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) =
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.58 { ! class_Rings_Oring__no__zero__divisors( X ), ! hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.96/1.58 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.58 { ! class_Rings_Oring__no__zero__divisors( X ), ! Z =
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.58 { ! class_Rings_Oring__no__zero__divisors( X ), ! Y =
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.58 { ! class_Rings_Ono__zero__divisors( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.58 X ), Z = c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) =
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.58 { ! class_Rings_Ono__zero__divisors( X ), ! hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.96/1.58 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.58 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Oone__class_Oone( X ) =
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.58 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.96/1.58 c_Groups_Oone__class_Oone( X ) }.
% 0.96/1.58 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ), Y ), Y = c_Groups_Ozero__class_Ozero( X
% 0.96/1.58 ) }.
% 0.96/1.58 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 0.96/1.58 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.96/1.58 ( X, Y ) ) }.
% 0.96/1.58 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 0.96/1.58 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.96/1.58 ) ), Y ) }.
% 0.96/1.58 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.96/1.58 , c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.96/1.58 ( X, Y ) ) }.
% 0.96/1.58 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.96/1.58 , c_Groups_Ouminus__class_Ouminus( X, Z ) ),
% 0.96/1.58 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 0.96/1.58 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.96/1.58 ), Z ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 0.96/1.58 Z = Y, Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.96/1.58 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.96/1.58 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.96/1.58 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.96/1.58 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Z,
% 0.96/1.58 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.96/1.58 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Z,
% 0.96/1.58 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.96/1.58 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.96/1.58 Y ), c_Rings_Odvd__class_Odvd( X, Z, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.96/1.58 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.96/1.58 Y ), c_Rings_Odvd__class_Odvd( X, Z, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.96/1.58 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.96/1.58 Y ), ! c_Rings_Odvd__class_Odvd( X, U, T ), c_Rings_Odvd__class_Odvd( X,
% 0.96/1.58 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.96/1.58 { ! class_Rings_Odvd( X ), ! Z = hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.58 ( X ), Y ), T ), c_Rings_Odvd__class_Odvd( X, Y, Z ) }.
% 0.96/1.58 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.96/1.58 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), Y ),
% 0.96/1.58 c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 0.96/1.58 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.96/1.58 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ),
% 0.96/1.58 c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 0.96/1.58 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X,
% 0.96/1.58 c_Groups_Oone__class_Oone( X ), Y ) }.
% 0.96/1.58 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 0.96/1.58 , ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X, Z,
% 0.96/1.58 c_Groups_Ominus__class_Ominus( X, Y, T ) ) }.
% 0.96/1.58 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.96/1.58 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Rings_Odvd__class_Odvd( X, Z
% 0.96/1.58 , Y ) }.
% 0.96/1.58 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 0.96/1.58 , c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.96/1.58 ) }.
% 0.96/1.58 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.96/1.58 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ), c_Rings_Odvd__class_Odvd( X
% 0.96/1.58 , Z, Y ) }.
% 0.96/1.58 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 0.96/1.58 , c_Rings_Odvd__class_Odvd( X, c_Groups_Ouminus__class_Ouminus( X, Z ), Y
% 0.96/1.58 ) }.
% 0.96/1.58 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 0.96/1.58 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, U, T ),
% 0.96/1.58 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 0.96/1.58 c_Groups_Ominus__class_Ominus( X, U, Z ), c_Groups_Ominus__class_Ominus(
% 0.96/1.58 tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 0.96/1.58 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.96/1.58 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 0.96/1.58 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.96/1.58 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) }.
% 0.96/1.58 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.96/1.58 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 0.96/1.58 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.96/1.58 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) }.
% 0.96/1.58 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Odegree( X,
% 0.96/1.58 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ) =
% 0.96/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.58 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 0.96/1.58 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.96/1.58 c_Groups_Oone__class_Oone( X ) }.
% 0.96/1.58 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 0.96/1.58 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.96/1.58 c_Groups_Ominus__class_Ominus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 0.96/1.58 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.96/1.58 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 0.96/1.58 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ) ), Y ) =
% 0.96/1.58 c_Groups_Ouminus__class_Ouminus( X, hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 0.96/1.58 ) }.
% 0.96/1.58 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 0.96/1.58 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 0.96/1.58 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y =
% 0.96/1.58 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.58 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Y =
% 0.96/1.58 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.96/1.58 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 0.96/1.58 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.96/1.58 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.96/1.58 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.96/1.58 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.58 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 0.96/1.58 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.96/1.58 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 0.96/1.58 X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.58 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), alpha2( X, Y
% 0.96/1.58 , Z ), alpha16( X, Y, Z ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha2( X, Y, Z ),
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.58 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha16( X, Y, Z ),
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.58 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.96/1.58 { ! alpha16( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.58 { ! alpha16( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.58 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.96/1.58 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ) ), alpha16( X, Y, Z ) }.
% 0.96/1.58 { ! alpha2( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.96/1.58 { ! alpha2( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.96/1.58 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.96/1.58 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ), Y ), alpha2( X, Y, Z ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.96/1.58 ( X ) ), alpha3( X, Y, Z ), alpha17( X, Y, Z ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha3( X, Y, Z ),
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.96/1.58 ( X ) ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha17( X, Y, Z ),
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.96/1.58 ( X ) ) }.
% 0.96/1.58 { ! alpha17( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.58 { ! alpha17( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.96/1.58 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.96/1.58 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 0.96/1.58 ( X ), Y ), alpha17( X, Y, Z ) }.
% 0.96/1.58 { ! alpha3( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.96/1.58 { ! alpha3( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.58 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.96/1.58 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ) ), alpha3( X, Y, Z ) }.
% 0.96/1.58 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.96/1.58 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.96/1.58 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.96/1.58 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.96/1.58 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.96/1.58 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ),
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.58 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.96/1.58 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.96/1.58 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.58 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.96/1.58 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.96/1.58 X ), Z ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.96/1.58 ( X ) ) }.
% 0.96/1.58 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.96/1.58 , Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 0.96/1.58 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.96/1.58 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.96/1.58 { ! class_Rings_Oordered__semiring( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.96/1.58 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.96/1.58 { ! class_Rings_Oordered__semiring( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.96/1.58 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.96/1.58 { ! class_Rings_Oordered__comm__semiring( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.96/1.58 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.96/1.58 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.96/1.58 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.96/1.58 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.96/1.58 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.96/1.58 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.96/1.58 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 0.96/1.58 { ! class_Rings_Oordered__semiring( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.96/1.58 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.96/1.58 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.96/1.58 { ! class_Rings_Oordered__semiring( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.96/1.58 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.96/1.58 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.96/1.58 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.96/1.58 , c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.96/1.58 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.96/1.58 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.96/1.58 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.96/1.58 , Z, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.96/1.58 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.96/1.58 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.96/1.58 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.96/1.58 ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.96/1.58 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.58 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 0.96/1.58 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.96/1.58 X ), Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.96/1.58 ( X ) ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.96/1.58 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha4( X, Y, Z, T ),
% 0.96/1.58 alpha18( X, Y, Z, T ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha4( X, Y, Z, T ),
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha18( X, Y, Z, T ),
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.96/1.58 { ! alpha18( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z,
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.58 { ! alpha18( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, T ) }.
% 0.96/1.58 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.58 , ! c_Orderings_Oord__class_Oless( X, Y, T ), alpha18( X, Y, Z, T ) }.
% 0.96/1.58 { ! alpha4( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.96/1.58 { ! alpha4( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.96/1.58 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.96/1.58 , ! c_Orderings_Oord__class_Oless( X, T, Y ), alpha4( X, Y, Z, T ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha5( X, Y, Z, T ),
% 0.96/1.58 alpha19( X, Y, Z, T ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha5( X, Y, Z, T ),
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha19( X, Y, Z, T ),
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.96/1.58 { ! alpha19( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.58 { ! alpha19( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.96/1.58 { ! c_Orderings_Oord__class_Oless( X, T, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.58 , ! c_Orderings_Oord__class_Oless( X, Y, Z ), alpha19( X, Y, Z, T ) }.
% 0.96/1.58 { ! alpha5( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ), T ) }.
% 0.96/1.58 { ! alpha5( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.96/1.58 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T )
% 0.96/1.58 , ! c_Orderings_Oord__class_Oless( X, Z, Y ), alpha5( X, Y, Z, T ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.96/1.58 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.96/1.58 ! c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless
% 0.96/1.58 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.96/1.58 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.96/1.58 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.96/1.58 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.58 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.96/1.58 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.58 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.96/1.58 ( X ) ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.96/1.58 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.58 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.96/1.58 ( X ) ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.96/1.58 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.96/1.58 .
% 0.96/1.58 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.96/1.58 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ) }
% 0.96/1.58 .
% 0.96/1.58 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.96/1.58 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.96/1.58 ! c_Orderings_Oord__class_Oless( X, Z, T ), c_Orderings_Oord__class_Oless
% 0.96/1.58 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.96/1.58 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.96/1.58 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.96/1.58 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.96/1.58 ( X ) ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.96/1.58 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.58 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.58 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.96/1.58 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.96/1.58 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP
% 0.96/1.58 ( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.96/1.58 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.96/1.58 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.96/1.58 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__comm__semiring__strict( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.96/1.58 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.96/1.58 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.96/1.58 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.96/1.58 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.96/1.58 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.96/1.58 ( c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.96/1.58 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.96/1.58 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP
% 0.96/1.58 ( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__semidom( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__semidom( X ),
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.58 c_Groups_Oone__class_Oone( X ) ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.58 ( X, c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero( X ) ) }
% 0.96/1.58 .
% 0.96/1.58 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.96/1.58 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.96/1.58 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.96/1.58 .
% 0.96/1.58 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.96/1.58 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.96/1.58 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.58 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.96/1.58 ( X, c_Groups_Oone__class_Oone( X ), Z ), c_Orderings_Oord__class_Oless(
% 0.96/1.58 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.96/1.58 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Z =
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, T, Y ) }.
% 0.96/1.58 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.58 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.96/1.58 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) )
% 0.96/1.58 }.
% 0.96/1.58 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, T, Y ),
% 0.96/1.58 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.96/1.58 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) )
% 0.96/1.58 }.
% 0.96/1.58 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), T =
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 0.96/1.58 { ! class_Rings_Oidom( X ), ! T = c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.58 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.96/1.58 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) )
% 0.96/1.58 }.
% 0.96/1.58 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y ),
% 0.96/1.58 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.96/1.58 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) )
% 0.96/1.58 }.
% 0.96/1.58 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = c_Groups_Oone__class_Oone
% 0.96/1.58 ( X ), Y = c_Groups_Oone__class_Oone( X ), Y =
% 0.96/1.58 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) }.
% 0.96/1.58 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.96/1.58 c_Groups_Oone__class_Oone( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.58 ( X ), Y ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.96/1.58 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.96/1.58 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ),
% 0.96/1.58 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) =
% 0.96/1.58 c_Groups_Oone__class_Oone( X ) }.
% 0.96/1.58 { ! class_Groups_Ozero( X ), c_Polynomial_OpCons( X,
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero(
% 0.96/1.58 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 0.96/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.58 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 0.96/1.58 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.58 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 0.96/1.58 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y =
% 0.96/1.58 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.58 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 0.96/1.58 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.96/1.58 c_Polynomial_OpCons( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.96/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.58 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oone__class_Oone(
% 0.96/1.58 tc_Polynomial_Opoly( X ) ) = c_Polynomial_OpCons( X,
% 0.96/1.58 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.96/1.58 tc_Polynomial_Opoly( X ) ) ) }.
% 0.96/1.58 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.96/1.58 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.58 { ! class_Groups_Ozero( X ), c_Polynomial_Odegree( X,
% 0.96/1.58 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.96/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.58 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 0.96/1.58 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Z
% 0.96/1.58 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP(
% 0.96/1.58 c_Polynomial_Opoly( X, T ), Y ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 0.96/1.58 ) }.
% 0.96/1.58 { ! class_Rings_Ocomm__semiring__1( X ), c_Orderings_Oord__class_Oless__eq
% 0.96/1.58 ( tc_Nat_Onat, c_Polynomial_Odegree( X, hAPP( hAPP(
% 0.96/1.58 c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), Z ), Y ) ),
% 0.96/1.58 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.58 c_Polynomial_Odegree( X, Z ) ), Y ) ) }.
% 0.96/1.58 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 0.96/1.58 ( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), T ), Z
% 0.96/1.58 ) ), Y ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), hAPP(
% 0.96/1.58 c_Polynomial_Opoly( X, T ), Y ) ), Z ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.96/1.58 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.96/1.58 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.96/1.58 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.96/1.58 ! c_Orderings_Oord__class_Oless__eq( X, Z, T ),
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.96/1.58 ( X, U, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.96/1.58 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.96/1.58 ( X, U, T ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.96/1.58 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.96/1.58 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.96/1.58 , U ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, U, T ), ! c_Orderings_Oord__class_Oless
% 0.96/1.58 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.96/1.58 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.58 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.96/1.58 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.96/1.58 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.96/1.58 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.58 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.96/1.58 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.96/1.58 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.96/1.58 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.96/1.58 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.96/1.58 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 0.96/1.58 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.96/1.58 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.96/1.58 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 0.96/1.58 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) }.
% 0.96/1.58 { ! class_Groups_Ozero( X ), c_Polynomial_Odegree( X, c_Polynomial_OpCons(
% 0.96/1.58 X, Y, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) =
% 0.96/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.58 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.96/1.58 ( X ), Z, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X )
% 0.96/1.58 ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree
% 0.96/1.58 ( X, Z ), c_Polynomial_Odegree( X, Y ) ) }.
% 0.96/1.58 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.58 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless__eq(
% 0.96/1.58 tc_Nat_Onat, c_Polynomial_Oorder( X, Z, Y ), c_Polynomial_Odegree( X, Y )
% 0.96/1.58 ) }.
% 0.96/1.58 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.58 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) =
% 0.96/1.58 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.96/1.58 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.58 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) = hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 0.96/1.58 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ),
% 0.96/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 0.96/1.58 ( tc_Nat_Onat ) ) ) ) }.
% 0.96/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.58 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.96/1.58 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) }.
% 0.96/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.58 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.58 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP
% 0.96/1.58 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ) }.
% 0.96/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.58 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z
% 0.96/1.58 , Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.96/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.58 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.96/1.58 , Y ), X ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.96/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.58 tc_Nat_Onat ), Y ) }.
% 0.96/1.58 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.96/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.58 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 0.96/1.58 ), X ) ) }.
% 0.96/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.58 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.58 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.96/1.58 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 0.96/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.96/1.58 ( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) }.
% 0.96/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.58 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 0.96/1.58 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.96/1.58 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.96/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.58 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ),
% 0.96/1.58 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.96/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.58 ( tc_Nat_Onat ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.96/1.58 tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.96/1.58 tc_Nat_Onat ), X ), Y ), Z = Y }.
% 0.96/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.58 ( tc_Nat_Onat ), X ), ! Z = Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.58 ( tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.96/1.58 tc_Nat_Onat ), X ), Y ) }.
% 0.96/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.58 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 0.96/1.58 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP(
% 0.96/1.58 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.96/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.96/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.58 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 0.96/1.58 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.96/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( c_Nat_OSuc(
% 0.96/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), X =
% 0.96/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X = c_Nat_OSuc(
% 0.96/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.96/1.58 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, X ) }.
% 0.96/1.58 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.96/1.58 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.96/1.58 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.96/1.58 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 0.96/1.58 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), alpha6( X, Y ), Y = X }
% 0.96/1.58 .
% 0.96/1.58 { ! alpha6( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.96/1.58 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.96/1.58 { ! alpha6( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.96/1.58 { ! alpha6( X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.96/1.58 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.96/1.58 ( tc_Nat_Onat, X, Y ), alpha6( X, Y ) }.
% 0.96/1.58 { ! alpha7( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.96/1.58 { ! alpha7( X, Y ), ! Y = X }.
% 0.96/1.58 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X, alpha7( X, Y ) }
% 0.96/1.58 .
% 0.96/1.58 { ! alpha7( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.96/1.58 { ! alpha7( X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.96/1.58 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.96/1.58 ( tc_Nat_Onat, X, Y ), alpha7( X, Y ) }.
% 0.96/1.58 { Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ),
% 0.96/1.58 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.96/1.58 { Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.96/1.58 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.96/1.58 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.96/1.58 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.96/1.58 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), X = Y }.
% 0.96/1.58 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), ! X = Y,
% 0.96/1.58 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.96/1.58 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.96/1.58 ( tc_Nat_Onat, Y, X ), Y = X }.
% 0.96/1.58 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.96/1.58 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 0.96/1.58 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X,
% 0.96/1.58 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.96/1.58 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X, !
% 0.96/1.58 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.96/1.58 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.96/1.58 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 0.96/1.58 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), ! X = Z,
% 0.96/1.58 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 0.96/1.58 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.96/1.58 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 0.96/1.58 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.96/1.58 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 0.96/1.58 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.96/1.58 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 0.96/1.58 tc_Nat_Onat, Y, Z ) }.
% 0.96/1.58 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.96/1.58 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd(
% 0.96/1.58 tc_Nat_Onat, Y, Z ) }.
% 0.96/1.58 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.96/1.58 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd
% 0.96/1.58 ( tc_Nat_Onat, Z, Y ) }.
% 0.96/1.58 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.96/1.58 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 0.96/1.58 tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 0.96/1.58 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.96/1.58 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 0.96/1.58 tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.96/1.58 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.96/1.58 ( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.96/1.58 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.96/1.58 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 0.96/1.58 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.96/1.58 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.96/1.58 ( tc_Nat_Onat, X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.96/1.58 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.96/1.58 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 0.96/1.58 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.96/1.58 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.96/1.58 ( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.96/1.58 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.96/1.58 ( tc_Nat_Onat, X, Y ), ! X = Y }.
% 0.96/1.58 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.96/1.58 ( tc_Nat_Onat, X, Y ), ! X = Z, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 0.96/1.58 , Z ) }.
% 0.96/1.58 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.96/1.58 ( tc_Nat_Onat, X, Y ), ! X = Z, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat,
% 0.96/1.58 Z, Y ) }.
% 0.96/1.58 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.96/1.58 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.96/1.58 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 0.96/1.58 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.96/1.58 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), !
% 0.96/1.58 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.96/1.58 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.96/1.58 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 0.96/1.58 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.96/1.58 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.96/1.58 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.96/1.58 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd(
% 0.96/1.58 tc_Nat_Onat, Y, Z ) }.
% 0.96/1.58 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.96/1.58 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.96/1.58 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd
% 0.96/1.58 ( tc_Nat_Onat, Z, Y ) }.
% 0.96/1.58 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.96/1.58 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 0.96/1.58 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.96/1.58 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 0.96/1.58 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 0.96/1.58 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.96/1.58 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 0.96/1.58 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.96/1.58 tc_Polynomial_Opoly( X ) ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.96/1.58 tc_Polynomial_Opoly( X ), Y ) }.
% 0.96/1.58 { ! class_Groups_Oab__group__add( X ), ! c_Orderings_Oord__class_Oless(
% 0.96/1.58 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, T )
% 0.96/1.58 , Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree(
% 0.96/1.58 X, c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Z, T ) ), Y )
% 0.96/1.58 }.
% 0.96/1.58 { ! class_Groups_Oab__group__add( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.96/1.58 ( tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 0.96/1.58 T ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.58 c_Polynomial_Odegree( X, c_Groups_Ominus__class_Ominus(
% 0.96/1.58 tc_Polynomial_Opoly( X ), Z, T ) ), Y ) }.
% 0.96/1.58 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.96/1.58 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Z =
% 0.96/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.96/1.58 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.96/1.58 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.96/1.58 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.96/1.58 .
% 0.96/1.58 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), Z =
% 0.96/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 0.96/1.58 tc_Nat_Onat, Y, X ) }.
% 0.96/1.58 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.96/1.58 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.96/1.58 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.96/1.58 ( tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.58 Z ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.96/1.58 X ) ) }.
% 0.96/1.58 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.96/1.58 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.58 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.96/1.58 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ),
% 0.96/1.58 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.96/1.58 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.96/1.58 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ), c_Rings_Odvd__class_Odvd(
% 0.96/1.58 tc_Nat_Onat, hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Z )
% 0.96/1.58 , X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X )
% 0.96/1.58 ) }.
% 0.96/1.58 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.58 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.96/1.58 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ), Y =
% 0.96/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 0.96/1.58 tc_Nat_Onat, Z, X ) }.
% 0.96/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.58 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ),
% 0.96/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.58 tc_Nat_Onat ), Y ) }.
% 0.96/1.58 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.58 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ozero__class_Ozero(
% 0.96/1.58 tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.96/1.58 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.58 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 0.96/1.58 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 0.96/1.58 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 0.96/1.58 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.96/1.58 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) }.
% 0.96/1.58 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.96/1.58 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Z ) }.
% 0.96/1.58 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), U ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 0.96/1.58 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), Y ) ) }.
% 0.96/1.58 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.96/1.58 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.58 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.96/1.58 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ), Y =
% 0.96/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 0.96/1.58 tc_Int_Oint, Z, X ) }.
% 0.96/1.58 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.96/1.58 c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.58 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.96/1.58 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ) ),
% 0.96/1.58 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 0.96/1.58 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.96/1.58 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd(
% 0.96/1.58 tc_Int_Oint, hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z )
% 0.96/1.58 , X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X )
% 0.96/1.58 ) }.
% 0.96/1.58 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.96/1.58 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.58 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.96/1.58 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.58 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.96/1.58 = Y }.
% 0.96/1.58 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.96/1.58 = Y }.
% 0.96/1.58 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.58 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.58 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.96/1.58 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.96/1.58 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero(
% 0.96/1.58 tc_Nat_Onat ) ) }.
% 0.96/1.58 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.58 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.96/1.58 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.96/1.58 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) }.
% 0.96/1.58 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.58 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.96/1.58 tc_Nat_Onat ) ) = Y }.
% 0.96/1.58 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 0.96/1.58 tc_Nat_Onat ), X ) }.
% 0.96/1.58 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ouminus__class_Ouminus( X, Y
% 0.96/1.58 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.96/1.58 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) ), Y
% 0.96/1.58 ) }.
% 0.96/1.58 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.58 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.96/1.58 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.96/1.58 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.96/1.58 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.96/1.58 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 0.96/1.58 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.96/1.58 X, Y ) }.
% 0.96/1.58 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.58 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.96/1.58 ( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.58 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.58 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.96/1.58 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.96/1.58 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.96/1.58 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.96/1.58 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.58 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.96/1.58 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.96/1.58 , Y ) }.
% 0.96/1.58 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.96/1.58 , Y ) }.
% 0.96/1.58 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.58 c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.96/1.58 ) }.
% 0.96/1.58 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.96/1.58 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.96/1.58 ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.96/1.58 { ! class_Groups_Ozero( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y, Y =
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.58 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ) = Y }.
% 0.96/1.58 { ! class_Groups_Oab__semigroup__mult( X ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.96/1.58 { ! class_Groups_Oone( X ), ! c_Groups_Oone__class_Oone( X ) = Y, Y =
% 0.96/1.58 c_Groups_Oone__class_Oone( X ) }.
% 0.96/1.58 { ! class_Groups_Oone( X ), ! Y = c_Groups_Oone__class_Oone( X ),
% 0.96/1.58 c_Groups_Oone__class_Oone( X ) = Y }.
% 0.96/1.58 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.96/1.58 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! U = T, Z = Y }.
% 0.96/1.58 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.96/1.58 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! Z = Y, U = T }.
% 0.96/1.58 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 0.96/1.58 ) = c_Groups_Ouminus__class_Ouminus( X, Y ), Z = Y }.
% 0.96/1.58 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ouminus__class_Ouminus
% 0.96/1.58 ( X, Z ) = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.96/1.58 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 0.96/1.58 ) = Y, c_Groups_Ouminus__class_Ouminus( X, Y ) = Z }.
% 0.96/1.58 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 0.96/1.58 ) = Z, c_Groups_Ouminus__class_Ouminus( X, Z ) = Y }.
% 0.96/1.58 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 0.96/1.58 , Y ), Y = c_Groups_Ouminus__class_Ouminus( X, Z ) }.
% 0.96/1.58 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 0.96/1.58 , Z ), Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.96/1.58 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.96/1.58 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 0.96/1.58 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.96/1.58 ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.96/1.58 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ominus__class_Ominus(
% 0.96/1.58 X, Z, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.58 { ! class_Groups_Oab__group__add( X ), ! Z = Y,
% 0.96/1.58 c_Groups_Ominus__class_Ominus( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.96/1.58 ) }.
% 0.96/1.58 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.96/1.58 Z, Y ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.96/1.58 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y, Y )
% 0.96/1.58 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.58 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y,
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.96/1.58 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.58 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.96/1.58 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.96/1.58 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.58 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.96/1.58 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, U, T ) }.
% 0.96/1.58 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.58 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.96/1.58 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, U, T ),
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.96/1.58 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.58 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.96/1.58 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, U, T ) }.
% 0.96/1.58 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.96/1.58 c_Groups_Ouminus__class_Ouminus( X, Y ) = Y, Y =
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.58 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.96/1.58 = Y }.
% 0.96/1.58 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 0.96/1.58 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.96/1.58 ) }.
% 0.96/1.58 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.58 c_Groups_Ouminus__class_Ouminus( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.96/1.58 ) }.
% 0.96/1.58 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.96/1.58 c_Groups_Ouminus__class_Ouminus( X, Y ), Y = c_Groups_Ozero__class_Ozero
% 0.96/1.58 ( X ) }.
% 0.96/1.58 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus( X
% 0.96/1.58 , Y ) }.
% 0.96/1.58 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.96/1.58 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Groups_Ozero__class_Ozero( X )
% 0.96/1.58 = Y }.
% 0.96/1.58 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y,
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Ouminus__class_Ouminus( X, Y
% 0.96/1.58 ) }.
% 0.96/1.58 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.58 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.96/1.58 = Y }.
% 0.96/1.58 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.96/1.58 = Y }.
% 0.96/1.58 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.96/1.58 = Y }.
% 0.96/1.58 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.96/1.58 = Y }.
% 0.96/1.58 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.96/1.58 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.96/1.58 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.96/1.58 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.96/1.58 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.96/1.58 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.96/1.58 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.96/1.58 , Z ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.58 c_Groups_Ouminus__class_Ouminus( X, Y ), Z ) }.
% 0.96/1.58 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.96/1.58 , Y ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.58 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.96/1.58 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ouminus__class_Ouminus
% 0.96/1.58 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.96/1.58 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.96/1.58 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 0.96/1.58 ( X, Z ) ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.96/1.58 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.96/1.58 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.96/1.58 , c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.96/1.58 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, Y, Z ), c_Orderings_Oord__class_Oless(
% 0.96/1.58 X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.96/1.58 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.96/1.58 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.96/1.58 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 0.96/1.58 ( X, Y ), Z ) }.
% 0.96/1.58 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.96/1.58 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 0.96/1.58 ( X, Z ), Y ) }.
% 0.96/1.58 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ouminus__class_Ouminus( X,
% 0.96/1.58 Y ) ), c_Orderings_Oord__class_Oless( X, Y,
% 0.96/1.58 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.96/1.58 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ouminus__class_Ouminus( X,
% 0.96/1.58 Z ) ), c_Orderings_Oord__class_Oless( X, Z,
% 0.96/1.58 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.96/1.58 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.96/1.58 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) =
% 0.96/1.58 c_Groups_Ominus__class_Ominus( X, Y, Z ) }.
% 0.96/1.58 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 0.96/1.58 , Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.58 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 0.96/1.58 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.96/1.58 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.96/1.58 X, c_Groups_Ominus__class_Ominus( X, Z, Y ), c_Groups_Ozero__class_Ozero
% 0.96/1.58 ( X ) ) }.
% 0.96/1.58 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.96/1.58 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.96/1.58 , Z, Y ) }.
% 0.96/1.58 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.96/1.58 , Y ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.96/1.58 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.96/1.58 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 0.96/1.58 ( X, Y ), Y ) }.
% 0.96/1.58 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.96/1.58 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.96/1.58 ) }.
% 0.96/1.58 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.96/1.58 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 0.96/1.58 ( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.58 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 0.96/1.58 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.58 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.96/1.58 ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.96/1.58 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.96/1.58 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.58 tc_Polynomial_Opoly( X ) ),
% 0.96/1.58 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.96/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.58 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.58 tc_Polynomial_Opoly( X ) ),
% 0.96/1.58 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) = c_Nat_OSuc(
% 0.96/1.58 c_Polynomial_Odegree( X, Y ) ) }.
% 0.96/1.58 { ! class_Orderings_Opreorder( X ), c_Orderings_Oord__class_Oless__eq( X, Y
% 0.96/1.58 , Y ) }.
% 0.96/1.58 { ! class_Power_Opower( X ), c_Power_Opower__class_Opower( X ) =
% 0.96/1.58 c_Power_Opower_Opower( X, c_Groups_Oone__class_Oone( X ),
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ) ) }.
% 0.96/1.58 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), hAPP( hAPP(
% 0.96/1.58 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 0.96/1.58 ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.96/1.58 { ! class_Rings_Ocomm__semiring__0( X ), c_Orderings_Oord__class_Oless__eq
% 0.96/1.58 ( tc_Nat_Onat, c_Polynomial_Odegree( X, c_Polynomial_Opcompose( X, Z, Y )
% 0.96/1.58 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.58 c_Polynomial_Odegree( X, Z ) ), c_Polynomial_Odegree( X, Y ) ) ) }.
% 0.96/1.58 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 0.96/1.58 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.96/1.58 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.58 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.96/1.58 c_Polynomial_Opcompose( X, T, Z ) ), Y ) = hAPP( c_Polynomial_Opoly( X, T
% 0.96/1.58 ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.96/1.58 { hAPP( hAPP( c_Power_Opower_Opower( T, Z, Y ), X ),
% 0.96/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = Z }.
% 0.96/1.58 { hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), c_Nat_OSuc( X ) ) =
% 0.96/1.58 hAPP( hAPP( Z, Y ), hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), X
% 0.96/1.58 ) ) }.
% 0.96/1.58 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.96/1.58 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.96/1.58 hAPP( Y, U ) ) }.
% 0.96/1.58 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, hAPP
% 0.96/1.58 ( Z, skol9( X, Y, Z ) ), hAPP( Y, skol9( X, Y, Z ) ) ),
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }.
% 0.96/1.58 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.96/1.58 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.96/1.58 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.96/1.58 ( X, Z, Y ) }.
% 0.96/1.58 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.96/1.58 ( X, Y, Z ) }.
% 0.96/1.58 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.96/1.58 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 0.96/1.58 { ! class_Orderings_Opreorder( X ), ! Z = Y,
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.96/1.58 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.96/1.58 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.96/1.58 hAPP( Y, U ) ) }.
% 0.96/1.58 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.96/1.58 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 0.96/1.58 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.96/1.58 , Y ), ! Y = Z, c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.96/1.58 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.96/1.58 ( X, Y, T ), c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.96/1.58 { ! class_Orderings_Oorder( X ), ! Z = Y, !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 0.96/1.58 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y
% 0.96/1.58 ), ! Y = T, c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.96/1.58 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.96/1.58 , Y ), ! Z = T, c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.96/1.58 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.96/1.58 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 0.96/1.58 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.96/1.58 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.96/1.58 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.96/1.58 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 0.96/1.58 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.96/1.58 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.96/1.58 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.96/1.58 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.96/1.58 hAPP( Y, U ) ) }.
% 0.96/1.58 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.96/1.58 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.96/1.58 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.96/1.58 Y ) }.
% 0.96/1.58 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 0.96/1.58 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.96/1.58 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.96/1.58 Y ), ! Z = Y }.
% 0.96/1.58 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.96/1.58 Z ), ! Z = Y }.
% 0.96/1.58 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.96/1.58 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Z = Y }.
% 0.96/1.58 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.96/1.58 Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.96/1.58 { ! class_Orderings_Olinorder( X ), ! Z = Y, !
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.96/1.58 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.96/1.58 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.96/1.58 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.96/1.58 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Y = Z }.
% 0.96/1.58 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.96/1.58 ), ! Y = Z, ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.96/1.58 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 0.96/1.58 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.96/1.58 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.96/1.58 , ! Z = Y }.
% 0.96/1.58 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.96/1.58 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.96/1.58 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.96/1.58 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.96/1.58 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.96/1.58 , ! Z = Y }.
% 0.96/1.58 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.96/1.58 , ! Y = Z }.
% 0.96/1.58 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.96/1.58 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.96/1.58 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.96/1.58 , ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.96/1.58 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X
% 0.96/1.58 , Y, T ), c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.96/1.58 { ! class_Orderings_Oorder( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless(
% 0.96/1.58 X, T, Y ), c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.96/1.58 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 0.96/1.58 ! Y = T, c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.96/1.58 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.96/1.58 , ! Z = T, c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.96/1.58 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.96/1.58 Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.96/1.58 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.96/1.58 , ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.96/1.58 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.96/1.58 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.96/1.58 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.96/1.58 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.96/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), !
% 0.96/1.58 c_Rings_Odvd__class_Odvd( tc_Int_Oint, X, Y ), ! c_Rings_Odvd__class_Odvd
% 0.96/1.58 ( tc_Int_Oint, Y, X ), X = Y }.
% 0.96/1.58 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.58 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y
% 0.96/1.58 ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }.
% 0.96/1.58 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.96/1.58 tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 0.96/1.58 ) }.
% 0.96/1.58 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, c_Groups_Ominus__class_Ominus
% 0.96/1.58 ( tc_Int_Oint, Y, X ) ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, X )
% 0.96/1.58 , c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 0.96/1.58 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), Z =
% 0.96/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Rings_Odvd__class_Odvd(
% 0.96/1.58 tc_Int_Oint, Y, X ) }.
% 0.96/1.58 { ! class_Groups_Ozero( X ), !
% 0.96/1.58 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.96/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.96/1.58 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.58 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.58 tc_Polynomial_Opoly( X ) ),
% 0.96/1.58 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.96/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.58 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.96/1.58 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.96/1.58 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.96/1.58 , Y, Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.96/1.58 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.96/1.58 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.96/1.58 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.96/1.58 Z ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.96/1.58 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.96/1.58 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.96/1.58 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.96/1.58 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.96/1.58 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.96/1.58 , ! Z = Y }.
% 0.96/1.58 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.96/1.58 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.96/1.58 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.96/1.58 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.96/1.58 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.96/1.58 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.96/1.58 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.96/1.58 , Z, Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.96/1.58 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.96/1.58 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.96/1.58 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.96/1.58 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.96/1.58 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.96/1.58 ( X, Z, Y ) }.
% 0.96/1.58 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.96/1.58 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.96/1.58 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.96/1.58 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.96/1.58 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.96/1.58 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ), Z = Y }.
% 0.96/1.58 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.96/1.58 ), ! Z = Y, c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.96/1.58 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.96/1.58 ( X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.96/1.58 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.96/1.58 ( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.96/1.58 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.96/1.58 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.96/1.58 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.96/1.58 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.96/1.58 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.96/1.58 , Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.96/1.58 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.96/1.58 , Z, Y ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.96/1.58 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.96/1.58 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.96/1.58 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.96/1.58 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.96/1.58 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.96/1.58 , Y ), Y = Z, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.96/1.58 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.96/1.58 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.96/1.58 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.96/1.58 , ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.96/1.58 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.96/1.58 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.96/1.58 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.96/1.58 , Y ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.96/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.96/1.58 c_Polynomial_OpCons( X, Z, Y ) ), c_Polynomial_Opos__poly( X, Y ), alpha8
% 0.96/1.58 ( X, Y, Z ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.96/1.58 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__idom( X ), ! alpha8( X, Y, Z ),
% 0.96/1.58 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ) }.
% 0.96/1.58 { ! alpha8( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly
% 0.96/1.58 ( X ) ) }.
% 0.96/1.58 { ! alpha8( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.96/1.58 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.96/1.58 alpha8( X, Y, Z ) }.
% 0.96/1.58 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.96/1.58 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Ouminus__class_Ouminus
% 0.96/1.58 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.96/1.58 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) }.
% 0.96/1.58 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.96/1.58 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.96/1.58 { ! c_Groups_Ozero__class_Ozero( tc_Int_Oint ) = c_Groups_Oone__class_Oone
% 0.96/1.58 ( tc_Int_Oint ) }.
% 0.96/1.58 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.96/1.58 tc_Int_Oint ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.96/1.58 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.58 ( tc_Int_Oint ) ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.96/1.58 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.96/1.58 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) = X }.
% 0.96/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.58 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ),
% 0.96/1.58 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.96/1.58 tc_Int_Oint ), X ) }.
% 0.96/1.58 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.58 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.58 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) }.
% 0.96/1.58 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 0.96/1.58 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) = X }.
% 0.96/1.58 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) = hAPP
% 0.96/1.58 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) }.
% 0.96/1.58 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.96/1.58 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ominus__class_Ominus
% 0.96/1.58 ( tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.96/1.58 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.96/1.58 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ),
% 0.96/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.96/1.58 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.96/1.58 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.96/1.58 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) ) =
% 0.96/1.58 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.96/1.58 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.96/1.58 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ), X ) =
% 0.96/1.58 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.96/1.58 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP(
% 0.96/1.58 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.96/1.58 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.96/1.58 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ), X ) =
% 0.96/1.58 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.96/1.58 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.58 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.96/1.58 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), X =
% 0.96/1.58 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.96/1.58 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.58 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.96/1.58 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), Y =
% 0.96/1.58 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.96/1.58 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.58 ( tc_Int_Oint ), X ), ! X = c_Groups_Oone__class_Oone( tc_Int_Oint ), ! Y
% 0.96/1.58 = c_Groups_Oone__class_Oone( tc_Int_Oint ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 0.96/1.58 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.96/1.58 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.96/1.58 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 0.96/1.58 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP
% 0.96/1.58 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.96/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.96/1.58 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 0.96/1.58 ( tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 0.96/1.58 .
% 0.96/1.58 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.96/1.58 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 0.96/1.58 ( tc_Int_Oint ) ) ) }.
% 0.96/1.58 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, X ) }.
% 0.96/1.58 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ) }.
% 0.96/1.58 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 0.96/1.58 X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }
% 0.96/1.58 .
% 0.96/1.58 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 0.96/1.58 X ), Z, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z )
% 0.96/1.58 }.
% 0.96/1.58 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.96/1.58 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z
% 0.96/1.58 ), c_Orderings_Oord__class_Oless( tc_fun( T, X ), Z, Y ) }.
% 0.96/1.58 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 0.96/1.58 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), ! Y = X }.
% 0.96/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), Y = X,
% 0.96/1.58 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.96/1.58 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y = X,
% 0.96/1.58 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.96/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Z ),
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, Z ) }.
% 0.96/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ), Y = X }.
% 0.96/1.58 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.96/1.58 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.96/1.58 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X, hAPP( hAPP
% 0.96/1.58 ( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) }
% 0.96/1.58 .
% 0.96/1.58 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless(
% 0.96/1.58 tc_Polynomial_Opoly( X ), Z, Y ), c_Polynomial_Opos__poly( X,
% 0.96/1.58 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.96/1.58 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ),
% 0.96/1.58 c_Orderings_Oord__class_Oless( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.96/1.58 ( tc_Polynomial_Opoly( X ), Z, Y ), Z = Y, c_Polynomial_Opos__poly( X,
% 0.96/1.58 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__idom( X ), ! Z = Y,
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.96/1.58 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ),
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.58 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opos__poly( X, Y ),
% 0.96/1.58 c_Polynomial_Opos__poly( X, c_Groups_Ouminus__class_Ouminus(
% 0.96/1.58 tc_Polynomial_Opoly( X ), Y ) ) }.
% 0.96/1.58 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.96/1.58 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.58 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.96/1.58 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.58 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.96/1.58 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.58 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.96/1.58 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.58 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 0.96/1.58 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.96/1.58 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 0.96/1.58 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.96/1.58 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 0.96/1.58 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.96/1.58 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 0.96/1.58 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.96/1.58 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.96/1.58 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.96/1.58 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.96/1.58 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.96/1.58 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.96/1.58 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.96/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 0.96/1.58 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) }.
% 0.96/1.58 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.96/1.58 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd(
% 0.96/1.58 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X
% 0.96/1.58 ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y
% 0.96/1.58 ) ) }.
% 0.96/1.58 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.96/1.58 c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ),
% 0.96/1.58 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 0.96/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) }.
% 0.96/1.58 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Ozero__class_Ozero(
% 0.96/1.58 tc_Int_Oint ) ) }.
% 0.96/1.58 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint,
% 0.96/1.58 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) = X }.
% 0.96/1.58 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), c_Rings_Odvd__class_Odvd
% 0.96/1.58 ( tc_Int_Oint, Y, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.96/1.58 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y,
% 0.96/1.58 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ),
% 0.96/1.58 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }.
% 0.96/1.58 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), c_Rings_Odvd__class_Odvd
% 0.96/1.58 ( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) }.
% 0.96/1.58 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.96/1.58 ( tc_Int_Oint, Y ), X ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }
% 0.96/1.58 .
% 0.96/1.58 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 0.96/1.58 tc_Int_Oint ) ) }.
% 0.96/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.96/1.58 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ominus__class_Ominus(
% 0.96/1.58 tc_Int_Oint, X, Y ) }.
% 0.96/1.58 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.96/1.58 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint
% 0.96/1.58 ) }.
% 0.96/1.58 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.96/1.58 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.96/1.58 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.96/1.58 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.96/1.58 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.96/1.58 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.96/1.58 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 0.96/1.58 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 0.96/1.58 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 0.96/1.58 { ! class_Groups_Ominus( X ), hAPP( c_Groups_Ominus__class_Ominus( tc_fun(
% 0.96/1.58 U, X ), T, Z ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( T, Y ),
% 0.96/1.58 hAPP( Z, Y ) ) }.
% 0.96/1.58 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.96/1.58 c_Groups_Ouminus__class_Ouminus( X, Z ) = c_Groups_Ouminus__class_Ouminus
% 0.96/1.58 ( X, Y ), Z = Y }.
% 0.96/1.58 { ! class_Lattices_Oboolean__algebra( X ), ! Z = Y,
% 0.96/1.58 c_Groups_Ouminus__class_Ouminus( X, Z ) = c_Groups_Ouminus__class_Ouminus
% 0.96/1.58 ( X, Y ) }.
% 0.96/1.58 { ! class_Groups_Ouminus( X ), hAPP( c_Groups_Ouminus__class_Ouminus(
% 0.96/1.58 tc_fun( T, X ), Z ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( Z, Y
% 0.96/1.58 ) ) }.
% 0.96/1.58 { ! class_Lattices_Oboolean__algebra( X ), c_Groups_Ouminus__class_Ouminus
% 0.96/1.58 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 0.96/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Nat__Transfer_Otsub( X, Y )
% 0.96/1.58 ) }.
% 0.96/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.96/1.58 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ominus__class_Ominus(
% 0.96/1.58 tc_Int_Oint, X, Y ) }.
% 0.96/1.58 { ! class_Rings_Ocomm__ring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP(
% 0.96/1.58 hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.96/1.58 c_Polynomial_Omonom( X, c_Groups_Oone__class_Oone( X ), T ) ), Z ) ), Y )
% 0.96/1.58 = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.58 c_Power_Opower__class_Opower( X ), Y ), T ) ), hAPP( c_Polynomial_Opoly(
% 0.96/1.58 X, Z ), Y ) ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__idom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.58 tc_Polynomial_Opoly( X ) ), c_Groups_Osgn__class_Osgn(
% 0.96/1.58 tc_Polynomial_Opoly( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 0.96/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.58 tc_Polynomial_Opoly( X ) ), ! c_Orderings_Oord__class_Oless(
% 0.96/1.58 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.96/1.58 tc_Polynomial_Opoly( X ) ), Y ), c_Groups_Osgn__class_Osgn(
% 0.96/1.58 tc_Polynomial_Opoly( X ), Y ) = c_Groups_Oone__class_Oone(
% 0.96/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.58 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless(
% 0.96/1.58 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.96/1.58 tc_Polynomial_Opoly( X ) ), Y ), c_Groups_Osgn__class_Osgn(
% 0.96/1.58 tc_Polynomial_Opoly( X ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.96/1.58 tc_Polynomial_Opoly( X ), c_Groups_Oone__class_Oone( tc_Polynomial_Opoly
% 0.96/1.58 ( X ) ) ) }.
% 0.96/1.58 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.58 ( tc_Int_Oint ), X ), hBOOL( hAPP( Y, skol10( Z, Y ) ) ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! hBOOL( hAPP( Y, U ) )
% 0.96/1.58 , hBOOL( hAPP( Y, c_Groups_Ominus__class_Ominus( tc_Int_Oint, U, hAPP(
% 0.96/1.58 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), T ), X ) ) ) ) }.
% 0.96/1.58 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.58 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( Y, c_Groups_Ominus__class_Ominus(
% 0.96/1.58 tc_Int_Oint, skol10( X, Y ), X ) ) ), ! c_Orderings_Oord__class_Oless__eq
% 0.96/1.58 ( tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), ! hBOOL(
% 0.96/1.58 hAPP( Y, T ) ), hBOOL( hAPP( Y, c_Groups_Ominus__class_Ominus(
% 0.96/1.58 tc_Int_Oint, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 0.96/1.58 , Z ), X ) ) ) ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 0.96/1.58 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.58 }.
% 0.96/1.58 { ! class_Rings_Olinordered__idom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.58 X ), c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.58 }.
% 0.96/1.58 { ! class_Groups_Osgn__if( X ), c_Groups_Osgn__class_Osgn( X,
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__idom( X ), c_Groups_Osgn__class_Osgn( X, hAPP
% 0.96/1.58 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Osgn__class_Osgn( X, Z ) ),
% 0.96/1.58 c_Groups_Osgn__class_Osgn( X, Y ) ) }.
% 0.96/1.58 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 0.96/1.58 c_Groups_Osgn__class_Osgn( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.96/1.58 X ), Z ), Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.96/1.58 c_Groups_Osgn__class_Osgn( X, Z ) ), c_Groups_Osgn__class_Osgn( X, Y ) )
% 0.96/1.58 }.
% 0.96/1.58 { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Osgn__class_Osgn
% 0.96/1.58 ( X, c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X
% 0.96/1.58 ) }.
% 0.96/1.58 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.96/1.58 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.58 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) =
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__idom( X ), c_Groups_Osgn__class_Osgn( X,
% 0.96/1.58 c_Groups_Osgn__class_Osgn( X, Y ) ) = c_Groups_Osgn__class_Osgn( X, Y ) }
% 0.96/1.58 .
% 0.96/1.58 { ! class_Groups_Ozero( X ), ! c_Polynomial_Omonom( X, T, Z ) =
% 0.96/1.58 c_Polynomial_Omonom( X, Y, Z ), T = Y }.
% 0.96/1.58 { ! class_Groups_Ozero( X ), ! T = Y, c_Polynomial_Omonom( X, T, Z ) =
% 0.96/1.58 c_Polynomial_Omonom( X, Y, Z ) }.
% 0.96/1.58 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 0.96/1.58 c_Groups_Osgn__class_Osgn( X, c_Groups_Oone__class_Oone( X ) ) =
% 0.96/1.58 c_Groups_Oone__class_Oone( X ) }.
% 0.96/1.58 { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Osgn__class_Osgn
% 0.96/1.58 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 0.96/1.58 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Osgn__class_Osgn( X, Y ) ) }
% 0.96/1.58 .
% 0.96/1.58 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.96/1.58 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) ),
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.96/1.58 .
% 0.96/1.58 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.96/1.58 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless( X
% 0.96/1.58 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) ) }
% 0.96/1.58 .
% 0.96/1.58 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.96/1.58 , c_Groups_Osgn__class_Osgn( X, Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.96/1.58 .
% 0.96/1.58 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.96/1.58 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.96/1.58 , c_Groups_Osgn__class_Osgn( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }
% 0.96/1.58 .
% 0.96/1.58 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X,
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 0.96/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.58 { ! class_Groups_Ozero( X ), ! c_Polynomial_Omonom( X, Z, Y ) =
% 0.96/1.58 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.58 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.58 c_Polynomial_Omonom( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.96/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.58 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.58 c_Polynomial_Odegree( X, c_Polynomial_Omonom( X, Y, Z ) ) = Z }.
% 0.96/1.58 { ! class_Groups_Ozero( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat
% 0.96/1.58 , c_Polynomial_Odegree( X, c_Polynomial_Omonom( X, Z, Y ) ), Y ) }.
% 0.96/1.58 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.96/1.58 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, Z, Y ) ) =
% 0.96/1.58 c_Polynomial_Omonom( X, c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.96/1.58 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 0.96/1.58 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, T, Z ),
% 0.96/1.58 c_Polynomial_Omonom( X, Y, Z ) ) = c_Polynomial_Omonom( X,
% 0.96/1.58 c_Groups_Ominus__class_Ominus( X, T, Y ), Z ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 0.96/1.58 = c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless( X,
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.96/1.58 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Groups_Osgn__class_Osgn( X, Y
% 0.96/1.58 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.96/1.58 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Groups_Osgn__class_Osgn( X, Y
% 0.96/1.58 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.96/1.58 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X, Z, c_Nat_OSuc( Y ) ) =
% 0.96/1.58 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.58 c_Polynomial_Omonom( X, Z, Y ) ) }.
% 0.96/1.58 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 0.96/1.58 c_Polynomial_Omonom( X, T, Z ) ), Y ) = hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.96/1.58 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.96/1.58 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X, Y,
% 0.96/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = c_Polynomial_OpCons( X, Y
% 0.96/1.58 , c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 0.96/1.58 = c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ),
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.96/1.58 .
% 0.96/1.58 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.96/1.58 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Osgn__class_Osgn( X, Y
% 0.96/1.58 ) = c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) )
% 0.96/1.58 }.
% 0.96/1.58 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.96/1.58 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Osgn__class_Osgn( X, Y
% 0.96/1.58 ) = c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) )
% 0.96/1.58 }.
% 0.96/1.58 { ! class_Groups_Osgn__if( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.58 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.58 { ! class_Groups_Osgn__if( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.96/1.58 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.96/1.58 { ! class_Groups_Osgn__if( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.96/1.58 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.96/1.58 c_Groups_Oone__class_Oone( X ) ) }.
% 0.96/1.58 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 0.96/1.58 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( W, X, Y,
% 0.96/1.58 Z, c_Polynomial_OpCons( X, U, T ) ) = hAPP( hAPP( hAPP( Z, U ), T ),
% 0.96/1.58 c_Polynomial_Opoly__rec( W, X, Y, Z, T ) ) }.
% 0.96/1.58 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Odegree( X,
% 0.96/1.58 c_Polynomial_Osynthetic__div( X, Z, Y ) ) = c_Groups_Ominus__class_Ominus
% 0.96/1.58 ( tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Groups_Oone__class_Oone(
% 0.96/1.58 tc_Nat_Onat ) ) }.
% 0.96/1.58 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Osynthetic__div( X
% 0.96/1.58 , Z, Y ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.96/1.58 c_Polynomial_Odegree( X, Z ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.96/1.58 }.
% 0.96/1.58 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Odegree( X, Z ) =
% 0.96/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Polynomial_Osynthetic__div
% 0.96/1.58 ( X, Z, Y ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.58 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 0.96/1.58 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.96/1.58 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.58 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 0.96/1.58 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Polynomial_OpCons( X, hAPP(
% 0.96/1.58 c_Polynomial_Opoly( X, Z ), Y ), c_Polynomial_Osynthetic__div( X, Z, Y )
% 0.96/1.58 ) }.
% 0.96/1.58 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 0.96/1.58 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( T, X, Y,
% 0.96/1.58 Z, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.96/1.58 { ! class_Groups_Ozero( X ), c_Polynomial_Opoly__rec( W, X, U, T,
% 0.96/1.58 c_Polynomial_OpCons( X, Z, Y ) ) = hAPP( hAPP( hAPP( T, Z ), Y ), c_If( W
% 0.96/1.58 , c_fequal( Y, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) )
% 0.96/1.58 , U, c_Polynomial_Opoly__rec( W, X, U, T, Y ) ) ) }.
% 0.96/1.58 { ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.96/1.58 c_Groups_Osgn__class_Osgn( tc_Int_Oint, X ) = c_Groups_Ozero__class_Ozero
% 0.96/1.58 ( tc_Int_Oint ) }.
% 0.96/1.58 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.96/1.58 tc_Int_Oint ), X ), c_Groups_Osgn__class_Osgn( tc_Int_Oint, X ) =
% 0.96/1.58 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.96/1.58 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.96/1.58 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.96/1.58 tc_Int_Oint ), X ), c_Groups_Osgn__class_Osgn( tc_Int_Oint, X ) =
% 0.96/1.58 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Oone__class_Oone(
% 0.96/1.58 tc_Int_Oint ) ) }.
% 0.96/1.58 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Oplus__class_Oplus(
% 0.96/1.58 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.96/1.58 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.96/1.58 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 0.96/1.58 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.96/1.58 tc_Polynomial_Opoly( X ) ) ) ) ), c_Polynomial_Osynthetic__div( X, Y, Z )
% 0.96/1.58 ), c_Polynomial_OpCons( X, hAPP( c_Polynomial_Opoly( X, Y ), Z ),
% 0.96/1.58 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) = Y }.
% 0.96/1.58 { ! class_Groups_Ozero( X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.96/1.58 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), ! hAPP(
% 0.96/1.58 c_Polynomial_Ocoeff( X, Z ), Y ) = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.96/1.58 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.96/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, Z )
% 0.96/1.58 , Y ) }.
% 0.96/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.58 ( tc_Nat_Onat ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ),
% 0.96/1.58 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) = c_Nat_OSuc(
% 0.96/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.96/1.58 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ),
% 0.96/1.58 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) }.
% 0.96/1.58 { ! class_Int_Onumber( X ), ! class_Rings_Osemiring( X ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.96/1.58 T ) ), c_Groups_Oplus__class_Oplus( X, Z, Y ) ) =
% 0.96/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.58 ( X ), c_Int_Onumber__class_Onumber__of( X, T ) ), Z ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.96/1.58 T ) ), Y ) ) }.
% 0.96/1.58 { ! class_Int_Onumber( X ), ! class_Rings_Osemiring( X ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.96/1.58 ) ), c_Int_Onumber__class_Onumber__of( X, Y ) ) =
% 0.96/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.58 ( X ), T ), c_Int_Onumber__class_Onumber__of( X, Y ) ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), c_Int_Onumber__class_Onumber__of
% 0.96/1.58 ( X, Y ) ) ) }.
% 0.96/1.58 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.96/1.58 c_Groups_Oplus__class_Oplus( X, Y, Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.58 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.58 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.96/1.58 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.58 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.96/1.58 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.96/1.58 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ), hAPP
% 0.96/1.58 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y
% 0.96/1.58 ) ) }.
% 0.96/1.58 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.58 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.96/1.58 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.96/1.58 ( X ), U = T, Z = Y, ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.96/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.58 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.96/1.58 ) }.
% 0.96/1.58 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.96/1.58 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.96/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.58 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.96/1.58 ), ! U = T }.
% 0.96/1.58 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.96/1.58 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.96/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.58 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.96/1.58 ), ! Z = Y }.
% 0.96/1.58 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.96/1.58 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.96/1.58 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.58 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Y
% 0.96/1.58 ) ), Z ) }.
% 0.96/1.58 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.96/1.58 ( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.96/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.58 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.96/1.58 ), U = Z, T = Y }.
% 0.96/1.58 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.96/1.58 ( X ), ! U = Z, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.96/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.58 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.96/1.58 ) }.
% 0.96/1.58 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.96/1.58 ( X ), ! T = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.96/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.58 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.96/1.58 ) }.
% 0.96/1.58 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.96/1.58 ( X ), ! Z = c_Groups_Oplus__class_Oplus( X, Z, Y ), Y =
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.58 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.96/1.58 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.96/1.58 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 0.96/1.58 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.96/1.58 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.96/1.58 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.96/1.58 { ! class_Rings_Ocomm__semiring( X ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.96/1.58 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.96/1.58 { ! class_Rings_Osemiring( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP
% 0.96/1.58 ( c_Groups_Otimes__class_Otimes( X ), U ), T ),
% 0.96/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.58 ( X ), Z ), T ), Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, U, Z
% 0.96/1.58 ) ), T ), Y ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.96/1.58 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X,
% 0.96/1.58 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 0.96/1.58 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.96/1.58 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.96/1.58 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.96/1.58 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.96/1.58 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.58 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.96/1.58 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.58 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.96/1.58 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.96/1.58 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.96/1.58 tc_Polynomial_Opoly( X ) ), Y ) = Y }.
% 0.96/1.58 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.96/1.58 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 0.96/1.58 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.96/1.58 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.96/1.58 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.96/1.58 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.96/1.58 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.96/1.58 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.58 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero( X ) =
% 0.96/1.58 c_Groups_Oplus__class_Oplus( X, Y, Y ) }.
% 0.96/1.58 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.96/1.58 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.96/1.58 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.96/1.58 Y ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X,
% 0.96/1.58 Z, c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.96/1.58 { ! class_Groups_Oab__semigroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.58 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.96/1.58 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.96/1.58 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.96/1.58 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.96/1.58 T, Y ), Z = Y }.
% 0.96/1.58 { ! class_Groups_Ocancel__semigroup__add( X ), ! Z = Y,
% 0.96/1.58 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.96/1.58 T, Y ) }.
% 0.96/1.58 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.96/1.58 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.96/1.58 Y, Z ), T = Y }.
% 0.96/1.58 { ! class_Groups_Ocancel__semigroup__add( X ), ! T = Y,
% 0.96/1.58 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.96/1.58 Y, Z ) }.
% 0.96/1.58 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.96/1.58 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.96/1.58 T, Y ), Z = Y }.
% 0.96/1.58 { ! class_Groups_Ocancel__ab__semigroup__add( X ), !
% 0.96/1.58 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.96/1.58 T, Y ), Z = Y }.
% 0.96/1.58 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.96/1.58 c_Groups_Oplus__class_Oplus( X, Z, T ) = c_Groups_Oplus__class_Oplus( X,
% 0.96/1.58 Y, T ), Z = Y }.
% 0.96/1.58 { ! class_Groups_Ozero( X ), ! Z = Y, hAPP( c_Polynomial_Ocoeff( X, Z ), T
% 0.96/1.58 ) = hAPP( c_Polynomial_Ocoeff( X, Y ), T ) }.
% 0.96/1.58 { ! class_Groups_Ozero( X ), ! hAPP( c_Polynomial_Ocoeff( X, Z ), skol11( X
% 0.96/1.58 , Y, Z ) ) = hAPP( c_Polynomial_Ocoeff( X, Y ), skol11( X, Y, Z ) ), Z =
% 0.96/1.58 Y }.
% 0.96/1.58 { ! class_Groups_Ozero( X ), ! c_Polynomial_Ocoeff( X, Z ) =
% 0.96/1.58 c_Polynomial_Ocoeff( X, Y ), Z = Y }.
% 0.96/1.58 { ! class_Groups_Ozero( X ), ! Z = Y, c_Polynomial_Ocoeff( X, Z ) =
% 0.96/1.58 c_Polynomial_Ocoeff( X, Y ) }.
% 0.96/1.58 { ! class_Groups_Ocomm__monoid__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.96/1.58 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.96/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( c_Polynomial_Ocoeff( X, T ), Y ),
% 0.96/1.58 hAPP( c_Polynomial_Ocoeff( X, Z ), Y ) ) }.
% 0.96/1.58 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.96/1.58 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, U, T ),
% 0.96/1.58 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 0.96/1.58 c_Groups_Oplus__class_Oplus( X, U, Z ), c_Groups_Oplus__class_Oplus(
% 0.96/1.58 tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 0.96/1.58 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.96/1.58 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.96/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 0.96/1.58 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.96/1.58 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.96/1.58 , Y ) = c_Groups_Oplus__class_Oplus( X, Y, Z ) }.
% 0.96/1.58 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.96/1.58 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.96/1.58 ( X, Z, c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.96/1.58 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.96/1.58 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.96/1.58 ( X, c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) }.
% 0.96/1.58 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.58 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.96/1.58 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.96/1.58 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.58 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.96/1.58 ( X, c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 0.96/1.58 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.58 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.96/1.58 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X
% 0.96/1.58 , U, Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.96/1.58 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.96/1.58 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ) ) =
% 0.96/1.58 c_Groups_Oplus__class_Oplus( X, c_Int_Onumber__class_Onumber__of( X, Z )
% 0.96/1.58 , c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.96/1.58 { ! class_Int_Onumber( X ), ! c_Int_Onumber__class_Onumber__of( X, Z ) = Y
% 0.96/1.58 , Y = c_Int_Onumber__class_Onumber__of( X, Z ) }.
% 0.96/1.58 { ! class_Int_Onumber( X ), ! Y = c_Int_Onumber__class_Onumber__of( X, Z )
% 0.96/1.58 , c_Int_Onumber__class_Onumber__of( X, Z ) = Y }.
% 0.96/1.58 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.58 c_Int_Onumber__class_Onumber__of( X, Z ),
% 0.96/1.58 c_Int_Onumber__class_Onumber__of( X, Y ) ) =
% 0.96/1.58 c_Int_Onumber__class_Onumber__of( X, c_Groups_Oplus__class_Oplus(
% 0.96/1.58 tc_Int_Oint, Z, Y ) ) }.
% 0.96/1.58 { ! class_Int_Onumber__ring( X ), ! class_Int_Oring__char__0( X ), !
% 0.96/1.58 c_Int_Onumber__class_Onumber__of( X, Z ) =
% 0.96/1.58 c_Int_Onumber__class_Onumber__of( X, Y ), Z = Y }.
% 0.96/1.58 { ! class_Int_Onumber__ring( X ), ! class_Int_Oring__char__0( X ), ! Z = Y
% 0.96/1.58 , c_Int_Onumber__class_Onumber__of( X, Z ) =
% 0.96/1.58 c_Int_Onumber__class_Onumber__of( X, Y ) }.
% 0.96/1.58 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.58 c_Int_Onumber__class_Onumber__of( X, T ), c_Groups_Oplus__class_Oplus( X
% 0.96/1.58 , c_Int_Onumber__class_Onumber__of( X, Z ), Y ) ) =
% 0.96/1.58 c_Groups_Oplus__class_Oplus( X, c_Int_Onumber__class_Onumber__of( X,
% 0.96/1.58 c_Groups_Oplus__class_Oplus( tc_Int_Oint, T, Z ) ), Y ) }.
% 0.96/1.58 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.96/1.58 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ),
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.96/1.58 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.96/1.58 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.96/1.58 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.96/1.58 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.96/1.58 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.96/1.58 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.96/1.58 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.96/1.58 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.96/1.58 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.96/1.58 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.96/1.58 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.96/1.58 U ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.96/1.58 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.96/1.58 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ),
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.96/1.58 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.96/1.58 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.96/1.58 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.96/1.58 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ), c_Orderings_Oord__class_Oless
% 0.96/1.58 ( X, T, Y ) }.
% 0.96/1.58 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, T, Y ), c_Orderings_Oord__class_Oless(
% 0.96/1.58 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.96/1.58 , Y, Z ) ) }.
% 0.96/1.58 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.96/1.58 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.96/1.58 ( X, Z, Y ) }.
% 0.96/1.58 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.96/1.58 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.96/1.58 , T, Y ) ) }.
% 0.96/1.58 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.96/1.58 X, c_Groups_Oplus__class_Oplus( X, Z, T ), c_Groups_Oplus__class_Oplus( X
% 0.96/1.58 , Y, T ) ) }.
% 0.96/1.58 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.96/1.58 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.96/1.58 , T, Y ) ) }.
% 0.96/1.58 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.96/1.58 ( X, U, T ), c_Orderings_Oord__class_Oless( X,
% 0.96/1.58 c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X, Y
% 0.96/1.58 , T ) ) }.
% 0.96/1.58 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, T )
% 0.96/1.58 , c_Groups_Oplus__class_Oplus( X, Y, T ) ), c_Orderings_Oord__class_Oless
% 0.96/1.58 ( X, Z, Y ) }.
% 0.96/1.58 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.96/1.58 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.96/1.58 ( X, Z, Y ) }.
% 0.96/1.58 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.58 c_Int_Onumber__class_Onumber__of( X, T ), c_Groups_Ominus__class_Ominus(
% 0.96/1.58 X, Z, c_Int_Onumber__class_Onumber__of( X, Y ) ) ) =
% 0.96/1.58 c_Groups_Oplus__class_Oplus( X, c_Int_Onumber__class_Onumber__of( X,
% 0.96/1.58 c_Groups_Oplus__class_Oplus( tc_Int_Oint, T,
% 0.96/1.58 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ) ), Z ) }.
% 0.96/1.58 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.58 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.58 Z, Y ) ) = Y }.
% 0.96/1.58 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Z,
% 0.96/1.58 c_Groups_Oplus__class_Oplus( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.96/1.58 Y ) ) = Y }.
% 0.96/1.58 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.96/1.58 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 0.96/1.58 , c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.96/1.58 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.96/1.58 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.96/1.58 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 0.96/1.58 , c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.96/1.58 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.96/1.58 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.96/1.58 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, T, Z ),
% 0.96/1.58 c_Polynomial_Omonom( X, Y, Z ) ) = c_Polynomial_Omonom( X,
% 0.96/1.58 c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 0.96/1.58 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.96/1.58 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = Z }.
% 0.96/1.58 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.58 c_Groups_Ominus__class_Ominus( X, Z, Y ), Y ) = Z }.
% 0.96/1.58 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.58 c_Int_Onumber__class_Onumber__of( X, T ), c_Groups_Ominus__class_Ominus(
% 0.96/1.58 X, c_Int_Onumber__class_Onumber__of( X, Z ), Y ) ) =
% 0.96/1.58 c_Groups_Ominus__class_Ominus( X, c_Int_Onumber__class_Onumber__of( X,
% 0.96/1.58 c_Groups_Oplus__class_Oplus( tc_Int_Oint, T, Z ) ), Y ) }.
% 0.96/1.58 { ! class_Int_Onumber( X ), ! class_Orderings_Olinorder( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 0.96/1.58 , Z ), c_Int_Onumber__class_Onumber__of( X, Y ) ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Y
% 0.96/1.58 ), c_Int_Onumber__class_Onumber__of( X, Z ) ) }.
% 0.96/1.58 { ! class_Int_Onumber( X ), ! class_Orderings_Olinorder( X ),
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Y
% 0.96/1.58 ), c_Int_Onumber__class_Onumber__of( X, Z ) ),
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 0.96/1.58 , Z ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.96/1.58 { ! class_Int_Onumber( X ), ! class_Rings_Oring( X ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 0.96/1.58 Z ) ), c_Int_Onumber__class_Onumber__of( X, Y ) ) =
% 0.96/1.58 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), T ), c_Int_Onumber__class_Onumber__of
% 0.96/1.58 ( X, Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 0.96/1.58 c_Int_Onumber__class_Onumber__of( X, Y ) ) ) }.
% 0.96/1.58 { ! class_Int_Onumber( X ), ! class_Rings_Oring( X ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.96/1.58 T ) ), c_Groups_Ominus__class_Ominus( X, Z, Y ) ) =
% 0.96/1.58 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.96/1.58 T ) ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.96/1.58 c_Int_Onumber__class_Onumber__of( X, T ) ), Y ) ) }.
% 0.96/1.58 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 0.96/1.58 , Z ), c_Int_Onumber__class_Onumber__of( X, Y ) ),
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z, Y ) }.
% 0.96/1.58 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z, Y ),
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 0.96/1.58 , Z ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.96/1.58 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.58 c_Groups_Oplus__class_Oplus( X, Y, Y ) ),
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.96/1.58 ) }.
% 0.96/1.58 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.96/1.58 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.96/1.58 ), c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.96/1.58 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Y,
% 0.96/1.58 Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.96/1.58 ) }.
% 0.96/1.58 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.96/1.58 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X
% 0.96/1.58 , Y, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.58 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.96/1.58 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.96/1.58 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.96/1.58 ) }.
% 0.96/1.58 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.96/1.58 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.96/1.58 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 0.96/1.58 .
% 0.96/1.58 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.96/1.58 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.96/1.58 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.96/1.58 .
% 0.96/1.58 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.96/1.58 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.96/1.58 X ), Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), ! Z =
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.96/1.58 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.58 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.96/1.58 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 0.96/1.58 Y, Z ) ) }.
% 0.96/1.58 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.96/1.58 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 0.96/1.58 Z, Y ) ) }.
% 0.96/1.58 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.96/1.58 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.96/1.58 , c_Groups_Oplus__class_Oplus( X, Y, Z ), c_Groups_Ozero__class_Ozero( X
% 0.96/1.58 ) ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.96/1.58 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.96/1.58 ) ), c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 0.96/1.58 ) ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.96/1.58 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.96/1.58 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.96/1.58 ) ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.58 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless(
% 0.96/1.58 X, T, c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.96/1.58 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.58 c_Groups_Oplus__class_Oplus( X, Y, Y ) ), c_Orderings_Oord__class_Oless(
% 0.96/1.58 X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.96/1.58 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.58 c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.96/1.58 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.96/1.58 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Y
% 0.96/1.58 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.58 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.96/1.58 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.58 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.96/1.58 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.96/1.58 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.58 c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.96/1.58 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.96/1.58 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.58 , c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.96/1.58 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.58 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Z
% 0.96/1.58 ), c_Int_Onumber__class_Onumber__of( X, Y ) ),
% 0.96/1.58 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, Y ) }.
% 0.96/1.58 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, Y ),
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Z
% 0.96/1.58 ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.96/1.58 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, U )
% 0.96/1.58 , c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.96/1.58 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, U, T ), c_Orderings_Oord__class_Oless(
% 0.96/1.58 X, c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X
% 0.96/1.58 , Y, T ) ) }.
% 0.96/1.58 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.96/1.58 ( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! W = U, T = Z, !
% 0.96/1.58 c_Groups_Oplus__class_Oplus( X, W, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) =
% 0.96/1.58 c_Groups_Oplus__class_Oplus( X, U, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.58 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.96/1.58 ) = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X
% 0.96/1.58 ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.58 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.96/1.58 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.96/1.58 ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.58 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.58 { ! class_Int_Onumber__ring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.58 ( X ), c_Int_Onumber__class_Onumber__of( X, T ) ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.96/1.58 Z ) ), Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.96/1.58 c_Int_Onumber__class_Onumber__of( X, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), T ), Z ) ) ), Y ) }.
% 0.96/1.58 { ! class_Int_Onumber__ring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.58 ( X ), c_Int_Onumber__class_Onumber__of( X, Z ) ),
% 0.96/1.58 c_Int_Onumber__class_Onumber__of( X, Y ) ) =
% 0.96/1.58 c_Int_Onumber__class_Onumber__of( X, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ) }.
% 0.96/1.58 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X, hAPP
% 0.96/1.58 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ) = hAPP(
% 0.96/1.58 hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.96/1.58 c_Int_Onumber__class_Onumber__of( X, Z ) ),
% 0.96/1.58 c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.96/1.58 , Y, c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) )
% 0.96/1.58 ) }.
% 0.96/1.58 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.96/1.58 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus
% 0.96/1.58 ( X, Z ) }.
% 0.96/1.58 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 0.96/1.58 , Z ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.58 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.96/1.58 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Ozero__class_Ozero(
% 0.96/1.58 X ) }.
% 0.96/1.58 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 0.96/1.58 , Y ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.58 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.96/1.58 = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ouminus__class_Ouminus
% 0.96/1.58 ( X, Y ) }.
% 0.96/1.58 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.58 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.58 { ! class_Groups_Oab__group__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.58 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.58 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.96/1.58 = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.96/1.58 Z ) = Y }.
% 0.96/1.58 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.96/1.58 , Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.96/1.58 c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.96/1.58 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.96/1.58 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.96/1.58 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP
% 0.96/1.58 ( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.96/1.58 c_Groups_Oone__class_Oone( X ) ) ), Z ) }.
% 0.96/1.58 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.58 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = hAPP(
% 0.96/1.58 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X
% 0.96/1.58 , Z, c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.96/1.58 { ! class_Rings_Oring( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.96/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.58 ( X ), U ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 0.96/1.58 Z ) ), Y ) ) }.
% 0.96/1.58 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.96/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.58 ( X ), Z ), U ), Y ), T = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.96/1.58 W ) ), U ), Y ) }.
% 0.96/1.58 { ! class_Rings_Oring( X ), ! T = c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.96/1.58 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.96/1.58 X, Z, W ) ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.96/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.58 ( X ), Z ), U ), Y ) }.
% 0.96/1.58 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.96/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.58 ( X ), Z ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.96/1.58 Z ) ), U ), T ) = Y }.
% 0.96/1.58 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.96/1.58 Z ) ), U ), T ) = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.96/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.58 ( X ), Z ), U ), Y ) }.
% 0.96/1.58 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.96/1.58 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.96/1.58 c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.96/1.58 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.96/1.58 X, U, Z ) ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 0.96/1.58 Z ) ), Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 0.96/1.58 c_Groups_Ominus__class_Ominus( X, T, Y ) ) ) }.
% 0.96/1.58 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.96/1.58 ) = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus(
% 0.96/1.58 X, Y ) ) }.
% 0.96/1.58 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z, Y )
% 0.96/1.58 = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus( X
% 0.96/1.58 , Y ) ) }.
% 0.96/1.58 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X, Z
% 0.96/1.58 , Y ) = c_Groups_Oplus__class_Oplus( X, Z,
% 0.96/1.58 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.96/1.58 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.96/1.58 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Oplus__class_Oplus(
% 0.96/1.58 X, Z, Y ) }.
% 0.96/1.58 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.96/1.58 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ) =
% 0.96/1.58 c_Groups_Ominus__class_Ominus( X, c_Int_Onumber__class_Onumber__of( X, Z
% 0.96/1.58 ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.96/1.58 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.96/1.58 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ) =
% 0.96/1.58 c_Groups_Ouminus__class_Ouminus( X, c_Int_Onumber__class_Onumber__of( X,
% 0.96/1.58 Y ) ) }.
% 0.96/1.58 { ! class_Int_Onumber__ring( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.96/1.58 c_Int_Onumber__class_Onumber__of( X, Y ) ) =
% 0.96/1.58 c_Int_Onumber__class_Onumber__of( X, c_Groups_Ouminus__class_Ouminus(
% 0.96/1.58 tc_Int_Oint, Y ) ) }.
% 0.96/1.58 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.96/1.58 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.58 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.96/1.58 c_Polynomial_OpCons( X, Z, Y ) ), c_Groups_Ozero__class_Ozero(
% 0.96/1.58 tc_Nat_Onat ) ) = Z }.
% 0.96/1.58 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.96/1.58 c_Polynomial_OpCons( X, T, Z ) ), c_Nat_OSuc( Y ) ) = hAPP(
% 0.96/1.58 c_Polynomial_Ocoeff( X, Z ), Y ) }.
% 0.96/1.58 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 0.96/1.58 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) )
% 0.96/1.58 , c_Polynomial_Odegree( X, c_Groups_Oplus__class_Oplus(
% 0.96/1.58 tc_Polynomial_Opoly( X ), Y, Z ) ) = c_Polynomial_Odegree( X, Y ) }.
% 0.96/1.58 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 0.96/1.58 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) )
% 0.96/1.58 , c_Polynomial_Odegree( X, c_Groups_Oplus__class_Oplus(
% 0.96/1.58 tc_Polynomial_Opoly( X ), Z, Y ) ) = c_Polynomial_Odegree( X, Y ) }.
% 0.96/1.58 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 0.96/1.58 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, T )
% 0.96/1.58 , Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree(
% 0.96/1.58 X, c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Z, T ) ), Y ) }
% 0.96/1.58 .
% 0.96/1.58 { ! class_Groups_Ocomm__monoid__add( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 0.96/1.58 Z ), Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.58 c_Polynomial_Odegree( X, T ), Y ), c_Orderings_Oord__class_Oless__eq(
% 0.96/1.58 tc_Nat_Onat, c_Polynomial_Odegree( X, c_Groups_Oplus__class_Oplus(
% 0.96/1.58 tc_Polynomial_Opoly( X ), Z, T ) ), Y ) }.
% 0.96/1.58 { ! class_Groups_Ozero( X ), ! T = Z, hAPP( c_Polynomial_Ocoeff( X,
% 0.96/1.58 c_Polynomial_Omonom( X, Y, T ) ), Z ) = Y }.
% 0.96/1.58 { ! class_Groups_Ozero( X ), T = Z, hAPP( c_Polynomial_Ocoeff( X,
% 0.96/1.58 c_Polynomial_Omonom( X, Y, T ) ), Z ) = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.58 }.
% 0.96/1.58 { ! class_Groups_Oab__group__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.96/1.58 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ) ), Y ) =
% 0.96/1.58 c_Groups_Ouminus__class_Ouminus( X, hAPP( c_Polynomial_Ocoeff( X, Z ), Y
% 0.96/1.58 ) ) }.
% 0.96/1.58 { ! class_Groups_Oab__group__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.96/1.58 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.96/1.58 c_Groups_Ominus__class_Ominus( X, hAPP( c_Polynomial_Ocoeff( X, T ), Y )
% 0.96/1.58 , hAPP( c_Polynomial_Ocoeff( X, Z ), Y ) ) }.
% 0.96/1.58 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Ocoeff( X, Z ),
% 0.96/1.58 c_Polynomial_Odegree( X, Z ) ) = hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.96/1.58 c_Polynomial_Odegree( X, Y ) ), ! c_Rings_Odvd__class_Odvd(
% 0.96/1.58 tc_Polynomial_Opoly( X ), Z, Y ), ! c_Rings_Odvd__class_Odvd(
% 0.96/1.58 tc_Polynomial_Opoly( X ), Y, Z ), Z = Y }.
% 0.96/1.58 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.96/1.58 ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.96/1.58 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.96/1.58 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.96/1.58 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.96/1.58 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.96/1.58 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.96/1.58 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.96/1.58 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.96/1.58 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.96/1.58 ) ) }.
% 0.96/1.58 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.96/1.58 ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.96/1.58 ) ) }.
% 0.96/1.58 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.96/1.58 ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.96/1.58 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.96/1.58 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.58 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.96/1.58 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.96/1.58 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.96/1.58 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 0.96/1.58 X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 0.96/1.58 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.96/1.58 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ) ), Z = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.58 }.
% 0.96/1.58 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.96/1.58 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.58 }.
% 0.96/1.58 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.58 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.96/1.58 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.96/1.58 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.58 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.96/1.58 ) ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__ring__strict( X ), Z =
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.96/1.58 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__ring__strict( X ), Y =
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.96/1.58 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.96/1.58 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.96/1.58 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.58 c_Groups_Oone__class_Oone( X ), c_Groups_Oone__class_Oone( X ) ) ) }.
% 0.96/1.58 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.96/1.58 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.96/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.58 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X, T,
% 0.96/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.58 ( X ), c_Groups_Ominus__class_Ominus( X, Z, W ) ), U ), Y ) ) }.
% 0.96/1.58 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.96/1.58 , T, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.96/1.58 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.58 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.96/1.58 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.96/1.58 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.96/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.58 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.58 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ) }.
% 0.96/1.58 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.96/1.58 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.96/1.58 Z ) ), U ), T ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.58 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.96/1.58 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.96/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.58 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, hAPP
% 0.96/1.58 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus
% 0.96/1.58 ( X, Z, W ) ), U ), Y ) ) }.
% 0.96/1.58 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X, T
% 0.96/1.58 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.96/1.58 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless( X,
% 0.96/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.58 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.96/1.58 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.96/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.58 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.96/1.58 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.96/1.58 X, W, Z ) ), U ), T ), Y ) }.
% 0.96/1.58 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.96/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.58 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ),
% 0.96/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.96/1.58 hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.96/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.58 ( X ), Z ), U ), Y ) ) }.
% 0.96/1.58 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 0.96/1.58 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ), hBOOL(
% 0.96/1.58 hAPP( Z, skol12( U, W, Z ) ) ) }.
% 0.96/1.58 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 0.96/1.58 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ),
% 0.96/1.58 c_Rings_Odvd__class_Odvd( X, Y, c_Groups_Oplus__class_Oplus( X, skol12( X
% 0.96/1.58 , Y, Z ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.96/1.58 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), !
% 0.96/1.58 c_Rings_Odvd__class_Odvd( X, Y, c_Groups_Oplus__class_Oplus( X, T,
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ) ) ), ! hBOOL( hAPP( Z, T ) ), hBOOL(
% 0.96/1.58 hAPP( Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), skol24( X,
% 0.96/1.58 Y, Z ) ) ) ) }.
% 0.96/1.58 { ! class_Rings_Oring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP
% 0.96/1.58 ( c_Groups_Otimes__class_Otimes( X ), Y ), Y ), c_Groups_Oone__class_Oone
% 0.96/1.58 ( X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.96/1.58 c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) ) ),
% 0.96/1.58 c_Groups_Ominus__class_Ominus( X, Y, c_Groups_Oone__class_Oone( X ) ) ) }
% 0.96/1.58 .
% 0.96/1.58 { ! class_Int_Onumber__ring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.58 ( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.96/1.58 c_Int_Onumber__class_Onumber__of( X, Z ) ) ), Y ) = hAPP( hAPP(
% 0.96/1.58 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.96/1.58 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Z ) ) ), Y ) }.
% 0.96/1.58 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 0.96/1.58 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.96/1.58 c_Groups_Oplus__class_Oplus( X, U, T ) ), c_Rings_Odvd__class_Odvd( X, Z
% 0.96/1.58 , c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U,
% 0.96/1.58 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) }.
% 0.96/1.58 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 0.96/1.58 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.96/1.58 c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U, hAPP
% 0.96/1.58 ( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ),
% 0.96/1.58 c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oplus__class_Oplus( X, U, T ) )
% 0.96/1.58 }.
% 0.96/1.58 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 0.96/1.58 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.96/1.58 c_Groups_Oplus__class_Oplus( X, U, T ) ), c_Rings_Odvd__class_Odvd( X, Z
% 0.96/1.58 , c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U,
% 0.96/1.58 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) }.
% 0.96/1.58 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 0.96/1.58 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.96/1.58 c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U, hAPP
% 0.96/1.58 ( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ),
% 0.96/1.58 c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oplus__class_Oplus( X, U, T ) )
% 0.96/1.58 }.
% 0.96/1.58 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.96/1.58 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.96/1.58 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ),
% 0.96/1.58 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) ) =
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.96/1.58 .
% 0.96/1.58 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.96/1.58 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.96/1.58 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ),
% 0.96/1.58 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) ) =
% 0.96/1.58 c_Groups_Ozero__class_Ozero( X ), ! c_Int_Onumber__class_Onumber__of(
% 0.96/1.58 tc_Nat_Onat, Y ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.58 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.96/1.58 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.96/1.59 , ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.59 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.59 c_Power_Opower__class_Opower( X ), Z ), c_Int_Onumber__class_Onumber__of
% 0.96/1.59 ( tc_Nat_Onat, Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.59 { ! class_Groups_Ozero( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.59 c_Polynomial_Odegree( X, Z ), Y ), hAPP( c_Polynomial_Ocoeff( X, Z ), Y )
% 0.96/1.59 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.59 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X, Z ), Y ) =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless__eq(
% 0.96/1.59 tc_Nat_Onat, Y, c_Polynomial_Odegree( X, Z ) ) }.
% 0.96/1.59 { ! class_Groups_Ozero( X ), ! hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.96/1.59 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.59 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.96/1.59 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.59 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ), ! hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.96/1.59 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.96/1.59 c_Polynomial_OpCons( X, T, Z ) ), Y ) = c_Groups_Oplus__class_Oplus( X, T
% 0.96/1.59 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), hAPP(
% 0.96/1.59 c_Polynomial_Opoly( X, Z ), Y ) ) ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.59 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.96/1.59 , Y ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) ),
% 0.96/1.59 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Orderings_Oord__class_Oless
% 0.96/1.59 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 0.96/1.59 { ! c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Orderings_Oord__class_Oless
% 0.96/1.59 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.59 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ),
% 0.96/1.59 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.59 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.59 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ),
% 0.96/1.59 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) ) }.
% 0.96/1.59 { ! class_Rings_Olinordered__semiring__1( X ), !
% 0.96/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.96/1.59 c_Orderings_Oord__class_Oless__eq( X, T, Y ), !
% 0.96/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.96/1.59 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.96/1.59 X ), W ), ! c_Groups_Oplus__class_Oplus( X, U, W ) =
% 0.96/1.59 c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.59 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.59 ( X ), U ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), T )
% 0.96/1.59 ), Y ) }.
% 0.96/1.59 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), !
% 0.96/1.59 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.59 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.96/1.59 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) ) =
% 0.96/1.59 c_Groups_Oone__class_Oone( X ) }.
% 0.96/1.59 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ),
% 0.96/1.59 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.59 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.96/1.59 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) ) =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__1( X ), ! Y = c_Groups_Ozero__class_Ozero
% 0.96/1.59 ( tc_Nat_Onat ), hAPP( c_Polynomial_Ocoeff( X, c_Groups_Oone__class_Oone
% 0.96/1.59 ( tc_Polynomial_Opoly( X ) ) ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__1( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.59 tc_Nat_Onat ), hAPP( c_Polynomial_Ocoeff( X, c_Groups_Oone__class_Oone(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ) ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.59 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.96/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.96/1.59 ( c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) ) }.
% 0.96/1.59 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.96/1.59 , c_Groups_Ozero__class_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.96/1.59 c_Polynomial_Odegree( X, Y ) ) ), c_Polynomial_Opos__poly( X, Y ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Ocoeff( X, hAPP
% 0.96/1.59 ( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ),
% 0.96/1.59 c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 0.96/1.59 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ), Y ) = c_Groups_Oone__class_Oone
% 0.96/1.59 ( X ) }.
% 0.96/1.59 { ! class_Rings_Olinordered__semiring__1__strict( X ), !
% 0.96/1.59 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.96/1.59 ( X, T, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( X ), U ), !
% 0.96/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), W
% 0.96/1.59 ), ! c_Groups_Oplus__class_Oplus( X, U, W ) = c_Groups_Oone__class_Oone
% 0.96/1.59 ( X ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X,
% 0.96/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), W ), T ) ), Y ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 0.96/1.59 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus(
% 0.96/1.59 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, T,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 0.96/1.59 c_Polynomial_Opcompose( X, Z, Y ) ) ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP
% 0.96/1.59 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), hAPP( hAPP(
% 0.96/1.59 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) ) = hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.96/1.59 Y ) ), c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.96/1.59 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.96/1.59 , U = c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), T ), Y )
% 0.96/1.59 }.
% 0.96/1.59 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.96/1.59 , alpha27( X, Y, Z, T ) }.
% 0.96/1.59 { ! class_Fields_Ofield( X ), ! U = c_Groups_Oplus__class_Oplus(
% 0.96/1.59 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ), Z ), T ), Y ), ! alpha27( X, Y, Z, T ),
% 0.96/1.59 c_Polynomial_Opdivmod__rel( X, U, T, Z, Y ) }.
% 0.96/1.59 { ! alpha27( X, Y, Z, T ), alpha9( X, Z, T ) }.
% 0.96/1.59 { ! alpha27( X, Y, Z, T ), alpha20( X, Y, T ) }.
% 0.96/1.59 { ! alpha9( X, Z, T ), ! alpha20( X, Y, T ), alpha27( X, Y, Z, T ) }.
% 0.96/1.59 { ! alpha20( X, Y, Z ), Z = c_Groups_Ozero__class_Ozero(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ), alpha28( X, Y, Z ) }.
% 0.96/1.59 { ! Z = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha20( X
% 0.96/1.59 , Y, Z ) }.
% 0.96/1.59 { ! alpha28( X, Y, Z ), alpha20( X, Y, Z ) }.
% 0.96/1.59 { ! alpha28( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.59 c_Polynomial_Odegree( X, Y ), c_Polynomial_Odegree( X, Z ) ) }.
% 0.96/1.59 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha28( X
% 0.96/1.59 , Y, Z ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, Y
% 0.96/1.59 ), c_Polynomial_Odegree( X, Z ) ), alpha28( X, Y, Z ) }.
% 0.96/1.59 { ! alpha9( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ), Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.59 { Z = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha9( X, Y
% 0.96/1.59 , Z ) }.
% 0.96/1.59 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha9( X
% 0.96/1.59 , Y, Z ) }.
% 0.96/1.59 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.96/1.59 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.96/1.59 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus(
% 0.96/1.59 X, U, Z ), c_Groups_Ominus__class_Ominus( X, T, Y ) ) }.
% 0.96/1.59 { ! class_Groups_Ozero( X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z
% 0.96/1.59 , skol13( T, U, Z ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.59 c_Polynomial_Odegree( X, Y ), Z ) }.
% 0.96/1.59 { ! class_Groups_Ozero( X ), ! hAPP( c_Polynomial_Ocoeff( X, Y ), skol13( X
% 0.96/1.59 , Y, Z ) ) = c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 0.96/1.59 Y ), Z ) }.
% 0.96/1.59 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) =
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.96/1.59 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.96/1.59 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ) ),
% 0.96/1.59 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ) =
% 0.96/1.59 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.96/1.59 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ) ), X ) =
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.96/1.59 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero
% 0.96/1.59 ( tc_Int_Oint ) ) = X }.
% 0.96/1.59 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.96/1.59 tc_Int_Oint ), X ) = X }.
% 0.96/1.59 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.59 tc_Nat_Onat ), X ) = X }.
% 0.96/1.59 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero
% 0.96/1.59 ( tc_Nat_Onat ) ) = X }.
% 0.96/1.59 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.59 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.59 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.96/1.59 tc_Nat_Onat, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.59 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = Y, X =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.59 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.96/1.59 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.96/1.59 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), T ), Z ),
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), X ) ) =
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus
% 0.96/1.59 ( tc_Nat_Onat, T, Y ) ), Z ), X ) }.
% 0.96/1.59 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, c_Groups_Oplus__class_Oplus(
% 0.96/1.59 tc_Nat_Onat, X, Y ) ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.96/1.59 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.96/1.59 ( tc_Nat_Onat, Y, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.96/1.59 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.96/1.59 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.96/1.59 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.96/1.59 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 0.96/1.59 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.96/1.59 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) =
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ) }.
% 0.96/1.59 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus
% 0.96/1.59 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 0.96/1.59 { c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.96/1.59 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ),
% 0.96/1.59 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ) =
% 0.96/1.59 c_Int_Onumber__class_Onumber__of( tc_Int_Oint,
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 0.96/1.59 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.96/1.59 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.96/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.96/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ), X ),
% 0.96/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.96/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.96/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.96/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, T ),
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ),
% 0.96/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol14( X, Y ) ) }.
% 0.96/1.59 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.96/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.96/1.59 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.96/1.59 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.96/1.59 ( tc_Nat_Onat, Y, Z ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y
% 0.96/1.59 , X ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, X ) =
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.96/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.96/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ),
% 0.96/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.96/1.59 tc_Nat_Onat, Y, T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.96/1.59 .
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.96/1.59 tc_Nat_Onat, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.96/1.59 .
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.96/1.59 ( tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) )
% 0.96/1.59 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.96/1.59 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }
% 0.96/1.59 .
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.96/1.59 ( tc_Nat_Onat, Y, X ), X ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.96/1.59 ( tc_Nat_Onat, Y, X ), Y ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.96/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ),
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.96/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.96/1.59 tc_Int_Oint, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 0.96/1.59 .
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.59 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ),
% 0.96/1.59 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ),
% 0.96/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.96/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.59 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ),
% 0.96/1.59 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.96/1.59 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ),
% 0.96/1.59 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ),
% 0.96/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.96/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.96/1.59 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ),
% 0.96/1.59 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ) }.
% 0.96/1.59 { c_Groups_Ominus__class_Ominus( tc_Int_Oint,
% 0.96/1.59 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ),
% 0.96/1.59 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ) =
% 0.96/1.59 c_Int_Onumber__class_Onumber__of( tc_Int_Oint,
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.96/1.59 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) ) }.
% 0.96/1.59 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint,
% 0.96/1.59 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ) =
% 0.96/1.59 c_Int_Onumber__class_Onumber__of( tc_Int_Oint,
% 0.96/1.59 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.96/1.59 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.96/1.59 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.96/1.59 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ),
% 0.96/1.59 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.96/1.59 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.96/1.59 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) =
% 0.96/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ) }.
% 0.96/1.59 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.96/1.59 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) =
% 0.96/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 0.96/1.59 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.96/1.59 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.96/1.59 Z, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.96/1.59 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.96/1.59 tc_Nat_Onat, Y, X ), Y ) = X }.
% 0.96/1.59 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.96/1.59 tc_Nat_Onat, Y, X ), X ) = Y }.
% 0.96/1.59 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ), Z =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.59 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ), Y =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.59 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opdivmod__rel( X,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ) }.
% 0.96/1.59 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ), Z =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.59 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ), Y = T }
% 0.96/1.59 .
% 0.96/1.59 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ), ! Y = T, c_Polynomial_Opdivmod__rel( X, T,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ) }.
% 0.96/1.59 { ! class_Fields_Ofield( X ), c_Polynomial_Opdivmod__rel( X,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.96/1.59 { ! class_Fields_Ofield( X ), c_Polynomial_Opdivmod__rel( X, Y,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) }.
% 0.96/1.59 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.96/1.59 , ! c_Polynomial_Opdivmod__rel( X, U, T, V0, W ), Z = V0 }.
% 0.96/1.59 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.96/1.59 , ! c_Polynomial_Opdivmod__rel( X, U, T, V0, W ), Y = W }.
% 0.96/1.59 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, U, Y )
% 0.96/1.59 , ! c_Polynomial_Opdivmod__rel( X, T, Z, V0, W ), Y = W }.
% 0.96/1.59 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, Y, U )
% 0.96/1.59 , ! c_Polynomial_Opdivmod__rel( X, T, Z, W, V0 ), Y = W }.
% 0.96/1.59 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.96/1.59 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 0.96/1.59 tc_Nat_Onat, Z, Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.96/1.59 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.96/1.59 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.59 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.96/1.59 c_Power_Opower__class_Opower( X ), T ), Y ) ) = hAPP( hAPP(
% 0.96/1.59 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 0.96/1.59 tc_Nat_Onat, Z, Y ) ) }.
% 0.96/1.59 { ! c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ), alpha10( X, Y ),
% 0.96/1.59 alpha21( X, Y ) }.
% 0.96/1.59 { ! alpha10( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.96/1.59 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 0.96/1.59 { ! alpha21( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.96/1.59 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 0.96/1.59 { ! alpha21( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.59 { ! alpha21( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.96/1.59 tc_Nat_Onat ) ) }.
% 0.96/1.59 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha21( X, Y ) }.
% 0.96/1.59 { ! alpha10( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.96/1.59 tc_Nat_Onat ) ) }.
% 0.96/1.59 { ! alpha10( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.59 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha10( X, Y ) }.
% 0.96/1.59 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha11( X, Y ), alpha22( X
% 0.96/1.59 , Y ) }.
% 0.96/1.59 { ! alpha11( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.96/1.59 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.96/1.59 { ! alpha22( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.96/1.59 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.96/1.59 { ! alpha22( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.59 { ! alpha22( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.96/1.59 tc_Nat_Onat ) ) }.
% 0.96/1.59 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha22( X, Y ) }.
% 0.96/1.59 { ! alpha11( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.96/1.59 tc_Nat_Onat ) ) }.
% 0.96/1.59 { ! alpha11( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.59 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha11( X, Y ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.59 ( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ),
% 0.96/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.59 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.59 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.96/1.59 tc_Nat_Onat, Y, X ) ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.59 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.96/1.59 tc_Nat_Onat, Y, X ) ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.96/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.96/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.96/1.59 tc_Int_Oint, X, Y ) ) }.
% 0.96/1.59 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.96/1.59 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), X = c_Nat_OSuc(
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol15( X, Y ) ) ) }.
% 0.96/1.59 { ! X = c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ),
% 0.96/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.96/1.59 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.96/1.59 tc_Int_Oint, c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ) =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.96/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Z ),
% 0.96/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.96/1.59 tc_Int_Oint, Y, T ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 0.96/1.59 .
% 0.96/1.59 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y,
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.59 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Y )
% 0.96/1.59 ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.96/1.59 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), c_Nat_OSuc
% 0.96/1.59 ( X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.96/1.59 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y
% 0.96/1.59 = X }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.96/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.96/1.59 tc_Int_Oint ) ) ) }.
% 0.96/1.59 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.96/1.59 tc_Int_Oint ) ) ) }.
% 0.96/1.59 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.96/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) = Y }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z,
% 0.96/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 0.96/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.96/1.59 tc_Nat_Onat, Z, X ), Y ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.96/1.59 ( tc_Nat_Onat, Z, X ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z
% 0.96/1.59 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 0.96/1.59 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.96/1.59 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.96/1.59 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.96/1.59 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.96/1.59 tc_Nat_Onat, X, Z ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.96/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), Z ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.96/1.59 tc_Nat_Onat, X, Y ), Z ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ), Y ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.96/1.59 tc_Nat_Onat, Z, X ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.96/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.96/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z, X =
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X =
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.96/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.96/1.59 tc_Nat_Onat, X, Y ), Y ) = X }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.96/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.96/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ),
% 0.96/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.96/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.96/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.96/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.96/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 0.96/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.96/1.59 tc_Nat_Onat, Z, X ), Y ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 0.96/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = X }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.96/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.96/1.59 tc_Nat_Onat, X, Z ), Y ) ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ),
% 0.96/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ),
% 0.96/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z,
% 0.96/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 0.96/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.96/1.59 tc_Nat_Onat, Z, Y ), X ) }.
% 0.96/1.59 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.96/1.59 ( tc_Int_Oint, X ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.96/1.59 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 0.96/1.59 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 0.96/1.59 tc_Int_Oint, U, T ) ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y,
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.96/1.59 tc_Int_Oint, U, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 0.96/1.59 , Z ), X ) ), T ) ) }.
% 0.96/1.59 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 0.96/1.59 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 0.96/1.59 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), T ) ),
% 0.96/1.59 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 0.96/1.59 tc_Int_Oint, U, T ) ) }.
% 0.96/1.59 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus(
% 0.96/1.59 tc_Int_Oint, Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 0.96/1.59 , Z ), X ) ) ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 0.96/1.59 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd
% 0.96/1.59 ( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP( hAPP
% 0.96/1.59 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ) }.
% 0.96/1.59 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) =
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.96/1.59 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.96/1.59 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.96/1.59 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.96/1.59 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) }.
% 0.96/1.59 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ),
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) = hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.96/1.59 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 0.96/1.59 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ) }.
% 0.96/1.59 { ! class_Int_Onumber__ring( X ), c_Groups_Ominus__class_Ominus( X,
% 0.96/1.59 c_Int_Onumber__class_Onumber__of( X, Z ),
% 0.96/1.59 c_Int_Onumber__class_Onumber__of( X, Y ) ) =
% 0.96/1.59 c_Int_Onumber__class_Onumber__of( X, c_Groups_Oplus__class_Oplus(
% 0.96/1.59 tc_Int_Oint, Z, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ) ) }.
% 0.96/1.59 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.96/1.59 , alpha12( X, Y, Z ) }.
% 0.96/1.59 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.96/1.59 , alpha23( X, Y, Z ) }.
% 0.96/1.59 { ! alpha12( X, Y, Z ), ! alpha23( X, Y, Z ), hBOOL( hAPP( Z,
% 0.96/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.96/1.59 { ! alpha23( X, Y, Z ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.96/1.59 T ), hBOOL( hAPP( Z, T ) ) }.
% 0.96/1.59 { ! hBOOL( hAPP( Z, skol16( T, U, Z ) ) ), alpha23( X, Y, Z ) }.
% 0.96/1.59 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, skol16( X, Y, Z ) ),
% 0.96/1.59 alpha23( X, Y, Z ) }.
% 0.96/1.59 { ! alpha12( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 0.96/1.59 ), hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.96/1.59 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), alpha12( X, Y, Z ) }
% 0.96/1.59 .
% 0.96/1.59 { ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha12
% 0.96/1.59 ( X, Y, Z ) }.
% 0.96/1.59 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.96/1.59 , ! alpha13( X, Y, Z ) }.
% 0.96/1.59 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.96/1.59 , ! alpha24( X, Y, Z ) }.
% 0.96/1.59 { alpha13( X, Y, Z ), alpha24( X, Y, Z ), hBOOL( hAPP( Z,
% 0.96/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.96/1.59 { ! alpha24( X, Y, Z ), ! hBOOL( hAPP( Z, skol17( T, U, Z ) ) ) }.
% 0.96/1.59 { ! alpha24( X, Y, Z ), Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.96/1.59 skol17( X, Y, Z ) ) }.
% 0.96/1.59 { ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, T ), hBOOL( hAPP( Z, T
% 0.96/1.59 ) ), alpha24( X, Y, Z ) }.
% 0.96/1.59 { ! alpha13( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 0.96/1.59 }.
% 0.96/1.59 { ! alpha13( X, Y, Z ), ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero(
% 0.96/1.59 tc_Nat_Onat ) ) ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), hBOOL( hAPP( Z,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha13( X, Y, Z ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.96/1.59 ( tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.96/1.59 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.96/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.96/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.96/1.59 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.96/1.59 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.96/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.96/1.59 tc_Int_Oint ) ), X ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.96/1.59 tc_Int_Oint ) ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X )
% 0.96/1.59 }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.96/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.96/1.59 tc_Int_Oint ) ), X ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.96/1.59 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X )
% 0.96/1.59 }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.96/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.96/1.59 tc_Int_Oint ) ) ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc(
% 0.96/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), Z ) =
% 0.96/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, c_Nat_OSuc(
% 0.96/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) ) =
% 0.96/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.96/1.59 tc_Nat_Onat, Z, Y ), c_Nat_OSuc( X ) ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.96/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ),
% 0.96/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.96/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ),
% 0.96/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.96/1.59 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 0.96/1.59 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) =
% 0.96/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.96/1.59 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ) =
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ),
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ) = Z }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ) = Z,
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ) =
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.96/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ),
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ),
% 0.96/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T,
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.96/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T,
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ),
% 0.96/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ),
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.96/1.59 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 0.96/1.59 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) =
% 0.96/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, T,
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ) =
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ), T =
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! T =
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ),
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ) =
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) }.
% 0.96/1.59 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.96/1.59 , ! c_Polynomial_Opdivmod__rel( X, Z, V1, V0, W ),
% 0.96/1.59 c_Polynomial_Opdivmod__rel( X, U, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), V1 ), V0
% 0.96/1.59 , c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), W ), Y )
% 0.96/1.59 ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__0( X ), c_Orderings_Oord__class_Oless__eq
% 0.96/1.59 ( tc_Nat_Onat, c_Polynomial_Odegree( X, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y ) ),
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Polynomial_Odegree( X, Z ),
% 0.96/1.59 c_Polynomial_Odegree( X, Y ) ) ) }.
% 0.96/1.59 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ), Z = c_Groups_Ozero__class_Ozero(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) =
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Polynomial_Odegree( X, Y ),
% 0.96/1.59 c_Polynomial_Odegree( X, Z ) ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.96/1.59 c_Polynomial_Omonom( X, U, T ) ), c_Polynomial_Omonom( X, Z, Y ) ) =
% 0.96/1.59 c_Polynomial_Omonom( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U
% 0.96/1.59 ), Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, Y ) ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.96/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.96/1.59 tc_Int_Oint ), c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.96/1.59 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) ) }.
% 0.96/1.59 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = X }.
% 0.96/1.59 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.96/1.59 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.96/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.96/1.59 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 0.96/1.59 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ),
% 0.96/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.96/1.59 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.96/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.96/1.59 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ),
% 0.96/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.96/1.59 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 0.96/1.59 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.96/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.96/1.59 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 0.96/1.59 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ),
% 0.96/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T,
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.96/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T,
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ),
% 0.96/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.96/1.59 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 0.96/1.59 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) }.
% 0.96/1.59 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.59 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 0.96/1.59 ( tc_Nat_Onat ) ) ), X ) ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Ocoeff( X, hAPP
% 0.96/1.59 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y
% 0.96/1.59 ) ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 0.96/1.59 Z ), c_Polynomial_Odegree( X, Y ) ) ) = hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), hAPP( c_Polynomial_Ocoeff( X, Z ),
% 0.96/1.59 c_Polynomial_Odegree( X, Z ) ) ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.96/1.59 c_Polynomial_Odegree( X, Y ) ) ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.59 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.96/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 0.96/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ),
% 0.96/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oone__class_Oone
% 0.96/1.59 ( tc_Int_Oint ), Y ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.59 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.96/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 0.96/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ),
% 0.96/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.96/1.59 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.96/1.59 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.96/1.59 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, c_Groups_Oplus__class_Oplus
% 0.96/1.59 ( tc_Nat_Onat, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.96/1.59 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.96/1.59 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.96/1.59 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ), Y = X }.
% 0.96/1.59 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) }.
% 0.96/1.59 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ), Z = X }.
% 0.96/1.59 { ! Z = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.96/1.59 { c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) = X }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.96/1.59 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.96/1.59 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 0.96/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.96/1.59 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.96/1.59 ( tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.96/1.59 Z ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.96/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.96/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.96/1.59 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 0.96/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), !
% 0.96/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, U ), !
% 0.96/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, U ),
% 0.96/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Y ) }.
% 0.96/1.59 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 0.96/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.96/1.59 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.96/1.59 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 0.96/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), !
% 0.96/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.96/1.59 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.96/1.59 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, U, Y ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 0.96/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.96/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, X ), !
% 0.96/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, Z ),
% 0.96/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, T ) }.
% 0.96/1.59 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 0.96/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.96/1.59 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.96/1.59 ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.96/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, T, W ), !
% 0.96/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.96/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.96/1.59 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.96/1.59 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, U ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol18( X, Y ) ) }.
% 0.96/1.59 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.96/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.59 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.96/1.59 c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.59 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ), Y ) = hAPP( hAPP(
% 0.96/1.59 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ),
% 0.96/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.96/1.59 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.96/1.59 ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Divides_Odiv__class_Odiv( X
% 0.96/1.59 , c_Groups_Oplus__class_Oplus( X, Y, T ), Z ) =
% 0.96/1.59 c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Odiv( X, Y, Z ),
% 0.96/1.59 c_Divides_Odiv__class_Odiv( X, T, Z ) ) }.
% 0.96/1.59 { ! c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), alpha14( X, Y ) }.
% 0.96/1.59 { ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.96/1.59 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.96/1.59 { ! alpha14( X, Y ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.96/1.59 { ! alpha14( X, Y ), alpha25( X, Y ), alpha29( X, Y ) }.
% 0.96/1.59 { ! alpha25( X, Y ), alpha14( X, Y ) }.
% 0.96/1.59 { ! alpha29( X, Y ), alpha14( X, Y ) }.
% 0.96/1.59 { ! alpha29( X, Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.96/1.59 { ! alpha29( X, Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.96/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ), alpha29( X, Y ) }.
% 0.96/1.59 { ! alpha25( X, Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.96/1.59 { ! alpha25( X, Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), !
% 0.96/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), alpha25( X, Y ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.59 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.96/1.59 tc_Int_Oint, Y, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.59 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.96/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.96/1.59 tc_Int_Oint, Y, X ) ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.59 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.96/1.59 tc_Int_Oint, Y, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X
% 0.96/1.59 , Y ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.59 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X
% 0.96/1.59 , Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.96/1.59 tc_Int_Oint, Y, X ) ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.96/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.96/1.59 tc_Int_Oint ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ),
% 0.96/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.96/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.96/1.59 tc_Int_Oint ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ),
% 0.96/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.96/1.59 tc_Int_Oint ), Y ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.96/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.96/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.96/1.59 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.96/1.59 tc_Int_Oint, X, Y ) ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.96/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.96/1.59 tc_Int_Oint ), Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.96/1.59 Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.59 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ),
% 0.96/1.59 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.96/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.96/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.59 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.96/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ),
% 0.96/1.59 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.96/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.96/1.59 tc_Int_Oint, Y, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y
% 0.96/1.59 , c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.96/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.96/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.96/1.59 tc_Int_Oint, Y, X ) ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.96/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.96/1.59 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.59 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.96/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.96/1.59 tc_Int_Oint ), Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.96/1.59 Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.59 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 0.96/1.59 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ) ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.96/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.96/1.59 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.96/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.96/1.59 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.59 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, Z ),
% 0.96/1.59 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ) ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.96/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.96/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.59 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ),
% 0.96/1.59 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, Z ) ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.59 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.96/1.59 c_Groups_Oone__class_Oone( tc_Int_Oint ), Y ),
% 0.96/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.96/1.59 tc_Int_Oint, X, Y ), X ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.59 ( tc_Int_Oint ), X ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Z, hAPP(
% 0.96/1.59 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) =
% 0.96/1.59 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.96/1.59 tc_Int_Oint, Z, Y ), X ) }.
% 0.96/1.59 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.59 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, T, hAPP
% 0.96/1.59 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) =
% 0.96/1.59 c_Groups_Oplus__class_Oplus( X, Z, c_Divides_Odiv__class_Odiv( X, T, Y )
% 0.96/1.59 ) }.
% 0.96/1.59 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.59 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, T, hAPP
% 0.96/1.59 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) =
% 0.96/1.59 c_Groups_Oplus__class_Oplus( X, Z, c_Divides_Odiv__class_Odiv( X, T, Y )
% 0.96/1.59 ) }.
% 0.96/1.59 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.59 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, Z, Y ),
% 0.96/1.59 Y ) = c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Odiv( X, Z, Y
% 0.96/1.59 ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.96/1.59 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.59 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, Y, Z ),
% 0.96/1.59 Y ) = c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Odiv( X, Z, Y
% 0.96/1.59 ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.96/1.59 { ! class_Divides_Osemiring__div( X ), ! T = c_Groups_Ozero__class_Ozero( X
% 0.96/1.59 ), c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.59 { ! class_Divides_Osemiring__div( X ), T = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.59 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.96/1.59 c_Divides_Odiv__class_Odiv( X, Z, Y ) }.
% 0.96/1.59 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.59 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = Z }.
% 0.96/1.59 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.59 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) = Z }.
% 0.96/1.59 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.59 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.96/1.59 c_Divides_Odiv__class_Odiv( X, T, Z ) }.
% 0.96/1.59 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.59 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) =
% 0.96/1.59 c_Divides_Odiv__class_Odiv( X, T, Z ) }.
% 0.96/1.59 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.96/1.59 tc_Int_Oint ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.96/1.59 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.59 }.
% 0.96/1.59 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X, Y,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.59 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ),
% 0.96/1.59 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) = X }.
% 0.96/1.59 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.96/1.59 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 0.96/1.59 c_Divides_Odiv__class_Odiv( X, Y, Z ) ) = Y }.
% 0.96/1.59 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.96/1.59 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ),
% 0.96/1.59 c_Divides_Odiv__class_Odiv( X, Y, Z ) ) = c_Divides_Odiv__class_Odiv( X,
% 0.96/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.96/1.59 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.96/1.59 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.96/1.59 c_Divides_Odiv__class_Odiv( X, Y, Z ) ), Z ) = Y }.
% 0.96/1.59 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.96/1.59 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.96/1.59 c_Divides_Odiv__class_Odiv( X, Y, Z ) ), T ) = c_Divides_Odiv__class_Odiv
% 0.96/1.59 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), Z ) }.
% 0.96/1.59 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.96/1.59 ), ! c_Rings_Odvd__class_Odvd( X, U, T ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Odiv( X, Y, Z )
% 0.96/1.59 ), c_Divides_Odiv__class_Odiv( X, T, U ) ) = c_Divides_Odiv__class_Odiv
% 0.96/1.59 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.96/1.59 ( c_Groups_Otimes__class_Otimes( X ), Z ), U ) ) }.
% 0.96/1.59 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.96/1.59 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ),
% 0.96/1.59 c_Divides_Odiv__class_Odiv( X, Y, Z ) ), T ) = c_Divides_Odiv__class_Odiv
% 0.96/1.59 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.96/1.59 ( c_Power_Opower__class_Opower( X ), Z ), T ) ) }.
% 0.96/1.59 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.96/1.59 ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), ! c_Rings_Odvd__class_Odvd( X
% 0.96/1.59 , c_Divides_Odiv__class_Odiv( X, Y, Z ), c_Divides_Odiv__class_Odiv( X, T
% 0.96/1.59 , Z ) ), c_Rings_Odvd__class_Odvd( X, Y, T ) }.
% 0.96/1.59 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.96/1.59 ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), ! c_Rings_Odvd__class_Odvd( X
% 0.96/1.59 , Y, T ), c_Rings_Odvd__class_Odvd( X, c_Divides_Odiv__class_Odiv( X, Y,
% 0.96/1.59 Z ), c_Divides_Odiv__class_Odiv( X, T, Z ) ) }.
% 0.96/1.59 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X, Y,
% 0.96/1.59 c_Groups_Oone__class_Oone( X ) ) = Y }.
% 0.96/1.59 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.96/1.59 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, X ) =
% 0.96/1.59 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.96/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.96/1.59 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.96/1.59 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.96/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.96/1.59 tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.96/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.96/1.59 tc_Int_Oint ), Y ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.96/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.96/1.59 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.96/1.59 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ),
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.96/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.96/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.96/1.59 tc_Int_Oint, X, Y ) ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.59 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.96/1.59 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ),
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.96/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.59 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.96/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.96/1.59 tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.96/1.59 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.59 , c_Divides_Odiv__class_Odiv( X, Y, Y ) = c_Groups_Oone__class_Oone( X )
% 0.96/1.59 }.
% 0.96/1.59 { ! class_Divides_Oring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y ),
% 0.96/1.59 c_Divides_Odiv__class_Odiv( X, Y, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.96/1.59 ) = c_Groups_Ouminus__class_Ouminus( X, c_Divides_Odiv__class_Odiv( X, Y
% 0.96/1.59 , Z ) ) }.
% 0.96/1.59 { ! class_Divides_Oring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y ),
% 0.96/1.59 c_Divides_Odiv__class_Odiv( X, c_Groups_Ouminus__class_Ouminus( X, Y ), Z
% 0.96/1.59 ) = c_Groups_Ouminus__class_Ouminus( X, c_Divides_Odiv__class_Odiv( X, Y
% 0.96/1.59 , Z ) ) }.
% 0.96/1.59 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.96/1.59 ( tc_Int_Oint, Y ), c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.96/1.59 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) }.
% 0.96/1.59 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y,
% 0.96/1.59 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.96/1.59 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.96/1.59 ( tc_Int_Oint, Y ), X ) }.
% 0.96/1.59 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.59 , Z = c_Groups_Ozero__class_Ozero( X ), ! c_Rings_Odvd__class_Odvd( X, Y
% 0.96/1.59 , T ), ! c_Rings_Odvd__class_Odvd( X, Z, U ), !
% 0.96/1.59 c_Divides_Odiv__class_Odiv( X, T, Y ) = c_Divides_Odiv__class_Odiv( X, U
% 0.96/1.59 , Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ) = hAPP(
% 0.96/1.59 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), U ) }.
% 0.96/1.59 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.59 , Z = c_Groups_Ozero__class_Ozero( X ), ! c_Rings_Odvd__class_Odvd( X, Y
% 0.96/1.59 , T ), ! c_Rings_Odvd__class_Odvd( X, Z, U ), ! hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ) = hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), U ), c_Divides_Odiv__class_Odiv
% 0.96/1.59 ( X, T, Y ) = c_Divides_Odiv__class_Odiv( X, U, Z ) }.
% 0.96/1.59 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.59 , ! c_Rings_Odvd__class_Odvd( X, Y, Z ), ! c_Divides_Odiv__class_Odiv( X
% 0.96/1.59 , Z, Y ) = T, Z = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y
% 0.96/1.59 ) }.
% 0.96/1.59 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.59 , ! c_Rings_Odvd__class_Odvd( X, Y, Z ), ! Z = hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ), c_Divides_Odiv__class_Odiv
% 0.96/1.59 ( X, Z, Y ) = T }.
% 0.96/1.59 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ),
% 0.96/1.59 alpha15( X, Z ) }.
% 0.96/1.59 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ),
% 0.96/1.59 alpha26( X, Y, Z ) }.
% 0.96/1.59 { ! alpha15( X, Z ), ! alpha26( X, Y, Z ), hBOOL( hAPP( Z,
% 0.96/1.59 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ) }.
% 0.96/1.59 { ! alpha26( X, Y, Z ), alpha30( X, Y, Z ) }.
% 0.96/1.59 { ! alpha26( X, Y, Z ), alpha31( X, Y, Z ) }.
% 0.96/1.59 { ! alpha30( X, Y, Z ), ! alpha31( X, Y, Z ), alpha26( X, Y, Z ) }.
% 0.96/1.59 { ! alpha31( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha33( X, Y, Z ) }.
% 0.96/1.59 { c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha31( X, Y, Z ) }.
% 0.96/1.59 { ! alpha33( X, Y, Z ), alpha31( X, Y, Z ) }.
% 0.96/1.59 { ! alpha33( X, Y, Z ), ! alpha35( X, Y, T ), hBOOL( hAPP( Z, T ) ) }.
% 0.96/1.59 { ! hBOOL( hAPP( Z, skol19( T, U, Z ) ) ), alpha33( X, Y, Z ) }.
% 0.96/1.59 { alpha35( X, Y, skol19( X, Y, Z ) ), alpha33( X, Y, Z ) }.
% 0.96/1.59 { ! alpha35( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.96/1.59 skol20( X, T, U ) ) }.
% 0.96/1.59 { ! alpha35( X, Y, Z ), alpha37( X, Y, Z, skol20( X, Y, Z ) ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, T ), ! alpha37( X, Y, Z
% 0.96/1.59 , T ), alpha35( X, Y, Z ) }.
% 0.96/1.59 { ! alpha37( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.59 T, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.96/1.59 { ! alpha37( X, Y, Z, T ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.96/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ) }
% 0.96/1.59 .
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! Y =
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ), alpha37( X,
% 0.96/1.59 Y, Z, T ) }.
% 0.96/1.59 { ! alpha30( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), alpha32( X, Y, Z ) }.
% 0.96/1.59 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.96/1.59 tc_Int_Oint ), X ), alpha30( X, Y, Z ) }.
% 0.96/1.59 { ! alpha32( X, Y, Z ), alpha30( X, Y, Z ) }.
% 0.96/1.59 { ! alpha32( X, Y, Z ), ! alpha34( X, Y, T ), hBOOL( hAPP( Z, T ) ) }.
% 0.96/1.59 { ! hBOOL( hAPP( Z, skol21( T, U, Z ) ) ), alpha32( X, Y, Z ) }.
% 0.96/1.59 { alpha34( X, Y, skol21( X, Y, Z ) ), alpha32( X, Y, Z ) }.
% 0.96/1.59 { ! alpha34( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), skol22( T, U, W ) ) }.
% 0.96/1.59 { ! alpha34( X, Y, Z ), alpha36( X, Y, Z, skol22( X, Y, Z ) ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! alpha36( X, Y, Z, T )
% 0.96/1.59 , alpha34( X, Y, Z ) }.
% 0.96/1.59 { ! alpha36( X, Y, Z, T ), c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X
% 0.96/1.59 ) }.
% 0.96/1.59 { ! alpha36( X, Y, Z, T ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.96/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ) }
% 0.96/1.59 .
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X ), ! Y =
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ), alpha36( X,
% 0.96/1.59 Y, Z, T ) }.
% 0.96/1.59 { ! alpha15( X, Y ), ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.96/1.59 hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 0.96/1.59 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), alpha15( X, Y ) }.
% 0.96/1.59 { ! hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), alpha15
% 0.96/1.59 ( X, Y ) }.
% 0.96/1.59 { ! T = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), alpha39( X,
% 0.96/1.59 Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), Z =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.96/1.59 tc_Int_Oint, T, Z ) = Y }.
% 0.96/1.59 { ! T = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), alpha39( X,
% 0.96/1.59 Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ), !
% 0.96/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Z =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.96/1.59 tc_Int_Oint, T, Z ) = Y }.
% 0.96/1.59 { ! alpha39( X, Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.96/1.59 { ! alpha39( X, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.96/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.59 ( tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), alpha39( X, Y ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.59 ( tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y )
% 0.96/1.59 , alpha39( X, Y ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), c_SMT_Oz3div( X, Y ) =
% 0.96/1.59 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) }.
% 0.96/1.59 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), c_SMT_Oz3div( X, Y ) =
% 0.96/1.59 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Divides_Odiv__class_Odiv
% 0.96/1.59 ( tc_Int_Oint, X, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ) ) }
% 0.96/1.59 .
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.59 ( tc_Int_Oint ), X ), hBOOL( hAPP( Y, skol23( Z, Y ) ) ), !
% 0.96/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! hBOOL( hAPP( Y, U ) )
% 0.96/1.59 , hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, hAPP( hAPP
% 0.96/1.59 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), T ), X ) ) ) ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.59 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus(
% 0.96/1.59 tc_Int_Oint, skol23( X, Y ), X ) ) ), ! c_Orderings_Oord__class_Oless__eq
% 0.96/1.59 ( tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), ! hBOOL(
% 0.96/1.59 hAPP( Y, T ) ), hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus( tc_Int_Oint
% 0.96/1.59 , T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) )
% 0.96/1.59 ) ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.59 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X
% 0.96/1.59 , Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.59 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, Y ),
% 0.96/1.59 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, X ) ) }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.59 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 0.96/1.59 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ) = Y }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.59 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 0.96/1.59 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ) = Y }.
% 0.96/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 0.96/1.59 tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 0.96/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 0.96/1.59 tc_Nat_Onat, Y, X ), Y ) }.
% 0.96/1.59 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) =
% 0.96/1.59 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 0.96/1.59 tc_Nat_Onat, Z, Y ), X ) }.
% 0.96/1.59 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) = X }.
% 0.96/1.59 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.96/1.59 class_Groups_Ocancel__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.59 { class_Groups_Ocancel__comm__monoid__add( tc_Complex_Ocomplex ) }.
% 0.96/1.59 { class_Groups_Ocancel__comm__monoid__add( tc_Nat_Onat ) }.
% 0.96/1.59 { class_Groups_Ocancel__comm__monoid__add( tc_Int_Oint ) }.
% 0.96/1.59 { ! class_Lattices_Oboolean__algebra( X ), class_Lattices_Oboolean__algebra
% 0.96/1.59 ( tc_fun( Y, X ) ) }.
% 0.96/1.59 { ! class_Orderings_Opreorder( X ), class_Orderings_Opreorder( tc_fun( Y, X
% 0.96/1.59 ) ) }.
% 0.96/1.59 { ! class_Orderings_Oorder( X ), class_Orderings_Oorder( tc_fun( Y, X ) ) }
% 0.96/1.59 .
% 0.96/1.59 { ! class_Orderings_Oord( X ), class_Orderings_Oord( tc_fun( Y, X ) ) }.
% 0.96/1.59 { ! class_Groups_Ouminus( X ), class_Groups_Ouminus( tc_fun( Y, X ) ) }.
% 0.96/1.59 { ! class_Groups_Ominus( X ), class_Groups_Ominus( tc_fun( Y, X ) ) }.
% 0.96/1.59 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.96/1.59 tc_Int_Oint ) }.
% 0.96/1.59 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.96/1.59 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Int_Oint ) }.
% 0.96/1.59 { class_Rings_Olinordered__comm__semiring__strict( tc_Int_Oint ) }.
% 0.96/1.59 { class_Rings_Olinordered__semiring__1__strict( tc_Int_Oint ) }.
% 0.96/1.59 { class_Rings_Olinordered__semiring__strict( tc_Int_Oint ) }.
% 0.96/1.59 { class_Groups_Oordered__ab__semigroup__add( tc_Int_Oint ) }.
% 0.96/1.59 { class_Groups_Oordered__comm__monoid__add( tc_Int_Oint ) }.
% 0.96/1.59 { class_Groups_Olinordered__ab__group__add( tc_Int_Oint ) }.
% 0.96/1.59 { class_Groups_Ocancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.96/1.59 { class_Rings_Oring__1__no__zero__divisors( tc_Int_Oint ) }.
% 0.96/1.59 { class_Rings_Oordered__cancel__semiring( tc_Int_Oint ) }.
% 0.96/1.59 { class_Rings_Olinordered__ring__strict( tc_Int_Oint ) }.
% 0.96/1.59 { class_Rings_Oring__no__zero__divisors( tc_Int_Oint ) }.
% 0.96/1.59 { class_Rings_Oordered__comm__semiring( tc_Int_Oint ) }.
% 0.96/1.59 { class_Rings_Olinordered__semiring__1( tc_Int_Oint ) }.
% 0.96/1.59 { class_Groups_Oordered__ab__group__add( tc_Int_Oint ) }.
% 0.96/1.59 { class_Groups_Ocancel__semigroup__add( tc_Int_Oint ) }.
% 0.96/1.59 { class_Rings_Olinordered__semiring( tc_Int_Oint ) }.
% 0.96/1.59 { class_Rings_Olinordered__semidom( tc_Int_Oint ) }.
% 0.96/1.59 { class_Groups_Oab__semigroup__mult( tc_Int_Oint ) }.
% 0.96/1.59 { class_Groups_Ocomm__monoid__mult( tc_Int_Oint ) }.
% 0.96/1.59 { class_Groups_Oab__semigroup__add( tc_Int_Oint ) }.
% 0.96/1.59 { class_Rings_Oordered__semiring( tc_Int_Oint ) }.
% 0.96/1.59 { class_Rings_Ono__zero__divisors( tc_Int_Oint ) }.
% 0.96/1.59 { class_Groups_Ocomm__monoid__add( tc_Int_Oint ) }.
% 0.96/1.59 { class_Rings_Olinordered__ring( tc_Int_Oint ) }.
% 0.96/1.59 { class_Rings_Olinordered__idom( tc_Int_Oint ) }.
% 0.96/1.59 { class_Rings_Ocomm__semiring__1( tc_Int_Oint ) }.
% 0.96/1.59 { class_Rings_Ocomm__semiring__0( tc_Int_Oint ) }.
% 0.96/1.59 { class_Divides_Osemiring__div( tc_Int_Oint ) }.
% 0.96/1.59 { class_Rings_Ocomm__semiring( tc_Int_Oint ) }.
% 0.96/1.59 { class_Groups_Oab__group__add( tc_Int_Oint ) }.
% 0.96/1.59 { class_Rings_Ozero__neq__one( tc_Int_Oint ) }.
% 0.96/1.59 { class_Rings_Oordered__ring( tc_Int_Oint ) }.
% 0.96/1.59 { class_Orderings_Opreorder( tc_Int_Oint ) }.
% 0.96/1.59 { class_Orderings_Olinorder( tc_Int_Oint ) }.
% 0.96/1.59 { class_Groups_Omonoid__mult( tc_Int_Oint ) }.
% 0.96/1.59 { class_Rings_Ocomm__ring__1( tc_Int_Oint ) }.
% 0.96/1.59 { class_Groups_Omonoid__add( tc_Int_Oint ) }.
% 0.96/1.59 { class_Rings_Osemiring__0( tc_Int_Oint ) }.
% 0.96/1.59 { class_Groups_Ogroup__add( tc_Int_Oint ) }.
% 0.96/1.59 { class_Divides_Oring__div( tc_Int_Oint ) }.
% 0.96/1.59 { class_Rings_Omult__zero( tc_Int_Oint ) }.
% 0.96/1.59 { class_Rings_Ocomm__ring( tc_Int_Oint ) }.
% 0.96/1.59 { class_Orderings_Oorder( tc_Int_Oint ) }.
% 0.96/1.59 { class_Int_Oring__char__0( tc_Int_Oint ) }.
% 0.96/1.59 { class_Int_Onumber__ring( tc_Int_Oint ) }.
% 0.96/1.59 { class_Rings_Osemiring( tc_Int_Oint ) }.
% 0.96/1.59 { class_Orderings_Oord( tc_Int_Oint ) }.
% 0.96/1.59 { class_Groups_Ouminus( tc_Int_Oint ) }.
% 0.96/1.59 { class_Groups_Osgn__if( tc_Int_Oint ) }.
% 0.96/1.59 { class_Rings_Oring__1( tc_Int_Oint ) }.
% 0.96/1.59 { class_Groups_Ominus( tc_Int_Oint ) }.
% 0.96/1.59 { class_Power_Opower( tc_Int_Oint ) }.
% 0.96/1.59 { class_Groups_Ozero( tc_Int_Oint ) }.
% 0.96/1.59 { class_Rings_Oring( tc_Int_Oint ) }.
% 0.96/1.59 { class_Rings_Oidom( tc_Int_Oint ) }.
% 0.96/1.59 { class_Int_Onumber( tc_Int_Oint ) }.
% 0.96/1.59 { class_Groups_Oone( tc_Int_Oint ) }.
% 0.96/1.59 { class_Rings_Odvd( tc_Int_Oint ) }.
% 0.96/1.59 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.96/1.59 tc_Nat_Onat ) }.
% 0.96/1.59 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.96/1.59 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Nat_Onat ) }.
% 0.96/1.59 { class_Rings_Olinordered__comm__semiring__strict( tc_Nat_Onat ) }.
% 0.96/1.59 { class_Rings_Olinordered__semiring__strict( tc_Nat_Onat ) }.
% 0.96/1.59 { class_Groups_Oordered__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.96/1.59 { class_Groups_Oordered__comm__monoid__add( tc_Nat_Onat ) }.
% 0.96/1.59 { class_Groups_Ocancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.96/1.59 { class_Rings_Oordered__cancel__semiring( tc_Nat_Onat ) }.
% 0.96/1.59 { class_Rings_Oordered__comm__semiring( tc_Nat_Onat ) }.
% 0.96/1.59 { class_Groups_Ocancel__semigroup__add( tc_Nat_Onat ) }.
% 0.96/1.59 { class_Rings_Olinordered__semiring( tc_Nat_Onat ) }.
% 0.96/1.59 { class_Rings_Olinordered__semidom( tc_Nat_Onat ) }.
% 0.96/1.59 { class_Groups_Oab__semigroup__mult( tc_Nat_Onat ) }.
% 0.96/1.59 { class_Groups_Ocomm__monoid__mult( tc_Nat_Onat ) }.
% 0.96/1.59 { class_Groups_Oab__semigroup__add( tc_Nat_Onat ) }.
% 0.96/1.59 { class_Rings_Oordered__semiring( tc_Nat_Onat ) }.
% 0.96/1.59 { class_Rings_Ono__zero__divisors( tc_Nat_Onat ) }.
% 0.96/1.59 { class_Groups_Ocomm__monoid__add( tc_Nat_Onat ) }.
% 0.96/1.59 { class_Rings_Ocomm__semiring__1( tc_Nat_Onat ) }.
% 0.96/1.59 { class_Rings_Ocomm__semiring__0( tc_Nat_Onat ) }.
% 0.96/1.59 { class_Divides_Osemiring__div( tc_Nat_Onat ) }.
% 0.96/1.59 { class_Rings_Ocomm__semiring( tc_Nat_Onat ) }.
% 0.96/1.59 { class_Rings_Ozero__neq__one( tc_Nat_Onat ) }.
% 0.96/1.59 { class_Orderings_Opreorder( tc_Nat_Onat ) }.
% 0.96/1.59 { class_Orderings_Olinorder( tc_Nat_Onat ) }.
% 0.96/1.59 { class_Groups_Omonoid__mult( tc_Nat_Onat ) }.
% 0.96/1.59 { class_Groups_Omonoid__add( tc_Nat_Onat ) }.
% 0.96/1.59 { class_Rings_Osemiring__0( tc_Nat_Onat ) }.
% 0.96/1.59 { class_Rings_Omult__zero( tc_Nat_Onat ) }.
% 0.96/1.59 { class_Orderings_Oorder( tc_Nat_Onat ) }.
% 0.96/1.59 { class_Rings_Osemiring( tc_Nat_Onat ) }.
% 0.96/1.59 { class_Orderings_Oord( tc_Nat_Onat ) }.
% 0.96/1.59 { class_Groups_Ominus( tc_Nat_Onat ) }.
% 0.96/1.59 { class_Power_Opower( tc_Nat_Onat ) }.
% 0.96/1.59 { class_Groups_Ozero( tc_Nat_Onat ) }.
% 0.96/1.59 { class_Int_Onumber( tc_Nat_Onat ) }.
% 0.96/1.59 { class_Groups_Oone( tc_Nat_Onat ) }.
% 0.96/1.59 { class_Rings_Odvd( tc_Nat_Onat ) }.
% 0.96/1.59 { class_Lattices_Oboolean__algebra( tc_HOL_Obool ) }.
% 0.96/1.59 { class_Orderings_Opreorder( tc_HOL_Obool ) }.
% 0.96/1.59 { class_Orderings_Oorder( tc_HOL_Obool ) }.
% 0.96/1.59 { class_Orderings_Oord( tc_HOL_Obool ) }.
% 0.96/1.59 { class_Groups_Ouminus( tc_HOL_Obool ) }.
% 0.96/1.59 { class_Groups_Ominus( tc_HOL_Obool ) }.
% 0.96/1.59 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.96/1.59 tc_Complex_Ocomplex ) }.
% 0.96/1.59 { class_RealVector_Oreal__normed__div__algebra( tc_Complex_Ocomplex ) }.
% 0.96/1.59 { class_RealVector_Oreal__normed__algebra__1( tc_Complex_Ocomplex ) }.
% 0.96/1.59 { class_RealVector_Oreal__normed__algebra( tc_Complex_Ocomplex ) }.
% 0.96/1.59 { class_Groups_Ocancel__ab__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.96/1.59 { class_Rings_Oring__1__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.96/1.59 { class_RealVector_Oreal__normed__vector( tc_Complex_Ocomplex ) }.
% 0.96/1.59 { class_Rings_Oring__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.96/1.59 { class_Groups_Ocancel__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.96/1.59 { class_Groups_Oab__semigroup__mult( tc_Complex_Ocomplex ) }.
% 0.96/1.59 { class_Groups_Ocomm__monoid__mult( tc_Complex_Ocomplex ) }.
% 0.96/1.59 { class_Groups_Oab__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.96/1.59 { class_Rings_Ono__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.96/1.59 { class_Groups_Ocomm__monoid__add( tc_Complex_Ocomplex ) }.
% 0.96/1.59 { class_Rings_Ocomm__semiring__1( tc_Complex_Ocomplex ) }.
% 0.96/1.59 { class_Rings_Ocomm__semiring__0( tc_Complex_Ocomplex ) }.
% 0.96/1.59 { class_Rings_Ocomm__semiring( tc_Complex_Ocomplex ) }.
% 0.96/1.59 { class_Groups_Oab__group__add( tc_Complex_Ocomplex ) }.
% 0.96/1.59 { class_Rings_Ozero__neq__one( tc_Complex_Ocomplex ) }.
% 0.96/1.59 { class_Groups_Omonoid__mult( tc_Complex_Ocomplex ) }.
% 0.96/1.59 { class_Rings_Ocomm__ring__1( tc_Complex_Ocomplex ) }.
% 0.96/1.59 { class_Groups_Omonoid__add( tc_Complex_Ocomplex ) }.
% 0.96/1.59 { class_Rings_Osemiring__0( tc_Complex_Ocomplex ) }.
% 0.96/1.59 { class_Groups_Ogroup__add( tc_Complex_Ocomplex ) }.
% 0.96/1.59 { class_Rings_Omult__zero( tc_Complex_Ocomplex ) }.
% 0.96/1.59 { class_Rings_Ocomm__ring( tc_Complex_Ocomplex ) }.
% 0.96/1.59 { class_Int_Oring__char__0( tc_Complex_Ocomplex ) }.
% 0.96/1.59 { class_Int_Onumber__ring( tc_Complex_Ocomplex ) }.
% 0.96/1.59 { class_Rings_Osemiring( tc_Complex_Ocomplex ) }.
% 0.96/1.59 { class_Groups_Ouminus( tc_Complex_Ocomplex ) }.
% 0.96/1.59 { class_Rings_Oring__1( tc_Complex_Ocomplex ) }.
% 0.96/1.59 { class_Groups_Ominus( tc_Complex_Ocomplex ) }.
% 0.96/1.59 { class_Fields_Ofield( tc_Complex_Ocomplex ) }.
% 0.96/1.59 { class_Power_Opower( tc_Complex_Ocomplex ) }.
% 0.96/1.59 { class_Groups_Ozero( tc_Complex_Ocomplex ) }.
% 0.96/1.59 { class_Rings_Oring( tc_Complex_Ocomplex ) }.
% 0.96/1.59 { class_Rings_Oidom( tc_Complex_Ocomplex ) }.
% 0.96/1.59 { class_Int_Onumber( tc_Complex_Ocomplex ) }.
% 0.96/1.59 { class_Groups_Oone( tc_Complex_Ocomplex ) }.
% 0.96/1.59 { class_Rings_Odvd( tc_Complex_Ocomplex ) }.
% 0.96/1.59 { ! class_Rings_Oidom( X ),
% 0.96/1.59 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.59 { ! class_Rings_Olinordered__idom( X ),
% 0.96/1.59 class_Groups_Oordered__cancel__ab__semigroup__add( tc_Polynomial_Opoly( X
% 0.96/1.59 ) ) }.
% 0.96/1.59 { ! class_Rings_Olinordered__idom( X ),
% 0.96/1.59 class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Polynomial_Opoly(
% 0.96/1.59 X ) ) }.
% 0.96/1.59 { ! class_Rings_Olinordered__idom( X ),
% 0.96/1.59 class_Rings_Olinordered__comm__semiring__strict( tc_Polynomial_Opoly( X )
% 0.96/1.59 ) }.
% 0.96/1.59 { ! class_Rings_Olinordered__idom( X ),
% 0.96/1.59 class_Rings_Olinordered__semiring__1__strict( tc_Polynomial_Opoly( X ) )
% 0.96/1.59 }.
% 0.96/1.59 { ! class_Rings_Olinordered__idom( X ),
% 0.96/1.59 class_Rings_Olinordered__semiring__strict( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.59 { ! class_Rings_Olinordered__idom( X ),
% 0.96/1.59 class_Groups_Oordered__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.59 { ! class_Rings_Olinordered__idom( X ),
% 0.96/1.59 class_Groups_Oordered__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.59 { ! class_Rings_Olinordered__idom( X ),
% 0.96/1.59 class_Groups_Olinordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.59 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.96/1.59 class_Groups_Ocancel__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.59 { ! class_Rings_Oidom( X ), class_Rings_Oring__1__no__zero__divisors(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.59 { ! class_Rings_Olinordered__idom( X ),
% 0.96/1.59 class_Rings_Oordered__cancel__semiring( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.59 { ! class_Rings_Olinordered__idom( X ),
% 0.96/1.59 class_Rings_Olinordered__ring__strict( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.59 { ! class_Rings_Oidom( X ), class_Rings_Oring__no__zero__divisors(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.59 { ! class_Rings_Olinordered__idom( X ),
% 0.96/1.59 class_Rings_Oordered__comm__semiring( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.59 { ! class_Rings_Olinordered__idom( X ),
% 0.96/1.59 class_Rings_Olinordered__semiring__1( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.59 { ! class_Rings_Olinordered__idom( X ),
% 0.96/1.59 class_Groups_Oordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.59 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.96/1.59 class_Groups_Ocancel__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.59 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semiring(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.59 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semidom(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Oab__semigroup__mult
% 0.96/1.59 ( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Ocomm__monoid__mult(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.59 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Oab__semigroup__add
% 0.96/1.59 ( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.59 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__semiring(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.59 { ! class_Rings_Oidom( X ), class_Rings_Ono__zero__divisors(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.59 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Ocomm__monoid__add(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.59 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__ring(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.59 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__idom(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ocomm__semiring__1(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring__0(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.59 { ! class_Fields_Ofield( X ), class_Divides_Osemiring__div(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.59 { ! class_Groups_Oab__group__add( X ), class_Groups_Oab__group__add(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ozero__neq__one(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.59 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__ring(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.59 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Opreorder(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.59 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Olinorder(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Omonoid__mult(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Ocomm__ring__1(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.59 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Omonoid__add(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring__0(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.59 { ! class_Groups_Oab__group__add( X ), class_Groups_Ogroup__add(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.59 { ! class_Fields_Ofield( X ), class_Divides_Oring__div( tc_Polynomial_Opoly
% 0.96/1.59 ( X ) ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Omult__zero(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__ring( X ), class_Rings_Ocomm__ring(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.59 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oorder(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.59 { ! class_Rings_Olinordered__idom( X ), class_Int_Oring__char__0(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__ring__1( X ), class_Int_Onumber__ring(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.59 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oord(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.59 { ! class_Groups_Oab__group__add( X ), class_Groups_Ouminus(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.59 { ! class_Rings_Olinordered__idom( X ), class_Groups_Osgn__if(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Oring__1(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.59 { ! class_Groups_Oab__group__add( X ), class_Groups_Ominus(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__1( X ), class_Power_Opower(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.59 { ! class_Groups_Ozero( X ), class_Groups_Ozero( tc_Polynomial_Opoly( X ) )
% 0.96/1.59 }.
% 0.96/1.59 { ! class_Rings_Ocomm__ring( X ), class_Rings_Oring( tc_Polynomial_Opoly( X
% 0.96/1.59 ) ) }.
% 0.96/1.59 { ! class_Rings_Oidom( X ), class_Rings_Oidom( tc_Polynomial_Opoly( X ) ) }
% 0.96/1.59 .
% 0.96/1.59 { ! class_Rings_Ocomm__ring__1( X ), class_Int_Onumber( tc_Polynomial_Opoly
% 0.96/1.59 ( X ) ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Oone(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Odvd(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.59 { ! hBOOL( c_fequal( Y, X ) ), Y = X }.
% 0.96/1.59 { ! Y = X, hBOOL( c_fequal( Y, X ) ) }.
% 0.96/1.59 { ! v_r____ = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.96/1.59 tc_Complex_Ocomplex ) ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), v_na____ ) }.
% 0.96/1.59 { ! hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly(
% 0.96/1.59 tc_Complex_Ocomplex ) ), c_Polynomial_OpCons( tc_Complex_Ocomplex,
% 0.96/1.59 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, v_a____ ),
% 0.96/1.59 c_Polynomial_OpCons( tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(
% 0.96/1.59 tc_Complex_Ocomplex ), c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.96/1.59 tc_Complex_Ocomplex ) ) ) ) ), v_na____ ) = hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( tc_Complex_Ocomplex )
% 0.96/1.59 ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly(
% 0.96/1.59 tc_Complex_Ocomplex ) ), c_Polynomial_OpCons( tc_Complex_Ocomplex,
% 0.96/1.59 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, v_a____ ),
% 0.96/1.59 c_Polynomial_OpCons( tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(
% 0.96/1.59 tc_Complex_Ocomplex ), c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.96/1.59 tc_Complex_Ocomplex ) ) ) ) ), c_Polynomial_Oorder( tc_Complex_Ocomplex,
% 0.96/1.59 v_a____, v_pa____ ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.96/1.59 tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ), c_Polynomial_OpCons(
% 0.96/1.59 tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex
% 0.96/1.59 , v_a____ ), c_Polynomial_OpCons( tc_Complex_Ocomplex,
% 0.96/1.59 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ),
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) )
% 0.96/1.59 ) ) ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, v_na____,
% 0.96/1.59 c_Polynomial_Oorder( tc_Complex_Ocomplex, v_a____, v_pa____ ) ) ) ) }.
% 0.96/1.59
% 0.96/1.59 *** allocated 15000 integers for clauses
% 0.96/1.59 *** allocated 22500 integers for clauses
% 0.96/1.59 *** allocated 33750 integers for clauses
% 0.96/1.59 *** allocated 50625 integers for clauses
% 0.96/1.59 *** allocated 75937 integers for clauses
% 0.96/1.59 percentage equality = 0.265638, percentage horn = 0.909337
% 0.96/1.59 This is a problem with some equality
% 0.96/1.59
% 0.96/1.59
% 0.96/1.59
% 0.96/1.59 Options Used:
% 0.96/1.59
% 0.96/1.59 useres = 1
% 0.96/1.59 useparamod = 1
% 0.96/1.59 useeqrefl = 1
% 0.96/1.59 useeqfact = 1
% 0.96/1.59 usefactor = 1
% 0.96/1.59 usesimpsplitting = 0
% 0.96/1.59 usesimpdemod = 5
% 0.96/1.59 usesimpres = 3
% 0.96/1.59
% 0.96/1.59 resimpinuse = 1000
% 0.96/1.59 resimpclauses = 20000
% 0.96/1.59 substype = eqrewr
% 0.96/1.59 backwardsubs = 1
% 0.96/1.59 selectoldest = 5
% 0.96/1.59
% 0.96/1.59 litorderings [0] = split
% 0.96/1.59 litorderings [1] = extend the termordering, first sorting on arguments
% 0.96/1.59
% 0.96/1.59 termordering = kbo
% 0.96/1.59
% 0.96/1.59 litapriori = 0
% 0.96/1.59 termapriori = 1
% 0.96/1.59 litaposteriori = 0
% 0.96/1.59 termaposteriori = 0
% 0.96/1.59 demodaposteriori = 0
% 0.96/1.59 ordereqreflfact = 0
% 0.96/1.59
% 0.96/1.59 litselect = negord
% 0.96/1.59
% 0.96/1.59 maxweight = 15
% 0.96/1.59 maxdepth = 30000
% 0.96/1.59 maxlength = 115
% 0.96/1.59 maxnrvars = 195
% 0.96/1.59 excuselevel = 1
% 0.96/1.59 increasemaxweight = 1
% 0.96/1.59
% 0.96/1.59 maxselected = 10000000
% 0.96/1.59 maxnrclauses = 10000000
% 0.96/1.59
% 0.96/1.59 showgenerated = 0
% 0.96/1.59 showkept = 0
% 0.96/1.59 showselected = 0
% 0.96/1.59 showdeleted = 0
% 0.96/1.59 showresimp = 1
% 0.96/1.59 showstatus = 2000
% 0.96/1.59
% 0.96/1.59 prologoutput = 0
% 0.96/1.59 nrgoals = 5000000
% 0.96/1.59 totalproof = 1
% 0.96/1.59
% 0.96/1.59 Symbols occurring in the translation:
% 0.96/1.59
% 0.96/1.59 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.96/1.59 . [1, 2] (w:1, o:199, a:1, s:1, b:0),
% 0.96/1.59 ! [4, 1] (w:0, o:117, a:1, s:1, b:0),
% 0.96/1.59 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.96/1.59 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.96/1.59 hAPP [38, 2] (w:1, o:223, a:1, s:1, b:0),
% 0.96/1.59 v_n [39, 0] (w:1, o:11, a:1, s:1, b:0),
% 0.96/1.59 tc_Nat_Onat [40, 0] (w:1, o:16, a:1, s:1, b:0),
% 0.96/1.59 c_Groups_Ozero__class_Ozero [41, 1] (w:1, o:122, a:1, s:1, b:0),
% 0.96/1.59 v_na____ [42, 0] (w:1, o:17, a:1, s:1, b:0),
% 0.96/1.59 v_qa____ [43, 0] (w:1, o:20, a:1, s:1, b:0),
% 0.96/1.59 tc_Complex_Ocomplex [44, 0] (w:1, o:21, a:1, s:1, b:0),
% 0.96/1.59 tc_Polynomial_Opoly [45, 1] (w:1, o:124, a:1, s:1, b:0),
% 0.96/1.59 v_a____ [46, 0] (w:1, o:22, a:1, s:1, b:0),
% 0.96/1.59 v_pa____ [47, 0] (w:1, o:18, a:1, s:1, b:0),
% 0.96/1.59 c_Polynomial_Oorder [48, 3] (w:1, o:258, a:1, s:1, b:0),
% 0.96/1.59 v_k____ [49, 0] (w:1, o:23, a:1, s:1, b:0),
% 0.96/1.59 c_Orderings_Oord__class_Oless__eq [51, 3] (w:1, o:256, a:1, s:1, b:0)
% 0.96/1.59 ,
% 0.96/1.59 v_s____ [52, 0] (w:1, o:27, a:1, s:1, b:0),
% 0.96/1.59 c_Polynomial_OpCons [53, 3] (w:1, o:259, a:1, s:1, b:0),
% 0.96/1.59 c_Groups_Otimes__class_Otimes [54, 1] (w:1, o:125, a:1, s:1, b:0),
% 0.96/1.59 c_Power_Opower__class_Opower [55, 1] (w:1, o:126, a:1, s:1, b:0),
% 0.96/1.59 c_Groups_Ouminus__class_Ouminus [56, 2] (w:1, o:225, a:1, s:1, b:0),
% 0.96/1.59
% 0.96/1.59 c_Groups_Oone__class_Oone [57, 1] (w:1, o:127, a:1, s:1, b:0),
% 0.96/1.59 v_r____ [58, 0] (w:1, o:26, a:1, s:1, b:0),
% 0.96/1.59 c_Polynomial_Opoly [59, 2] (w:1, o:226, a:1, s:1, b:0),
% 0.96/1.59 c_Polynomial_Odegree [60, 2] (w:1, o:228, a:1, s:1, b:0),
% 0.96/1.59 c_Rings_Odvd__class_Odvd [62, 3] (w:1, o:260, a:1, s:1, b:0),
% 0.96/1.59 class_Rings_Olinordered__semidom [66, 1] (w:1, o:130, a:1, s:1, b:0)
% 0.96/1.59 ,
% 0.96/1.59 c_Orderings_Oord__class_Oless [67, 3] (w:1, o:257, a:1, s:1, b:0),
% 0.96/1.59 class_Power_Opower [69, 1] (w:1, o:135, a:1, s:1, b:0),
% 0.96/1.59 c_Groups_Ominus__class_Ominus [70, 3] (w:1, o:261, a:1, s:1, b:0),
% 0.96/1.59 v_p [75, 0] (w:1, o:19, a:1, s:1, b:0),
% 0.96/1.59 v_q [76, 0] (w:1, o:25, a:1, s:1, b:0),
% 0.96/1.59 class_Rings_Ocomm__semiring__1 [84, 1] (w:1, o:139, a:1, s:1, b:0),
% 0.96/1.59 class_Groups_Omonoid__mult [86, 1] (w:1, o:142, a:1, s:1, b:0),
% 0.96/1.59 hBOOL [92, 1] (w:1, o:143, a:1, s:1, b:0),
% 0.96/1.59 class_Rings_Oring__1__no__zero__divisors [95, 1] (w:1, o:144, a:1, s:
% 0.96/1.59 1, b:0),
% 0.96/1.59 class_Groups_Ocomm__monoid__mult [96, 1] (w:1, o:145, a:1, s:1, b:0)
% 0.96/1.59 ,
% 0.96/1.59 class_Rings_Omult__zero [98, 1] (w:1, o:152, a:1, s:1, b:0),
% 0.96/1.59 class_Rings_Ono__zero__divisors [99, 1] (w:1, o:153, a:1, s:1, b:0),
% 0.96/1.59
% 0.96/1.59 class_Rings_Ozero__neq__one [100, 1] (w:1, o:154, a:1, s:1, b:0),
% 0.96/1.59 class_Rings_Osemiring__0 [102, 1] (w:1, o:158, a:1, s:1, b:0),
% 0.96/1.59 class_Rings_Oring__1 [103, 1] (w:1, o:155, a:1, s:1, b:0),
% 0.96/1.59 c_Nat_OSuc [105, 1] (w:1, o:159, a:1, s:1, b:0),
% 0.96/1.59 class_Rings_Oidom [107, 1] (w:1, o:160, a:1, s:1, b:0),
% 0.96/1.59 class_Groups_Oab__group__add [113, 1] (w:1, o:161, a:1, s:1, b:0),
% 0.96/1.59 class_Groups_Ozero [117, 1] (w:1, o:162, a:1, s:1, b:0),
% 0.96/1.59 class_Rings_Olinordered__idom [119, 1] (w:1, o:146, a:1, s:1, b:0),
% 0.96/1.59 class_Int_Oring__char__0 [121, 1] (w:1, o:163, a:1, s:1, b:0),
% 0.96/1.59 class_Rings_Oring__no__zero__divisors [122, 1] (w:1, o:156, a:1, s:1
% 0.96/1.59 , b:0),
% 0.96/1.59 class_Rings_Oring [123, 1] (w:1, o:157, a:1, s:1, b:0),
% 0.96/1.59 class_Rings_Odvd [125, 1] (w:1, o:165, a:1, s:1, b:0),
% 0.96/1.59 class_Rings_Ocomm__ring__1 [127, 1] (w:1, o:136, a:1, s:1, b:0),
% 0.96/1.59 class_Rings_Ocomm__ring [130, 1] (w:1, o:137, a:1, s:1, b:0),
% 0.96/1.59 class_Rings_Ocomm__semiring__0 [131, 1] (w:1, o:138, a:1, s:1, b:0),
% 0.96/1.59
% 0.96/1.59 class_Rings_Olinordered__ring [132, 1] (w:1, o:128, a:1, s:1, b:0),
% 0.96/1.59 class_Rings_Olinordered__ring__strict [133, 1] (w:1, o:129, a:1, s:1
% 0.96/1.59 , b:0),
% 0.96/1.59 class_Rings_Oordered__cancel__semiring [134, 1] (w:1, o:166, a:1, s:1
% 0.96/1.59 , b:0),
% 0.96/1.59 class_Rings_Oordered__ring [135, 1] (w:1, o:167, a:1, s:1, b:0),
% 0.96/1.59 class_Rings_Oordered__semiring [136, 1] (w:1, o:168, a:1, s:1, b:0),
% 0.96/1.59
% 0.96/1.59 class_Rings_Oordered__comm__semiring [137, 1] (w:1, o:169, a:1, s:1
% 0.96/1.59 , b:0),
% 0.96/1.59 class_Rings_Olinordered__semiring__strict [138, 1] (w:1, o:147, a:1
% 0.96/1.59 , s:1, b:0),
% 0.96/1.59 class_Rings_Olinordered__comm__semiring__strict [139, 1] (w:1, o:148
% 1.30/1.64 , a:1, s:1, b:0),
% 1.30/1.64 class_Rings_Olinordered__semiring [140, 1] (w:1, o:149, a:1, s:1, b:0
% 1.30/1.64 ),
% 1.30/1.64 tc_Int_Oint [145, 0] (w:1, o:101, a:1, s:1, b:0),
% 1.30/1.64 class_Groups_Ogroup__add [146, 1] (w:1, o:170, a:1, s:1, b:0),
% 1.30/1.64 class_Groups_Oordered__ab__group__add [147, 1] (w:1, o:171, a:1, s:1
% 1.30/1.64 , b:0),
% 1.30/1.64 class_Groups_Olinordered__ab__group__add [148, 1] (w:1, o:141, a:1
% 1.30/1.64 , s:1, b:0),
% 1.30/1.64 class_Groups_Oab__semigroup__mult [149, 1] (w:1, o:172, a:1, s:1, b:0
% 1.30/1.64 ),
% 1.30/1.64 class_Groups_Oone [150, 1] (w:1, o:173, a:1, s:1, b:0),
% 1.30/1.64 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize [152, 2] (w:1, o:
% 1.30/1.64 224, a:1, s:1, b:0),
% 1.30/1.64 class_Orderings_Opreorder [153, 1] (w:1, o:133, a:1, s:1, b:0),
% 1.30/1.64 c_Power_Opower_Opower [154, 3] (w:1, o:262, a:1, s:1, b:0),
% 1.30/1.64 c_Polynomial_Opcompose [155, 3] (w:1, o:263, a:1, s:1, b:0),
% 1.30/1.64 class_Orderings_Oord [158, 1] (w:1, o:131, a:1, s:1, b:0),
% 1.30/1.64 tc_fun [159, 2] (w:1, o:237, a:1, s:1, b:0),
% 1.30/1.64 class_Orderings_Olinorder [160, 1] (w:1, o:134, a:1, s:1, b:0),
% 1.30/1.64 class_Orderings_Oorder [161, 1] (w:1, o:132, a:1, s:1, b:0),
% 1.30/1.64 c_Polynomial_Opos__poly [162, 2] (w:1, o:238, a:1, s:1, b:0),
% 1.30/1.64 class_RealVector_Oreal__normed__algebra [163, 1] (w:1, o:174, a:1, s:
% 1.30/1.64 1, b:0),
% 1.30/1.64 c_Nat__Transfer_Otsub [176, 2] (w:1, o:239, a:1, s:1, b:0),
% 1.30/1.64 class_Lattices_Oboolean__algebra [177, 1] (w:1, o:176, a:1, s:1, b:0)
% 1.30/1.64 ,
% 1.30/1.64 class_Lattices_Oab__semigroup__idem__mult [178, 1] (w:1, o:175, a:1
% 1.30/1.64 , s:1, b:0),
% 1.30/1.64 class_Groups_Ominus [181, 1] (w:1, o:177, a:1, s:1, b:0),
% 1.30/1.64 class_Groups_Ouminus [182, 1] (w:1, o:178, a:1, s:1, b:0),
% 1.30/1.64 c_Polynomial_Omonom [183, 3] (w:1, o:264, a:1, s:1, b:0),
% 1.30/1.64 c_Groups_Osgn__class_Osgn [184, 2] (w:1, o:240, a:1, s:1, b:0),
% 1.30/1.64 class_Groups_Osgn__if [185, 1] (w:1, o:179, a:1, s:1, b:0),
% 1.30/1.64 class_RealVector_Oreal__normed__div__algebra [186, 1] (w:1, o:180, a:
% 1.30/1.64 1, s:1, b:0),
% 1.30/1.64 class_RealVector_Oreal__normed__vector [187, 1] (w:1, o:181, a:1, s:1
% 1.30/1.64 , b:0),
% 1.30/1.64 class_RealVector_Oreal__normed__algebra__1 [188, 1] (w:1, o:182, a:1
% 1.30/1.64 , s:1, b:0),
% 1.30/1.64 c_Polynomial_Opoly__rec [189, 5] (w:1, o:308, a:1, s:1, b:0),
% 1.30/1.64 c_Polynomial_Osynthetic__div [190, 3] (w:1, o:265, a:1, s:1, b:0),
% 1.30/1.64 c_fequal [191, 2] (w:1, o:241, a:1, s:1, b:0),
% 1.30/1.64 c_If [192, 4] (w:1, o:300, a:1, s:1, b:0),
% 1.30/1.64 c_Groups_Oplus__class_Oplus [193, 3] (w:1, o:266, a:1, s:1, b:0),
% 1.30/1.64 c_Polynomial_Ocoeff [194, 2] (w:1, o:227, a:1, s:1, b:0),
% 1.30/1.64 c_Int_Onumber__class_Onumber__of [196, 2] (w:1, o:242, a:1, s:1, b:0)
% 1.30/1.64 ,
% 1.30/1.64 class_Int_Onumber [197, 1] (w:1, o:183, a:1, s:1, b:0),
% 1.30/1.64 class_Rings_Osemiring [198, 1] (w:1, o:184, a:1, s:1, b:0),
% 1.30/1.64 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct [
% 1.30/1.64 199, 1] (w:1, o:185, a:1, s:1, b:0),
% 1.30/1.64 class_Rings_Ocomm__semiring [200, 1] (w:1, o:164, a:1, s:1, b:0),
% 1.30/1.64 class_Groups_Ocomm__monoid__add [202, 1] (w:1, o:186, a:1, s:1, b:0)
% 1.30/1.64 ,
% 1.30/1.64 class_Groups_Omonoid__add [203, 1] (w:1, o:187, a:1, s:1, b:0),
% 1.30/1.64 class_Groups_Oab__semigroup__add [204, 1] (w:1, o:188, a:1, s:1, b:0)
% 1.30/1.64 ,
% 1.30/1.64 class_Groups_Ocancel__semigroup__add [205, 1] (w:1, o:189, a:1, s:1
% 1.30/1.64 , b:0),
% 1.30/1.64 class_Groups_Ocancel__ab__semigroup__add [206, 1] (w:1, o:190, a:1
% 1.30/1.64 , s:1, b:0),
% 1.30/1.64 class_Int_Onumber__ring [208, 1] (w:1, o:191, a:1, s:1, b:0),
% 1.30/1.64 class_Groups_Oordered__ab__semigroup__add__imp__le [209, 1] (w:1, o:
% 1.30/1.64 192, a:1, s:1, b:0),
% 1.30/1.64 class_Groups_Oordered__ab__semigroup__add [210, 1] (w:1, o:193, a:1
% 1.30/1.64 , s:1, b:0),
% 1.30/1.64 class_Groups_Oordered__cancel__ab__semigroup__add [211, 1] (w:1, o:
% 1.30/1.64 194, a:1, s:1, b:0),
% 1.30/1.64 class_Groups_Oordered__comm__monoid__add [213, 1] (w:1, o:195, a:1
% 1.30/1.64 , s:1, b:0),
% 1.30/1.64 class_Rings_Olinordered__semiring__1 [217, 1] (w:1, o:150, a:1, s:1
% 1.30/1.64 , b:0),
% 1.30/1.64 class_Rings_Olinordered__semiring__1__strict [218, 1] (w:1, o:151, a:
% 1.30/1.64 1, s:1, b:0),
% 1.30/1.64 class_Fields_Ofield [220, 1] (w:1, o:140, a:1, s:1, b:0),
% 1.30/1.64 c_Polynomial_Opdivmod__rel [221, 5] (w:1, o:309, a:1, s:1, b:0),
% 12.32/12.67 c_Divides_Odiv__class_Odiv [235, 3] (w:1, o:267, a:1, s:1, b:0),
% 12.32/12.67 class_Divides_Osemiring__div [236, 1] (w:1, o:197, a:1, s:1, b:0),
% 12.32/12.67 class_Divides_Oring__div [237, 1] (w:1, o:196, a:1, s:1, b:0),
% 12.32/12.67 c_SMT_Oz3div [241, 2] (w:1, o:243, a:1, s:1, b:0),
% 12.32/12.67 class_Groups_Ocancel__comm__monoid__add [243, 1] (w:1, o:198, a:1, s:
% 12.32/12.67 1, b:0),
% 12.32/12.67 tc_HOL_Obool [245, 0] (w:1, o:100, a:1, s:1, b:0),
% 12.32/12.67 alpha1 [246, 2] (w:1, o:244, a:1, s:1, b:1),
% 12.32/12.67 alpha2 [247, 3] (w:1, o:272, a:1, s:1, b:1),
% 12.32/12.67 alpha3 [248, 3] (w:1, o:278, a:1, s:1, b:1),
% 12.32/12.67 alpha4 [249, 4] (w:1, o:303, a:1, s:1, b:1),
% 12.32/12.67 alpha5 [250, 4] (w:1, o:304, a:1, s:1, b:1),
% 12.32/12.67 alpha6 [251, 2] (w:1, o:245, a:1, s:1, b:1),
% 12.32/12.67 alpha7 [252, 2] (w:1, o:246, a:1, s:1, b:1),
% 12.32/12.67 alpha8 [253, 3] (w:1, o:279, a:1, s:1, b:1),
% 12.32/12.67 alpha9 [254, 3] (w:1, o:280, a:1, s:1, b:1),
% 12.32/12.67 alpha10 [255, 2] (w:1, o:247, a:1, s:1, b:1),
% 12.32/12.67 alpha11 [256, 2] (w:1, o:248, a:1, s:1, b:1),
% 12.32/12.67 alpha12 [257, 3] (w:1, o:268, a:1, s:1, b:1),
% 12.32/12.67 alpha13 [258, 3] (w:1, o:269, a:1, s:1, b:1),
% 12.32/12.67 alpha14 [259, 2] (w:1, o:249, a:1, s:1, b:1),
% 12.32/12.67 alpha15 [260, 2] (w:1, o:250, a:1, s:1, b:1),
% 12.32/12.67 alpha16 [261, 3] (w:1, o:270, a:1, s:1, b:1),
% 12.32/12.67 alpha17 [262, 3] (w:1, o:271, a:1, s:1, b:1),
% 12.32/12.67 alpha18 [263, 4] (w:1, o:305, a:1, s:1, b:1),
% 12.32/12.67 alpha19 [264, 4] (w:1, o:306, a:1, s:1, b:1),
% 12.32/12.67 alpha20 [265, 3] (w:1, o:273, a:1, s:1, b:1),
% 12.32/12.67 alpha21 [266, 2] (w:1, o:251, a:1, s:1, b:1),
% 12.32/12.67 alpha22 [267, 2] (w:1, o:252, a:1, s:1, b:1),
% 12.32/12.67 alpha23 [268, 3] (w:1, o:274, a:1, s:1, b:1),
% 12.32/12.67 alpha24 [269, 3] (w:1, o:275, a:1, s:1, b:1),
% 12.32/12.67 alpha25 [270, 2] (w:1, o:253, a:1, s:1, b:1),
% 12.32/12.67 alpha26 [271, 3] (w:1, o:276, a:1, s:1, b:1),
% 12.32/12.67 alpha27 [272, 4] (w:1, o:307, a:1, s:1, b:1),
% 12.32/12.67 alpha28 [273, 3] (w:1, o:277, a:1, s:1, b:1),
% 12.32/12.67 alpha29 [274, 2] (w:1, o:254, a:1, s:1, b:1),
% 12.32/12.67 alpha30 [275, 3] (w:1, o:281, a:1, s:1, b:1),
% 12.32/12.67 alpha31 [276, 3] (w:1, o:282, a:1, s:1, b:1),
% 12.32/12.67 alpha32 [277, 3] (w:1, o:283, a:1, s:1, b:1),
% 12.32/12.67 alpha33 [278, 3] (w:1, o:284, a:1, s:1, b:1),
% 12.32/12.67 alpha34 [279, 3] (w:1, o:285, a:1, s:1, b:1),
% 12.32/12.67 alpha35 [280, 3] (w:1, o:286, a:1, s:1, b:1),
% 12.32/12.67 alpha36 [281, 4] (w:1, o:301, a:1, s:1, b:1),
% 12.32/12.67 alpha37 [282, 4] (w:1, o:302, a:1, s:1, b:1),
% 12.32/12.67 alpha38 [283, 3] (w:1, o:287, a:1, s:1, b:1),
% 12.32/12.67 alpha39 [284, 2] (w:1, o:255, a:1, s:1, b:1),
% 12.32/12.67 alpha40 [285, 3] (w:1, o:288, a:1, s:1, b:1),
% 12.32/12.67 skol1 [286, 2] (w:1, o:229, a:1, s:1, b:1),
% 12.32/12.67 skol2 [287, 0] (w:1, o:12, a:1, s:1, b:1),
% 12.32/12.67 skol3 [288, 2] (w:1, o:231, a:1, s:1, b:1),
% 12.32/12.67 skol4 [289, 0] (w:1, o:13, a:1, s:1, b:1),
% 12.32/12.67 skol5 [290, 0] (w:1, o:14, a:1, s:1, b:1),
% 12.32/12.67 skol6 [291, 0] (w:1, o:15, a:1, s:1, b:1),
% 12.32/12.67 skol7 [292, 1] (w:1, o:123, a:1, s:1, b:1),
% 12.32/12.67 skol8 [293, 2] (w:1, o:232, a:1, s:1, b:1),
% 12.32/12.67 skol9 [294, 3] (w:1, o:289, a:1, s:1, b:1),
% 12.32/12.67 skol10 [295, 2] (w:1, o:233, a:1, s:1, b:1),
% 12.32/12.67 skol11 [296, 3] (w:1, o:290, a:1, s:1, b:1),
% 12.32/12.67 skol12 [297, 3] (w:1, o:291, a:1, s:1, b:1),
% 12.32/12.67 skol13 [298, 3] (w:1, o:292, a:1, s:1, b:1),
% 12.32/12.67 skol14 [299, 2] (w:1, o:234, a:1, s:1, b:1),
% 12.32/12.67 skol15 [300, 2] (w:1, o:235, a:1, s:1, b:1),
% 12.32/12.67 skol16 [301, 3] (w:1, o:293, a:1, s:1, b:1),
% 12.32/12.67 skol17 [302, 3] (w:1, o:294, a:1, s:1, b:1),
% 12.32/12.67 skol18 [303, 2] (w:1, o:236, a:1, s:1, b:1),
% 12.32/12.67 skol19 [304, 3] (w:1, o:295, a:1, s:1, b:1),
% 12.32/12.67 skol20 [305, 3] (w:1, o:296, a:1, s:1, b:1),
% 12.32/12.67 skol21 [306, 3] (w:1, o:297, a:1, s:1, b:1),
% 12.32/12.67 skol22 [307, 3] (w:1, o:298, a:1, s:1, b:1),
% 12.32/12.67 skol23 [308, 2] (w:1, o:230, a:1, s:1, b:1),
% 12.32/12.67 skol24 [309, 3] (w:1, o:299, a:1, s:1, b:1).
% 12.32/12.67
% 12.32/12.67
% 12.32/12.67 Starting Search:
% 12.32/12.67
% 12.32/12.67 *** allocated 113905 integers for clauses
% 12.32/12.67 *** allocated 170857 integers for clauses
% 12.32/12.67 Resimplifying inuse:
% 12.32/12.67 Done
% 12.32/12.67
% 12.32/12.67
% 12.32/12.67 Intermediate Status:
% 12.32/12.67 Generated: 3100
% 12.32/12.67 Kept: 2000
% 12.32/12.67 Inuse: 73
% 12.32/12.67 Deleted: 0
% 12.32/12.67 Deletedinuse: 0
% 12.32/12.67
% 12.32/12.67 *** allocated 256285 integers for clauses
% 12.32/12.67 *** allocated 170857 integers for termspace/termends
% 60.34/60.74 Resimplifying inuse:
% 60.34/60.74 Done
% 60.34/60.74
% 60.34/60.74 *** allocated 256285 integers for termspace/termends
% 60.34/60.74 *** allocated 384427 integers for clauses
% 60.34/60.74
% 60.34/60.74 Intermediate Status:
% 60.34/60.74 Generated: 8863
% 60.34/60.74 Kept: 4220
% 60.34/60.74 Inuse: 180
% 60.34/60.74 Deleted: 1
% 60.34/60.74 Deletedinuse: 0
% 60.34/60.74
% 60.34/60.74 Resimplifying inuse:
% 60.34/60.74 Done
% 60.34/60.74
% 60.34/60.74 Resimplifying inuse:
% 60.34/60.74 Done
% 60.34/60.74
% 60.34/60.74
% 60.34/60.74 Intermediate Status:
% 60.34/60.74 Generated: 18023
% 60.34/60.74 Kept: 6222
% 60.34/60.74 Inuse: 210
% 60.34/60.74 Deleted: 1
% 60.34/60.74 Deletedinuse: 0
% 60.34/60.74
% 60.34/60.74 Resimplifying inuse:
% 60.34/60.74 Done
% 60.34/60.74
% 60.34/60.74 *** allocated 384427 integers for termspace/termends
% 60.34/60.74 *** allocated 576640 integers for clauses
% 60.34/60.74 Resimplifying inuse:
% 60.34/60.74 Done
% 60.34/60.74
% 60.34/60.74
% 60.34/60.74 Intermediate Status:
% 60.34/60.74 Generated: 29836
% 60.34/60.74 Kept: 8242
% 60.34/60.74 Inuse: 238
% 60.34/60.74 Deleted: 4
% 60.34/60.74 Deletedinuse: 1
% 60.34/60.74
% 60.34/60.74 Resimplifying inuse:
% 60.34/60.74 Done
% 60.34/60.74
% 60.34/60.74 Resimplifying inuse:
% 60.34/60.74 Done
% 60.34/60.74
% 60.34/60.74
% 60.34/60.74 Intermediate Status:
% 60.34/60.74 Generated: 37113
% 60.34/60.74 Kept: 10254
% 60.34/60.74 Inuse: 317
% 60.34/60.74 Deleted: 5
% 60.34/60.74 Deletedinuse: 1
% 60.34/60.74
% 60.34/60.74 Resimplifying inuse:
% 60.34/60.74 Done
% 60.34/60.74
% 60.34/60.74 *** allocated 576640 integers for termspace/termends
% 60.34/60.74 Resimplifying inuse:
% 60.34/60.74 Done
% 60.34/60.74
% 60.34/60.74 *** allocated 864960 integers for clauses
% 60.34/60.74
% 60.34/60.74 Intermediate Status:
% 60.34/60.74 Generated: 44845
% 60.34/60.74 Kept: 12258
% 60.34/60.74 Inuse: 378
% 60.34/60.74 Deleted: 6
% 60.34/60.74 Deletedinuse: 1
% 60.34/60.74
% 60.34/60.74 Resimplifying inuse:
% 60.34/60.74 Done
% 60.34/60.74
% 60.34/60.74
% 60.34/60.74 Intermediate Status:
% 60.34/60.74 Generated: 51807
% 60.34/60.74 Kept: 15305
% 60.34/60.74 Inuse: 416
% 60.34/60.74 Deleted: 6
% 60.34/60.74 Deletedinuse: 1
% 60.34/60.74
% 60.34/60.74 Resimplifying inuse:
% 60.34/60.74 Done
% 60.34/60.74
% 60.34/60.74 Resimplifying inuse:
% 60.34/60.74 Done
% 60.34/60.74
% 60.34/60.74 *** allocated 1297440 integers for clauses
% 60.34/60.74
% 60.34/60.74 Intermediate Status:
% 60.34/60.74 Generated: 62846
% 60.34/60.74 Kept: 18317
% 60.34/60.74 Inuse: 460
% 60.34/60.74 Deleted: 14
% 60.34/60.74 Deletedinuse: 8
% 60.34/60.74
% 60.34/60.74 Resimplifying inuse:
% 60.34/60.74 Done
% 60.34/60.74
% 60.34/60.74 *** allocated 864960 integers for termspace/termends
% 60.34/60.74 Resimplifying inuse:
% 60.34/60.74 Done
% 60.34/60.74
% 60.34/60.74 Resimplifying clauses:
% 60.34/60.74 Done
% 60.34/60.74
% 60.34/60.74
% 60.34/60.74 Intermediate Status:
% 60.34/60.74 Generated: 69204
% 60.34/60.74 Kept: 20324
% 60.34/60.74 Inuse: 498
% 60.34/60.74 Deleted: 618
% 60.34/60.74 Deletedinuse: 8
% 60.34/60.74
% 60.34/60.74 Resimplifying inuse:
% 60.34/60.74 Done
% 60.34/60.74
% 60.34/60.74
% 60.34/60.74 Intermediate Status:
% 60.34/60.74 Generated: 73908
% 60.34/60.74 Kept: 22722
% 60.34/60.74 Inuse: 510
% 60.34/60.74 Deleted: 619
% 60.34/60.74 Deletedinuse: 9
% 60.34/60.74
% 60.34/60.74 Resimplifying inuse:
% 60.34/60.74 Done
% 60.34/60.74
% 60.34/60.74
% 60.34/60.74 Intermediate Status:
% 60.34/60.74 Generated: 78207
% 60.34/60.74 Kept: 25160
% 60.34/60.74 Inuse: 520
% 60.34/60.74 Deleted: 619
% 60.34/60.74 Deletedinuse: 9
% 60.34/60.74
% 60.34/60.74 Resimplifying inuse:
% 60.34/60.74 Done
% 60.34/60.74
% 60.34/60.74 Resimplifying inuse:
% 60.34/60.74 Done
% 60.34/60.74
% 60.34/60.74
% 60.34/60.74 Intermediate Status:
% 60.34/60.74 Generated: 86285
% 60.34/60.74 Kept: 27173
% 60.34/60.74 Inuse: 559
% 60.34/60.74 Deleted: 619
% 60.34/60.74 Deletedinuse: 9
% 60.34/60.74
% 60.34/60.74 *** allocated 1946160 integers for clauses
% 60.34/60.74 Resimplifying inuse:
% 60.34/60.74 Done
% 60.34/60.74
% 60.34/60.74 Resimplifying inuse:
% 60.34/60.74 Done
% 60.34/60.74
% 60.34/60.74
% 60.34/60.74 Intermediate Status:
% 60.34/60.74 Generated: 96089
% 60.34/60.74 Kept: 29203
% 60.34/60.74 Inuse: 588
% 60.34/60.74 Deleted: 619
% 60.34/60.74 Deletedinuse: 9
% 60.34/60.74
% 60.34/60.74 Resimplifying inuse:
% 60.34/60.74 Done
% 60.34/60.74
% 60.34/60.74 *** allocated 1297440 integers for termspace/termends
% 60.34/60.74
% 60.34/60.74 Intermediate Status:
% 60.34/60.74 Generated: 107327
% 60.34/60.74 Kept: 31928
% 60.34/60.74 Inuse: 610
% 60.34/60.74 Deleted: 619
% 60.34/60.74 Deletedinuse: 9
% 60.34/60.74
% 60.34/60.74 Resimplifying inuse:
% 60.34/60.74 Done
% 60.34/60.74
% 60.34/60.74 Resimplifying inuse:
% 60.34/60.74 Done
% 60.34/60.74
% 60.34/60.74
% 60.34/60.74 Intermediate Status:
% 60.34/60.74 Generated: 118300
% 60.34/60.74 Kept: 33938
% 60.34/60.74 Inuse: 635
% 60.34/60.74 Deleted: 619
% 60.34/60.74 Deletedinuse: 9
% 60.34/60.74
% 60.34/60.74 Resimplifying inuse:
% 60.34/60.74 Done
% 60.34/60.74
% 60.34/60.74 Resimplifying inuse:
% 60.34/60.74 Done
% 60.34/60.74
% 60.34/60.74
% 60.34/60.74 Intermediate Status:
% 60.34/60.74 Generated: 125830
% 60.34/60.74 Kept: 35965
% 60.34/60.74 Inuse: 671
% 60.34/60.74 Deleted: 620
% 60.34/60.74 Deletedinuse: 10
% 60.34/60.74
% 60.34/60.74 Resimplifying inuse:
% 60.34/60.74 Done
% 60.34/60.74
% 60.34/60.74 Resimplifying inuse:
% 60.34/60.74 Done
% 60.34/60.74
% 60.34/60.74
% 60.34/60.74 Intermediate Status:
% 60.34/60.74 Generated: 133417
% 60.34/60.74 Kept: 37965
% 60.34/60.74 Inuse: 689
% 60.34/60.74 Deleted: 620
% 60.34/60.74 Deletedinuse: 10
% 60.34/60.74
% 60.34/60.74 Resimplifying inuse:
% 60.34/60.74 Done
% 60.34/60.74
% 60.34/60.74 Resimplifying inuse:
% 60.34/60.74 Done
% 60.34/60.74
% 60.34/60.74
% 60.34/60.74 Intermediate Status:
% 60.34/60.74 Generated: 140821
% 60.34/60.74 Kept: 39999
% 60.34/60.74 Inuse: 714
% 60.34/60.74 Deleted: 620
% 60.34/60.74 Deletedinuse: 10
% 60.34/60.74
% 60.34/60.74 Resimplifying clauses:
% 60.34/60.74 Done
% 60.34/60.74
% 60.34/60.74 Resimplifying inuse:
% 60.34/60.74 Done
% 60.34/60.74
% 60.34/60.74 *** allocated 2919240 integers for clauses
% 60.34/60.74
% 60.34/60.74 Intermediate Status:
% 60.34/60.74 Generated: 152568
% 60.34/60.74 Kept: 43124
% 60.34/60.74 Inuse: 733
% 60.34/60.74 Deleted: 1086
% 60.34/60.74 Deletedinuse: 10
% 60.34/60.74
% 60.34/60.74 Resimplifying inuse:
% 60.34/60.74 Done
% 60.34/60.74
% 60.34/60.74 Resimplifying inuse:
% 60.34/60.74 Done
% 60.34/60.74
% 60.34/60.74 *** allocated 1946160 integers for termspace/termends
% 60.34/60.74
% 60.34/60.74 Intermediate Status:
% 60.34/60.74 Generated: 160036
% 60.34/60.74 Kept: 45400
% 60.34/60.74 Inuse: 760
% 60.34/60.74 Deleted: 1087
% 60.34/60.74 Deletedinuse: 11
% 60.34/60.74
% 60.34/60.74 Resimplifying inuse:
% 60.34/60.74 Done
% 60.34/60.74
% 60.34/60.74
% 60.34/60.74 Intermediate Status:
% 60.34/60.74 Generated: 171586
% 60.34/60.74 Kept: 48353
% 60.34/60.74 Inuse: 795
% 60.34/60.74 Deleted: 1087
% 60.34/60.74 Deletedinuse: 11
% 60.34/60.74
% 60.34/60.74 Resimplifying inuse:
% 60.34/60.74 Done
% 60.34/60.74
% 60.34/60.74 Resimplifying inuse:
% 60.34/60.74 Done
% 60.34/60.74
% 60.34/60.74
% 60.34/60.74 Intermediate Status:
% 60.34/60.74 Generated: 183035
% 60.34/60.74 Kept: 50413
% 60.34/60.74 Inuse: 830
% 60.34/60.74 Deleted: 1087
% 60.34/60.74 Deletedinuse: 11
% 60.34/60.74
% 60.34/60.74
% 60.34/60.74 Intermediate Status:
% 60.34/60.74 Generated: 190027
% 60.34/60.74 Kept: 54153
% 146.30/146.73 Inuse: 835
% 146.30/146.73 Deleted: 1087
% 146.30/146.73 Deletedinuse: 11
% 146.30/146.73
% 146.30/146.73 Resimplifying inuse:
% 146.30/146.73 Done
% 146.30/146.73
% 146.30/146.73
% 146.30/146.73 Intermediate Status:
% 146.30/146.73 Generated: 195942
% 146.30/146.73 Kept: 56405
% 146.30/146.73 Inuse: 855
% 146.30/146.73 Deleted: 1087
% 146.30/146.73 Deletedinuse: 11
% 146.30/146.73
% 146.30/146.73 Resimplifying inuse:
% 146.30/146.73 Done
% 146.30/146.73
% 146.30/146.73 Resimplifying inuse:
% 146.30/146.73 Done
% 146.30/146.73
% 146.30/146.73
% 146.30/146.73 Intermediate Status:
% 146.30/146.73 Generated: 203729
% 146.30/146.73 Kept: 59206
% 146.30/146.73 Inuse: 885
% 146.30/146.73 Deleted: 1087
% 146.30/146.73 Deletedinuse: 11
% 146.30/146.73
% 146.30/146.73 Resimplifying inuse:
% 146.30/146.73 Done
% 146.30/146.73
% 146.30/146.73 Resimplifying inuse:
% 146.30/146.73 Done
% 146.30/146.73
% 146.30/146.73 Resimplifying clauses:
% 146.30/146.73 Done
% 146.30/146.73
% 146.30/146.73
% 146.30/146.73 Intermediate Status:
% 146.30/146.73 Generated: 212277
% 146.30/146.73 Kept: 62697
% 146.30/146.73 Inuse: 920
% 146.30/146.73 Deleted: 1397
% 146.30/146.73 Deletedinuse: 11
% 146.30/146.73
% 146.30/146.73 Resimplifying inuse:
% 146.30/146.73 Done
% 146.30/146.73
% 146.30/146.73 Resimplifying inuse:
% 146.30/146.73 Done
% 146.30/146.73
% 146.30/146.73 *** allocated 4378860 integers for clauses
% 146.30/146.73
% 146.30/146.73 Intermediate Status:
% 146.30/146.73 Generated: 219589
% 146.30/146.73 Kept: 64729
% 146.30/146.73 Inuse: 960
% 146.30/146.73 Deleted: 1399
% 146.30/146.73 Deletedinuse: 13
% 146.30/146.73
% 146.30/146.73 Resimplifying inuse:
% 146.30/146.73 Done
% 146.30/146.73
% 146.30/146.73
% 146.30/146.73 Intermediate Status:
% 146.30/146.73 Generated: 224785
% 146.30/146.73 Kept: 67089
% 146.30/146.73 Inuse: 970
% 146.30/146.73 Deleted: 1399
% 146.30/146.73 Deletedinuse: 13
% 146.30/146.73
% 146.30/146.73 Resimplifying inuse:
% 146.30/146.73 Done
% 146.30/146.73
% 146.30/146.73 Resimplifying inuse:
% 146.30/146.73 Done
% 146.30/146.73
% 146.30/146.73
% 146.30/146.73 Intermediate Status:
% 146.30/146.73 Generated: 239318
% 146.30/146.73 Kept: 73063
% 146.30/146.73 Inuse: 1020
% 146.30/146.73 Deleted: 1399
% 146.30/146.73 Deletedinuse: 13
% 146.30/146.73
% 146.30/146.73 Resimplifying inuse:
% 146.30/146.73 Done
% 146.30/146.73
% 146.30/146.73 Resimplifying inuse:
% 146.30/146.73 Done
% 146.30/146.73
% 146.30/146.73 *** allocated 2919240 integers for termspace/termends
% 146.30/146.73
% 146.30/146.73 Intermediate Status:
% 146.30/146.73 Generated: 247639
% 146.30/146.73 Kept: 75073
% 146.30/146.73 Inuse: 1053
% 146.30/146.73 Deleted: 1401
% 146.30/146.73 Deletedinuse: 13
% 146.30/146.73
% 146.30/146.73 Resimplifying inuse:
% 146.30/146.73 Done
% 146.30/146.73
% 146.30/146.73 Resimplifying inuse:
% 146.30/146.73 Done
% 146.30/146.73
% 146.30/146.73
% 146.30/146.73 Intermediate Status:
% 146.30/146.73 Generated: 261775
% 146.30/146.73 Kept: 77572
% 146.30/146.73 Inuse: 1068
% 146.30/146.73 Deleted: 1401
% 146.30/146.73 Deletedinuse: 13
% 146.30/146.73
% 146.30/146.73 Resimplifying inuse:
% 146.30/146.73 Done
% 146.30/146.73
% 146.30/146.73 Resimplifying inuse:
% 146.30/146.73 Done
% 146.30/146.73
% 146.30/146.73
% 146.30/146.73 Intermediate Status:
% 146.30/146.73 Generated: 269951
% 146.30/146.73 Kept: 79921
% 146.30/146.73 Inuse: 1088
% 146.30/146.73 Deleted: 1401
% 146.30/146.73 Deletedinuse: 13
% 146.30/146.73
% 146.30/146.73 Resimplifying inuse:
% 146.30/146.73 Done
% 146.30/146.73
% 146.30/146.73 Resimplifying inuse:
% 146.30/146.73 Done
% 146.30/146.73
% 146.30/146.73 Resimplifying clauses:
% 146.30/146.73 Done
% 146.30/146.73
% 146.30/146.73
% 146.30/146.73 Intermediate Status:
% 146.30/146.73 Generated: 285817
% 146.30/146.73 Kept: 83699
% 146.30/146.73 Inuse: 1103
% 146.30/146.73 Deleted: 1955
% 146.30/146.73 Deletedinuse: 13
% 146.30/146.73
% 146.30/146.73 Resimplifying inuse:
% 146.30/146.73 Done
% 146.30/146.73
% 146.30/146.73
% 146.30/146.73 Intermediate Status:
% 146.30/146.73 Generated: 295930
% 146.30/146.73 Kept: 85796
% 146.30/146.73 Inuse: 1113
% 146.30/146.73 Deleted: 1955
% 146.30/146.73 Deletedinuse: 13
% 146.30/146.73
% 146.30/146.73 Resimplifying inuse:
% 146.30/146.73 Done
% 146.30/146.73
% 146.30/146.73 Resimplifying inuse:
% 146.30/146.73 Done
% 146.30/146.73
% 146.30/146.73
% 146.30/146.73 Intermediate Status:
% 146.30/146.73 Generated: 306085
% 146.30/146.73 Kept: 87799
% 146.30/146.73 Inuse: 1121
% 146.30/146.73 Deleted: 1955
% 146.30/146.73 Deletedinuse: 13
% 146.30/146.73
% 146.30/146.73
% 146.30/146.73 Intermediate Status:
% 146.30/146.73 Generated: 316975
% 146.30/146.73 Kept: 89967
% 146.30/146.73 Inuse: 1128
% 146.30/146.73 Deleted: 1955
% 146.30/146.73 Deletedinuse: 13
% 146.30/146.73
% 146.30/146.73 Resimplifying inuse:
% 146.30/146.73 Done
% 146.30/146.73
% 146.30/146.73
% 146.30/146.73 Intermediate Status:
% 146.30/146.73 Generated: 326280
% 146.30/146.73 Kept: 92421
% 146.30/146.73 Inuse: 1143
% 146.30/146.73 Deleted: 1955
% 146.30/146.73 Deletedinuse: 13
% 146.30/146.73
% 146.30/146.73 Resimplifying inuse:
% 146.30/146.73 Done
% 146.30/146.73
% 146.30/146.73
% 146.30/146.73 Intermediate Status:
% 146.30/146.73 Generated: 345292
% 146.30/146.73 Kept: 95610
% 146.30/146.73 Inuse: 1158
% 146.30/146.73 Deleted: 1955
% 146.30/146.73 Deletedinuse: 13
% 146.30/146.73
% 146.30/146.73 Resimplifying inuse:
% 146.30/146.73 Done
% 146.30/146.73
% 146.30/146.73
% 146.30/146.73 Intermediate Status:
% 146.30/146.73 Generated: 365717
% 146.30/146.73 Kept: 98876
% 146.30/146.73 Inuse: 1173
% 146.30/146.73 Deleted: 1955
% 146.30/146.73 Deletedinuse: 13
% 146.30/146.73
% 146.30/146.73 Resimplifying inuse:
% 146.30/146.73 Done
% 146.30/146.73
% 146.30/146.73 *** allocated 6568290 integers for clauses
% 146.30/146.73
% 146.30/146.73 Intermediate Status:
% 146.30/146.73 Generated: 372275
% 146.30/146.73 Kept: 102105
% 146.30/146.73 Inuse: 1183
% 146.30/146.73 Deleted: 1955
% 146.30/146.73 Deletedinuse: 13
% 146.30/146.73
% 146.30/146.73 Resimplifying inuse:
% 146.30/146.73 Done
% 146.30/146.73
% 146.30/146.73 Resimplifying clauses:
% 146.30/146.73 Done
% 146.30/146.73
% 146.30/146.73 *** allocated 4378860 integers for termspace/termends
% 146.30/146.73
% 146.30/146.73 Intermediate Status:
% 146.30/146.73 Generated: 399468
% 146.30/146.73 Kept: 106290
% 146.30/146.73 Inuse: 1193
% 146.30/146.73 Deleted: 2022
% 146.30/146.73 Deletedinuse: 13
% 146.30/146.73
% 146.30/146.73 Resimplifying inuse:
% 146.30/146.73 Done
% 146.30/146.73
% 146.30/146.73 Resimplifying inuse:
% 146.30/146.73 Done
% 146.30/146.73
% 146.30/146.73
% 146.30/146.73 Intermediate Status:
% 146.30/146.73 Generated: 408274
% 146.30/146.73 Kept: 108311
% 146.30/146.73 Inuse: 1217
% 146.30/146.73 Deleted: 2022
% 146.30/146.73 Deletedinuse: 13
% 146.30/146.73
% 146.30/146.73 Resimplifying inuse:
% 146.30/146.73 Done
% 146.30/146.73
% 146.30/146.73 Resimplifying inuse:
% 146.30/146.73 Done
% 146.30/146.73
% 146.30/146.73
% 146.30/146.73 Intermediate Status:
% 146.30/146.73 Generated: 416116
% 146.30/146.73 Kept: 110363
% 146.30/146.73 Inuse: 1243
% 146.30/146.73 Deleted: 2022
% 146.30/146.73 Deletedinuse: 13
% 146.30/146.73
% 146.30/146.73 Resimplifying inuse:
% 146.30/146.73 Done
% 146.30/146.73
% 146.30/146.73 Resimplifying inuse:
% 146.30/146.73 Done
% 146.30/146.73
% 146.30/146.73
% 146.30/146.73 Intermediate Status:
% 146.30/146.73 Generated: 425777
% 146.30/146.73 Kept: 112389
% 146.30/146.73 Inuse: 1284
% 146.30/146.73 Deleted: 2023
% 146.30/146.73 Deletedinuse: 14
% 146.30/146.73
% 146.30/146.73 Resimplifying inuse:
% 146.30/146.73 Done
% 146.30/146.73
% 146.30/146.73 Resimplifying inuse:
% 146.30/146.73 Done
% 146.30/146.73
% 146.30/146.73
% 146.30/146.73 Intermediate Status:
% 146.30/146.73 Generated: 434744
% 146.30/146.73 Kept: 114405
% 146.30/146.73 Inuse: 1314
% 146.30/146.73 Deleted: 2023
% 146.30/146.73 Deletedinuse: 14
% 146.30/146.73
% 146.30/146.73 Resimplifying inuse:
% 146.30/146.73 Done
% 146.30/146.73
% 146.30/146.73 Resimplifying inuse:
% 146.30/146.73 Done
% 146.30/146.73
% 146.30/146.73
% 146.30/146.73 Intermediate Status:
% 146.30/146.73 Generated: 441913
% 146.30/146.73 Kept: 116416
% 146.30/146.73 Inuse: 1352
% 146.30/146.73 Deleted: 2023
% 146.30/146.73 Deletedinuse: 14
% 146.30/146.73
% 146.30/146.73 Resimplifying inuse:
% 146.30/146.73 Done
% 146.30/146.73
% 146.30/146.73 Resimplifying inuseCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------