TSTP Solution File: SWW249+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWW249+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n021.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 23:21:33 EDT 2022
% Result : Timeout 300.04s 300.53s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW249+1 : TPTP v8.1.0. Released v5.2.0.
% 0.07/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n021.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 : Sun Jun 5 13:44:49 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.97/1.64 *** allocated 10000 integers for termspace/termends
% 0.97/1.64 *** allocated 10000 integers for clauses
% 0.97/1.64 *** allocated 10000 integers for justifications
% 0.97/1.64 *** allocated 15000 integers for termspace/termends
% 0.97/1.64 *** allocated 22500 integers for termspace/termends
% 0.97/1.64 *** allocated 33750 integers for termspace/termends
% 0.97/1.64 Bliksem 1.12
% 0.97/1.64
% 0.97/1.64
% 0.97/1.64 Automatic Strategy Selection
% 0.97/1.64
% 0.97/1.64 *** allocated 50625 integers for termspace/termends
% 0.97/1.64 *** allocated 75937 integers for termspace/termends
% 0.97/1.64 *** allocated 113905 integers for termspace/termends
% 0.97/1.64 *** allocated 170857 integers for termspace/termends
% 0.97/1.64
% 0.97/1.64 Clauses:
% 0.97/1.64
% 0.97/1.64 { ! hAPP( Y, skol1( X, Y ) ) = hAPP( X, skol1( X, Y ) ), Y = X }.
% 0.97/1.64 { ! class_Rings_Oidom( t_a ), !
% 0.97/1.64 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( t_a, t_a,
% 0.97/1.64 c_Polynomial_Opoly( t_a, v_p ) ) }.
% 0.97/1.64 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( c_Nat_OSuc, X ) ) ) }
% 0.97/1.64 .
% 0.97/1.64 { ! class_Rings_Oidom( t_a ), ! skol2 = c_Groups_Ozero__class_Ozero( t_a )
% 0.97/1.64 }.
% 0.97/1.64 { ! class_Rings_Oidom( t_a ), ! hAPP( c_Polynomial_Opoly( t_a, v_cs____ ),
% 0.97/1.64 skol2 ) = c_Groups_Ozero__class_Ozero( t_a ) }.
% 0.97/1.64 { ! class_Rings_Oidom( t_a ), ! skol3 = c_Groups_Ozero__class_Ozero( t_a )
% 0.97/1.64 }.
% 0.97/1.64 { ! class_Rings_Oidom( t_a ), ! hAPP( c_Polynomial_Opoly( t_a, v_cs____ ),
% 0.97/1.64 skol3 ) = c_Groups_Ozero__class_Ozero( t_a ) }.
% 0.97/1.64 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), hAPP(
% 0.97/1.64 c_Nat_OSuc, X ) ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 0.97/1.64 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Nat_OSuc
% 0.97/1.64 , Y ) ), hAPP( c_Nat_OSuc, X ) ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ),
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), Y ) )
% 0.97/1.64 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Z ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), hAPP
% 0.97/1.64 ( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z ), Y ) ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), T )
% 0.97/1.64 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, T ),
% 0.97/1.64 c_Groups_Oone__class_Oone( X ) ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.64 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.97/1.64 c_Power_Opower__class_Opower( X ), T ), Z ) ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 0.97/1.64 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Y ),
% 0.97/1.64 c_Groups_Oone__class_Oone( X ) ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.64 c_Power_Opower__class_Opower( X ), Y ), hAPP( c_Nat_OSuc, Z ) ) ),
% 0.97/1.64 c_Groups_Oone__class_Oone( X ) ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 0.97/1.64 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Y ),
% 0.97/1.64 c_Groups_Oone__class_Oone( X ) ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.97/1.64 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ), hAPP( hAPP(
% 0.97/1.64 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 0.97/1.64 ( hAPP( c_Polynomial_OpCons( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), T ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( c_Polynomial_Opoly( X, Z )
% 0.97/1.64 , Y ) ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), Y ) )
% 0.97/1.64 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.64 c_Power_Opower__class_Opower( X ), Y ), T ) ), hAPP( hAPP(
% 0.97/1.64 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T ), Z ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), Y ) )
% 0.97/1.64 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, T ), Z ) ),
% 0.97/1.64 hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.64 c_Power_Opower__class_Opower( X ), Y ), T ) ), hAPP( hAPP(
% 0.97/1.64 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.97/1.64 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.97/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z = X
% 0.97/1.64 , Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.64 { ! Z = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.97/1.64 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }
% 0.97/1.64 .
% 0.97/1.64 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.97/1.64 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.97/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Y = X
% 0.97/1.64 , Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.64 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.97/1.64 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.97/1.64 .
% 0.97/1.64 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.97/1.64 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.64 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.64 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) =
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.64 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.97/1.64 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.64 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.97/1.64 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) }.
% 0.97/1.64 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP(
% 0.97/1.64 c_Nat_OSuc, Z ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.64 tc_Nat_Onat ), hAPP( c_Nat_OSuc, Z ) ), X ), Y = X }.
% 0.97/1.64 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP(
% 0.97/1.64 c_Nat_OSuc, Z ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.64 tc_Nat_Onat ), hAPP( c_Nat_OSuc, Z ) ), X ) }.
% 0.97/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP( hAPP
% 0.97/1.64 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP
% 0.97/1.64 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.97/1.64 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y = c_Groups_Oone__class_Oone(
% 0.97/1.64 tc_Nat_Onat ) }.
% 0.97/1.64 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X = c_Groups_Oone__class_Oone(
% 0.97/1.64 tc_Nat_Onat ) }.
% 0.97/1.64 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.97/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.97/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.97/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 0.97/1.64 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), Y =
% 0.97/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.97/1.64 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X =
% 0.97/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.97/1.64 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.97/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Groups_Oone__class_Oone(
% 0.97/1.64 tc_Nat_Onat ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.97/1.64 , Y ), X ) }.
% 0.97/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) = X }.
% 0.97/1.64 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 0.97/1.64 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y =
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Y =
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.97/1.64 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.97/1.64 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( Z, Y, X ), hAPP(
% 0.97/1.64 X, T ) = hAPP( X, U ) }.
% 0.97/1.64 { ! hAPP( X, skol4( X ) ) = hAPP( X, skol30( X ) ),
% 0.97/1.64 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( Z, Y, X ) }.
% 0.97/1.64 { ! hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.64 hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = hAPP( c_Nat_OSuc,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.64 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.64 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = hAPP( c_Nat_OSuc
% 0.97/1.64 , c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.64 { ! Y = hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 0.97/1.64 hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = hAPP
% 0.97/1.64 ( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.64 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), hAPP( c_Nat_OSuc
% 0.97/1.64 , c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) = hAPP( c_Nat_OSuc
% 0.97/1.64 , c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.64 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Z ) ), hAPP( hAPP(
% 0.97/1.64 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z ), Y ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.97/1.64 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.64 tc_Nat_Onat ) ), Y ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 0.97/1.64 .
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.64 tc_Nat_Onat ) ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.97/1.64 , Y ), X ) ) ) }.
% 0.97/1.64 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.64 tc_Nat_Onat ) ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.97/1.64 , Y ), X ) ) ) }.
% 0.97/1.64 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.64 hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y = hAPP
% 0.97/1.64 ( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.64 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.64 hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X = hAPP
% 0.97/1.64 ( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.64 { ! Y = hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X
% 0.97/1.64 = hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP(
% 0.97/1.64 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP(
% 0.97/1.64 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), !
% 0.97/1.64 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Z ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), !
% 0.97/1.64 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Z ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.64 tc_Nat_Onat ) ), Y ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z ), X ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z ), X ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.64 tc_Nat_Onat ) ), Z ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Z ) ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.64 tc_Nat_Onat ) ), Y ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.64 tc_Nat_Onat ) ), X ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.64 tc_Nat_Onat ) ), X ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.97/1.64 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( c_Nat_OSuc, Z ) ), Y
% 0.97/1.64 ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP(
% 0.97/1.64 c_Nat_OSuc, Z ) ), X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.97/1.64 tc_Nat_Onat, Y ), X ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 0.97/1.64 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( c_Nat_OSuc, Z ) ), Y
% 0.97/1.64 ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP(
% 0.97/1.64 c_Nat_OSuc, Z ) ), X ) ) ) }.
% 0.97/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP(
% 0.97/1.64 c_Nat_OSuc, Y ) ), X ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 0.97/1.64 tc_Nat_Onat ), X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.64 tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), hAPP(
% 0.97/1.64 c_Nat_OSuc, X ) ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat
% 0.97/1.64 ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X
% 0.97/1.64 ) ) }.
% 0.97/1.64 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X )
% 0.97/1.64 , X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y =
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oone__class_Oone(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) = hAPP( hAPP( c_Polynomial_OpCons( X ),
% 0.97/1.64 c_Groups_Oone__class_Oone( X ) ), c_Groups_Ozero__class_Ozero(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.97/1.64 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) ), !
% 0.97/1.64 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Nat_OSuc
% 0.97/1.64 , c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), Y ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Nat_OSuc,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.97/1.64 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) ), !
% 0.97/1.64 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Nat_OSuc
% 0.97/1.64 , c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), Y ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.97/1.64 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) ), !
% 0.97/1.64 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Nat_OSuc
% 0.97/1.64 , c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), Y ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) ) }.
% 0.97/1.64 { ! class_Groups_Ozero( X ), !
% 0.97/1.64 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ),
% 0.97/1.64 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.64 { ! hAPP( c_Nat_OSuc, Y ) = hAPP( c_Nat_OSuc, X ), Y = X }.
% 0.97/1.64 { ! hAPP( c_Nat_OSuc, Y ) = hAPP( c_Nat_OSuc, X ), Y = X }.
% 0.97/1.64 { ! Y = X, hAPP( c_Nat_OSuc, Y ) = hAPP( c_Nat_OSuc, X ) }.
% 0.97/1.64 { ! hAPP( c_Nat_OSuc, X ) = X }.
% 0.97/1.64 { ! X = hAPP( c_Nat_OSuc, X ) }.
% 0.97/1.64 { alpha47( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.97/1.64 tc_Nat_Onat, Y ), Z ) ), hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.97/1.64 { alpha47( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP
% 0.97/1.64 ( X, Y ), Z ) ) }.
% 0.97/1.64 { ! alpha47( X, Y, Z ), alpha50( X, Y, Z ), Z = Y }.
% 0.97/1.64 { ! alpha47( X, Y, Z ), alpha50( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z
% 0.97/1.64 ) ) }.
% 0.97/1.64 { ! alpha50( X, Y, Z ), alpha47( X, Y, Z ) }.
% 0.97/1.64 { ! Z = Y, hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha47( X, Y, Z ) }.
% 0.97/1.64 { ! alpha50( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.97/1.64 tc_Nat_Onat, Z ), Y ) ) }.
% 0.97/1.64 { ! alpha50( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z ), Y ) ),
% 0.97/1.64 hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha50( X, Y, Z ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), !
% 0.97/1.64 Y = X }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), !
% 0.97/1.64 X = Y }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), X ) ) }.
% 0.97/1.64 { Y = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X )
% 0.97/1.64 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), Y ) ) }
% 0.97/1.64 .
% 0.97/1.64 { Y = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X )
% 0.97/1.64 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), Y ) ) }
% 0.97/1.64 .
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), !
% 0.97/1.64 Y = X }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), Y ) ), !
% 0.97/1.64 Y = X }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), X ) ) }.
% 0.97/1.64 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) = hAPP
% 0.97/1.64 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Y ), Z = X }.
% 0.97/1.64 { ! Z = X, hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y )
% 0.97/1.64 = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Y ) }.
% 0.97/1.64 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) = hAPP
% 0.97/1.64 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ), Y = X }.
% 0.97/1.64 { ! Y = X, hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y )
% 0.97/1.64 = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) }.
% 0.97/1.64 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP( hAPP
% 0.97/1.64 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.64 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) }.
% 0.97/1.64 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) = hAPP(
% 0.97/1.64 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Y ) }.
% 0.97/1.64 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( c_Polynomial_OpCons( X ), U ), T
% 0.97/1.64 ) = hAPP( hAPP( c_Polynomial_OpCons( X ), Z ), Y ), U = Z }.
% 0.97/1.64 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( c_Polynomial_OpCons( X ), U ), T
% 0.97/1.64 ) = hAPP( hAPP( c_Polynomial_OpCons( X ), Z ), Y ), T = Y }.
% 0.97/1.64 { ! class_Groups_Ozero( X ), ! U = Z, ! T = Y, hAPP( hAPP(
% 0.97/1.64 c_Polynomial_OpCons( X ), U ), T ) = hAPP( hAPP( c_Polynomial_OpCons( X )
% 0.97/1.64 , Z ), Y ) }.
% 0.97/1.64 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 0.97/1.64 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ), Z = Y }.
% 0.97/1.64 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Z = Y,
% 0.97/1.64 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ) }.
% 0.97/1.64 { ! class_Rings_Oring__1__no__zero__divisors( X ), Y =
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.97/1.64 c_Power_Opower__class_Opower( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 0.97/1.64 ( X ) }.
% 0.97/1.64 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.97/1.64 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.64 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.97/1.64 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.97/1.64 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.64 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.97/1.64 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.97/1.64 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.97/1.64 c_Power_Opower__class_Opower( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.97/1.64 = c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.64 { ! hAPP( c_Nat_OSuc, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.64 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = hAPP( c_Nat_OSuc, X ) }.
% 0.97/1.64 { ! hAPP( c_Nat_OSuc, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.64 { ! hAPP( c_Nat_OSuc, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.64 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = hAPP( c_Nat_OSuc, X ) }.
% 0.97/1.64 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = hAPP( c_Nat_OSuc, X ) }.
% 0.97/1.64 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.64 tc_Nat_Onat ) ), X ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), !
% 0.97/1.64 X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ),
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.97/1.64 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.64 tc_Nat_Onat ) ), X ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! X =
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ),
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.97/1.64 c_Nat_OSuc, Y ) ), hAPP( c_Nat_OSuc, X ) ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.97/1.64 c_Nat_OSuc, Y ) ), X ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.97/1.64 tc_Nat_Onat, Y ), X ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), hAPP(
% 0.97/1.64 c_Nat_OSuc, X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.97/1.64 tc_Nat_Onat, Y ), X ) ), Y = X }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), !
% 0.97/1.64 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), Z ) ),
% 0.97/1.64 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Nat_OSuc
% 0.97/1.64 , Y ) ), Z ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 0.97/1.64 hAPP( c_Nat_OSuc, Y ) = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.97/1.64 tc_Nat_Onat, hAPP( c_Nat_OSuc, Y ) ), X ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 0.97/1.64 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), hAPP(
% 0.97/1.64 c_Nat_OSuc, X ) ) ) }.
% 0.97/1.64 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), !
% 0.97/1.64 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), hAPP(
% 0.97/1.64 c_Nat_OSuc, X ) ) ), X = Y }.
% 0.97/1.64 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), !
% 0.97/1.64 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), hAPP(
% 0.97/1.64 c_Nat_OSuc, X ) ) ), Y = X }.
% 0.97/1.64 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), ! Y
% 0.97/1.64 = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), hAPP(
% 0.97/1.64 c_Nat_OSuc, X ) ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.97/1.64 c_Nat_OSuc, Y ) ), hAPP( c_Nat_OSuc, X ) ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 0.97/1.64 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Nat_OSuc
% 0.97/1.64 , Y ) ), hAPP( c_Nat_OSuc, X ) ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), hAPP(
% 0.97/1.64 c_Nat_OSuc, X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.97/1.64 tc_Nat_Onat, Y ), X ) ), Y = X }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 0.97/1.64 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), hAPP(
% 0.97/1.64 c_Nat_OSuc, X ) ) ) }.
% 0.97/1.64 { ! Y = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ),
% 0.97/1.64 hAPP( c_Nat_OSuc, X ) ) ) }.
% 0.97/1.64 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 0.97/1.64 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), hAPP(
% 0.97/1.64 c_Nat_OSuc, Y ) ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), hAPP(
% 0.97/1.64 c_Nat_OSuc, Y ) ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.97/1.64 tc_Nat_Onat, Y ), X ) ) }.
% 0.97/1.64 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) = Y, X
% 0.97/1.64 = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.64 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.64 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.64 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X =
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.64 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ),
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = X }.
% 0.97/1.64 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ),
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) = X }.
% 0.97/1.64 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( c_Nat_OSuc
% 0.97/1.64 , Y ) ), X ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y
% 0.97/1.64 ), hAPP( c_Nat_OSuc, X ) ) }.
% 0.97/1.64 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( c_Nat_OSuc
% 0.97/1.64 , Y ) ), X ) = hAPP( c_Nat_OSuc, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.97/1.64 ( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.64 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), hAPP(
% 0.97/1.64 c_Nat_OSuc, X ) ) = hAPP( c_Nat_OSuc, hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), Z ) ), X ) ), hBOOL(
% 0.97/1.64 hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), !
% 0.97/1.64 hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), T ), X ) = hAPP(
% 0.97/1.64 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), Z ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T ), Z ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), !
% 0.97/1.64 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, T ), Z ) ),
% 0.97/1.64 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), T ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 0.97/1.64 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), Z ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 0.97/1.64 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), hAPP( hAPP
% 0.97/1.64 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 0.97/1.64 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), hAPP( hAPP
% 0.97/1.64 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 0.97/1.64 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ), X ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ), Y ) ) }.
% 0.97/1.64 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.97/1.64 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.97/1.64 tc_Nat_Onat ) ) = Y }.
% 0.97/1.64 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( c_Polynomial_OpCons( X ), Z ), Y
% 0.97/1.64 ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.64 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( c_Polynomial_OpCons( X ), Z ), Y
% 0.97/1.64 ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y =
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 0.97/1.64 c_Polynomial_OpCons( X ), Z ), Y ) = c_Groups_Ozero__class_Ozero(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Groups_Ozero( X ), hAPP( hAPP( c_Polynomial_OpCons( X ),
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Groups_Ocomm__monoid__add( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 0.97/1.64 c_Polynomial_OpCons( X ), U ), T ) ), hAPP( hAPP( c_Polynomial_OpCons( X
% 0.97/1.64 ), Z ), Y ) ) = hAPP( hAPP( c_Polynomial_OpCons( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), U ), Z ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), T ), Y ) ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 0.97/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Z
% 0.97/1.64 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP(
% 0.97/1.64 c_Polynomial_Opoly( X, T ), Y ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 0.97/1.64 ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 0.97/1.64 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), T ), Z )
% 0.97/1.64 ), Y ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP(
% 0.97/1.64 c_Polynomial_Opoly( X, T ), Y ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 0.97/1.64 ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 0.97/1.64 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.97/1.64 c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 0.97/1.64 ( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), T ), Z
% 0.97/1.64 ) ), Y ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), hAPP(
% 0.97/1.64 c_Polynomial_Opoly( X, T ), Y ) ), Z ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 0.97/1.64 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) ), hAPP( hAPP(
% 0.97/1.64 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.97/1.64 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.97/1.64 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.97/1.64 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.97/1.64 .
% 0.97/1.64 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.97/1.64 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.97/1.64 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.64 tc_Nat_Onat ) }.
% 0.97/1.64 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.97/1.64 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.97/1.64 , ! Z = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 0.97/1.64 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y )
% 0.97/1.64 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), Y ) )
% 0.97/1.64 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP
% 0.97/1.64 ( c_Power_Opower__class_Opower( X ), Y ), Z ), T = Z }.
% 0.97/1.64 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), Y ) )
% 0.97/1.64 , ! T = Z, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP
% 0.97/1.64 ( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) }.
% 0.97/1.64 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), hAPP( hAPP(
% 0.97/1.64 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.64 hAPP( c_Nat_OSuc, Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.64 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.97/1.64 c_Power_Opower__class_Opower( X ), Z ), hAPP( c_Nat_OSuc, Y ) ) = hAPP(
% 0.97/1.64 hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.64 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) }.
% 0.97/1.64 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.97/1.64 , Z ), hAPP( c_Nat_OSuc, Y ) ) = hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.97/1.64 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.97/1.64 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.97/1.64 , Y ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.97/1.64 c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.64 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.97/1.64 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.64 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.97/1.64 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), hAPP(
% 0.97/1.64 c_Nat_OSuc, X ) ) ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.64 alpha1( X, Y ) }.
% 0.97/1.64 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), hAPP( c_Nat_OSuc, X ) )
% 0.97/1.64 ) }.
% 0.97/1.64 { ! alpha1( X, Y ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 0.97/1.64 , Y ), hAPP( c_Nat_OSuc, X ) ) ) }.
% 0.97/1.64 { ! alpha1( X, Y ), Y = hAPP( c_Nat_OSuc, skol5( Z, Y ) ) }.
% 0.97/1.64 { ! alpha1( X, Y ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 0.97/1.64 , skol5( X, Y ) ), X ) ) }.
% 0.97/1.64 { ! Y = hAPP( c_Nat_OSuc, Z ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless
% 0.97/1.64 ( tc_Nat_Onat, Z ), X ) ), alpha1( X, Y ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), hAPP(
% 0.97/1.64 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), X =
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.64 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), hAPP( c_Nat_OSuc,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), X = hAPP( c_Nat_OSuc
% 0.97/1.64 , skol6( X ) ) }.
% 0.97/1.64 { ! X = hAPP( c_Nat_OSuc, Y ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.97/1.64 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ) }.
% 0.97/1.64 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) = hAPP
% 0.97/1.64 ( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha2( X, Y
% 0.97/1.64 ), alpha20( X, Y ) }.
% 0.97/1.64 { ! alpha2( X, Y ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat )
% 0.97/1.64 , Y ), X ) = hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.97/1.64 ) }.
% 0.97/1.64 { ! alpha20( X, Y ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat )
% 0.97/1.64 , Y ), X ) = hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.97/1.64 ) }.
% 0.97/1.64 { ! alpha20( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.64 { ! alpha20( X, Y ), X = hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero(
% 0.97/1.64 tc_Nat_Onat ) ) }.
% 0.97/1.64 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = hAPP( c_Nat_OSuc
% 0.97/1.64 , c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha20( X, Y ) }.
% 0.97/1.64 { ! alpha2( X, Y ), Y = hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero(
% 0.97/1.64 tc_Nat_Onat ) ) }.
% 0.97/1.64 { ! alpha2( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.64 { ! Y = hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X
% 0.97/1.64 = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha2( X, Y ) }.
% 0.97/1.64 { ! hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = hAPP(
% 0.97/1.64 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ), alpha3( X, Y
% 0.97/1.64 ), alpha21( X, Y ) }.
% 0.97/1.64 { ! alpha3( X, Y ), hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero(
% 0.97/1.64 tc_Nat_Onat ) ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat )
% 0.97/1.64 , Y ), X ) }.
% 0.97/1.64 { ! alpha21( X, Y ), hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero(
% 0.97/1.64 tc_Nat_Onat ) ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat )
% 0.97/1.64 , Y ), X ) }.
% 0.97/1.64 { ! alpha21( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.64 { ! alpha21( X, Y ), X = hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero(
% 0.97/1.64 tc_Nat_Onat ) ) }.
% 0.97/1.64 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = hAPP( c_Nat_OSuc
% 0.97/1.64 , c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha21( X, Y ) }.
% 0.97/1.64 { ! alpha3( X, Y ), Y = hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero(
% 0.97/1.64 tc_Nat_Onat ) ) }.
% 0.97/1.64 { ! alpha3( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.64 { ! Y = hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X
% 0.97/1.64 = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha3( X, Y ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.64 tc_Nat_Onat ) ), Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.97/1.64 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.64 tc_Nat_Onat ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ),
% 0.97/1.64 Y ), X ) ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.64 tc_Nat_Onat ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ),
% 0.97/1.64 Y ), X ) ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), X
% 0.97/1.64 = hAPP( c_Nat_OSuc, hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat
% 0.97/1.64 ), Y ), skol7( X, Y ) ) ) }.
% 0.97/1.64 { ! X = hAPP( c_Nat_OSuc, hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 0.97/1.64 tc_Nat_Onat ), Y ), Z ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.97/1.64 tc_Nat_Onat, Y ), X ) ) }.
% 0.97/1.64 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), hAPP(
% 0.97/1.64 c_Nat_OSuc, hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ),
% 0.97/1.64 Y ) ) ) ) }.
% 0.97/1.64 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), hAPP(
% 0.97/1.64 c_Nat_OSuc, hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ),
% 0.97/1.64 X ) ) ) ) }.
% 0.97/1.64 { c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( c_Nat_OSuc,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), Y ) )
% 0.97/1.64 , hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.64 c_Power_Opower__class_Opower( X ), Y ), Z ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.97/1.64 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), Y ) )
% 0.97/1.64 , hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 0.97/1.64 c_Groups_Oone__class_Oone( X ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.97/1.64 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) ) }.
% 0.97/1.64 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), ! Y =
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.64 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.97/1.64 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.64 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), Y =
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.64 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.97/1.64 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), Y ) )
% 0.97/1.64 , hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 0.97/1.64 c_Groups_Oone__class_Oone( X ) ), hAPP( hAPP(
% 0.97/1.64 c_Power_Opower__class_Opower( X ), Y ), hAPP( c_Nat_OSuc, Z ) ) ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z ), Y ) ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), T ) )
% 0.97/1.64 , hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.64 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.97/1.64 c_Power_Opower__class_Opower( X ), T ), Y ) ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), Y ) )
% 0.97/1.64 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.64 c_Power_Opower__class_Opower( X ), Y ), T ) ), hAPP( hAPP(
% 0.97/1.64 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T ), Z ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__semidom( X ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.64 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), c_Groups_Oone__class_Oone(
% 0.97/1.64 X ) ), c_Groups_Oone__class_Oone( X ) ) ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.64 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) ), ! Z =
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.64 }.
% 0.97/1.64 { ! class_Rings_Olinordered__ring__strict( X ), Z =
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.64 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__ring__strict( X ), Y =
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.64 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__ring( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.97/1.64 ( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP(
% 0.97/1.64 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ),
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.97/1.64 { ! class_Rings_Oidom( t_a ), !
% 0.97/1.64 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( t_a, t_a,
% 0.97/1.64 c_Polynomial_Opoly( t_a, hAPP( hAPP( c_Polynomial_OpCons( t_a ), v_c____
% 0.97/1.64 ), v_cs____ ) ) ) }.
% 0.97/1.64 { hAPP( c_Nat_OSuc, X ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 0.97/1.64 tc_Nat_Onat ), X ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.97/1.64 { hAPP( c_Nat_OSuc, X ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 0.97/1.64 tc_Nat_Onat ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), hAPP(
% 0.97/1.64 c_Nat_OSuc, hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.97/1.64 ) ) ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X = hAPP(
% 0.97/1.64 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.64 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.97/1.64 c_Power_Opower__class_Opower( X ), T ), Y ) ) = hAPP( hAPP(
% 0.97/1.64 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.64 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ozero__class_Ozero(
% 0.97/1.64 tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.64 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 0.97/1.64 c_Power_Opower__class_Opower( X ), Z ), hAPP( c_Nat_OSuc, Y ) ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.97/1.64 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.64 c_Power_Opower__class_Opower( X ), Z ), hAPP( c_Nat_OSuc, Y ) ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.64 c_Power_Opower__class_Opower( X ), Z ), hAPP( c_Nat_OSuc, Y ) ) = hAPP(
% 0.97/1.64 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.97/1.64 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Groups_Ocomm__monoid__add( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ),
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) = Y }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Groups_Ocomm__monoid__add( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), Y ),
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.97/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP
% 0.97/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.97/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 0.97/1.64 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), T ), Z ) ), Y )
% 0.97/1.64 = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ),
% 0.97/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T
% 0.97/1.64 ), Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly
% 0.97/1.64 ( X ) ), Z ), Y ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__idom( X ), Z = Y, hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Z ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), U ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), Y ) ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) = hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), T ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), Z ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), T ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.97/1.64 ( X ), T ), Z ) ), Y ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.97/1.64 ( X ), T ), Z ) ), Y ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), T
% 0.97/1.64 ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.97/1.64 ( X ), T ), Z ) ), Y ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ),
% 0.97/1.64 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), T ), Y ) ), Z ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.97/1.64 ( X ), U ), T ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), Y )
% 0.97/1.64 ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), U ), Z ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.64 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.97/1.64 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.64 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) }.
% 0.97/1.64 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.64 ( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) =
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.97/1.64 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.64 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.64 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) =
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.97/1.64 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.64 { ! class_Rings_Oring__no__zero__divisors( X ), ! hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.64 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.64 { ! class_Rings_Oring__no__zero__divisors( X ), ! Z =
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.64 { ! class_Rings_Oring__no__zero__divisors( X ), ! Y =
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.64 { ! class_Rings_Ono__zero__divisors( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.64 X ), Z = c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) =
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.64 { ! class_Rings_Ono__zero__divisors( X ), ! hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.64 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), c_Groups_Ozero__class_Ozero( X ) ), Y )
% 0.97/1.64 = Y }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), Y ), c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.64 = Y }.
% 0.97/1.64 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.64 ( X ), ! Z = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), Y ), Y =
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.64 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.64 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z = hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) }.
% 0.97/1.64 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Oone__class_Oone( X ) =
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.64 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.97/1.64 c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.64 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.64 ( X ), U = T, Z = Y, ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP
% 0.97/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) = hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), U ), Y ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 0.97/1.64 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.64 ( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) = hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), U ), Y ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), ! U = T }.
% 0.97/1.64 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.64 ( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) = hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), U ), Y ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), ! Z = Y }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ), Z ) }.
% 0.97/1.64 { ! class_Rings_Osemiring( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X
% 0.97/1.64 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP(
% 0.97/1.64 hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ), Y ) ) = hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), U ), Z ) ), T ) ), Y ) }.
% 0.97/1.64 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.64 ( X ), ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), U ), Y ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ), U = Z, T = Y }.
% 0.97/1.64 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.64 ( X ), ! U = Z, hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP
% 0.97/1.64 ( c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), U ), Y ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.97/1.64 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.64 ( X ), ! T = Y, hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP
% 0.97/1.64 ( c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), U ), Y ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.97/1.64 = Y }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.97/1.64 = Y }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.64 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.64 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.97/1.64 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.97/1.64 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) ), X =
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.64 tc_Nat_Onat ) ), Y ) ) }.
% 0.97/1.64 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.64 tc_Nat_Onat ) ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.97/1.64 , Y ), X ) ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.64 tc_Nat_Onat ) ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.97/1.64 , Y ), X ) ) ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.64 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.97/1.64 tc_Nat_Onat ) ) = Y }.
% 0.97/1.64 { ! class_Rings_Olinordered__ring( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), alpha4( X, Y, Z, T ),
% 0.97/1.64 alpha22( X, Y, Z, T ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha4( X, Y, Z, T ),
% 0.97/1.64 hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha22( X, Y, Z, T ),
% 0.97/1.64 hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 0.97/1.64 { ! alpha22( X, Y, Z, T ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Z
% 0.97/1.64 ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.97/1.64 { ! alpha22( X, Y, Z, T ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Y
% 0.97/1.64 ), T ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Z ),
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) ) ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, Y ), T ) ), alpha22( X, Y, Z, T ) }.
% 0.97/1.64 { ! alpha4( X, Y, Z, T ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) ), Z ) ) }.
% 0.97/1.64 { ! alpha4( X, Y, Z, T ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, T
% 0.97/1.64 ), Y ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, T ), Y ) ), alpha4( X, Y, Z, T ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ), alpha5( X, Y, Z, T ),
% 0.97/1.64 alpha23( X, Y, Z, T ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha5( X, Y, Z, T ),
% 0.97/1.64 hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha23( X, Y, Z, T ),
% 0.97/1.64 hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 0.97/1.64 { ! alpha23( X, Y, Z, T ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, T
% 0.97/1.64 ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.97/1.64 { ! alpha23( X, Y, Z, T ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Y
% 0.97/1.64 ), Z ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, T ),
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) ) ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, Y ), Z ) ), alpha23( X, Y, Z, T ) }.
% 0.97/1.64 { ! alpha5( X, Y, Z, T ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) ), T ) ) }.
% 0.97/1.64 { ! alpha5( X, Y, Z, T ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Z
% 0.97/1.64 ), Y ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) ), T ) ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), alpha5( X, Y, Z, T ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 0.97/1.64 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, T ), Z ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 0.97/1.64 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, T ), Z ) ), hBOOL(
% 0.97/1.64 hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 0.97/1.64 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 0.97/1.64 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Z ),
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 0.97/1.64 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Z ),
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ), ! hBOOL(
% 0.97/1.64 hAPP( c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.64 ), Z ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) ), Y ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ), ! hBOOL(
% 0.97/1.64 hAPP( c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.64 ), Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) ), Z ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.64 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, Z ), T ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.64 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Z ), T ) ), hBOOL(
% 0.97/1.64 hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.64 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.64 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Z ),
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), T )
% 0.97/1.64 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), T )
% 0.97/1.64 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__comm__semiring__strict( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), T )
% 0.97/1.64 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, T ), c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.64 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, T ), c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.64 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 0.97/1.64 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, T ), Z ) ), hBOOL(
% 0.97/1.64 hAPP( c_Orderings_Oord__class_Oless( X, T ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__ring__strict( X ), ! hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.97/1.64 .
% 0.97/1.64 { ! class_Rings_Olinordered__ring__strict( X ), ! hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 0.97/1.64 .
% 0.97/1.64 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.64 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.64 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.64 ( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! W = U, T = Z, ! hAPP( hAPP
% 0.97/1.64 ( c_Groups_Oplus__class_Oplus( X ), W ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) = hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), U ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ),
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__semidom( X ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.64 c_Groups_Oone__class_Oone( X ) ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), Y ) )
% 0.97/1.64 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 0.97/1.64 c_Groups_Oone__class_Oone( X ) ), Z ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), hAPP
% 0.97/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__semidom( X ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, Y ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), Y ), c_Groups_Oone__class_Oone( X ) ) )
% 0.97/1.64 ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), Y ), Y ) = hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), c_Groups_Oone__class_Oone( X ) ),
% 0.97/1.64 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), Z ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), Y ), c_Groups_Oone__class_Oone( X ) ) )
% 0.97/1.64 , Z ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) = hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), Z ), c_Groups_Oone__class_Oone( X ) ) )
% 0.97/1.64 , Y ) }.
% 0.97/1.64 { ! class_Rings_Oidom( t_a ),
% 0.97/1.64 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( t_a, t_a,
% 0.97/1.64 c_Polynomial_Opoly( t_a, v_cs____ ) ), ! skol8 =
% 0.97/1.64 c_Groups_Ozero__class_Ozero( t_a ) }.
% 0.97/1.64 { ! class_Rings_Oidom( t_a ),
% 0.97/1.64 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( t_a, t_a,
% 0.97/1.64 c_Polynomial_Opoly( t_a, v_cs____ ) ), alpha48( skol8 ) }.
% 0.97/1.64 { ! alpha48( X ), ! skol9( Y ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.97/1.64 }.
% 0.97/1.64 { ! alpha48( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ),
% 0.97/1.64 hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ),
% 0.97/1.64 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( t_a, skol31( X ) ) ),
% 0.97/1.64 skol9( X ) ) ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) =
% 0.97/1.64 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( t_a, v_cs____ ) }.
% 0.97/1.64 { ! alpha48( X ), hAPP( c_Polynomial_Opoly( t_a, v_cs____ ), Y ) = hAPP(
% 0.97/1.64 hAPP( c_Groups_Oplus__class_Oplus( t_a ), hAPP( c_Polynomial_Opoly( t_a,
% 0.97/1.64 v_cs____ ), c_Groups_Ozero__class_Ozero( t_a ) ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( t_a ), hAPP( hAPP(
% 0.97/1.64 c_Power_Opower__class_Opower( t_a ), Y ), skol9( X ) ) ), hAPP(
% 0.97/1.64 c_Polynomial_Opoly( t_a, hAPP( hAPP( c_Polynomial_OpCons( t_a ), X ),
% 0.97/1.64 skol31( X ) ) ), Y ) ) ) }.
% 0.97/1.64 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ),
% 0.97/1.64 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( t_a, Z ) ), Y ) ),
% 0.97/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) =
% 0.97/1.64 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( t_a, v_cs____ ), !
% 0.97/1.64 hAPP( c_Polynomial_Opoly( t_a, v_cs____ ), skol36( X, Y, Z ) ) = hAPP(
% 0.97/1.64 hAPP( c_Groups_Oplus__class_Oplus( t_a ), hAPP( c_Polynomial_Opoly( t_a,
% 0.97/1.64 v_cs____ ), c_Groups_Ozero__class_Ozero( t_a ) ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( t_a ), hAPP( hAPP(
% 0.97/1.64 c_Power_Opower__class_Opower( t_a ), skol36( X, Y, Z ) ), Y ) ), hAPP(
% 0.97/1.64 c_Polynomial_Opoly( t_a, hAPP( hAPP( c_Polynomial_OpCons( t_a ), X ), Z )
% 0.97/1.64 ), skol36( X, Y, Z ) ) ) ), alpha48( X ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) = hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z = Y }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! Z = Y, hAPP( hAPP
% 0.97/1.64 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) = hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z ), Y ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z ), Y ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X, hAPP(
% 0.97/1.64 hAPP( c_Polynomial_OpCons( X ), T ), Z ), Y ) = hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 0.97/1.64 c_Polynomial_OpCons( X ), T ), c_Groups_Ozero__class_Ozero(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.64 ( tc_Polynomial_Opoly( X ) ), Y ), c_Polynomial_Opcompose( X, Z, Y ) ) )
% 0.97/1.64 }.
% 0.97/1.64 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.64 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Y ) ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 0.97/1.64 ) }.
% 0.97/1.64 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 0.97/1.64 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), Y ), Y ) ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.97/1.64 ( X ), Y ), Y ) ), c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.64 ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.64 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), Y ), Y ) ), c_Groups_Ozero__class_Ozero
% 0.97/1.64 ( X ) ) ) }.
% 0.97/1.64 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.97/1.64 ( X ), Y ), Y ) ), c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.64 ) }.
% 0.97/1.64 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.64 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), Y ), Y ) ), c_Groups_Ozero__class_Ozero
% 0.97/1.64 ( X ) ) ) }.
% 0.97/1.64 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 0.97/1.64 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.64 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.97/1.64 c_Polynomial_Opcompose( X, T, Z ) ), Y ) = hAPP( c_Polynomial_Opoly( X, T
% 0.97/1.64 ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.97/1.64 { ! class_Groups_Ozero( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y, Y =
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.64 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) = Y }.
% 0.97/1.64 { ! class_Groups_Oab__semigroup__mult( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.64 { ! class_Groups_Ocancel__semigroup__add( X ), ! hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), Z ), T ) = hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), Y ), T ), Z = Y }.
% 0.97/1.64 { ! class_Groups_Ocancel__ab__semigroup__add( X ), ! hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), T ), Z ) = hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), T ), Y ), Z = Y }.
% 0.97/1.64 { ! class_Groups_Ocancel__semigroup__add( X ), ! hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), T ), Z ) = hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), T ), Y ), Z = Y }.
% 0.97/1.64 { ! class_Groups_Ocancel__semigroup__add( X ), ! hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), T ), Z ) = hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), Y ), Z ), T = Y }.
% 0.97/1.64 { ! class_Groups_Ocancel__semigroup__add( X ), ! T = Y, hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), T ), Z ) = hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) }.
% 0.97/1.64 { ! class_Groups_Ocancel__semigroup__add( X ), ! hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), T ), Z ) = hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), T ), Y ), Z = Y }.
% 0.97/1.64 { ! class_Groups_Ocancel__semigroup__add( X ), ! Z = Y, hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), T ), Z ) = hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), T ), Y ) }.
% 0.97/1.64 { ! class_Groups_Oab__semigroup__add( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.97/1.64 ( X ), T ), Z ) ), Y ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), T
% 0.97/1.64 ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) }.
% 0.97/1.64 { ! class_Groups_Oone( X ), ! c_Groups_Oone__class_Oone( X ) = Y, Y =
% 0.97/1.64 c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.64 { ! class_Groups_Oone( X ), ! Y = c_Groups_Oone__class_Oone( X ),
% 0.97/1.64 c_Groups_Oone__class_Oone( X ) = Y }.
% 0.97/1.64 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), hAPP( hAPP
% 0.97/1.64 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.64 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.64 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ) }.
% 0.97/1.64 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.64 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 0.97/1.64 ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.64 { ! class_Groups_Olinordered__ab__group__add( X ), ! hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), Y ), Y ) = c_Groups_Ozero__class_Ozero
% 0.97/1.64 ( X ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.64 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.97/1.64 ( X ), Y ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.64 { ! class_Groups_Ocomm__monoid__add( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), Y ), c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.64 = Y }.
% 0.97/1.64 { ! class_Groups_Omonoid__add( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.97/1.64 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.97/1.64 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) = hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), Y ), Y ), Y =
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.64 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero( X ) = hAPP
% 0.97/1.64 ( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Y ) }.
% 0.97/1.64 { ! class_Groups_Ocomm__monoid__add( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), c_Groups_Ozero__class_Ozero( X ) ), Y )
% 0.97/1.64 = Y }.
% 0.97/1.64 { ! class_Groups_Omonoid__add( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.97/1.64 ( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) = Y }.
% 0.97/1.64 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 0.97/1.64 ( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 0.97/1.64 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 0.97/1.64 ( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), Z ), T ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), Y ), T ) ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 0.97/1.64 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, U ), T ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.97/1.64 ( X ), Z ), U ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), T )
% 0.97/1.64 ) ) }.
% 0.97/1.64 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.97/1.64 ( X ), T ), Z ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), T ), Y )
% 0.97/1.64 ) ) }.
% 0.97/1.64 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.97/1.64 ( X ), Z ), T ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), T )
% 0.97/1.64 ) ) }.
% 0.97/1.64 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 0.97/1.64 ( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 0.97/1.64 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 0.97/1.64 ( c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.97/1.64 ( X ), T ), Z ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), T ), Y )
% 0.97/1.64 ) ) }.
% 0.97/1.64 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 0.97/1.64 ( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, T ), Y ) ) }.
% 0.97/1.64 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 0.97/1.64 ( c_Orderings_Oord__class_Oless( X, T ), Y ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.97/1.64 ( X ), T ), Z ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Z )
% 0.97/1.64 ) ) }.
% 0.97/1.64 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.97/1.64 = Y }.
% 0.97/1.64 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.97/1.64 = Y }.
% 0.97/1.64 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.97/1.64 = Y }.
% 0.97/1.64 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.97/1.64 = Y }.
% 0.97/1.64 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.97/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Z =
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.97/1.64 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.97/1.64 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.97/1.64 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.97/1.64 .
% 0.97/1.64 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), T ), Z ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ) ), X ) ) = hAPP(
% 0.97/1.64 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), T ), Y ) ), Z ) ), X ) }.
% 0.97/1.64 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.64 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Z ),
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.97/1.64 ( X ), Y ), Z ) ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X, Z, Y )
% 0.97/1.64 = c_Polynomial_Opoly__rec( tc_Polynomial_Opoly( X ), X,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 0.97/1.64 c_COMBB( tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ) ),
% 0.97/1.64 tc_fun( tc_Polynomial_Opoly( X ), tc_fun( tc_Polynomial_Opoly( X ),
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) ), X ), c_COMBK( tc_fun( tc_Polynomial_Opoly(
% 0.97/1.64 X ), tc_Polynomial_Opoly( X ) ), tc_Polynomial_Opoly( X ) ) ), hAPP(
% 0.97/1.64 c_COMBC( X, tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ) )
% 0.97/1.64 , tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ) ), hAPP(
% 0.97/1.64 hAPP( c_COMBB( tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X )
% 0.97/1.64 ), tc_fun( tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ) )
% 0.97/1.64 , tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ) ) ), X ),
% 0.97/1.64 c_COMBB( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ),
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) ), hAPP( hAPP( c_COMBB( tc_Polynomial_Opoly( X
% 0.97/1.64 ), tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ) ), X ),
% 0.97/1.64 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ) ), hAPP( c_COMBC
% 0.97/1.64 ( X, tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ),
% 0.97/1.64 c_Polynomial_OpCons( X ) ), c_Groups_Ozero__class_Ozero(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) ) ) ) ), hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ), Y ) ) ), Z ) }.
% 0.97/1.64 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ), ! c_Polynomial_Oorder( X, Y, Z ) =
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.64 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.64 { ! class_Rings_Oidom( X ), c_Polynomial_Oorder( X, Y, Z ) =
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( c_Polynomial_Opoly( X,
% 0.97/1.64 Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.64 { ! class_Power_Opower( X ), c_Power_Opower__class_Opower( X ) =
% 0.97/1.64 c_Power_Opower_Opower( X, c_Groups_Oone__class_Oone( X ),
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ) ) }.
% 0.97/1.64 { ! class_Rings_Oidom( t_a ), ! skol10 = c_Groups_Ozero__class_Ozero( t_a )
% 0.97/1.64 }.
% 0.97/1.64 { ! class_Rings_Oidom( t_a ), hAPP( c_Nat_OSuc, hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ),
% 0.97/1.64 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( t_a, skol37 ) ),
% 0.97/1.64 skol32 ) ) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( t_a,
% 0.97/1.64 v_cs____ ) }.
% 0.97/1.64 { ! class_Rings_Oidom( t_a ), hAPP( c_Polynomial_Opoly( t_a, v_cs____ ), X
% 0.97/1.64 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( t_a ), hAPP( hAPP(
% 0.97/1.64 c_Power_Opower__class_Opower( t_a ), X ), skol32 ) ), hAPP(
% 0.97/1.64 c_Polynomial_Opoly( t_a, hAPP( hAPP( c_Polynomial_OpCons( t_a ), skol10 )
% 0.97/1.64 , skol37 ) ), X ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 0.97/1.64 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), hAPP( hAPP
% 0.97/1.64 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 0.97/1.64 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), hAPP( hAPP
% 0.97/1.64 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, hAPP
% 0.97/1.64 ( hAPP( c_Polynomial_OpCons( X ), Z ), Y ) ), c_Polynomial_Opos__poly( X
% 0.97/1.64 , Y ), alpha6( X, Y, Z ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.97/1.64 c_Polynomial_Opos__poly( X, hAPP( hAPP( c_Polynomial_OpCons( X ), Z ), Y
% 0.97/1.64 ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__idom( X ), ! alpha6( X, Y, Z ),
% 0.97/1.64 c_Polynomial_Opos__poly( X, hAPP( hAPP( c_Polynomial_OpCons( X ), Z ), Y
% 0.97/1.64 ) ) }.
% 0.97/1.64 { ! alpha6( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly
% 0.97/1.64 ( X ) ) }.
% 0.97/1.64 { ! alpha6( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) ), Z ) ) }.
% 0.97/1.64 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), ! hBOOL(
% 0.97/1.64 hAPP( c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.64 ), Z ) ), alpha6( X, Y, Z ) }.
% 0.97/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.97/1.64 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) = X }.
% 0.97/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 0.97/1.64 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) = X }.
% 0.97/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) = hAPP
% 0.97/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) }.
% 0.97/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP
% 0.97/1.64 ( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), X ) ) = hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.97/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP(
% 0.97/1.64 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.97/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 0.97/1.64 ( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 0.97/1.64 c_Groups_Oone__class_Oone( tc_Int_Oint ), X = c_Groups_Oone__class_Oone(
% 0.97/1.64 tc_Int_Oint ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 0.97/1.64 c_Groups_Oone__class_Oone( tc_Int_Oint ), Y = c_Groups_Oone__class_Oone(
% 0.97/1.64 tc_Int_Oint ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! X =
% 0.97/1.64 c_Groups_Oone__class_Oone( tc_Int_Oint ), ! Y = c_Groups_Oone__class_Oone
% 0.97/1.64 ( tc_Int_Oint ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 0.97/1.64 , X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ), !
% 0.97/1.64 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Z ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.97/1.64 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X, hAPP( hAPP
% 0.97/1.64 ( c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.97/1.64 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X, hAPP( hAPP
% 0.97/1.64 ( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) }
% 0.97/1.64 .
% 0.97/1.64 { hAPP( hAPP( c_Power_Opower_Opower( T, Z, Y ), X ),
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = Z }.
% 0.97/1.64 { hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), hAPP( c_Nat_OSuc, X )
% 0.97/1.64 ) = hAPP( hAPP( Z, Y ), hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y
% 0.97/1.64 ), X ) ) }.
% 0.97/1.64 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( T, X, Y,
% 0.97/1.64 Z, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.97/1.64 { ! class_Groups_Ozero( X ), c_Polynomial_Opoly__rec( W, X, U, T, hAPP(
% 0.97/1.64 hAPP( c_Polynomial_OpCons( X ), Z ), Y ) ) = hAPP( hAPP( hAPP( T, Z ), Y
% 0.97/1.64 ), c_If( W, c_fequal( Y, c_Groups_Ozero__class_Ozero(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) ), U, c_Polynomial_Opoly__rec( W, X, U, T, Y )
% 0.97/1.64 ) ) }.
% 0.97/1.64 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( W, X, Y,
% 0.97/1.64 Z, hAPP( hAPP( c_Polynomial_OpCons( X ), U ), T ) ) = hAPP( hAPP( hAPP( Z
% 0.97/1.64 , U ), T ), c_Polynomial_Opoly__rec( W, X, Y, Z, T ) ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y ) =
% 0.97/1.64 c_Polynomial_Opoly__rec( tc_Polynomial_Opoly( X ), X,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 0.97/1.64 c_COMBB( tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ) ),
% 0.97/1.64 tc_fun( tc_Polynomial_Opoly( X ), tc_fun( tc_Polynomial_Opoly( X ),
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) ), X ), c_COMBK( tc_fun( tc_Polynomial_Opoly(
% 0.97/1.64 X ), tc_Polynomial_Opoly( X ) ), tc_Polynomial_Opoly( X ) ) ), hAPP(
% 0.97/1.64 c_COMBC( X, tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ) )
% 0.97/1.64 , tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ) ), hAPP(
% 0.97/1.64 hAPP( c_COMBB( tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X )
% 0.97/1.64 ), tc_fun( tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ) )
% 0.97/1.64 , tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ) ) ), X ),
% 0.97/1.64 c_COMBB( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ),
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) ), hAPP( hAPP( c_COMBB( tc_Polynomial_Opoly( X
% 0.97/1.64 ), tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ) ), X ),
% 0.97/1.64 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ) ), hAPP( c_COMBC
% 0.97/1.64 ( X, tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ),
% 0.97/1.64 c_Polynomial_Osmult( X ) ), Y ) ) ) ), hAPP( c_Polynomial_OpCons( X ),
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) ) ) ), Z ) }.
% 0.97/1.64 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.64 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.64 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.64 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__ring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP(
% 0.97/1.64 hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.97/1.64 c_Polynomial_Omonom( X, c_Groups_Oone__class_Oone( X ), T ) ), Z ) ), Y )
% 0.97/1.64 = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.64 c_Power_Opower__class_Opower( X ), Y ), T ) ), hAPP( c_Polynomial_Opoly(
% 0.97/1.64 X, Z ), Y ) ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP( c_Polynomial_Osmult( X
% 0.97/1.64 ), T ), c_Polynomial_Omonom( X, Z, Y ) ) = c_Polynomial_Omonom( X, hAPP
% 0.97/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 0.97/1.64 { ! class_Groups_Ozero( X ), ! c_Polynomial_Omonom( X, T, Z ) =
% 0.97/1.64 c_Polynomial_Omonom( X, Y, Z ), T = Y }.
% 0.97/1.64 { ! class_Groups_Ozero( X ), ! T = Y, c_Polynomial_Omonom( X, T, Z ) =
% 0.97/1.64 c_Polynomial_Omonom( X, Y, Z ) }.
% 0.97/1.64 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ), Y =
% 0.97/1.64 X, hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, X ), Y ) ) }
% 0.97/1.64 .
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ),
% 0.97/1.64 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), Z ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ), Z ) ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 0.97/1.64 tc_Int_Oint ) ), X ) ), X ) ), c_Groups_Ozero__class_Ozero( tc_Int_Oint )
% 0.97/1.64 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, X ),
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, X ),
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 0.97/1.64 tc_Int_Oint ) ), X ) ), X ) ), c_Groups_Ozero__class_Ozero( tc_Int_Oint )
% 0.97/1.64 ) ) }.
% 0.97/1.64 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 0.97/1.64 ( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), X ) ) }.
% 0.97/1.64 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), X ) ) = hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), X ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), hAPP(
% 0.97/1.64 hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ),
% 0.97/1.64 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ), Y = X }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ),
% 0.97/1.64 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), hAPP( hAPP
% 0.97/1.64 ( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ),
% 0.97/1.64 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ) ) }.
% 0.97/1.64 { ! Y = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ),
% 0.97/1.64 hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ),
% 0.97/1.64 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ) ) }.
% 0.97/1.64 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), X ) = hAPP(
% 0.97/1.64 hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ), Y ) }.
% 0.97/1.64 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ),
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) = X }.
% 0.97/1.64 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ),
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) = X }.
% 0.97/1.64 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Groups_Oone__class_Oone(
% 0.97/1.64 tc_Int_Oint ) ) ) }.
% 0.97/1.64 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 0.97/1.64 tc_Int_Oint ) ), X ) ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint )
% 0.97/1.64 }.
% 0.97/1.64 { ! c_Groups_Ozero__class_Ozero( tc_Int_Oint ) = c_Groups_Oone__class_Oone
% 0.97/1.64 ( tc_Int_Oint ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP( c_Polynomial_Osmult( X
% 0.97/1.64 ), T ), hAPP( hAPP( c_Polynomial_Osmult( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.64 c_Polynomial_Osmult( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.97/1.64 , T ), Z ) ), Y ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP( c_Polynomial_Osmult( X
% 0.97/1.64 ), c_Groups_Oone__class_Oone( X ) ), Y ) = Y }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP( c_Polynomial_Osmult( X
% 0.97/1.64 ), Y ), c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP( c_Polynomial_Osmult( X
% 0.97/1.64 ), T ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X
% 0.97/1.64 ) ), Z ), Y ) ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Polynomial_Osmult( X ), T ), Z
% 0.97/1.64 ) ), hAPP( hAPP( c_Polynomial_Osmult( X ), T ), Y ) ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 0.97/1.64 c_Polynomial_Osmult( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.64 c_Polynomial_Osmult( X ), T ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.64 ( tc_Polynomial_Opoly( X ) ), Z ), Y ) ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), hAPP(
% 0.97/1.64 hAPP( c_Polynomial_Osmult( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.64 c_Polynomial_Osmult( X ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.64 ( tc_Polynomial_Opoly( X ) ), T ), Y ) ) }.
% 0.97/1.64 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Polynomial_Osmult( X ), Z ), Y
% 0.97/1.64 ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ), hAPP(
% 0.97/1.64 hAPP( c_Polynomial_Osmult( X ), Z ), Y ) = c_Groups_Ozero__class_Ozero(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Rings_Oidom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Polynomial_Osmult( X ), Z ), Y
% 0.97/1.64 ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP( c_Polynomial_Osmult( X
% 0.97/1.64 ), c_Groups_Ozero__class_Ozero( X ) ), Y ) = c_Groups_Ozero__class_Ozero
% 0.97/1.64 ( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP( c_Polynomial_Osmult( X
% 0.97/1.64 ), T ), hAPP( hAPP( c_Polynomial_OpCons( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.64 c_Polynomial_OpCons( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.97/1.64 , T ), Z ) ), hAPP( hAPP( c_Polynomial_Osmult( X ), T ), Y ) ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 0.97/1.64 ( hAPP( c_Polynomial_Osmult( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( c_Polynomial_Opoly( X, Z )
% 0.97/1.64 , Y ) ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__0( X ), ! hAPP( hAPP( c_Polynomial_Osmult
% 0.97/1.64 ( X ), T ), Y ) = hAPP( hAPP( c_Polynomial_OpCons( X ), Z ), Y ), Y =
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP( c_Polynomial_Osmult( X
% 0.97/1.64 ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), Y ) = hAPP
% 0.97/1.64 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), hAPP(
% 0.97/1.64 hAPP( c_Polynomial_Osmult( X ), T ), Y ) ), hAPP( hAPP(
% 0.97/1.64 c_Polynomial_Osmult( X ), Z ), Y ) ) }.
% 0.97/1.64 { ! class_Groups_Ozero( X ), ! c_Polynomial_Omonom( X, Z, Y ) =
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.64 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.64 c_Polynomial_Omonom( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Groups_Ocomm__monoid__add( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ),
% 0.97/1.64 c_Polynomial_Omonom( X, T, Z ) ), c_Polynomial_Omonom( X, Y, Z ) ) =
% 0.97/1.64 c_Polynomial_Omonom( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), T )
% 0.97/1.64 , Y ), Z ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__0( X ), ! hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 0.97/1.64 c_Polynomial_Osmult( X ), T ), Y ) ), hAPP( hAPP( c_Polynomial_OpCons( X
% 0.97/1.64 ), Z ), Y ) ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) )
% 0.97/1.64 , Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X, Z, hAPP( c_Nat_OSuc, Y
% 0.97/1.64 ) ) = hAPP( hAPP( c_Polynomial_OpCons( X ), c_Groups_Ozero__class_Ozero
% 0.97/1.64 ( X ) ), c_Polynomial_Omonom( X, Z, Y ) ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 0.97/1.64 c_Polynomial_Omonom( X, T, Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.97/1.64 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.97/1.64 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X, Y,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = hAPP( hAPP(
% 0.97/1.64 c_Polynomial_OpCons( X ), Y ), c_Groups_Ozero__class_Ozero(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.97/1.64 c_Polynomial_Omonom( X, U, T ) ), c_Polynomial_Omonom( X, Z, Y ) ) =
% 0.97/1.64 c_Polynomial_Omonom( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U
% 0.97/1.64 ), Z ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), T ), Y )
% 0.97/1.64 ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 0.97/1.64 c_Polynomial_OpCons( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 0.97/1.64 c_Polynomial_Osmult( X ), T ), Y ) ), hAPP( hAPP( c_Polynomial_OpCons( X
% 0.97/1.64 ), c_Groups_Ozero__class_Ozero( X ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y ) ) ) }
% 0.97/1.64 .
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), hAPP(
% 0.97/1.64 hAPP( c_Polynomial_OpCons( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 0.97/1.64 c_Polynomial_Osmult( X ), Z ), T ) ), hAPP( hAPP( c_Polynomial_OpCons( X
% 0.97/1.64 ), c_Groups_Ozero__class_Ozero( X ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ) ) ) }
% 0.97/1.64 .
% 0.97/1.64 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.97/1.64 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.64 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.97/1.64 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.64 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.97/1.64 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.64 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.97/1.64 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__0( X ),
% 0.97/1.64 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) =
% 0.97/1.64 c_Polynomial_Opoly__rec( tc_Polynomial_Opoly( X ), X,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 0.97/1.64 c_COMBB( tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ) ),
% 0.97/1.64 tc_fun( tc_Polynomial_Opoly( X ), tc_fun( tc_Polynomial_Opoly( X ),
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) ), X ), c_COMBK( tc_fun( tc_Polynomial_Opoly(
% 0.97/1.64 X ), tc_Polynomial_Opoly( X ) ), tc_Polynomial_Opoly( X ) ) ), hAPP( hAPP
% 0.97/1.64 ( c_COMBB( tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ) ),
% 0.97/1.64 tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ) ), X ), hAPP(
% 0.97/1.64 c_COMBS( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ),
% 0.97/1.64 tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_COMBB( tc_Polynomial_Opoly( X )
% 0.97/1.64 , tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ) ),
% 0.97/1.64 tc_Polynomial_Opoly( X ) ), c_Groups_Oplus__class_Oplus(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) ), hAPP( c_Polynomial_Osmult( X ), Y ) ) ) ),
% 0.97/1.64 c_Polynomial_OpCons( X ) ) ), Z ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__0( X ), ! hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), U ), hAPP( hAPP
% 0.97/1.64 ( c_Polynomial_Osmult( X ), T ), Z ) ) = hAPP( hAPP( c_Polynomial_OpCons
% 0.97/1.64 ( X ), Y ), Z ), Y = hAPP( c_Polynomial_Opoly( X, U ), T ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__0( X ), ! hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), U ), hAPP( hAPP
% 0.97/1.64 ( c_Polynomial_Osmult( X ), T ), Z ) ) = hAPP( hAPP( c_Polynomial_OpCons
% 0.97/1.64 ( X ), Y ), Z ), Z = c_Polynomial_Osynthetic__div( X, U, T ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), Z ), hAPP( hAPP
% 0.97/1.64 ( c_Polynomial_Osmult( X ), Y ), c_Polynomial_Osynthetic__div( X, Z, Y )
% 0.97/1.64 ) ) = hAPP( hAPP( c_Polynomial_OpCons( X ), hAPP( c_Polynomial_Opoly( X
% 0.97/1.64 , Z ), Y ) ), c_Polynomial_Osynthetic__div( X, Z, Y ) ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__0( X ),
% 0.97/1.64 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, hAPP( hAPP(
% 0.97/1.64 c_Polynomial_OpCons( X ), T ), Z ), Y ) = hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 0.97/1.64 c_Polynomial_Osmult( X ), Y ),
% 0.97/1.64 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) ) ),
% 0.97/1.64 hAPP( hAPP( c_Polynomial_OpCons( X ), T ),
% 0.97/1.64 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) ) ) }
% 0.97/1.64 .
% 0.97/1.64 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.64 , Z ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), T ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.64 c_Power_Opower__class_Opower( X ), Z ), T ) ), hAPP( hAPP(
% 0.97/1.64 c_Power_Opower__class_Opower( X ), Y ), T ) ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__semiring__1__strict( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, T ), Y ) ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.64 , U ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) ), W ) ), ! hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), U ), W ) = c_Groups_Oone__class_Oone( X
% 0.97/1.64 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), W ), T ) ) ), Y ) ) }.
% 0.97/1.64 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), Y ) ), ! hBOOL( hAPP
% 0.97/1.64 ( c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ) )
% 0.97/1.64 , T ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.64 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.97/1.64 c_Power_Opower__class_Opower( X ), T ), Y ) ) ) }.
% 0.97/1.64 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 0.97/1.64 ( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 0.97/1.64 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 0.97/1.64 ( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), Z ), T ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), Y ), T ) ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 0.97/1.64 { ! class_Groups_Oordered__ab__semigroup__add( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, U ), T ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), Z ), U ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), Y ), T ) ) ) }.
% 0.97/1.64 { ! class_Groups_Oordered__ab__semigroup__add( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ) ) }.
% 0.97/1.64 { ! class_Groups_Oordered__ab__semigroup__add( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), Z ), T ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), Y ), T ) ) ) }.
% 0.97/1.64 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 0.97/1.64 ( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 0.97/1.64 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 0.97/1.64 ( c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ) ) }.
% 0.97/1.64 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 0.97/1.64 ( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, T ), Y ) ) }.
% 0.97/1.64 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 0.97/1.64 ( c_Orderings_Oord__class_Oless__eq( X, T ), Y ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) ) }.
% 0.97/1.64 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ),
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X =
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.64 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ),
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 0.97/1.64 c_Nat_OSuc, X ) ), X ) ) }.
% 0.97/1.64 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ),
% 0.97/1.64 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 0.97/1.64 c_Nat_OSuc, X ) ), Y ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 0.97/1.64 c_Nat_OSuc, X ) ), Y ) ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), hAPP
% 0.97/1.64 ( c_Nat_OSuc, X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.97/1.64 tc_Nat_Onat, Y ), X ) ), Y = hAPP( c_Nat_OSuc, X ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.97/1.64 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), hAPP
% 0.97/1.64 ( c_Nat_OSuc, X ) ) ) }.
% 0.97/1.64 { ! Y = hAPP( c_Nat_OSuc, X ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), hAPP( c_Nat_OSuc, X
% 0.97/1.64 ) ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 0.97/1.64 c_Nat_OSuc, Y ) ), hAPP( c_Nat_OSuc, X ) ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.97/1.64 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 0.97/1.64 c_Nat_OSuc, Y ) ), hAPP( c_Nat_OSuc, X ) ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.97/1.64 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), hAPP
% 0.97/1.64 ( c_Nat_OSuc, X ) ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), hAPP
% 0.97/1.64 ( c_Nat_OSuc, X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.97/1.64 tc_Nat_Onat, Y ), X ) ), Y = hAPP( c_Nat_OSuc, X ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 0.97/1.64 c_Nat_OSuc, Y ) ), X ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 0.97/1.64 ( tc_Nat_Onat, Y ), X ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 0.97/1.64 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }
% 0.97/1.64 .
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 0.97/1.64 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }
% 0.97/1.64 .
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), !
% 0.97/1.64 Y = X }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.97/1.64 , Y = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X
% 0.97/1.64 ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.97/1.64 , hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), Y
% 0.97/1.64 = X }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 0.97/1.64 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }
% 0.97/1.64 .
% 0.97/1.64 { ! Y = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y )
% 0.97/1.64 , X ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 0.97/1.64 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }
% 0.97/1.64 .
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.97/1.64 , Y = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X
% 0.97/1.64 ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 0.97/1.64 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }
% 0.97/1.64 .
% 0.97/1.64 { ! Y = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y )
% 0.97/1.64 , X ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.97/1.64 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), hAPP
% 0.97/1.64 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.97/1.64 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), hAPP
% 0.97/1.64 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ) ) }.
% 0.97/1.64 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), hAPP(
% 0.97/1.64 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Y ) ) ) }.
% 0.97/1.64 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), hAPP(
% 0.97/1.64 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.97/1.64 , X = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), skol11
% 0.97/1.64 ( X, Y ) ) }.
% 0.97/1.64 { ! X = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), Z ),
% 0.97/1.64 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }
% 0.97/1.64 .
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 0.97/1.64 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.97/1.64 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 0.97/1.64 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.97/1.64 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), hAPP
% 0.97/1.64 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.97/1.64 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), hAPP
% 0.97/1.64 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.97/1.64 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 0.97/1.64 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), Z ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.97/1.64 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T ), Z )
% 0.97/1.64 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 0.97/1.64 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), T ) ), hAPP( hAPP
% 0.97/1.64 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 0.97/1.64 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), X ) ), hBOOL(
% 0.97/1.64 hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 0.97/1.64 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), Z ) ), X ) ), hBOOL(
% 0.97/1.64 hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 0.97/1.64 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), X ) ), hBOOL(
% 0.97/1.64 hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), X ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 0.97/1.64 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), X ) ), hBOOL(
% 0.97/1.64 hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ),
% 0.97/1.64 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) ) }
% 0.97/1.64 .
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ), !
% 0.97/1.64 Y = X }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) )
% 0.97/1.64 , Y = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X
% 0.97/1.64 ) ) }.
% 0.97/1.64 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), hAPP(
% 0.97/1.64 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) ) }.
% 0.97/1.64 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), hAPP(
% 0.97/1.64 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.97/1.64 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 0.97/1.64 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.97/1.64 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 0.97/1.64 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.97/1.64 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T ), Z )
% 0.97/1.64 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 0.97/1.64 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), T ) ), hAPP(
% 0.97/1.64 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) )
% 0.97/1.64 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP( hAPP
% 0.97/1.64 ( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), X ) ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), Y ) ), ! hBOOL( hAPP
% 0.97/1.64 ( c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.64 ), T ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, T ),
% 0.97/1.64 c_Groups_Oone__class_Oone( X ) ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.64 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.97/1.64 c_Power_Opower__class_Opower( X ), T ), Z ) ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), Y ) )
% 0.97/1.64 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.64 c_Power_Opower__class_Opower( X ), Y ), T ) ), hAPP( hAPP(
% 0.97/1.64 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T ), Z ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), Y ) )
% 0.97/1.64 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T ), Z )
% 0.97/1.64 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.64 c_Power_Opower__class_Opower( X ), Y ), T ) ), hAPP( hAPP(
% 0.97/1.64 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), Y ) )
% 0.97/1.64 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.64 c_Power_Opower__class_Opower( X ), Y ), T ) ), hAPP( hAPP(
% 0.97/1.64 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T ), Z ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__ring( X ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.64 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.64 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ), alpha7( X
% 0.97/1.64 , Y, Z ), alpha24( X, Y, Z ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha7( X, Y, Z ), hBOOL
% 0.97/1.64 ( hAPP( c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 0.97/1.64 ( X ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha24( X, Y, Z ), hBOOL
% 0.97/1.64 ( hAPP( c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 0.97/1.64 ( X ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 0.97/1.64 { ! alpha24( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.64 Z ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.97/1.64 { ! alpha24( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.64 Y ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ),
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) ) ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 0.97/1.64 ) ) ), alpha24( X, Y, Z ) }.
% 0.97/1.64 { ! alpha7( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) ), Z ) ) }.
% 0.97/1.64 { ! alpha7( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) ), Y ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.64 , Y ) ), alpha7( X, Y, Z ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) ) ), alpha8( X, Y, Z ), alpha25( X, Y, Z
% 0.97/1.64 ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha8( X, Y, Z ), hBOOL
% 0.97/1.64 ( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha25( X, Y, Z ), hBOOL
% 0.97/1.64 ( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.97/1.64 { ! alpha25( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.64 Z ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.97/1.64 { ! alpha25( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) ), Y ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ),
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) ) ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.64 , Y ) ), alpha25( X, Y, Z ) }.
% 0.97/1.64 { ! alpha8( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) ), Z ) ) }.
% 0.97/1.64 { ! alpha8( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Y
% 0.97/1.64 ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 0.97/1.64 ) ) ), alpha8( X, Y, Z ) }.
% 0.97/1.64 { ! class_Rings_Oordered__cancel__semiring( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.64 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.64 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 0.97/1.64 { ! class_Rings_Oordered__cancel__semiring( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.64 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ),
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.97/1.64 { ! class_Rings_Oordered__cancel__semiring( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.64 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ),
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.97/1.64 { ! class_Rings_Oordered__cancel__semiring( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 0.97/1.64 ) ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.97/1.64 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 0.97/1.64 ) ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ),
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.64 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 0.97/1.64 { ! class_Rings_Oordered__semiring( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.64 , T ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ) }.
% 0.97/1.64 { ! class_Rings_Oordered__semiring( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.64 , T ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 0.97/1.64 { ! class_Rings_Oordered__comm__semiring( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.64 , T ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 0.97/1.64 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, T ), c_Groups_Ozero__class_Ozero( X
% 0.97/1.64 ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) ) }.
% 0.97/1.64 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, T ), c_Groups_Ozero__class_Ozero( X
% 0.97/1.64 ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) ) }.
% 0.97/1.64 { ! class_Rings_Oordered__semiring( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, U ), T ) ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.64 , Z ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) ), U ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ) }.
% 0.97/1.64 { ! class_Rings_Oordered__semiring( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, U ), T ) ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.64 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) ), U ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ) }.
% 0.97/1.64 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.64 , Z ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) ), Y ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.64 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 0.97/1.64 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, Z ), c_Groups_Ozero__class_Ozero( X
% 0.97/1.64 ) ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Y ),
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.64 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 0.97/1.64 { ! class_Rings_Oordered__cancel__semiring( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.64 , Z ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Y ),
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.97/1.64 { ! class_Rings_Oordered__cancel__semiring( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, Z ), c_Groups_Ozero__class_Ozero( X
% 0.97/1.64 ) ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) ), Y ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.97/1.64 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.64 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Y ) ) ), hBOOL( hAPP
% 0.97/1.64 ( c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.64 ), Y ) ) }.
% 0.97/1.64 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.64 , Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), Y ), Y ) ) ) }.
% 0.97/1.64 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), Y ), Y ) ), c_Groups_Ozero__class_Ozero
% 0.97/1.64 ( X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Y ),
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.97/1.64 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 0.97/1.64 ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), Y ), Y ) ), c_Groups_Ozero__class_Ozero
% 0.97/1.64 ( X ) ) ) }.
% 0.97/1.64 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.64 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.64 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) ) }.
% 0.97/1.64 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.64 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), ! hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 0.97/1.64 ( X ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.64 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.64 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), ! hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 0.97/1.64 ( X ), Z = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.64 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.64 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), ! Y =
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.64 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Z ) =
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.64 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.64 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, T ), Z ) )
% 0.97/1.64 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, T ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) ) }.
% 0.97/1.64 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.64 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, T ), Z ) )
% 0.97/1.64 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, T ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) ) }.
% 0.97/1.64 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 0.97/1.64 ) ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ),
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ), c_Groups_Ozero__class_Ozero
% 0.97/1.64 ( X ) ) ) }.
% 0.97/1.64 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, U ), T ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.97/1.64 ( X ), Z ), U ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), T )
% 0.97/1.64 ) ) }.
% 0.97/1.64 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, U ), T ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.97/1.64 ( X ), Z ), U ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), T )
% 0.97/1.64 ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ) ),
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__semidom( X ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.64 , c_Groups_Oone__class_Oone( X ) ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.64 , Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) ), hAPP( hAPP(
% 0.97/1.64 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.64 , Z ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.64 c_Power_Opower__class_Opower( X ), Z ), T ) ), hAPP( hAPP(
% 0.97/1.64 c_Power_Opower__class_Opower( X ), Y ), T ) ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ) ), Y
% 0.97/1.64 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.64 c_Groups_Oone__class_Oone( X ) ), hAPP( hAPP(
% 0.97/1.64 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 0.97/1.64 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 0.97/1.64 c_Nat_OSuc, Y ) ), X ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 0.97/1.64 c_Nat_OSuc, Y ) ), X ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.97/1.64 tc_Nat_Onat, Y ), X ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), hAPP(
% 0.97/1.64 c_Nat_OSuc, X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.97/1.64 tc_Nat_Onat, Y ), X ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.97/1.64 , hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), hAPP(
% 0.97/1.64 c_Nat_OSuc, X ) ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 0.97/1.64 c_Nat_OSuc, Y ) ), X ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.97/1.64 tc_Nat_Onat, Y ), X ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 0.97/1.64 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 0.97/1.64 c_Nat_OSuc, Y ) ), X ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.97/1.64 , hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), hAPP(
% 0.97/1.64 c_Nat_OSuc, X ) ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 0.97/1.64 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 0.97/1.64 c_Nat_OSuc, Y ) ), X ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.97/1.64 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), hAPP(
% 0.97/1.64 c_Nat_OSuc, Y ) ) ), X = Y }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.97/1.64 , ! X = Y, hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ),
% 0.97/1.64 hAPP( c_Nat_OSuc, Y ) ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 0.97/1.64 c_Nat_OSuc, Y ) ), X ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.97/1.64 tc_Nat_Onat, Y ), X ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 0.97/1.64 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( c_Nat_OSuc, Z ) ),
% 0.97/1.64 Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP(
% 0.97/1.64 c_Nat_OSuc, Z ) ), X ) ) ), hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.97/1.64 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 0.97/1.64 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( c_Nat_OSuc, Z ) ),
% 0.97/1.64 Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP(
% 0.97/1.64 c_Nat_OSuc, Z ) ), X ) ) ) }.
% 0.97/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ), !
% 0.97/1.64 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T ), Z ) ),
% 0.97/1.64 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), T ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ), Z ) ) ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__0( X ), !
% 0.97/1.64 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) =
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__0( X ), ! Z = c_Groups_Ozero__class_Ozero
% 0.97/1.64 ( tc_Polynomial_Opoly( X ) ),
% 0.97/1.64 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) =
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__0( X ),
% 0.97/1.64 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ) =
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( c_Nat_OSuc, X ) ) }
% 0.97/1.64 .
% 0.97/1.64 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 0.97/1.64 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, T ), Z ) ) }.
% 0.97/1.65 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 0.97/1.65 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, T ), Z ) ),
% 0.97/1.65 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 0.97/1.65 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.65 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), T ) ) }.
% 0.97/1.65 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.65 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ), T ) ),
% 0.97/1.65 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 0.97/1.65 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, U ), T ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 0.97/1.65 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( X ) ), U ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ) }.
% 0.97/1.65 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, U ), T ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.65 , Z ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( X ) ), U ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ) }.
% 0.97/1.65 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, U ), T ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.65 , Z ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( X ) ), U ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ) }.
% 0.97/1.65 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, U ), T ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Z )
% 0.97/1.65 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( X ) ), U ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ) }.
% 0.97/1.65 { ! class_Rings_Olinordered__semiring( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.65 , Z ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, T ), Y ) ) }.
% 0.97/1.65 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.65 , Z ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, T ), Y ) ) }.
% 0.97/1.65 { ! class_Rings_Olinordered__semiring( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.65 , T ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 0.97/1.65 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.65 , T ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 0.97/1.65 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Z )
% 0.97/1.65 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, T ), Y ) ) }.
% 0.97/1.65 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), T )
% 0.97/1.65 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 0.97/1.65 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 0.97/1.65 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.65 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) ) }.
% 0.97/1.65 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.65 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.65 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) ) }.
% 0.97/1.65 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 0.97/1.65 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, T ), Z ) ),
% 0.97/1.65 hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, T ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) ) }.
% 0.97/1.65 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.65 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, T ), Z ) ),
% 0.97/1.65 hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, T ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) ) }.
% 0.97/1.65 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.65 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ),
% 0.97/1.65 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.97/1.65 ( X ), Y ), Z ) ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.97/1.65 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 0.97/1.65 ) ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Z ),
% 0.97/1.65 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.97/1.65 ( X ), Y ), Z ) ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.97/1.65 { ! class_Rings_Olinordered__ring( X ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.65 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) ) }.
% 0.97/1.65 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ),
% 0.97/1.65 c_Groups_Ozero__class_Ozero( X ) ) ), Z = c_Groups_Ozero__class_Ozero( X
% 0.97/1.65 ) }.
% 0.97/1.65 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ),
% 0.97/1.65 c_Groups_Ozero__class_Ozero( X ) ) ), Y = c_Groups_Ozero__class_Ozero( X
% 0.97/1.65 ) }.
% 0.97/1.65 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.97/1.65 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.65 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ),
% 0.97/1.65 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.97/1.65 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.65 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), c_Groups_Oone__class_Oone( X )
% 0.97/1.65 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) ) }.
% 0.97/1.65 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.65 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), c_Groups_Oone__class_Oone( X )
% 0.97/1.65 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) ) }.
% 0.97/1.65 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.65 c_Power_Opower__class_Opower( X ), Z ), T ) ), hAPP( hAPP(
% 0.97/1.65 c_Power_Opower__class_Opower( X ), Y ), T ) ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.65 , Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 0.97/1.65 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.65 c_Power_Opower__class_Opower( X ), Z ), hAPP( c_Nat_OSuc, T ) ) ), hAPP(
% 0.97/1.65 hAPP( c_Power_Opower__class_Opower( X ), Y ), hAPP( c_Nat_OSuc, T ) ) ) )
% 0.97/1.65 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( X ) ), Y ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 0.97/1.65 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 0.97/1.65 c_Power_Opower__class_Opower( X ), Z ), hAPP( c_Nat_OSuc, T ) ) = hAPP(
% 0.97/1.65 hAPP( c_Power_Opower__class_Opower( X ), Y ), hAPP( c_Nat_OSuc, T ) ), !
% 0.97/1.65 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.65 , Y ) ), Z = Y }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 0.97/1.65 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( c_Nat_OSuc,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), Y ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 0.97/1.65 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( c_Nat_OSuc,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 0.97/1.65 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), Y ) ), !
% 0.97/1.65 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 0.97/1.65 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) ), hBOOL
% 0.97/1.65 ( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( c_Nat_OSuc
% 0.97/1.65 , c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 0.97/1.65 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ), ! hBOOL( hAPP
% 0.97/1.65 ( c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.65 ( tc_Nat_Onat ) ), Z ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 0.97/1.65 ( tc_Nat_Onat, Y ), X ) ) }.
% 0.97/1.65 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Z ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.97/1.65 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 0.97/1.65 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 0.97/1.65 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ), ! hBOOL( hAPP
% 0.97/1.65 ( c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.65 ( tc_Nat_Onat ) ), Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 0.97/1.65 ( tc_Nat_Onat, Z ), X ) ) }.
% 0.97/1.65 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), X ) )
% 0.97/1.65 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 0.97/1.65 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), Y ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), Y ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.65 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.65 tc_Int_Oint ) ), X ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oone__class_Oone
% 0.97/1.65 ( tc_Int_Oint ) ), X ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), hAPP(
% 0.97/1.65 hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ),
% 0.97/1.65 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) )
% 0.97/1.65 , hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), hAPP(
% 0.97/1.65 hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ),
% 0.97/1.65 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP( hAPP
% 0.97/1.65 ( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ),
% 0.97/1.65 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ), X ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ),
% 0.97/1.65 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ),
% 0.97/1.65 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ), X ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ),
% 0.97/1.65 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ),
% 0.97/1.65 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ), X ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 0.97/1.65 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) ), hBOOL
% 0.97/1.65 ( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( c_Nat_OSuc
% 0.97/1.65 , c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), hAPP( hAPP(
% 0.97/1.65 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ) ) }.
% 0.97/1.65 { ! class_Rings_Olinordered__semiring__1( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, T ), Y ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.65 , U ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( X ) ), W ) ), ! hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( X ), U ), W ) = c_Groups_Oone__class_Oone( X
% 0.97/1.65 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), W ), T ) ) ), Y ) ) }.
% 0.97/1.65 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 0.97/1.65 c_Power_Opower__class_Opower( X ), T ), Z ) = hAPP( hAPP(
% 0.97/1.65 c_Power_Opower__class_Opower( X ), Y ), Z ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.65 , T ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( X ) ), Y ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.65 tc_Nat_Onat ) ), Z ) ), T = Y }.
% 0.97/1.65 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.97/1.65 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, T, Z ) ), Y
% 0.97/1.65 ) = hAPP( c_Polynomial_Opoly( X, T ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) }.
% 0.97/1.65 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 0.97/1.65 hAPP( hAPP( c_Polynomial_OpCons( X ), T ), Z ), Y ) = hAPP( hAPP(
% 0.97/1.65 c_Polynomial_OpCons( X ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) ),
% 0.97/1.65 c_Polynomial_Osynthetic__div( X, Z, Y ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.65 tc_Int_Oint ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ),
% 0.97/1.65 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) ) ) }.
% 0.97/1.65 { ! class_Rings_Ocomm__semiring__0( X ),
% 0.97/1.65 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, hAPP( hAPP(
% 0.97/1.65 c_Polynomial_OpCons( X ), Z ), c_Groups_Ozero__class_Ozero(
% 0.97/1.65 tc_Polynomial_Opoly( X ) ) ), Y ) = hAPP( hAPP( c_Polynomial_OpCons( X )
% 0.97/1.65 , Z ), c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! X = hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Z ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ),
% 0.97/1.65 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! X = hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z ), X ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oone__class_Oone
% 0.97/1.65 ( tc_Int_Oint ) ), Y ) ) }.
% 0.97/1.65 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.65 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Y ),
% 0.97/1.65 c_Groups_Oone__class_Oone( X ) ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.65 c_Power_Opower__class_Opower( X ), Y ), hAPP( c_Nat_OSuc, Z ) ) ), Y ) )
% 0.97/1.65 }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) ) ), !
% 0.97/1.65 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, X ), Z ) ), !
% 0.97/1.65 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Z ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) ),
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.65 tc_Int_Oint ) ), Z ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.97/1.65 tc_Int_Oint, Y ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 0.97/1.65 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ), X ) ) }
% 0.97/1.65 .
% 0.97/1.65 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) ),
% 0.97/1.65 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ), Y ) ) }
% 0.97/1.65 .
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) )
% 0.97/1.65 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ), Z )
% 0.97/1.65 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), Z )
% 0.97/1.65 ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) )
% 0.97/1.65 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ), Y )
% 0.97/1.65 ), Y = X }.
% 0.97/1.65 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), X ) ) }
% 0.97/1.65 .
% 0.97/1.65 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ),
% 0.97/1.65 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), Y ) ) }
% 0.97/1.65 .
% 0.97/1.65 { ! Y = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y )
% 0.97/1.65 , X ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.97/1.65 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), Z )
% 0.97/1.65 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), Z )
% 0.97/1.65 ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.97/1.65 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), Y )
% 0.97/1.65 ), Y = X }.
% 0.97/1.65 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ) ), T ) = hAPP(
% 0.97/1.65 hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ), ! hBOOL(
% 0.97/1.65 hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) ),
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, T ), W ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.65 tc_Int_Oint ) ), Z ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 0.97/1.65 ( tc_Int_Oint, Z ), W ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 0.97/1.65 ( tc_Int_Oint, Y ), U ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP( hAPP
% 0.97/1.65 ( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ) ), Z ) ), hAPP(
% 0.97/1.65 hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ) ), X ) ) ), !
% 0.97/1.65 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ),
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, U ), X ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, U ), Z ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), T ) ) }.
% 0.97/1.65 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ) ), T ) = hAPP(
% 0.97/1.65 hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ), ! hBOOL(
% 0.97/1.65 hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) ) ), !
% 0.97/1.65 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, X ), Z ) ), !
% 0.97/1.65 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), T ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.65 tc_Int_Oint ) ), Z ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 0.97/1.65 ( tc_Int_Oint, Z ), W ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 0.97/1.65 ( tc_Int_Oint, U ), Y ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP( hAPP
% 0.97/1.65 ( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ) ), Z ) ), hAPP(
% 0.97/1.65 hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ) ), X ) ) ), !
% 0.97/1.65 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Z ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z ), U ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, X ), U ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T ), Y ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), hAPP( hAPP(
% 0.97/1.65 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ), Y ) ) ) }.
% 0.97/1.65 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Groups_Oone__class_Oone(
% 0.97/1.65 tc_Int_Oint ) ) ) }.
% 0.97/1.65 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Groups_Ozero__class_Ozero
% 0.97/1.65 ( tc_Int_Oint ) ) ) }.
% 0.97/1.65 { ! class_Orderings_Opreorder( X ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, Y ), Y ) ) }.
% 0.97/1.65 { ! class_Rings_Ocomm__ring__1( X ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 0.97/1.65 c_Polynomial_OpCons( X ), c_Groups_Ouminus__class_Ouminus( X, Z ) ), hAPP
% 0.97/1.65 ( hAPP( c_Polynomial_OpCons( X ), c_Groups_Oone__class_Oone( X ) ),
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ),
% 0.97/1.65 c_Polynomial_Osynthetic__div( X, Y, Z ) ) ), hAPP( hAPP(
% 0.97/1.65 c_Polynomial_OpCons( X ), hAPP( c_Polynomial_Opoly( X, Y ), Z ) ),
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) = Y }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.97/1.65 , X = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), skol12
% 0.97/1.65 ( X, Y ) ) }.
% 0.97/1.65 { ! X = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), Z ),
% 0.97/1.65 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }
% 0.97/1.65 .
% 0.97/1.65 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ) }.
% 0.97/1.65 { ! class_Orderings_Olinorder( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 0.97/1.65 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.97/1.65 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Polynomial_OpCons( X ), Z ), Y )
% 0.97/1.65 ) = hAPP( hAPP( c_Polynomial_OpCons( X ),
% 0.97/1.65 c_Groups_Ouminus__class_Ouminus( X, Z ) ),
% 0.97/1.65 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) }.
% 0.97/1.65 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.97/1.65 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Polynomial_OpCons( X ), Z ), Y )
% 0.97/1.65 ) = hAPP( hAPP( c_Polynomial_OpCons( X ),
% 0.97/1.65 c_Groups_Ouminus__class_Ouminus( X, Z ) ),
% 0.97/1.65 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) }.
% 0.97/1.65 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 0.97/1.65 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ) ), Y ) =
% 0.97/1.65 c_Groups_Ouminus__class_Ouminus( X, hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 0.97/1.65 ) }.
% 0.97/1.65 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 0.97/1.65 ) = c_Groups_Ouminus__class_Ouminus( X, Y ), Z = Y }.
% 0.97/1.65 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ouminus__class_Ouminus
% 0.97/1.65 ( X, Z ) = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.97/1.65 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 0.97/1.65 ) = Y, c_Groups_Ouminus__class_Ouminus( X, Y ) = Z }.
% 0.97/1.65 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 0.97/1.65 ) = Z, c_Groups_Ouminus__class_Ouminus( X, Z ) = Y }.
% 0.97/1.65 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.65 , Y ), Y = c_Groups_Ouminus__class_Ouminus( X, Z ) }.
% 0.97/1.65 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.65 , Z ), Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.97/1.65 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.97/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 0.97/1.65 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.97/1.65 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, Z, Y ) ) =
% 0.97/1.65 c_Polynomial_Omonom( X, c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.97/1.65 { ! class_Rings_Ocomm__ring( X ), hAPP( hAPP( c_Polynomial_Osmult( X ),
% 0.97/1.65 c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) =
% 0.97/1.65 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 0.97/1.65 c_Polynomial_Osmult( X ), Z ), Y ) ) }.
% 0.97/1.65 { ! class_Rings_Ocomm__ring( X ), hAPP( hAPP( c_Polynomial_Osmult( X ), Z )
% 0.97/1.65 , c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) =
% 0.97/1.65 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 0.97/1.65 c_Polynomial_Osmult( X ), Z ), Y ) ) }.
% 0.97/1.65 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.97/1.65 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.97/1.65 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 0.97/1.65 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.65 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.97/1.65 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ), X ) =
% 0.97/1.65 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.97/1.65 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), X ) ) = hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint ),
% 0.97/1.65 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ),
% 0.97/1.65 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.97/1.65 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.65 ( tc_Int_Oint ) ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.97/1.65 { ! class_Groups_Ogroup__add( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.97/1.65 ( X ), c_Groups_Ouminus__class_Ouminus( X, Z ) ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) = Y }.
% 0.97/1.65 { ! class_Groups_Ogroup__add( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.97/1.65 ( X ), Z ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ),
% 0.97/1.65 c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) ) = Y }.
% 0.97/1.65 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP
% 0.97/1.65 ( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( X ), c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.97/1.65 ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.97/1.65 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.97/1.65 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( X ), c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.97/1.65 ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.97/1.65 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 0.97/1.65 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.97/1.65 ( X, Y ) ) }.
% 0.97/1.65 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 0.97/1.65 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.97/1.65 ) ), Y ) }.
% 0.97/1.65 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.97/1.65 , c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.97/1.65 ( X, Y ) ) }.
% 0.97/1.65 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.97/1.65 , c_Groups_Ouminus__class_Ouminus( X, Z ) ),
% 0.97/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 0.97/1.65 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.97/1.65 ), Z ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 0.97/1.65 Z = Y, Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.97/1.65 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.97/1.65 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.97/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.97/1.65 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.97/1.65 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.65 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.97/1.65 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.65 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.97/1.65 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.65 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.97/1.65 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.65 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.97/1.65 ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 0.97/1.65 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Y ), Z ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.97/1.65 ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) ) }.
% 0.97/1.65 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.97/1.65 ), Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 0.97/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ) ), Z ) ) }.
% 0.97/1.65 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.97/1.65 ), Z ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 0.97/1.65 c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) ) }.
% 0.97/1.65 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Z ), c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.65 , Y ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Y ),
% 0.97/1.65 c_Groups_Ouminus__class_Ouminus( X, Z ) ) ) }.
% 0.97/1.65 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.65 , Z ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Z ),
% 0.97/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ) ) ) }.
% 0.97/1.65 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ),
% 0.97/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ) ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, Y ),
% 0.97/1.65 c_Groups_Ouminus__class_Ouminus( X, Z ) ) ) }.
% 0.97/1.65 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, Y ),
% 0.97/1.65 c_Groups_Ouminus__class_Ouminus( X, Z ) ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ),
% 0.97/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ) ) ) }.
% 0.97/1.65 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.65 , Z ) ), Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ) ), Z ) ) }.
% 0.97/1.65 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.65 , Y ) ), Z ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.65 c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) ) }.
% 0.97/1.65 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.65 , Z ) ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ) }.
% 0.97/1.65 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.65 , Z ) ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) ) }.
% 0.97/1.65 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.65 , Y ) ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) ) }.
% 0.97/1.65 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ) = Y, Y =
% 0.97/1.65 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.65 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.97/1.65 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.97/1.65 = Y }.
% 0.97/1.65 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 0.97/1.65 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.97/1.65 ) }.
% 0.97/1.65 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.97/1.65 ) }.
% 0.97/1.65 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.97/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ), Y = c_Groups_Ozero__class_Ozero
% 0.97/1.65 ( X ) }.
% 0.97/1.65 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.97/1.65 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.65 , Y ) }.
% 0.97/1.65 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.97/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Groups_Ozero__class_Ozero( X )
% 0.97/1.65 = Y }.
% 0.97/1.65 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Ouminus__class_Ouminus( X, Y
% 0.97/1.65 ) }.
% 0.97/1.65 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.65 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.65 , c_Groups_Ouminus__class_Ouminus( X, Y ) ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 0.97/1.65 ) ) ) }.
% 0.97/1.65 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 0.97/1.65 ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ouminus__class_Ouminus( X, Y
% 0.97/1.65 ) ) ) }.
% 0.97/1.65 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, Y ),
% 0.97/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ) ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 0.97/1.65 ) ) ) }.
% 0.97/1.65 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 0.97/1.65 ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Y ),
% 0.97/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ) ) ) }.
% 0.97/1.65 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.65 , Y ) ), c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.65 , Y ) ) }.
% 0.97/1.65 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.65 , Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Groups_Ozero__class_Ozero( X
% 0.97/1.65 ) ) ) }.
% 0.97/1.65 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.65 , Y ) ), Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( X ) ), Y ) ) }.
% 0.97/1.65 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.65 , Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ) ), Y ) ) }.
% 0.97/1.65 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.97/1.65 ), Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( X ) ), Y ) ) }.
% 0.97/1.65 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 0.97/1.65 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 0.97/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ) ), Y ) ) }.
% 0.97/1.65 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.97/1.65 ), c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 0.97/1.65 ) }.
% 0.97/1.65 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 0.97/1.65 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 0.97/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Groups_Ozero__class_Ozero( X
% 0.97/1.65 ) ) ) }.
% 0.97/1.65 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ) ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.65 ) }.
% 0.97/1.65 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.65 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ouminus__class_Ouminus( X, Y
% 0.97/1.65 ) ) ) }.
% 0.97/1.65 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.65 , Y ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Y ),
% 0.97/1.65 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.97/1.65 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.65 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Y ),
% 0.97/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ) ) ) }.
% 0.97/1.65 { ! class_Groups_Ogroup__add( X ), ! hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) = c_Groups_Ozero__class_Ozero
% 0.97/1.65 ( X ), Y = c_Groups_Ouminus__class_Ouminus( X, Z ) }.
% 0.97/1.65 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.65 , Z ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), Y ) =
% 0.97/1.65 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.65 { ! class_Groups_Ogroup__add( X ), ! hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) = c_Groups_Ozero__class_Ozero
% 0.97/1.65 ( X ), c_Groups_Ouminus__class_Ouminus( X, Z ) = Y }.
% 0.97/1.65 { ! class_Groups_Oab__group__add( X ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( X ), c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.97/1.65 ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.65 { ! class_Groups_Ogroup__add( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.97/1.65 ( X ), c_Groups_Ouminus__class_Ouminus( X, Y ) ), Y ) =
% 0.97/1.65 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.65 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.65 , Y ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), Y ) =
% 0.97/1.65 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.65 { ! class_Groups_Ogroup__add( X ), ! hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) = c_Groups_Ozero__class_Ozero
% 0.97/1.65 ( X ), Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.97/1.65 { ! class_Groups_Ogroup__add( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.97/1.65 ( X ), Y ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 0.97/1.65 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.65 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = c_Groups_Oone__class_Oone
% 0.97/1.65 ( X ), Y = c_Groups_Oone__class_Oone( X ), Y =
% 0.97/1.65 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) }.
% 0.97/1.65 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.97/1.65 c_Groups_Oone__class_Oone( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.65 ( X ), Y ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.65 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.97/1.65 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ),
% 0.97/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) =
% 0.97/1.65 c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.65 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ouminus__class_Ouminus( X, Y
% 0.97/1.65 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.97/1.65 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) ), Y
% 0.97/1.65 ) }.
% 0.97/1.65 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ),
% 0.97/1.65 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ), X ) =
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.97/1.65 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.65 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opos__poly( X, Y ),
% 0.97/1.65 c_Polynomial_Opos__poly( X, c_Groups_Ouminus__class_Ouminus(
% 0.97/1.65 tc_Polynomial_Opoly( X ), Y ) ) }.
% 0.97/1.65 { ! class_Rings_Oring__1( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.97/1.65 ), c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.65 c_Power_Opower__class_Opower( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.97/1.65 c_Groups_Oone__class_Oone( X ) ) ), Y ) ), hAPP( hAPP(
% 0.97/1.65 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.97/1.65 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.97/1.65 , Z ), hAPP( c_Nat_OSuc, hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero(
% 0.97/1.65 tc_Nat_Onat ) ) ) ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y )
% 0.97/1.65 , hAPP( c_Nat_OSuc, hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero(
% 0.97/1.65 tc_Nat_Onat ) ) ) ), Z = Y, Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }
% 0.97/1.65 .
% 0.97/1.65 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 0.97/1.65 c_Power_Opower__class_Opower( X ), Z ), hAPP( c_Nat_OSuc, hAPP(
% 0.97/1.65 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP
% 0.97/1.65 ( c_Power_Opower__class_Opower( X ), Y ), hAPP( c_Nat_OSuc, hAPP(
% 0.97/1.65 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.97/1.65 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.97/1.65 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), hAPP( c_Nat_OSuc,
% 0.97/1.65 hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP
% 0.97/1.65 ( hAPP( c_Power_Opower__class_Opower( X ), Y ), hAPP( c_Nat_OSuc, hAPP(
% 0.97/1.65 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.97/1.65 { ! class_Orderings_Oord( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z ), Y ) ), hBOOL(
% 0.97/1.65 hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ) ), hAPP( Y, U )
% 0.97/1.65 ) ) }.
% 0.97/1.65 { ! class_Orderings_Oord( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, skol13( X, Y, Z ) ) ),
% 0.97/1.65 hAPP( Y, skol13( X, Y, Z ) ) ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z ), Y ) ) }.
% 0.97/1.65 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ) }.
% 0.97/1.65 { ! class_Orderings_Oorder( X ), ! Z = Y, hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 0.97/1.65 { ! class_Orderings_Oorder( X ), ! Z = Y, hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ) }.
% 0.97/1.65 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ), Z = Y }.
% 0.97/1.65 { ! class_Orderings_Opreorder( X ), ! Z = Y, hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 0.97/1.65 { ! class_Orderings_Oord( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z ), Y ) ), hBOOL(
% 0.97/1.65 hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ) ), hAPP( Y, U )
% 0.97/1.65 ) ) }.
% 0.97/1.65 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ), Y = Z }.
% 0.97/1.65 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! Y = Z, hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ) }.
% 0.97/1.65 { ! class_Orderings_Oord( X ), ! Z = Y, ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, Y ), T ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), T ) ) }.
% 0.97/1.65 { ! class_Orderings_Oorder( X ), ! Z = Y, ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, T ), Y ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, T ), Z ) ) }.
% 0.97/1.65 { ! class_Orderings_Oord( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! Y = T, hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), T ) ) }.
% 0.97/1.65 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! Z = T, hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, T ), Y ) ) }.
% 0.97/1.65 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ), Z = Y }.
% 0.97/1.65 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, Y ), T ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), T ) ) }.
% 0.97/1.65 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ), Y = Z }.
% 0.97/1.65 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, T ), Z ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, T ), Y ) ) }.
% 0.97/1.65 { ! class_Orderings_Oord( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z ), Y ) ), hBOOL(
% 0.97/1.65 hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ) ), hAPP( Y, U )
% 0.97/1.65 ) ) }.
% 0.97/1.65 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ) }.
% 0.97/1.65 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), Z = Y, hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 0.97/1.65 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 0.97/1.65 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, T ), Z ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, T ), Y ) ) }.
% 0.97/1.65 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Y ), T ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Z ), T ) ) }.
% 0.97/1.65 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! Z = T, hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, T ), Y ) ) }.
% 0.97/1.65 { ! class_Orderings_Oord( X ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless
% 0.97/1.65 ( X, Z ), Y ) ), ! Y = T, hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 0.97/1.65 Z ), T ) ) }.
% 0.97/1.65 { ! class_Orderings_Oorder( X ), ! Z = Y, ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, T ), Y ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, T ), Z ) ) }.
% 0.97/1.65 { ! class_Orderings_Oord( X ), ! Z = Y, ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Y ), T ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Z ), T ) ) }.
% 0.97/1.65 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 0.97/1.65 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 0.97/1.65 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! Y = Z }.
% 0.97/1.65 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! Z = Y }.
% 0.97/1.65 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 0.97/1.65 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 0.97/1.65 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! Z = Y }.
% 0.97/1.65 { ! class_Orderings_Olinorder( X ), Z = Y, hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 0.97/1.65 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Y ), Z ) ), Y = Z }.
% 0.97/1.65 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! Y = Z, ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 0.97/1.65 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), Z = Y, hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 0.97/1.65 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Y ), Z ) ), Z = Y }.
% 0.97/1.65 { ! class_Orderings_Olinorder( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Y ), Z ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 0.97/1.65 { ! class_Orderings_Olinorder( X ), ! Z = Y, ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 0.97/1.65 { ! class_Orderings_Olinorder( X ), Z = Y, hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 0.97/1.65 { ! class_Orderings_Olinorder( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! Z = Y }.
% 0.97/1.65 { ! class_Orderings_Olinorder( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Y ), Z ) ), ! Z = Y }.
% 0.97/1.65 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Y ), Y ) ) }.
% 0.97/1.65 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, T ), Z ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, T ), Y ) ) }.
% 0.97/1.65 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Y ), T ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Z ), T ) ) }.
% 0.97/1.65 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, T ), Z ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, T ), Y ) ) }.
% 0.97/1.65 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, Y ), T ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Z ), T ) ) }.
% 0.97/1.65 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), Y = Z, hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 0.97/1.65 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), Z = Y, hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 0.97/1.65 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), Z = Y }.
% 0.97/1.65 { ! class_Orderings_Olinorder( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), Z = Y }.
% 0.97/1.65 { ! class_Orderings_Olinorder( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! Z = Y, ! hBOOL( hAPP
% 0.97/1.65 ( c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 0.97/1.65 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 0.97/1.65 { ! class_Orderings_Olinorder( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 0.97/1.65 { ! class_Orderings_Oorder( X ), Z = Y, ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 0.97/1.65 { ! class_Orderings_Oorder( X ), Z = Y, ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 0.97/1.65 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), Z = Y }.
% 0.97/1.65 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! Z = Y, hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 0.97/1.65 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 0.97/1.65 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ) }.
% 0.97/1.65 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), Z = Y }.
% 0.97/1.65 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 0.97/1.65 { ! class_Orderings_Oorder( X ), ! Z = Y, hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 0.97/1.65 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 0.97/1.65 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ) }.
% 0.97/1.65 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 0.97/1.65 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 0.97/1.65 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! Z = Y }.
% 0.97/1.65 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), Z = Y, hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 0.97/1.65 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 0.97/1.65 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 0.97/1.65 { ! class_Orderings_Olinorder( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Y ), Z ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 0.97/1.65 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.65 tc_Polynomial_Opoly( X ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.97/1.65 tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.97/1.65 tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Polynomial_OpCons( X ),
% 0.97/1.65 c_Groups_Ouminus__class_Ouminus( X, Z ) ), hAPP( hAPP(
% 0.97/1.65 c_Polynomial_OpCons( X ), c_Groups_Oone__class_Oone( X ) ),
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ),
% 0.97/1.65 c_Polynomial_Oorder( X, Z, Y ) ) ), Y ) ) }.
% 0.97/1.65 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.65 tc_Polynomial_Opoly( X ) ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 0.97/1.65 ( tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.97/1.65 tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Polynomial_OpCons( X ),
% 0.97/1.65 c_Groups_Ouminus__class_Ouminus( X, Z ) ), hAPP( hAPP(
% 0.97/1.65 c_Polynomial_OpCons( X ), c_Groups_Oone__class_Oone( X ) ),
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ), hAPP(
% 0.97/1.65 c_Nat_OSuc, c_Polynomial_Oorder( X, Z, Y ) ) ) ), Y ) ) }.
% 0.97/1.65 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.65 tc_Polynomial_Opoly( X ) ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 0.97/1.65 ( tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.97/1.65 tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Polynomial_OpCons( X ),
% 0.97/1.65 c_Groups_Ouminus__class_Ouminus( X, Z ) ), hAPP( hAPP(
% 0.97/1.65 c_Polynomial_OpCons( X ), c_Groups_Oone__class_Oone( X ) ),
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ), hAPP(
% 0.97/1.65 c_Nat_OSuc, c_Polynomial_Oorder( X, Z, Y ) ) ) ), Y ) ) }.
% 0.97/1.65 { ! class_Lattices_Oboolean__algebra( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.65 , Z ) ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ) }.
% 0.97/1.65 { ! class_Lattices_Oboolean__algebra( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.65 , Z ) ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) ) }.
% 0.97/1.65 { ! class_Lattices_Oboolean__algebra( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.65 , Y ) ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) ) }.
% 0.97/1.65 { ! class_Rings_Ocomm__semiring__1( X ), hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) )
% 0.97/1.65 }.
% 0.97/1.65 { ! class_Rings_Ocomm__ring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( X ), c_Groups_Ouminus__class_Ouminus( X, Z ) )
% 0.97/1.65 , Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ) }.
% 0.97/1.65 { ! class_Rings_Ocomm__ring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( X ), c_Groups_Ouminus__class_Ouminus( X, Z ) )
% 0.97/1.65 , Y ) ) }.
% 0.97/1.65 { ! class_Rings_Ocomm__ring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( X ), Z ), c_Groups_Ouminus__class_Ouminus( X, Y
% 0.97/1.65 ) ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ) }.
% 0.97/1.65 { ! class_Rings_Ocomm__ring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( X ), Z ), c_Groups_Ouminus__class_Ouminus( X, Y
% 0.97/1.65 ) ) ) }.
% 0.97/1.65 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint,
% 0.97/1.65 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) = X }.
% 0.97/1.65 { ! class_Orderings_Oord( X ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless
% 0.97/1.65 ( tc_fun( T, X ), Z ), Y ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z ), Y ) ) }.
% 0.97/1.65 { ! class_Orderings_Oord( X ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless
% 0.97/1.65 ( tc_fun( T, X ), Z ), Y ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y ), Z ) ) }.
% 0.97/1.65 { ! class_Orderings_Oord( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z ), Y ) ), hBOOL(
% 0.97/1.65 hAPP( c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y ), Z ) ),
% 0.97/1.65 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_fun( T, X ), Z ), Y ) ) }
% 0.97/1.65 .
% 0.97/1.65 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 0.97/1.65 c_Polynomial_Osmult( X ), T ), Z ) ), Y ) ), hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Z ), Y ) ) }.
% 0.97/1.65 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Z ), Y ) ), hBOOL(
% 0.97/1.65 hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Z ),
% 0.97/1.65 hAPP( hAPP( c_Polynomial_Osmult( X ), T ), Y ) ) ) }.
% 0.97/1.65 { ! class_Rings_Ocomm__semiring__1( X ), hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( X ), Y ), Y ) ) }.
% 0.97/1.65 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( X ), Y ), T ) ), hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( X ), Z ), T ) ) }.
% 0.97/1.65 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.97/1.65 X ), Z ), T ) ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T )
% 0.97/1.65 ) ) }.
% 0.97/1.65 { ! class_Rings_Ocomm__semiring__1( X ), hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( X ), c_Groups_Oone__class_Oone( X ) ), Y ) ) }
% 0.97/1.65 .
% 0.97/1.65 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( X ), Z ), T ) ), hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( X ), Y ), T ) ) ) }.
% 0.97/1.65 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.65 ( X ), T ), Z ) ), Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X
% 0.97/1.65 ), Z ), Y ) ) }.
% 0.97/1.65 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.65 ( X ), Z ), T ) ), Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X
% 0.97/1.65 ), Z ), Y ) ) }.
% 0.97/1.65 { ! class_Rings_Odvd( X ), ! Z = hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.65 ( X ), Y ), T ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Y ), Z
% 0.97/1.65 ) ) }.
% 0.97/1.65 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( X ), U ), T ) ), hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.65 ( X ), Z ), U ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T
% 0.97/1.65 ) ) ) }.
% 0.97/1.65 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 0.97/1.65 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ) }.
% 0.97/1.65 { ! class_Rings_Ocomm__semiring__1( X ), hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 0.97/1.65 { ! class_Rings_Ocomm__semiring__1( X ), hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 0.97/1.65 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) )
% 0.97/1.65 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.65 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.97/1.65 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP(
% 0.97/1.65 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), Z =
% 0.97/1.65 c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( X ), T ), Y ) ) }.
% 0.97/1.65 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ), hBOOL(
% 0.97/1.65 hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 0.97/1.65 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.97/1.65 X ), T ), Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), hAPP(
% 0.97/1.65 hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 0.97/1.65 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.97/1.65 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP(
% 0.97/1.65 hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ), T =
% 0.97/1.65 c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ) }.
% 0.97/1.65 { ! class_Rings_Oidom( X ), ! T = c_Groups_Ozero__class_Ozero( X ), hBOOL(
% 0.97/1.65 hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 0.97/1.65 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.97/1.65 X ), Z ), Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), hAPP(
% 0.97/1.65 hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 0.97/1.65 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), Y ) ), hBOOL( hAPP(
% 0.97/1.65 hAPP( c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP(
% 0.97/1.65 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.97/1.65 c_Power_Opower__class_Opower( X ), T ), Y ) ) ) }.
% 0.97/1.65 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, U ), T ) ), hBOOL( hAPP(
% 0.97/1.65 hAPP( c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP(
% 0.97/1.65 c_Power_Opower__class_Opower( X ), Z ), U ) ), hAPP( hAPP(
% 0.97/1.65 c_Power_Opower__class_Opower( X ), Y ), T ) ) ) }.
% 0.97/1.65 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.97/1.65 X ), T ), Z ) ), Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 0.97/1.65 ( tc_Nat_Onat, U ), Z ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X
% 0.97/1.65 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), U ) ), Y ) ) }.
% 0.97/1.65 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! hBOOL
% 0.97/1.65 ( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), T ),
% 0.97/1.65 hAPP( hAPP( c_Polynomial_Osmult( X ), Y ), Z ) ) ), hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), T ), Z ) ) }.
% 0.97/1.65 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! hBOOL
% 0.97/1.65 ( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), T ),
% 0.97/1.65 Z ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly(
% 0.97/1.65 X ) ), T ), hAPP( hAPP( c_Polynomial_Osmult( X ), Y ), Z ) ) ) }.
% 0.97/1.65 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 0.97/1.65 ( tc_Polynomial_Opoly( X ) ), Z ), Y ) ), T = c_Groups_Ozero__class_Ozero
% 0.97/1.65 ( X ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly(
% 0.97/1.65 X ) ), hAPP( hAPP( c_Polynomial_Osmult( X ), T ), Z ) ), Y ) ) }.
% 0.97/1.65 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 0.97/1.65 ( tc_Polynomial_Opoly( X ) ), T ), hAPP( hAPP( c_Polynomial_Osmult( X ),
% 0.97/1.65 Z ), Y ) ) ), Z = c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), T ), Y ) ) }.
% 0.97/1.65 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 0.97/1.65 ( tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Polynomial_Osmult( X ), T ),
% 0.97/1.65 Z ) ), Y ) ), alpha9( X, Y, T ) }.
% 0.97/1.65 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 0.97/1.65 ( tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Polynomial_Osmult( X ), T ),
% 0.97/1.65 Z ) ), Y ) ), alpha26( X, Y, Z, T ) }.
% 0.97/1.65 { ! class_Fields_Ofield( X ), ! alpha9( X, Y, T ), ! alpha26( X, Y, Z, T )
% 0.97/1.65 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) )
% 0.97/1.65 , hAPP( hAPP( c_Polynomial_Osmult( X ), T ), Z ) ), Y ) ) }.
% 0.97/1.65 { ! alpha26( X, Y, Z, T ), T = c_Groups_Ozero__class_Ozero( X ), hBOOL(
% 0.97/1.65 hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Z ), Y
% 0.97/1.65 ) ) }.
% 0.97/1.65 { ! T = c_Groups_Ozero__class_Ozero( X ), alpha26( X, Y, Z, T ) }.
% 0.97/1.65 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) )
% 0.97/1.65 , Z ), Y ) ), alpha26( X, Y, Z, T ) }.
% 0.97/1.65 { ! alpha9( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.65 { Z = c_Groups_Ozero__class_Ozero( X ), alpha9( X, Y, Z ) }.
% 0.97/1.65 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha9( X
% 0.97/1.65 , Y, Z ) }.
% 0.97/1.65 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 0.97/1.65 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 0.97/1.65 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 0.97/1.65 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.97/1.65 c_Groups_Ouminus__class_Ouminus( X, Z ) = c_Groups_Ouminus__class_Ouminus
% 0.97/1.65 ( X, Y ), Z = Y }.
% 0.97/1.65 { ! class_Lattices_Oboolean__algebra( X ), ! Z = Y,
% 0.97/1.65 c_Groups_Ouminus__class_Ouminus( X, Z ) = c_Groups_Ouminus__class_Ouminus
% 0.97/1.65 ( X, Y ) }.
% 0.97/1.65 { ! class_Groups_Ouminus( X ), hAPP( c_Groups_Ouminus__class_Ouminus(
% 0.97/1.65 tc_fun( T, X ), Z ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( Z, Y
% 0.97/1.65 ) ) }.
% 0.97/1.65 { ! class_Lattices_Oboolean__algebra( X ), c_Groups_Ouminus__class_Ouminus
% 0.97/1.65 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 0.97/1.65 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.65 tc_Nat_Onat ) ), Z ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X )
% 0.97/1.65 , Y ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.97/1.65 { ! class_Rings_Ocomm__semiring__1( X ), ! Y = c_Groups_Oone__class_Oone( X
% 0.97/1.65 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Y ), hAPP( hAPP(
% 0.97/1.65 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.97/1.65 { ! class_Groups_Ouminus( X ), hAPP( c_Groups_Ouminus__class_Ouminus(
% 0.97/1.65 tc_fun( T, X ), Z ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( Z, Y
% 0.97/1.65 ) ) }.
% 0.97/1.65 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.97/1.65 c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 0.97/1.65 c_Polynomial_OpCons( X ), c_Groups_Ouminus__class_Ouminus( X, Y ) ), hAPP
% 0.97/1.65 ( hAPP( c_Polynomial_OpCons( X ), c_Groups_Oone__class_Oone( X ) ),
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ), Z ) ) }.
% 0.97/1.65 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.97/1.65 tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Polynomial_OpCons( X ),
% 0.97/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ) ), hAPP( hAPP(
% 0.97/1.65 c_Polynomial_OpCons( X ), c_Groups_Oone__class_Oone( X ) ),
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ), Z ) ),
% 0.97/1.65 hAPP( c_Polynomial_Opoly( X, Z ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.65 }.
% 0.97/1.65 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.97/1.65 tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Polynomial_OpCons( X ), Z ),
% 0.97/1.65 hAPP( hAPP( c_Polynomial_OpCons( X ), c_Groups_Oone__class_Oone( X ) ),
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ),
% 0.97/1.65 hAPP( c_Polynomial_Opoly( X, Y ), c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.97/1.65 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.65 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Y ),
% 0.97/1.65 c_Groups_Ouminus__class_Ouminus( X, Z ) ) = c_Groups_Ozero__class_Ozero(
% 0.97/1.65 X ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X
% 0.97/1.65 ) ), hAPP( hAPP( c_Polynomial_OpCons( X ), Z ), hAPP( hAPP(
% 0.97/1.65 c_Polynomial_OpCons( X ), c_Groups_Oone__class_Oone( X ) ),
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ) }.
% 0.97/1.65 { ! class_Rings_Oidom( X ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.97/1.65 tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.97/1.65 tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Polynomial_OpCons( X ),
% 0.97/1.65 c_Groups_Ouminus__class_Ouminus( X, Z ) ), hAPP( hAPP(
% 0.97/1.65 c_Polynomial_OpCons( X ), c_Groups_Oone__class_Oone( X ) ),
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ),
% 0.97/1.65 c_Polynomial_Oorder( X, Z, Y ) ) ), Y ) ) }.
% 0.97/1.65 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 0.97/1.65 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ), hBOOL(
% 0.97/1.65 hAPP( Z, skol14( U, W, Z ) ) ) }.
% 0.97/1.65 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 0.97/1.65 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ), hBOOL(
% 0.97/1.65 hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Y ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( X ), skol14( X, Y, Z ) ),
% 0.97/1.65 c_Groups_Ozero__class_Ozero( X ) ) ) ) }.
% 0.97/1.65 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 0.97/1.65 hAPP( c_Rings_Odvd__class_Odvd( X ), Y ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( X ), T ), c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.65 ) ), ! hBOOL( hAPP( Z, T ) ), hBOOL( hAPP( Z, hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), skol33( X, Y, Z ) ) ) ) }.
% 0.97/1.65 { ! class_Rings_Oidom( X ), c_Polynomial_Oorder( X, Z, Y ) =
% 0.97/1.65 c_Orderings_Oord__class_OLeast( tc_Nat_Onat, hAPP( hAPP( c_COMBB(
% 0.97/1.65 tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat ), c_fNot ), hAPP( c_COMBC(
% 0.97/1.65 tc_Nat_Onat, tc_Polynomial_Opoly( X ), tc_HOL_Obool, hAPP( hAPP( c_COMBB
% 0.97/1.65 ( tc_Polynomial_Opoly( X ), tc_fun( tc_Polynomial_Opoly( X ),
% 0.97/1.65 tc_HOL_Obool ), tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 0.97/1.65 tc_Polynomial_Opoly( X ) ) ), hAPP( hAPP( c_COMBB( tc_Nat_Onat,
% 0.97/1.65 tc_Polynomial_Opoly( X ), tc_Nat_Onat ), hAPP(
% 0.97/1.65 c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 0.97/1.65 c_Polynomial_OpCons( X ), c_Groups_Ouminus__class_Ouminus( X, Z ) ), hAPP
% 0.97/1.65 ( hAPP( c_Polynomial_OpCons( X ), c_Groups_Oone__class_Oone( X ) ),
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ) ),
% 0.97/1.65 c_Nat_OSuc ) ) ), Y ) ) ) }.
% 0.97/1.65 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.97/1.65 hAPP( X, Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.65 skol15( Z, Y ) ), Y ) ) }.
% 0.97/1.65 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.97/1.65 hAPP( X, Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.97/1.65 tc_Nat_Onat, Z ), skol15( X, Y ) ) ), ! hBOOL( hAPP( X, Z ) ) }.
% 0.97/1.65 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.97/1.65 hAPP( X, Y ) ), hBOOL( hAPP( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 0.97/1.65 tc_Nat_Onat ), skol15( X, Y ) ), c_Groups_Oone__class_Oone( tc_Nat_Onat )
% 0.97/1.65 ) ) ) }.
% 0.97/1.65 { hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP(
% 0.97/1.65 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) )
% 0.97/1.65 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ),
% 0.97/1.65 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ),
% 0.97/1.65 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) ), hBOOL( hAPP( hAPP
% 0.97/1.65 ( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) )
% 0.97/1.65 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ),
% 0.97/1.65 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ), X ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ),
% 0.97/1.65 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ), X ) ), hBOOL( hAPP(
% 0.97/1.65 hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), hAPP(
% 0.97/1.65 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Y ) ) ), hBOOL(
% 0.97/1.65 hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.65 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), hAPP(
% 0.97/1.65 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Y ) ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ),
% 0.97/1.65 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ), X =
% 0.97/1.65 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.97/1.65 { ! X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), c_Groups_Oone__class_Oone(
% 0.97/1.65 tc_Nat_Onat ) ) ) }.
% 0.97/1.65 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), ! hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ) ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) ) }.
% 0.97/1.65 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), ! hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ) ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) ), hBOOL( hAPP(
% 0.97/1.65 hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ) }.
% 0.97/1.65 { ! class_Orderings_Owellorder( X ), ! hBOOL( hAPP( Y, Z ) ), hBOOL( hAPP(
% 0.97/1.65 Y, c_Orderings_Oord__class_OLeast( X, Y ) ) ) }.
% 0.97/1.65 { ! class_Orderings_Owellorder( X ), ! hBOOL( hAPP( Y, Z ) ), hBOOL( hAPP(
% 0.97/1.65 Y, c_Orderings_Oord__class_OLeast( X, Y ) ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), ! hBOOL( hAPP( hAPP
% 0.97/1.65 ( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), X ), Y ) ), ! hBOOL( hAPP(
% 0.97/1.65 hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) ), X = Y }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, X ), Y ) ), ! hBOOL( hAPP(
% 0.97/1.65 hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP( hAPP
% 0.97/1.65 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ), Z =
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) )
% 0.97/1.65 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), hAPP
% 0.97/1.65 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), U ), T ) ) ), hBOOL(
% 0.97/1.65 hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), U ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ), T ) ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) )
% 0.97/1.65 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), hAPP
% 0.97/1.65 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), U ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ), T ) ) ),
% 0.97/1.65 hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), hAPP(
% 0.97/1.65 hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), U ), T ) ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), hAPP(
% 0.97/1.65 hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ) ), hBOOL( hAPP
% 0.97/1.65 ( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) )
% 0.97/1.65 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), hAPP(
% 0.97/1.65 hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), hAPP(
% 0.97/1.65 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), X = hAPP(
% 0.97/1.65 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.65 { ! X = hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 0.97/1.65 hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), hAPP(
% 0.97/1.65 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), Y ) ), ! hBOOL( hAPP(
% 0.97/1.65 hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP
% 0.97/1.65 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ), Z =
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.65 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.65 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP
% 0.97/1.65 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ) }.
% 0.97/1.65 { ! class_Orderings_Owellorder( X ), ! hBOOL( hAPP( Z, Y ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Orderings_Oord__class_OLeast( X,
% 0.97/1.65 Z ) ), Y ) ) }.
% 0.97/1.65 { ! class_Orderings_Owellorder( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Z ), c_Orderings_Oord__class_OLeast( X
% 0.97/1.65 , Y ) ) ), ! hBOOL( hAPP( Y, Z ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) )
% 0.97/1.65 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.65 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP( hAPP
% 0.97/1.65 ( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ), hBOOL( hAPP(
% 0.97/1.65 hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP( hAPP
% 0.97/1.65 ( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y ) ), hBOOL( hAPP( hAPP
% 0.97/1.65 ( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP
% 0.97/1.65 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ), ! hBOOL( hAPP
% 0.97/1.65 ( c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.65 ( tc_Nat_Onat ) ), Z ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.97/1.65 tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.65 tc_Nat_Onat ) ) ), c_Orderings_Oord__class_OLeast( tc_Nat_Onat, X ) =
% 0.97/1.65 hAPP( c_Nat_OSuc, c_Orderings_Oord__class_OLeast( tc_Nat_Onat, hAPP( hAPP
% 0.97/1.65 ( c_COMBB( tc_Nat_Onat, tc_HOL_Obool, tc_Nat_Onat ), X ), c_Nat_OSuc ) )
% 0.97/1.65 ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP( hAPP
% 0.97/1.65 ( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ), X ) ), Y =
% 0.97/1.65 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! Y =
% 0.97/1.65 c_Groups_Oone__class_Oone( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ), X ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP( hAPP
% 0.97/1.65 ( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), X ) ), Y =
% 0.97/1.65 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! Y =
% 0.97/1.65 c_Groups_Oone__class_Oone( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), X ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP
% 0.97/1.65 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.65 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ) ) ), ! hBOOL( hAPP
% 0.97/1.65 ( c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 0.97/1.65 tc_Nat_Onat ) ), Z ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.97/1.65 tc_Nat_Onat, Y ), X ) ) }.
% 0.97/1.65 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.65 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ) ), hAPP( hAPP(
% 0.97/1.65 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) ), hBOOL( hAPP(
% 0.97/1.65 hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y ) ) }.
% 0.97/1.65 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.65 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ) ), hAPP( hAPP(
% 0.97/1.65 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP
% 0.97/1.65 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.65 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ) ), Y =
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP( hAPP
% 0.97/1.65 ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.65 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) ), Y =
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), X ) ) }.
% 0.97/1.65 { hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), X ) ) }
% 0.97/1.65 .
% 0.97/1.65 { ! Y = X, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 0.97/1.65 , X ) ) }.
% 0.97/1.65 { ! Y = X, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X )
% 0.97/1.65 , Y ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.65 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 0.97/1.65 ), Y = X }.
% 0.97/1.65 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.65 , alpha10( X, Y ), Y = X }.
% 0.97/1.65 { ! alpha10( X, Y ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.97/1.65 tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.65 { ! Y = X, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 0.97/1.65 , X ) ) }.
% 0.97/1.65 { ! alpha10( X, Y ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.97/1.65 tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.65 { ! alpha10( X, Y ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.97/1.65 tc_Nat_Onat ), X ), Y ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.65 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.97/1.65 , alpha10( X, Y ) }.
% 0.97/1.65 { ! alpha11( X, Y ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.97/1.65 tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.65 { ! alpha11( X, Y ), ! Y = X }.
% 0.97/1.65 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.65 , Y = X, alpha11( X, Y ) }.
% 0.97/1.65 { ! alpha11( X, Y ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.97/1.65 tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.65 { ! alpha11( X, Y ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.97/1.65 tc_Nat_Onat ), X ), Y ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.65 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.97/1.65 , alpha11( X, Y ) }.
% 0.97/1.65 { Y = X, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 0.97/1.65 , X ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 0.97/1.65 , X ) ) }.
% 0.97/1.65 { Y = X, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 0.97/1.65 , X ) ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X
% 0.97/1.65 ), Y ) ) }.
% 0.97/1.65 { ! Y = X, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 0.97/1.65 , X ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.65 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 0.97/1.65 ), X = Y }.
% 0.97/1.65 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.65 , ! X = Y, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X
% 0.97/1.65 ), Y ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.65 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.65 , Y = X }.
% 0.97/1.65 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.65 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 0.97/1.65 ), Y = X }.
% 0.97/1.65 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.65 , Y = X, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 0.97/1.65 , X ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.65 , Y = X, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X
% 0.97/1.65 ), Y ) ) }.
% 0.97/1.65 { ! Y = X, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X
% 0.97/1.65 ), Z ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y
% 0.97/1.65 ), Z ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.65 , ! X = Z, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y
% 0.97/1.65 ), Z ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.65 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 0.97/1.65 ), Y = X }.
% 0.97/1.65 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.65 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 0.97/1.65 ), Y = X }.
% 0.97/1.65 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.65 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 0.97/1.65 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), Z )
% 0.97/1.65 ) }.
% 0.97/1.65 { ! Y = X, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X
% 0.97/1.65 ), Z ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z
% 0.97/1.65 ), X ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y
% 0.97/1.65 ), Z ) ) }.
% 0.97/1.65 { ! Y = X, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X
% 0.97/1.65 ), Z ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z
% 0.97/1.65 ), X ) ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ),
% 0.97/1.65 Z ), Y ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.65 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 0.97/1.65 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X )
% 0.97/1.65 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), Z )
% 0.97/1.65 ) }.
% 0.97/1.65 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.65 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 0.97/1.65 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X )
% 0.97/1.65 ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y
% 0.97/1.65 ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.65 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.97/1.65 , ! Y = X }.
% 0.97/1.65 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.65 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.97/1.65 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 0.97/1.65 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X )
% 0.97/1.65 ) }.
% 0.97/1.65 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.65 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.97/1.65 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.65 }.
% 0.97/1.65 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.65 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.97/1.65 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 0.97/1.65 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X )
% 0.97/1.65 ) }.
% 0.97/1.65 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.65 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.97/1.65 , ! Y = X }.
% 0.97/1.65 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.65 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.97/1.65 , ! X = Y }.
% 0.97/1.65 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.65 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.97/1.65 , ! X = Z, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y
% 0.97/1.65 ), Z ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.65 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.97/1.65 , ! X = Z, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ),
% 0.97/1.65 Z ), Y ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.65 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.97/1.65 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 0.97/1.65 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), Z )
% 0.97/1.65 ) }.
% 0.97/1.65 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.65 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.97/1.65 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 0.97/1.65 ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y
% 0.97/1.65 ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.65 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.97/1.65 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 0.97/1.65 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X )
% 0.97/1.65 ) }.
% 0.97/1.65 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.65 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.97/1.65 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 0.97/1.65 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X )
% 0.97/1.65 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), Z )
% 0.97/1.65 ) }.
% 0.97/1.65 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.65 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.97/1.65 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 0.97/1.65 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X )
% 0.97/1.65 ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y
% 0.97/1.65 ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.65 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.97/1.65 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 0.97/1.65 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X )
% 0.97/1.65 ) }.
% 0.97/1.65 { hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ),
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.97/1.65 { hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ),
% 0.97/1.65 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP( hAPP
% 0.97/1.65 ( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.65 tc_Nat_Onat ) ), Y ) ) }.
% 0.97/1.65 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.65 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ), hAPP( hAPP(
% 0.97/1.65 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ) ) ), hBOOL( hAPP(
% 0.97/1.65 hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ) }.
% 0.97/1.65 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.65 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ), hAPP( hAPP(
% 0.97/1.65 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ) ) ) }.
% 0.97/1.65 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oorder_Ostrict__mono(
% 0.97/1.65 tc_Nat_Onat, X, hAPP( hAPP( c_COMBS( tc_Nat_Onat, tc_fun( tc_Nat_Onat,
% 0.97/1.65 tc_HOL_Obool ), tc_fun( tc_Nat_Onat, tc_HOL_Obool ) ), hAPP( hAPP(
% 0.97/1.65 c_COMBB( tc_fun( tc_Nat_Onat, tc_fun( tc_HOL_Obool, tc_HOL_Obool ) ),
% 0.97/1.65 tc_fun( tc_fun( tc_Nat_Onat, tc_HOL_Obool ), tc_fun( tc_Nat_Onat,
% 0.97/1.65 tc_HOL_Obool ) ), tc_Nat_Onat ), c_COMBS( tc_Nat_Onat, tc_HOL_Obool,
% 0.97/1.65 tc_HOL_Obool ) ), hAPP( hAPP( c_COMBB( tc_fun( tc_Nat_Onat, tc_HOL_Obool
% 0.97/1.65 ), tc_fun( tc_Nat_Onat, tc_fun( tc_HOL_Obool, tc_HOL_Obool ) ),
% 0.97/1.65 tc_Nat_Onat ), hAPP( c_COMBB( tc_HOL_Obool, tc_fun( tc_HOL_Obool,
% 0.97/1.65 tc_HOL_Obool ), tc_Nat_Onat ), c_fconj ) ), c_Rings_Odvd__class_Odvd(
% 0.97/1.65 tc_Nat_Onat ) ) ) ), hAPP( hAPP( c_COMBB( tc_fun( tc_Nat_Onat,
% 0.97/1.65 tc_HOL_Obool ), tc_fun( tc_Nat_Onat, tc_HOL_Obool ), tc_Nat_Onat ), hAPP
% 0.97/1.65 ( c_COMBB( tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat ), c_fNot ) ), c_COMBC
% 0.97/1.65 ( tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool, c_Rings_Odvd__class_Odvd(
% 0.97/1.65 tc_Nat_Onat ) ) ) ), Y ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.97/1.65 tc_Nat_Onat ), T ), Z ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.97/1.65 tc_Nat_Onat ), Z ), T ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X
% 0.97/1.65 , hAPP( Y, T ) ), hAPP( Y, Z ) ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), hBOOL( hAPP( Y,
% 0.97/1.65 skol16( Z, Y ) ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.97/1.65 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), T ) ), ! hBOOL
% 0.97/1.65 ( hAPP( Y, U ) ), hBOOL( hAPP( Y, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.97/1.65 ( tc_Int_Oint ), U ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.65 tc_Int_Oint ), T ), X ) ) ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP( Y,
% 0.97/1.65 hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), skol16( X, Y ) )
% 0.97/1.65 , X ) ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint
% 0.97/1.65 , c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Z ) ), ! hBOOL( hAPP( Y,
% 0.97/1.65 T ) ), hBOOL( hAPP( Y, hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 0.97/1.65 tc_Int_Oint ), T ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.65 tc_Int_Oint ), Z ), X ) ) ) ) }.
% 0.97/1.65 { ! class_Groups_Omonoid__mult( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.65 tc_Nat_Onat ) ), Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.97/1.65 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ),
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 0.97/1.65 ( tc_Nat_Onat ) ) ) ), Z ) = hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.97/1.65 ), Z ), Y ) }.
% 0.97/1.65 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ),
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ), ! hBOOL( hAPP(
% 0.97/1.65 hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y ) ), ! hBOOL( hAPP
% 0.97/1.65 ( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), Y ) ), hBOOL( hAPP
% 0.97/1.65 ( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ),
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ), ! hBOOL( hAPP(
% 0.97/1.65 hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X ) ), ! hBOOL( hAPP
% 0.97/1.65 ( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), Y ) ), hBOOL( hAPP
% 0.97/1.65 ( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.65 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), Z )
% 0.97/1.65 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ),
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) ) }.
% 0.97/1.65 { ! class_Rings_Ocomm__ring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( X ), Z ), T ) ), hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( X ), Z ), c_Groups_Ominus__class_Ominus( X, Y,
% 0.97/1.65 T ) ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), Y ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), Y ) ),
% 0.97/1.65 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.65 tc_Nat_Onat ) ), Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.97/1.65 tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ), Y ) )
% 0.97/1.65 }.
% 0.97/1.65 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ), hAPP( c_Nat_OSuc, Y
% 0.97/1.65 ) ) ) }.
% 0.97/1.65 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) =
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.97/1.65 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.65 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.97/1.65 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.97/1.65 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( c_Nat_OSuc, X ), Y )
% 0.97/1.65 = hAPP( c_Nat_OSuc, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) )
% 0.97/1.65 }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z ),
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ), Y ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ), Y ) ), hBOOL(
% 0.97/1.65 hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z ),
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.97/1.65 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), hAPP
% 0.97/1.65 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ),
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) = Y }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.97/1.65 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), Z )
% 0.97/1.65 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ),
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), Z ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.97/1.65 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), Z )
% 0.97/1.65 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), Z ) )
% 0.97/1.65 , hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ),
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), !
% 0.97/1.65 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), Y ) ),
% 0.97/1.65 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, Z ) ),
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.97/1.65 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ), Y ) = hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), c_Groups_Ominus__class_Ominus
% 0.97/1.65 ( tc_Nat_Onat, X, Y ) ), Z ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.97/1.65 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ),
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), Z ) =
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ), Y ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.97/1.65 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ), Y ) = hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ),
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.97/1.65 , ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z, X = hAPP(
% 0.97/1.65 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.97/1.65 , ! X = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y )
% 0.97/1.65 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.97/1.65 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ),
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), Y ) = X }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.97/1.65 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ),
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), X ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.97/1.65 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 0.97/1.65 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), X ) ),
% 0.97/1.65 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ),
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.97/1.65 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ),
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ), Y ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.97/1.65 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ),
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = X }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.97/1.65 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ),
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ), Y ) ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ), X ) ), hBOOL( hAPP
% 0.97/1.65 ( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Y ) ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), hAPP
% 0.97/1.65 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Y ) ) ), hBOOL(
% 0.97/1.65 hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ), X ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.97/1.65 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z,
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ), X ) }.
% 0.97/1.65 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, hAPP( c_Nat_OSuc, X ) ) =
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.65 ( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) }.
% 0.97/1.65 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( c_Nat_OSuc, X ),
% 0.97/1.65 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 0.97/1.65 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ), Y ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.97/1.65 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ) ),
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.97/1.65 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, Z ) ),
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.97/1.65 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = Y }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.97/1.65 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), Z )
% 0.97/1.65 ), ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X = Z }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.97/1.65 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), Z )
% 0.97/1.65 ), ! X = Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.97/1.65 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), Z )
% 0.97/1.65 ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) =
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.97/1.65 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), Z )
% 0.97/1.65 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ),
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), Z ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.97/1.65 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), Z )
% 0.97/1.65 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), Z
% 0.97/1.65 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ),
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) ) }.
% 0.97/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.65 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.97/1.65 ( X, Z, Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, U ), T
% 0.97/1.65 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 0.97/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.65 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.97/1.65 ( X, Z, Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ), Y
% 0.97/1.65 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, U ), T ) ) }.
% 0.97/1.65 { ! class_Groups_Ominus( X ), hAPP( c_Groups_Ominus__class_Ominus( tc_fun(
% 0.97/1.65 U, X ), T, Z ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( T, Y ),
% 0.97/1.65 hAPP( Z, Y ) ) }.
% 0.97/1.65 { ! class_Groups_Ominus( X ), hAPP( c_Groups_Ominus__class_Ominus( tc_fun(
% 0.97/1.65 U, X ), T, Z ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( T, Y ),
% 0.97/1.65 hAPP( Z, Y ) ) }.
% 0.97/1.65 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 0.97/1.65 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Polynomial_OpCons( X ), U ), T )
% 0.97/1.65 , hAPP( hAPP( c_Polynomial_OpCons( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.65 c_Polynomial_OpCons( X ), c_Groups_Ominus__class_Ominus( X, U, Z ) ),
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 0.97/1.65 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.97/1.65 c_Groups_Ominus__class_Ominus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 0.97/1.65 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.97/1.65 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.65 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ), Y ) }.
% 0.97/1.65 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.97/1.65 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! U = T, Z = Y }.
% 0.97/1.65 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.97/1.65 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! Z = Y, U = T }.
% 0.97/1.65 { ! class_Rings_Ocomm__ring( X ), hAPP( hAPP( c_Polynomial_Osmult( X ),
% 0.97/1.65 c_Groups_Ominus__class_Ominus( X, T, Z ) ), Y ) =
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 0.97/1.65 c_Polynomial_Osmult( X ), T ), Y ), hAPP( hAPP( c_Polynomial_Osmult( X )
% 0.97/1.65 , Z ), Y ) ) }.
% 0.97/1.65 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 0.97/1.65 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, T, Z ),
% 0.97/1.65 c_Polynomial_Omonom( X, Y, Z ) ) = c_Polynomial_Omonom( X,
% 0.97/1.65 c_Groups_Ominus__class_Ominus( X, T, Y ), Z ) }.
% 0.97/1.65 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) =
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.97/1.65 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.65 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ), X ) = Y }.
% 0.97/1.65 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ), Y ) = X }.
% 0.97/1.65 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.65 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.97/1.65 Z, hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.65 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) =
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 0.97/1.65 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Y ) ) =
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ) }.
% 0.97/1.65 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( c_Nat_OSuc, Y ), hAPP(
% 0.97/1.65 c_Nat_OSuc, X ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }
% 0.97/1.65 .
% 0.97/1.65 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.65 ( tc_Nat_Onat, hAPP( c_Nat_OSuc, Z ), Y ), hAPP( c_Nat_OSuc, X ) ) =
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.65 ( tc_Nat_Onat, Z, Y ), X ) }.
% 0.97/1.65 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.65 tc_Nat_Onat ), X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.65 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = X }.
% 0.97/1.65 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, X ) =
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.65 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.97/1.65 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, hAPP(
% 0.97/1.65 hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), Y ), Y ) = Z }.
% 0.97/1.65 { ! class_Groups_Ogroup__add( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.97/1.65 ( X ), c_Groups_Ominus__class_Ominus( X, Z, Y ) ), Y ) = Z }.
% 0.97/1.65 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 0.97/1.65 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.65 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 0.97/1.65 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.65 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 0.97/1.65 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.65 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 0.97/1.65 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.65 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.97/1.65 ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.97/1.65 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ominus__class_Ominus(
% 0.97/1.65 X, Z, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.65 { ! class_Groups_Oab__group__add( X ), ! Z = Y,
% 0.97/1.65 c_Groups_Ominus__class_Ominus( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.97/1.65 ) }.
% 0.97/1.65 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.97/1.65 Z, Y ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.97/1.65 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y, Y )
% 0.97/1.65 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.65 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.97/1.65 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.97/1.65 ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ),
% 0.97/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.97/1.65 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.97/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) }.
% 0.97/1.65 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X, Z
% 0.97/1.65 , Y ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ),
% 0.97/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.97/1.65 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z, Y )
% 0.97/1.65 = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ),
% 0.97/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.97/1.65 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.97/1.65 X, Y ) }.
% 0.97/1.65 { ! class_Rings_Oring( X ), ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( X )
% 0.97/1.65 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) = hAPP
% 0.97/1.65 ( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ), T = hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.97/1.65 W ) ), U ) ), Y ) }.
% 0.97/1.65 { ! class_Rings_Oring( X ), ! T = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 0.97/1.65 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.97/1.65 c_Groups_Ominus__class_Ominus( X, Z, W ) ), U ) ), Y ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) = hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) }.
% 0.97/1.65 { ! class_Rings_Oring( X ), ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( X )
% 0.97/1.65 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) = hAPP
% 0.97/1.65 ( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.97/1.65 Z ) ), U ) ), T ) = Y }.
% 0.97/1.65 { ! class_Rings_Oring( X ), ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( X )
% 0.97/1.65 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.97/1.65 c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ) ), T ) = Y, hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) = hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) }.
% 0.97/1.65 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.97/1.65 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.97/1.65 ( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.97/1.65 c_Groups_Ominus__class_Ominus( X, U, Z ) ), c_Groups_Ominus__class_Ominus
% 0.97/1.65 ( X, T, Y ) ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.97/1.65 c_Groups_Ominus__class_Ominus( X, U, Z ) ), Y ) ) ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ominus__class_Ominus( X
% 0.97/1.65 , T, Y ) ) ) }.
% 0.97/1.65 { ! class_Rings_Oring( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), U ), c_Groups_Ominus__class_Ominus( X
% 0.97/1.65 , T, Y ) ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.97/1.65 c_Groups_Ominus__class_Ominus( X, U, Z ) ), Y ) ) }.
% 0.97/1.65 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.97/1.65 ) ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.97/1.65 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.97/1.65 ) ), c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 0.97/1.65 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 0.97/1.65 , Y ) ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.97/1.65 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 0.97/1.65 , Y ) ), c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 0.97/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.65 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.97/1.65 ( X, Z, Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, U ), T ) )
% 0.97/1.65 , hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 0.97/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.65 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.97/1.65 ( X, Z, Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Z ), Y ) )
% 0.97/1.65 , hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, U ), T ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), !
% 0.97/1.65 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), Z ) ),
% 0.97/1.65 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ) ),
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 0.97/1.65 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, Z ) ), X ) ) }.
% 0.97/1.65 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.97/1.65 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) =
% 0.97/1.65 c_Groups_Ominus__class_Ominus( X, Y, Z ) }.
% 0.97/1.65 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, T ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.97/1.65 W ) ), U ) ), Y ) ) ) }.
% 0.97/1.65 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, T ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.97/1.65 W ) ), U ) ), Y ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.65 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) ) ) }.
% 0.97/1.65 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.97/1.65 Z ) ), U ) ), T ) ), Y ) ) }.
% 0.97/1.65 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.97/1.65 Z ) ), U ) ), T ) ), Y ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) ) ) }.
% 0.97/1.65 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.97/1.65 ( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) )
% 0.97/1.65 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.97/1.65 ( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.97/1.65 c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ) ), T ) ), Y ) ) }.
% 0.97/1.65 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.97/1.65 ( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.97/1.65 c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ) ), T ) ), Y ) ), hBOOL(
% 0.97/1.65 hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) ) ) }.
% 0.97/1.65 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.97/1.65 ( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) )
% 0.97/1.65 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, T ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.97/1.65 W ) ), U ) ), Y ) ) ) }.
% 0.97/1.65 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( X, T ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.97/1.65 W ) ), U ) ), Y ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 0.97/1.65 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) ) ) }.
% 0.97/1.65 { ! class_Rings_Oring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP
% 0.97/1.65 ( c_Groups_Otimes__class_Otimes( X ), Y ), Y ), c_Groups_Oone__class_Oone
% 0.97/1.65 ( X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( X ), Y ), c_Groups_Oone__class_Oone( X ) ) )
% 0.97/1.65 , c_Groups_Ominus__class_Ominus( X, Y, c_Groups_Oone__class_Oone( X ) ) )
% 0.97/1.65 }.
% 0.97/1.65 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), ! hBOOL( hAPP(
% 0.97/1.65 hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( X ), U ), T ) ) ), hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( X ), c_Groups_Ominus__class_Ominus( X, U,
% 0.97/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ) ), T ) ) ) }.
% 0.97/1.65 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), ! hBOOL( hAPP(
% 0.97/1.65 hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( X ), c_Groups_Ominus__class_Ominus( X, U,
% 0.97/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ) ), T ) ) ),
% 0.97/1.65 hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( X ), U ), T ) ) ) }.
% 0.97/1.65 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), ! hBOOL( hAPP(
% 0.97/1.65 hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( X ), U ), T ) ) ), hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( X ), c_Groups_Ominus__class_Ominus( X, U,
% 0.97/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ) ), T ) ) ) }.
% 0.97/1.65 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), ! hBOOL( hAPP(
% 0.97/1.65 hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( X ), c_Groups_Ominus__class_Ominus( X, U,
% 0.97/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ) ), T ) ) ),
% 0.97/1.65 hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( X ), U ), T ) ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.65 ( tc_Nat_Onat, X, hAPP( c_Nat_OSuc, Y ) ) ), X ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), hAPP( c_Nat_OSuc,
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, hAPP( c_Nat_OSuc,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = X }.
% 0.97/1.65 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.97/1.65 , alpha12( X, Y, Z ) }.
% 0.97/1.65 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.97/1.65 , alpha27( X, Y, Z ) }.
% 0.97/1.65 { ! alpha12( X, Y, Z ), ! alpha27( X, Y, Z ), hBOOL( hAPP( Z,
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.97/1.65 { ! alpha27( X, Y, Z ), ! Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 0.97/1.65 tc_Nat_Onat ), X ), T ), hBOOL( hAPP( Z, T ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( Z, skol17( T, U, Z ) ) ), alpha27( X, Y, Z ) }.
% 0.97/1.65 { Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), skol17(
% 0.97/1.65 X, Y, Z ) ), alpha27( X, Y, Z ) }.
% 0.97/1.65 { ! alpha12( X, Y, Z ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.97/1.65 tc_Nat_Onat, Y ), X ) ), hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero(
% 0.97/1.65 tc_Nat_Onat ) ) ) }.
% 0.97/1.65 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 0.97/1.65 alpha12( X, Y, Z ) }.
% 0.97/1.65 { ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha12
% 0.97/1.65 ( X, Y, Z ) }.
% 0.97/1.65 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.97/1.65 , ! alpha13( X, Y, Z ) }.
% 0.97/1.65 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.97/1.65 , ! alpha28( X, Y, Z ) }.
% 0.97/1.65 { alpha13( X, Y, Z ), alpha28( X, Y, Z ), hBOOL( hAPP( Z,
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.97/1.65 { ! alpha28( X, Y, Z ), ! hBOOL( hAPP( Z, skol18( T, U, Z ) ) ) }.
% 0.97/1.65 { ! alpha28( X, Y, Z ), Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 0.97/1.65 tc_Nat_Onat ), X ), skol18( X, Y, Z ) ) }.
% 0.97/1.65 { ! Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), T ),
% 0.97/1.65 hBOOL( hAPP( Z, T ) ), alpha28( X, Y, Z ) }.
% 0.97/1.65 { ! alpha13( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.97/1.65 tc_Nat_Onat, Y ), X ) ) }.
% 0.97/1.65 { ! alpha13( X, Y, Z ), ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero(
% 0.97/1.65 tc_Nat_Onat ) ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 0.97/1.65 hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha13(
% 0.97/1.65 X, Y, Z ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.97/1.65 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( c_Nat_OSuc,
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), Z ) =
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( c_Nat_OSuc, X ), hAPP(
% 0.97/1.65 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), Z ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.97/1.65 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, hAPP( c_Nat_OSuc,
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) ) =
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ), hAPP( c_Nat_OSuc, X
% 0.97/1.65 ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.97/1.65 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 0.97/1.65 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), T ) ), hAPP(
% 0.97/1.65 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), Z ) ) ), hBOOL
% 0.97/1.65 ( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ) ), T ) ), Z ) )
% 0.97/1.65 }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.97/1.65 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 0.97/1.65 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ) ), T ) ), Z ) )
% 0.97/1.65 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 0.97/1.65 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), T ) ), hAPP(
% 0.97/1.65 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), Z ) ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.97/1.65 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), T ), hAPP( hAPP
% 0.97/1.65 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), Z ) ) =
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ) ), T ), Z ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.97/1.65 , ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), T ) = hAPP(
% 0.97/1.65 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), Z ), hAPP( hAPP
% 0.97/1.65 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ) ), T ) = Z }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.97/1.65 , ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ) ), T ) = Z,
% 0.97/1.65 hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), T ) = hAPP(
% 0.97/1.65 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), Z ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.97/1.65 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 0.97/1.65 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), T ) ), hAPP(
% 0.97/1.65 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), Z ) ) ), hBOOL
% 0.97/1.65 ( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ) ), Z ) ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.97/1.65 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T ),
% 0.97/1.65 hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ) ), Z ) ) ),
% 0.97/1.65 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), T ) ), hAPP(
% 0.97/1.65 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), Z ) ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.97/1.65 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), T ), hAPP( hAPP
% 0.97/1.65 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), Z ) ) =
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, T, hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ) ), Z ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.97/1.65 , ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), T ) = hAPP(
% 0.97/1.65 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), Z ), T = hAPP(
% 0.97/1.65 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ) ), Z ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.97/1.65 , ! T = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP(
% 0.97/1.65 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ) ), Z ), hAPP(
% 0.97/1.65 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), T ) = hAPP(
% 0.97/1.65 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), Z ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), X = hAPP( c_Nat_OSuc
% 0.97/1.65 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 0.97/1.65 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), hAPP( c_Nat_OSuc,
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Groups_Oone__class_Oone
% 0.97/1.65 ( tc_Nat_Onat ) ) ) = X }.
% 0.97/1.65 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) = X }.
% 0.97/1.65 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) = hAPP( c_Nat_OSuc,
% 0.97/1.65 hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ),
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 0.97/1.65 ( tc_Nat_Onat ) ) ), X ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.97/1.65 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), T ) ), hAPP(
% 0.97/1.65 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), Z ) ) ), hBOOL
% 0.97/1.65 ( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ) ), T ) ), Z ) )
% 0.97/1.65 }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.97/1.65 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ) ), T ) ), Z ) )
% 0.97/1.65 , hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), T ) ), hAPP(
% 0.97/1.65 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), Z ) ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.97/1.65 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), T ) ), hAPP(
% 0.97/1.65 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), Z ) ) ), hBOOL
% 0.97/1.65 ( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, T ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ) ), Z ) ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.97/1.65 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, T ), hAPP(
% 0.97/1.65 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ) ), Z ) ) ),
% 0.97/1.65 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), T ) ), hAPP(
% 0.97/1.65 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), Z ) ) ) }.
% 0.97/1.65 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.65 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 0.97/1.65 ( tc_Nat_Onat ) ) ), X ) ) }.
% 0.97/1.65 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.65 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) =
% 0.97/1.65 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.97/1.65 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.65 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) = hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 0.97/1.65 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ),
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 0.97/1.65 ( tc_Nat_Onat ) ) ) ) }.
% 0.97/1.65 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP
% 0.97/1.65 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), hAPP( c_Nat_OSuc, hAPP(
% 0.97/1.65 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), hAPP( hAPP
% 0.97/1.65 ( c_Power_Opower__class_Opower( X ), Y ), hAPP( c_Nat_OSuc, hAPP(
% 0.97/1.65 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) ) = hAPP(
% 0.97/1.65 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.97/1.65 X, Z, Y ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) }.
% 0.97/1.65 { ! class_Power_Opower( X ), ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 0.97/1.65 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) =
% 0.97/1.65 c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.65 { ! class_Power_Opower( X ), Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.97/1.65 , hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) = hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.97/1.65 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ominus__class_Ominus(
% 0.97/1.65 tc_Nat_Onat, Z, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 0.97/1.65 { ! class_Groups_Omonoid__mult( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), Y ) ), hAPP( hAPP(
% 0.97/1.65 c_Power_Opower__class_Opower( X ), T ), c_Groups_Ominus__class_Ominus(
% 0.97/1.65 tc_Nat_Onat, hAPP( c_Nat_OSuc, Y ), Z ) ) = hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.65 c_Power_Opower__class_Opower( X ), T ), c_Groups_Ominus__class_Ominus(
% 0.97/1.65 tc_Nat_Onat, Y, Z ) ) ), T ) }.
% 0.97/1.65 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ),
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) ) ), ! hBOOL( hAPP(
% 0.97/1.65 hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), X ) ), hBOOL( hAPP(
% 0.97/1.65 hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ),
% 0.97/1.65 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) ),
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) ),
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ) }.
% 0.97/1.65 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( tc_Polynomial_Opoly( X ), Z ), Y ) ),
% 0.97/1.65 Z = Y, c_Polynomial_Opos__poly( X, c_Groups_Ominus__class_Ominus(
% 0.97/1.65 tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 0.97/1.65 { ! class_Rings_Olinordered__idom( X ), ! Z = Y, hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( tc_Polynomial_Opoly( X ), Z ), Y ) ) }
% 0.97/1.65 .
% 0.97/1.65 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ), hBOOL
% 0.97/1.65 ( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Polynomial_Opoly( X ), Z )
% 0.97/1.65 , Y ) ) }.
% 0.97/1.65 { ! class_Rings_Ocomm__ring( X ), hAPP( hAPP( c_Polynomial_Osmult( X ), T )
% 0.97/1.65 , c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Z, Y ) ) =
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 0.97/1.65 c_Polynomial_Osmult( X ), T ), Z ), hAPP( hAPP( c_Polynomial_Osmult( X )
% 0.97/1.65 , T ), Y ) ) }.
% 0.97/1.65 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 0.97/1.65 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 0.97/1.65 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.97/1.65 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) ) =
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.97/1.65 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ), X ) =
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.97/1.65 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( tc_Polynomial_Opoly( X ), Z ), Y ) ),
% 0.97/1.65 c_Polynomial_Opos__poly( X, c_Groups_Ominus__class_Ominus(
% 0.97/1.65 tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 0.97/1.65 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ), hBOOL
% 0.97/1.65 ( hAPP( c_Orderings_Oord__class_Oless( tc_Polynomial_Opoly( X ), Z ), Y )
% 0.97/1.65 ) }.
% 0.97/1.65 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ),
% 0.97/1.65 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) }.
% 0.97/1.65 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) = hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ),
% 0.97/1.65 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.97/1.65 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 0.97/1.65 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.97/1.65 tc_Polynomial_Opoly( X ) ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.97/1.65 tc_Polynomial_Opoly( X ), Y ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ),
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 0.97/1.65 ( tc_Int_Oint ) ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.97/1.65 tc_Int_Oint, Y ), X ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ),
% 0.97/1.65 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ),
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 0.97/1.65 ( tc_Int_Oint ) ) ) ) }.
% 0.97/1.65 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oorder_Ostrict__mono(
% 0.97/1.65 tc_Nat_Onat, X, hAPP( hAPP( c_COMBS( tc_Nat_Onat, tc_fun( tc_Nat_Onat,
% 0.97/1.65 tc_HOL_Obool ), tc_fun( tc_Nat_Onat, tc_HOL_Obool ) ), hAPP( hAPP(
% 0.97/1.65 c_COMBB( tc_fun( tc_Nat_Onat, tc_fun( tc_HOL_Obool, tc_HOL_Obool ) ),
% 0.97/1.65 tc_fun( tc_fun( tc_Nat_Onat, tc_HOL_Obool ), tc_fun( tc_Nat_Onat,
% 0.97/1.65 tc_HOL_Obool ) ), tc_Nat_Onat ), c_COMBS( tc_Nat_Onat, tc_HOL_Obool,
% 0.97/1.65 tc_HOL_Obool ) ), hAPP( hAPP( c_COMBB( tc_fun( tc_Nat_Onat, tc_HOL_Obool
% 0.97/1.65 ), tc_fun( tc_Nat_Onat, tc_fun( tc_HOL_Obool, tc_HOL_Obool ) ),
% 0.97/1.65 tc_Nat_Onat ), hAPP( c_COMBB( tc_HOL_Obool, tc_fun( tc_HOL_Obool,
% 0.97/1.65 tc_HOL_Obool ), tc_Nat_Onat ), c_fconj ) ), c_Rings_Odvd__class_Odvd(
% 0.97/1.65 tc_Nat_Onat ) ) ) ), hAPP( hAPP( c_COMBB( tc_fun( tc_Nat_Onat,
% 0.97/1.65 tc_HOL_Obool ), tc_fun( tc_Nat_Onat, tc_HOL_Obool ), tc_Nat_Onat ), hAPP
% 0.97/1.65 ( c_COMBB( tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat ), c_fNot ) ), c_COMBC
% 0.97/1.65 ( tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool, c_Rings_Odvd__class_Odvd(
% 0.97/1.65 tc_Nat_Onat ) ) ) ), Y ), c_Orderings_Oorder_Omono( tc_Nat_Onat, X,
% 0.97/1.65 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ) }.
% 0.97/1.65 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.97/1.65 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Ouminus__class_Ouminus
% 0.97/1.65 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.97/1.65 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) }.
% 0.97/1.65 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oorder_Omono( tc_Nat_Onat, X
% 0.97/1.65 , c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), ! hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), T ), Z ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, T ) ), hAPP( Y, Z ) ) ) }
% 0.97/1.65 .
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) )
% 0.97/1.65 , c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ominus__class_Ominus(
% 0.97/1.65 tc_Int_Oint, X, Y ) }.
% 0.97/1.65 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) ),
% 0.97/1.65 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint
% 0.97/1.65 ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.65 tc_Int_Oint ) ), Y ) ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP(
% 0.97/1.65 hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ), Y ) = hAPP(
% 0.97/1.65 hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Y ),
% 0.97/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, hAPP( c_Nat_OSuc,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, X ),
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.65 tc_Int_Oint ) ), Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.97/1.65 tc_Int_Oint, c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ),
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, X ),
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.97/1.65 tc_Int_Oint, Y, X ) ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ),
% 0.97/1.65 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, X ),
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.65 tc_Int_Oint ) ), Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.97/1.65 tc_Int_Oint, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.97/1.65 tc_Int_Oint, Y, X ) ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ),
% 0.97/1.65 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ),
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ),
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.97/1.65 tc_Int_Oint, Y, X ) ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Divides_Odiv__class_Odiv
% 0.97/1.65 ( tc_Int_Oint, X, Y ) ) ) }.
% 0.97/1.65 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.65 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) =
% 0.97/1.65 c_Divides_Odiv__class_Odiv( X, T, Z ) }.
% 0.97/1.65 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.65 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.97/1.65 c_Divides_Odiv__class_Odiv( X, T, Z ) }.
% 0.97/1.65 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.65 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) = Z }.
% 0.97/1.65 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.65 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = Z }.
% 0.97/1.65 { ! class_Divides_Osemiring__div( X ), ! T = c_Groups_Ozero__class_Ozero( X
% 0.97/1.65 ), c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.97/1.65 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.65 { ! class_Divides_Osemiring__div( X ), T = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.65 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.97/1.65 c_Divides_Odiv__class_Odiv( X, Z, Y ) }.
% 0.97/1.65 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.65 , c_Divides_Odiv__class_Odiv( X, Y, Y ) = c_Groups_Oone__class_Oone( X )
% 0.97/1.65 }.
% 0.97/1.65 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), c_Divides_Odiv__class_Odiv( X, Y
% 0.97/1.65 , Z ) ) = Y }.
% 0.97/1.65 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), T ), c_Divides_Odiv__class_Odiv( X, Y
% 0.97/1.65 , Z ) ) = c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.97/1.65 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Odiv( X, Y, Z )
% 0.97/1.65 ), Z ) = Y }.
% 0.97/1.65 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Odiv( X, Y, Z )
% 0.97/1.65 ), T ) = c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), T ), Z ) }.
% 0.97/1.65 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( X ), U ), T ) ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Odiv( X, Y, Z )
% 0.97/1.65 ), c_Divides_Odiv__class_Odiv( X, T, U ) ) = c_Divides_Odiv__class_Odiv
% 0.97/1.65 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.97/1.65 ( c_Groups_Otimes__class_Otimes( X ), Z ), U ) ) }.
% 0.97/1.65 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( X ), Z ), T ) ), c_Divides_Odiv__class_Odiv( X
% 0.97/1.65 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), T ), Z ) = hAPP(
% 0.97/1.65 hAPP( c_Groups_Oplus__class_Oplus( X ), c_Divides_Odiv__class_Odiv( X, Y
% 0.97/1.65 , Z ) ), c_Divides_Odiv__class_Odiv( X, T, Z ) ) }.
% 0.97/1.65 { ! class_Divides_Oring__div( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), c_Divides_Odiv__class_Odiv( X
% 0.97/1.65 , Y, c_Groups_Ouminus__class_Ouminus( X, Z ) ) =
% 0.97/1.65 c_Groups_Ouminus__class_Ouminus( X, c_Divides_Odiv__class_Odiv( X, Y, Z )
% 0.97/1.65 ) }.
% 0.97/1.65 { ! class_Divides_Oring__div( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), c_Divides_Odiv__class_Odiv( X
% 0.97/1.65 , c_Groups_Ouminus__class_Ouminus( X, Y ), Z ) =
% 0.97/1.65 c_Groups_Ouminus__class_Ouminus( X, c_Divides_Odiv__class_Odiv( X, Y, Z )
% 0.97/1.65 ) }.
% 0.97/1.65 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.65 c_Power_Opower__class_Opower( X ), c_Divides_Odiv__class_Odiv( X, Y, Z )
% 0.97/1.65 ), T ) = c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.97/1.65 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.65 c_Power_Opower__class_Opower( X ), Z ), T ) ) }.
% 0.97/1.65 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.97/1.65 ( tc_Int_Oint, Y ), c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.97/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) }.
% 0.97/1.65 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y,
% 0.97/1.65 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.97/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.97/1.65 ( tc_Int_Oint, Y ), X ) }.
% 0.97/1.65 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.97/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, X ) =
% 0.97/1.65 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.97/1.65 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X, Y,
% 0.97/1.65 c_Groups_Oone__class_Oone( X ) ) = Y }.
% 0.97/1.65 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X, Y,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.65 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.65 }.
% 0.97/1.65 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.65 tc_Int_Oint ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.97/1.65 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( X ), Z ), T ) ), ! hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( X ), c_Divides_Odiv__class_Odiv( X, Y, Z ) ),
% 0.97/1.65 c_Divides_Odiv__class_Odiv( X, T, Z ) ) ), hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( X ), Y ), T ) ) }.
% 0.97/1.65 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( X ), Z ), T ) ), ! hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( X ), Y ), T ) ), hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( X ), c_Divides_Odiv__class_Odiv( X, Y, Z ) ),
% 0.97/1.65 c_Divides_Odiv__class_Odiv( X, T, Z ) ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) )
% 0.97/1.65 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ),
% 0.97/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) = X }.
% 0.97/1.65 { ! c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X =
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), alpha14( X, Y ) }.
% 0.97/1.65 { ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.97/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.97/1.65 { ! alpha14( X, Y ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.97/1.65 { ! alpha14( X, Y ), alpha29( X, Y ), alpha35( X, Y ) }.
% 0.97/1.65 { ! alpha29( X, Y ), alpha14( X, Y ) }.
% 0.97/1.65 { ! alpha35( X, Y ), alpha14( X, Y ) }.
% 0.97/1.65 { ! alpha35( X, Y ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.97/1.65 tc_Int_Oint, Y ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 0.97/1.65 { ! alpha35( X, Y ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.97/1.65 tc_Int_Oint, X ), Y ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ),
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, X ), Y ) ), alpha35( X, Y ) }
% 0.97/1.65 .
% 0.97/1.65 { ! alpha29( X, Y ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.97/1.65 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ) }.
% 0.97/1.65 { ! alpha29( X, Y ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.97/1.65 tc_Int_Oint, Y ), X ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ), alpha29( X, Y ) }
% 0.97/1.65 .
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Divides_Odiv__class_Odiv
% 0.97/1.65 ( tc_Int_Oint, Y, X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 0.97/1.65 ( tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Divides_Odiv__class_Odiv
% 0.97/1.65 ( tc_Int_Oint, Y, X ) ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.65 tc_Int_Oint ) ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ),
% 0.97/1.65 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ), Y ) ) }
% 0.97/1.65 .
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ), Y ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.65 tc_Int_Oint ) ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.65 tc_Int_Oint ) ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) ),
% 0.97/1.65 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) ) }
% 0.97/1.65 .
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.65 tc_Int_Oint ) ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) ),
% 0.97/1.65 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) ), ! hBOOL( hAPP
% 0.97/1.65 ( c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.65 ( tc_Int_Oint ) ), Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.97/1.65 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.97/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.65 tc_Int_Oint ) ), Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 0.97/1.65 ( tc_Int_Oint, Y ), Z ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 0.97/1.65 ( tc_Int_Oint, c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ) ),
% 0.97/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ),
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ),
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, X ), Y ) ),
% 0.97/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) =
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, X ),
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Divides_Odiv__class_Odiv
% 0.97/1.65 ( tc_Int_Oint, Y, X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 0.97/1.65 ( tc_Int_Oint, Y ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, X ),
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ),
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Divides_Odiv__class_Odiv
% 0.97/1.65 ( tc_Int_Oint, Y, X ) ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ),
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.65 tc_Int_Oint ) ), Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.97/1.65 tc_Int_Oint, c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ),
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, X ),
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.65 tc_Int_Oint ) ), Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 0.97/1.65 ( tc_Int_Oint, Y ), Z ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 0.97/1.65 ( tc_Int_Oint, c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ),
% 0.97/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ) ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ),
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ),
% 0.97/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) =
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) )
% 0.97/1.65 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Z ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, Z ) ),
% 0.97/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ) ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) )
% 0.97/1.65 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Z ),
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ) ),
% 0.97/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, Z ) ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oone__class_Oone(
% 0.97/1.65 tc_Int_Oint ) ), Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.97/1.65 tc_Int_Oint, c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ), X ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ),
% 0.97/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Z, hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) =
% 0.97/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.97/1.65 tc_Int_Oint, Z, Y ), X ) }.
% 0.97/1.65 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.65 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.97/1.65 ( X ), T ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y
% 0.97/1.65 ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ),
% 0.97/1.65 c_Divides_Odiv__class_Odiv( X, T, Y ) ) }.
% 0.97/1.65 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.65 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.97/1.65 ( X ), T ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y
% 0.97/1.65 ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ),
% 0.97/1.65 c_Divides_Odiv__class_Odiv( X, T, Y ) ) }.
% 0.97/1.65 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.65 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.97/1.65 ( X ), Z ), Y ), Y ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ),
% 0.97/1.65 c_Divides_Odiv__class_Odiv( X, Z, Y ) ), c_Groups_Oone__class_Oone( X ) )
% 0.97/1.65 }.
% 0.97/1.65 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.65 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.97/1.65 ( X ), Y ), Z ), Y ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ),
% 0.97/1.65 c_Divides_Odiv__class_Odiv( X, Z, Y ) ), c_Groups_Oone__class_Oone( X ) )
% 0.97/1.65 }.
% 0.97/1.65 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.65 , Z = c_Groups_Ozero__class_Ozero( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( X ), Y ), T ) ), ! hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( X ), Z ), U ) ), ! c_Divides_Odiv__class_Odiv(
% 0.97/1.65 X, T, Y ) = c_Divides_Odiv__class_Odiv( X, U, Z ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ) = hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), U ) }.
% 0.97/1.65 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.65 , Z = c_Groups_Ozero__class_Ozero( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( X ), Y ), T ) ), ! hBOOL( hAPP( hAPP(
% 0.97/1.65 c_Rings_Odvd__class_Odvd( X ), Z ), U ) ), ! hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ) = hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), U ), c_Divides_Odiv__class_Odiv
% 0.97/1.65 ( X, T, Y ) = c_Divides_Odiv__class_Odiv( X, U, Z ) }.
% 0.97/1.65 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.65 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Y ), Z ) ), !
% 0.97/1.65 c_Divides_Odiv__class_Odiv( X, Z, Y ) = T, Z = hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ) }.
% 0.97/1.65 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.65 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Y ), Z ) ), ! Z =
% 0.97/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ),
% 0.97/1.65 c_Divides_Odiv__class_Odiv( X, Z, Y ) = T }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), hBOOL( hAPP(
% 0.97/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Nat__Transfer_Otsub( X, Y
% 0.97/1.65 ) ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ),
% 0.97/1.65 alpha15( X, Z ) }.
% 0.97/1.65 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ),
% 0.97/1.65 alpha30( X, Y, Z ) }.
% 0.97/1.65 { ! alpha15( X, Z ), ! alpha30( X, Y, Z ), hBOOL( hAPP( Z,
% 0.97/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ) }.
% 0.97/1.65 { ! alpha30( X, Y, Z ), alpha36( X, Y, Z ) }.
% 0.97/1.65 { ! alpha30( X, Y, Z ), alpha39( X, Y, Z ) }.
% 0.97/1.65 { ! alpha36( X, Y, Z ), ! alpha39( X, Y, Z ), alpha30( X, Y, Z ) }.
% 0.97/1.65 { ! alpha39( X, Y, Z ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.97/1.65 tc_Int_Oint, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), alpha42
% 0.97/1.65 ( X, Y, Z ) }.
% 0.97/1.65 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, X ),
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), alpha39( X, Y, Z ) }.
% 0.97/1.65 { ! alpha42( X, Y, Z ), alpha39( X, Y, Z ) }.
% 0.97/1.65 { ! alpha42( X, Y, Z ), ! alpha44( X, Y, T ), hBOOL( hAPP( Z, T ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( Z, skol19( T, U, Z ) ) ), alpha42( X, Y, Z ) }.
% 0.97/1.65 { alpha44( X, Y, skol19( X, Y, Z ) ), alpha42( X, Y, Z ) }.
% 0.97/1.65 { ! alpha44( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.97/1.65 tc_Int_Oint, X ), skol20( X, T, U ) ) ) }.
% 0.97/1.65 { ! alpha44( X, Y, Z ), alpha46( X, Y, Z, skol20( X, Y, Z ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, X ), T ) ), !
% 0.97/1.65 alpha46( X, Y, Z, T ), alpha44( X, Y, Z ) }.
% 0.97/1.65 { ! alpha46( X, Y, Z, T ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.97/1.65 tc_Int_Oint, T ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 0.97/1.65 { ! alpha46( X, Y, Z, T ), Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 0.97/1.65 tc_Int_Oint ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.97/1.65 X ), Z ) ), T ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T ),
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), ! Y = hAPP( hAPP(
% 0.97/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ) ), T ), alpha46( X
% 0.97/1.65 , Y, Z, T ) }.
% 0.97/1.65 { ! alpha36( X, Y, Z ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.97/1.65 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), alpha40
% 0.97/1.65 ( X, Y, Z ) }.
% 0.97/1.65 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), alpha36( X, Y, Z ) }
% 0.97/1.65 .
% 0.97/1.65 { ! alpha40( X, Y, Z ), alpha36( X, Y, Z ) }.
% 0.97/1.65 { ! alpha40( X, Y, Z ), ! alpha43( X, Y, T ), hBOOL( hAPP( Z, T ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( Z, skol21( T, U, Z ) ) ), alpha40( X, Y, Z ) }.
% 0.97/1.65 { alpha43( X, Y, skol21( X, Y, Z ) ), alpha40( X, Y, Z ) }.
% 0.97/1.65 { ! alpha43( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.97/1.65 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), skol22( T, U,
% 0.97/1.65 W ) ) ) }.
% 0.97/1.65 { ! alpha43( X, Y, Z ), alpha45( X, Y, Z, skol22( X, Y, Z ) ) }.
% 0.97/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), T ) ), ! alpha45( X, Y, Z,
% 0.97/1.66 T ), alpha43( X, Y, Z ) }.
% 0.97/1.66 { ! alpha45( X, Y, Z, T ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.97/1.66 tc_Int_Oint, T ), X ) ) }.
% 0.97/1.66 { ! alpha45( X, Y, Z, T ), Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 0.97/1.66 tc_Int_Oint ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.97/1.66 X ), Z ) ), T ) }.
% 0.97/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, T ), X ) ), !
% 0.97/1.66 Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ) ), T ), alpha45( X
% 0.97/1.66 , Y, Z, T ) }.
% 0.97/1.66 { ! alpha15( X, Y ), ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.97/1.66 hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 0.97/1.66 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), alpha15( X, Y ) }.
% 0.97/1.66 { ! hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), alpha15
% 0.97/1.66 ( X, Y ) }.
% 0.97/1.66 { ! T = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP
% 0.97/1.66 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ), alpha49
% 0.97/1.66 ( X, Z ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Z ) ), Z =
% 0.97/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.97/1.66 tc_Int_Oint, T, Z ) = Y }.
% 0.97/1.66 { ! T = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP
% 0.97/1.66 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ), alpha49
% 0.97/1.66 ( X, Z ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Z )
% 0.97/1.66 , X ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X
% 0.97/1.66 ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), Z =
% 0.97/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.97/1.66 tc_Int_Oint, T, Z ) = Y }.
% 0.97/1.66 { ! alpha49( X, Y ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.97/1.66 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ) }.
% 0.97/1.66 { ! alpha49( X, Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.97/1.66 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL
% 0.97/1.66 ( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, X ), Y ) ) }.
% 0.97/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), hBOOL( hAPP(
% 0.97/1.66 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), alpha49( X, Y ) }.
% 0.97/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), hBOOL( hAPP(
% 0.97/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, X ), Y ) ), alpha49( X, Y ) }
% 0.97/1.66 .
% 0.97/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) )
% 0.97/1.66 , c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ominus__class_Ominus(
% 0.97/1.66 tc_Int_Oint, X, Y ) }.
% 0.97/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), c_SMT_Oz3div( X, Y )
% 0.97/1.66 = c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) }.
% 0.97/1.66 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), c_SMT_Oz3div( X, Y )
% 0.97/1.66 = c_Groups_Ouminus__class_Ouminus( tc_Int_Oint,
% 0.97/1.66 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X,
% 0.97/1.66 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ) ) }.
% 0.97/1.66 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.97/1.66 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), U ), T ), hAPP( hAPP(
% 0.97/1.66 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.66 c_Groups_Oplus__class_Oplus( X ), c_Groups_Ominus__class_Ominus( X, U, Z
% 0.97/1.66 ) ), c_Groups_Ominus__class_Ominus( X, T, Y ) ) }.
% 0.97/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.97/1.66 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.66 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, Z ) ),
% 0.97/1.66 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, X, Z ) ) ) }.
% 0.97/1.66 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.66 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ), Y ) ) }.
% 0.97/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 0.97/1.66 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) =
% 0.97/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.66 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Odiv(
% 0.97/1.66 tc_Polynomial_Opoly( X ), c_Groups_Ouminus__class_Ouminus(
% 0.97/1.66 tc_Polynomial_Opoly( X ), Z ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.97/1.66 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly
% 0.97/1.66 ( X ), Z, Y ) ) }.
% 0.97/1.66 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Odiv(
% 0.97/1.66 tc_Polynomial_Opoly( X ), Z, c_Groups_Ouminus__class_Ouminus(
% 0.97/1.66 tc_Polynomial_Opoly( X ), Y ) ) = c_Groups_Ouminus__class_Ouminus(
% 0.97/1.66 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly
% 0.97/1.66 ( X ), Z, Y ) ) }.
% 0.97/1.66 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, X, hAPP( c_Nat_OSuc,
% 0.97/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) = X }.
% 0.97/1.66 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.66 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) =
% 0.97/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.66 { Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.66 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) =
% 0.97/1.66 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) }.
% 0.97/1.66 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, hAPP( hAPP(
% 0.97/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) =
% 0.97/1.66 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 0.97/1.66 tc_Nat_Onat, Z, Y ), X ) }.
% 0.97/1.66 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Odiv(
% 0.97/1.66 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Polynomial_Osmult( X ), T ), Z )
% 0.97/1.66 , Y ) = hAPP( hAPP( c_Polynomial_Osmult( X ), T ),
% 0.97/1.66 c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly( X ), Z, Y ) ) }.
% 0.97/1.66 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Odiv(
% 0.97/1.66 tc_Polynomial_Opoly( X ), T, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.66 tc_Polynomial_Opoly( X ) ), Z ), Y ) ) = c_Divides_Odiv__class_Odiv(
% 0.97/1.66 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly
% 0.97/1.66 ( X ), T, Z ), Y ) }.
% 0.97/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 0.97/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), Y ) ), hBOOL( hAPP(
% 0.97/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.66 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, Y ) ),
% 0.97/1.66 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, X ) ) ) }.
% 0.97/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ),
% 0.97/1.66 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ) = Y }.
% 0.97/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ),
% 0.97/1.66 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ) = Y }.
% 0.97/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ),
% 0.97/1.66 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.97/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) =
% 0.97/1.66 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, Y ) }.
% 0.97/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.66 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 0.97/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.66 tc_Nat_Onat ) ), Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.97/1.66 tc_Nat_Onat, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ), Y ) ) }.
% 0.97/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 0.97/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 0.97/1.66 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) =
% 0.97/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), hBOOL( hAPP(
% 0.97/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 0.97/1.66 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) = hAPP( c_Nat_OSuc,
% 0.97/1.66 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.97/1.66 tc_Nat_Onat, Y, X ), X ) ) }.
% 0.97/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), hBOOL( hAPP(
% 0.97/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 0.97/1.66 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) = hAPP( c_Nat_OSuc,
% 0.97/1.66 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.97/1.66 tc_Nat_Onat, Y, X ), X ) ) }.
% 0.97/1.66 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ),
% 0.97/1.66 alpha16( X, Z ) }.
% 0.97/1.66 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ),
% 0.97/1.66 alpha31( X, Y, Z ) }.
% 0.97/1.66 { ! alpha16( X, Z ), ! alpha31( X, Y, Z ), hBOOL( hAPP( Z,
% 0.97/1.66 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ) }.
% 0.97/1.66 { ! alpha31( X, Y, Z ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.66 alpha37( X, Y, Z ) }.
% 0.97/1.66 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha31( X, Y, Z ) }.
% 0.97/1.66 { ! alpha37( X, Y, Z ), alpha31( X, Y, Z ) }.
% 0.97/1.66 { ! alpha37( X, Y, Z ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.97/1.66 tc_Nat_Onat, T ), X ) ), alpha41( X, Y, Z, T ) }.
% 0.97/1.66 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol23( X, T, U
% 0.97/1.66 ) ), X ) ), alpha37( X, Y, Z ) }.
% 0.97/1.66 { ! alpha41( X, Y, Z, skol23( X, Y, Z ) ), alpha37( X, Y, Z ) }.
% 0.97/1.66 { ! alpha41( X, Y, Z, T ), ! Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 0.97/1.66 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.66 X ), U ) ), T ), hBOOL( hAPP( Z, U ) ) }.
% 0.97/1.66 { ! hBOOL( hAPP( Z, skol24( U, W, Z, V0 ) ) ), alpha41( X, Y, Z, T ) }.
% 0.97/1.66 { Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol24( X, Y, Z, T ) )
% 0.97/1.66 ), T ), alpha41( X, Y, Z, T ) }.
% 0.97/1.66 { ! alpha16( X, Y ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.66 hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.97/1.66 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha16( X, Y ) }.
% 0.97/1.66 { ! hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha16
% 0.97/1.66 ( X, Y ) }.
% 0.97/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 0.97/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ), Y ) ), ! hBOOL
% 0.97/1.66 ( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), hAPP( hAPP(
% 0.97/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( c_Nat_OSuc, Z )
% 0.97/1.66 ) ) ), Z = c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) }.
% 0.97/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! Z =
% 0.97/1.66 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ), hBOOL( hAPP(
% 0.97/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ), Y ) ) }.
% 0.97/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! Z =
% 0.97/1.66 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ), hBOOL( hAPP(
% 0.97/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), hAPP( hAPP(
% 0.97/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( c_Nat_OSuc, Z )
% 0.97/1.66 ) ) ) }.
% 0.97/1.66 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ),
% 0.97/1.66 alpha17( X, Z ), alpha32( X, Y, Z ) }.
% 0.97/1.66 { ! alpha17( X, Z ), hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv(
% 0.97/1.66 tc_Nat_Onat, Y, X ) ) ) }.
% 0.97/1.66 { ! alpha32( X, Y, Z ), hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv(
% 0.97/1.66 tc_Nat_Onat, Y, X ) ) ) }.
% 0.97/1.66 { ! alpha32( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.97/1.66 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 0.97/1.66 ), skol25( X, Y, T ) ) ), Y ) ) }.
% 0.97/1.66 { ! alpha32( X, Y, Z ), alpha38( X, Y, Z, skol25( X, Y, Z ) ) }.
% 0.97/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 0.97/1.66 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), T ) ), Y ) ), !
% 0.97/1.66 alpha38( X, Y, Z, T ), alpha32( X, Y, Z ) }.
% 0.97/1.66 { ! alpha38( X, Y, Z, T ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.97/1.66 tc_Nat_Onat, Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat
% 0.97/1.66 ), X ), hAPP( c_Nat_OSuc, T ) ) ) ) }.
% 0.97/1.66 { ! alpha38( X, Y, Z, T ), hBOOL( hAPP( Z, T ) ) }.
% 0.97/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), hAPP(
% 0.97/1.66 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( c_Nat_OSuc
% 0.97/1.66 , T ) ) ) ), ! hBOOL( hAPP( Z, T ) ), alpha38( X, Y, Z, T ) }.
% 0.97/1.66 { ! alpha17( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.66 { ! alpha17( X, Y ), hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero(
% 0.97/1.66 tc_Nat_Onat ) ) ) }.
% 0.97/1.66 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! hBOOL( hAPP( Y,
% 0.97/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha17( X, Y ) }.
% 0.97/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 0.97/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), Y ) ),
% 0.97/1.66 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) = hAPP( c_Nat_OSuc,
% 0.97/1.66 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.97/1.66 tc_Nat_Onat, Y, X ), X ) ) }.
% 0.97/1.66 { ! class_Rings_Olinordered__idom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.66 tc_Polynomial_Opoly( X ) ), c_Groups_Osgn__class_Osgn(
% 0.97/1.66 tc_Polynomial_Opoly( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 0.97/1.66 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.66 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.66 tc_Polynomial_Opoly( X ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless
% 0.97/1.66 ( tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.97/1.66 tc_Polynomial_Opoly( X ) ) ), Y ) ), c_Groups_Osgn__class_Osgn(
% 0.97/1.66 tc_Polynomial_Opoly( X ), Y ) = c_Groups_Oone__class_Oone(
% 0.97/1.66 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.66 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.66 tc_Polynomial_Opoly( X ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.97/1.66 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.97/1.66 tc_Polynomial_Opoly( X ) ) ), Y ) ), c_Groups_Osgn__class_Osgn(
% 0.97/1.66 tc_Polynomial_Opoly( X ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.97/1.66 tc_Polynomial_Opoly( X ), c_Groups_Oone__class_Oone( tc_Polynomial_Opoly
% 0.97/1.66 ( X ) ) ) }.
% 0.97/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), hBOOL( hAPP( Y,
% 0.97/1.66 skol26( Z, Y ) ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.97/1.66 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), T ) ), ! hBOOL
% 0.97/1.66 ( hAPP( Y, U ) ), hBOOL( hAPP( Y, c_Groups_Ominus__class_Ominus(
% 0.97/1.66 tc_Int_Oint, U, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 0.97/1.66 , T ), X ) ) ) ) }.
% 0.97/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP( Y,
% 0.97/1.66 c_Groups_Ominus__class_Ominus( tc_Int_Oint, skol26( X, Y ), X ) ) ), !
% 0.97/1.66 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Z ) ), ! hBOOL( hAPP( Y, T
% 0.97/1.66 ) ), hBOOL( hAPP( Y, c_Groups_Ominus__class_Ominus( tc_Int_Oint, T, hAPP
% 0.97/1.66 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ) ) }.
% 0.97/1.66 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 0.97/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.66 c_Groups_Osgn__class_Osgn( X, Y ) ) ), hBOOL( hAPP(
% 0.97/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 0.97/1.66 ) }.
% 0.97/1.66 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 0.97/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 0.97/1.66 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 0.97/1.66 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Osgn__class_Osgn( X, Y ) ) )
% 0.97/1.66 }.
% 0.97/1.66 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 0.97/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Osgn__class_Osgn( X, Y ) ),
% 0.97/1.66 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 0.97/1.66 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.66 ) }.
% 0.97/1.66 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 0.97/1.66 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.66 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 0.97/1.66 c_Groups_Osgn__class_Osgn( X, Y ) ), c_Groups_Ozero__class_Ozero( X ) ) )
% 0.97/1.66 }.
% 0.97/1.66 { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Osgn__class_Osgn
% 0.97/1.66 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 0.97/1.66 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Osgn__class_Osgn( X, Y ) ) }
% 0.97/1.66 .
% 0.97/1.66 { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Osgn__class_Osgn
% 0.97/1.66 ( X, c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X
% 0.97/1.66 ) }.
% 0.97/1.66 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.97/1.66 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.97/1.66 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.66 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.97/1.66 c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) =
% 0.97/1.66 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.66 { ! class_Groups_Osgn__if( X ), c_Groups_Osgn__class_Osgn( X,
% 0.97/1.66 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.66 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 0.97/1.66 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.66 }.
% 0.97/1.66 { ! class_Rings_Olinordered__idom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.66 X ), c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.66 }.
% 0.97/1.66 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 0.97/1.66 c_Groups_Osgn__class_Osgn( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.66 X ), Z ), Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.97/1.66 c_Groups_Osgn__class_Osgn( X, Z ) ), c_Groups_Osgn__class_Osgn( X, Y ) )
% 0.97/1.66 }.
% 0.97/1.66 { ! class_Rings_Olinordered__idom( X ), c_Groups_Osgn__class_Osgn( X, hAPP
% 0.97/1.66 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.66 c_Groups_Otimes__class_Otimes( X ), c_Groups_Osgn__class_Osgn( X, Z ) ),
% 0.97/1.66 c_Groups_Osgn__class_Osgn( X, Y ) ) }.
% 0.97/1.66 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 0.97/1.66 c_Groups_Osgn__class_Osgn( X, c_Groups_Oone__class_Oone( X ) ) =
% 0.97/1.66 c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.66 { ! class_Rings_Olinordered__idom( X ), c_Groups_Osgn__class_Osgn( X,
% 0.97/1.66 c_Groups_Osgn__class_Osgn( X, Y ) ) = c_Groups_Osgn__class_Osgn( X, Y ) }
% 0.97/1.66 .
% 0.97/1.66 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 0.97/1.66 = c_Groups_Oone__class_Oone( X ), hBOOL( hAPP(
% 0.97/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 0.97/1.66 ) }.
% 0.97/1.66 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 0.97/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 0.97/1.66 ), c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Oone__class_Oone( X ) }
% 0.97/1.66 .
% 0.97/1.66 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 0.97/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 0.97/1.66 ), c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Oone__class_Oone( X ) }
% 0.97/1.66 .
% 0.97/1.66 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 0.97/1.66 = c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ),
% 0.97/1.66 hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Y ),
% 0.97/1.66 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.97/1.66 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 0.97/1.66 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.66 ), c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.97/1.66 X, c_Groups_Oone__class_Oone( X ) ) }.
% 0.97/1.66 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 0.97/1.66 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.66 ), c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.97/1.66 X, c_Groups_Oone__class_Oone( X ) ) }.
% 0.97/1.66 { ! class_Groups_Osgn__if( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.66 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.66 { ! class_Groups_Osgn__if( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 0.97/1.66 hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 0.97/1.66 c_Groups_Ozero__class_Ozero( X ) ), Y ) ), c_Groups_Osgn__class_Osgn( X,
% 0.97/1.66 Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.66 { ! class_Groups_Osgn__if( X ), Y = c_Groups_Ozero__class_Ozero( X ), hBOOL
% 0.97/1.66 ( hAPP( c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X
% 0.97/1.66 ) ), Y ) ), c_Groups_Osgn__class_Osgn( X, Y ) =
% 0.97/1.66 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) }.
% 0.97/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP( hAPP
% 0.97/1.66 ( Z, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 0.97/1.66 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ), ! alpha18( X, Y, T,
% 0.97/1.66 U ), hBOOL( hAPP( hAPP( Z, T ), U ) ) }.
% 0.97/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), alpha18( X, Y,
% 0.97/1.66 skol27( X, Y, Z ), skol34( X, Y, Z ) ), hBOOL( hAPP( hAPP( Z,
% 0.97/1.66 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 0.97/1.66 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 0.97/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP( hAPP
% 0.97/1.66 ( Z, skol27( X, Y, Z ) ), skol34( X, Y, Z ) ) ), hBOOL( hAPP( hAPP( Z,
% 0.97/1.66 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 0.97/1.66 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 0.97/1.66 { ! alpha18( X, Y, Z, T ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.97/1.66 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), T ) ) }.
% 0.97/1.66 { ! alpha18( X, Y, Z, T ), alpha33( X, Y, Z, T ) }.
% 0.97/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), T ) ), ! alpha33( X, Y, Z,
% 0.97/1.66 T ), alpha18( X, Y, Z, T ) }.
% 0.97/1.66 { ! alpha33( X, Y, Z, T ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.97/1.66 tc_Int_Oint, T ), X ) ) }.
% 0.97/1.66 { ! alpha33( X, Y, Z, T ), Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 0.97/1.66 tc_Int_Oint ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.97/1.66 X ), Z ) ), T ) }.
% 0.97/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, T ), X ) ), !
% 0.97/1.66 Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ) ), T ), alpha33( X
% 0.97/1.66 , Y, Z, T ) }.
% 0.97/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, X ),
% 0.97/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), ! hBOOL( hAPP( hAPP( Z,
% 0.97/1.66 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 0.97/1.66 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ), ! alpha19( X, Y, T,
% 0.97/1.66 U ), hBOOL( hAPP( hAPP( Z, T ), U ) ) }.
% 0.97/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, X ),
% 0.97/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), alpha19( X, Y, skol28( X
% 0.97/1.66 , Y, Z ), skol35( X, Y, Z ) ), hBOOL( hAPP( hAPP( Z,
% 0.97/1.66 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 0.97/1.66 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 0.97/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, X ),
% 0.97/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), ! hBOOL( hAPP( hAPP( Z,
% 0.97/1.66 skol28( X, Y, Z ) ), skol35( X, Y, Z ) ) ), hBOOL( hAPP( hAPP( Z,
% 0.97/1.66 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 0.97/1.66 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 0.97/1.66 { ! alpha19( X, Y, Z, T ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.97/1.66 tc_Int_Oint, X ), T ) ) }.
% 0.97/1.66 { ! alpha19( X, Y, Z, T ), alpha34( X, Y, Z, T ) }.
% 0.97/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, X ), T ) ), !
% 0.97/1.66 alpha34( X, Y, Z, T ), alpha19( X, Y, Z, T ) }.
% 0.97/1.66 { ! alpha34( X, Y, Z, T ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.97/1.66 tc_Int_Oint, T ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 0.97/1.66 { ! alpha34( X, Y, Z, T ), Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 0.97/1.66 tc_Int_Oint ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.97/1.66 X ), Z ) ), T ) }.
% 0.97/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T ),
% 0.97/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), ! Y = hAPP( hAPP(
% 0.97/1.66 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ) ), T ), alpha34( X
% 0.97/1.66 , Y, Z, T ) }.
% 0.97/1.66 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.66 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), Y ), X ) = hAPP( hAPP(
% 0.97/1.66 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.66 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.97/1.66 tc_Int_Oint, Z, X ) ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) )
% 0.97/1.66 ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.66 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.97/1.66 tc_Int_Oint, Z, X ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) )
% 0.97/1.66 , X ) ) }.
% 0.97/1.66 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Divides_Odiv__class_Omod(
% 0.97/1.66 tc_Int_Oint, Y, X ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.97/1.66 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X,
% 0.97/1.66 c_Divides_Odiv__class_Omod( X, Z, Y ), Y ) = c_Groups_Ozero__class_Ozero
% 0.97/1.66 ( X ) }.
% 0.97/1.66 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero(
% 0.97/1.66 tc_Int_Oint ) ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.97/1.66 { c_Divides_Odiv__class_Omod( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero(
% 0.97/1.66 tc_Int_Oint ) ) = X }.
% 0.97/1.66 { ! class_Divides_Osemiring__div( X ), hAPP( hAPP(
% 0.97/1.66 c_Groups_Oplus__class_Oplus( X ), c_Divides_Odiv__class_Omod( X, Z, Y ) )
% 0.97/1.66 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.97/1.66 c_Divides_Odiv__class_Odiv( X, Z, Y ) ), Y ) ) = Z }.
% 0.97/1.66 { ! class_Divides_Osemiring__div( X ), hAPP( hAPP(
% 0.97/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), c_Divides_Odiv__class_Odiv( X, Y
% 0.97/1.66 , Z ) ) ), c_Divides_Odiv__class_Omod( X, Y, Z ) ) = Y }.
% 0.97/1.66 { ! class_Divides_Osemiring__div( X ), hAPP( hAPP(
% 0.97/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.66 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Odiv( X, Z, Y )
% 0.97/1.66 ), Y ) ), c_Divides_Odiv__class_Omod( X, Z, Y ) ) = Z }.
% 0.97/1.66 { ! class_Divides_Osemiring__div( X ), hAPP( hAPP(
% 0.97/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.97/1.66 ( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ),
% 0.97/1.66 c_Divides_Odiv__class_Odiv( X, Z, T ) ) ), c_Divides_Odiv__class_Omod( X
% 0.97/1.66 , Z, T ) ) ), Y ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), Y
% 0.97/1.66 ) }.
% 0.97/1.66 { ! class_Divides_Osemiring__div( X ), hAPP( hAPP(
% 0.97/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.97/1.66 ( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.97/1.66 c_Divides_Odiv__class_Odiv( X, T, Z ) ), Z ) ),
% 0.97/1.66 c_Divides_Odiv__class_Omod( X, T, Z ) ) ), Y ) = hAPP( hAPP(
% 0.97/1.66 c_Groups_Oplus__class_Oplus( X ), T ), Y ) }.
% 0.97/1.66 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.66 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), c_Divides_Odiv__class_Odiv
% 0.97/1.66 ( tc_Int_Oint, Z, Y ) ), Y ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint,
% 0.97/1.66 Z, Y ) ) ), X ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint )
% 0.97/1.66 , Z ), X ) }.
% 0.97/1.66 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.66 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.97/1.66 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, Z ) ) ),
% 0.97/1.66 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, Z ) ) ), X ) = hAPP( hAPP(
% 0.97/1.66 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), X ) }.
% 0.97/1.66 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ) = hAPP( hAPP
% 0.97/1.66 ( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.97/1.66 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ),
% 0.97/1.66 c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.97/1.66 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) ) }.
% 0.97/1.66 { Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 0.97/1.66 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ),
% 0.97/1.66 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) }.
% 0.97/1.66 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ),
% 0.97/1.66 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) =
% 0.97/1.66 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Divides_Odiv__class_Omod
% 0.97/1.66 ( tc_Int_Oint, X, Y ) ) }.
% 0.97/1.66 { c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.97/1.66 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, hAPP( hAPP(
% 0.97/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), c_Divides_Odiv__class_Odiv
% 0.97/1.66 ( tc_Int_Oint, Y, X ) ), X ) ) }.
% 0.97/1.66 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.66 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 0.97/1.66 c_Rings_Odvd__class_Odvd( X ), Z ), c_Divides_Odiv__class_Omod( X, T, Y )
% 0.97/1.66 ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), T ) ) }.
% 0.97/1.66 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.66 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 0.97/1.66 c_Rings_Odvd__class_Odvd( X ), Z ), T ) ), hBOOL( hAPP( hAPP(
% 0.97/1.66 c_Rings_Odvd__class_Odvd( X ), Z ), c_Divides_Odiv__class_Omod( X, T, Y )
% 0.97/1.66 ) ) }.
% 0.97/1.66 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.66 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), c_Divides_Odiv__class_Omod( X
% 0.97/1.66 , c_Divides_Odiv__class_Omod( X, T, Y ), Z ) = c_Divides_Odiv__class_Omod
% 0.97/1.66 ( X, T, Z ) }.
% 0.97/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) )
% 0.97/1.66 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), Z )
% 0.97/1.66 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ),
% 0.97/1.66 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Z ) ) ) }.
% 0.97/1.66 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.66 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 0.97/1.66 c_Rings_Odvd__class_Odvd( X ), Z ), T ) ), hBOOL( hAPP( hAPP(
% 0.97/1.66 c_Rings_Odvd__class_Odvd( X ), Z ), c_Divides_Odiv__class_Omod( X, Y, T )
% 0.97/1.66 ) ) }.
% 0.97/1.66 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.66 c_Rings_Odvd__class_Odvd( X ), T ), c_Divides_Odiv__class_Omod( X, Z, Y )
% 0.97/1.66 ) ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), T ), Y ) ),
% 0.97/1.66 hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), T ), Z ) ) }.
% 0.97/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ),
% 0.97/1.66 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ), ! hBOOL( hAPP( hAPP
% 0.97/1.66 ( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), X ) ), hBOOL( hAPP( hAPP
% 0.97/1.66 ( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ) }.
% 0.97/1.66 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.66 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), c_Divides_Odiv__class_Omod( X
% 0.97/1.66 , Y, Z ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.66 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.66 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), c_Divides_Odiv__class_Omod( X
% 0.97/1.66 , Y, Z ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.66 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, Y,
% 0.97/1.66 Z ) = c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP( hAPP(
% 0.97/1.66 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ) }.
% 0.97/1.66 { c_Divides_Odiv__class_Omod( tc_Int_Oint, Y,
% 0.97/1.66 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.97/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), ! c_Divides_Odiv__class_Omod
% 0.97/1.66 ( tc_Int_Oint, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.97/1.66 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.97/1.66 ( tc_Int_Oint, Y ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.97/1.66 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.97/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.97/1.66 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.97/1.66 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) =
% 0.97/1.66 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.66 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.97/1.66 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Z ) =
% 0.97/1.66 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.66 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y,
% 0.97/1.66 c_Groups_Oone__class_Oone( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.66 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.97/1.66 ( hAPP( c_Groups_Oplus__class_Oplus( X ), T ), hAPP( hAPP(
% 0.97/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Z ) =
% 0.97/1.66 c_Divides_Odiv__class_Omod( X, T, Z ) }.
% 0.97/1.66 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.97/1.66 ( hAPP( c_Groups_Oplus__class_Oplus( X ), T ), hAPP( hAPP(
% 0.97/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) =
% 0.97/1.66 c_Divides_Odiv__class_Omod( X, T, Y ) }.
% 0.97/1.66 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.66 tc_Int_Oint ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.97/1.66 { c_Divides_Odiv__class_Omod( tc_Int_Oint, X, X ) =
% 0.97/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.97/1.66 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.97/1.66 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.66 }.
% 0.97/1.66 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y,
% 0.97/1.66 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.97/1.66 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y, Y
% 0.97/1.66 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.66 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.97/1.66 ( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), Y ), Y ) =
% 0.97/1.66 c_Divides_Odiv__class_Omod( X, Z, Y ) }.
% 0.97/1.66 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.97/1.66 ( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), Y ), Z ) =
% 0.97/1.66 c_Divides_Odiv__class_Omod( X, Y, Z ) }.
% 0.97/1.66 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.97/1.66 ( hAPP( c_Groups_Oplus__class_Oplus( X ), T ), Z ), Y ) =
% 0.97/1.66 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus( X
% 0.97/1.66 ), T ), c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 0.97/1.66 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.97/1.66 ( hAPP( c_Groups_Oplus__class_Oplus( X ), T ), Z ), Y ) =
% 0.97/1.66 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus( X
% 0.97/1.66 ), c_Divides_Odiv__class_Omod( X, T, Y ) ), Z ), Y ) }.
% 0.97/1.66 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.97/1.66 ( hAPP( c_Groups_Oplus__class_Oplus( X ), T ), Z ), Y ) =
% 0.97/1.66 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus( X
% 0.97/1.66 ), c_Divides_Odiv__class_Omod( X, T, Y ) ), c_Divides_Odiv__class_Omod(
% 0.97/1.66 X, Z, Y ) ), Y ) }.
% 0.97/1.66 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.97/1.66 ( hAPP( c_Groups_Oplus__class_Oplus( X ), T ), c_Divides_Odiv__class_Omod
% 0.97/1.66 ( X, Z, Y ) ), Y ) = c_Divides_Odiv__class_Omod( X, hAPP( hAPP(
% 0.97/1.66 c_Groups_Oplus__class_Oplus( X ), T ), Z ), Y ) }.
% 0.97/1.66 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.97/1.66 ( hAPP( c_Groups_Oplus__class_Oplus( X ), c_Divides_Odiv__class_Omod( X,
% 0.97/1.66 T, Z ) ), Y ), Z ) = c_Divides_Odiv__class_Omod( X, hAPP( hAPP(
% 0.97/1.66 c_Groups_Oplus__class_Oplus( X ), T ), Y ), Z ) }.
% 0.97/1.66 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, T,
% 0.97/1.66 Z ) = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod
% 0.97/1.66 ( X, W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 0.97/1.66 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus( X
% 0.97/1.66 ), T ), W ), Z ) = c_Divides_Odiv__class_Omod( X, hAPP( hAPP(
% 0.97/1.66 c_Groups_Oplus__class_Oplus( X ), Y ), U ), Z ) }.
% 0.97/1.66 { ! class_Rings_Oidom( X ),
% 0.97/1.66 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct( X
% 0.97/1.66 ) }.
% 0.97/1.66 { ! class_Rings_Oidom( X ), class_Groups_Ocancel__ab__semigroup__add( X ) }
% 0.97/1.66 .
% 0.97/1.66 { ! class_Rings_Oidom( X ), class_Rings_Oring__1__no__zero__divisors( X ) }
% 0.97/1.66 .
% 0.97/1.66 { ! class_Rings_Oidom( X ), class_Rings_Oring__no__zero__divisors( X ) }.
% 0.97/1.66 { ! class_Rings_Oidom( X ), class_Groups_Ocancel__semigroup__add( X ) }.
% 0.97/1.66 { ! class_Rings_Oidom( X ), class_Groups_Oab__semigroup__mult( X ) }.
% 0.97/1.66 { ! class_Rings_Oidom( X ), class_Groups_Ocomm__monoid__mult( X ) }.
% 0.97/1.66 { ! class_Rings_Oidom( X ), class_Groups_Oab__semigroup__add( X ) }.
% 0.97/1.66 { ! class_Rings_Oidom( X ), class_Rings_Ono__zero__divisors( X ) }.
% 0.97/1.66 { ! class_Rings_Oidom( X ), class_Groups_Ocomm__monoid__add( X ) }.
% 0.97/1.66 { ! class_Rings_Oidom( X ), class_Rings_Ocomm__semiring__1( X ) }.
% 0.97/1.66 { ! class_Rings_Oidom( X ), class_Rings_Ocomm__semiring__0( X ) }.
% 0.97/1.66 { ! class_Rings_Oidom( X ), class_Rings_Ocomm__semiring( X ) }.
% 0.97/1.66 { ! class_Rings_Oidom( X ), class_Groups_Oab__group__add( X ) }.
% 0.97/1.66 { ! class_Rings_Oidom( X ), class_Rings_Ozero__neq__one( X ) }.
% 0.97/1.66 { ! class_Rings_Oidom( X ), class_Groups_Omonoid__mult( X ) }.
% 0.97/1.66 { ! class_Rings_Oidom( X ), class_Rings_Ocomm__ring__1( X ) }.
% 0.97/1.66 { ! class_Rings_Oidom( X ), class_Groups_Omonoid__add( X ) }.
% 0.97/1.66 { ! class_Rings_Oidom( X ), class_Rings_Osemiring__0( X ) }.
% 0.97/1.66 { ! class_Rings_Oidom( X ), class_Groups_Ogroup__add( X ) }.
% 0.97/1.66 { ! class_Rings_Oidom( X ), class_Rings_Omult__zero( X ) }.
% 0.97/1.66 { ! class_Rings_Oidom( X ), class_Rings_Ocomm__ring( X ) }.
% 0.97/1.66 { ! class_Rings_Oidom( X ), class_Rings_Osemiring( X ) }.
% 0.97/1.66 { ! class_Rings_Oidom( X ), class_Groups_Ouminus( X ) }.
% 0.97/1.66 { ! class_Rings_Oidom( X ), class_Rings_Oring__1( X ) }.
% 0.97/1.66 { ! class_Rings_Oidom( X ), class_Groups_Ominus( X ) }.
% 0.97/1.66 { ! class_Rings_Oidom( X ), class_Power_Opower( X ) }.
% 0.97/1.66 { ! class_Rings_Oidom( X ), class_Groups_Ozero( X ) }.
% 0.97/1.66 { ! class_Rings_Oidom( X ), class_Rings_Oring( X ) }.
% 0.97/1.66 { ! class_Rings_Oidom( X ), class_Groups_Oone( X ) }.
% 0.97/1.66 { ! class_Rings_Oidom( X ), class_Rings_Odvd( X ) }.
% 0.97/1.66 { ! class_Rings_Oidom( X ), class_Groups_Ocancel__comm__monoid__add( X ) }
% 0.97/1.66 .
% 0.97/1.66 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.97/1.66 class_Groups_Ocancel__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.66 { class_Groups_Ocancel__comm__monoid__add( tc_Nat_Onat ) }.
% 0.97/1.66 { class_Groups_Ocancel__comm__monoid__add( tc_Int_Oint ) }.
% 0.97/1.66 { ! class_Lattices_Oboolean__algebra( X ), class_Lattices_Oboolean__algebra
% 0.97/1.66 ( tc_fun( Y, X ) ) }.
% 0.97/1.66 { ! class_Orderings_Opreorder( X ), class_Orderings_Opreorder( tc_fun( Y, X
% 0.97/1.66 ) ) }.
% 0.97/1.66 { ! class_Orderings_Oorder( X ), class_Orderings_Oorder( tc_fun( Y, X ) ) }
% 0.97/1.66 .
% 0.97/1.66 { ! class_Orderings_Oord( X ), class_Orderings_Oord( tc_fun( Y, X ) ) }.
% 0.97/1.66 { ! class_Groups_Ouminus( X ), class_Groups_Ouminus( tc_fun( Y, X ) ) }.
% 0.97/1.66 { ! class_Groups_Ominus( X ), class_Groups_Ominus( tc_fun( Y, X ) ) }.
% 0.97/1.66 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.97/1.66 tc_Int_Oint ) }.
% 0.97/1.66 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.97/1.66 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Int_Oint ) }.
% 0.97/1.66 { class_Rings_Olinordered__comm__semiring__strict( tc_Int_Oint ) }.
% 0.97/1.66 { class_Rings_Olinordered__semiring__1__strict( tc_Int_Oint ) }.
% 0.97/1.66 { class_Rings_Olinordered__semiring__strict( tc_Int_Oint ) }.
% 0.97/1.66 { class_Groups_Oordered__ab__semigroup__add( tc_Int_Oint ) }.
% 0.97/1.66 { class_Groups_Oordered__comm__monoid__add( tc_Int_Oint ) }.
% 0.97/1.66 { class_Groups_Olinordered__ab__group__add( tc_Int_Oint ) }.
% 0.97/1.66 { class_Groups_Ocancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.97/1.66 { class_Rings_Oring__1__no__zero__divisors( tc_Int_Oint ) }.
% 0.97/1.66 { class_Rings_Oordered__cancel__semiring( tc_Int_Oint ) }.
% 0.97/1.66 { class_Rings_Olinordered__ring__strict( tc_Int_Oint ) }.
% 0.97/1.66 { class_Rings_Oring__no__zero__divisors( tc_Int_Oint ) }.
% 0.97/1.66 { class_Rings_Oordered__comm__semiring( tc_Int_Oint ) }.
% 0.97/1.66 { class_Rings_Olinordered__semiring__1( tc_Int_Oint ) }.
% 0.97/1.66 { class_Groups_Oordered__ab__group__add( tc_Int_Oint ) }.
% 0.97/1.66 { class_Groups_Ocancel__semigroup__add( tc_Int_Oint ) }.
% 0.97/1.66 { class_Rings_Olinordered__semiring( tc_Int_Oint ) }.
% 0.97/1.66 { class_Rings_Olinordered__semidom( tc_Int_Oint ) }.
% 0.97/1.66 { class_Groups_Oab__semigroup__mult( tc_Int_Oint ) }.
% 0.97/1.66 { class_Groups_Ocomm__monoid__mult( tc_Int_Oint ) }.
% 0.97/1.66 { class_Groups_Oab__semigroup__add( tc_Int_Oint ) }.
% 0.97/1.66 { class_Rings_Oordered__semiring( tc_Int_Oint ) }.
% 0.97/1.66 { class_Rings_Ono__zero__divisors( tc_Int_Oint ) }.
% 0.97/1.66 { class_Groups_Ocomm__monoid__add( tc_Int_Oint ) }.
% 0.97/1.66 { class_Rings_Olinordered__ring( tc_Int_Oint ) }.
% 0.97/1.66 { class_Rings_Olinordered__idom( tc_Int_Oint ) }.
% 0.97/1.66 { class_Rings_Ocomm__semiring__1( tc_Int_Oint ) }.
% 0.97/1.66 { class_Rings_Ocomm__semiring__0( tc_Int_Oint ) }.
% 0.97/1.66 { class_Divides_Osemiring__div( tc_Int_Oint ) }.
% 0.97/1.66 { class_Rings_Ocomm__semiring( tc_Int_Oint ) }.
% 0.97/1.66 { class_Groups_Oab__group__add( tc_Int_Oint ) }.
% 0.97/1.66 { class_Rings_Ozero__neq__one( tc_Int_Oint ) }.
% 0.97/1.66 { class_Rings_Oordered__ring( tc_Int_Oint ) }.
% 0.97/1.66 { class_Orderings_Opreorder( tc_Int_Oint ) }.
% 0.97/1.66 { class_Orderings_Olinorder( tc_Int_Oint ) }.
% 0.97/1.66 { class_Groups_Omonoid__mult( tc_Int_Oint ) }.
% 0.97/1.66 { class_Rings_Ocomm__ring__1( tc_Int_Oint ) }.
% 0.97/1.66 { class_Groups_Omonoid__add( tc_Int_Oint ) }.
% 0.97/1.66 { class_Rings_Osemiring__0( tc_Int_Oint ) }.
% 0.97/1.66 { class_Groups_Ogroup__add( tc_Int_Oint ) }.
% 0.97/1.66 { class_Divides_Oring__div( tc_Int_Oint ) }.
% 0.97/1.66 { class_Rings_Omult__zero( tc_Int_Oint ) }.
% 0.97/1.66 { class_Rings_Ocomm__ring( tc_Int_Oint ) }.
% 0.97/1.66 { class_Orderings_Oorder( tc_Int_Oint ) }.
% 0.97/1.66 { class_Int_Oring__char__0( tc_Int_Oint ) }.
% 0.97/1.66 { class_Rings_Osemiring( tc_Int_Oint ) }.
% 0.97/1.66 { class_Orderings_Oord( tc_Int_Oint ) }.
% 0.97/1.66 { class_Groups_Ouminus( tc_Int_Oint ) }.
% 0.97/1.66 { class_Groups_Osgn__if( tc_Int_Oint ) }.
% 0.97/1.66 { class_Rings_Oring__1( tc_Int_Oint ) }.
% 0.97/1.66 { class_Groups_Ominus( tc_Int_Oint ) }.
% 0.97/1.66 { class_Power_Opower( tc_Int_Oint ) }.
% 0.97/1.66 { class_Groups_Ozero( tc_Int_Oint ) }.
% 0.97/1.66 { class_Rings_Oring( tc_Int_Oint ) }.
% 0.97/1.66 { class_Rings_Oidom( tc_Int_Oint ) }.
% 0.97/1.66 { class_Groups_Oone( tc_Int_Oint ) }.
% 0.97/1.66 { class_Rings_Odvd( tc_Int_Oint ) }.
% 0.97/1.66 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.97/1.66 tc_Nat_Onat ) }.
% 0.97/1.66 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.97/1.66 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Nat_Onat ) }.
% 0.97/1.66 { class_Rings_Olinordered__comm__semiring__strict( tc_Nat_Onat ) }.
% 0.97/1.66 { class_Rings_Olinordered__semiring__strict( tc_Nat_Onat ) }.
% 0.97/1.66 { class_Groups_Oordered__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.97/1.66 { class_Groups_Oordered__comm__monoid__add( tc_Nat_Onat ) }.
% 0.97/1.66 { class_Groups_Ocancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.97/1.66 { class_Rings_Oordered__cancel__semiring( tc_Nat_Onat ) }.
% 0.97/1.66 { class_Rings_Oordered__comm__semiring( tc_Nat_Onat ) }.
% 0.97/1.66 { class_Groups_Ocancel__semigroup__add( tc_Nat_Onat ) }.
% 0.97/1.66 { class_Rings_Olinordered__semiring( tc_Nat_Onat ) }.
% 0.97/1.66 { class_Rings_Olinordered__semidom( tc_Nat_Onat ) }.
% 0.97/1.66 { class_Groups_Oab__semigroup__mult( tc_Nat_Onat ) }.
% 0.97/1.66 { class_Groups_Ocomm__monoid__mult( tc_Nat_Onat ) }.
% 0.97/1.66 { class_Groups_Oab__semigroup__add( tc_Nat_Onat ) }.
% 0.97/1.66 { class_Rings_Oordered__semiring( tc_Nat_Onat ) }.
% 0.97/1.66 { class_Rings_Ono__zero__divisors( tc_Nat_Onat ) }.
% 0.97/1.66 { class_Groups_Ocomm__monoid__add( tc_Nat_Onat ) }.
% 0.97/1.66 { class_Rings_Ocomm__semiring__1( tc_Nat_Onat ) }.
% 0.97/1.66 { class_Rings_Ocomm__semiring__0( tc_Nat_Onat ) }.
% 0.97/1.66 { class_Divides_Osemiring__div( tc_Nat_Onat ) }.
% 0.97/1.66 { class_Rings_Ocomm__semiring( tc_Nat_Onat ) }.
% 0.97/1.66 { class_Orderings_Owellorder( tc_Nat_Onat ) }.
% 0.97/1.66 { class_Rings_Ozero__neq__one( tc_Nat_Onat ) }.
% 0.97/1.66 { class_Orderings_Opreorder( tc_Nat_Onat ) }.
% 0.97/1.66 { class_Orderings_Olinorder( tc_Nat_Onat ) }.
% 0.97/1.66 { class_Groups_Omonoid__mult( tc_Nat_Onat ) }.
% 0.97/1.66 { class_Groups_Omonoid__add( tc_Nat_Onat ) }.
% 0.97/1.66 { class_Rings_Osemiring__0( tc_Nat_Onat ) }.
% 0.97/1.66 { class_Rings_Omult__zero( tc_Nat_Onat ) }.
% 0.97/1.66 { class_Orderings_Oorder( tc_Nat_Onat ) }.
% 0.97/1.66 { class_Rings_Osemiring( tc_Nat_Onat ) }.
% 0.97/1.66 { class_Orderings_Oord( tc_Nat_Onat ) }.
% 0.97/1.66 { class_Groups_Ominus( tc_Nat_Onat ) }.
% 0.97/1.66 { class_Power_Opower( tc_Nat_Onat ) }.
% 0.97/1.66 { class_Groups_Ozero( tc_Nat_Onat ) }.
% 0.97/1.66 { class_Groups_Oone( tc_Nat_Onat ) }.
% 0.97/1.66 { class_Rings_Odvd( tc_Nat_Onat ) }.
% 0.97/1.66 { class_Lattices_Oboolean__algebra( tc_HOL_Obool ) }.
% 0.97/1.66 { class_Orderings_Opreorder( tc_HOL_Obool ) }.
% 0.97/1.66 { class_Orderings_Oorder( tc_HOL_Obool ) }.
% 0.97/1.66 { class_Orderings_Oord( tc_HOL_Obool ) }.
% 0.97/1.66 { class_Groups_Ouminus( tc_HOL_Obool ) }.
% 0.97/1.66 { class_Groups_Ominus( tc_HOL_Obool ) }.
% 0.97/1.66 { ! class_Rings_Oidom( X ),
% 0.97/1.66 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.97/1.66 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.66 { ! class_Rings_Olinordered__idom( X ),
% 0.97/1.66 class_Groups_Oordered__cancel__ab__semigroup__add( tc_Polynomial_Opoly( X
% 0.97/1.66 ) ) }.
% 0.97/1.66 { ! class_Rings_Olinordered__idom( X ),
% 0.97/1.66 class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Polynomial_Opoly(
% 0.97/1.66 X ) ) }.
% 0.97/1.66 { ! class_Rings_Olinordered__idom( X ),
% 0.97/1.66 class_Rings_Olinordered__comm__semiring__strict( tc_Polynomial_Opoly( X )
% 0.97/1.66 ) }.
% 0.97/1.66 { ! class_Rings_Olinordered__idom( X ),
% 0.97/1.66 class_Rings_Olinordered__semiring__1__strict( tc_Polynomial_Opoly( X ) )
% 0.97/1.66 }.
% 0.97/1.66 { ! class_Rings_Olinordered__idom( X ),
% 0.97/1.66 class_Rings_Olinordered__semiring__strict( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.66 { ! class_Rings_Olinordered__idom( X ),
% 0.97/1.66 class_Groups_Oordered__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.66 { ! class_Rings_Olinordered__idom( X ),
% 0.97/1.66 class_Groups_Oordered__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.66 { ! class_Rings_Olinordered__idom( X ),
% 0.97/1.66 class_Groups_Olinordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.66 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.97/1.66 class_Groups_Ocancel__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.66 { ! class_Rings_Oidom( X ), class_Rings_Oring__1__no__zero__divisors(
% 0.97/1.66 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.66 { ! class_Rings_Olinordered__idom( X ),
% 0.97/1.66 class_Rings_Oordered__cancel__semiring( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.66 { ! class_Rings_Olinordered__idom( X ),
% 0.97/1.66 class_Rings_Olinordered__ring__strict( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.66 { ! class_Rings_Oidom( X ), class_Rings_Oring__no__zero__divisors(
% 0.97/1.66 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.66 { ! class_Rings_Olinordered__idom( X ),
% 0.97/1.66 class_Rings_Oordered__comm__semiring( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.66 { ! class_Rings_Olinordered__idom( X ),
% 0.97/1.66 class_Rings_Olinordered__semiring__1( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.66 { ! class_Rings_Olinordered__idom( X ),
% 0.97/1.66 class_Groups_Oordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.66 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.97/1.66 class_Groups_Ocancel__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.66 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semiring(
% 0.97/1.66 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.66 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semidom(
% 0.97/1.66 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.66 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Oab__semigroup__mult
% 0.97/1.66 ( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.66 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Ocomm__monoid__mult(
% 0.97/1.66 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.66 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Oab__semigroup__add
% 0.97/1.66 ( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.66 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__semiring(
% 0.97/1.66 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.66 { ! class_Rings_Oidom( X ), class_Rings_Ono__zero__divisors(
% 0.97/1.66 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.66 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Ocomm__monoid__add(
% 0.97/1.66 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.66 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__ring(
% 0.97/1.66 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.66 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__idom(
% 0.97/1.66 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.66 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ocomm__semiring__1(
% 0.97/1.66 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.66 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring__0(
% 0.97/1.66 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.66 { ! class_Fields_Ofield( X ), class_Divides_Osemiring__div(
% 0.97/1.66 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.66 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring(
% 0.97/1.66 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.66 { ! class_Groups_Oab__group__add( X ), class_Groups_Oab__group__add(
% 0.97/1.66 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.66 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ozero__neq__one(
% 0.97/1.66 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.66 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__ring(
% 0.97/1.66 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.66 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Opreorder(
% 0.97/1.66 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.66 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Olinorder(
% 0.97/1.66 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.66 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Omonoid__mult(
% 0.97/1.66 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.66 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Ocomm__ring__1(
% 0.97/1.66 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.66 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Omonoid__add(
% 0.97/1.66 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.66 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring__0(
% 0.97/1.66 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.66 { ! class_Groups_Oab__group__add( X ), class_Groups_Ogroup__add(
% 0.97/1.66 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.66 { ! class_Fields_Ofield( X ), class_Divides_Oring__div( tc_Polynomial_Opoly
% 0.97/1.66 ( X ) ) }.
% 0.97/1.66 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Omult__zero(
% 0.97/1.66 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.66 { ! class_Rings_Ocomm__ring( X ), class_Rings_Ocomm__ring(
% 0.97/1.66 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.66 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oorder(
% 0.97/1.66 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.66 { ! class_Rings_Olinordered__idom( X ), class_Int_Oring__char__0(
% 0.97/1.66 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.66 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring(
% 0.97/1.66 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.66 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oord(
% 0.97/1.66 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.66 { ! class_Groups_Oab__group__add( X ), class_Groups_Ouminus(
% 0.97/1.66 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.66 { ! class_Rings_Olinordered__idom( X ), class_Groups_Osgn__if(
% 0.97/1.66 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.66 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Oring__1(
% 0.97/1.66 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.66 { ! class_Groups_Oab__group__add( X ), class_Groups_Ominus(
% 0.97/1.66 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.66 { ! class_Rings_Ocomm__semiring__1( X ), class_Power_Opower(
% 0.97/1.66 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.66 { ! class_Groups_Ozero( X ), class_Groups_Ozero( tc_Polynomial_Opoly( X ) )
% 0.97/1.66 }.
% 0.97/1.66 { ! class_Rings_Ocomm__ring( X ), class_Rings_Oring( tc_Polynomial_Opoly( X
% 0.97/1.66 ) ) }.
% 0.97/1.66 { ! class_Rings_Oidom( X ), class_Rings_Oidom( tc_Polynomial_Opoly( X ) ) }
% 0.97/1.66 .
% 0.97/1.66 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Oone(
% 0.97/1.66 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.66 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Odvd(
% 0.97/1.66 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.66 { hAPP( hAPP( c_COMBK( T, Z ), Y ), X ) = Y }.
% 0.97/1.66 { hAPP( hAPP( hAPP( c_COMBB( W, U, T ), Z ), Y ), X ) = hAPP( Z, hAPP( Y, X
% 0.97/1.66 ) ) }.
% 0.97/1.66 { hAPP( hAPP( c_COMBC( W, U, T, Z ), Y ), X ) = hAPP( hAPP( Z, X ), Y ) }.
% 0.97/1.66 { hAPP( hAPP( hAPP( c_COMBS( W, U, T ), Z ), Y ), X ) = hAPP( hAPP( Z, X )
% 0.97/1.66 , hAPP( Y, X ) ) }.
% 0.97/1.66 { ! hBOOL( c_fequal( Y, X ) ), Y = X }.
% 0.97/1.66 { ! Y = X, hBOOL( c_fequal( Y, X ) ) }.
% 0.97/1.66 { ! hBOOL( hAPP( c_fNot, X ) ), ! hBOOL( X ) }.
% 0.97/1.66 { hBOOL( X ), hBOOL( hAPP( c_fNot, X ) ) }.
% 0.97/1.66 { ! hBOOL( X ), ! hBOOL( Y ), hBOOL( hAPP( hAPP( c_fconj, X ), Y ) ) }.
% 0.97/1.66 { ! hBOOL( hAPP( hAPP( c_fconj, X ), Y ) ), hBOOL( X ) }.
% 0.97/1.66 { ! hBOOL( hAPP( hAPP( c_fconj, Y ), X ) ), hBOOL( X ) }.
% 0.97/1.66 { ! v_a = c_Groups_Ozero__class_Ozero( t_a ) }.
% 0.97/1.66 { hAPP( c_Nat_OSuc, hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat )
% 0.97/1.66 , c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( t_a, v_q ) ), v_k )
% 0.97/1.66 ) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( t_a, v_cs____ ) }
% 0.97/1.66 .
% 0.97/1.66 { hAPP( c_Polynomial_Opoly( t_a, v_cs____ ), X ) = hAPP( hAPP(
% 0.97/1.66 c_Groups_Otimes__class_Otimes( t_a ), hAPP( hAPP(
% 0.97/1.66 c_Power_Opower__class_Opower( t_a ), X ), v_k ) ), hAPP( hAPP(
% 0.97/1.66 c_Groups_Oplus__class_Oplus( t_a ), v_a ), hAPP( hAPP(
% 0.97/1.66 c_Groups_Otimes__class_Otimes( t_a ), X ), hAPP( c_Polynomial_Opoly( t_a
% 0.97/1.66 , v_q ), X ) ) ) ) }.
% 0.97/1.66 { X = c_Groups_Ozero__class_Ozero( t_a ), ! hBOOL( hAPP(
% 0.97/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.66 tc_Nat_Onat ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ),
% 0.97/1.66 v_k ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ), ! hAPP( c_Nat_OSuc
% 0.97/1.66 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ),
% 0.97/1.66 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( t_a, Y ) ), hAPP( hAPP
% 0.97/1.66 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), v_k ),
% 0.97/1.66 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) =
% 0.97/1.66 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( t_a, hAPP( hAPP(
% 0.97/1.66 c_Polynomial_OpCons( t_a ), v_c____ ), v_cs____ ) ), ! hAPP( hAPP(
% 0.97/1.66 c_Groups_Otimes__class_Otimes( t_a ), skol29( X, Y ) ), hAPP( hAPP(
% 0.97/1.66 c_Groups_Otimes__class_Otimes( t_a ), hAPP( hAPP(
% 0.97/1.66 c_Power_Opower__class_Opower( t_a ), skol29( X, Y ) ), v_k ) ), hAPP(
% 0.97/1.66 hAPP( c_Groups_Oplus__class_Oplus( t_a ), v_a ), hAPP( hAPP(
% 0.97/1.66 c_Groups_Otimes__class_Otimes( t_a ), skol29( X, Y ) ), hAPP(
% 0.97/1.66 c_Polynomial_Opoly( t_a, v_q ), skol29( X, Y ) ) ) ) ) ) = hAPP( hAPP(
% 0.97/1.66 c_Groups_Otimes__class_Otimes( t_a ), hAPP( hAPP(
% 0.97/1.66 c_Power_Opower__class_Opower( t_a ), skol29( X, Y ) ), hAPP( hAPP(
% 0.97/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), v_k ),
% 0.97/1.66 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ), hAPP( hAPP(
% 0.97/1.66 c_Groups_Oplus__class_Oplus( t_a ), X ), hAPP( hAPP(
% 0.97/1.66 c_Groups_Otimes__class_Otimes( t_a ), skol29( X, Y ) ), hAPP(
% 0.97/1.66 c_Polynomial_Opoly( t_a, Y ), skol29( X, Y ) ) ) ) ) }.
% 0.97/1.66 { class_Rings_Oidom( t_a ) }.
% 0.97/1.66
% 0.97/1.66 *** allocated 15000 integers for clauses
% 0.97/1.66 *** allocated 22500 integers for clauses
% 0.97/1.66 *** allocated 33750 integers for clauses
% 0.97/1.66 *** allocated 50625 integers for clauses
% 0.97/1.66 *** allocated 75937 integers for clauses
% 0.97/1.66 *** allocated 113905 integers for clauses
% 0.97/1.66 percentage equality = 0.260558, percentage horn = 0.908016
% 0.97/1.66 This is a problem with some equality
% 0.97/1.66
% 0.97/1.66
% 0.97/1.66
% 0.97/1.66 Options Used:
% 0.97/1.66
% 0.97/1.66 useres = 1
% 0.97/1.66 useparamod = 1
% 0.97/1.66 useeqrefl = 1
% 0.97/1.66 useeqfact = 1
% 0.97/1.66 usefactor = 1
% 0.97/1.66 usesimpsplitting = 0
% 0.97/1.66 usesimpdemod = 5
% 0.97/1.66 usesimpres = 3
% 0.97/1.66
% 0.97/1.66 resimpinuse = 1000
% 0.97/1.66 resimpclauses = 20000
% 0.97/1.66 substype = eqrewr
% 0.97/1.66 backwardsubs = 1
% 0.97/1.66 selectoldest = 5
% 0.97/1.66
% 0.97/1.66 litorderings [0] = split
% 0.97/1.66 litorderings [1] = extend the termordering, first sorting on arguments
% 0.97/1.66
% 0.97/1.66 termordering = kbo
% 0.97/1.66
% 0.97/1.66 litapriori = 0
% 0.97/1.66 termapriori = 1
% 0.97/1.66 litaposteriori = 0
% 0.97/1.66 termaposteriori = 0
% 0.97/1.66 demodaposteriori = 0
% 0.97/1.66 ordereqreflfact = 0
% 0.97/1.66
% 0.97/1.66 litselect = negord
% 0.97/1.66
% 0.97/1.66 maxweight = 15
% 0.97/1.66 maxdepth = 30000
% 0.97/1.66 maxlength = 115
% 0.97/1.66 maxnrvars = 195
% 0.97/1.66 excuselevel = 1
% 0.97/1.66 increasemaxweight = 1
% 0.97/1.66
% 0.97/1.66 maxselected = 10000000
% 0.97/1.66 maxnrclauses = 10000000
% 0.97/1.66
% 0.97/1.66 showgenerated = 0
% 0.97/1.66 showkept = 0
% 0.97/1.66 showselected = 0
% 0.97/1.66 showdeleted = 0
% 0.97/1.66 showresimp = 1
% 0.97/1.66 showstatus = 2000
% 0.97/1.66
% 0.97/1.66 prologoutput = 0
% 0.97/1.66 nrgoals = 5000000
% 0.97/1.66 totalproof = 1
% 0.97/1.66
% 0.97/1.66 Symbols occurring in the translation:
% 0.97/1.66
% 0.97/1.66 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.97/1.66 . [1, 2] (w:1, o:212, a:1, s:1, b:0),
% 0.97/1.66 ! [4, 1] (w:0, o:123, a:1, s:1, b:0),
% 0.97/1.66 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.97/1.66 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.97/1.66 hAPP [38, 2] (w:1, o:236, a:1, s:1, b:0),
% 0.97/1.66 t_a [39, 0] (w:1, o:18, a:1, s:1, b:0),
% 0.97/1.66 class_Rings_Oidom [40, 1] (w:1, o:128, a:1, s:1, b:0),
% 0.97/1.66 v_p [41, 0] (w:1, o:19, a:1, s:1, b:0),
% 0.97/1.66 c_Polynomial_Opoly [42, 2] (w:1, o:241, a:1, s:1, b:0),
% 0.97/1.66 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant [43, 3] (w:1, o:
% 0.97/1.66 273, a:1, s:1, b:0),
% 0.97/1.66 tc_Nat_Onat [45, 0] (w:1, o:27, a:1, s:1, b:0),
% 0.97/1.66 c_Groups_Ozero__class_Ozero [46, 1] (w:1, o:129, a:1, s:1, b:0),
% 0.97/1.66 c_Orderings_Oord__class_Oless [47, 2] (w:1, o:238, a:1, s:1, b:0),
% 0.97/1.66 c_Nat_OSuc [48, 0] (w:1, o:28, a:1, s:1, b:0),
% 0.97/1.66 hBOOL [49, 1] (w:1, o:130, a:1, s:1, b:0),
% 0.97/1.66 v_cs____ [51, 0] (w:1, o:32, a:1, s:1, b:0),
% 0.97/1.66 class_Rings_Olinordered__semidom [55, 1] (w:1, o:133, a:1, s:1, b:0)
% 0.97/1.66 ,
% 0.97/1.66 c_Groups_Oone__class_Oone [56, 1] (w:1, o:134, a:1, s:1, b:0),
% 0.97/1.66 c_Power_Opower__class_Opower [57, 1] (w:1, o:135, a:1, s:1, b:0),
% 0.97/1.66 c_Groups_Otimes__class_Otimes [59, 1] (w:1, o:136, a:1, s:1, b:0),
% 0.97/1.66 class_Rings_Ocomm__semiring__0 [62, 1] (w:1, o:139, a:1, s:1, b:0),
% 0.97/1.66 c_Polynomial_OpCons [63, 1] (w:1, o:140, a:1, s:1, b:0),
% 0.97/1.66 c_Groups_Oplus__class_Oplus [64, 1] (w:1, o:141, a:1, s:1, b:0),
% 0.97/1.66 class_Groups_Omonoid__mult [72, 1] (w:1, o:144, a:1, s:1, b:0),
% 0.97/1.66 class_Int_Oring__char__0 [75, 1] (w:1, o:145, a:1, s:1, b:0),
% 0.97/1.66 tc_Polynomial_Opoly [76, 1] (w:1, o:151, a:1, s:1, b:0),
% 0.97/1.66 class_Rings_Ocomm__semiring__1 [81, 1] (w:1, o:152, a:1, s:1, b:0),
% 0.97/1.66 class_Groups_Ozero [82, 1] (w:1, o:153, a:1, s:1, b:0),
% 0.97/1.66 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize [83, 2] (w:1, o:242
% 0.97/1.66 , a:1, s:1, b:0),
% 0.97/1.66 class_Rings_Oring__1__no__zero__divisors [93, 1] (w:1, o:154, a:1, s:
% 0.97/1.66 1, b:0),
% 0.97/1.66 class_Groups_Ocomm__monoid__mult [95, 1] (w:1, o:155, a:1, s:1, b:0)
% 0.97/1.66 ,
% 0.97/1.66 class_Groups_Ocomm__monoid__add [100, 1] (w:1, o:156, a:1, s:1, b:0)
% 0.97/1.66 ,
% 0.97/1.66 class_Power_Opower [101, 1] (w:1, o:162, a:1, s:1, b:0),
% 0.97/1.66 class_Rings_Omult__zero [102, 1] (w:1, o:169, a:1, s:1, b:0),
% 0.97/1.66 class_Rings_Ono__zero__divisors [103, 1] (w:1, o:170, a:1, s:1, b:0)
% 0.97/1.66 ,
% 0.97/1.66 class_Rings_Ozero__neq__one [104, 1] (w:1, o:171, a:1, s:1, b:0),
% 0.97/1.66 class_Rings_Osemiring__0 [105, 1] (w:1, o:175, a:1, s:1, b:0),
% 0.97/1.66 class_Rings_Olinordered__ring__strict [109, 1] (w:1, o:131, a:1, s:1
% 0.97/1.66 , b:0),
% 0.97/1.66 class_Rings_Olinordered__ring [110, 1] (w:1, o:132, a:1, s:1, b:0),
% 0.97/1.66 v_c____ [111, 0] (w:1, o:87, a:1, s:1, b:0),
% 0.97/1.66 class_Rings_Olinordered__idom [113, 1] (w:1, o:163, a:1, s:1, b:0),
% 0.97/1.66 class_Rings_Oring__no__zero__divisors [120, 1] (w:1, o:172, a:1, s:1
% 0.97/1.66 , b:0),
% 0.97/1.66 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct [
% 0.97/1.66 121, 1] (w:1, o:187, a:1, s:1, b:0),
% 0.97/1.66 class_Rings_Ocomm__semiring [124, 1] (w:1, o:176, a:1, s:1, b:0),
% 0.97/1.66 class_Rings_Osemiring [126, 1] (w:1, o:177, a:1, s:1, b:0),
% 0.97/1.66 class_Rings_Olinordered__semiring__strict [129, 1] (w:1, o:164, a:1
% 0.97/1.66 , s:1, b:0),
% 0.97/1.66 class_Rings_Olinordered__comm__semiring__strict [130, 1] (w:1, o:165
% 0.97/1.66 , a:1, s:1, b:0),
% 0.97/1.66 c_Polynomial_Opcompose [133, 3] (w:1, o:275, a:1, s:1, b:0),
% 0.97/1.66 class_Groups_Olinordered__ab__group__add [134, 1] (w:1, o:143, a:1
% 0.97/1.66 , s:1, b:0),
% 0.97/1.66 class_Groups_Oordered__comm__monoid__add [135, 1] (w:1, o:188, a:1
% 0.97/1.66 , s:1, b:0),
% 0.97/1.66 class_Groups_Oab__semigroup__mult [136, 1] (w:1, o:189, a:1, s:1, b:0
% 0.97/1.66 ),
% 0.97/1.66 class_Groups_Ocancel__semigroup__add [137, 1] (w:1, o:190, a:1, s:1
% 0.97/1.66 , b:0),
% 0.97/1.66 class_Groups_Ocancel__ab__semigroup__add [138, 1] (w:1, o:191, a:1
% 0.97/1.66 , s:1, b:0),
% 0.97/1.66 class_Groups_Oab__semigroup__add [139, 1] (w:1, o:192, a:1, s:1, b:0)
% 0.97/1.66 ,
% 0.97/1.66 class_Groups_Oone [140, 1] (w:1, o:193, a:1, s:1, b:0),
% 0.97/1.66 tc_Int_Oint [141, 0] (w:1, o:97, a:1, s:1, b:0),
% 0.97/1.66 class_Groups_Omonoid__add [142, 1] (w:1, o:194, a:1, s:1, b:0),
% 0.97/1.66 class_Groups_Oordered__ab__semigroup__add__imp__le [143, 1] (w:1, o:
% 0.97/1.66 195, a:1, s:1, b:0),
% 0.97/1.66 class_Groups_Oordered__cancel__ab__semigroup__add [144, 1] (w:1, o:
% 0.97/1.66 196, a:1, s:1, b:0),
% 0.97/1.66 tc_fun [146, 2] (w:1, o:252, a:1, s:1, b:0),
% 0.97/1.66 c_COMBB [147, 3] (w:1, o:276, a:1, s:1, b:0),
% 0.97/1.66 c_COMBK [148, 2] (w:1, o:253, a:1, s:1, b:0),
% 0.97/1.66 c_COMBC [149, 4] (w:1, o:323, a:1, s:1, b:0),
% 0.97/1.66 c_Polynomial_Opoly__rec [150, 5] (w:1, o:341, a:1, s:1, b:0),
% 0.97/1.66 c_Polynomial_Oorder [151, 3] (w:1, o:274, a:1, s:1, b:0),
% 0.97/1.66 c_Power_Opower_Opower [152, 3] (w:1, o:277, a:1, s:1, b:0),
% 0.97/1.66 c_Polynomial_Opos__poly [153, 2] (w:1, o:254, a:1, s:1, b:0),
% 0.97/1.66 c_fequal [160, 2] (w:1, o:255, a:1, s:1, b:0),
% 0.97/1.66 c_If [161, 4] (w:1, o:324, a:1, s:1, b:0),
% 0.97/1.66 c_Polynomial_Osmult [162, 1] (w:1, o:197, a:1, s:1, b:0),
% 0.97/1.66 class_RealVector_Oreal__normed__algebra [164, 1] (w:1, o:178, a:1, s:
% 0.97/1.66 1, b:0),
% 0.97/1.66 class_Rings_Ocomm__ring__1 [168, 1] (w:1, o:137, a:1, s:1, b:0),
% 0.97/1.66 c_Polynomial_Omonom [169, 3] (w:1, o:278, a:1, s:1, b:0),
% 0.97/1.66 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly [171, 3] (w:
% 0.97/1.66 1, o:279, a:1, s:1, b:0),
% 0.97/1.66 c_COMBS [172, 3] (w:1, o:280, a:1, s:1, b:0),
% 0.97/1.66 c_Polynomial_Osynthetic__div [173, 3] (w:1, o:281, a:1, s:1, b:0),
% 0.97/1.66 c_Orderings_Oord__class_Oless__eq [175, 2] (w:1, o:239, a:1, s:1, b:0
% 0.97/1.66 ),
% 0.97/1.66 class_Rings_Olinordered__semiring__1__strict [177, 1] (w:1, o:166, a:
% 0.97/1.66 1, s:1, b:0),
% 0.97/1.66 class_Groups_Oordered__ab__semigroup__add [178, 1] (w:1, o:198, a:1
% 0.97/1.66 , s:1, b:0),
% 0.97/1.66 class_Rings_Oordered__cancel__semiring [179, 1] (w:1, o:179, a:1, s:1
% 0.97/1.66 , b:0),
% 0.97/1.66 class_Rings_Oordered__ring [180, 1] (w:1, o:180, a:1, s:1, b:0),
% 0.97/1.66 class_Rings_Oordered__semiring [181, 1] (w:1, o:181, a:1, s:1, b:0),
% 0.97/1.66
% 0.97/1.66 class_Rings_Oordered__comm__semiring [182, 1] (w:1, o:182, a:1, s:1
% 0.97/1.66 , b:0),
% 0.97/1.66 class_Rings_Olinordered__semiring [185, 1] (w:1, o:167, a:1, s:1, b:0
% 0.97/1.66 ),
% 0.97/1.66 class_Rings_Olinordered__semiring__1 [186, 1] (w:1, o:168, a:1, s:1
% 0.97/1.66 , b:0),
% 0.97/1.66 class_Orderings_Opreorder [189, 1] (w:1, o:159, a:1, s:1, b:0),
% 0.97/1.66 c_Groups_Ouminus__class_Ouminus [190, 2] (w:1, o:256, a:1, s:1, b:0)
% 0.97/1.66 ,
% 0.97/1.66 class_Orderings_Olinorder [193, 1] (w:1, o:160, a:1, s:1, b:0),
% 0.97/1.66 class_Groups_Oab__group__add [194, 1] (w:1, o:199, a:1, s:1, b:0),
% 0.97/1.66 class_Rings_Ocomm__ring [195, 1] (w:1, o:138, a:1, s:1, b:0),
% 0.97/1.66 class_Groups_Ogroup__add [196, 1] (w:1, o:200, a:1, s:1, b:0),
% 0.97/1.66 class_Rings_Oring [197, 1] (w:1, o:173, a:1, s:1, b:0),
% 0.97/1.66 class_Groups_Oordered__ab__group__add [198, 1] (w:1, o:201, a:1, s:1
% 0.97/1.66 , b:0),
% 0.97/1.66 class_Rings_Oring__1 [199, 1] (w:1, o:174, a:1, s:1, b:0),
% 0.97/1.66 class_Orderings_Oord [200, 1] (w:1, o:157, a:1, s:1, b:0),
% 0.97/1.66 class_Orderings_Oorder [201, 1] (w:1, o:158, a:1, s:1, b:0),
% 0.97/1.66 c_Rings_Odvd__class_Odvd [202, 1] (w:1, o:202, a:1, s:1, b:0),
% 0.97/1.66 class_Lattices_Oboolean__algebra [203, 1] (w:1, o:204, a:1, s:1, b:0)
% 0.97/1.66 ,
% 0.97/1.66 class_Rings_Odvd [204, 1] (w:1, o:183, a:1, s:1, b:0),
% 0.97/1.66 class_Fields_Ofield [205, 1] (w:1, o:142, a:1, s:1, b:0),
% 0.97/1.66 class_Lattices_Oab__semigroup__idem__mult [206, 1] (w:1, o:203, a:1
% 0.97/1.66 , s:1, b:0),
% 0.97/1.66 class_Groups_Ouminus [208, 1] (w:1, o:205, a:1, s:1, b:0),
% 0.97/1.66 tc_HOL_Obool [209, 0] (w:1, o:96, a:1, s:1, b:0),
% 0.97/1.66 c_fNot [210, 0] (w:1, o:107, a:1, s:1, b:0),
% 0.97/1.66 c_Orderings_Oord__class_OLeast [211, 2] (w:1, o:240, a:1, s:1, b:0),
% 0.97/1.66
% 0.97/1.66 class_Orderings_Owellorder [214, 1] (w:1, o:161, a:1, s:1, b:0),
% 0.97/1.66 c_fconj [216, 0] (w:1, o:108, a:1, s:1, b:0),
% 4.39/4.75 c_Orderings_Oorder_Ostrict__mono [217, 4] (w:1, o:325, a:1, s:1, b:0)
% 4.39/4.75 ,
% 4.39/4.75 c_Groups_Ominus__class_Ominus [218, 3] (w:1, o:282, a:1, s:1, b:0),
% 4.39/4.75 class_Groups_Ominus [222, 1] (w:1, o:206, a:1, s:1, b:0),
% 4.39/4.75 c_Orderings_Oorder_Omono [227, 4] (w:1, o:326, a:1, s:1, b:0),
% 4.39/4.75 c_Nat__Transfer_Otsub [228, 2] (w:1, o:237, a:1, s:1, b:0),
% 4.39/4.75 c_Divides_Odiv__class_Odiv [229, 3] (w:1, o:283, a:1, s:1, b:0),
% 4.39/4.75 class_Divides_Osemiring__div [230, 1] (w:1, o:208, a:1, s:1, b:0),
% 4.39/4.75 class_Divides_Oring__div [231, 1] (w:1, o:207, a:1, s:1, b:0),
% 4.39/4.75 c_SMT_Oz3div [235, 2] (w:1, o:257, a:1, s:1, b:0),
% 4.39/4.75 c_Groups_Osgn__class_Osgn [236, 2] (w:1, o:258, a:1, s:1, b:0),
% 4.39/4.75 class_RealVector_Oreal__normed__vector [237, 1] (w:1, o:184, a:1, s:1
% 4.39/4.75 , b:0),
% 4.39/4.75 class_Groups_Osgn__if [238, 1] (w:1, o:209, a:1, s:1, b:0),
% 4.39/4.75 class_RealVector_Oreal__normed__div__algebra [239, 1] (w:1, o:185, a:
% 4.39/4.75 1, s:1, b:0),
% 4.39/4.75 class_RealVector_Oreal__normed__algebra__1 [240, 1] (w:1, o:186, a:1
% 4.39/4.75 , s:1, b:0),
% 4.39/4.75 c_Divides_Odiv__class_Omod [241, 3] (w:1, o:284, a:1, s:1, b:0),
% 4.39/4.75 class_Groups_Ocancel__comm__monoid__add [244, 1] (w:1, o:210, a:1, s:
% 4.39/4.75 1, b:0),
% 4.39/4.75 v_a [252, 0] (w:1, o:120, a:1, s:1, b:0),
% 4.39/4.75 v_q [253, 0] (w:1, o:121, a:1, s:1, b:0),
% 4.39/4.75 v_k [254, 0] (w:1, o:122, a:1, s:1, b:0),
% 4.39/4.75 alpha1 [255, 2] (w:1, o:259, a:1, s:1, b:1),
% 4.39/4.75 alpha2 [256, 2] (w:1, o:266, a:1, s:1, b:1),
% 4.39/4.75 alpha3 [257, 2] (w:1, o:270, a:1, s:1, b:1),
% 4.39/4.75 alpha4 [258, 4] (w:1, o:330, a:1, s:1, b:1),
% 4.39/4.75 alpha5 [259, 4] (w:1, o:334, a:1, s:1, b:1),
% 4.39/4.75 alpha6 [260, 3] (w:1, o:286, a:1, s:1, b:1),
% 4.39/4.75 alpha7 [261, 3] (w:1, o:287, a:1, s:1, b:1),
% 4.39/4.75 alpha8 [262, 3] (w:1, o:288, a:1, s:1, b:1),
% 4.39/4.75 alpha9 [263, 3] (w:1, o:289, a:1, s:1, b:1),
% 4.39/4.75 alpha10 [264, 2] (w:1, o:260, a:1, s:1, b:1),
% 4.39/4.75 alpha11 [265, 2] (w:1, o:261, a:1, s:1, b:1),
% 4.39/4.75 alpha12 [266, 3] (w:1, o:290, a:1, s:1, b:1),
% 4.39/4.75 alpha13 [267, 3] (w:1, o:291, a:1, s:1, b:1),
% 4.39/4.75 alpha14 [268, 2] (w:1, o:262, a:1, s:1, b:1),
% 4.39/4.75 alpha15 [269, 2] (w:1, o:263, a:1, s:1, b:1),
% 4.39/4.75 alpha16 [270, 2] (w:1, o:264, a:1, s:1, b:1),
% 4.39/4.75 alpha17 [271, 2] (w:1, o:265, a:1, s:1, b:1),
% 4.39/4.75 alpha18 [272, 4] (w:1, o:335, a:1, s:1, b:1),
% 4.39/4.75 alpha19 [273, 4] (w:1, o:336, a:1, s:1, b:1),
% 4.39/4.75 alpha20 [274, 2] (w:1, o:267, a:1, s:1, b:1),
% 4.39/4.75 alpha21 [275, 2] (w:1, o:268, a:1, s:1, b:1),
% 4.39/4.75 alpha22 [276, 4] (w:1, o:337, a:1, s:1, b:1),
% 4.39/4.75 alpha23 [277, 4] (w:1, o:338, a:1, s:1, b:1),
% 4.39/4.75 alpha24 [278, 3] (w:1, o:292, a:1, s:1, b:1),
% 4.39/4.75 alpha25 [279, 3] (w:1, o:293, a:1, s:1, b:1),
% 4.39/4.75 alpha26 [280, 4] (w:1, o:339, a:1, s:1, b:1),
% 4.39/4.75 alpha27 [281, 3] (w:1, o:294, a:1, s:1, b:1),
% 4.39/4.75 alpha28 [282, 3] (w:1, o:295, a:1, s:1, b:1),
% 4.39/4.75 alpha29 [283, 2] (w:1, o:269, a:1, s:1, b:1),
% 4.39/4.75 alpha30 [284, 3] (w:1, o:296, a:1, s:1, b:1),
% 4.39/4.75 alpha31 [285, 3] (w:1, o:297, a:1, s:1, b:1),
% 4.39/4.75 alpha32 [286, 3] (w:1, o:298, a:1, s:1, b:1),
% 4.39/4.75 alpha33 [287, 4] (w:1, o:327, a:1, s:1, b:1),
% 4.39/4.75 alpha34 [288, 4] (w:1, o:328, a:1, s:1, b:1),
% 4.39/4.75 alpha35 [289, 2] (w:1, o:271, a:1, s:1, b:1),
% 4.39/4.75 alpha36 [290, 3] (w:1, o:299, a:1, s:1, b:1),
% 4.39/4.75 alpha37 [291, 3] (w:1, o:300, a:1, s:1, b:1),
% 4.39/4.75 alpha38 [292, 4] (w:1, o:329, a:1, s:1, b:1),
% 4.39/4.75 alpha39 [293, 3] (w:1, o:301, a:1, s:1, b:1),
% 4.39/4.75 alpha40 [294, 3] (w:1, o:302, a:1, s:1, b:1),
% 4.39/4.75 alpha41 [295, 4] (w:1, o:331, a:1, s:1, b:1),
% 4.39/4.75 alpha42 [296, 3] (w:1, o:303, a:1, s:1, b:1),
% 4.39/4.75 alpha43 [297, 3] (w:1, o:304, a:1, s:1, b:1),
% 4.39/4.75 alpha44 [298, 3] (w:1, o:305, a:1, s:1, b:1),
% 4.39/4.75 alpha45 [299, 4] (w:1, o:332, a:1, s:1, b:1),
% 4.39/4.75 alpha46 [300, 4] (w:1, o:333, a:1, s:1, b:1),
% 4.39/4.75 alpha47 [301, 3] (w:1, o:306, a:1, s:1, b:1),
% 4.39/4.75 alpha48 [302, 1] (w:1, o:211, a:1, s:1, b:1),
% 4.39/4.75 alpha49 [303, 2] (w:1, o:272, a:1, s:1, b:1),
% 4.39/4.75 alpha50 [304, 3] (w:1, o:285, a:1, s:1, b:1),
% 4.39/4.75 skol1 [305, 2] (w:1, o:243, a:1, s:1, b:1),
% 4.39/4.75 skol2 [306, 0] (w:1, o:13, a:1, s:1, b:1),
% 19.57/19.93 skol3 [307, 0] (w:1, o:14, a:1, s:1, b:1),
% 19.57/19.93 skol4 [308, 1] (w:1, o:148, a:1, s:1, b:1),
% 19.57/19.93 skol5 [309, 2] (w:1, o:244, a:1, s:1, b:1),
% 19.57/19.93 skol6 [310, 1] (w:1, o:149, a:1, s:1, b:1),
% 19.57/19.93 skol7 [311, 2] (w:1, o:245, a:1, s:1, b:1),
% 19.57/19.93 skol8 [312, 0] (w:1, o:15, a:1, s:1, b:1),
% 19.57/19.93 skol9 [313, 1] (w:1, o:150, a:1, s:1, b:1),
% 19.57/19.93 skol10 [314, 0] (w:1, o:12, a:1, s:1, b:1),
% 19.57/19.93 skol11 [315, 2] (w:1, o:246, a:1, s:1, b:1),
% 19.57/19.93 skol12 [316, 2] (w:1, o:247, a:1, s:1, b:1),
% 19.57/19.93 skol13 [317, 3] (w:1, o:307, a:1, s:1, b:1),
% 19.57/19.93 skol14 [318, 3] (w:1, o:308, a:1, s:1, b:1),
% 19.57/19.93 skol15 [319, 2] (w:1, o:248, a:1, s:1, b:1),
% 19.57/19.93 skol16 [320, 2] (w:1, o:249, a:1, s:1, b:1),
% 19.57/19.93 skol17 [321, 3] (w:1, o:309, a:1, s:1, b:1),
% 19.57/19.93 skol18 [322, 3] (w:1, o:310, a:1, s:1, b:1),
% 19.57/19.93 skol19 [323, 3] (w:1, o:311, a:1, s:1, b:1),
% 19.57/19.93 skol20 [324, 3] (w:1, o:312, a:1, s:1, b:1),
% 19.57/19.93 skol21 [325, 3] (w:1, o:313, a:1, s:1, b:1),
% 19.57/19.93 skol22 [326, 3] (w:1, o:314, a:1, s:1, b:1),
% 19.57/19.93 skol23 [327, 3] (w:1, o:315, a:1, s:1, b:1),
% 19.57/19.93 skol24 [328, 4] (w:1, o:340, a:1, s:1, b:1),
% 19.57/19.93 skol25 [329, 3] (w:1, o:316, a:1, s:1, b:1),
% 19.57/19.93 skol26 [330, 2] (w:1, o:250, a:1, s:1, b:1),
% 19.57/19.93 skol27 [331, 3] (w:1, o:317, a:1, s:1, b:1),
% 19.57/19.93 skol28 [332, 3] (w:1, o:318, a:1, s:1, b:1),
% 19.57/19.93 skol29 [333, 2] (w:1, o:251, a:1, s:1, b:1),
% 19.57/19.93 skol30 [334, 1] (w:1, o:146, a:1, s:1, b:1),
% 19.57/19.93 skol31 [335, 1] (w:1, o:147, a:1, s:1, b:1),
% 19.57/19.93 skol32 [336, 0] (w:1, o:16, a:1, s:1, b:1),
% 19.57/19.93 skol33 [337, 3] (w:1, o:319, a:1, s:1, b:1),
% 19.57/19.93 skol34 [338, 3] (w:1, o:320, a:1, s:1, b:1),
% 19.57/19.93 skol35 [339, 3] (w:1, o:321, a:1, s:1, b:1),
% 19.57/19.93 skol36 [340, 3] (w:1, o:322, a:1, s:1, b:1),
% 19.57/19.93 skol37 [341, 0] (w:1, o:17, a:1, s:1, b:1).
% 19.57/19.93
% 19.57/19.93
% 19.57/19.93 Starting Search:
% 19.57/19.93
% 19.57/19.93 *** allocated 170857 integers for clauses
% 19.57/19.93 Resimplifying inuse:
% 19.57/19.93 Done
% 19.57/19.93
% 19.57/19.93
% 19.57/19.93 Intermediate Status:
% 19.57/19.93 Generated: 3139
% 19.57/19.93 Kept: 2020
% 19.57/19.93 Inuse: 61
% 19.57/19.93 Deleted: 5
% 19.57/19.93 Deletedinuse: 0
% 19.57/19.93
% 19.57/19.93 *** allocated 256285 integers for clauses
% 19.57/19.93 Resimplifying inuse:
% 19.57/19.93 Done
% 19.57/19.93
% 19.57/19.93 *** allocated 256285 integers for termspace/termends
% 19.57/19.93 *** allocated 384427 integers for clauses
% 19.57/19.93
% 19.57/19.93 Intermediate Status:
% 19.57/19.93 Generated: 13780
% 19.57/19.93 Kept: 4303
% 19.57/19.93 Inuse: 143
% 19.57/19.93 Deleted: 8
% 19.57/19.93 Deletedinuse: 0
% 19.57/19.93
% 19.57/19.93 Resimplifying inuse:
% 19.57/19.93 Done
% 19.57/19.93
% 19.57/19.93 Resimplifying inuse:
% 19.57/19.93 Done
% 19.57/19.93
% 19.57/19.93 *** allocated 384427 integers for termspace/termends
% 19.57/19.93
% 19.57/19.93 Intermediate Status:
% 19.57/19.93 Generated: 20719
% 19.57/19.93 Kept: 6333
% 19.57/19.93 Inuse: 227
% 19.57/19.93 Deleted: 15
% 19.57/19.93 Deletedinuse: 1
% 19.57/19.93
% 19.57/19.93 Resimplifying inuse:
% 19.57/19.93 Done
% 19.57/19.93
% 19.57/19.93 *** allocated 576640 integers for clauses
% 19.57/19.93 Resimplifying inuse:
% 19.57/19.93 Done
% 19.57/19.93
% 19.57/19.93
% 19.57/19.93 Intermediate Status:
% 19.57/19.93 Generated: 27700
% 19.57/19.93 Kept: 8337
% 19.57/19.93 Inuse: 302
% 19.57/19.93 Deleted: 18
% 19.57/19.93 Deletedinuse: 1
% 19.57/19.93
% 19.57/19.93 Resimplifying inuse:
% 19.57/19.93 Done
% 19.57/19.93
% 19.57/19.93
% 19.57/19.93 Intermediate Status:
% 19.57/19.93 Generated: 34741
% 19.57/19.93 Kept: 10361
% 19.57/19.93 Inuse: 326
% 19.57/19.93 Deleted: 21
% 19.57/19.93 Deletedinuse: 1
% 19.57/19.93
% 19.57/19.93 Resimplifying inuse:
% 19.57/19.93 Done
% 19.57/19.93
% 19.57/19.93 *** allocated 576640 integers for termspace/termends
% 19.57/19.93 *** allocated 864960 integers for clauses
% 19.57/19.93 Resimplifying inuse:
% 19.57/19.93 Done
% 19.57/19.93
% 19.57/19.93
% 19.57/19.93 Intermediate Status:
% 19.57/19.93 Generated: 42443
% 19.57/19.93 Kept: 13243
% 19.57/19.93 Inuse: 351
% 19.57/19.93 Deleted: 21
% 19.57/19.93 Deletedinuse: 1
% 19.57/19.93
% 19.57/19.93 Resimplifying inuse:
% 19.57/19.93 Done
% 19.57/19.93
% 19.57/19.93 Resimplifying inuse:
% 19.57/19.93 Done
% 19.57/19.93
% 19.57/19.93
% 19.57/19.93 Intermediate Status:
% 19.57/19.93 Generated: 52990
% 19.57/19.93 Kept: 15695
% 19.57/19.93 Inuse: 400
% 19.57/19.93 Deleted: 22
% 19.57/19.93 Deletedinuse: 1
% 19.57/19.93
% 19.57/19.93 Resimplifying inuse:
% 19.57/19.93 Done
% 19.57/19.93
% 19.57/19.93 Resimplifying inuse:
% 19.57/19.93 Done
% 19.57/19.93
% 19.57/19.93 *** allocated 1297440 integers for clauses
% 19.57/19.93
% 19.57/19.93 Intermediate Status:
% 19.57/19.93 Generated: 64239
% 19.57/19.93 Kept: 17735
% 19.57/19.93 Inuse: 435
% 19.57/19.93 Deleted: 27
% 19.57/19.93 Deletedinuse: 6
% 19.57/19.93
% 19.57/19.93 Resimplifying inuse:
% 19.57/19.93 Done
% 19.57/19.93
% 19.57/19.93 *** allocated 864960 integers for termspace/termends
% 19.57/19.93 Resimplifying inuse:
% 19.57/19.93 Done
% 19.57/19.93
% 19.57/19.93
% 19.57/19.93 Intermediate Status:
% 19.57/19.93 Generated: 73656
% 19.57/19.93 Kept: 19737
% 19.57/19.93 Inuse: 453
% 19.57/19.93 Deleted: 27
% 19.57/19.93 Deletedinuse: 6
% 19.57/19.93
% 19.57/19.93 Resimplifying inuse:
% 19.57/19.93 Done
% 19.57/19.93
% 19.57/19.93 Resimplifying clauses:
% 19.57/19.93 Done
% 19.57/19.93
% 19.57/19.93
% 19.57/19.93 Intermediate Status:
% 19.57/19.93 Generated: 81211
% 19.57/19.93 Kept: 22603
% 19.57/19.93 Inuse: 480
% 19.57/19.93 Deleted: 569
% 19.57/19.93 Deletedinuse: 6
% 19.57/19.93
% 19.57/19.93 Resimplifying inuse:
% 19.57/19.93 Done
% 19.57/19.93
% 19.57/19.93
% 19.57/19.93 Intermediate Status:
% 19.57/19.93 Generated: 88567
% 19.57/19.93 Kept: 24842
% 19.57/19.93 Inuse: 500
% 19.57/19.93 Deleted: 570
% 19.57/19.93 Deletedinuse: 7
% 19.57/19.93
% 19.57/19.93 Resimplifying inuse:
% 19.57/19.93 Done
% 19.57/19.93
% 19.57/19.93 Resimplifying inuse:
% 70.46/70.91 Done
% 70.46/70.91
% 70.46/70.91
% 70.46/70.91 Intermediate Status:
% 70.46/70.91 Generated: 95351
% 70.46/70.91 Kept: 26858
% 70.46/70.91 Inuse: 525
% 70.46/70.91 Deleted: 570
% 70.46/70.91 Deletedinuse: 7
% 70.46/70.91
% 70.46/70.91 Resimplifying inuse:
% 70.46/70.91 Done
% 70.46/70.91
% 70.46/70.91 *** allocated 1946160 integers for clauses
% 70.46/70.91 Resimplifying inuse:
% 70.46/70.91 Done
% 70.46/70.91
% 70.46/70.91 *** allocated 1297440 integers for termspace/termends
% 70.46/70.91
% 70.46/70.91 Intermediate Status:
% 70.46/70.91 Generated: 101582
% 70.46/70.91 Kept: 29888
% 70.46/70.91 Inuse: 540
% 70.46/70.91 Deleted: 570
% 70.46/70.91 Deletedinuse: 7
% 70.46/70.91
% 70.46/70.91 Resimplifying inuse:
% 70.46/70.91 Done
% 70.46/70.91
% 70.46/70.91 Resimplifying inuse:
% 70.46/70.91 Done
% 70.46/70.91
% 70.46/70.91
% 70.46/70.91 Intermediate Status:
% 70.46/70.91 Generated: 106217
% 70.46/70.91 Kept: 31888
% 70.46/70.91 Inuse: 559
% 70.46/70.91 Deleted: 570
% 70.46/70.91 Deletedinuse: 7
% 70.46/70.91
% 70.46/70.91 Resimplifying inuse:
% 70.46/70.91 Done
% 70.46/70.91
% 70.46/70.91 Resimplifying inuse:
% 70.46/70.91 Done
% 70.46/70.91
% 70.46/70.91
% 70.46/70.91 Intermediate Status:
% 70.46/70.91 Generated: 112039
% 70.46/70.91 Kept: 33911
% 70.46/70.91 Inuse: 581
% 70.46/70.91 Deleted: 575
% 70.46/70.91 Deletedinuse: 12
% 70.46/70.91
% 70.46/70.91 Resimplifying inuse:
% 70.46/70.91 Done
% 70.46/70.91
% 70.46/70.91 Resimplifying inuse:
% 70.46/70.91 Done
% 70.46/70.91
% 70.46/70.91
% 70.46/70.91 Intermediate Status:
% 70.46/70.91 Generated: 117774
% 70.46/70.91 Kept: 36038
% 70.46/70.91 Inuse: 605
% 70.46/70.91 Deleted: 575
% 70.46/70.91 Deletedinuse: 12
% 70.46/70.91
% 70.46/70.91 Resimplifying inuse:
% 70.46/70.91 Done
% 70.46/70.91
% 70.46/70.91
% 70.46/70.91 Intermediate Status:
% 70.46/70.91 Generated: 124319
% 70.46/70.91 Kept: 38067
% 70.46/70.91 Inuse: 625
% 70.46/70.91 Deleted: 575
% 70.46/70.91 Deletedinuse: 12
% 70.46/70.91
% 70.46/70.91 Resimplifying inuse:
% 70.46/70.91 Done
% 70.46/70.91
% 70.46/70.91 Resimplifying inuse:
% 70.46/70.91 Done
% 70.46/70.91
% 70.46/70.91
% 70.46/70.91 Intermediate Status:
% 70.46/70.91 Generated: 131988
% 70.46/70.91 Kept: 40245
% 70.46/70.91 Inuse: 640
% 70.46/70.91 Deleted: 575
% 70.46/70.91 Deletedinuse: 12
% 70.46/70.91
% 70.46/70.91 Resimplifying inuse:
% 70.46/70.91 Done
% 70.46/70.91
% 70.46/70.91 Resimplifying clauses:
% 70.46/70.91 Done
% 70.46/70.91
% 70.46/70.91 Resimplifying inuse:
% 70.46/70.91 Done
% 70.46/70.91
% 70.46/70.91 *** allocated 2919240 integers for clauses
% 70.46/70.91
% 70.46/70.91 Intermediate Status:
% 70.46/70.91 Generated: 141779
% 70.46/70.91 Kept: 43066
% 70.46/70.91 Inuse: 670
% 70.46/70.91 Deleted: 910
% 70.46/70.91 Deletedinuse: 12
% 70.46/70.91
% 70.46/70.91 Resimplifying inuse:
% 70.46/70.91 Done
% 70.46/70.91
% 70.46/70.91 *** allocated 1946160 integers for termspace/termends
% 70.46/70.91 Resimplifying inuse:
% 70.46/70.91 Done
% 70.46/70.91
% 70.46/70.91
% 70.46/70.91 Intermediate Status:
% 70.46/70.91 Generated: 155669
% 70.46/70.91 Kept: 45402
% 70.46/70.91 Inuse: 680
% 70.46/70.91 Deleted: 910
% 70.46/70.91 Deletedinuse: 12
% 70.46/70.91
% 70.46/70.91 Resimplifying inuse:
% 70.46/70.91 Done
% 70.46/70.91
% 70.46/70.91 Resimplifying inuse:
% 70.46/70.91 Done
% 70.46/70.91
% 70.46/70.91
% 70.46/70.91 Intermediate Status:
% 70.46/70.91 Generated: 163791
% 70.46/70.91 Kept: 47413
% 70.46/70.91 Inuse: 708
% 70.46/70.91 Deleted: 910
% 70.46/70.91 Deletedinuse: 12
% 70.46/70.91
% 70.46/70.91 Resimplifying inuse:
% 70.46/70.91 Done
% 70.46/70.91
% 70.46/70.91 Resimplifying inuse:
% 70.46/70.91 Done
% 70.46/70.91
% 70.46/70.91
% 70.46/70.91 Intermediate Status:
% 70.46/70.91 Generated: 170594
% 70.46/70.91 Kept: 49417
% 70.46/70.91 Inuse: 721
% 70.46/70.91 Deleted: 910
% 70.46/70.91 Deletedinuse: 12
% 70.46/70.91
% 70.46/70.91 Resimplifying inuse:
% 70.46/70.91 Done
% 70.46/70.91
% 70.46/70.91
% 70.46/70.91 Intermediate Status:
% 70.46/70.91 Generated: 181995
% 70.46/70.91 Kept: 52380
% 70.46/70.91 Inuse: 747
% 70.46/70.91 Deleted: 910
% 70.46/70.91 Deletedinuse: 12
% 70.46/70.91
% 70.46/70.91 Resimplifying inuse:
% 70.46/70.91 Done
% 70.46/70.91
% 70.46/70.91
% 70.46/70.91 Intermediate Status:
% 70.46/70.91 Generated: 186035
% 70.46/70.91 Kept: 54632
% 70.46/70.91 Inuse: 755
% 70.46/70.91 Deleted: 911
% 70.46/70.91 Deletedinuse: 13
% 70.46/70.91
% 70.46/70.91 Resimplifying inuse:
% 70.46/70.91 Done
% 70.46/70.91
% 70.46/70.91
% 70.46/70.91 Intermediate Status:
% 70.46/70.91 Generated: 189097
% 70.46/70.91 Kept: 56635
% 70.46/70.91 Inuse: 760
% 70.46/70.91 Deleted: 911
% 70.46/70.91 Deletedinuse: 13
% 70.46/70.91
% 70.46/70.91 Resimplifying inuse:
% 70.46/70.91 Done
% 70.46/70.91
% 70.46/70.91
% 70.46/70.91 Intermediate Status:
% 70.46/70.91 Generated: 192198
% 70.46/70.91 Kept: 58649
% 70.46/70.91 Inuse: 765
% 70.46/70.91 Deleted: 911
% 70.46/70.91 Deletedinuse: 13
% 70.46/70.91
% 70.46/70.91 Resimplifying inuse:
% 70.46/70.91 Done
% 70.46/70.91
% 70.46/70.91
% 70.46/70.91 Intermediate Status:
% 70.46/70.91 Generated: 195299
% 70.46/70.91 Kept: 60670
% 70.46/70.91 Inuse: 770
% 70.46/70.91 Deleted: 911
% 70.46/70.91 Deletedinuse: 13
% 70.46/70.91
% 70.46/70.91 Resimplifying inuse:
% 70.46/70.91 Done
% 70.46/70.91
% 70.46/70.91 Resimplifying clauses:
% 70.46/70.91 Done
% 70.46/70.91
% 70.46/70.91 Resimplifying inuse:
% 70.46/70.91 Done
% 70.46/70.91
% 70.46/70.91
% 70.46/70.91 Intermediate Status:
% 70.46/70.91 Generated: 207207
% 70.46/70.91 Kept: 63250
% 70.46/70.91 Inuse: 810
% 70.46/70.91 Deleted: 1127
% 70.46/70.91 Deletedinuse: 13
% 70.46/70.91
% 70.46/70.91 Resimplifying inuse:
% 70.46/70.91 Done
% 70.46/70.91
% 70.46/70.91
% 70.46/70.91 Intermediate Status:
% 70.46/70.91 Generated: 214560
% 70.46/70.91 Kept: 65626
% 70.46/70.91 Inuse: 825
% 70.46/70.91 Deleted: 1127
% 70.46/70.91 Deletedinuse: 13
% 70.46/70.91
% 70.46/70.91 Resimplifying inuse:
% 70.46/70.91 Done
% 70.46/70.91
% 70.46/70.91 *** allocated 4378860 integers for clauses
% 70.46/70.91 Resimplifying inuse:
% 70.46/70.91 Done
% 70.46/70.91
% 70.46/70.91
% 70.46/70.91 Intermediate Status:
% 70.46/70.91 Generated: 221125
% 70.46/70.91 Kept: 67743
% 70.46/70.91 Inuse: 835
% 70.46/70.91 Deleted: 1127
% 70.46/70.91 Deletedinuse: 13
% 70.46/70.91
% 70.46/70.91 Resimplifying inuse:
% 70.46/70.91 Done
% 70.46/70.91
% 70.46/70.91 *** allocated 2919240 integers for termspace/termends
% 70.46/70.91 Resimplifying inuse:
% 70.46/70.91 Done
% 70.46/70.91
% 70.46/70.91
% 70.46/70.91 Intermediate Status:
% 70.46/70.91 Generated: 234707
% 70.46/70.91 Kept: 69889
% 70.46/70.91 Inuse: 880
% 70.46/70.91 Deleted: 1128
% 70.46/70.91 Deletedinuse: 14
% 70.46/70.91
% 70.46/70.91 Resimplifying inuse:
% 70.46/70.91 Done
% 70.46/70.91
% 70.46/70.91
% 70.46/70.91 Intermediate Status:
% 70.46/70.91 Generated: 246433
% 70.46/70.91 Kept: 72080
% 70.46/70.91 Inuse: 900
% 70.46/70.91 Deleted: 1128
% 70.46/70.91 Deletedinuse: 14
% 70.46/70.91
% 70.46/70.91 Resimplifying inuse:
% 70.46/70.91 Done
% 70.46/70.91
% 70.46/70.91 Resimplifying inuse:
% 70.46/70.91 Done
% 70.46/70.91
% 70.46/70.91
% 70.46/70.91 Intermediate Status:
% 70.46/70.91 Generated: 259621
% 70.46/70.91 Kept: 74095
% 70.46/70.91 Inuse: 948
% 70.46/70.91 Deleted: 1128
% 70.46/70.91 Deletedinuse: 14
% 70.46/70.91
% 70.46/70.91 Resimplifying inuse:
% 70.46/70.91 Done
% 70.46/70.91
% 70.46/70.91 Resimplifying inuse:
% 70.46/70.91 Done
% 70.46/70.91
% 70.46/70.91
% 70.46/70.91 Intermediate Status:
% 70.46/70.91 Generated: 281164
% 70.46/70.91 Kept: 78382
% 70.46/70.91 Inuse: 975
% 70.46/70.91 Deleted: 1128
% 70.46/70.91 Deletedinuse: 14
% 70.46/70.91
% 70.46/70.91 Resimplifying inuse:
% 70.46/70.91 Done
% 70.46/70.91
% 70.46/70.91
% 70.46/70.91 Intermediate Status:
% 70.46/70.91 Generated: 300655
% 174.67/175.13 Kept: 81479
% 174.67/175.13 Inuse: 990
% 174.67/175.13 Deleted: 1128
% 174.67/175.13 Deletedinuse: 14
% 174.67/175.13
% 174.67/175.13 Resimplifying inuse:
% 174.67/175.13 Done
% 174.67/175.13
% 174.67/175.13 Resimplifying clauses:
% 174.67/175.13 Done
% 174.67/175.13
% 174.67/175.13
% 174.67/175.13 Intermediate Status:
% 174.67/175.13 Generated: 308314
% 174.67/175.13 Kept: 84096
% 174.67/175.13 Inuse: 1005
% 174.67/175.13 Deleted: 1330
% 174.67/175.13 Deletedinuse: 14
% 174.67/175.13
% 174.67/175.13 Resimplifying inuse:
% 174.67/175.13 Done
% 174.67/175.13
% 174.67/175.13 Resimplifying inuse:
% 174.67/175.13 Done
% 174.67/175.13
% 174.67/175.13
% 174.67/175.13 Intermediate Status:
% 174.67/175.13 Generated: 351384
% 174.67/175.13 Kept: 88819
% 174.67/175.13 Inuse: 1025
% 174.67/175.13 Deleted: 1330
% 174.67/175.13 Deletedinuse: 14
% 174.67/175.13
% 174.67/175.13 Resimplifying inuse:
% 174.67/175.13 Done
% 174.67/175.13
% 174.67/175.13 Resimplifying inuse:
% 174.67/175.13 Done
% 174.67/175.13
% 174.67/175.13
% 174.67/175.13 Intermediate Status:
% 174.67/175.13 Generated: 363388
% 174.67/175.13 Kept: 91120
% 174.67/175.13 Inuse: 1045
% 174.67/175.13 Deleted: 1330
% 174.67/175.13 Deletedinuse: 14
% 174.67/175.13
% 174.67/175.13 Resimplifying inuse:
% 174.67/175.13 Done
% 174.67/175.13
% 174.67/175.13 Resimplifying inuse:
% 174.67/175.13 Done
% 174.67/175.13
% 174.67/175.13
% 174.67/175.13 Intermediate Status:
% 174.67/175.13 Generated: 371479
% 174.67/175.13 Kept: 93123
% 174.67/175.13 Inuse: 1070
% 174.67/175.13 Deleted: 1330
% 174.67/175.13 Deletedinuse: 14
% 174.67/175.13
% 174.67/175.13 Resimplifying inuse:
% 174.67/175.13 Done
% 174.67/175.13
% 174.67/175.13 Resimplifying inuse:
% 174.67/175.13 Done
% 174.67/175.13
% 174.67/175.13
% 174.67/175.13 Intermediate Status:
% 174.67/175.13 Generated: 377896
% 174.67/175.13 Kept: 95217
% 174.67/175.13 Inuse: 1095
% 174.67/175.13 Deleted: 1330
% 174.67/175.13 Deletedinuse: 14
% 174.67/175.13
% 174.67/175.13 Resimplifying inuse:
% 174.67/175.13 Done
% 174.67/175.13
% 174.67/175.13 *** allocated 4378860 integers for termspace/termends
% 174.67/175.13 Resimplifying inuse:
% 174.67/175.13 Done
% 174.67/175.13
% 174.67/175.13
% 174.67/175.13 Intermediate Status:
% 174.67/175.13 Generated: 385389
% 174.67/175.13 Kept: 97519
% 174.67/175.13 Inuse: 1125
% 174.67/175.13 Deleted: 1330
% 174.67/175.13 Deletedinuse: 14
% 174.67/175.13
% 174.67/175.13 Resimplifying inuse:
% 174.67/175.13 Done
% 174.67/175.13
% 174.67/175.13 Resimplifying inuse:
% 174.67/175.13 Done
% 174.67/175.13
% 174.67/175.13 *** allocated 6568290 integers for clauses
% 174.67/175.13
% 174.67/175.13 Intermediate Status:
% 174.67/175.13 Generated: 393209
% 174.67/175.13 Kept: 99866
% 174.67/175.13 Inuse: 1160
% 174.67/175.13 Deleted: 1330
% 174.67/175.13 Deletedinuse: 14
% 174.67/175.13
% 174.67/175.13 Resimplifying inuse:
% 174.67/175.13 Done
% 174.67/175.13
% 174.67/175.13 Resimplifying inuse:
% 174.67/175.13 Done
% 174.67/175.13
% 174.67/175.13 Resimplifying clauses:
% 174.67/175.13 Done
% 174.67/175.13
% 174.67/175.13
% 174.67/175.13 Intermediate Status:
% 174.67/175.13 Generated: 400749
% 174.67/175.13 Kept: 102059
% 174.67/175.13 Inuse: 1175
% 174.67/175.13 Deleted: 1513
% 174.67/175.13 Deletedinuse: 14
% 174.67/175.13
% 174.67/175.13 Resimplifying inuse:
% 174.67/175.13 Done
% 174.67/175.13
% 174.67/175.13 Resimplifying inuse:
% 174.67/175.13 Done
% 174.67/175.13
% 174.67/175.13
% 174.67/175.13 Intermediate Status:
% 174.67/175.13 Generated: 408099
% 174.67/175.13 Kept: 104082
% 174.67/175.13 Inuse: 1191
% 174.67/175.13 Deleted: 1513
% 174.67/175.13 Deletedinuse: 14
% 174.67/175.13
% 174.67/175.13 Resimplifying inuse:
% 174.67/175.13 Done
% 174.67/175.13
% 174.67/175.13
% 174.67/175.13 Intermediate Status:
% 174.67/175.13 Generated: 415095
% 174.67/175.13 Kept: 106242
% 174.67/175.13 Inuse: 1205
% 174.67/175.13 Deleted: 1513
% 174.67/175.13 Deletedinuse: 14
% 174.67/175.13
% 174.67/175.13 Resimplifying inuse:
% 174.67/175.13 Done
% 174.67/175.13
% 174.67/175.13
% 174.67/175.13 Intermediate Status:
% 174.67/175.13 Generated: 423175
% 174.67/175.13 Kept: 108579
% 174.67/175.13 Inuse: 1220
% 174.67/175.13 Deleted: 1513
% 174.67/175.13 Deletedinuse: 14
% 174.67/175.13
% 174.67/175.13 Resimplifying inuse:
% 174.67/175.13 Done
% 174.67/175.13
% 174.67/175.13 Resimplifying inuse:
% 174.67/175.13 Done
% 174.67/175.13
% 174.67/175.13
% 174.67/175.13 Intermediate Status:
% 174.67/175.13 Generated: 431163
% 174.67/175.13 Kept: 110870
% 174.67/175.13 Inuse: 1235
% 174.67/175.13 Deleted: 1513
% 174.67/175.13 Deletedinuse: 14
% 174.67/175.13
% 174.67/175.13
% 174.67/175.13 Intermediate Status:
% 174.67/175.13 Generated: 439062
% 174.67/175.13 Kept: 112965
% 174.67/175.13 Inuse: 1240
% 174.67/175.13 Deleted: 1513
% 174.67/175.13 Deletedinuse: 14
% 174.67/175.13
% 174.67/175.13 Resimplifying inuse:
% 174.67/175.13 Done
% 174.67/175.13
% 174.67/175.13
% 174.67/175.13 Intermediate Status:
% 174.67/175.13 Generated: 447093
% 174.67/175.13 Kept: 115075
% 174.67/175.13 Inuse: 1245
% 174.67/175.13 Deleted: 1513
% 174.67/175.13 Deletedinuse: 14
% 174.67/175.13
% 174.67/175.13 Resimplifying inuse:
% 174.67/175.13 Done
% 174.67/175.13
% 174.67/175.13
% 174.67/175.13 Intermediate Status:
% 174.67/175.13 Generated: 490635
% 174.67/175.13 Kept: 119250
% 174.67/175.13 Inuse: 1255
% 174.67/175.13 Deleted: 1513
% 174.67/175.13 Deletedinuse: 14
% 174.67/175.13
% 174.67/175.13 Resimplifying inuse:
% 174.67/175.13 Done
% 174.67/175.13
% 174.67/175.13 Resimplifying inuse:
% 174.67/175.13 Done
% 174.67/175.13
% 174.67/175.13
% 174.67/175.13 Intermediate Status:
% 174.67/175.13 Generated: 500076
% 174.67/175.13 Kept: 121890
% 174.67/175.13 Inuse: 1280
% 174.67/175.13 Deleted: 1513
% 174.67/175.13 Deletedinuse: 14
% 174.67/175.13
% 174.67/175.13 Resimplifying inuse:
% 174.67/175.13 Done
% 174.67/175.13
% 174.67/175.13 Resimplifying clauses:
% 174.67/175.13 Done
% 174.67/175.13
% 174.67/175.13 Resimplifying inuse:
% 174.67/175.13 Done
% 174.67/175.13
% 174.67/175.13
% 174.67/175.13 Intermediate Status:
% 174.67/175.13 Generated: 508958
% 174.67/175.13 Kept: 123891
% 174.67/175.13 Inuse: 1300
% 174.67/175.13 Deleted: 1613
% 174.67/175.13 Deletedinuse: 14
% 174.67/175.13
% 174.67/175.13 Resimplifying inuse:
% 174.67/175.13 Done
% 174.67/175.13
% 174.67/175.13
% 174.67/175.13 Intermediate Status:
% 174.67/175.13 Generated: 524079
% 174.67/175.13 Kept: 125997
% 174.67/175.13 Inuse: 1315
% 174.67/175.13 Deleted: 1613
% 174.67/175.13 Deletedinuse: 14
% 174.67/175.13
% 174.67/175.13 Resimplifying inuse:
% 174.67/175.13 Done
% 174.67/175.13
% 174.67/175.13 Resimplifying inuse:
% 174.67/175.13 Done
% 174.67/175.13
% 174.67/175.13
% 174.67/175.13 Intermediate Status:
% 174.67/175.13 Generated: 531615
% 174.67/175.13 Kept: 128418
% 174.67/175.13 Inuse: 1335
% 174.67/175.13 Deleted: 1613
% 174.67/175.13 Deletedinuse: 14
% 174.67/175.13
% 174.67/175.13 Resimplifying inuse:
% 174.67/175.13 Done
% 174.67/175.13
% 174.67/175.13 Resimplifying inuse:
% 174.67/175.13 Done
% 174.67/175.13
% 174.67/175.13
% 174.67/175.13 Intermediate Status:
% 174.67/175.13 Generated: 539355
% 174.67/175.13 Kept: 130544
% 174.67/175.13 Inuse: 1355
% 174.67/175.13 Deleted: 1613
% 174.67/175.13 Deletedinuse: 14
% 174.67/175.13
% 174.67/175.13 *** allocated 6568290 integers for termspace/termends
% 174.67/175.13 Resimplifying inuse:
% 174.67/175.13 Done
% 174.67/175.13
% 174.67/175.13
% 174.67/175.13 Intermediate Status:
% 174.67/175.13 Generated: 555641
% 174.67/175.13 Kept: 133099
% 174.67/175.13 Inuse: 1370
% 174.67/175.13 Deleted: 1613
% 174.67/175.13 Deletedinuse: 14
% 174.67/175.13
% 174.67/175.13 Resimplifying inuse:
% 174.67/175.13 Done
% 174.67/175.13
% 174.67/175.13 Resimplifying inuse:
% 174.67/175.13 Done
% 174.67/175.13
% 174.67/175.13
% 174.67/175.13 Intermediate Status:
% 174.67/175.13 Generated: 581833
% 174.67/175.13 Kept: 136861
% 174.67/175.13 Inuse: 1380
% 174.67/175.13 Deleted: 1613
% 174.67/175.13 Deletedinuse: 14
% 174.67/175.13
% 174.67/175.13 Resimplifying inuse:
% 174.67/175.13 Done
% 174.67/175.13
% 174.67/175.13 Resimplifying inuse:
% 174.67/175.13 Done
% 174.67/175.13
% 174.67/175.13
% 174.67/175.13 Intermediate Status:
% 174.67/175.13 Generated: 593920
% 174.67/175.13 Kept: 139231
% 174.67/175.13 Inuse: 1405
% 174.67/175.13 Deleted: 1613
% 174.67/175.13 Deletedinuse: 14
% 174.67/175.13
% 174.67/175.13 Resimplifying inCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------