TSTP Solution File: SWW250+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWW250+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Wed Jul 20 23:21:34 EDT 2022
% Result : Timeout 300.02s 300.41s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SWW250+1 : TPTP v8.1.0. Released v5.2.0.
% 0.11/0.13 % Command : bliksem %s
% 0.13/0.35 % Computer : n017.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % DateTime : Sat Jun 4 13:14:14 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.04/1.69 *** allocated 10000 integers for termspace/termends
% 1.04/1.69 *** allocated 10000 integers for clauses
% 1.04/1.69 *** allocated 10000 integers for justifications
% 1.04/1.69 *** allocated 15000 integers for termspace/termends
% 1.04/1.69 *** allocated 22500 integers for termspace/termends
% 1.04/1.69 *** allocated 33750 integers for termspace/termends
% 1.04/1.69 Bliksem 1.12
% 1.04/1.69
% 1.04/1.69
% 1.04/1.69 Automatic Strategy Selection
% 1.04/1.69
% 1.04/1.69 *** allocated 50625 integers for termspace/termends
% 1.04/1.69 *** allocated 75937 integers for termspace/termends
% 1.04/1.69 *** allocated 113905 integers for termspace/termends
% 1.04/1.69 *** allocated 170857 integers for termspace/termends
% 1.04/1.69
% 1.04/1.69 Clauses:
% 1.04/1.69
% 1.04/1.69 { ! hAPP( Y, skol1( X, Y ) ) = hAPP( X, skol1( X, Y ) ), Y = X }.
% 1.04/1.69 { ! class_Rings_Oidom( t_a ), !
% 1.04/1.69 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( t_a, t_a,
% 1.04/1.69 c_Polynomial_Opoly( t_a, v_p ) ) }.
% 1.04/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.04/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( c_Nat_OSuc, X ) ) ) }
% 1.04/1.69 .
% 1.04/1.69 { ! class_Rings_Oidom( t_a ), ! skol2 = c_Groups_Ozero__class_Ozero( t_a )
% 1.04/1.69 }.
% 1.04/1.69 { ! class_Rings_Oidom( t_a ), ! hAPP( c_Polynomial_Opoly( t_a, v_cs____ ),
% 1.04/1.69 skol2 ) = c_Groups_Ozero__class_Ozero( t_a ) }.
% 1.04/1.69 { ! class_Rings_Oidom( t_a ), ! skol3 = c_Groups_Ozero__class_Ozero( t_a )
% 1.04/1.69 }.
% 1.04/1.69 { ! class_Rings_Oidom( t_a ), ! hAPP( c_Polynomial_Opoly( t_a, v_cs____ ),
% 1.04/1.69 skol3 ) = c_Groups_Ozero__class_Ozero( t_a ) }.
% 1.04/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), hAPP(
% 1.04/1.69 c_Nat_OSuc, X ) ) ) }.
% 1.04/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.04/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Nat_OSuc
% 1.04/1.69 , Y ) ), hAPP( c_Nat_OSuc, X ) ) ) }.
% 1.04/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ),
% 1.04/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.04/1.69 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 1.04/1.69 ( hAPP( c_Polynomial_OpCons( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.04/1.69 c_Groups_Oplus__class_Oplus( X ), T ), hAPP( hAPP(
% 1.04/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( c_Polynomial_Opoly( X, Z )
% 1.04/1.69 , Y ) ) ) }.
% 1.04/1.69 { ! class_Rings_Olinordered__ring( X ), ! hBOOL( hAPP(
% 1.04/1.69 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.04/1.69 ( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP(
% 1.04/1.69 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ),
% 1.04/1.69 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.04/1.69 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 1.04/1.69 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 1.04/1.69 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.04/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 1.04/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) ), ! Z =
% 1.04/1.69 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 1.04/1.69 }.
% 1.04/1.69 { ! class_Rings_Olinordered__ring__strict( X ), Z =
% 1.04/1.69 c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP(
% 1.04/1.69 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 1.04/1.69 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.04/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 1.04/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) ) }.
% 1.04/1.69 { ! class_Rings_Olinordered__ring__strict( X ), Y =
% 1.04/1.69 c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP(
% 1.04/1.69 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 1.04/1.69 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.04/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 1.04/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) ) }.
% 1.04/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), hAPP(
% 1.04/1.69 c_Nat_OSuc, hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ),
% 1.04/1.69 X ) ) ) ) }.
% 1.04/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), hAPP(
% 1.04/1.69 c_Nat_OSuc, hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ),
% 1.04/1.69 Y ) ) ) ) }.
% 1.04/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), X
% 1.04/1.69 = hAPP( c_Nat_OSuc, hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat
% 1.04/1.69 ), Y ), skol4( X, Y ) ) ) }.
% 1.04/1.69 { ! X = hAPP( c_Nat_OSuc, hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.04/1.69 tc_Nat_Onat ), Y ), Z ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.04/1.69 tc_Nat_Onat, Y ), X ) ) }.
% 1.04/1.69 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 1.04/1.69 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z = X
% 1.04/1.69 , Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.04/1.69 { ! Z = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 1.04/1.69 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }
% 1.04/1.69 .
% 1.04/1.69 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 1.04/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 1.04/1.69 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 1.04/1.69 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Y = X
% 1.04/1.69 , Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.04/1.69 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 1.04/1.69 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 1.04/1.69 .
% 1.04/1.69 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 1.04/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 1.04/1.69 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.04/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 1.04/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 1.04/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.04/1.69 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.04/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.04/1.69 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.04/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.04/1.69 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 1.04/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 1.04/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.04/1.69 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.04/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) =
% 1.04/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.04/1.69 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP(
% 1.04/1.69 c_Nat_OSuc, Z ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.04/1.69 tc_Nat_Onat ), hAPP( c_Nat_OSuc, Z ) ), X ), Y = X }.
% 1.04/1.69 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP(
% 1.04/1.69 c_Nat_OSuc, Z ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.04/1.69 tc_Nat_Onat ), hAPP( c_Nat_OSuc, Z ) ), X ) }.
% 1.04/1.69 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.69 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP( hAPP
% 1.04/1.69 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), hAPP( hAPP(
% 1.04/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.04/1.69 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP
% 1.04/1.69 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP(
% 1.04/1.69 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.04/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.04/1.69 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 1.04/1.69 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 1.04/1.69 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y =
% 1.04/1.69 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.04/1.69 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Y =
% 1.04/1.69 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.04/1.69 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 1.04/1.69 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 1.04/1.69 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( Z, Y, X ), hAPP(
% 1.04/1.69 X, T ) = hAPP( X, U ) }.
% 1.04/1.69 { ! hAPP( X, skol5( X ) ) = hAPP( X, skol31( X ) ),
% 1.04/1.69 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( Z, Y, X ) }.
% 1.04/1.69 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.04/1.69 hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y = hAPP
% 1.04/1.69 ( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.04/1.69 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.04/1.69 hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X = hAPP
% 1.04/1.69 ( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.04/1.69 { ! Y = hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X
% 1.04/1.69 = hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP(
% 1.04/1.69 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP(
% 1.04/1.69 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.04/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), !
% 1.04/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.04/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Z ) ), hBOOL( hAPP(
% 1.04/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.04/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.04/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ) }.
% 1.04/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), !
% 1.04/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.04/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Z ) ), hBOOL( hAPP(
% 1.04/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.04/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ) ), hAPP( hAPP(
% 1.04/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) ) }.
% 1.04/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.04/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.04/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ), hBOOL( hAPP(
% 1.04/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.04/1.69 tc_Nat_Onat ) ), Y ) ) }.
% 1.04/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.04/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.04/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ), hBOOL( hAPP(
% 1.04/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z ), X ) ) }.
% 1.04/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.04/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) ), ! hBOOL( hAPP(
% 1.04/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z ), X ) ), hBOOL( hAPP(
% 1.04/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.04/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.04/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ) }.
% 1.04/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.04/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.04/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ), hBOOL( hAPP(
% 1.04/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.04/1.69 tc_Nat_Onat ) ), Z ) ) }.
% 1.04/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.04/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.04/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ), hBOOL( hAPP(
% 1.04/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ) }.
% 1.04/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.04/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Z ) ), ! hBOOL( hAPP(
% 1.04/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), hBOOL( hAPP(
% 1.04/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.04/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.04/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ) }.
% 1.04/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.04/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.04/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) ), hBOOL( hAPP(
% 1.04/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.04/1.69 tc_Nat_Onat ) ), Y ) ) }.
% 1.04/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.04/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.04/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) ), hBOOL( hAPP(
% 1.04/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.04/1.69 tc_Nat_Onat ) ), X ) ) }.
% 1.04/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.04/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) ), ! hBOOL( hAPP(
% 1.04/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.04/1.69 tc_Nat_Onat ) ), X ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.04/1.69 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.04/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) ) }.
% 1.04/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.04/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( c_Nat_OSuc, Z ) ), Y
% 1.04/1.69 ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP(
% 1.04/1.69 c_Nat_OSuc, Z ) ), X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.04/1.69 tc_Nat_Onat, Y ), X ) ) }.
% 1.04/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.04/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.04/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( c_Nat_OSuc, Z ) ), Y
% 1.04/1.69 ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP(
% 1.04/1.69 c_Nat_OSuc, Z ) ), X ) ) ) }.
% 1.04/1.69 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP(
% 1.04/1.69 c_Nat_OSuc, Y ) ), X ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.04/1.69 tc_Nat_Onat ), X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.04/1.69 tc_Nat_Onat ), Y ), X ) ) }.
% 1.04/1.69 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), hAPP(
% 1.04/1.69 c_Nat_OSuc, X ) ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat
% 1.04/1.69 ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X
% 1.04/1.69 ) ) }.
% 1.04/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 1.04/1.69 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) ), !
% 1.04/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Nat_OSuc
% 1.04/1.69 , c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), Y ) ), hBOOL( hAPP(
% 1.04/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Nat_OSuc,
% 1.04/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), hAPP( hAPP(
% 1.04/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) ) }.
% 1.04/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 1.04/1.69 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) ), !
% 1.04/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Nat_OSuc
% 1.04/1.69 , c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), Y ) ), hBOOL( hAPP(
% 1.04/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), hAPP( hAPP(
% 1.04/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ) }.
% 1.04/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 1.04/1.69 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) ), !
% 1.04/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Nat_OSuc
% 1.04/1.69 , c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), Y ) ), hBOOL( hAPP(
% 1.04/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), hAPP( hAPP(
% 1.04/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) ) }.
% 1.04/1.69 { ! class_Groups_Ozero( X ), !
% 1.04/1.69 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 1.04/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 1.04/1.69 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.04/1.69 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.04/1.69 tc_Polynomial_Opoly( X ) ),
% 1.04/1.69 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 1.04/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.04/1.69 { ! hAPP( c_Nat_OSuc, Y ) = hAPP( c_Nat_OSuc, X ), Y = X }.
% 1.04/1.69 { ! hAPP( c_Nat_OSuc, Y ) = hAPP( c_Nat_OSuc, X ), Y = X }.
% 1.04/1.69 { ! Y = X, hAPP( c_Nat_OSuc, Y ) = hAPP( c_Nat_OSuc, X ) }.
% 1.04/1.69 { ! hAPP( c_Nat_OSuc, X ) = X }.
% 1.04/1.69 { ! X = hAPP( c_Nat_OSuc, X ) }.
% 1.04/1.69 { alpha43( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.04/1.69 tc_Nat_Onat, Y ), Z ) ), hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 1.04/1.69 { alpha43( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP
% 1.04/1.69 ( X, Y ), Z ) ) }.
% 1.04/1.69 { ! alpha43( X, Y, Z ), alpha48( X, Y, Z ), Z = Y }.
% 1.04/1.69 { ! alpha43( X, Y, Z ), alpha48( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z
% 1.04/1.69 ) ) }.
% 1.04/1.69 { ! alpha48( X, Y, Z ), alpha43( X, Y, Z ) }.
% 1.04/1.69 { ! Z = Y, hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha43( X, Y, Z ) }.
% 1.04/1.69 { ! alpha48( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.04/1.69 tc_Nat_Onat, Z ), Y ) ) }.
% 1.04/1.69 { ! alpha48( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 1.04/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z ), Y ) ),
% 1.04/1.69 hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha48( X, Y, Z ) }.
% 1.04/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), !
% 1.04/1.69 Y = X }.
% 1.04/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), !
% 1.04/1.69 X = Y }.
% 1.04/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), X ) ) }.
% 1.04/1.69 { Y = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X )
% 1.04/1.69 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), Y ) ) }
% 1.04/1.69 .
% 1.04/1.69 { Y = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X )
% 1.04/1.69 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), Y ) ) }
% 1.04/1.69 .
% 1.04/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), !
% 1.04/1.69 Y = X }.
% 1.04/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), Y ) ), !
% 1.04/1.69 Y = X }.
% 1.04/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), X ) ) }.
% 1.04/1.69 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) = hAPP
% 1.04/1.69 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Y ), Z = X }.
% 1.04/1.69 { ! Z = X, hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y )
% 1.04/1.69 = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Y ) }.
% 1.04/1.69 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) = hAPP
% 1.04/1.69 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ), Y = X }.
% 1.04/1.69 { ! Y = X, hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y )
% 1.04/1.69 = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) }.
% 1.04/1.69 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.69 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP( hAPP
% 1.04/1.69 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 1.04/1.69 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) }.
% 1.04/1.69 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 1.04/1.69 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP(
% 1.04/1.69 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), hAPP( hAPP(
% 1.04/1.69 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) }.
% 1.04/1.69 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) = hAPP(
% 1.04/1.69 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Y ) }.
% 1.04/1.69 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( c_Polynomial_OpCons( X ), U ), T
% 1.04/1.69 ) = hAPP( hAPP( c_Polynomial_OpCons( X ), Z ), Y ), U = Z }.
% 1.04/1.69 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( c_Polynomial_OpCons( X ), U ), T
% 1.04/1.69 ) = hAPP( hAPP( c_Polynomial_OpCons( X ), Z ), Y ), T = Y }.
% 1.04/1.69 { ! class_Groups_Ozero( X ), ! U = Z, ! T = Y, hAPP( hAPP(
% 1.04/1.69 c_Polynomial_OpCons( X ), U ), T ) = hAPP( hAPP( c_Polynomial_OpCons( X )
% 1.04/1.69 , Z ), Y ) }.
% 1.04/1.69 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 1.04/1.69 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ), Z = Y }.
% 1.04/1.69 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Z = Y,
% 1.04/1.69 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ) }.
% 1.04/1.69 { ! hAPP( c_Nat_OSuc, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.04/1.69 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = hAPP( c_Nat_OSuc, X ) }.
% 1.04/1.69 { ! hAPP( c_Nat_OSuc, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.04/1.69 { ! hAPP( c_Nat_OSuc, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.04/1.69 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = hAPP( c_Nat_OSuc, X ) }.
% 1.04/1.69 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = hAPP( c_Nat_OSuc, X ) }.
% 1.04/1.69 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP(
% 1.04/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.04/1.69 tc_Nat_Onat ) ), X ) ) }.
% 1.04/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), !
% 1.04/1.69 X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.04/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ),
% 1.04/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.04/1.69 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP(
% 1.04/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.04/1.69 tc_Nat_Onat ) ), X ) ) }.
% 1.04/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.04/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! X =
% 1.04/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.04/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ),
% 1.04/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.04/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 1.04/1.69 c_Nat_OSuc, Y ) ), hAPP( c_Nat_OSuc, X ) ) ), hBOOL( hAPP(
% 1.04/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ) }.
% 1.04/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 1.04/1.69 c_Nat_OSuc, Y ) ), X ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.04/1.69 tc_Nat_Onat, Y ), X ) ) }.
% 1.04/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), hAPP(
% 1.04/1.69 c_Nat_OSuc, X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.04/1.69 tc_Nat_Onat, Y ), X ) ), Y = X }.
% 1.04/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), !
% 1.04/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), Z ) ),
% 1.04/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Nat_OSuc
% 1.04/1.69 , Y ) ), Z ) ) }.
% 1.04/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.04/1.69 hAPP( c_Nat_OSuc, Y ) = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.04/1.69 tc_Nat_Onat, hAPP( c_Nat_OSuc, Y ) ), X ) ) }.
% 1.04/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.04/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), hAPP(
% 1.04/1.69 c_Nat_OSuc, X ) ) ) }.
% 1.04/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), !
% 1.04/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), hAPP(
% 1.04/1.69 c_Nat_OSuc, X ) ) ), X = Y }.
% 1.04/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), !
% 1.04/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), hAPP(
% 1.04/1.69 c_Nat_OSuc, X ) ) ), Y = X }.
% 1.04/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), ! Y
% 1.04/1.69 = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), hAPP(
% 1.04/1.69 c_Nat_OSuc, X ) ) ) }.
% 1.04/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 1.04/1.69 c_Nat_OSuc, Y ) ), hAPP( c_Nat_OSuc, X ) ) ), hBOOL( hAPP(
% 1.04/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ) }.
% 1.04/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.04/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Nat_OSuc
% 1.04/1.69 , Y ) ), hAPP( c_Nat_OSuc, X ) ) ) }.
% 1.04/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), hAPP(
% 1.04/1.69 c_Nat_OSuc, X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.04/1.69 tc_Nat_Onat, Y ), X ) ), Y = X }.
% 1.04/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.04/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), hAPP(
% 1.04/1.69 c_Nat_OSuc, X ) ) ) }.
% 1.04/1.69 { ! Y = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ),
% 1.04/1.69 hAPP( c_Nat_OSuc, X ) ) ) }.
% 1.04/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.04/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), hAPP(
% 1.04/1.69 c_Nat_OSuc, Y ) ) ) }.
% 1.04/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), hAPP(
% 1.04/1.69 c_Nat_OSuc, Y ) ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.04/1.69 tc_Nat_Onat, Y ), X ) ) }.
% 1.04/1.69 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) = Y, X
% 1.04/1.69 = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.04/1.69 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) =
% 1.04/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 1.04/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.04/1.69 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) =
% 1.04/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 1.04/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.04/1.69 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X =
% 1.04/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.69 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) =
% 1.04/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.04/1.69 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ),
% 1.04/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = X }.
% 1.04/1.69 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ),
% 1.04/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) = X }.
% 1.04/1.69 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( c_Nat_OSuc
% 1.04/1.69 , Y ) ), X ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y
% 1.04/1.69 ), hAPP( c_Nat_OSuc, X ) ) }.
% 1.04/1.69 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( c_Nat_OSuc
% 1.04/1.69 , Y ) ), X ) = hAPP( c_Nat_OSuc, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.04/1.69 ( tc_Nat_Onat ), Y ), X ) ) }.
% 1.04/1.70 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), hAPP(
% 1.04/1.70 c_Nat_OSuc, X ) ) = hAPP( c_Nat_OSuc, hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), Z ) ), X ) ), hBOOL(
% 1.04/1.70 hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), !
% 1.04/1.70 hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), T ), X ) = hAPP(
% 1.04/1.70 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), Z ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T ), Z ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), !
% 1.04/1.70 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, T ), Z ) ),
% 1.04/1.70 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), T ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.04/1.70 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), Z ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.04/1.70 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), hAPP( hAPP
% 1.04/1.70 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.04/1.70 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), hAPP( hAPP
% 1.04/1.70 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.04/1.70 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ), X ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ), Y ) ) }.
% 1.04/1.70 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( c_Polynomial_OpCons( X ), Z ), Y
% 1.04/1.70 ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) }.
% 1.04/1.70 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( c_Polynomial_OpCons( X ), Z ), Y
% 1.04/1.70 ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y =
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.04/1.70 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 1.04/1.70 c_Polynomial_OpCons( X ), Z ), Y ) = c_Groups_Ozero__class_Ozero(
% 1.04/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.04/1.70 { ! class_Groups_Ozero( X ), hAPP( hAPP( c_Polynomial_OpCons( X ),
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 1.04/1.70 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 1.04/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.04/1.70 { ! class_Groups_Ocomm__monoid__add( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 1.04/1.70 c_Polynomial_OpCons( X ), U ), T ) ), hAPP( hAPP( c_Polynomial_OpCons( X
% 1.04/1.70 ), Z ), Y ) ) = hAPP( hAPP( c_Polynomial_OpCons( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), U ), Z ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), T ), Y ) ) }.
% 1.04/1.70 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) }.
% 1.04/1.70 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 1.04/1.70 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Z
% 1.04/1.70 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP(
% 1.04/1.70 c_Polynomial_Opoly( X, T ), Y ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 1.04/1.70 ) }.
% 1.04/1.70 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 1.04/1.70 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), T ), Z )
% 1.04/1.70 ), Y ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP(
% 1.04/1.70 c_Polynomial_Opoly( X, T ), Y ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 1.04/1.70 ) }.
% 1.04/1.70 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 1.04/1.70 ( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), T ), Z
% 1.04/1.70 ) ), Y ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), hAPP(
% 1.04/1.70 c_Polynomial_Opoly( X, T ), Y ) ), Z ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__ring__strict( X ), ! hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 1.04/1.70 .
% 1.04/1.70 { ! class_Rings_Olinordered__ring__strict( X ), ! hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 1.04/1.70 .
% 1.04/1.70 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 1.04/1.70 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), hAPP(
% 1.04/1.70 c_Nat_OSuc, X ) ) ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.04/1.70 alpha1( X, Y ) }.
% 1.04/1.70 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), hAPP( c_Nat_OSuc, X ) )
% 1.04/1.70 ) }.
% 1.04/1.70 { ! alpha1( X, Y ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 1.04/1.70 , Y ), hAPP( c_Nat_OSuc, X ) ) ) }.
% 1.04/1.70 { ! alpha1( X, Y ), Y = hAPP( c_Nat_OSuc, skol6( Z, Y ) ) }.
% 1.04/1.70 { ! alpha1( X, Y ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 1.04/1.70 , skol6( X, Y ) ), X ) ) }.
% 1.04/1.70 { ! Y = hAPP( c_Nat_OSuc, Z ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless
% 1.04/1.70 ( tc_Nat_Onat, Z ), X ) ), alpha1( X, Y ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), hAPP(
% 1.04/1.70 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), X =
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.04/1.70 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), hAPP( c_Nat_OSuc,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), X = hAPP( c_Nat_OSuc
% 1.04/1.70 , skol7( X ) ) }.
% 1.04/1.70 { ! X = hAPP( c_Nat_OSuc, Y ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.04/1.70 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ) }.
% 1.04/1.70 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) = hAPP
% 1.04/1.70 ( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha2( X, Y
% 1.04/1.70 ), alpha18( X, Y ) }.
% 1.04/1.70 { ! alpha2( X, Y ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat )
% 1.04/1.70 , Y ), X ) = hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.04/1.70 ) }.
% 1.04/1.70 { ! alpha18( X, Y ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat )
% 1.04/1.70 , Y ), X ) = hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.04/1.70 ) }.
% 1.04/1.70 { ! alpha18( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.04/1.70 { ! alpha18( X, Y ), X = hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero(
% 1.04/1.70 tc_Nat_Onat ) ) }.
% 1.04/1.70 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = hAPP( c_Nat_OSuc
% 1.04/1.70 , c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha18( X, Y ) }.
% 1.04/1.70 { ! alpha2( X, Y ), Y = hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero(
% 1.04/1.70 tc_Nat_Onat ) ) }.
% 1.04/1.70 { ! alpha2( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.04/1.70 { ! Y = hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X
% 1.04/1.70 = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha2( X, Y ) }.
% 1.04/1.70 { ! hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = hAPP(
% 1.04/1.70 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ), alpha3( X, Y
% 1.04/1.70 ), alpha19( X, Y ) }.
% 1.04/1.70 { ! alpha3( X, Y ), hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero(
% 1.04/1.70 tc_Nat_Onat ) ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat )
% 1.04/1.70 , Y ), X ) }.
% 1.04/1.70 { ! alpha19( X, Y ), hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero(
% 1.04/1.70 tc_Nat_Onat ) ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat )
% 1.04/1.70 , Y ), X ) }.
% 1.04/1.70 { ! alpha19( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.04/1.70 { ! alpha19( X, Y ), X = hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero(
% 1.04/1.70 tc_Nat_Onat ) ) }.
% 1.04/1.70 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = hAPP( c_Nat_OSuc
% 1.04/1.70 , c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha19( X, Y ) }.
% 1.04/1.70 { ! alpha3( X, Y ), Y = hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero(
% 1.04/1.70 tc_Nat_Onat ) ) }.
% 1.04/1.70 { ! alpha3( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.04/1.70 { ! Y = hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X
% 1.04/1.70 = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha3( X, Y ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.04/1.70 tc_Nat_Onat ) ), Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.04/1.70 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.04/1.70 tc_Nat_Onat ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ),
% 1.04/1.70 Y ), X ) ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.04/1.70 tc_Nat_Onat ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ),
% 1.04/1.70 Y ), X ) ) ) }.
% 1.04/1.70 { ! class_Rings_Oidom( t_a ), !
% 1.04/1.70 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( t_a, t_a,
% 1.04/1.70 c_Polynomial_Opoly( t_a, hAPP( hAPP( c_Polynomial_OpCons( t_a ), v_c____
% 1.04/1.70 ), v_cs____ ) ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), hAPP(
% 1.04/1.70 c_Nat_OSuc, hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.04/1.70 ) ) ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X = hAPP(
% 1.04/1.70 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.04/1.70 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( X ), T ), Y ) ) = hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ) }.
% 1.04/1.70 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 1.04/1.70 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( X ), Z ), hAPP( c_Nat_OSuc, Y ) ) }.
% 1.04/1.70 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( X ), Z ), hAPP( c_Nat_OSuc, Y ) ) }.
% 1.04/1.70 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( X ), Z ), hAPP( c_Nat_OSuc, Y ) ) = hAPP(
% 1.04/1.70 hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) }.
% 1.04/1.70 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( X ), Z ), hAPP( c_Nat_OSuc, Y ) ) = hAPP(
% 1.04/1.70 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.04/1.70 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 1.04/1.70 , Z ), hAPP( c_Nat_OSuc, Y ) ) = hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.04/1.70 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.04/1.70 hAPP( c_Nat_OSuc, Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.04/1.70 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.04/1.70 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.04/1.70 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 1.04/1.70 .
% 1.04/1.70 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.04/1.70 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.04/1.70 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.04/1.70 tc_Nat_Onat ) }.
% 1.04/1.70 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.04/1.70 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.04/1.70 , ! Z = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 1.04/1.70 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y )
% 1.04/1.70 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 1.04/1.70 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) ), hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.04/1.70 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.04/1.70 { ! class_Groups_Ocomm__monoid__add( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ),
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) = Y }.
% 1.04/1.70 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.04/1.70 { ! class_Groups_Ocomm__monoid__add( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), Y ),
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) = Y }.
% 1.04/1.70 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP
% 1.04/1.70 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 1.04/1.70 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 1.04/1.70 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.04/1.70 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), T ), Z ) ), Y )
% 1.04/1.70 = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ),
% 1.04/1.70 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T
% 1.04/1.70 ), Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly
% 1.04/1.70 ( X ) ), Z ), Y ) ) }.
% 1.04/1.70 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), hAPP( c_Nat_OSuc
% 1.04/1.70 , c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) = hAPP( c_Nat_OSuc
% 1.04/1.70 , c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.04/1.70 { ! hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) =
% 1.04/1.70 hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = hAPP( c_Nat_OSuc,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.04/1.70 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = hAPP( c_Nat_OSuc
% 1.04/1.70 , c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.04/1.70 { ! Y = hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 1.04/1.70 hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = hAPP
% 1.04/1.70 ( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.04/1.70 tc_Nat_Onat ) ), Y ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 1.04/1.70 .
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.04/1.70 tc_Nat_Onat ) ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 1.04/1.70 , Y ), X ) ) ) }.
% 1.04/1.70 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.04/1.70 tc_Nat_Onat ) ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 1.04/1.70 , Y ), X ) ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) ), X =
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.04/1.70 tc_Nat_Onat ) ), Y ) ) }.
% 1.04/1.70 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.04/1.70 tc_Nat_Onat ) ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 1.04/1.70 , Y ), X ) ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.04/1.70 tc_Nat_Onat ) ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 1.04/1.70 , Y ), X ) ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Z ) ), hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z ), Y ) ) }.
% 1.04/1.70 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 1.04/1.70 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.04/1.70 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) }.
% 1.04/1.70 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.04/1.70 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Z ) }.
% 1.04/1.70 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), U ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 1.04/1.70 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), Y ) ) }.
% 1.04/1.70 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.04/1.70 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) = hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) }.
% 1.04/1.70 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), T ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), Z ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ) }.
% 1.04/1.70 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), T ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.04/1.70 ( X ), T ), Z ) ), Y ) }.
% 1.04/1.70 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.04/1.70 ( X ), T ), Z ) ), Y ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), T
% 1.04/1.70 ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) }.
% 1.04/1.70 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.04/1.70 ( X ), T ), Z ) ), Y ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ),
% 1.04/1.70 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), T ), Y ) ), Z ) }.
% 1.04/1.70 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.04/1.70 ( X ), U ), T ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), Y )
% 1.04/1.70 ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), U ), Z ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ) }.
% 1.04/1.70 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) }.
% 1.04/1.70 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) }.
% 1.04/1.70 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.04/1.70 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.04/1.70 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.04/1.70 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.04/1.70 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), c_Groups_Ozero__class_Ozero( X ) ), Y )
% 1.04/1.70 = Y }.
% 1.04/1.70 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), Y ), c_Groups_Ozero__class_Ozero( X ) )
% 1.04/1.70 = Y }.
% 1.04/1.70 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.04/1.70 ( X ), ! Z = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), Y ), Y =
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) }.
% 1.04/1.70 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.04/1.70 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z = hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) }.
% 1.04/1.70 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.04/1.70 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.04/1.70 ( X ), U = T, Z = Y, ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP
% 1.04/1.70 ( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) = hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), U ), Y ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 1.04/1.70 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.04/1.70 ( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) = hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), U ), Y ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), ! U = T }.
% 1.04/1.70 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.04/1.70 ( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) = hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), U ), Y ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), ! Z = Y }.
% 1.04/1.70 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.04/1.70 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ), Z ) }.
% 1.04/1.70 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.04/1.70 ( X ), ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), U ), Y ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ), U = Z, T = Y }.
% 1.04/1.70 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.04/1.70 ( X ), ! U = Z, hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP
% 1.04/1.70 ( c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), U ), Y ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 1.04/1.70 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.04/1.70 ( X ), ! T = Y, hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP
% 1.04/1.70 ( c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), U ), Y ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 1.04/1.70 { ! class_Rings_Oring__1__no__zero__divisors( X ), Y =
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 1.04/1.70 ( X ) }.
% 1.04/1.70 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.04/1.70 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.04/1.70 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.04/1.70 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.04/1.70 ( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! W = U, T = Z, ! hAPP( hAPP
% 1.04/1.70 ( c_Groups_Oplus__class_Oplus( X ), W ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) = hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), U ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) = hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z = Y }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! Z = Y, hAPP( hAPP
% 1.04/1.70 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) = hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z ), Y ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z ), Y ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ) }.
% 1.04/1.70 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X, hAPP(
% 1.04/1.70 hAPP( c_Polynomial_OpCons( X ), T ), Z ), Y ) = hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 1.04/1.70 c_Polynomial_OpCons( X ), T ), c_Groups_Ozero__class_Ozero(
% 1.04/1.70 tc_Polynomial_Opoly( X ) ) ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.04/1.70 ( tc_Polynomial_Opoly( X ) ), Y ), c_Polynomial_Opcompose( X, Z, Y ) ) )
% 1.04/1.70 }.
% 1.04/1.70 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 1.04/1.70 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Y ) ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 1.04/1.70 ) }.
% 1.04/1.70 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 1.04/1.70 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), Y ), Y ) ) ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.04/1.70 ( X ), Y ), Y ) ), c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 1.04/1.70 ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 1.04/1.70 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), Y ), Y ) ), c_Groups_Ozero__class_Ozero
% 1.04/1.70 ( X ) ) ) }.
% 1.04/1.70 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.04/1.70 ( X ), Y ), Y ) ), c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 1.04/1.70 ) }.
% 1.04/1.70 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 1.04/1.70 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), Y ), Y ) ), c_Groups_Ozero__class_Ozero
% 1.04/1.70 ( X ) ) ) }.
% 1.04/1.70 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 1.04/1.70 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 1.04/1.70 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 1.04/1.70 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, T ), Z ) ), hBOOL(
% 1.04/1.70 hAPP( c_Orderings_Oord__class_Oless( X, T ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) ) }.
% 1.04/1.70 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 1.04/1.70 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Z ),
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.04/1.70 ( X ), Y ), Z ) ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.04/1.70 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.04/1.70 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.04/1.70 c_Polynomial_Opcompose( X, T, Z ) ), Y ) = hAPP( c_Polynomial_Opoly( X, T
% 1.04/1.70 ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 1.04/1.70 { ! class_Groups_Ozero( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y, Y =
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) }.
% 1.04/1.70 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) = Y }.
% 1.04/1.70 { ! class_Rings_Olinordered__idom( X ), Z = Y, hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 1.04/1.70 { ! class_Groups_Oab__semigroup__mult( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.04/1.70 { ! class_Groups_Ocancel__semigroup__add( X ), ! hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), Z ), T ) = hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), Y ), T ), Z = Y }.
% 1.04/1.70 { ! class_Groups_Ocancel__ab__semigroup__add( X ), ! hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), T ), Z ) = hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), T ), Y ), Z = Y }.
% 1.04/1.70 { ! class_Groups_Ocancel__semigroup__add( X ), ! hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), T ), Z ) = hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), T ), Y ), Z = Y }.
% 1.04/1.70 { ! class_Groups_Ocancel__semigroup__add( X ), ! hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), T ), Z ) = hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), Y ), Z ), T = Y }.
% 1.04/1.70 { ! class_Groups_Ocancel__semigroup__add( X ), ! T = Y, hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), T ), Z ) = hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) }.
% 1.04/1.70 { ! class_Groups_Ocancel__semigroup__add( X ), ! hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), T ), Z ) = hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), T ), Y ), Z = Y }.
% 1.04/1.70 { ! class_Groups_Ocancel__semigroup__add( X ), ! Z = Y, hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), T ), Z ) = hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), T ), Y ) }.
% 1.04/1.70 { ! class_Groups_Oab__semigroup__add( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.04/1.70 ( X ), T ), Z ) ), Y ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), T
% 1.04/1.70 ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) }.
% 1.04/1.70 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), hAPP( hAPP
% 1.04/1.70 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ) }.
% 1.04/1.70 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 1.04/1.70 ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.04/1.70 { ! class_Rings_Ono__zero__divisors( X ), ! hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 1.04/1.70 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.04/1.70 { ! class_Rings_Ono__zero__divisors( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.04/1.70 X ), Z = c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) =
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) }.
% 1.04/1.70 { ! class_Rings_Oring__no__zero__divisors( X ), ! hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 1.04/1.70 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.04/1.70 { ! class_Rings_Oring__no__zero__divisors( X ), ! Z =
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) }.
% 1.04/1.70 { ! class_Rings_Oring__no__zero__divisors( X ), ! Y =
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) }.
% 1.04/1.70 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.04/1.70 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) =
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) }.
% 1.04/1.70 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.04/1.70 ( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) =
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) }.
% 1.04/1.70 { ! class_Groups_Olinordered__ab__group__add( X ), ! hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), Y ), Y ) = c_Groups_Ozero__class_Ozero
% 1.04/1.70 ( X ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.04/1.70 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.04/1.70 ( X ), Y ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.04/1.70 { ! class_Groups_Ocomm__monoid__add( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), Y ), c_Groups_Ozero__class_Ozero( X ) )
% 1.04/1.70 = Y }.
% 1.04/1.70 { ! class_Groups_Omonoid__add( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.04/1.70 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.04/1.70 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) = hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), Y ), Y ), Y =
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) }.
% 1.04/1.70 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero( X ) = hAPP
% 1.04/1.70 ( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Y ) }.
% 1.04/1.70 { ! class_Groups_Ocomm__monoid__add( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), c_Groups_Ozero__class_Ozero( X ) ), Y )
% 1.04/1.70 = Y }.
% 1.04/1.70 { ! class_Groups_Omonoid__add( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.04/1.70 ( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) = Y }.
% 1.04/1.70 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 1.04/1.70 ( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 1.04/1.70 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 1.04/1.70 ( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), Z ), T ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), Y ), T ) ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 1.04/1.70 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, U ), T ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.04/1.70 ( X ), Z ), U ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), T )
% 1.04/1.70 ) ) }.
% 1.04/1.70 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.04/1.70 ( X ), T ), Z ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), T ), Y )
% 1.04/1.70 ) ) }.
% 1.04/1.70 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.04/1.70 ( X ), Z ), T ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), T )
% 1.04/1.70 ) ) }.
% 1.04/1.70 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 1.04/1.70 ( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 1.04/1.70 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 1.04/1.70 ( c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.04/1.70 ( X ), T ), Z ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), T ), Y )
% 1.04/1.70 ) ) }.
% 1.04/1.70 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 1.04/1.70 ( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, T ), Y ) ) }.
% 1.04/1.70 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 1.04/1.70 ( c_Orderings_Oord__class_Oless( X, T ), Y ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.04/1.70 ( X ), T ), Z ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Z )
% 1.04/1.70 ) ) }.
% 1.04/1.70 { ! class_Rings_Osemiring( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X
% 1.04/1.70 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP(
% 1.04/1.70 hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ), Y ) ) = hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), U ), Z ) ), T ) ), Y ) }.
% 1.04/1.70 { ! class_Rings_Ocomm__semiring( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.04/1.70 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 1.04/1.70 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Z =
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 1.04/1.70 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 1.04/1.70 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 1.04/1.70 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 1.04/1.70 .
% 1.04/1.70 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), T ), Z ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ) ), X ) ) = hAPP(
% 1.04/1.70 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), T ), Y ) ), Z ) ), X ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, T ), c_Groups_Ozero__class_Ozero( X ) )
% 1.04/1.70 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, T ), c_Groups_Ozero__class_Ozero( X ) )
% 1.04/1.70 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__comm__semiring__strict( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), T )
% 1.04/1.70 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), T )
% 1.04/1.70 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), T )
% 1.04/1.70 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 1.04/1.70 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Z ),
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 1.04/1.70 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 1.04/1.70 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 1.04/1.70 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Z ), T ) ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 1.04/1.70 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Z ), T ) ), hBOOL(
% 1.04/1.70 hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 1.04/1.70 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ), ! hBOOL(
% 1.04/1.70 hAPP( c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.04/1.70 ), Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) ), Z ) ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 1.04/1.70 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ), ! hBOOL(
% 1.04/1.70 hAPP( c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.04/1.70 ), Z ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) ), Y ) ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 1.04/1.70 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Z ),
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 1.04/1.70 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Z ),
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 1.04/1.70 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 1.04/1.70 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 1.04/1.70 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, T ), Z ) ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 1.04/1.70 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, T ), Z ) ), hBOOL(
% 1.04/1.70 hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ), alpha4( X, Y, Z, T ),
% 1.04/1.70 alpha20( X, Y, Z, T ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha4( X, Y, Z, T ),
% 1.04/1.70 hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha20( X, Y, Z, T ),
% 1.04/1.70 hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 1.04/1.70 { ! alpha20( X, Y, Z, T ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, T
% 1.04/1.70 ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.04/1.70 { ! alpha20( X, Y, Z, T ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Y
% 1.04/1.70 ), Z ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, T ),
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Y ), Z ) ), alpha20( X, Y, Z, T ) }.
% 1.04/1.70 { ! alpha4( X, Y, Z, T ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) ), T ) ) }.
% 1.04/1.70 { ! alpha4( X, Y, Z, T ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Z
% 1.04/1.70 ), Y ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) ), T ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), alpha4( X, Y, Z, T ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), alpha5( X, Y, Z, T ),
% 1.04/1.70 alpha21( X, Y, Z, T ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha5( X, Y, Z, T ),
% 1.04/1.70 hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha21( X, Y, Z, T ),
% 1.04/1.70 hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 1.04/1.70 { ! alpha21( X, Y, Z, T ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Z
% 1.04/1.70 ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.04/1.70 { ! alpha21( X, Y, Z, T ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Y
% 1.04/1.70 ), T ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Z ),
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Y ), T ) ), alpha21( X, Y, Z, T ) }.
% 1.04/1.70 { ! alpha5( X, Y, Z, T ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) ), Z ) ) }.
% 1.04/1.70 { ! alpha5( X, Y, Z, T ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, T
% 1.04/1.70 ), Y ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, T ), Y ) ), alpha5( X, Y, Z, T ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__ring( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.04/1.70 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X, Z, Y )
% 1.04/1.70 = c_Polynomial_Opoly__rec( tc_Polynomial_Opoly( X ), X,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 1.04/1.70 c_COMBB( tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ) ),
% 1.04/1.70 tc_fun( tc_Polynomial_Opoly( X ), tc_fun( tc_Polynomial_Opoly( X ),
% 1.04/1.70 tc_Polynomial_Opoly( X ) ) ), X ), c_COMBK( tc_fun( tc_Polynomial_Opoly(
% 1.04/1.70 X ), tc_Polynomial_Opoly( X ) ), tc_Polynomial_Opoly( X ) ) ), hAPP(
% 1.04/1.70 c_COMBC( X, tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ) )
% 1.04/1.70 , tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ) ), hAPP(
% 1.04/1.70 hAPP( c_COMBB( tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X )
% 1.04/1.70 ), tc_fun( tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ) )
% 1.04/1.70 , tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ) ) ), X ),
% 1.04/1.70 c_COMBB( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ),
% 1.04/1.70 tc_Polynomial_Opoly( X ) ) ), hAPP( hAPP( c_COMBB( tc_Polynomial_Opoly( X
% 1.04/1.70 ), tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ) ), X ),
% 1.04/1.70 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ) ), hAPP( c_COMBC
% 1.04/1.70 ( X, tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ),
% 1.04/1.70 c_Polynomial_OpCons( X ) ), c_Groups_Ozero__class_Ozero(
% 1.04/1.70 tc_Polynomial_Opoly( X ) ) ) ) ) ), hAPP( c_Groups_Otimes__class_Otimes(
% 1.04/1.70 tc_Polynomial_Opoly( X ) ), Y ) ) ), Z ) }.
% 1.04/1.70 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 1.04/1.70 tc_Polynomial_Opoly( X ) ), ! c_Polynomial_Oorder( X, Y, Z ) =
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.04/1.70 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.04/1.70 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) }.
% 1.04/1.70 { ! class_Rings_Oidom( X ), c_Polynomial_Oorder( X, Y, Z ) =
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( c_Polynomial_Opoly( X,
% 1.04/1.70 Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.04/1.70 { ! class_Rings_Oidom( t_a ),
% 1.04/1.70 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( t_a, t_a,
% 1.04/1.70 c_Polynomial_Opoly( t_a, v_cs____ ) ), ! skol8 =
% 1.04/1.70 c_Groups_Ozero__class_Ozero( t_a ) }.
% 1.04/1.70 { ! class_Rings_Oidom( t_a ),
% 1.04/1.70 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( t_a, t_a,
% 1.04/1.70 c_Polynomial_Opoly( t_a, v_cs____ ) ), alpha44( skol8 ) }.
% 1.04/1.70 { ! alpha44( X ), ! skol9( Y ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.04/1.70 }.
% 1.04/1.70 { ! alpha44( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ),
% 1.04/1.70 hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ),
% 1.04/1.70 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( t_a, skol32( X ) ) ),
% 1.04/1.70 skol9( X ) ) ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) =
% 1.04/1.70 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( t_a, v_cs____ ) }.
% 1.04/1.70 { ! alpha44( X ), hAPP( c_Polynomial_Opoly( t_a, v_cs____ ), Y ) = hAPP(
% 1.04/1.70 hAPP( c_Groups_Oplus__class_Oplus( t_a ), hAPP( c_Polynomial_Opoly( t_a,
% 1.04/1.70 v_cs____ ), c_Groups_Ozero__class_Ozero( t_a ) ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( t_a ), hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( t_a ), Y ), skol9( X ) ) ), hAPP(
% 1.04/1.70 c_Polynomial_Opoly( t_a, hAPP( hAPP( c_Polynomial_OpCons( t_a ), X ),
% 1.04/1.70 skol32( X ) ) ), Y ) ) ) }.
% 1.04/1.70 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ),
% 1.04/1.70 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( t_a, Z ) ), Y ) ),
% 1.04/1.70 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) =
% 1.04/1.70 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( t_a, v_cs____ ), !
% 1.04/1.70 hAPP( c_Polynomial_Opoly( t_a, v_cs____ ), skol38( X, Y, Z ) ) = hAPP(
% 1.04/1.70 hAPP( c_Groups_Oplus__class_Oplus( t_a ), hAPP( c_Polynomial_Opoly( t_a,
% 1.04/1.70 v_cs____ ), c_Groups_Ozero__class_Ozero( t_a ) ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( t_a ), hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( t_a ), skol38( X, Y, Z ) ), Y ) ), hAPP(
% 1.04/1.70 c_Polynomial_Opoly( t_a, hAPP( hAPP( c_Polynomial_OpCons( t_a ), X ), Z )
% 1.04/1.70 ), skol38( X, Y, Z ) ) ) ), alpha44( X ) }.
% 1.04/1.70 { ! class_Rings_Oidom( t_a ), ! skol10 = c_Groups_Ozero__class_Ozero( t_a )
% 1.04/1.70 }.
% 1.04/1.70 { ! class_Rings_Oidom( t_a ), hAPP( c_Nat_OSuc, hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ),
% 1.04/1.70 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( t_a, skol39 ) ),
% 1.04/1.70 skol33 ) ) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( t_a,
% 1.04/1.70 v_cs____ ) }.
% 1.04/1.70 { ! class_Rings_Oidom( t_a ), hAPP( c_Polynomial_Opoly( t_a, v_cs____ ), X
% 1.04/1.70 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( t_a ), hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( t_a ), X ), skol33 ) ), hAPP(
% 1.04/1.70 c_Polynomial_Opoly( t_a, hAPP( hAPP( c_Polynomial_OpCons( t_a ), skol10 )
% 1.04/1.70 , skol39 ) ), X ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.04/1.70 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), hAPP( hAPP
% 1.04/1.70 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.04/1.70 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), hAPP( hAPP
% 1.04/1.70 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ) ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, hAPP
% 1.04/1.70 ( hAPP( c_Polynomial_OpCons( X ), Z ), Y ) ), c_Polynomial_Opos__poly( X
% 1.04/1.70 , Y ), alpha6( X, Y, Z ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 1.04/1.70 c_Polynomial_Opos__poly( X, hAPP( hAPP( c_Polynomial_OpCons( X ), Z ), Y
% 1.04/1.70 ) ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__idom( X ), ! alpha6( X, Y, Z ),
% 1.04/1.70 c_Polynomial_Opos__poly( X, hAPP( hAPP( c_Polynomial_OpCons( X ), Z ), Y
% 1.04/1.70 ) ) }.
% 1.04/1.70 { ! alpha6( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly
% 1.04/1.70 ( X ) ) }.
% 1.04/1.70 { ! alpha6( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) ), Z ) ) }.
% 1.04/1.70 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), ! hBOOL(
% 1.04/1.70 hAPP( c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.04/1.70 ), Z ) ), alpha6( X, Y, Z ) }.
% 1.04/1.70 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.04/1.70 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) = hAPP
% 1.04/1.70 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) }.
% 1.04/1.70 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP
% 1.04/1.70 ( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), X ) ) = hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 1.04/1.70 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP(
% 1.04/1.70 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.04/1.70 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 1.04/1.70 ( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ), !
% 1.04/1.70 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Z ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ) }.
% 1.04/1.70 { ! class_Groups_Oone( X ), ! c_Groups_Oone__class_Oone( X ) = Y, Y =
% 1.04/1.70 c_Groups_Oone__class_Oone( X ) }.
% 1.04/1.70 { ! class_Groups_Oone( X ), ! Y = c_Groups_Oone__class_Oone( X ),
% 1.04/1.70 c_Groups_Oone__class_Oone( X ) = Y }.
% 1.04/1.70 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 1.04/1.70 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 1.04/1.70 c_Groups_Oone__class_Oone( X ) }.
% 1.04/1.70 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oone__class_Oone(
% 1.04/1.70 tc_Polynomial_Opoly( X ) ) = hAPP( hAPP( c_Polynomial_OpCons( X ),
% 1.04/1.70 c_Groups_Oone__class_Oone( X ) ), c_Groups_Ozero__class_Ozero(
% 1.04/1.70 tc_Polynomial_Opoly( X ) ) ) }.
% 1.04/1.70 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 1.04/1.70 c_Groups_Oone__class_Oone( X ) }.
% 1.04/1.70 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Oone__class_Oone( X ) =
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) }.
% 1.04/1.70 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.04/1.70 = Y }.
% 1.04/1.70 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 1.04/1.70 = Y }.
% 1.04/1.70 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 1.04/1.70 = Y }.
% 1.04/1.70 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 1.04/1.70 = Y }.
% 1.04/1.70 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.04/1.70 = Y }.
% 1.04/1.70 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.04/1.70 = Y }.
% 1.04/1.70 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.04/1.70 = c_Groups_Oone__class_Oone( X ) }.
% 1.04/1.70 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 1.04/1.70 tc_Nat_Onat ) ) = Y }.
% 1.04/1.70 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 1.04/1.70 tc_Nat_Onat ) ) = Y }.
% 1.04/1.70 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.04/1.70 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) = X }.
% 1.04/1.70 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), Y =
% 1.04/1.70 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.04/1.70 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X =
% 1.04/1.70 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.04/1.70 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 1.04/1.70 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Groups_Oone__class_Oone(
% 1.04/1.70 tc_Nat_Onat ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 1.04/1.70 , Y ), X ) }.
% 1.04/1.70 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 1.04/1.70 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 1.04/1.70 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.04/1.70 c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y = c_Groups_Oone__class_Oone(
% 1.04/1.70 tc_Nat_Onat ) }.
% 1.04/1.70 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.04/1.70 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X = c_Groups_Oone__class_Oone(
% 1.04/1.70 tc_Nat_Onat ) }.
% 1.04/1.70 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 1.04/1.70 c_Groups_Oone__class_Oone( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.04/1.70 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ),
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__semidom( X ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 1.04/1.70 c_Groups_Oone__class_Oone( X ) ) ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), Y ) )
% 1.04/1.70 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 1.04/1.70 c_Groups_Oone__class_Oone( X ) ), Z ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), hAPP
% 1.04/1.70 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__semidom( X ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Y ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), Y ), c_Groups_Oone__class_Oone( X ) ) )
% 1.04/1.70 ) }.
% 1.04/1.70 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), Y ), Y ) = hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), c_Groups_Oone__class_Oone( X ) ),
% 1.04/1.70 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 1.04/1.70 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), Z ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), Y ), c_Groups_Oone__class_Oone( X ) ) )
% 1.04/1.70 , Z ) }.
% 1.04/1.70 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) = hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), Z ), c_Groups_Oone__class_Oone( X ) ) )
% 1.04/1.70 , Y ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), Y ) )
% 1.04/1.70 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP
% 1.04/1.70 ( c_Power_Opower__class_Opower( X ), Y ), Z ), T = Z }.
% 1.04/1.70 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), Y ) )
% 1.04/1.70 , ! T = Z, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP
% 1.04/1.70 ( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) }.
% 1.04/1.70 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 1.04/1.70 , Y ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 1.04/1.70 c_Groups_Oone__class_Oone( X ) }.
% 1.04/1.70 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ozero__class_Ozero(
% 1.04/1.70 tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone( X ) }.
% 1.04/1.70 { c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( c_Nat_OSuc,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.04/1.70 { hAPP( c_Nat_OSuc, X ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.04/1.70 tc_Nat_Onat ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) }.
% 1.04/1.70 { hAPP( c_Nat_OSuc, X ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.04/1.70 tc_Nat_Onat ), X ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 1.04/1.70 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X )
% 1.04/1.70 , X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y =
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 1.04/1.70 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X, hAPP( hAPP
% 1.04/1.70 ( c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 1.04/1.70 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X, hAPP( hAPP
% 1.04/1.70 ( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) }
% 1.04/1.70 .
% 1.04/1.70 { ! class_Rings_Olinordered__semidom( X ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 1.04/1.70 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), c_Groups_Oone__class_Oone(
% 1.04/1.70 X ) ), c_Groups_Oone__class_Oone( X ) ) ) ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), Y ) )
% 1.04/1.70 , hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 1.04/1.70 c_Groups_Oone__class_Oone( X ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), Y ) )
% 1.04/1.70 , hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( X ), Y ), Z ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) ) }.
% 1.04/1.70 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), ! Y =
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.04/1.70 ) = c_Groups_Oone__class_Oone( X ) }.
% 1.04/1.70 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), Y =
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.04/1.70 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), Y ) )
% 1.04/1.70 , hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 1.04/1.70 c_Groups_Oone__class_Oone( X ) ), hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( X ), Y ), hAPP( c_Nat_OSuc, Z ) ) ) ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), Y ) )
% 1.04/1.70 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( X ), Y ), T ) ), hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T ), Z ) ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), Y ) )
% 1.04/1.70 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, T ), Z ) ),
% 1.04/1.70 hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( X ), Y ), T ) ), hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), Y ) )
% 1.04/1.70 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( X ), Y ), T ) ), hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T ), Z ) ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z ), Y ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), T ) )
% 1.04/1.70 , hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( X ), T ), Y ) ) ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 1.04/1.70 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Y ),
% 1.04/1.70 c_Groups_Oone__class_Oone( X ) ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ), hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 1.04/1.70 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Y ),
% 1.04/1.70 c_Groups_Oone__class_Oone( X ) ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( X ), Y ), hAPP( c_Nat_OSuc, Z ) ) ),
% 1.04/1.70 c_Groups_Oone__class_Oone( X ) ) ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z ), Y ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), T )
% 1.04/1.70 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, T ),
% 1.04/1.70 c_Groups_Oone__class_Oone( X ) ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( X ), T ), Z ) ) ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), Y ) )
% 1.04/1.70 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Z ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), hAPP
% 1.04/1.70 ( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.04/1.70 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 1.04/1.70 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( T, X, Y,
% 1.04/1.70 Z, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) = Y }.
% 1.04/1.70 { ! class_Groups_Ozero( X ), c_Polynomial_Opoly__rec( W, X, U, T, hAPP(
% 1.04/1.70 hAPP( c_Polynomial_OpCons( X ), Z ), Y ) ) = hAPP( hAPP( hAPP( T, Z ), Y
% 1.04/1.70 ), hAPP( hAPP( hAPP( c_If( W ), hAPP( c_fequal( Y ),
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ), U ),
% 1.04/1.70 c_Polynomial_Opoly__rec( W, X, U, T, Y ) ) ) }.
% 1.04/1.70 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 1.04/1.70 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( W, X, Y,
% 1.04/1.70 Z, hAPP( hAPP( c_Polynomial_OpCons( X ), U ), T ) ) = hAPP( hAPP( hAPP( Z
% 1.04/1.70 , U ), T ), c_Polynomial_Opoly__rec( W, X, Y, Z, T ) ) }.
% 1.04/1.70 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.04/1.70 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.04/1.70 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.04/1.70 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.04/1.70 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.04/1.70 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.04/1.70 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.04/1.70 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.04/1.70 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.04/1.70 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.04/1.70 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.04/1.70 { ! class_Power_Opower( X ), c_Power_Opower__class_Opower( X ) =
% 1.04/1.70 c_Power_Opower_Opower( X, c_Groups_Oone__class_Oone( X ),
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ) ) }.
% 1.04/1.70 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y ) =
% 1.04/1.70 c_Polynomial_Opoly__rec( tc_Polynomial_Opoly( X ), X,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 1.04/1.70 c_COMBB( tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ) ),
% 1.04/1.70 tc_fun( tc_Polynomial_Opoly( X ), tc_fun( tc_Polynomial_Opoly( X ),
% 1.04/1.70 tc_Polynomial_Opoly( X ) ) ), X ), c_COMBK( tc_fun( tc_Polynomial_Opoly(
% 1.04/1.70 X ), tc_Polynomial_Opoly( X ) ), tc_Polynomial_Opoly( X ) ) ), hAPP(
% 1.04/1.70 c_COMBC( X, tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ) )
% 1.04/1.70 , tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ) ), hAPP(
% 1.04/1.70 hAPP( c_COMBB( tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X )
% 1.04/1.70 ), tc_fun( tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ) )
% 1.04/1.70 , tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ) ) ), X ),
% 1.04/1.70 c_COMBB( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ),
% 1.04/1.70 tc_Polynomial_Opoly( X ) ) ), hAPP( hAPP( c_COMBB( tc_Polynomial_Opoly( X
% 1.04/1.70 ), tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ) ), X ),
% 1.04/1.70 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ) ), hAPP( c_COMBC
% 1.04/1.70 ( X, tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ),
% 1.04/1.70 c_Polynomial_Osmult( X ) ), Y ) ) ) ), hAPP( c_Polynomial_OpCons( X ),
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) ) ) ), Z ) }.
% 1.04/1.70 { ! class_Rings_Ocomm__ring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP(
% 1.04/1.70 hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.04/1.70 c_Polynomial_Omonom( X, c_Groups_Oone__class_Oone( X ), T ) ), Z ) ), Y )
% 1.04/1.70 = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( X ), Y ), T ) ), hAPP( c_Polynomial_Opoly(
% 1.04/1.70 X, Z ), Y ) ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.04/1.70 , Z ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), T ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( X ), Z ), T ) ), hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( X ), Y ), T ) ) ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__semiring__1__strict( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, T ), Y ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.04/1.70 , U ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) ), W ) ), ! hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), U ), W ) = c_Groups_Oone__class_Oone( X
% 1.04/1.70 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), W ), T ) ) ), Y ) ) }.
% 1.04/1.70 { c_Nat_Onat_Onat__size( hAPP( c_Nat_OSuc, X ) ) = hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), c_Nat_Onat_Onat__size( X ) )
% 1.04/1.70 , hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.04/1.70 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Ocoeff( X, hAPP
% 1.04/1.70 ( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), hAPP(
% 1.04/1.70 hAPP( c_Polynomial_OpCons( X ), Z ), hAPP( hAPP( c_Polynomial_OpCons( X )
% 1.04/1.70 , c_Groups_Oone__class_Oone( X ) ), c_Groups_Ozero__class_Ozero(
% 1.04/1.70 tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ), Y ) = c_Groups_Oone__class_Oone
% 1.04/1.70 ( X ) }.
% 1.04/1.70 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ) }.
% 1.04/1.70 { ! c_Groups_Ozero__class_Ozero( tc_Int_Oint ) = c_Groups_Oone__class_Oone
% 1.04/1.70 ( tc_Int_Oint ) }.
% 1.04/1.70 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 1.04/1.70 tc_Int_Oint ) ), X ) ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint )
% 1.04/1.70 }.
% 1.04/1.70 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Groups_Oone__class_Oone(
% 1.04/1.70 tc_Int_Oint ) ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.70 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.04/1.70 tc_Int_Oint ) ), X ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oone__class_Oone
% 1.04/1.70 ( tc_Int_Oint ) ), X ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), hAPP(
% 1.04/1.70 hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ),
% 1.04/1.70 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) )
% 1.04/1.70 , hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), hAPP(
% 1.04/1.70 hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ),
% 1.04/1.70 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), hAPP(
% 1.04/1.70 hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ),
% 1.04/1.70 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ), Y = X }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ),
% 1.04/1.70 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), hAPP( hAPP
% 1.04/1.70 ( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ),
% 1.04/1.70 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ) ) }.
% 1.04/1.70 { ! Y = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ),
% 1.04/1.70 hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ),
% 1.04/1.70 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP( hAPP
% 1.04/1.70 ( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ),
% 1.04/1.70 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ), X ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ),
% 1.04/1.70 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ),
% 1.04/1.70 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ), X ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 1.04/1.70 tc_Int_Oint ) ), X ) ), X ) ), c_Groups_Ozero__class_Ozero( tc_Int_Oint )
% 1.04/1.70 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, X ),
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, X ),
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 1.04/1.70 tc_Int_Oint ) ), X ) ), X ) ), c_Groups_Ozero__class_Ozero( tc_Int_Oint )
% 1.04/1.70 ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.04/1.70 tc_Int_Oint ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ),
% 1.04/1.70 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ),
% 1.04/1.70 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ),
% 1.04/1.70 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ), X ) ) }.
% 1.04/1.70 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP( c_Polynomial_Osmult( X
% 1.04/1.70 ), T ), c_Polynomial_Omonom( X, Z, Y ) ) = c_Polynomial_Omonom( X, hAPP
% 1.04/1.70 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 1.04/1.70 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Ocoeff( X, hAPP
% 1.04/1.70 ( hAPP( c_Polynomial_Osmult( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( c_Polynomial_Ocoeff( X, Z
% 1.04/1.70 ), Y ) ) }.
% 1.04/1.70 { ! class_Groups_Ozero( X ), ! T = Z, hAPP( c_Polynomial_Ocoeff( X,
% 1.04/1.70 c_Polynomial_Omonom( X, Y, T ) ), Z ) = Y }.
% 1.04/1.70 { ! class_Groups_Ozero( X ), T = Z, hAPP( c_Polynomial_Ocoeff( X,
% 1.04/1.70 c_Polynomial_Omonom( X, Y, T ) ), Z ) = c_Groups_Ozero__class_Ozero( X )
% 1.04/1.70 }.
% 1.04/1.70 { ! class_Groups_Ozero( X ), ! c_Polynomial_Omonom( X, T, Z ) =
% 1.04/1.70 c_Polynomial_Omonom( X, Y, Z ), T = Y }.
% 1.04/1.70 { ! class_Groups_Ozero( X ), ! T = Y, c_Polynomial_Omonom( X, T, Z ) =
% 1.04/1.70 c_Polynomial_Omonom( X, Y, Z ) }.
% 1.04/1.70 { ! class_Groups_Ozero( X ), ! c_Polynomial_Ocoeff( X, Z ) =
% 1.04/1.70 c_Polynomial_Ocoeff( X, Y ), Z = Y }.
% 1.04/1.70 { ! class_Groups_Ozero( X ), ! Z = Y, c_Polynomial_Ocoeff( X, Z ) =
% 1.04/1.70 c_Polynomial_Ocoeff( X, Y ) }.
% 1.04/1.70 { ! class_Groups_Ozero( X ), ! Z = Y, hAPP( c_Polynomial_Ocoeff( X, Z ), T
% 1.04/1.70 ) = hAPP( c_Polynomial_Ocoeff( X, Y ), T ) }.
% 1.04/1.70 { ! class_Groups_Ozero( X ), ! hAPP( c_Polynomial_Ocoeff( X, Z ), skol11( X
% 1.04/1.70 , Y, Z ) ) = hAPP( c_Polynomial_Ocoeff( X, Y ), skol11( X, Y, Z ) ), Z =
% 1.04/1.70 Y }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ),
% 1.04/1.70 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) ) }
% 1.04/1.70 .
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ), !
% 1.04/1.70 Y = X }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) )
% 1.04/1.70 , Y = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X
% 1.04/1.70 ) ) }.
% 1.04/1.70 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ), Y =
% 1.04/1.70 X, hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, X ), Y ) ) }
% 1.04/1.70 .
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ), !
% 1.04/1.70 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T ), Z ) ),
% 1.04/1.70 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), T ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ), Z ) ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) )
% 1.04/1.70 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP( hAPP
% 1.04/1.70 ( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), X ) ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ),
% 1.04/1.70 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), Z ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ), Z ) ) ) }.
% 1.04/1.70 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 1.04/1.70 ( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), X ) ) }.
% 1.04/1.70 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), X ) ) = hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), X ) ) }.
% 1.04/1.70 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), X ) = hAPP(
% 1.04/1.70 hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ), Y ) }.
% 1.04/1.70 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ),
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) = X }.
% 1.04/1.70 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ),
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) = X }.
% 1.04/1.70 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), Y ) ), ! hBOOL( hAPP
% 1.04/1.70 ( c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ) )
% 1.04/1.70 , T ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( X ), T ), Y ) ) ) }.
% 1.04/1.70 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP( c_Polynomial_Osmult( X
% 1.04/1.70 ), T ), hAPP( hAPP( c_Polynomial_Osmult( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.04/1.70 c_Polynomial_Osmult( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 1.04/1.70 , T ), Z ) ), Y ) }.
% 1.04/1.70 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP( c_Polynomial_Osmult( X
% 1.04/1.70 ), c_Groups_Oone__class_Oone( X ) ), Y ) = Y }.
% 1.04/1.70 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 1.04/1.70 ( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, T ), Y ) ) }.
% 1.04/1.70 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 1.04/1.70 ( c_Orderings_Oord__class_Oless__eq( X, T ), Y ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) ) }.
% 1.04/1.70 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 1.04/1.70 ( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 1.04/1.70 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 1.04/1.70 ( c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ) ) }.
% 1.04/1.70 { ! class_Groups_Oordered__ab__semigroup__add( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), Z ), T ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), Y ), T ) ) ) }.
% 1.04/1.70 { ! class_Groups_Oordered__ab__semigroup__add( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ) ) }.
% 1.04/1.70 { ! class_Groups_Oordered__ab__semigroup__add( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, U ), T ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), Z ), U ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), Y ), T ) ) ) }.
% 1.04/1.70 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 1.04/1.70 ( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), Z ), T ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), Y ), T ) ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 1.04/1.70 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 1.04/1.70 ( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ),
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X =
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.04/1.70 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ),
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.04/1.70 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 1.04/1.70 c_Nat_OSuc, Y ) ), X ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 1.04/1.70 ( tc_Nat_Onat, Y ), X ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), hAPP
% 1.04/1.70 ( c_Nat_OSuc, X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.04/1.70 tc_Nat_Onat, Y ), X ) ), Y = hAPP( c_Nat_OSuc, X ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.04/1.70 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), hAPP
% 1.04/1.70 ( c_Nat_OSuc, X ) ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 1.04/1.70 c_Nat_OSuc, Y ) ), hAPP( c_Nat_OSuc, X ) ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.04/1.70 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 1.04/1.70 c_Nat_OSuc, Y ) ), hAPP( c_Nat_OSuc, X ) ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), hAPP
% 1.04/1.70 ( c_Nat_OSuc, X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.04/1.70 tc_Nat_Onat, Y ), X ) ), Y = hAPP( c_Nat_OSuc, X ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.04/1.70 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), hAPP
% 1.04/1.70 ( c_Nat_OSuc, X ) ) ) }.
% 1.04/1.70 { ! Y = hAPP( c_Nat_OSuc, X ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), hAPP( c_Nat_OSuc, X
% 1.04/1.70 ) ) ) }.
% 1.04/1.70 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ),
% 1.04/1.70 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 1.04/1.70 c_Nat_OSuc, X ) ), Y ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 1.04/1.70 c_Nat_OSuc, X ) ), Y ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 1.04/1.70 c_Nat_OSuc, X ) ), X ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.04/1.70 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }
% 1.04/1.70 .
% 1.04/1.70 { ! Y = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y )
% 1.04/1.70 , X ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.04/1.70 , Y = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X
% 1.04/1.70 ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.04/1.70 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }
% 1.04/1.70 .
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.04/1.70 , hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), Y
% 1.04/1.70 = X }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.04/1.70 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }
% 1.04/1.70 .
% 1.04/1.70 { ! Y = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y )
% 1.04/1.70 , X ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.04/1.70 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }
% 1.04/1.70 .
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), !
% 1.04/1.70 Y = X }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.04/1.70 , Y = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X
% 1.04/1.70 ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.04/1.70 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }
% 1.04/1.70 .
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 1.04/1.70 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), X ) ), hBOOL(
% 1.04/1.70 hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), X ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 1.04/1.70 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), X ) ), hBOOL(
% 1.04/1.70 hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 1.04/1.70 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), Z ) ), X ) ), hBOOL(
% 1.04/1.70 hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 1.04/1.70 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), X ) ), hBOOL(
% 1.04/1.70 hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.04/1.70 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T ), Z )
% 1.04/1.70 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 1.04/1.70 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), T ) ), hAPP( hAPP
% 1.04/1.70 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.04/1.70 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 1.04/1.70 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), Z ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.04/1.70 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), hAPP
% 1.04/1.70 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.04/1.70 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), hAPP
% 1.04/1.70 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 1.04/1.70 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.04/1.70 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 1.04/1.70 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.04/1.70 , X = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), skol12
% 1.04/1.70 ( X, Y ) ) }.
% 1.04/1.70 { ! X = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), Z ),
% 1.04/1.70 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }
% 1.04/1.70 .
% 1.04/1.70 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), hAPP(
% 1.04/1.70 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) ) }.
% 1.04/1.70 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), hAPP(
% 1.04/1.70 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Y ) ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.04/1.70 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), hAPP
% 1.04/1.70 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.04/1.70 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), hAPP
% 1.04/1.70 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) ) }.
% 1.04/1.70 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP( c_Polynomial_Osmult( X
% 1.04/1.70 ), Y ), c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.04/1.70 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T ), Z )
% 1.04/1.70 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 1.04/1.70 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), T ) ), hAPP(
% 1.04/1.70 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.04/1.70 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 1.04/1.70 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.04/1.70 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 1.04/1.70 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) ) }.
% 1.04/1.70 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), hAPP(
% 1.04/1.70 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) ) ) }.
% 1.04/1.70 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), hAPP(
% 1.04/1.70 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 1.04/1.70 c_Groups_Oone__class_Oone( tc_Int_Oint ), X = c_Groups_Oone__class_Oone(
% 1.04/1.70 tc_Int_Oint ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 1.04/1.70 c_Groups_Oone__class_Oone( tc_Int_Oint ), Y = c_Groups_Oone__class_Oone(
% 1.04/1.70 tc_Int_Oint ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! X =
% 1.04/1.70 c_Groups_Oone__class_Oone( tc_Int_Oint ), ! Y = c_Groups_Oone__class_Oone
% 1.04/1.70 ( tc_Int_Oint ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 1.04/1.70 , X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.04/1.70 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 1.04/1.70 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) = X }.
% 1.04/1.70 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.04/1.70 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) = X }.
% 1.04/1.70 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP( c_Polynomial_Osmult( X
% 1.04/1.70 ), T ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X
% 1.04/1.70 ) ), Z ), Y ) ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.04/1.70 tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Polynomial_Osmult( X ), T ), Z
% 1.04/1.70 ) ), hAPP( hAPP( c_Polynomial_Osmult( X ), T ), Y ) ) }.
% 1.04/1.70 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 1.04/1.70 c_Polynomial_Osmult( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.04/1.70 c_Polynomial_Osmult( X ), T ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.04/1.70 ( tc_Polynomial_Opoly( X ) ), Z ), Y ) ) }.
% 1.04/1.70 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), hAPP(
% 1.04/1.70 hAPP( c_Polynomial_Osmult( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.04/1.70 c_Polynomial_Osmult( X ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.04/1.70 ( tc_Polynomial_Opoly( X ) ), T ), Y ) ) }.
% 1.04/1.70 { c_Nat_Onat_Onat__size( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), Y ) ), ! hBOOL( hAPP
% 1.04/1.70 ( c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.04/1.70 ), T ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, T ),
% 1.04/1.70 c_Groups_Oone__class_Oone( X ) ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( X ), T ), Z ) ) ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), Y ) )
% 1.04/1.70 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( X ), Y ), T ) ), hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T ), Z ) ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), Y ) )
% 1.04/1.70 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T ), Z )
% 1.04/1.70 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( X ), Y ), T ) ), hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), Y ) )
% 1.04/1.70 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( X ), Y ), T ) ), hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T ), Z ) ) }.
% 1.04/1.70 { ! class_Rings_Oordered__cancel__semiring( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.04/1.70 , Z ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Y ),
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.04/1.70 { ! class_Rings_Oordered__cancel__semiring( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Z ), c_Groups_Ozero__class_Ozero( X
% 1.04/1.70 ) ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) ), Y ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.04/1.70 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.04/1.70 , Z ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) ), Y ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.04/1.70 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 1.04/1.70 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Z ), c_Groups_Ozero__class_Ozero( X
% 1.04/1.70 ) ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Y ),
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.04/1.70 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 1.04/1.70 { ! class_Rings_Oordered__semiring( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, U ), T ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.04/1.70 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) ), U ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ) }.
% 1.04/1.70 { ! class_Rings_Oordered__semiring( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, U ), T ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.04/1.70 , Z ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) ), U ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ) }.
% 1.04/1.70 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, T ), c_Groups_Ozero__class_Ozero( X
% 1.04/1.70 ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) ) }.
% 1.04/1.70 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, T ), c_Groups_Ozero__class_Ozero( X
% 1.04/1.70 ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) ) }.
% 1.04/1.70 { ! class_Rings_Oordered__comm__semiring( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.04/1.70 , T ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 1.04/1.70 { ! class_Rings_Oordered__semiring( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.04/1.70 , T ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 1.04/1.70 { ! class_Rings_Oordered__semiring( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.04/1.70 , T ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ) }.
% 1.04/1.70 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 1.04/1.70 ) ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ),
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.04/1.70 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 1.04/1.70 { ! class_Rings_Oordered__cancel__semiring( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 1.04/1.70 ) ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.04/1.70 { ! class_Rings_Oordered__cancel__semiring( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.04/1.70 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ),
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.04/1.70 { ! class_Rings_Oordered__cancel__semiring( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.04/1.70 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ),
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.04/1.70 { ! class_Rings_Oordered__cancel__semiring( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.04/1.70 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.04/1.70 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) ) ), alpha7( X, Y, Z ), alpha22( X, Y, Z
% 1.04/1.70 ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha7( X, Y, Z ), hBOOL
% 1.04/1.70 ( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha22( X, Y, Z ), hBOOL
% 1.04/1.70 ( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.04/1.70 { ! alpha22( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.04/1.70 Z ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.04/1.70 { ! alpha22( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) ), Y ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ),
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.04/1.70 , Y ) ), alpha22( X, Y, Z ) }.
% 1.04/1.70 { ! alpha7( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) ), Z ) ) }.
% 1.04/1.70 { ! alpha7( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Y
% 1.04/1.70 ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 1.04/1.70 ) ) ), alpha7( X, Y, Z ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.04/1.70 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ), alpha8( X
% 1.04/1.70 , Y, Z ), alpha23( X, Y, Z ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha8( X, Y, Z ), hBOOL
% 1.04/1.70 ( hAPP( c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 1.04/1.70 ( X ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha23( X, Y, Z ), hBOOL
% 1.04/1.70 ( hAPP( c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 1.04/1.70 ( X ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 1.04/1.70 { ! alpha23( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.04/1.70 Z ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.04/1.70 { ! alpha23( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.04/1.70 Y ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ),
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 1.04/1.70 ) ) ), alpha23( X, Y, Z ) }.
% 1.04/1.70 { ! alpha8( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) ), Z ) ) }.
% 1.04/1.70 { ! alpha8( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) ), Y ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.04/1.70 , Y ) ), alpha8( X, Y, Z ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__ring( X ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.04/1.70 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 1.04/1.70 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 1.04/1.70 ) ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ),
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ), c_Groups_Ozero__class_Ozero
% 1.04/1.70 ( X ) ) ) }.
% 1.04/1.70 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.04/1.70 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, T ), Z ) )
% 1.04/1.70 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, T ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) ) }.
% 1.04/1.70 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.04/1.70 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, T ), Z ) )
% 1.04/1.70 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, T ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) ) }.
% 1.04/1.70 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.04/1.70 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), ! hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 1.04/1.70 ( X ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.04/1.70 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.04/1.70 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), ! hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 1.04/1.70 ( X ), Z = c_Groups_Ozero__class_Ozero( X ) }.
% 1.04/1.70 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.04/1.70 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), ! Y =
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X )
% 1.04/1.70 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Z ) =
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) }.
% 1.04/1.70 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.04/1.70 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.04/1.70 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) ) }.
% 1.04/1.70 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), Y ), Y ) ), c_Groups_Ozero__class_Ozero
% 1.04/1.70 ( X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Y ),
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.04/1.70 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 1.04/1.70 ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), Y ), Y ) ), c_Groups_Ozero__class_Ozero
% 1.04/1.70 ( X ) ) ) }.
% 1.04/1.70 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.04/1.70 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Y ) ) ), hBOOL( hAPP
% 1.04/1.70 ( c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.04/1.70 ), Y ) ) }.
% 1.04/1.70 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.04/1.70 , Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), Y ), Y ) ) ) }.
% 1.04/1.70 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, U ), T ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.04/1.70 ( X ), Z ), U ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), T )
% 1.04/1.70 ) ) }.
% 1.04/1.70 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, U ), T ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.04/1.70 ( X ), Z ), U ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), T )
% 1.04/1.70 ) ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__semidom( X ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.04/1.70 , c_Groups_Oone__class_Oone( X ) ) ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ) ),
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.04/1.70 , Z ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( X ), Z ), T ) ), hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( X ), Y ), T ) ) ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.04/1.70 , Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) ), hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.04/1.70 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Polynomial_Osmult( X ), Z ), Y
% 1.04/1.70 ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.04/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.04/1.70 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ), hAPP(
% 1.04/1.70 hAPP( c_Polynomial_Osmult( X ), Z ), Y ) = c_Groups_Ozero__class_Ozero(
% 1.04/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.04/1.70 { ! class_Rings_Oidom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.04/1.70 tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Polynomial_Osmult( X ), Z ), Y
% 1.04/1.70 ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.04/1.70 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP( c_Polynomial_Osmult( X
% 1.04/1.70 ), c_Groups_Ozero__class_Ozero( X ) ), Y ) = c_Groups_Ozero__class_Ozero
% 1.04/1.70 ( tc_Polynomial_Opoly( X ) ) }.
% 1.04/1.70 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ) ), Y
% 1.04/1.70 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.04/1.70 c_Groups_Oone__class_Oone( X ) ), hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.04/1.70 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP( c_Polynomial_Osmult( X
% 1.04/1.70 ), T ), hAPP( hAPP( c_Polynomial_OpCons( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.04/1.70 c_Polynomial_OpCons( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 1.04/1.70 , T ), Z ) ), hAPP( hAPP( c_Polynomial_Osmult( X ), T ), Y ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 1.04/1.70 c_Nat_OSuc, Y ) ), X ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.04/1.70 tc_Nat_Onat, Y ), X ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.04/1.70 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), hAPP(
% 1.04/1.70 c_Nat_OSuc, Y ) ) ), X = Y }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.04/1.70 , ! X = Y, hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ),
% 1.04/1.70 hAPP( c_Nat_OSuc, Y ) ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.04/1.70 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 1.04/1.70 c_Nat_OSuc, Y ) ), X ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.04/1.70 , hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), hAPP(
% 1.04/1.70 c_Nat_OSuc, X ) ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 1.04/1.70 c_Nat_OSuc, Y ) ), X ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.04/1.70 tc_Nat_Onat, Y ), X ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.04/1.70 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 1.04/1.70 c_Nat_OSuc, Y ) ), X ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), hAPP(
% 1.04/1.70 c_Nat_OSuc, X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.04/1.70 tc_Nat_Onat, Y ), X ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.04/1.70 , hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), hAPP(
% 1.04/1.70 c_Nat_OSuc, X ) ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.04/1.70 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 1.04/1.70 c_Nat_OSuc, Y ) ), X ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 1.04/1.70 c_Nat_OSuc, Y ) ), X ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.04/1.70 tc_Nat_Onat, Y ), X ) ) }.
% 1.04/1.70 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X, hAPP( hAPP(
% 1.04/1.70 c_Polynomial_OpCons( X ), Z ), Y ) ), c_Groups_Ozero__class_Ozero(
% 1.04/1.70 tc_Nat_Onat ) ) = Z }.
% 1.04/1.70 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X, hAPP( hAPP(
% 1.04/1.70 c_Polynomial_OpCons( X ), T ), Z ) ), hAPP( c_Nat_OSuc, Y ) ) = hAPP(
% 1.04/1.70 c_Polynomial_Ocoeff( X, Z ), Y ) }.
% 1.04/1.70 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 1.04/1.70 ( hAPP( c_Polynomial_Osmult( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( c_Polynomial_Opoly( X, Z )
% 1.04/1.70 , Y ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 1.04/1.70 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( c_Nat_OSuc, Z ) ),
% 1.04/1.70 Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP(
% 1.04/1.70 c_Nat_OSuc, Z ) ), X ) ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.04/1.70 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 1.04/1.70 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( c_Nat_OSuc, Z ) ),
% 1.04/1.70 Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP(
% 1.04/1.70 c_Nat_OSuc, Z ) ), X ) ) ) }.
% 1.04/1.70 { ! class_Rings_Ocomm__semiring__0( X ), ! hAPP( hAPP( c_Polynomial_Osmult
% 1.04/1.70 ( X ), T ), Y ) = hAPP( hAPP( c_Polynomial_OpCons( X ), Z ), Y ), Y =
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.04/1.70 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP( c_Polynomial_Osmult( X
% 1.04/1.70 ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), Y ) = hAPP
% 1.04/1.70 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), hAPP(
% 1.04/1.70 hAPP( c_Polynomial_Osmult( X ), T ), Y ) ), hAPP( hAPP(
% 1.04/1.70 c_Polynomial_Osmult( X ), Z ), Y ) ) }.
% 1.04/1.70 { ! class_Groups_Ocomm__monoid__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 1.04/1.70 hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), T )
% 1.04/1.70 , Z ) ), Y ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP(
% 1.04/1.70 c_Polynomial_Ocoeff( X, T ), Y ) ), hAPP( c_Polynomial_Ocoeff( X, Z ), Y
% 1.04/1.70 ) ) }.
% 1.04/1.70 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ) =
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( c_Nat_OSuc, X ) ) }
% 1.04/1.70 .
% 1.04/1.70 { ! class_Groups_Ozero( X ), ! c_Polynomial_Omonom( X, Z, Y ) =
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) }.
% 1.04/1.70 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 1.04/1.70 c_Polynomial_Omonom( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 1.04/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.04/1.70 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 1.04/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.04/1.70 { ! class_Groups_Ocomm__monoid__add( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ),
% 1.04/1.70 c_Polynomial_Omonom( X, T, Z ) ), c_Polynomial_Omonom( X, Y, Z ) ) =
% 1.04/1.70 c_Polynomial_Omonom( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), T )
% 1.04/1.70 , Y ), Z ) }.
% 1.04/1.70 { ! class_Rings_Ocomm__semiring__1( X ), ! Y = c_Groups_Ozero__class_Ozero
% 1.04/1.70 ( tc_Nat_Onat ), hAPP( c_Polynomial_Ocoeff( X, c_Groups_Oone__class_Oone
% 1.04/1.70 ( tc_Polynomial_Opoly( X ) ) ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 1.04/1.70 { ! class_Rings_Ocomm__semiring__1( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.04/1.70 tc_Nat_Onat ), hAPP( c_Polynomial_Ocoeff( X, c_Groups_Oone__class_Oone(
% 1.04/1.70 tc_Polynomial_Opoly( X ) ) ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), T )
% 1.04/1.70 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Z )
% 1.04/1.70 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, T ), Y ) ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.04/1.70 , T ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__semiring( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.04/1.70 , T ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.04/1.70 , Z ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, T ), Y ) ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__semiring( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.04/1.70 , Z ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, T ), Y ) ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, U ), T ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Z )
% 1.04/1.70 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) ), U ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, U ), T ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.04/1.70 , Z ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) ), U ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, U ), T ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.04/1.70 , Z ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) ), U ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, U ), T ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 1.04/1.70 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) ), U ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 1.04/1.70 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Z ), T ) ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 1.04/1.70 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ), T ) ),
% 1.04/1.70 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 1.04/1.70 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, T ), Z ) ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 1.04/1.70 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, T ), Z ) ),
% 1.04/1.70 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 1.04/1.70 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 1.04/1.70 ) ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Z ),
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.04/1.70 ( X ), Y ), Z ) ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.04/1.70 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 1.04/1.70 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ),
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.04/1.70 ( X ), Y ), Z ) ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.04/1.70 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.04/1.70 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, T ), Z ) ),
% 1.04/1.70 hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, T ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) ) }.
% 1.04/1.70 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 1.04/1.70 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, T ), Z ) ),
% 1.04/1.70 hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, T ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) ) }.
% 1.04/1.70 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.04/1.70 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 1.04/1.70 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) ) }.
% 1.04/1.70 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 1.04/1.70 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 1.04/1.70 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ),
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) ) ), Z = c_Groups_Ozero__class_Ozero( X
% 1.04/1.70 ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ),
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) ) ), Y = c_Groups_Ozero__class_Ozero( X
% 1.04/1.70 ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 1.04/1.70 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ),
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__ring( X ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.04/1.70 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.04/1.70 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Z ), c_Groups_Oone__class_Oone( X )
% 1.04/1.70 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.04/1.70 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Z ), c_Groups_Oone__class_Oone( X )
% 1.04/1.70 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( X ), Z ), T ) ), hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( X ), Y ), T ) ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.04/1.70 , Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( X ), Z ), hAPP( c_Nat_OSuc, T ) ) = hAPP(
% 1.04/1.70 hAPP( c_Power_Opower__class_Opower( X ), Y ), hAPP( c_Nat_OSuc, T ) ), !
% 1.04/1.70 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.04/1.70 , Y ) ), Z = Y }.
% 1.04/1.70 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( X ), Z ), hAPP( c_Nat_OSuc, T ) ) ), hAPP(
% 1.04/1.70 hAPP( c_Power_Opower__class_Opower( X ), Y ), hAPP( c_Nat_OSuc, T ) ) ) )
% 1.04/1.70 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) ), Y ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 1.04/1.70 { hAPP( hAPP( c_Power_Opower_Opower( T, Z, Y ), X ),
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = Z }.
% 1.04/1.70 { hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), hAPP( c_Nat_OSuc, X )
% 1.04/1.70 ) = hAPP( hAPP( Z, Y ), hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y
% 1.04/1.70 ), X ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 1.04/1.70 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( c_Nat_OSuc,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), Y ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 1.04/1.70 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( c_Nat_OSuc,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 1.04/1.70 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), Y ) ), !
% 1.04/1.70 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 1.04/1.70 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) ), hBOOL
% 1.04/1.70 ( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( c_Nat_OSuc
% 1.04/1.70 , c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), Y ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), Y ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 1.04/1.70 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ), ! hBOOL( hAPP
% 1.04/1.70 ( c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.04/1.70 ( tc_Nat_Onat ) ), Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 1.04/1.70 ( tc_Nat_Onat, Z ), X ) ) }.
% 1.04/1.70 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), X ) )
% 1.04/1.70 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 1.04/1.70 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 1.04/1.70 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ), ! hBOOL( hAPP
% 1.04/1.70 ( c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.04/1.70 ( tc_Nat_Onat ) ), Z ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 1.04/1.70 ( tc_Nat_Onat, Y ), X ) ) }.
% 1.04/1.70 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Z ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.04/1.70 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 1.04/1.70 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 1.04/1.70 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) ), hBOOL
% 1.04/1.70 ( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( c_Nat_OSuc
% 1.04/1.70 , c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ) ) }.
% 1.04/1.70 { ! class_Rings_Ocomm__semiring__0( X ), ! hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 1.04/1.70 c_Polynomial_Osmult( X ), T ), Y ) ), hAPP( hAPP( c_Polynomial_OpCons( X
% 1.04/1.70 ), Z ), Y ) ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) )
% 1.04/1.70 , Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.04/1.70 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X, Z, hAPP( c_Nat_OSuc, Y
% 1.04/1.70 ) ) = hAPP( hAPP( c_Polynomial_OpCons( X ), c_Groups_Ozero__class_Ozero
% 1.04/1.70 ( X ) ), c_Polynomial_Omonom( X, Z, Y ) ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__semiring__1( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, T ), Y ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.04/1.70 , U ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) ), W ) ), ! hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), U ), W ) = c_Groups_Oone__class_Oone( X
% 1.04/1.70 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), W ), T ) ) ), Y ) ) }.
% 1.04/1.70 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 1.04/1.70 c_Polynomial_Omonom( X, T, Z ) ), Y ) = hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.04/1.70 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( X ), T ), Z ) = hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( X ), Y ), Z ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.04/1.70 , T ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) ), Y ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.04/1.70 tc_Nat_Onat ) ), Z ) ), T = Y }.
% 1.04/1.70 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X, Y,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = hAPP( hAPP(
% 1.04/1.70 c_Polynomial_OpCons( X ), Y ), c_Groups_Ozero__class_Ozero(
% 1.04/1.70 tc_Polynomial_Opoly( X ) ) ) }.
% 1.04/1.70 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.04/1.70 c_Polynomial_Omonom( X, U, T ) ), c_Polynomial_Omonom( X, Z, Y ) ) =
% 1.04/1.70 c_Polynomial_Omonom( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U
% 1.04/1.70 ), Z ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), T ), Y )
% 1.04/1.70 ) }.
% 1.04/1.70 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 1.04/1.70 c_Polynomial_OpCons( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 1.04/1.70 c_Polynomial_Osmult( X ), T ), Y ) ), hAPP( hAPP( c_Polynomial_OpCons( X
% 1.04/1.70 ), c_Groups_Ozero__class_Ozero( X ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y ) ) ) }
% 1.04/1.70 .
% 1.04/1.70 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), hAPP(
% 1.04/1.70 hAPP( c_Polynomial_OpCons( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 1.04/1.70 c_Polynomial_Osmult( X ), Z ), T ) ), hAPP( hAPP( c_Polynomial_OpCons( X
% 1.04/1.70 ), c_Groups_Ozero__class_Ozero( X ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ) ) ) }
% 1.04/1.70 .
% 1.04/1.70 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.04/1.70 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Y ),
% 1.04/1.70 c_Groups_Oone__class_Oone( X ) ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( X ), Y ), hAPP( c_Nat_OSuc, Z ) ) ), Y ) )
% 1.04/1.70 }.
% 1.04/1.70 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ) ), T ) = hAPP(
% 1.04/1.70 hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ), ! hBOOL(
% 1.04/1.70 hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) ),
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( tc_Int_Oint, T ), W ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.04/1.70 tc_Int_Oint ) ), Z ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 1.04/1.70 ( tc_Int_Oint, Z ), W ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 1.04/1.70 ( tc_Int_Oint, Y ), U ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP( hAPP
% 1.04/1.70 ( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ) ), Z ) ), hAPP(
% 1.04/1.70 hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ) ), X ) ) ), !
% 1.04/1.70 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ),
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( tc_Int_Oint, U ), X ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( tc_Int_Oint, U ), Z ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), T ) ) }.
% 1.04/1.70 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ) ), T ) = hAPP(
% 1.04/1.70 hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ), ! hBOOL(
% 1.04/1.70 hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) ) ), !
% 1.04/1.70 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, X ), Z ) ), !
% 1.04/1.70 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), T ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.04/1.70 tc_Int_Oint ) ), Z ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 1.04/1.70 ( tc_Int_Oint, Z ), W ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 1.04/1.70 ( tc_Int_Oint, U ), Y ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP( hAPP
% 1.04/1.70 ( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ) ), Z ) ), hAPP(
% 1.04/1.70 hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ) ), X ) ) ), !
% 1.04/1.70 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Z ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z ), U ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( tc_Int_Oint, X ), U ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T ), Y ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) ),
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.04/1.70 tc_Int_Oint ) ), Z ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.04/1.70 tc_Int_Oint, Y ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.04/1.70 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), Y )
% 1.04/1.70 ), Y = X }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.04/1.70 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), Z )
% 1.04/1.70 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), Z )
% 1.04/1.70 ) }.
% 1.04/1.70 { ! Y = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y )
% 1.04/1.70 , X ) ) }.
% 1.04/1.70 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ),
% 1.04/1.70 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), Y ) ) }
% 1.04/1.70 .
% 1.04/1.70 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), X ) ) }
% 1.04/1.70 .
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) )
% 1.04/1.70 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ), Y )
% 1.04/1.70 ), Y = X }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) )
% 1.04/1.70 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ), Z )
% 1.04/1.70 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), Z )
% 1.04/1.70 ) }.
% 1.04/1.70 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) ),
% 1.04/1.70 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ), Y ) ) }
% 1.04/1.70 .
% 1.04/1.70 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ), X ) ) }
% 1.04/1.70 .
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! X = hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Z ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ),
% 1.04/1.70 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! X = hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z ), X ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oone__class_Oone
% 1.04/1.70 ( tc_Int_Oint ) ), Y ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) ) ), !
% 1.04/1.70 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, X ), Z ) ), !
% 1.04/1.70 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Z ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ) }.
% 1.04/1.70 { ! class_Rings_Ocomm__semiring__0( X ),
% 1.04/1.70 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) =
% 1.04/1.70 c_Polynomial_Opoly__rec( tc_Polynomial_Opoly( X ), X,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 1.04/1.70 c_COMBB( tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ) ),
% 1.04/1.70 tc_fun( tc_Polynomial_Opoly( X ), tc_fun( tc_Polynomial_Opoly( X ),
% 1.04/1.70 tc_Polynomial_Opoly( X ) ) ), X ), c_COMBK( tc_fun( tc_Polynomial_Opoly(
% 1.04/1.70 X ), tc_Polynomial_Opoly( X ) ), tc_Polynomial_Opoly( X ) ) ), hAPP( hAPP
% 1.04/1.70 ( c_COMBB( tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ) ),
% 1.04/1.70 tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ) ), X ), hAPP(
% 1.04/1.70 c_COMBS( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ),
% 1.04/1.70 tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_COMBB( tc_Polynomial_Opoly( X )
% 1.04/1.70 , tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ) ),
% 1.04/1.70 tc_Polynomial_Opoly( X ) ), c_Groups_Oplus__class_Oplus(
% 1.04/1.70 tc_Polynomial_Opoly( X ) ) ), hAPP( c_Polynomial_Osmult( X ), Y ) ) ) ),
% 1.04/1.70 c_Polynomial_OpCons( X ) ) ), Z ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), hAPP( hAPP(
% 1.04/1.70 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) ) }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ), Y ) ) ) }.
% 1.04/1.70 { ! class_Rings_Ocomm__semiring__0( X ),
% 1.04/1.70 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.04/1.70 { ! class_Rings_Ocomm__semiring__0( X ), !
% 1.04/1.70 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) =
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.04/1.70 { ! class_Rings_Ocomm__semiring__0( X ), ! Z = c_Groups_Ozero__class_Ozero
% 1.04/1.70 ( tc_Polynomial_Opoly( X ) ),
% 1.04/1.70 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) =
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.04/1.70 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.04/1.70 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, T, Z ) ), Y
% 1.04/1.70 ) = hAPP( c_Polynomial_Opoly( X, T ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) }.
% 1.04/1.70 { ! class_Rings_Ocomm__semiring__0( X ),
% 1.04/1.70 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, hAPP( hAPP(
% 1.04/1.70 c_Polynomial_OpCons( X ), Z ), c_Groups_Ozero__class_Ozero(
% 1.04/1.70 tc_Polynomial_Opoly( X ) ) ), Y ) = hAPP( hAPP( c_Polynomial_OpCons( X )
% 1.04/1.70 , Z ), c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 1.04/1.70 { ! class_Rings_Ocomm__semiring__0( X ),
% 1.04/1.70 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, hAPP( hAPP(
% 1.04/1.70 c_Polynomial_OpCons( X ), T ), Z ), Y ) = hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 1.04/1.70 c_Polynomial_Osmult( X ), Y ),
% 1.04/1.70 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) ) ),
% 1.04/1.70 hAPP( hAPP( c_Polynomial_OpCons( X ), T ),
% 1.04/1.70 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) ) ) }
% 1.04/1.70 .
% 1.04/1.70 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Groups_Ozero__class_Ozero
% 1.04/1.70 ( tc_Int_Oint ) ) ) }.
% 1.04/1.70 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Groups_Oone__class_Oone(
% 1.04/1.70 tc_Int_Oint ) ) ) }.
% 1.04/1.70 { ! class_Orderings_Opreorder( X ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Y ), Y ) ) }.
% 1.04/1.70 { ! class_Rings_Ocomm__semiring__0( X ), ! hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), U ), hAPP( hAPP
% 1.04/1.70 ( c_Polynomial_Osmult( X ), T ), Z ) ) = hAPP( hAPP( c_Polynomial_OpCons
% 1.04/1.70 ( X ), Y ), Z ), Y = hAPP( c_Polynomial_Opoly( X, U ), T ) }.
% 1.04/1.70 { ! class_Rings_Ocomm__semiring__0( X ), ! hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), U ), hAPP( hAPP
% 1.04/1.70 ( c_Polynomial_Osmult( X ), T ), Z ) ) = hAPP( hAPP( c_Polynomial_OpCons
% 1.04/1.70 ( X ), Y ), Z ), Z = c_Polynomial_Osynthetic__div( X, U, T ) }.
% 1.04/1.70 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), Z ), hAPP( hAPP
% 1.04/1.70 ( c_Polynomial_Osmult( X ), Y ), c_Polynomial_Osynthetic__div( X, Z, Y )
% 1.04/1.70 ) ) = hAPP( hAPP( c_Polynomial_OpCons( X ), hAPP( c_Polynomial_Opoly( X
% 1.04/1.70 , Z ), Y ) ), c_Polynomial_Osynthetic__div( X, Z, Y ) ) }.
% 1.04/1.70 { c_Nat_Osize__class_Osize( tc_Nat_Onat, hAPP( c_Nat_OSuc, X ) ) = hAPP(
% 1.04/1.70 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ),
% 1.04/1.70 c_Nat_Osize__class_Osize( tc_Nat_Onat, X ) ), hAPP( c_Nat_OSuc,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.04/1.70 { c_Nat_Osize__class_Osize( tc_Nat_Onat, X ) = X }.
% 1.04/1.70 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.04/1.70 { c_Nat_Osize__class_Osize( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.04/1.70 tc_Nat_Onat ) ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.04/1.70 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ) }.
% 1.04/1.70 { ! class_Orderings_Oord( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z ), Y ) ), hBOOL(
% 1.04/1.70 hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ) ), hAPP( Y, U )
% 1.04/1.70 ) ) }.
% 1.04/1.70 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, T ), Z ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, T ), Y ) ) }.
% 1.04/1.70 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ), Y = Z }.
% 1.04/1.70 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Y ), T ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Z ), T ) ) }.
% 1.04/1.70 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ), Z = Y }.
% 1.04/1.70 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! Z = T, hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, T ), Y ) ) }.
% 1.04/1.70 { ! class_Orderings_Oord( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! Y = T, hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Z ), T ) ) }.
% 1.04/1.70 { ! class_Orderings_Oorder( X ), ! Z = Y, ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, T ), Y ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, T ), Z ) ) }.
% 1.04/1.70 { ! class_Orderings_Oord( X ), ! Z = Y, ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Y ), T ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Z ), T ) ) }.
% 1.04/1.70 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ), Y = Z }.
% 1.04/1.70 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! Y = Z, hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ) }.
% 1.04/1.70 { ! class_Orderings_Oord( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z ), Y ) ), hBOOL(
% 1.04/1.70 hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ) ), hAPP( Y, U )
% 1.04/1.70 ) ) }.
% 1.04/1.70 { ! class_Orderings_Opreorder( X ), ! Z = Y, hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 1.04/1.70 { ! class_Orderings_Oorder( X ), ! Z = Y, hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 1.04/1.70 { ! class_Orderings_Oorder( X ), ! Z = Y, hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ) }.
% 1.04/1.70 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ), Z = Y }.
% 1.04/1.70 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ) }.
% 1.04/1.70 { ! class_Orderings_Oord( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z ), Y ) ), hBOOL(
% 1.04/1.70 hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ) ), hAPP( Y, U )
% 1.04/1.70 ) ) }.
% 1.04/1.70 { ! class_Orderings_Oord( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, skol13( X, Y, Z ) ) ),
% 1.04/1.70 hAPP( Y, skol13( X, Y, Z ) ) ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z ), Y ) ) }.
% 1.04/1.70 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Y ), Y ) ) }.
% 1.04/1.70 { ! class_Orderings_Olinorder( X ), Z = Y, hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 1.04/1.70 { ! class_Orderings_Olinorder( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! Z = Y }.
% 1.04/1.70 { ! class_Orderings_Olinorder( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Y ), Z ) ), ! Z = Y }.
% 1.04/1.70 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Y ), Z ) ), Z = Y }.
% 1.04/1.70 { ! class_Orderings_Olinorder( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Y ), Z ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 1.04/1.70 { ! class_Orderings_Olinorder( X ), ! Z = Y, ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 1.04/1.70 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), Z = Y, hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 1.04/1.70 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Y ), Z ) ), Y = Z }.
% 1.04/1.70 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! Y = Z, ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 1.04/1.70 { ! class_Orderings_Olinorder( X ), Z = Y, hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 1.04/1.70 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! Z = Y }.
% 1.04/1.70 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 1.04/1.70 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 1.04/1.70 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! Z = Y }.
% 1.04/1.70 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! Y = Z }.
% 1.04/1.70 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 1.04/1.70 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 1.04/1.70 { ! class_Orderings_Oord( X ), ! Z = Y, ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Y ), T ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Z ), T ) ) }.
% 1.04/1.70 { ! class_Orderings_Oorder( X ), ! Z = Y, ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, T ), Y ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, T ), Z ) ) }.
% 1.04/1.70 { ! class_Orderings_Oord( X ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless
% 1.04/1.70 ( X, Z ), Y ) ), ! Y = T, hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 1.04/1.70 Z ), T ) ) }.
% 1.04/1.70 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! Z = T, hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, T ), Y ) ) }.
% 1.04/1.70 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Y ), T ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Z ), T ) ) }.
% 1.04/1.70 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, T ), Z ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, T ), Y ) ) }.
% 1.04/1.70 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 1.04/1.70 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), Z = Y, hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 1.04/1.70 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 1.04/1.70 hAPP( hAPP( c_Polynomial_OpCons( X ), T ), Z ), Y ) = hAPP( hAPP(
% 1.04/1.70 c_Polynomial_OpCons( X ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) ),
% 1.04/1.70 c_Polynomial_Osynthetic__div( X, Z, Y ) ) }.
% 1.04/1.70 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, T ), Z ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, T ), Y ) ) }.
% 1.04/1.70 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Y ), T ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Z ), T ) ) }.
% 1.04/1.70 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, T ), Z ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, T ), Y ) ) }.
% 1.04/1.70 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Y ), T ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Z ), T ) ) }.
% 1.04/1.70 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), Y = Z, hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 1.04/1.70 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), Z = Y, hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 1.04/1.70 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), Z = Y }.
% 1.04/1.70 { ! class_Orderings_Olinorder( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), Z = Y }.
% 1.04/1.70 { ! class_Orderings_Olinorder( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! Z = Y, ! hBOOL( hAPP
% 1.04/1.70 ( c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 1.04/1.70 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 1.04/1.70 { ! class_Orderings_Olinorder( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 1.04/1.70 { ! class_Orderings_Oorder( X ), Z = Y, ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 1.04/1.70 { ! class_Orderings_Oorder( X ), Z = Y, ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 1.04/1.70 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), Z = Y }.
% 1.04/1.70 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! Z = Y, hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 1.04/1.70 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 1.04/1.70 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ) }.
% 1.04/1.70 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), Z = Y }.
% 1.04/1.70 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 1.04/1.70 { ! class_Orderings_Oorder( X ), ! Z = Y, hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 1.04/1.70 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 1.04/1.70 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ) }.
% 1.04/1.70 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 1.04/1.70 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 1.04/1.70 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! Z = Y }.
% 1.04/1.70 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), Z = Y, hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 1.04/1.70 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 1.04/1.70 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 1.04/1.70 { ! class_Orderings_Olinorder( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Y ), Z ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 1.04/1.70 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ) }.
% 1.04/1.70 { ! class_Orderings_Olinorder( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 1.04/1.70 { ! class_Rings_Ocomm__ring__1( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 1.04/1.70 c_Polynomial_OpCons( X ), hAPP( c_Groups_Ouminus__class_Ouminus( X ), Z )
% 1.04/1.70 ), hAPP( hAPP( c_Polynomial_OpCons( X ), c_Groups_Oone__class_Oone( X )
% 1.04/1.70 ), c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ),
% 1.04/1.70 c_Polynomial_Osynthetic__div( X, Y, Z ) ) ), hAPP( hAPP(
% 1.04/1.70 c_Polynomial_OpCons( X ), hAPP( c_Polynomial_Opoly( X, Y ), Z ) ),
% 1.04/1.70 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) = Y }.
% 1.04/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.04/1.70 , X = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), skol14
% 1.04/1.70 ( X, Y ) ) }.
% 1.04/1.70 { ! X = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), Z ),
% 1.04/1.70 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }
% 1.04/1.70 .
% 1.04/1.70 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 1.04/1.70 hAPP( X, Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.04/1.70 skol15( Z, Y ) ), Y ) ) }.
% 1.04/1.70 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 1.04/1.70 hAPP( X, Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.04/1.70 tc_Nat_Onat, Z ), skol15( X, Y ) ) ), ! hBOOL( hAPP( X, Z ) ) }.
% 1.04/1.70 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 1.04/1.70 hAPP( X, Y ) ), hBOOL( hAPP( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.04/1.70 tc_Nat_Onat ), skol15( X, Y ) ), c_Groups_Oone__class_Oone( tc_Nat_Onat )
% 1.04/1.70 ) ) ) }.
% 1.04/1.70 { ! class_Groups_Ocomm__monoid__add( X ), hAPP( hAPP(
% 1.04/1.70 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), Z ), Y ) =
% 1.04/1.70 c_Polynomial_OAbs__poly( X, hAPP( hAPP( c_COMBS( tc_Nat_Onat, X, X ),
% 1.04/1.70 hAPP( hAPP( c_COMBB( X, tc_fun( X, X ), tc_Nat_Onat ),
% 1.04/1.70 c_Groups_Oplus__class_Oplus( X ) ), c_Polynomial_Ocoeff( X, Z ) ) ),
% 1.04/1.70 c_Polynomial_Ocoeff( X, Y ) ) ) }.
% 1.04/1.70 { ! class_Orderings_Oord( X ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless
% 1.04/1.70 ( tc_fun( T, X ), Z ), Y ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z ), Y ) ) }.
% 1.04/1.70 { ! class_Orderings_Oord( X ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless
% 1.04/1.70 ( tc_fun( T, X ), Z ), Y ) ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y ), Z ) ) }.
% 1.04/1.70 { ! class_Orderings_Oord( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z ), Y ) ), hBOOL(
% 1.04/1.70 hAPP( c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y ), Z ) ),
% 1.04/1.70 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_fun( T, X ), Z ), Y ) ) }
% 1.04/1.70 .
% 1.04/1.70 { ! class_Groups_Olinordered__ab__group__add( X ), ! hAPP(
% 1.04/1.70 c_Groups_Ouminus__class_Ouminus( X ), Y ) = Y, Y =
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) }.
% 1.04/1.70 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ), hAPP( c_Groups_Ouminus__class_Ouminus(
% 1.04/1.70 X ), Y ) = Y }.
% 1.04/1.70 { ! class_Groups_Ogroup__add( X ), ! hAPP( c_Groups_Ouminus__class_Ouminus
% 1.04/1.70 ( X ), Y ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) }.
% 1.04/1.70 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 1.04/1.70 hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ) =
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) }.
% 1.04/1.70 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y = hAPP(
% 1.04/1.70 c_Groups_Ouminus__class_Ouminus( X ), Y ), Y =
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) }.
% 1.04/1.70 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ), Y = hAPP(
% 1.04/1.70 c_Groups_Ouminus__class_Ouminus( X ), Y ) }.
% 1.04/1.70 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 1.04/1.70 hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ),
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) = Y }.
% 1.04/1.70 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y,
% 1.04/1.70 c_Groups_Ozero__class_Ozero( X ) = hAPP( c_Groups_Ouminus__class_Ouminus
% 1.04/1.70 ( X ), Y ) }.
% 1.04/1.70 { ! class_Groups_Ogroup__add( X ), hAPP( c_Groups_Ouminus__class_Ouminus( X
% 1.04/1.70 ), c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X )
% 1.04/1.70 }.
% 1.04/1.70 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Z ), hAPP(
% 1.04/1.70 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Y ), hAPP(
% 1.04/1.70 c_Groups_Ouminus__class_Ouminus( X ), Z ) ) ) }.
% 1.04/1.70 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Y ), hAPP(
% 1.04/1.70 c_Groups_Ouminus__class_Ouminus( X ), Z ) ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Z ), hAPP(
% 1.04/1.70 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) ) }.
% 1.04/1.70 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 1.04/1.70 c_Groups_Ouminus__class_Ouminus( X ), Z ) ), Y ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 1.04/1.70 c_Groups_Ouminus__class_Ouminus( X ), Y ) ), Z ) ) }.
% 1.04/1.70 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 1.04/1.70 c_Groups_Ouminus__class_Ouminus( X ), Y ) ), Z ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 1.04/1.70 c_Groups_Ouminus__class_Ouminus( X ), Z ) ), Y ) ) }.
% 1.04/1.70 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 1.04/1.70 c_Groups_Ouminus__class_Ouminus( X ), Z ) ), hAPP(
% 1.04/1.70 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ) }.
% 1.04/1.70 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 1.04/1.70 c_Groups_Ouminus__class_Ouminus( X ), Z ) ), hAPP(
% 1.04/1.70 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) ) }.
% 1.04/1.70 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 1.04/1.70 c_Groups_Ouminus__class_Ouminus( X ), Y ) ), hAPP(
% 1.04/1.70 c_Groups_Ouminus__class_Ouminus( X ), Z ) ) ) }.
% 1.04/1.70 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, hAPP( c_Groups_Ouminus__class_Ouminus(
% 1.04/1.70 X ), Z ) ), hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ) ) ), hBOOL(
% 1.04/1.70 hAPP( c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 1.04/1.70 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Y ), Z ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, hAPP( c_Groups_Ouminus__class_Ouminus(
% 1.04/1.70 X ), Z ) ), hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ) ) ) }.
% 1.04/1.70 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, hAPP( c_Groups_Ouminus__class_Ouminus(
% 1.04/1.70 X ), Z ) ), Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP(
% 1.04/1.70 c_Groups_Ouminus__class_Ouminus( X ), Y ) ), Z ) ) }.
% 1.04/1.70 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, hAPP( c_Groups_Ouminus__class_Ouminus(
% 1.04/1.70 X ), Y ) ), Z ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP(
% 1.04/1.70 c_Groups_Ouminus__class_Ouminus( X ), Z ) ), Y ) ) }.
% 1.04/1.70 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Z ), hAPP(
% 1.04/1.70 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) ), hBOOL( hAPP(
% 1.04/1.70 c_Orderings_Oord__class_Oless( X, Y ), hAPP(
% 1.04/1.70 c_Groups_Ouminus__class_Ouminus( X ), Z ) ) ) }.
% 1.04/1.70 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless( X, Y ), hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( X ), Z ) ) ), hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless( X, Z ), hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) ) }.
% 1.04/1.71 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), hAPP( c_Groups_Ouminus__class_Ouminus
% 1.04/1.71 ( X ), Z ) ), Y ) = hAPP( c_Groups_Ouminus__class_Ouminus( X ), hAPP(
% 1.04/1.71 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.04/1.71 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), hAPP( c_Groups_Ouminus__class_Ouminus
% 1.04/1.71 ( X ), Z ) ), Y ) = hAPP( c_Groups_Ouminus__class_Ouminus( X ), hAPP(
% 1.04/1.71 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.04/1.71 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) = hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.04/1.71 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) = hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.04/1.71 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 1.04/1.71 ), Z ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 1.04/1.71 Z = Y, Z = hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ) }.
% 1.04/1.71 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 1.04/1.71 { ! class_Rings_Oidom( X ), ! Z = hAPP( c_Groups_Ouminus__class_Ouminus( X
% 1.04/1.71 ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP
% 1.04/1.71 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 1.04/1.71 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 1.04/1.71 , hAPP( c_Groups_Ouminus__class_Ouminus( X ), Z ) ), hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) = hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 1.04/1.71 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 1.04/1.71 , hAPP( c_Groups_Ouminus__class_Ouminus( X ), Z ) ), Y ) = hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) }.
% 1.04/1.71 { ! class_Rings_Oring( X ), hAPP( c_Groups_Ouminus__class_Ouminus( X ),
% 1.04/1.71 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), hAPP( c_Groups_Ouminus__class_Ouminus
% 1.04/1.71 ( X ), Z ) ), Y ) }.
% 1.04/1.71 { ! class_Rings_Oring( X ), hAPP( c_Groups_Ouminus__class_Ouminus( X ),
% 1.04/1.71 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) }.
% 1.04/1.71 { ! class_Groups_Ogroup__add( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.04/1.71 ( X ), hAPP( c_Groups_Ouminus__class_Ouminus( X ), Z ) ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) = Y }.
% 1.04/1.71 { ! class_Groups_Ogroup__add( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.04/1.71 ( X ), Z ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( X ), Z ) ), Y ) ) = Y }.
% 1.04/1.71 { ! class_Groups_Ogroup__add( X ), hAPP( c_Groups_Ouminus__class_Ouminus( X
% 1.04/1.71 ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) = hAPP( hAPP
% 1.04/1.71 ( c_Groups_Oplus__class_Oplus( X ), hAPP( c_Groups_Ouminus__class_Ouminus
% 1.04/1.71 ( X ), Y ) ), hAPP( c_Groups_Ouminus__class_Ouminus( X ), Z ) ) }.
% 1.04/1.71 { ! class_Groups_Oab__group__add( X ), hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( X ), hAPP( c_Groups_Ouminus__class_Ouminus(
% 1.04/1.71 X ), Z ) ), hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ) ) }.
% 1.04/1.71 { hAPP( c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ),
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) =
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.04/1.71 { hAPP( c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), X ) ) = hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), Y ) ), hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), X ) ) }.
% 1.04/1.71 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), Y ) ), X ) = hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.04/1.71 { ! class_Groups_Oab__group__add( X ), hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ) ),
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.04/1.71 { ! class_Rings_Ocomm__ring( X ), hAPP( hAPP( c_Polynomial_Osmult( X ), Z )
% 1.04/1.71 , hAPP( c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ) ), Y )
% 1.04/1.71 ) = hAPP( c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ) ),
% 1.04/1.71 hAPP( hAPP( c_Polynomial_Osmult( X ), Z ), Y ) ) }.
% 1.04/1.71 { ! class_Groups_Oab__group__add( X ), hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 1.04/1.71 c_Polynomial_OpCons( X ), Z ), Y ) ) = hAPP( hAPP( c_Polynomial_OpCons( X
% 1.04/1.71 ), hAPP( c_Groups_Ouminus__class_Ouminus( X ), Z ) ), hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ) ), Y ) ) }.
% 1.04/1.71 { ! class_Groups_Oab__group__add( X ), hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 1.04/1.71 c_Polynomial_OpCons( X ), Z ), Y ) ) = hAPP( hAPP( c_Polynomial_OpCons( X
% 1.04/1.71 ), hAPP( c_Groups_Ouminus__class_Ouminus( X ), Z ) ), hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ) ), Y ) ) }.
% 1.04/1.71 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X, hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ) ), Z ) ), Y ) =
% 1.04/1.71 hAPP( c_Groups_Ouminus__class_Ouminus( X ), hAPP( c_Polynomial_Opoly( X
% 1.04/1.71 , Z ), Y ) ) }.
% 1.04/1.71 { ! class_Groups_Ogroup__add( X ), ! hAPP( c_Groups_Ouminus__class_Ouminus
% 1.04/1.71 ( X ), Z ) = hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ), Z = Y }.
% 1.04/1.71 { ! class_Groups_Ogroup__add( X ), ! Z = Y, hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( X ), Z ) = hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( X ), Y ) }.
% 1.04/1.71 { ! class_Groups_Ogroup__add( X ), ! hAPP( c_Groups_Ouminus__class_Ouminus
% 1.04/1.71 ( X ), Z ) = Y, hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ) = Z }.
% 1.04/1.71 { ! class_Groups_Ogroup__add( X ), ! hAPP( c_Groups_Ouminus__class_Ouminus
% 1.04/1.71 ( X ), Y ) = Z, hAPP( c_Groups_Ouminus__class_Ouminus( X ), Z ) = Y }.
% 1.04/1.71 { ! class_Groups_Ogroup__add( X ), ! Z = hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( X ), Y ), Y = hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( X ), Z ) }.
% 1.04/1.71 { ! class_Groups_Ogroup__add( X ), ! Y = hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( X ), Z ), Z = hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( X ), Y ) }.
% 1.04/1.71 { ! class_Groups_Ogroup__add( X ), hAPP( c_Groups_Ouminus__class_Ouminus( X
% 1.04/1.71 ), hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ) ) = Y }.
% 1.04/1.71 { ! class_Groups_Oab__group__add( X ), hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ) ),
% 1.04/1.71 c_Polynomial_Omonom( X, Z, Y ) ) = c_Polynomial_Omonom( X, hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( X ), Z ), Y ) }.
% 1.04/1.71 { ! class_Groups_Oab__group__add( X ), hAPP( c_Polynomial_Ocoeff( X, hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ) ), Z ) ), Y ) =
% 1.04/1.71 hAPP( c_Groups_Ouminus__class_Ouminus( X ), hAPP( c_Polynomial_Ocoeff( X
% 1.04/1.71 , Z ), Y ) ) }.
% 1.04/1.71 { ! class_Rings_Ocomm__ring( X ), hAPP( hAPP( c_Polynomial_Osmult( X ),
% 1.04/1.71 hAPP( c_Groups_Ouminus__class_Ouminus( X ), Z ) ), Y ) = hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 1.04/1.71 c_Polynomial_Osmult( X ), Z ), Y ) ) }.
% 1.04/1.71 { ! class_Groups_Oab__group__add( X ), hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ) ), Y ) =
% 1.04/1.71 c_Polynomial_OAbs__poly( X, hAPP( hAPP( c_COMBB( X, X, tc_Nat_Onat ),
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( X ) ), c_Polynomial_Ocoeff( X, Y ) ) ) }
% 1.04/1.71 .
% 1.04/1.71 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( X ), Y ) ), Y ) ), hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.04/1.71 , Y ) ) }.
% 1.04/1.71 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.04/1.71 , Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( X ), Y ) ), Y ) ) }.
% 1.04/1.71 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( X ), Y ) ), c_Groups_Ozero__class_Ozero
% 1.04/1.71 ( X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( X ) ), Y ) ) }.
% 1.04/1.71 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.04/1.71 , Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( X ), Y ) ), c_Groups_Ozero__class_Ozero
% 1.04/1.71 ( X ) ) ) }.
% 1.04/1.71 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless__eq( X, Y ), hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) ), hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 1.04/1.71 ) ) ) }.
% 1.04/1.71 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 1.04/1.71 ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Y ), hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) ) }.
% 1.04/1.71 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.04/1.71 , hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ) ) ), hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 1.04/1.71 ) ) ) }.
% 1.04/1.71 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 1.04/1.71 ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( X ) ), hAPP( c_Groups_Ouminus__class_Ouminus
% 1.04/1.71 ( X ), Y ) ) ) }.
% 1.04/1.71 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless( X, hAPP( c_Groups_Ouminus__class_Ouminus(
% 1.04/1.71 X ), Y ) ), Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( X ) ), Y ) ) }.
% 1.04/1.71 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 1.04/1.71 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( X ), Y ) ), Y ) ) }.
% 1.04/1.71 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless( X, hAPP( c_Groups_Ouminus__class_Ouminus(
% 1.04/1.71 X ), Y ) ), c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 1.04/1.71 ) }.
% 1.04/1.71 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 1.04/1.71 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( X ), Y ) ), c_Groups_Ozero__class_Ozero
% 1.04/1.71 ( X ) ) ) }.
% 1.04/1.71 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless( X, Y ), hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) ), hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 1.04/1.71 ) }.
% 1.04/1.71 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 1.04/1.71 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Y ), hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) ) }.
% 1.04/1.71 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 1.04/1.71 hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ) ) ), hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 1.04/1.71 ) }.
% 1.04/1.71 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 1.04/1.71 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( X ) ), hAPP( c_Groups_Ouminus__class_Ouminus
% 1.04/1.71 ( X ), Y ) ) ) }.
% 1.04/1.71 { ! class_Groups_Ozero( X ), c_Polynomial_OAbs__poly( X,
% 1.04/1.71 c_Polynomial_Ocoeff( X, Y ) ) = Y }.
% 1.04/1.71 { ! class_Groups_Ogroup__add( X ), ! hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) = c_Groups_Ozero__class_Ozero
% 1.04/1.71 ( X ), hAPP( c_Groups_Ouminus__class_Ouminus( X ), Z ) = Y }.
% 1.04/1.71 { ! class_Groups_Oab__group__add( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( X ), hAPP( c_Groups_Ouminus__class_Ouminus(
% 1.04/1.71 X ), Y ) ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.04/1.71 { ! class_Groups_Ogroup__add( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.04/1.71 ( X ), hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ) ), Y ) =
% 1.04/1.71 c_Groups_Ozero__class_Ozero( X ) }.
% 1.04/1.71 { ! class_Groups_Ogroup__add( X ), ! Z = hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( X ), Y ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) = c_Groups_Ozero__class_Ozero
% 1.04/1.71 ( X ) }.
% 1.04/1.71 { ! class_Groups_Ogroup__add( X ), ! hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) = c_Groups_Ozero__class_Ozero
% 1.04/1.71 ( X ), Z = hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ) }.
% 1.04/1.71 { ! class_Groups_Ogroup__add( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.04/1.71 ( X ), Y ), hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ) ) =
% 1.04/1.71 c_Groups_Ozero__class_Ozero( X ) }.
% 1.04/1.71 { ! class_Groups_Ogroup__add( X ), ! hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) = c_Groups_Ozero__class_Ozero
% 1.04/1.71 ( X ), Y = hAPP( c_Groups_Ouminus__class_Ouminus( X ), Z ) }.
% 1.04/1.71 { ! class_Groups_Ogroup__add( X ), ! Y = hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( X ), Z ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) = c_Groups_Ozero__class_Ozero
% 1.04/1.71 ( X ) }.
% 1.04/1.71 { ! class_Rings_Ocomm__ring__1( X ), hAPP( c_Groups_Ouminus__class_Ouminus
% 1.04/1.71 ( X ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( X ), c_Groups_Oone__class_Oone( X ) ) )
% 1.04/1.71 , Y ) }.
% 1.04/1.71 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = c_Groups_Oone__class_Oone
% 1.04/1.71 ( X ), Y = c_Groups_Oone__class_Oone( X ), Y = hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( X ), c_Groups_Oone__class_Oone( X ) ) }
% 1.04/1.71 .
% 1.04/1.71 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 1.04/1.71 c_Groups_Oone__class_Oone( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.04/1.71 ( X ), Y ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 1.04/1.71 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y = hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( X ), c_Groups_Oone__class_Oone( X ) ),
% 1.04/1.71 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) =
% 1.04/1.71 c_Groups_Oone__class_Oone( X ) }.
% 1.04/1.71 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), X ) ), X ) =
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.04/1.71 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.04/1.71 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opos__poly( X, Y ),
% 1.04/1.71 c_Polynomial_Opos__poly( X, hAPP( c_Groups_Ouminus__class_Ouminus(
% 1.04/1.71 tc_Polynomial_Opoly( X ) ), Y ) ) }.
% 1.04/1.71 { ! class_Rings_Oring__1( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X
% 1.04/1.71 ), hAPP( c_Groups_Ouminus__class_Ouminus( X ), Z ) ), Y ) = hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.04/1.71 c_Power_Opower__class_Opower( X ), hAPP( c_Groups_Ouminus__class_Ouminus
% 1.04/1.71 ( X ), c_Groups_Oone__class_Oone( X ) ) ), Y ) ), hAPP( hAPP(
% 1.04/1.71 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.04/1.71 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 1.04/1.71 , Z ), hAPP( c_Nat_OSuc, hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero(
% 1.04/1.71 tc_Nat_Onat ) ) ) ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y )
% 1.04/1.71 , hAPP( c_Nat_OSuc, hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero(
% 1.04/1.71 tc_Nat_Onat ) ) ) ), Z = Y, Z = hAPP( c_Groups_Ouminus__class_Ouminus( X
% 1.04/1.71 ), Y ) }.
% 1.04/1.71 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 1.04/1.71 c_Power_Opower__class_Opower( X ), Z ), hAPP( c_Nat_OSuc, hAPP(
% 1.04/1.71 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP
% 1.04/1.71 ( c_Power_Opower__class_Opower( X ), Y ), hAPP( c_Nat_OSuc, hAPP(
% 1.04/1.71 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 1.04/1.71 { ! class_Rings_Oidom( X ), ! Z = hAPP( c_Groups_Ouminus__class_Ouminus( X
% 1.04/1.71 ), Y ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), hAPP(
% 1.04/1.71 c_Nat_OSuc, hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.04/1.71 ) ) ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), hAPP(
% 1.04/1.71 c_Nat_OSuc, hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.04/1.71 ) ) ) }.
% 1.04/1.71 { ! class_Groups_Ozero( X ), c_Groups_Ozero__class_Ozero(
% 1.04/1.71 tc_Polynomial_Opoly( X ) ) = c_Polynomial_OAbs__poly( X, hAPP( c_COMBK( X
% 1.04/1.71 , tc_Nat_Onat ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.04/1.71 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X, Z, Y ) =
% 1.04/1.71 c_Polynomial_OAbs__poly( X, hAPP( c_COMBC( tc_Nat_Onat, X, X, hAPP(
% 1.04/1.71 c_COMBC( tc_Nat_Onat, X, tc_fun( X, X ), hAPP( hAPP( c_COMBB(
% 1.04/1.71 tc_HOL_Obool, tc_fun( X, tc_fun( X, X ) ), tc_Nat_Onat ), c_If( X ) ),
% 1.04/1.71 c_fequal( Y ) ) ), Z ) ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.04/1.71 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP( c_Polynomial_Osmult( X
% 1.04/1.71 ), Z ), Y ) = c_Polynomial_OAbs__poly( X, hAPP( hAPP( c_COMBB( X, X,
% 1.04/1.71 tc_Nat_Onat ), hAPP( c_Groups_Otimes__class_Otimes( X ), Z ) ),
% 1.04/1.71 c_Polynomial_Ocoeff( X, Y ) ) ) }.
% 1.04/1.71 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.04/1.71 tc_Polynomial_Opoly( X ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.04/1.71 tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.04/1.71 tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Polynomial_OpCons( X ), hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( X ), Z ) ), hAPP( hAPP(
% 1.04/1.71 c_Polynomial_OpCons( X ), c_Groups_Oone__class_Oone( X ) ),
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ),
% 1.04/1.71 c_Polynomial_Oorder( X, Z, Y ) ) ), Y ) ) }.
% 1.04/1.71 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.04/1.71 tc_Polynomial_Opoly( X ) ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 1.04/1.71 ( tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.04/1.71 tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Polynomial_OpCons( X ), hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( X ), Z ) ), hAPP( hAPP(
% 1.04/1.71 c_Polynomial_OpCons( X ), c_Groups_Oone__class_Oone( X ) ),
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ), hAPP(
% 1.04/1.71 c_Nat_OSuc, c_Polynomial_Oorder( X, Z, Y ) ) ) ), Y ) ) }.
% 1.04/1.71 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.04/1.71 tc_Polynomial_Opoly( X ) ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 1.04/1.71 ( tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.04/1.71 tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Polynomial_OpCons( X ), hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( X ), Z ) ), hAPP( hAPP(
% 1.04/1.71 c_Polynomial_OpCons( X ), c_Groups_Oone__class_Oone( X ) ),
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ), hAPP(
% 1.04/1.71 c_Nat_OSuc, c_Polynomial_Oorder( X, Z, Y ) ) ) ), Y ) ) }.
% 1.04/1.71 { ! class_Lattices_Oboolean__algebra( X ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( X ), Z ) ), hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) ), hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ) }.
% 1.04/1.71 { ! class_Lattices_Oboolean__algebra( X ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ), hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( X ), Z ) ), hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) ) }.
% 1.04/1.71 { ! class_Rings_Ocomm__semiring__1( X ), hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) )
% 1.04/1.71 }.
% 1.04/1.71 { ! class_Rings_Ocomm__ring__1( X ), ! hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( X ), hAPP( c_Groups_Ouminus__class_Ouminus( X )
% 1.04/1.71 , Z ) ), Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y
% 1.04/1.71 ) ) }.
% 1.04/1.71 { ! class_Rings_Ocomm__ring__1( X ), ! hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( X ), hAPP( c_Groups_Ouminus__class_Ouminus( X )
% 1.04/1.71 , Z ) ), Y ) ) }.
% 1.04/1.71 { ! class_Rings_Ocomm__ring__1( X ), ! hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( c_Groups_Ouminus__class_Ouminus
% 1.04/1.71 ( X ), Y ) ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y
% 1.04/1.71 ) ) }.
% 1.04/1.71 { ! class_Rings_Ocomm__ring__1( X ), ! hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( c_Groups_Ouminus__class_Ouminus
% 1.04/1.71 ( X ), Y ) ) ) }.
% 1.04/1.71 { hAPP( c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), X ) ) = X }.
% 1.04/1.71 { ! class_Rings_Ocomm__semiring__1( X ), hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( X ), Y ), Y ) ) }.
% 1.04/1.71 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( X ), Y ), T ) ), hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( X ), Z ), T ) ) }.
% 1.04/1.71 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 1.04/1.71 c_Polynomial_Osmult( X ), T ), Z ) ), Y ) ), hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Z ), Y ) ) }.
% 1.04/1.71 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Z ), Y ) ), hBOOL(
% 1.04/1.71 hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Z ),
% 1.04/1.71 hAPP( hAPP( c_Polynomial_Osmult( X ), T ), Y ) ) ) }.
% 1.04/1.71 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.04/1.71 X ), Z ), T ) ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T )
% 1.04/1.71 ) ) }.
% 1.04/1.71 { ! class_Rings_Ocomm__semiring__1( X ), hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( X ), c_Groups_Oone__class_Oone( X ) ), Y ) ) }
% 1.04/1.71 .
% 1.04/1.71 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( X ), Z ), T ) ), hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( X ), Y ), T ) ) ) }.
% 1.04/1.71 { ! class_Rings_Ocomm__semiring__1( X ), hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 1.04/1.71 { ! class_Rings_Ocomm__semiring__1( X ), hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 1.04/1.71 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ) }.
% 1.04/1.71 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 1.04/1.71 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( X ), U ), T ) ), hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.04/1.71 ( X ), Z ), U ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T
% 1.04/1.71 ) ) ) }.
% 1.04/1.71 { ! class_Rings_Odvd( X ), ! Z = hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.04/1.71 ( X ), Y ), T ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Y ), Z
% 1.04/1.71 ) ) }.
% 1.04/1.71 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.04/1.71 ( X ), Z ), T ) ), Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X
% 1.04/1.71 ), Z ), Y ) ) }.
% 1.04/1.71 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.04/1.71 ( X ), T ), Z ) ), Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X
% 1.04/1.71 ), Z ), Y ) ) }.
% 1.04/1.71 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) )
% 1.04/1.71 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.04/1.71 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.04/1.71 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP(
% 1.04/1.71 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), Z =
% 1.04/1.71 c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( X ), T ), Y ) ) }.
% 1.04/1.71 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ), hBOOL(
% 1.04/1.71 hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 1.04/1.71 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.04/1.71 X ), T ), Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), hAPP(
% 1.04/1.71 hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 1.04/1.71 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.04/1.71 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP(
% 1.04/1.71 hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ), T =
% 1.04/1.71 c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ) }.
% 1.04/1.71 { ! class_Rings_Oidom( X ), ! T = c_Groups_Ozero__class_Ozero( X ), hBOOL(
% 1.04/1.71 hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 1.04/1.71 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.04/1.71 X ), Z ), Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), hAPP(
% 1.04/1.71 hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 1.04/1.71 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), Y ) ), hBOOL( hAPP(
% 1.04/1.71 hAPP( c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP(
% 1.04/1.71 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 1.04/1.71 c_Power_Opower__class_Opower( X ), T ), Y ) ) ) }.
% 1.04/1.71 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, U ), T ) ), hBOOL( hAPP(
% 1.04/1.71 hAPP( c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP(
% 1.04/1.71 c_Power_Opower__class_Opower( X ), Z ), U ) ), hAPP( hAPP(
% 1.04/1.71 c_Power_Opower__class_Opower( X ), Y ), T ) ) ) }.
% 1.04/1.71 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.04/1.71 X ), T ), Z ) ), Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 1.04/1.71 ( tc_Nat_Onat, U ), Z ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X
% 1.04/1.71 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), U ) ), Y ) ) }.
% 1.04/1.71 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! hBOOL
% 1.04/1.71 ( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), T ),
% 1.04/1.71 hAPP( hAPP( c_Polynomial_Osmult( X ), Y ), Z ) ) ), hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), T ), Z ) ) }.
% 1.04/1.71 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! hBOOL
% 1.04/1.71 ( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), T ),
% 1.04/1.71 Z ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly(
% 1.04/1.71 X ) ), T ), hAPP( hAPP( c_Polynomial_Osmult( X ), Y ), Z ) ) ) }.
% 1.04/1.71 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 1.04/1.71 ( tc_Polynomial_Opoly( X ) ), Z ), Y ) ), T = c_Groups_Ozero__class_Ozero
% 1.04/1.71 ( X ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly(
% 1.04/1.71 X ) ), hAPP( hAPP( c_Polynomial_Osmult( X ), T ), Z ) ), Y ) ) }.
% 1.04/1.71 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 1.04/1.71 ( tc_Polynomial_Opoly( X ) ), T ), hAPP( hAPP( c_Polynomial_Osmult( X ),
% 1.04/1.71 Z ), Y ) ) ), Z = c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), T ), Y ) ) }.
% 1.04/1.71 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 1.04/1.71 ( tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Polynomial_Osmult( X ), T ),
% 1.04/1.71 Z ) ), Y ) ), alpha9( X, Y, T ) }.
% 1.04/1.71 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 1.04/1.71 ( tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Polynomial_Osmult( X ), T ),
% 1.04/1.71 Z ) ), Y ) ), alpha24( X, Y, Z, T ) }.
% 1.04/1.71 { ! class_Fields_Ofield( X ), ! alpha9( X, Y, T ), ! alpha24( X, Y, Z, T )
% 1.04/1.71 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) )
% 1.04/1.71 , hAPP( hAPP( c_Polynomial_Osmult( X ), T ), Z ) ), Y ) ) }.
% 1.04/1.71 { ! alpha24( X, Y, Z, T ), T = c_Groups_Ozero__class_Ozero( X ), hBOOL(
% 1.04/1.71 hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Z ), Y
% 1.04/1.71 ) ) }.
% 1.04/1.71 { ! T = c_Groups_Ozero__class_Ozero( X ), alpha24( X, Y, Z, T ) }.
% 1.04/1.71 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) )
% 1.04/1.71 , Z ), Y ) ), alpha24( X, Y, Z, T ) }.
% 1.04/1.71 { ! alpha9( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero( X ), Y =
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.04/1.71 { Z = c_Groups_Ozero__class_Ozero( X ), alpha9( X, Y, Z ) }.
% 1.04/1.71 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha9( X
% 1.04/1.71 , Y, Z ) }.
% 1.04/1.71 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 1.04/1.71 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 1.04/1.71 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 1.04/1.71 { ! class_Lattices_Oboolean__algebra( X ), ! hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( X ), Z ) = hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( X ), Y ), Z = Y }.
% 1.04/1.71 { ! class_Lattices_Oboolean__algebra( X ), ! Z = Y, hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( X ), Z ) = hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( X ), Y ) }.
% 1.04/1.71 { ! class_Groups_Ouminus( X ), hAPP( hAPP( c_Groups_Ouminus__class_Ouminus
% 1.04/1.71 ( tc_fun( T, X ) ), Z ), Y ) = hAPP( c_Groups_Ouminus__class_Ouminus( X )
% 1.04/1.71 , hAPP( Z, Y ) ) }.
% 1.04/1.71 { ! class_Lattices_Oboolean__algebra( X ), hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( X ), hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) = Y }.
% 1.04/1.71 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.04/1.71 tc_Nat_Onat ) ), Z ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X )
% 1.04/1.71 , Y ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.04/1.71 { ! class_Rings_Ocomm__semiring__1( X ), ! Y = c_Groups_Oone__class_Oone( X
% 1.04/1.71 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Y ), hAPP( hAPP(
% 1.04/1.71 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.04/1.71 { ! class_Groups_Ouminus( X ), hAPP( hAPP( c_Groups_Ouminus__class_Ouminus
% 1.04/1.71 ( tc_fun( T, X ) ), Z ), Y ) = hAPP( c_Groups_Ouminus__class_Ouminus( X )
% 1.04/1.71 , hAPP( Z, Y ) ) }.
% 1.04/1.71 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 1.04/1.71 c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 1.04/1.71 c_Polynomial_OpCons( X ), hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y )
% 1.04/1.71 ), hAPP( hAPP( c_Polynomial_OpCons( X ), c_Groups_Oone__class_Oone( X )
% 1.04/1.71 ), c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ), Z ) )
% 1.04/1.71 }.
% 1.04/1.71 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.04/1.71 tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Polynomial_OpCons( X ), hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( X ), Y ) ), hAPP( hAPP(
% 1.04/1.71 c_Polynomial_OpCons( X ), c_Groups_Oone__class_Oone( X ) ),
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ), Z ) ),
% 1.04/1.71 hAPP( c_Polynomial_Opoly( X, Z ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 1.04/1.71 }.
% 1.04/1.71 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.04/1.71 tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Polynomial_OpCons( X ), Z ),
% 1.04/1.71 hAPP( hAPP( c_Polynomial_OpCons( X ), c_Groups_Oone__class_Oone( X ) ),
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ),
% 1.04/1.71 hAPP( c_Polynomial_Opoly( X, Y ), hAPP( c_Groups_Ouminus__class_Ouminus(
% 1.04/1.71 X ), Z ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.04/1.71 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Y ), hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( X ), Z ) ) = c_Groups_Ozero__class_Ozero
% 1.04/1.71 ( X ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly(
% 1.04/1.71 X ) ), hAPP( hAPP( c_Polynomial_OpCons( X ), Z ), hAPP( hAPP(
% 1.04/1.71 c_Polynomial_OpCons( X ), c_Groups_Oone__class_Oone( X ) ),
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ) }.
% 1.04/1.71 { ! class_Rings_Oidom( X ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.04/1.71 tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.04/1.71 tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Polynomial_OpCons( X ), hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( X ), Z ) ), hAPP( hAPP(
% 1.04/1.71 c_Polynomial_OpCons( X ), c_Groups_Oone__class_Oone( X ) ),
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ),
% 1.04/1.71 c_Polynomial_Oorder( X, Z, Y ) ) ), Y ) ) }.
% 1.04/1.71 { ! class_Lattices_Oboolean__algebra( X ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( X ), Y ) ), hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( X ), Z ) ) ) }.
% 1.04/1.71 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 1.04/1.71 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ), hBOOL(
% 1.04/1.71 hAPP( Z, skol16( U, W, Z ) ) ) }.
% 1.04/1.71 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 1.04/1.71 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ), hBOOL(
% 1.04/1.71 hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Y ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( X ), skol16( X, Y, Z ) ),
% 1.04/1.71 c_Groups_Ozero__class_Ozero( X ) ) ) ) }.
% 1.04/1.71 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 1.04/1.71 hAPP( c_Rings_Odvd__class_Odvd( X ), Y ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( X ), T ), c_Groups_Ozero__class_Ozero( X ) )
% 1.04/1.71 ) ), ! hBOOL( hAPP( Z, T ) ), hBOOL( hAPP( Z, hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), Y ), skol34( X, Y, Z ) ) ) ) }.
% 1.04/1.71 { ! class_Rings_Oidom( X ), c_Polynomial_Oorder( X, Z, Y ) =
% 1.04/1.71 c_Orderings_Oord__class_OLeast( tc_Nat_Onat, hAPP( hAPP( c_COMBB(
% 1.04/1.71 tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat ), c_fNot ), hAPP( c_COMBC(
% 1.04/1.71 tc_Nat_Onat, tc_Polynomial_Opoly( X ), tc_HOL_Obool, hAPP( hAPP( c_COMBB
% 1.04/1.71 ( tc_Polynomial_Opoly( X ), tc_fun( tc_Polynomial_Opoly( X ),
% 1.04/1.71 tc_HOL_Obool ), tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 1.04/1.71 tc_Polynomial_Opoly( X ) ) ), hAPP( hAPP( c_COMBB( tc_Nat_Onat,
% 1.04/1.71 tc_Polynomial_Opoly( X ), tc_Nat_Onat ), hAPP(
% 1.04/1.71 c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 1.04/1.71 c_Polynomial_OpCons( X ), hAPP( c_Groups_Ouminus__class_Ouminus( X ), Z )
% 1.04/1.71 ), hAPP( hAPP( c_Polynomial_OpCons( X ), c_Groups_Oone__class_Oone( X )
% 1.04/1.71 ), c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ) ),
% 1.04/1.71 c_Nat_OSuc ) ) ), Y ) ) ) }.
% 1.04/1.71 { ! class_Groups_Ozero( X ), hAPP( hAPP( c_Polynomial_OpCons( X ), Z ), Y )
% 1.04/1.71 = c_Polynomial_OAbs__poly( X, c_Nat_Onat_Onat__case( X, Z,
% 1.04/1.71 c_Polynomial_Ocoeff( X, Y ) ) ) }.
% 1.04/1.71 { hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP(
% 1.04/1.71 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) )
% 1.04/1.71 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), X ) ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), X ) ) ), hBOOL( hAPP(
% 1.04/1.71 hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) )
% 1.04/1.71 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), Y ) ), X ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), Y ) ), X ) ), hBOOL( hAPP
% 1.04/1.71 ( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) ) }.
% 1.04/1.71 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), ! hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ) ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) ) }.
% 1.04/1.71 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), ! hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ) ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) ), hBOOL( hAPP(
% 1.04/1.71 hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ),
% 1.04/1.71 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ), X =
% 1.04/1.71 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.04/1.71 { ! X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), c_Groups_Oone__class_Oone(
% 1.04/1.71 tc_Nat_Onat ) ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), hAPP(
% 1.04/1.71 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Y ) ) ), hBOOL(
% 1.04/1.71 hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.04/1.71 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), hAPP(
% 1.04/1.71 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Y ) ) ) }.
% 1.04/1.71 { ! class_Orderings_Owellorder( X ), ! hBOOL( hAPP( Y, Z ) ), hBOOL( hAPP(
% 1.04/1.71 Y, c_Orderings_Oord__class_OLeast( X, Y ) ) ) }.
% 1.04/1.71 { ! class_Orderings_Owellorder( X ), ! hBOOL( hAPP( Y, Z ) ), hBOOL( hAPP(
% 1.04/1.71 Y, c_Orderings_Oord__class_OLeast( X, Y ) ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), ! hBOOL( hAPP( hAPP
% 1.04/1.71 ( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), X ), Y ) ), ! hBOOL( hAPP(
% 1.04/1.71 hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) ), X = Y }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless( tc_Int_Oint, X ), Y ) ), ! hBOOL( hAPP(
% 1.04/1.71 hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP( hAPP
% 1.04/1.71 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ), Z =
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) )
% 1.04/1.71 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), hAPP
% 1.04/1.71 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), U ), T ) ) ), hBOOL(
% 1.04/1.71 hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), U ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ), T ) ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) )
% 1.04/1.71 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), hAPP
% 1.04/1.71 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), U ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ), T ) ) ),
% 1.04/1.71 hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), hAPP(
% 1.04/1.71 hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), U ), T ) ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), hAPP(
% 1.04/1.71 hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ) ), hBOOL( hAPP
% 1.04/1.71 ( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) )
% 1.04/1.71 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), hAPP(
% 1.04/1.71 hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), hAPP(
% 1.04/1.71 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), X = hAPP(
% 1.04/1.71 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.04/1.71 { ! X = hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 1.04/1.71 hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), hAPP(
% 1.04/1.71 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), Y ) ), ! hBOOL( hAPP(
% 1.04/1.71 hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP
% 1.04/1.71 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ), Z =
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ) }.
% 1.04/1.71 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.04/1.71 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP
% 1.04/1.71 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ) }.
% 1.04/1.71 { hAPP( c_Nat_Onat_Onat__case( Z, Y, X ), c_Groups_Ozero__class_Ozero(
% 1.04/1.71 tc_Nat_Onat ) ) = Y }.
% 1.04/1.71 { hAPP( c_Nat_Onat_Onat__case( T, Z, Y ), hAPP( c_Nat_OSuc, X ) ) = hAPP( Y
% 1.04/1.71 , X ) }.
% 1.04/1.71 { ! class_Orderings_Owellorder( X ), ! hBOOL( hAPP( Z, Y ) ), hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless__eq( X, c_Orderings_Oord__class_OLeast( X,
% 1.04/1.71 Z ) ), Y ) ) }.
% 1.04/1.71 { ! class_Orderings_Owellorder( X ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless( X, Z ), c_Orderings_Oord__class_OLeast( X
% 1.04/1.71 , Y ) ) ), ! hBOOL( hAPP( Y, Z ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) )
% 1.04/1.71 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.04/1.71 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP( hAPP
% 1.04/1.71 ( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ), hBOOL( hAPP(
% 1.04/1.71 hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP( hAPP
% 1.04/1.71 ( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y ) ), hBOOL( hAPP( hAPP
% 1.04/1.71 ( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP
% 1.04/1.71 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ), ! hBOOL( hAPP
% 1.04/1.71 ( c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.04/1.71 ( tc_Nat_Onat ) ), Z ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.04/1.71 tc_Nat_Onat ), Y ), X ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero(
% 1.04/1.71 tc_Nat_Onat ) ) ), c_Orderings_Oord__class_OLeast( tc_Nat_Onat, X ) =
% 1.04/1.71 hAPP( c_Nat_OSuc, c_Orderings_Oord__class_OLeast( tc_Nat_Onat, hAPP( hAPP
% 1.04/1.71 ( c_COMBB( tc_Nat_Onat, tc_HOL_Obool, tc_Nat_Onat ), X ), c_Nat_OSuc ) )
% 1.04/1.71 ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP( hAPP
% 1.04/1.71 ( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ), X ) ), Y =
% 1.04/1.71 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! Y =
% 1.04/1.71 c_Groups_Oone__class_Oone( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ), X ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP( hAPP
% 1.04/1.71 ( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), X ) ), Y =
% 1.04/1.71 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! Y =
% 1.04/1.71 c_Groups_Oone__class_Oone( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), X ) ) }.
% 1.04/1.71 { ! class_Groups_Ozero( X ), c_Polynomial_Ocoeff( X, hAPP( hAPP(
% 1.04/1.71 c_Polynomial_OpCons( X ), Z ), Y ) ) = c_Nat_Onat_Onat__case( X, Z,
% 1.04/1.71 c_Polynomial_Ocoeff( X, Y ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP
% 1.04/1.71 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.04/1.71 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ) ) ), ! hBOOL( hAPP
% 1.04/1.71 ( c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 1.04/1.71 tc_Nat_Onat ) ), Z ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.04/1.71 tc_Nat_Onat, Y ), X ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 1.04/1.71 c_Nat_OSuc, Y ) ), X ) ), hBOOL( hAPP( c_Nat_Onat_Onat__case(
% 1.04/1.71 tc_HOL_Obool, c_fFalse, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 1.04/1.71 ) ), X ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Nat_Onat_Onat__case( tc_HOL_Obool, c_fFalse,
% 1.04/1.71 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ) ), X ) ), hBOOL( hAPP
% 1.04/1.71 ( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( c_Nat_OSuc, Y ) )
% 1.04/1.71 , X ) ) }.
% 1.04/1.71 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ) ), hAPP( hAPP(
% 1.04/1.71 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) ), hBOOL( hAPP(
% 1.04/1.71 hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y ) ) }.
% 1.04/1.71 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ) ), hAPP( hAPP(
% 1.04/1.71 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP
% 1.04/1.71 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.04/1.71 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ) ), Y =
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP( hAPP
% 1.04/1.71 ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 1.04/1.71 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) ), Y =
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), X ) ) }.
% 1.04/1.71 { hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), X ) ) }
% 1.04/1.71 .
% 1.04/1.71 { ! Y = X, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 1.04/1.71 , X ) ) }.
% 1.04/1.71 { ! Y = X, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X )
% 1.04/1.71 , Y ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.04/1.71 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 1.04/1.71 ), Y = X }.
% 1.04/1.71 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.04/1.71 , alpha10( X, Y ), Y = X }.
% 1.04/1.71 { ! alpha10( X, Y ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.04/1.71 tc_Nat_Onat ), Y ), X ) ) }.
% 1.04/1.71 { ! Y = X, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 1.04/1.71 , X ) ) }.
% 1.04/1.71 { ! alpha10( X, Y ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.04/1.71 tc_Nat_Onat ), Y ), X ) ) }.
% 1.04/1.71 { ! alpha10( X, Y ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.04/1.71 tc_Nat_Onat ), X ), Y ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.04/1.71 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 1.04/1.71 , alpha10( X, Y ) }.
% 1.04/1.71 { ! alpha11( X, Y ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.04/1.71 tc_Nat_Onat ), Y ), X ) ) }.
% 1.04/1.71 { ! alpha11( X, Y ), ! Y = X }.
% 1.04/1.71 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.04/1.71 , Y = X, alpha11( X, Y ) }.
% 1.04/1.71 { ! alpha11( X, Y ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.04/1.71 tc_Nat_Onat ), Y ), X ) ) }.
% 1.04/1.71 { ! alpha11( X, Y ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.04/1.71 tc_Nat_Onat ), X ), Y ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.04/1.71 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 1.04/1.71 , alpha11( X, Y ) }.
% 1.04/1.71 { Y = X, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 1.04/1.71 , X ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 1.04/1.71 , X ) ) }.
% 1.04/1.71 { Y = X, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 1.04/1.71 , X ) ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X
% 1.04/1.71 ), Y ) ) }.
% 1.04/1.71 { ! Y = X, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 1.04/1.71 , X ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.04/1.71 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 1.04/1.71 ), X = Y }.
% 1.04/1.71 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.04/1.71 , ! X = Y, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X
% 1.04/1.71 ), Y ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.04/1.71 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.04/1.71 , Y = X }.
% 1.04/1.71 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.04/1.71 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 1.04/1.71 ), Y = X }.
% 1.04/1.71 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.04/1.71 , Y = X, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 1.04/1.71 , X ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.04/1.71 , Y = X, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X
% 1.04/1.71 ), Y ) ) }.
% 1.04/1.71 { ! Y = X, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X
% 1.04/1.71 ), Z ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y
% 1.04/1.71 ), Z ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.04/1.71 , ! X = Z, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y
% 1.04/1.71 ), Z ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.04/1.71 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 1.04/1.71 ), Y = X }.
% 1.04/1.71 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.04/1.71 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 1.04/1.71 ), Y = X }.
% 1.04/1.71 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.04/1.71 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 1.04/1.71 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), Z )
% 1.04/1.71 ) }.
% 1.04/1.71 { ! Y = X, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X
% 1.04/1.71 ), Z ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z
% 1.04/1.71 ), X ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y
% 1.04/1.71 ), Z ) ) }.
% 1.04/1.71 { ! Y = X, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X
% 1.04/1.71 ), Z ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z
% 1.04/1.71 ), X ) ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ),
% 1.04/1.71 Z ), Y ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.04/1.71 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 1.04/1.71 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X )
% 1.04/1.71 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), Z )
% 1.04/1.71 ) }.
% 1.04/1.71 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.04/1.71 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 1.04/1.71 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X )
% 1.04/1.71 ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y
% 1.04/1.71 ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.04/1.71 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 1.04/1.71 , ! Y = X }.
% 1.04/1.71 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.04/1.71 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 1.04/1.71 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 1.04/1.71 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X )
% 1.04/1.71 ) }.
% 1.04/1.71 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.04/1.71 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 1.04/1.71 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.04/1.71 }.
% 1.04/1.71 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.04/1.71 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 1.04/1.71 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 1.04/1.71 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X )
% 1.04/1.71 ) }.
% 1.04/1.71 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.04/1.71 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 1.04/1.71 , ! Y = X }.
% 1.04/1.71 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.04/1.71 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 1.04/1.71 , ! X = Y }.
% 1.04/1.71 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.04/1.71 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 1.04/1.71 , ! X = Z, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y
% 1.04/1.71 ), Z ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.04/1.71 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 1.04/1.71 , ! X = Z, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ),
% 1.04/1.71 Z ), Y ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.04/1.71 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 1.04/1.71 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 1.04/1.71 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), Z )
% 1.04/1.71 ) }.
% 1.04/1.71 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.04/1.71 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 1.04/1.71 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 1.04/1.71 ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y
% 1.04/1.71 ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.04/1.71 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 1.04/1.71 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 1.04/1.71 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X )
% 1.04/1.71 ) }.
% 1.04/1.71 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.04/1.71 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 1.04/1.71 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 1.04/1.71 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X )
% 1.04/1.71 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), Z )
% 1.04/1.71 ) }.
% 1.04/1.71 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.04/1.71 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 1.04/1.71 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 1.04/1.71 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X )
% 1.04/1.71 ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y
% 1.04/1.71 ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.04/1.71 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 1.04/1.71 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 1.04/1.71 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X )
% 1.04/1.71 ) }.
% 1.04/1.71 { hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ),
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.04/1.71 { hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ),
% 1.04/1.71 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP( hAPP
% 1.04/1.71 ( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ), hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.04/1.71 tc_Nat_Onat ) ), Y ) ) }.
% 1.04/1.71 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP( hAPP(
% 1.04/1.71 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ), hAPP( hAPP(
% 1.04/1.71 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ) ) ), hBOOL( hAPP(
% 1.04/1.71 hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ) }.
% 1.04/1.71 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP( hAPP(
% 1.04/1.71 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ), hAPP( hAPP(
% 1.04/1.71 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ) ) ) }.
% 1.04/1.71 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oorder_Ostrict__mono(
% 1.04/1.71 tc_Nat_Onat, X, hAPP( hAPP( c_COMBS( tc_Nat_Onat, tc_fun( tc_Nat_Onat,
% 1.04/1.71 tc_HOL_Obool ), tc_fun( tc_Nat_Onat, tc_HOL_Obool ) ), hAPP( hAPP(
% 1.04/1.71 c_COMBB( tc_fun( tc_Nat_Onat, tc_fun( tc_HOL_Obool, tc_HOL_Obool ) ),
% 1.04/1.71 tc_fun( tc_fun( tc_Nat_Onat, tc_HOL_Obool ), tc_fun( tc_Nat_Onat,
% 1.04/1.71 tc_HOL_Obool ) ), tc_Nat_Onat ), c_COMBS( tc_Nat_Onat, tc_HOL_Obool,
% 1.04/1.71 tc_HOL_Obool ) ), hAPP( hAPP( c_COMBB( tc_fun( tc_Nat_Onat, tc_HOL_Obool
% 1.04/1.71 ), tc_fun( tc_Nat_Onat, tc_fun( tc_HOL_Obool, tc_HOL_Obool ) ),
% 1.04/1.71 tc_Nat_Onat ), hAPP( c_COMBB( tc_HOL_Obool, tc_fun( tc_HOL_Obool,
% 1.04/1.71 tc_HOL_Obool ), tc_Nat_Onat ), c_fconj ) ), c_Rings_Odvd__class_Odvd(
% 1.04/1.71 tc_Nat_Onat ) ) ) ), hAPP( hAPP( c_COMBB( tc_fun( tc_Nat_Onat,
% 1.04/1.71 tc_HOL_Obool ), tc_fun( tc_Nat_Onat, tc_HOL_Obool ), tc_Nat_Onat ), hAPP
% 1.04/1.71 ( c_COMBB( tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat ), c_fNot ) ), c_COMBC
% 1.04/1.71 ( tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool, c_Rings_Odvd__class_Odvd(
% 1.04/1.71 tc_Nat_Onat ) ) ) ), Y ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.04/1.71 tc_Nat_Onat ), T ), Z ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.04/1.71 tc_Nat_Onat ), Z ), T ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X
% 1.04/1.71 , hAPP( Y, T ) ), hAPP( Y, Z ) ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), hBOOL( hAPP( Y,
% 1.04/1.71 skol17( Z, Y ) ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.04/1.71 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), T ) ), ! hBOOL
% 1.04/1.71 ( hAPP( Y, U ) ), hBOOL( hAPP( Y, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.04/1.71 ( tc_Int_Oint ), U ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.04/1.71 tc_Int_Oint ), T ), X ) ) ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP( Y,
% 1.04/1.71 hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), skol17( X, Y ) )
% 1.04/1.71 , X ) ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint
% 1.04/1.71 , c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Z ) ), ! hBOOL( hAPP( Y,
% 1.04/1.71 T ) ), hBOOL( hAPP( Y, hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.04/1.71 tc_Int_Oint ), T ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.04/1.71 tc_Int_Oint ), Z ), X ) ) ) ) }.
% 1.04/1.71 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oorder_Ostrict__mono(
% 1.04/1.71 tc_Nat_Onat, X, hAPP( hAPP( c_COMBS( tc_Nat_Onat, tc_fun( tc_Nat_Onat,
% 1.04/1.71 tc_HOL_Obool ), tc_fun( tc_Nat_Onat, tc_HOL_Obool ) ), hAPP( hAPP(
% 1.04/1.71 c_COMBB( tc_fun( tc_Nat_Onat, tc_fun( tc_HOL_Obool, tc_HOL_Obool ) ),
% 1.04/1.71 tc_fun( tc_fun( tc_Nat_Onat, tc_HOL_Obool ), tc_fun( tc_Nat_Onat,
% 1.04/1.71 tc_HOL_Obool ) ), tc_Nat_Onat ), c_COMBS( tc_Nat_Onat, tc_HOL_Obool,
% 1.04/1.71 tc_HOL_Obool ) ), hAPP( hAPP( c_COMBB( tc_fun( tc_Nat_Onat, tc_HOL_Obool
% 1.04/1.71 ), tc_fun( tc_Nat_Onat, tc_fun( tc_HOL_Obool, tc_HOL_Obool ) ),
% 1.04/1.71 tc_Nat_Onat ), hAPP( c_COMBB( tc_HOL_Obool, tc_fun( tc_HOL_Obool,
% 1.04/1.71 tc_HOL_Obool ), tc_Nat_Onat ), c_fconj ) ), c_Rings_Odvd__class_Odvd(
% 1.04/1.71 tc_Nat_Onat ) ) ) ), hAPP( hAPP( c_COMBB( tc_fun( tc_Nat_Onat,
% 1.04/1.71 tc_HOL_Obool ), tc_fun( tc_Nat_Onat, tc_HOL_Obool ), tc_Nat_Onat ), hAPP
% 1.04/1.71 ( c_COMBB( tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat ), c_fNot ) ), c_COMBC
% 1.04/1.71 ( tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool, c_Rings_Odvd__class_Odvd(
% 1.04/1.71 tc_Nat_Onat ) ) ) ), Y ), c_Orderings_Oorder_Omono( tc_Nat_Onat, X,
% 1.04/1.71 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ) }.
% 1.04/1.71 { ! class_Orderings_Oorder( X ), hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), skol18( X, Y ) ), skol35( X, Y )
% 1.04/1.71 ) ), c_Orderings_Oorder_Ostrict__mono( tc_Nat_Onat, X, hAPP( hAPP(
% 1.04/1.71 c_COMBS( tc_Nat_Onat, tc_fun( tc_Nat_Onat, tc_HOL_Obool ), tc_fun(
% 1.04/1.71 tc_Nat_Onat, tc_HOL_Obool ) ), hAPP( hAPP( c_COMBB( tc_fun( tc_Nat_Onat,
% 1.04/1.71 tc_fun( tc_HOL_Obool, tc_HOL_Obool ) ), tc_fun( tc_fun( tc_Nat_Onat,
% 1.04/1.71 tc_HOL_Obool ), tc_fun( tc_Nat_Onat, tc_HOL_Obool ) ), tc_Nat_Onat ),
% 1.04/1.71 c_COMBS( tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool ) ), hAPP( hAPP( c_COMBB
% 1.04/1.71 ( tc_fun( tc_Nat_Onat, tc_HOL_Obool ), tc_fun( tc_Nat_Onat, tc_fun(
% 1.04/1.71 tc_HOL_Obool, tc_HOL_Obool ) ), tc_Nat_Onat ), hAPP( c_COMBB(
% 1.04/1.71 tc_HOL_Obool, tc_fun( tc_HOL_Obool, tc_HOL_Obool ), tc_Nat_Onat ),
% 1.04/1.71 c_fconj ) ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat ) ) ) ), hAPP( hAPP(
% 1.04/1.71 c_COMBB( tc_fun( tc_Nat_Onat, tc_HOL_Obool ), tc_fun( tc_Nat_Onat,
% 1.04/1.71 tc_HOL_Obool ), tc_Nat_Onat ), hAPP( c_COMBB( tc_HOL_Obool, tc_HOL_Obool
% 1.04/1.71 , tc_Nat_Onat ), c_fNot ) ), c_COMBC( tc_Nat_Onat, tc_Nat_Onat,
% 1.04/1.71 tc_HOL_Obool, c_Rings_Odvd__class_Odvd( tc_Nat_Onat ) ) ) ), Y ) }.
% 1.04/1.71 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), skol35( X, Y ) ), skol18( X, Y )
% 1.04/1.71 ) ), c_Orderings_Oorder_Ostrict__mono( tc_Nat_Onat, X, hAPP( hAPP(
% 1.04/1.71 c_COMBS( tc_Nat_Onat, tc_fun( tc_Nat_Onat, tc_HOL_Obool ), tc_fun(
% 1.04/1.71 tc_Nat_Onat, tc_HOL_Obool ) ), hAPP( hAPP( c_COMBB( tc_fun( tc_Nat_Onat,
% 1.04/1.71 tc_fun( tc_HOL_Obool, tc_HOL_Obool ) ), tc_fun( tc_fun( tc_Nat_Onat,
% 1.04/1.71 tc_HOL_Obool ), tc_fun( tc_Nat_Onat, tc_HOL_Obool ) ), tc_Nat_Onat ),
% 1.04/1.71 c_COMBS( tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool ) ), hAPP( hAPP( c_COMBB
% 1.04/1.71 ( tc_fun( tc_Nat_Onat, tc_HOL_Obool ), tc_fun( tc_Nat_Onat, tc_fun(
% 1.04/1.71 tc_HOL_Obool, tc_HOL_Obool ) ), tc_Nat_Onat ), hAPP( c_COMBB(
% 1.04/1.71 tc_HOL_Obool, tc_fun( tc_HOL_Obool, tc_HOL_Obool ), tc_Nat_Onat ),
% 1.04/1.71 c_fconj ) ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat ) ) ) ), hAPP( hAPP(
% 1.04/1.71 c_COMBB( tc_fun( tc_Nat_Onat, tc_HOL_Obool ), tc_fun( tc_Nat_Onat,
% 1.04/1.71 tc_HOL_Obool ), tc_Nat_Onat ), hAPP( c_COMBB( tc_HOL_Obool, tc_HOL_Obool
% 1.04/1.71 , tc_Nat_Onat ), c_fNot ) ), c_COMBC( tc_Nat_Onat, tc_Nat_Onat,
% 1.04/1.71 tc_HOL_Obool, c_Rings_Odvd__class_Odvd( tc_Nat_Onat ) ) ) ), Y ) }.
% 1.04/1.71 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless( X, hAPP( Y, skol18( X, Y ) ) ), hAPP( Y,
% 1.04/1.71 skol35( X, Y ) ) ) ), c_Orderings_Oorder_Ostrict__mono( tc_Nat_Onat, X,
% 1.04/1.71 hAPP( hAPP( c_COMBS( tc_Nat_Onat, tc_fun( tc_Nat_Onat, tc_HOL_Obool ),
% 1.04/1.71 tc_fun( tc_Nat_Onat, tc_HOL_Obool ) ), hAPP( hAPP( c_COMBB( tc_fun(
% 1.04/1.71 tc_Nat_Onat, tc_fun( tc_HOL_Obool, tc_HOL_Obool ) ), tc_fun( tc_fun(
% 1.04/1.71 tc_Nat_Onat, tc_HOL_Obool ), tc_fun( tc_Nat_Onat, tc_HOL_Obool ) ),
% 1.04/1.71 tc_Nat_Onat ), c_COMBS( tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool ) ), hAPP
% 1.04/1.71 ( hAPP( c_COMBB( tc_fun( tc_Nat_Onat, tc_HOL_Obool ), tc_fun( tc_Nat_Onat
% 1.04/1.71 , tc_fun( tc_HOL_Obool, tc_HOL_Obool ) ), tc_Nat_Onat ), hAPP( c_COMBB(
% 1.04/1.71 tc_HOL_Obool, tc_fun( tc_HOL_Obool, tc_HOL_Obool ), tc_Nat_Onat ),
% 1.04/1.71 c_fconj ) ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat ) ) ) ), hAPP( hAPP(
% 1.04/1.71 c_COMBB( tc_fun( tc_Nat_Onat, tc_HOL_Obool ), tc_fun( tc_Nat_Onat,
% 1.04/1.71 tc_HOL_Obool ), tc_Nat_Onat ), hAPP( c_COMBB( tc_HOL_Obool, tc_HOL_Obool
% 1.04/1.71 , tc_Nat_Onat ), c_fNot ) ), c_COMBC( tc_Nat_Onat, tc_Nat_Onat,
% 1.04/1.71 tc_HOL_Obool, c_Rings_Odvd__class_Odvd( tc_Nat_Onat ) ) ) ), Y ) }.
% 1.04/1.71 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oorder_Omono( tc_Nat_Onat, X
% 1.04/1.71 , c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), ! hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), T ), Z ) ), hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, T ) ), hAPP( Y, Z ) ) ) }
% 1.04/1.71 .
% 1.04/1.71 { ! class_Groups_Omonoid__mult( X ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.04/1.71 tc_Nat_Onat ) ), Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.04/1.71 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ),
% 1.04/1.71 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ), Z ) = hAPP( hAPP(
% 1.04/1.71 c_Power_Opower__class_Opower( X ), Z ), Y ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ),
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), hAPP( c_Int_Onat, hAPP(
% 1.04/1.71 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) = hAPP(
% 1.04/1.71 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( c_Int_Onat,
% 1.04/1.71 hAPP( c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), X ) ) ), hAPP(
% 1.04/1.71 c_Int_Onat, hAPP( c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), Y ) ) )
% 1.04/1.71 }.
% 1.04/1.71 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), hAPP(
% 1.04/1.71 hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ) ) ), ! hBOOL
% 1.04/1.71 ( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X ) ), !
% 1.04/1.71 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), Y ) ),
% 1.04/1.71 hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y ) ) }
% 1.04/1.71 .
% 1.04/1.71 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), hAPP(
% 1.04/1.71 hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ) ) ), ! hBOOL
% 1.04/1.71 ( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y ) ), !
% 1.04/1.71 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), Y ) ),
% 1.04/1.71 hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X ) ) }
% 1.04/1.71 .
% 1.04/1.71 { ! class_Rings_Ocomm__ring__1( X ), ! hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( X ), Z ), T ) ), hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( X ), Y ), T ) ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.04/1.71 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), Z )
% 1.04/1.71 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), hAPP
% 1.04/1.71 ( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Z ) ) ) }.
% 1.04/1.71 { hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), hAPP(
% 1.04/1.71 c_Nat_OSuc, X ) ) = hAPP( hAPP( c_Groups_Ominus__class_Ominus(
% 1.04/1.71 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ),
% 1.04/1.71 Y ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ), X ) }.
% 1.04/1.71 { hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP(
% 1.04/1.71 c_Nat_OSuc, X ) ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 1.04/1.71 { ! class_Groups_Ominus( X ), hAPP( hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( tc_fun( U, X ) ), T ), Z ), Y ) = hAPP(
% 1.04/1.71 hAPP( c_Groups_Ominus__class_Ominus( X ), hAPP( T, Y ) ), hAPP( Z, Y ) )
% 1.04/1.71 }.
% 1.04/1.71 { ! class_Groups_Ominus( X ), hAPP( hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( tc_fun( U, X ) ), T ), Z ), Y ) = hAPP(
% 1.04/1.71 hAPP( c_Groups_Ominus__class_Ominus( X ), hAPP( T, Y ) ), hAPP( Z, Y ) )
% 1.04/1.71 }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), !
% 1.04/1.71 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), Z ) ),
% 1.04/1.71 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ), X ) ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ), Y ) ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.04/1.71 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), Z ) ), X ) ) }.
% 1.04/1.71 { ! class_Groups_Oordered__ab__group__add( X ), ! hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( X ), U ), T ) = hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( X ), Z ), Y ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless( X, U ), T ) ), hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 1.04/1.71 { ! class_Groups_Oordered__ab__group__add( X ), ! hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( X ), U ), T ) = hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( X ), Z ), Y ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless( X, U ), T ) ) }.
% 1.04/1.71 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( X ), Z ), Y ) ),
% 1.04/1.71 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.04/1.71 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( X ), Z ), Y ) ),
% 1.04/1.71 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 1.04/1.71 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( X ), Z ), Y ) ),
% 1.04/1.71 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.04/1.71 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( X ), Z ), Y ) ),
% 1.04/1.71 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 1.04/1.71 { ! class_Groups_Ogroup__add( X ), ! hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( X ), Z ), Y ) =
% 1.04/1.71 c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 1.04/1.71 { ! class_Groups_Ogroup__add( X ), ! Z = Y, hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( X ), Z ), Y ) =
% 1.04/1.71 c_Groups_Ozero__class_Ozero( X ) }.
% 1.04/1.71 { ! class_Groups_Oab__group__add( X ), ! Z = Y, hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( X ), Z ), Y ) =
% 1.04/1.71 c_Groups_Ozero__class_Ozero( X ) }.
% 1.04/1.71 { ! class_Groups_Oab__group__add( X ), ! hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( X ), Z ), Y ) =
% 1.04/1.71 c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 1.04/1.71 { ! class_Groups_Ogroup__add( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( X ), Y ), Y ) =
% 1.04/1.71 c_Groups_Ozero__class_Ozero( X ) }.
% 1.04/1.71 { ! class_Groups_Ogroup__add( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.04/1.71 ) = Y }.
% 1.04/1.71 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.04/1.71 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.04/1.71 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.04/1.71 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.04/1.71 { ! class_Groups_Ogroup__add( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ), Y ) = Z }.
% 1.04/1.71 { ! class_Groups_Ogroup__add( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.04/1.71 ( X ), hAPP( hAPP( c_Groups_Ominus__class_Ominus( X ), Z ), Y ) ), Y ) =
% 1.04/1.71 Z }.
% 1.04/1.71 { hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ),
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) =
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.04/1.71 { hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ),
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = X }.
% 1.04/1.71 { hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), X ) =
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.04/1.71 { ! hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ) =
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) =
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 1.04/1.71 { hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP(
% 1.04/1.71 c_Nat_OSuc, Y ) ), hAPP( c_Nat_OSuc, X ) ) = hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ) }.
% 1.04/1.71 { hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( c_Nat_OSuc, Z ) ), Y
% 1.04/1.71 ) ), hAPP( c_Nat_OSuc, X ) ) = hAPP( hAPP( c_Groups_Ominus__class_Ominus
% 1.04/1.71 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat )
% 1.04/1.71 , Z ), Y ) ), X ) }.
% 1.04/1.71 { hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ), X ) = Y }.
% 1.04/1.71 { hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ), Y ) = X }.
% 1.04/1.71 { hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 1.04/1.71 hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) }.
% 1.04/1.71 { hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) = hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ) }.
% 1.04/1.71 { hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Y ) ) = hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ), X ) }.
% 1.04/1.71 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP
% 1.04/1.71 ( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.04/1.71 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 1.04/1.71 hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.04/1.71 { ! class_Groups_Oab__group__add( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 1.04/1.71 c_Polynomial_OpCons( X ), U ), T ) ), hAPP( hAPP( c_Polynomial_OpCons( X
% 1.04/1.71 ), Z ), Y ) ) = hAPP( hAPP( c_Polynomial_OpCons( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( X ), U ), Z ) ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ) ), T ), Y ) ) }.
% 1.04/1.71 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X, hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ) ), T ), Z ) ), Y
% 1.04/1.71 ) = hAPP( hAPP( c_Groups_Ominus__class_Ominus( X ), hAPP(
% 1.04/1.71 c_Polynomial_Opoly( X, T ), Y ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 1.04/1.71 ) }.
% 1.04/1.71 { hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 1.04/1.71 hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ), X ) ), Y ) }.
% 1.04/1.71 { ! class_Groups_Oab__group__add( X ), ! hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( X ), U ), T ) = hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( X ), Z ), Y ), ! U = T, Z = Y }.
% 1.04/1.71 { ! class_Groups_Oab__group__add( X ), ! hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( X ), U ), T ) = hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( X ), Z ), Y ), ! Z = Y, U = T }.
% 1.04/1.71 { ! class_Groups_Oab__group__add( X ), hAPP( c_Polynomial_Ocoeff( X, hAPP(
% 1.04/1.71 hAPP( c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ) ), T ), Z )
% 1.04/1.71 ), Y ) = hAPP( hAPP( c_Groups_Ominus__class_Ominus( X ), hAPP(
% 1.04/1.71 c_Polynomial_Ocoeff( X, T ), Y ) ), hAPP( c_Polynomial_Ocoeff( X, Z ), Y
% 1.04/1.71 ) ) }.
% 1.04/1.71 { ! class_Rings_Ocomm__ring( X ), hAPP( hAPP( c_Polynomial_Osmult( X ),
% 1.04/1.71 hAPP( hAPP( c_Groups_Ominus__class_Ominus( X ), T ), Z ) ), Y ) = hAPP(
% 1.04/1.71 hAPP( c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ) ), hAPP(
% 1.04/1.71 hAPP( c_Polynomial_Osmult( X ), T ), Y ) ), hAPP( hAPP(
% 1.04/1.71 c_Polynomial_Osmult( X ), Z ), Y ) ) }.
% 1.04/1.71 { ! class_Groups_Oab__group__add( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ) ),
% 1.04/1.71 c_Polynomial_Omonom( X, T, Z ) ), c_Polynomial_Omonom( X, Y, Z ) ) =
% 1.04/1.71 c_Polynomial_Omonom( X, hAPP( hAPP( c_Groups_Ominus__class_Ominus( X ), T
% 1.04/1.71 ), Y ), Z ) }.
% 1.04/1.71 { ! class_Groups_Oab__group__add( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ) ), Z ), Y ) =
% 1.04/1.71 c_Polynomial_OAbs__poly( X, hAPP( hAPP( c_COMBS( tc_Nat_Onat, X, X ),
% 1.04/1.71 hAPP( hAPP( c_COMBB( X, tc_fun( X, X ), tc_Nat_Onat ),
% 1.04/1.71 c_Groups_Ominus__class_Ominus( X ) ), c_Polynomial_Ocoeff( X, Z ) ) ),
% 1.04/1.71 c_Polynomial_Ocoeff( X, Y ) ) ) }.
% 1.04/1.71 { ! class_Groups_Oordered__ab__group__add( X ), ! hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( X ), U ), T ) = hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( X ), Z ), Y ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless__eq( X, U ), T ) ), hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 1.04/1.71 { ! class_Groups_Oordered__ab__group__add( X ), ! hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( X ), U ), T ) = hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( X ), Z ), Y ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless__eq( X, U ), T ) ) }.
% 1.04/1.71 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ) ), Y ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.04/1.71 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 1.04/1.71 ( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ), X ) ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ), Y ) ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.04/1.71 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 1.04/1.71 ( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), Z ) ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Z ) ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.04/1.71 , hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), hAPP(
% 1.04/1.71 hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ) = Y }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.04/1.71 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), Z )
% 1.04/1.71 ), ! hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y )
% 1.04/1.71 = hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ), Y ), X =
% 1.04/1.71 Z }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.04/1.71 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), Z )
% 1.04/1.71 ), ! X = Z, hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X
% 1.04/1.71 ), Y ) = hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ),
% 1.04/1.71 Y ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.04/1.71 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), Z )
% 1.04/1.71 ), hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP
% 1.04/1.71 ( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Z ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.04/1.71 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), Z )
% 1.04/1.71 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 1.04/1.71 hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ), hAPP(
% 1.04/1.71 hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ), Y ) ) ), hBOOL(
% 1.04/1.71 hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), Z ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.04/1.71 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), Z )
% 1.04/1.71 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), Z
% 1.04/1.71 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 1.04/1.71 hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ), hAPP(
% 1.04/1.71 hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ), Y ) ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.04/1.71 , hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ), hAPP(
% 1.04/1.71 hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ) = hAPP(
% 1.04/1.71 hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), X ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 1.04/1.71 ( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ), Y ) ), X ) ), hBOOL
% 1.04/1.71 ( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Y ) ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), hAPP
% 1.04/1.71 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Y ) ) ), hBOOL(
% 1.04/1.71 hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ), Y ) ), X ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.04/1.71 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), hAPP
% 1.04/1.71 ( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ), Y ) ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.04/1.71 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), hAPP( hAPP
% 1.04/1.71 ( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ) = X }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.04/1.71 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), hAPP( hAPP
% 1.04/1.71 ( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ) = hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ), Y ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.04/1.71 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ),
% 1.04/1.71 hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ) ),
% 1.04/1.71 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), X ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.04/1.71 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 1.04/1.71 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), X ) ),
% 1.04/1.71 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), hAPP(
% 1.04/1.71 hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.04/1.71 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ), Y ) = X }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.04/1.71 , ! hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) =
% 1.04/1.71 Z, X = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) }
% 1.04/1.71 .
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.04/1.71 , ! X = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y )
% 1.04/1.71 , hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) = Z
% 1.04/1.71 }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.04/1.71 , hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ), Y ) = hAPP( hAPP
% 1.04/1.71 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.04/1.71 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ), Z ) = hAPP(
% 1.04/1.71 hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ), Y ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.04/1.71 , hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ), Y ) = hAPP( hAPP
% 1.04/1.71 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ), Z ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), !
% 1.04/1.71 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), Y ) ),
% 1.04/1.71 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), Z ) ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Z ) ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.04/1.71 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), Z )
% 1.04/1.71 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP
% 1.04/1.71 ( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ), Y ) ) ), hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), Z ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.04/1.71 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), Z )
% 1.04/1.71 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), Z ) )
% 1.04/1.71 , hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ), Y ) ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z ), hAPP(
% 1.04/1.71 hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ) ) ), hBOOL(
% 1.04/1.71 hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ), Y ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ), Y ) ), hBOOL(
% 1.04/1.71 hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ) ) ) }.
% 1.04/1.71 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), hAPP
% 1.04/1.71 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ) ) = Y }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.04/1.71 , hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP(
% 1.04/1.71 c_Nat_OSuc, X ) ), Y ) = hAPP( c_Nat_OSuc, hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ) }.
% 1.04/1.71 { ! hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ) =
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.04/1.71 , hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ) =
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.04/1.71 , hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ) =
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.04/1.71 { hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), hAPP( hAPP
% 1.04/1.71 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) =
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.04/1.71 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ) ), hAPP(
% 1.04/1.71 c_Nat_OSuc, Y ) ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ) ) ), hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), Y ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), Y ) ),
% 1.04/1.71 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ) ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.04/1.71 tc_Nat_Onat ) ), Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.04/1.71 tc_Nat_Onat, hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y
% 1.04/1.71 ), X ) ), Y ) ) }.
% 1.04/1.71 { c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( c_Int_Onat,
% 1.04/1.71 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), ! hAPP( c_Int_Onat,
% 1.04/1.71 X ) = hAPP( c_Int_Onat, Y ), X = Y }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), ! X = Y, hAPP(
% 1.04/1.71 c_Int_Onat, X ) = hAPP( c_Int_Onat, Y ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), ! hAPP( c_Int_Onat,
% 1.04/1.71 X ) = hAPP( c_Int_Onat, Y ), X = Y }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), ! X = Y, hAPP(
% 1.04/1.71 c_Int_Onat, X ) = hAPP( c_Int_Onat, Y ) }.
% 1.04/1.71 { ! hBOOL( hAPP( X, skol19( X ) ) ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), hBOOL( hAPP( X, hAPP
% 1.04/1.71 ( c_Int_Onat, Y ) ) ) }.
% 1.04/1.71 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), skol36( Y ) ) ), hBOOL(
% 1.04/1.71 hAPP( X, Z ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( X, hAPP( c_Int_Onat, skol36( X ) ) ) ), hBOOL( hAPP( X, Y
% 1.04/1.71 ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.04/1.71 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), skol20( Z ) )
% 1.04/1.71 ) }.
% 1.04/1.71 { ! hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X, hAPP( c_Int_Onat, skol20( X ) )
% 1.04/1.71 ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), ! hBOOL( hAPP( X,
% 1.04/1.71 hAPP( c_Int_Onat, Y ) ) ), hBOOL( hAPP( X, skol37( X ) ) ) }.
% 1.04/1.71 { ! class_Rings_Ocomm__ring__1( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( X ), Z ), Y ) = hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( X ), Z ), hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) }.
% 1.04/1.71 { ! class_Groups_Ogroup__add( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( X ), Z ), hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) = hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) }.
% 1.04/1.71 { ! class_Groups_Oab__group__add( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( X ), Z ), Y ) = hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( X ), Z ), hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) }.
% 1.04/1.71 { ! class_Groups_Ogroup__add( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( X ), Z ), Y ) = hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( X ), Z ), hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) }.
% 1.04/1.71 { ! class_Groups_Ogroup__add( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.04/1.71 ) = hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ) }.
% 1.04/1.71 { hAPP( c_Int_Onat, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) =
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.04/1.71 { c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = hAPP( c_Int_Onat,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.04/1.71 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Ominus__class_Ominus( X )
% 1.04/1.71 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP
% 1.04/1.71 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), U ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( X ), T ), Y ) ) ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( X ), U ), Z ) ), Y ) ) }.
% 1.04/1.71 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.04/1.71 ( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( X ), U ), Z ) ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( X ), T ), Y ) ) ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( X ), U ), Z ) ), Y ) ) ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( X ), T ), Y ) ) ) }.
% 1.04/1.71 { ! class_Rings_Oring( X ), ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( X )
% 1.04/1.71 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) = hAPP
% 1.04/1.71 ( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ), T = hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( X ), Z ), W ) ), U ) ), Y ) }.
% 1.04/1.71 { ! class_Rings_Oring( X ), ! T = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.04/1.71 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( X ), Z ), W ) ), U ) ), Y ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) = hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) }.
% 1.04/1.71 { ! class_Rings_Oring( X ), ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( X )
% 1.04/1.71 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) = hAPP
% 1.04/1.71 ( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( X ), W ), Z ) ), U ) ), T ) = Y }.
% 1.04/1.71 { ! class_Rings_Oring( X ), ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( X )
% 1.04/1.71 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( X ), W ), Z ) ), U ) ), T ) = Y, hAPP(
% 1.04/1.71 hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) = hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) }.
% 1.04/1.71 { ! class_Groups_Oab__group__add( X ), hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( X ), Y ), Z ) }.
% 1.04/1.71 { hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), hAPP(
% 1.04/1.71 c_Nat_OSuc, X ) ) = hAPP( c_Nat_Onat_Onat__case( tc_Nat_Onat,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_COMBI( tc_Nat_Onat ) ),
% 1.04/1.71 hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ) ) }.
% 1.04/1.71 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) ) ), hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( X ), W ), Z ) ), U ) ), T ) ), Y ) ) }.
% 1.04/1.71 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( X ), W ), Z ) ), U ) ), T ) ), Y ) ),
% 1.04/1.71 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) ) ) }.
% 1.04/1.71 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) ) ), hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless__eq( X, T ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( X ), Z ), W ) ), U ) ), Y ) ) ) }.
% 1.04/1.71 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless__eq( X, T ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( X ), Z ), W ) ), U ) ), Y ) ) ), hBOOL(
% 1.04/1.71 hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) ) ) }.
% 1.04/1.71 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.04/1.71 ( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) )
% 1.04/1.71 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) ) ), hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.04/1.71 ( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( X ), W ), Z ) ), U ) ), T ) ), Y ) ) }.
% 1.04/1.71 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.04/1.71 ( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( X ), W ), Z ) ), U ) ), T ) ), Y ) ),
% 1.04/1.71 hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) ) ) }.
% 1.04/1.71 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.04/1.71 ( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) )
% 1.04/1.71 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) ) ), hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless( X, T ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( X ), Z ), W ) ), U ) ), Y ) ) ) }.
% 1.04/1.71 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless( X, T ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( X ), Z ), W ) ), U ) ), Y ) ) ), hBOOL(
% 1.04/1.71 hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) ) ) }.
% 1.04/1.71 { ! class_Rings_Oring__1( X ), hAPP( hAPP( c_Groups_Ominus__class_Ominus( X
% 1.04/1.71 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.04/1.71 c_Groups_Oone__class_Oone( X ) ) = hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( X ), Y ), c_Groups_Oone__class_Oone( X ) ) )
% 1.04/1.71 , hAPP( hAPP( c_Groups_Ominus__class_Ominus( X ), Y ),
% 1.04/1.71 c_Groups_Oone__class_Oone( X ) ) ) }.
% 1.04/1.71 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), ! hBOOL( hAPP(
% 1.04/1.71 hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( X ), U ), T ) ) ), hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( X ), U ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), W ), Y ) ) ), T ) ) ) }.
% 1.04/1.71 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), ! hBOOL( hAPP(
% 1.04/1.71 hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( X ), U ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), W ), Y ) ) ), T ) ) ), hBOOL( hAPP(
% 1.04/1.71 hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( X ), U ), T ) ) ) }.
% 1.04/1.71 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), ! hBOOL( hAPP(
% 1.04/1.71 hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( X ), U ), T ) ) ), hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( X ), U ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), W ), Y ) ) ), T ) ) ) }.
% 1.04/1.71 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), ! hBOOL( hAPP(
% 1.04/1.71 hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( X ), U ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), W ), Y ) ) ), T ) ) ), hBOOL( hAPP(
% 1.04/1.71 hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( X ), U ), T ) ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ),
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), hAPP( c_Int_Onat, X ) =
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.04/1.71 { ! hAPP( c_Int_Onat, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.04/1.71 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ),
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ),
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), hAPP( c_Int_Onat, X ) =
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.04/1.71 { hAPP( c_Int_Onat, c_Groups_Oone__class_Oone( tc_Int_Oint ) ) = hAPP(
% 1.04/1.71 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Int_Onat, Y ) ), hAPP
% 1.04/1.71 ( c_Int_Onat, X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.04/1.71 tc_Int_Oint, Y ), X ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ), hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Int_Onat, Y ) ), hAPP
% 1.04/1.71 ( c_Int_Onat, X ) ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 1.04/1.71 c_Int_Onat, Y ) ), hAPP( c_Int_Onat, X ) ) ), hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.04/1.71 tc_Int_Oint ) ), X ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 1.04/1.71 c_Int_Onat, Y ) ), hAPP( c_Int_Onat, X ) ) ), hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ), hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Int_Onat, Y ) ), hAPP
% 1.04/1.71 ( c_Int_Onat, X ) ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( c_Int_Onat, X ) ),
% 1.04/1.71 hAPP( c_Int_Onat, Y ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 1.04/1.71 ( tc_Int_Oint, X ), Y ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ), Y ) ), hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( c_Int_Onat, X ) ),
% 1.04/1.71 hAPP( c_Int_Onat, Y ) ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), hAPP( c_Nat_OSuc, Y )
% 1.04/1.71 ) ), X ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), hAPP( c_Nat_OSuc,
% 1.04/1.71 hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), hAPP(
% 1.04/1.71 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = X }.
% 1.04/1.71 { ! hBOOL( hAPP( Z, hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat
% 1.04/1.71 ), Y ), X ) ) ), alpha12( X, Y, Z ) }.
% 1.04/1.71 { ! hBOOL( hAPP( Z, hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat
% 1.04/1.71 ), Y ), X ) ) ), alpha25( X, Y, Z ) }.
% 1.04/1.71 { ! alpha12( X, Y, Z ), ! alpha25( X, Y, Z ), hBOOL( hAPP( Z, hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ) ) ) }.
% 1.04/1.71 { ! alpha25( X, Y, Z ), ! Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.04/1.71 tc_Nat_Onat ), X ), T ), hBOOL( hAPP( Z, T ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( Z, skol21( T, U, Z ) ) ), alpha25( X, Y, Z ) }.
% 1.04/1.71 { Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), skol21(
% 1.04/1.71 X, Y, Z ) ), alpha25( X, Y, Z ) }.
% 1.04/1.71 { ! alpha12( X, Y, Z ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.04/1.71 tc_Nat_Onat, Y ), X ) ), hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero(
% 1.04/1.71 tc_Nat_Onat ) ) ) }.
% 1.04/1.71 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.04/1.71 alpha12( X, Y, Z ) }.
% 1.04/1.71 { ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha12
% 1.04/1.71 ( X, Y, Z ) }.
% 1.04/1.71 { ! hBOOL( hAPP( Z, hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat
% 1.04/1.71 ), Y ), X ) ) ), ! alpha13( X, Y, Z ) }.
% 1.04/1.71 { ! hBOOL( hAPP( Z, hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat
% 1.04/1.71 ), Y ), X ) ) ), ! alpha26( X, Y, Z ) }.
% 1.04/1.71 { alpha13( X, Y, Z ), alpha26( X, Y, Z ), hBOOL( hAPP( Z, hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ) ) ) }.
% 1.04/1.71 { ! alpha26( X, Y, Z ), ! hBOOL( hAPP( Z, skol22( T, U, Z ) ) ) }.
% 1.04/1.71 { ! alpha26( X, Y, Z ), Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.04/1.71 tc_Nat_Onat ), X ), skol22( X, Y, Z ) ) }.
% 1.04/1.71 { ! Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), T ),
% 1.04/1.71 hBOOL( hAPP( Z, T ) ), alpha26( X, Y, Z ) }.
% 1.04/1.71 { ! alpha13( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.04/1.71 tc_Nat_Onat, Y ), X ) ) }.
% 1.04/1.71 { ! alpha13( X, Y, Z ), ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero(
% 1.04/1.71 tc_Nat_Onat ) ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.04/1.71 hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha13(
% 1.04/1.71 X, Y, Z ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.04/1.71 , hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP(
% 1.04/1.71 c_Nat_OSuc, hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X )
% 1.04/1.71 , Y ) ) ), Z ) = hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat )
% 1.04/1.71 , hAPP( c_Nat_OSuc, X ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.04/1.71 tc_Nat_Onat ), Y ), Z ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.04/1.71 , hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ), hAPP(
% 1.04/1.71 c_Nat_OSuc, hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X )
% 1.04/1.71 , Y ) ) ) = hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ),
% 1.04/1.71 hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), hAPP
% 1.04/1.71 ( c_Nat_OSuc, X ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.04/1.71 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 1.04/1.71 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), T ) ), hAPP(
% 1.04/1.71 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), Z ) ) ), hBOOL
% 1.04/1.71 ( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ), U ) ), T ) ), Z
% 1.04/1.71 ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.04/1.71 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 1.04/1.71 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ), U ) ), T ) ), Z
% 1.04/1.71 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 1.04/1.71 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), T ) ), hAPP(
% 1.04/1.71 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), Z ) ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.04/1.71 , hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), T ) ), hAPP(
% 1.04/1.71 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), Z ) ) = hAPP(
% 1.04/1.71 hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ), U ) ), T ) ), Z
% 1.04/1.71 ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.04/1.71 , ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), T ) = hAPP(
% 1.04/1.71 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), Z ), hAPP( hAPP
% 1.04/1.71 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ), U ) ), T ) = Z
% 1.04/1.71 }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.04/1.71 , ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ), U ) ), T ) = Z
% 1.04/1.71 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), T ) = hAPP(
% 1.04/1.71 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), Z ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.04/1.71 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 1.04/1.71 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), T ) ), hAPP(
% 1.04/1.71 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), Z ) ) ), hBOOL
% 1.04/1.71 ( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ), U ) ), Z ) ) )
% 1.04/1.71 }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.04/1.71 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T ),
% 1.04/1.71 hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ), U ) ), Z ) ) )
% 1.04/1.71 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 1.04/1.71 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), T ) ), hAPP(
% 1.04/1.71 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), Z ) ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.04/1.71 , hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), T ) ), hAPP(
% 1.04/1.71 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), Z ) ) = hAPP(
% 1.04/1.71 hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), T ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ), U ) ), Z ) ) }
% 1.04/1.71 .
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.04/1.71 , ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), T ) = hAPP(
% 1.04/1.71 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), Z ), T = hAPP(
% 1.04/1.71 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ), U ) ), Z ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.04/1.71 , ! T = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP(
% 1.04/1.71 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ), U ) ), Z ),
% 1.04/1.71 hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), T ) = hAPP(
% 1.04/1.71 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), Z ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( c_Int_Onat, X ) ) ),
% 1.04/1.71 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.04/1.71 tc_Nat_Onat ) ), hAPP( c_Int_Onat, X ) ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Int_Onat, X ) ), hAPP
% 1.04/1.71 ( c_Int_Onat, Y ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.04/1.71 tc_Int_Oint, X ), Y ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless( tc_Int_Oint, X ), Y ) ), hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Int_Onat, X ) ), hAPP
% 1.04/1.71 ( c_Int_Onat, Y ) ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Int_Onat, X ) ), hAPP
% 1.04/1.71 ( c_Int_Onat, Y ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.04/1.71 tc_Int_Oint, X ), Y ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless( tc_Int_Oint, X ), Y ) ), hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Int_Onat, X ) ), hAPP
% 1.04/1.71 ( c_Int_Onat, Y ) ) ) }.
% 1.04/1.71 { alpha45( X, Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.04/1.71 tc_Nat_Onat, hAPP( c_Int_Onat, Y ) ), hAPP( c_Int_Onat, X ) ) ), hBOOL(
% 1.04/1.71 hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) ) }.
% 1.04/1.71 { alpha45( X, Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.04/1.71 tc_Int_Oint, Y ), X ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.04/1.71 tc_Nat_Onat, hAPP( c_Int_Onat, Y ) ), hAPP( c_Int_Onat, X ) ) ) }.
% 1.04/1.71 { ! alpha45( X, Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.04/1.71 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ) }.
% 1.04/1.71 { ! alpha45( X, Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.04/1.71 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ) }.
% 1.04/1.71 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), alpha45( X, Y ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( c_Int_Onat, X ) ), hAPP
% 1.04/1.71 ( c_Int_Onat, Y ) ) = hAPP( c_Int_Onat, hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ), Y ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), hAPP( c_Int_Onat,
% 1.04/1.71 hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ), Y ) ) = hAPP
% 1.04/1.71 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( c_Int_Onat, X )
% 1.04/1.71 ), hAPP( c_Int_Onat, Y ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( c_Int_Onat, X ) ),
% 1.04/1.71 hAPP( c_Int_Onat, Y ) ) = hAPP( c_Int_Onat, hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), hAPP( c_Int_Onat,
% 1.04/1.71 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) =
% 1.04/1.71 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP(
% 1.04/1.71 c_Int_Onat, X ) ), hAPP( c_Int_Onat, Y ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), ! hBOOL( hAPP( hAPP
% 1.04/1.71 ( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( c_Int_Onat, X ) ), hAPP
% 1.04/1.71 ( c_Int_Onat, Y ) ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.04/1.71 tc_Int_Oint ), X ), Y ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), ! hBOOL( hAPP( hAPP
% 1.04/1.71 ( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), X ), Y ) ), hBOOL( hAPP( hAPP
% 1.04/1.71 ( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( c_Int_Onat, X ) ), hAPP
% 1.04/1.71 ( c_Int_Onat, Y ) ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), X = hAPP( c_Nat_OSuc
% 1.04/1.71 , hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ),
% 1.04/1.71 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), hAPP( c_Nat_OSuc,
% 1.04/1.71 hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ),
% 1.04/1.71 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) = X }.
% 1.04/1.71 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) = X }.
% 1.04/1.71 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) = hAPP( c_Nat_OSuc,
% 1.04/1.71 hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ),
% 1.04/1.71 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ), X ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.04/1.71 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), T ) ), hAPP(
% 1.04/1.71 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), Z ) ) ), hBOOL
% 1.04/1.71 ( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ), U ) ), T ) ), Z
% 1.04/1.71 ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.04/1.71 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ), U ) ), T ) ), Z
% 1.04/1.71 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP
% 1.04/1.71 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), T ) ), hAPP(
% 1.04/1.71 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), Z ) ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.04/1.71 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), T ) ), hAPP(
% 1.04/1.71 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), Z ) ) ), hBOOL
% 1.04/1.71 ( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, T ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ), U ) ), Z ) ) )
% 1.04/1.71 }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.04/1.71 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, T ), hAPP(
% 1.04/1.71 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ), U ) ), Z ) ) )
% 1.04/1.71 , hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), T ) ), hAPP(
% 1.04/1.71 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), Z ) ) ) }.
% 1.04/1.71 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.04/1.71 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ),
% 1.04/1.71 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ), X ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), hAPP( hAPP(
% 1.04/1.71 c_Power_Opower__class_Opower( tc_Nat_Onat ), hAPP( c_Int_Onat, X ) ), Y )
% 1.04/1.71 = hAPP( c_Int_Onat, hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.04/1.71 tc_Int_Oint ), X ), Y ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), hAPP( c_Int_Onat,
% 1.04/1.71 hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) =
% 1.04/1.71 hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), hAPP( c_Int_Onat
% 1.04/1.71 , X ) ), Y ) }.
% 1.04/1.71 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) =
% 1.04/1.71 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.04/1.71 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) = hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 1.04/1.71 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ),
% 1.04/1.71 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 1.04/1.71 { ! class_Rings_Ocomm__ring__1( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( X ), hAPP( hAPP(
% 1.04/1.71 c_Power_Opower__class_Opower( X ), Z ), hAPP( c_Nat_OSuc, hAPP(
% 1.04/1.71 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) ), hAPP(
% 1.04/1.71 hAPP( c_Power_Opower__class_Opower( X ), Y ), hAPP( c_Nat_OSuc, hAPP(
% 1.04/1.71 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) ) = hAPP(
% 1.04/1.71 hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( X ), Z ), Y ) ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 1.04/1.71 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), hAPP(
% 1.04/1.71 c_Int_Onat, X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.04/1.71 tc_Int_Oint, c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.04/1.71 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) ), hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Nat_OSuc,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), hAPP( c_Int_Onat, X ) ) )
% 1.04/1.71 }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), hAPP( c_Nat_OSuc,
% 1.04/1.71 hAPP( c_Int_Onat, X ) ) = hAPP( c_Int_Onat, hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 1.04/1.71 tc_Int_Oint ) ), X ) ) }.
% 1.04/1.71 { ! class_Power_Opower( X ), ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 1.04/1.71 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) =
% 1.04/1.71 c_Groups_Oone__class_Oone( X ) }.
% 1.04/1.71 { ! class_Power_Opower( X ), Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.04/1.71 , hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) = hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.04/1.71 c_Power_Opower__class_Opower( X ), Y ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ),
% 1.04/1.71 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 1.04/1.71 { ! class_Groups_Omonoid__mult( X ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), Y ) ), hAPP( hAPP(
% 1.04/1.71 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( c_Nat_OSuc, Y ) ), Z
% 1.04/1.71 ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.04/1.71 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), Z ) ) ), T ) }.
% 1.04/1.71 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), hAPP(
% 1.04/1.71 hAPP( c_Groups_Ominus__class_Ominus( tc_Int_Oint ), Y ), X ) ) ), ! hBOOL
% 1.04/1.71 ( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), X ) ), hBOOL
% 1.04/1.71 ( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ) }.
% 1.04/1.71 { hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Int_Oint ), Y ), X ) = hAPP
% 1.04/1.71 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), X ) ) }.
% 1.04/1.71 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), X ) ) = hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( tc_Int_Oint ), Y ), X ) }.
% 1.04/1.71 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless( tc_Polynomial_Opoly( X ), Z ), Y ) ),
% 1.04/1.71 c_Polynomial_Opos__poly( X, hAPP( hAPP( c_Groups_Ominus__class_Ominus(
% 1.04/1.71 tc_Polynomial_Opoly( X ) ), Y ), Z ) ) }.
% 1.04/1.71 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, hAPP
% 1.04/1.71 ( hAPP( c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ) ), Y ), Z
% 1.04/1.71 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Polynomial_Opoly( X
% 1.04/1.71 ), Z ), Y ) ) }.
% 1.04/1.71 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP
% 1.04/1.71 ( c_Groups_Ominus__class_Ominus( tc_Int_Oint ), Y ), X ) ) = hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( tc_Int_Oint ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 1.04/1.71 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP(
% 1.04/1.71 hAPP( c_Groups_Ominus__class_Ominus( tc_Int_Oint ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.04/1.71 { ! class_Groups_Oab__group__add( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ) ), Y ),
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) = Y }.
% 1.04/1.71 { ! class_Rings_Ocomm__ring( X ), hAPP( hAPP( c_Polynomial_Osmult( X ), T )
% 1.04/1.71 , hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ) ),
% 1.04/1.71 Z ), Y ) ) = hAPP( hAPP( c_Groups_Ominus__class_Ominus(
% 1.04/1.71 tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Polynomial_Osmult( X ), T ), Z
% 1.04/1.71 ) ), hAPP( hAPP( c_Polynomial_Osmult( X ), T ), Y ) ) }.
% 1.04/1.71 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless__eq( tc_Polynomial_Opoly( X ), Z ), Y ) ),
% 1.04/1.71 Z = Y, c_Polynomial_Opos__poly( X, hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) }.
% 1.04/1.71 { ! class_Rings_Olinordered__idom( X ), ! Z = Y, hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless__eq( tc_Polynomial_Opoly( X ), Z ), Y ) ) }
% 1.04/1.71 .
% 1.04/1.71 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, hAPP
% 1.04/1.71 ( hAPP( c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ) ), Y ), Z
% 1.04/1.71 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Polynomial_Opoly
% 1.04/1.71 ( X ), Z ), Y ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ),
% 1.04/1.71 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( tc_Int_Oint ), Y ), X ) ),
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( tc_Int_Oint ), Y ), X ) ),
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ) }.
% 1.04/1.71 { ! class_Groups_Oab__group__add( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ) ),
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) = hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ) ), Y ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), hAPP
% 1.04/1.71 ( hAPP( c_Groups_Ominus__class_Ominus( tc_Int_Oint ), X ),
% 1.04/1.71 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ) ), hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ),
% 1.04/1.71 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), hAPP(
% 1.04/1.71 hAPP( c_Groups_Ominus__class_Ominus( tc_Int_Oint ), X ),
% 1.04/1.71 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ), Y ) ), hAPP(
% 1.04/1.71 c_Int_Onat, hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Int_Oint ), Y )
% 1.04/1.71 , X ) ) = hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP
% 1.04/1.71 ( c_Int_Onat, Y ) ), hAPP( c_Int_Onat, X ) ) }.
% 1.04/1.71 { c_Int_Onat__aux( Y, X ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.04/1.71 tc_Nat_Onat ), hAPP( c_Int_Onat, Y ) ), X ) }.
% 1.04/1.71 { c_Nat__Transfer_Otransfer__morphism( tc_Int_Oint, tc_Nat_Onat, c_Int_Onat
% 1.04/1.71 , c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( c_Int_Onat, X ) ),
% 1.04/1.71 hAPP( c_Int_Onat, Y ) ) = hAPP( c_Int_Onat, c_Nat__Transfer_Otsub( X, Y )
% 1.04/1.71 ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) )
% 1.04/1.71 , c_Nat__Transfer_Otsub( X, Y ) = hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( tc_Int_Oint ), X ), Y ) }.
% 1.04/1.71 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) ),
% 1.04/1.71 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint
% 1.04/1.71 ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Nat__Transfer_Otsub( X, Y
% 1.04/1.71 ) ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) )
% 1.04/1.71 , c_Nat__Transfer_Otsub( X, Y ) = hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( tc_Int_Oint ), X ), Y ) }.
% 1.04/1.71 { ! class_Groups_Oab__group__add( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( X ), hAPP( c_Groups_Ouminus__class_Ouminus
% 1.04/1.71 ( X ), Z ) ), hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ) ) = hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( X ), Z ), Y ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.04/1.71 tc_Int_Oint ) ), Y ) ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP(
% 1.04/1.71 hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ), Y ) = hAPP(
% 1.04/1.71 hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), hAPP( c_Nat_OSuc,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) )
% 1.04/1.71 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ),
% 1.04/1.71 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) = X }.
% 1.04/1.71 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( X ), Z ), T ) ), ! hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( X ), c_Divides_Odiv__class_Odiv( X, Y, Z ) ),
% 1.04/1.71 c_Divides_Odiv__class_Odiv( X, T, Z ) ) ), hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( X ), Y ), T ) ) }.
% 1.04/1.71 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( X ), Z ), T ) ), ! hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( X ), Y ), T ) ), hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( X ), c_Divides_Odiv__class_Odiv( X, Y, Z ) ),
% 1.04/1.71 c_Divides_Odiv__class_Odiv( X, T, Z ) ) ) }.
% 1.04/1.71 { ! class_Divides_Osemiring__div( X ), ! T = c_Groups_Ozero__class_Ozero( X
% 1.04/1.71 ), c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.04/1.71 c_Groups_Ozero__class_Ozero( X ) }.
% 1.04/1.71 { ! class_Divides_Osemiring__div( X ), T = c_Groups_Ozero__class_Ozero( X )
% 1.04/1.71 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.04/1.71 c_Divides_Odiv__class_Odiv( X, Z, Y ) }.
% 1.04/1.71 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.04/1.71 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = Z }.
% 1.04/1.71 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.04/1.71 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) = Z }.
% 1.04/1.71 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.04/1.71 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.04/1.71 c_Divides_Odiv__class_Odiv( X, T, Z ) }.
% 1.04/1.71 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.04/1.71 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) =
% 1.04/1.71 c_Divides_Odiv__class_Odiv( X, T, Z ) }.
% 1.04/1.71 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.04/1.71 , c_Divides_Odiv__class_Odiv( X, Y, Y ) = c_Groups_Oone__class_Oone( X )
% 1.04/1.71 }.
% 1.04/1.71 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( X ), U ), T ) ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Odiv( X, Y, Z )
% 1.04/1.71 ), c_Divides_Odiv__class_Odiv( X, T, U ) ) = c_Divides_Odiv__class_Odiv
% 1.04/1.71 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 1.04/1.71 ( c_Groups_Otimes__class_Otimes( X ), Z ), U ) ) }.
% 1.04/1.71 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Odiv( X, Y, Z )
% 1.04/1.71 ), T ) = c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), Y ), T ), Z ) }.
% 1.04/1.71 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Odiv( X, Y, Z )
% 1.04/1.71 ), Z ) = Y }.
% 1.04/1.71 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), T ), c_Divides_Odiv__class_Odiv( X, Y
% 1.04/1.71 , Z ) ) = c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 1.04/1.71 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), Z ), c_Divides_Odiv__class_Odiv( X, Y
% 1.04/1.71 , Z ) ) = Y }.
% 1.04/1.71 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( X ), Z ), T ) ), c_Divides_Odiv__class_Odiv( X
% 1.04/1.71 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), T ), Z ) = hAPP(
% 1.04/1.71 hAPP( c_Groups_Oplus__class_Oplus( X ), c_Divides_Odiv__class_Odiv( X, Y
% 1.04/1.71 , Z ) ), c_Divides_Odiv__class_Odiv( X, T, Z ) ) }.
% 1.04/1.71 { ! class_Divides_Oring__div( X ), ! hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), c_Divides_Odiv__class_Odiv( X
% 1.04/1.71 , hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ), Z ) = hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( X ), c_Divides_Odiv__class_Odiv( X, Y, Z
% 1.04/1.71 ) ) }.
% 1.04/1.71 { ! class_Divides_Oring__div( X ), ! hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), c_Divides_Odiv__class_Odiv( X
% 1.04/1.71 , Y, hAPP( c_Groups_Ouminus__class_Ouminus( X ), Z ) ) = hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( X ), c_Divides_Odiv__class_Odiv( X, Y, Z
% 1.04/1.71 ) ) }.
% 1.04/1.71 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hAPP( hAPP(
% 1.04/1.71 c_Power_Opower__class_Opower( X ), c_Divides_Odiv__class_Odiv( X, Y, Z )
% 1.04/1.71 ), T ) = c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.04/1.71 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 1.04/1.71 c_Power_Opower__class_Opower( X ), Z ), T ) ) }.
% 1.04/1.71 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X, Y,
% 1.04/1.71 c_Groups_Oone__class_Oone( X ) ) = Y }.
% 1.04/1.71 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.04/1.71 tc_Int_Oint ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.04/1.71 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 1.04/1.71 }.
% 1.04/1.71 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X, Y,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.04/1.71 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 1.04/1.71 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, X ) =
% 1.04/1.71 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.04/1.71 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), X ) ) =
% 1.04/1.71 c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), Y ), X ) }.
% 1.04/1.71 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), Y ), hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), X ) ) =
% 1.04/1.71 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Divides_Odiv__class_Odiv
% 1.04/1.71 ( tc_Int_Oint, X, Y ) ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 1.04/1.71 tc_Int_Oint, Y, X ) ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ),
% 1.04/1.71 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ),
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ),
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 1.04/1.71 tc_Int_Oint, Y, X ) ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, X ),
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 1.04/1.71 tc_Int_Oint, Y, X ) ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ),
% 1.04/1.71 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, X ),
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.04/1.71 tc_Int_Oint ) ), Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.04/1.71 tc_Int_Oint, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, X ),
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.04/1.71 tc_Int_Oint ) ), Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.04/1.71 tc_Int_Oint, c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ),
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ),
% 1.04/1.71 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Z, hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) =
% 1.04/1.71 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 1.04/1.71 tc_Int_Oint, Z, Y ), X ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oone__class_Oone(
% 1.04/1.71 tc_Int_Oint ) ), Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.04/1.71 tc_Int_Oint, c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ), X ) ) }.
% 1.04/1.71 { ! c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X =
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), alpha14( X, Y ) }.
% 1.04/1.71 { ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 1.04/1.71 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.04/1.71 { ! alpha14( X, Y ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.04/1.71 { ! alpha14( X, Y ), alpha27( X, Y ), alpha31( X, Y ) }.
% 1.04/1.71 { ! alpha27( X, Y ), alpha14( X, Y ) }.
% 1.04/1.71 { ! alpha31( X, Y ), alpha14( X, Y ) }.
% 1.04/1.71 { ! alpha31( X, Y ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.04/1.71 tc_Int_Oint, Y ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 1.04/1.71 { ! alpha31( X, Y ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.04/1.71 tc_Int_Oint, X ), Y ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ),
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless( tc_Int_Oint, X ), Y ) ), alpha31( X, Y ) }
% 1.04/1.71 .
% 1.04/1.71 { ! alpha27( X, Y ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.04/1.71 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ) }.
% 1.04/1.71 { ! alpha27( X, Y ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.04/1.71 tc_Int_Oint, Y ), X ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ), alpha27( X, Y ) }
% 1.04/1.71 .
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Divides_Odiv__class_Odiv
% 1.04/1.71 ( tc_Int_Oint, Y, X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 1.04/1.71 ( tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Divides_Odiv__class_Odiv
% 1.04/1.71 ( tc_Int_Oint, Y, X ) ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.04/1.71 tc_Int_Oint ) ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ),
% 1.04/1.71 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ), Y ) ) }
% 1.04/1.71 .
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ), Y ) ), hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.04/1.71 tc_Int_Oint ) ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.04/1.71 tc_Int_Oint ) ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) ),
% 1.04/1.71 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) ) }
% 1.04/1.71 .
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.04/1.71 tc_Int_Oint ) ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) ),
% 1.04/1.71 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) ), ! hBOOL( hAPP
% 1.04/1.71 ( c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.04/1.71 ( tc_Int_Oint ) ), Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.04/1.71 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.04/1.71 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.04/1.71 tc_Int_Oint ) ), Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 1.04/1.71 ( tc_Int_Oint, Y ), Z ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 1.04/1.71 ( tc_Int_Oint, c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ) ),
% 1.04/1.71 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ),
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.71 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ),
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless( tc_Int_Oint, X ), Y ) ),
% 1.04/1.71 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) =
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, X ),
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Divides_Odiv__class_Odiv
% 1.04/1.71 ( tc_Int_Oint, Y, X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 1.04/1.71 ( tc_Int_Oint, Y ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, X ),
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ),
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Divides_Odiv__class_Odiv
% 1.04/1.71 ( tc_Int_Oint, Y, X ) ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ),
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.04/1.71 tc_Int_Oint ) ), Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.04/1.71 tc_Int_Oint, c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ),
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, X ),
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.04/1.71 tc_Int_Oint ) ), Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 1.04/1.71 ( tc_Int_Oint, Y ), Z ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 1.04/1.71 ( tc_Int_Oint, c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ),
% 1.04/1.71 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ) ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ),
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ),
% 1.04/1.71 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) =
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) )
% 1.04/1.71 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Z ) ), hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.71 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, Z ) ),
% 1.04/1.71 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ) ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) )
% 1.04/1.71 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Z ),
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.71 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ) ),
% 1.04/1.71 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, Z ) ) ) }.
% 1.04/1.71 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.04/1.71 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.04/1.71 ( X ), T ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y
% 1.04/1.71 ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ),
% 1.04/1.71 c_Divides_Odiv__class_Odiv( X, T, Y ) ) }.
% 1.04/1.71 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.04/1.71 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.04/1.71 ( X ), T ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y
% 1.04/1.71 ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ),
% 1.04/1.71 c_Divides_Odiv__class_Odiv( X, T, Y ) ) }.
% 1.04/1.71 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.04/1.71 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.04/1.71 ( X ), Z ), Y ), Y ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ),
% 1.04/1.71 c_Divides_Odiv__class_Odiv( X, Z, Y ) ), c_Groups_Oone__class_Oone( X ) )
% 1.04/1.71 }.
% 1.04/1.71 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.04/1.71 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.04/1.71 ( X ), Y ), Z ), Y ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ),
% 1.04/1.71 c_Divides_Odiv__class_Odiv( X, Z, Y ) ), c_Groups_Oone__class_Oone( X ) )
% 1.04/1.71 }.
% 1.04/1.71 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.04/1.71 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Y ), Z ) ), !
% 1.04/1.71 c_Divides_Odiv__class_Odiv( X, Z, Y ) = T, Z = hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), T ), Y ) }.
% 1.04/1.71 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.04/1.71 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Y ), Z ) ), ! Z =
% 1.04/1.71 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ),
% 1.04/1.71 c_Divides_Odiv__class_Odiv( X, Z, Y ) = T }.
% 1.04/1.71 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.04/1.71 , Z = c_Groups_Ozero__class_Ozero( X ), ! hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( X ), Y ), T ) ), ! hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( X ), Z ), U ) ), ! c_Divides_Odiv__class_Odiv(
% 1.04/1.71 X, T, Y ) = c_Divides_Odiv__class_Odiv( X, U, Z ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), T ), Z ) = hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), Y ), U ) }.
% 1.04/1.71 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.04/1.71 , Z = c_Groups_Ozero__class_Ozero( X ), ! hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( X ), Y ), T ) ), ! hBOOL( hAPP( hAPP(
% 1.04/1.71 c_Rings_Odvd__class_Odvd( X ), Z ), U ) ), ! hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), T ), Z ) = hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( X ), Y ), U ), c_Divides_Odiv__class_Odiv
% 1.04/1.71 ( X, T, Y ) = c_Divides_Odiv__class_Odiv( X, U, Z ) }.
% 1.04/1.71 { ! T = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP
% 1.04/1.71 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ), alpha46
% 1.04/1.71 ( X, Z ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Z ) ), Z =
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.04/1.71 tc_Int_Oint, T, Z ) = Y }.
% 1.04/1.71 { ! T = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP
% 1.04/1.71 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ), alpha46
% 1.04/1.71 ( X, Z ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Z )
% 1.04/1.71 , X ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X
% 1.04/1.71 ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), Z =
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.04/1.71 tc_Int_Oint, T, Z ) = Y }.
% 1.04/1.71 { ! alpha46( X, Y ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.04/1.71 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ) }.
% 1.04/1.71 { ! alpha46( X, Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.04/1.71 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL
% 1.04/1.71 ( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, X ), Y ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), alpha46( X, Y ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless( tc_Int_Oint, X ), Y ) ), alpha46( X, Y ) }
% 1.04/1.71 .
% 1.04/1.71 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ),
% 1.04/1.71 alpha15( X, Z ) }.
% 1.04/1.71 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ),
% 1.04/1.71 alpha28( X, Y, Z ) }.
% 1.04/1.71 { ! alpha15( X, Z ), ! alpha28( X, Y, Z ), hBOOL( hAPP( Z,
% 1.04/1.71 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ) }.
% 1.04/1.71 { ! alpha28( X, Y, Z ), alpha32( X, Y, Z ) }.
% 1.04/1.71 { ! alpha28( X, Y, Z ), alpha35( X, Y, Z ) }.
% 1.04/1.71 { ! alpha32( X, Y, Z ), ! alpha35( X, Y, Z ), alpha28( X, Y, Z ) }.
% 1.04/1.71 { ! alpha35( X, Y, Z ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.04/1.71 tc_Int_Oint, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), alpha38
% 1.04/1.71 ( X, Y, Z ) }.
% 1.04/1.71 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, X ),
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), alpha35( X, Y, Z ) }.
% 1.04/1.71 { ! alpha38( X, Y, Z ), alpha35( X, Y, Z ) }.
% 1.04/1.71 { ! alpha38( X, Y, Z ), ! alpha40( X, Y, T ), hBOOL( hAPP( Z, T ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( Z, skol23( T, U, Z ) ) ), alpha38( X, Y, Z ) }.
% 1.04/1.71 { alpha40( X, Y, skol23( X, Y, Z ) ), alpha38( X, Y, Z ) }.
% 1.04/1.71 { ! alpha40( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.04/1.71 tc_Int_Oint, X ), skol24( X, T, U ) ) ) }.
% 1.04/1.71 { ! alpha40( X, Y, Z ), alpha42( X, Y, Z, skol24( X, Y, Z ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, X ), T ) ), !
% 1.04/1.71 alpha42( X, Y, Z, T ), alpha40( X, Y, Z ) }.
% 1.04/1.71 { ! alpha42( X, Y, Z, T ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.04/1.71 tc_Int_Oint, T ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 1.04/1.71 { ! alpha42( X, Y, Z, T ), Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.04/1.71 tc_Int_Oint ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.04/1.71 X ), Z ) ), T ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T ),
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), ! Y = hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ) ), T ), alpha42( X
% 1.04/1.71 , Y, Z, T ) }.
% 1.04/1.71 { ! alpha32( X, Y, Z ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.04/1.71 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), alpha36
% 1.04/1.71 ( X, Y, Z ) }.
% 1.04/1.71 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), alpha32( X, Y, Z ) }
% 1.04/1.71 .
% 1.04/1.71 { ! alpha36( X, Y, Z ), alpha32( X, Y, Z ) }.
% 1.04/1.71 { ! alpha36( X, Y, Z ), ! alpha39( X, Y, T ), hBOOL( hAPP( Z, T ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( Z, skol25( T, U, Z ) ) ), alpha36( X, Y, Z ) }.
% 1.04/1.71 { alpha39( X, Y, skol25( X, Y, Z ) ), alpha36( X, Y, Z ) }.
% 1.04/1.71 { ! alpha39( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.04/1.71 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), skol26( T, U,
% 1.04/1.71 W ) ) ) }.
% 1.04/1.71 { ! alpha39( X, Y, Z ), alpha41( X, Y, Z, skol26( X, Y, Z ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), T ) ), ! alpha41( X, Y, Z,
% 1.04/1.71 T ), alpha39( X, Y, Z ) }.
% 1.04/1.71 { ! alpha41( X, Y, Z, T ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.04/1.71 tc_Int_Oint, T ), X ) ) }.
% 1.04/1.71 { ! alpha41( X, Y, Z, T ), Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.04/1.71 tc_Int_Oint ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.04/1.71 X ), Z ) ), T ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, T ), X ) ), !
% 1.04/1.71 Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ) ), T ), alpha41( X
% 1.04/1.71 , Y, Z, T ) }.
% 1.04/1.71 { ! alpha15( X, Y ), ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 1.04/1.71 hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 1.04/1.71 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), alpha15( X, Y ) }.
% 1.04/1.71 { ! hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), alpha15
% 1.04/1.71 ( X, Y ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), c_SMT_Oz3div( X, Y )
% 1.04/1.71 = c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) }.
% 1.04/1.71 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), c_SMT_Oz3div( X, Y )
% 1.04/1.71 = hAPP( c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ),
% 1.04/1.71 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), Y ) ) ) }.
% 1.04/1.71 { ! class_Groups_Oab__group__add( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( X ), U ), T ) ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.04/1.71 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( X ), U ), Z ) ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( X ), T ), Y ) ) }.
% 1.04/1.71 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, X, hAPP( c_Nat_OSuc,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) = X }.
% 1.04/1.71 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) =
% 1.04/1.71 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 1.04/1.71 tc_Nat_Onat, Z, Y ), X ) }.
% 1.04/1.71 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Odiv(
% 1.04/1.71 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Polynomial_Osmult( X ), T ), Z )
% 1.04/1.71 , Y ) = hAPP( hAPP( c_Polynomial_Osmult( X ), T ),
% 1.04/1.71 c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly( X ), Z, Y ) ) }.
% 1.04/1.71 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Odiv(
% 1.04/1.71 tc_Polynomial_Opoly( X ), T, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.04/1.71 tc_Polynomial_Opoly( X ) ), Z ), Y ) ) = c_Divides_Odiv__class_Odiv(
% 1.04/1.71 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly
% 1.04/1.71 ( X ), T, Z ), Y ) }.
% 1.04/1.71 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.04/1.71 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) =
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.04/1.71 { Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.04/1.71 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) =
% 1.04/1.71 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) }.
% 1.04/1.71 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Odiv(
% 1.04/1.71 tc_Polynomial_Opoly( X ), Z, hAPP( c_Groups_Ouminus__class_Ouminus(
% 1.04/1.71 tc_Polynomial_Opoly( X ) ), Y ) ) = hAPP( c_Groups_Ouminus__class_Ouminus
% 1.04/1.71 ( tc_Polynomial_Opoly( X ) ), c_Divides_Odiv__class_Odiv(
% 1.04/1.71 tc_Polynomial_Opoly( X ), Z, Y ) ) }.
% 1.04/1.71 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Odiv(
% 1.04/1.71 tc_Polynomial_Opoly( X ), hAPP( c_Groups_Ouminus__class_Ouminus(
% 1.04/1.71 tc_Polynomial_Opoly( X ) ), Z ), Y ) = hAPP(
% 1.04/1.71 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ) ),
% 1.04/1.71 c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly( X ), Z, Y ) ) }.
% 1.04/1.71 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.04/1.71 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ), Y ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.04/1.71 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.04/1.71 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, Z ) ),
% 1.04/1.71 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, X, Z ) ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.04/1.71 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) =
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.04/1.71 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.04/1.71 tc_Nat_Onat ) ), Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.04/1.71 tc_Nat_Onat, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ), Y ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ),
% 1.04/1.71 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) =
% 1.04/1.71 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, Y ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ),
% 1.04/1.71 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ) = Y }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ),
% 1.04/1.71 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ) = Y }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), Y ) ), hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.04/1.71 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, Y ) ),
% 1.04/1.71 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, X ) ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.04/1.71 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) =
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.04/1.71 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) = hAPP( c_Nat_OSuc,
% 1.04/1.71 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ), X ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.04/1.71 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) = hAPP( c_Nat_OSuc,
% 1.04/1.71 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 1.04/1.71 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ), X ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ),
% 1.04/1.71 alpha16( X, Z ) }.
% 1.04/1.71 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ),
% 1.04/1.71 alpha29( X, Y, Z ) }.
% 1.04/1.71 { ! alpha16( X, Z ), ! alpha29( X, Y, Z ), hBOOL( hAPP( Z,
% 1.04/1.71 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ) }.
% 1.04/1.71 { ! alpha29( X, Y, Z ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.04/1.71 alpha33( X, Y, Z ) }.
% 1.04/1.71 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha29( X, Y, Z ) }.
% 1.04/1.71 { ! alpha33( X, Y, Z ), alpha29( X, Y, Z ) }.
% 1.04/1.71 { ! alpha33( X, Y, Z ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.04/1.71 tc_Nat_Onat, T ), X ) ), alpha37( X, Y, Z, T ) }.
% 1.04/1.71 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol27( X, T, U
% 1.04/1.71 ) ), X ) ), alpha33( X, Y, Z ) }.
% 1.04/1.71 { ! alpha37( X, Y, Z, skol27( X, Y, Z ) ), alpha33( X, Y, Z ) }.
% 1.04/1.71 { ! alpha37( X, Y, Z, T ), ! Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.04/1.71 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.04/1.71 X ), U ) ), T ), hBOOL( hAPP( Z, U ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( Z, skol28( U, W, Z, V0 ) ) ), alpha37( X, Y, Z, T ) }.
% 1.04/1.71 { Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol28( X, Y, Z, T ) )
% 1.04/1.71 ), T ), alpha37( X, Y, Z, T ) }.
% 1.04/1.71 { ! alpha16( X, Y ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.04/1.71 hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.04/1.71 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha16( X, Y ) }.
% 1.04/1.71 { ! hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha16
% 1.04/1.71 ( X, Y ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), hAPP( c_Int_Onat,
% 1.04/1.71 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) =
% 1.04/1.71 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( c_Int_Onat, X ), hAPP(
% 1.04/1.71 c_Int_Onat, Y ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ),
% 1.04/1.71 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( c_Int_Onat, X ), hAPP(
% 1.04/1.71 c_Int_Onat, Y ) ) = hAPP( c_Int_Onat, c_Divides_Odiv__class_Odiv(
% 1.04/1.71 tc_Int_Oint, X, Y ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ),
% 1.04/1.71 alpha17( X, Z ), alpha30( X, Y, Z ) }.
% 1.04/1.71 { ! alpha17( X, Z ), hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv(
% 1.04/1.71 tc_Nat_Onat, Y, X ) ) ) }.
% 1.04/1.71 { ! alpha30( X, Y, Z ), hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv(
% 1.04/1.71 tc_Nat_Onat, Y, X ) ) ) }.
% 1.04/1.71 { ! alpha30( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.04/1.71 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 1.04/1.71 ), skol29( X, Y, T ) ) ), Y ) ) }.
% 1.04/1.71 { ! alpha30( X, Y, Z ), alpha34( X, Y, Z, skol29( X, Y, Z ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 1.04/1.71 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), T ) ), Y ) ), !
% 1.04/1.71 alpha34( X, Y, Z, T ), alpha30( X, Y, Z ) }.
% 1.04/1.71 { ! alpha34( X, Y, Z, T ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.04/1.71 tc_Nat_Onat, Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat
% 1.04/1.71 ), X ), hAPP( c_Nat_OSuc, T ) ) ) ) }.
% 1.04/1.71 { ! alpha34( X, Y, Z, T ), hBOOL( hAPP( Z, T ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), hAPP(
% 1.04/1.71 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( c_Nat_OSuc
% 1.04/1.71 , T ) ) ) ), ! hBOOL( hAPP( Z, T ) ), alpha34( X, Y, Z, T ) }.
% 1.04/1.71 { ! alpha17( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.04/1.71 { ! alpha17( X, Y ), hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero(
% 1.04/1.71 tc_Nat_Onat ) ) ) }.
% 1.04/1.71 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! hBOOL( hAPP( Y,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha17( X, Y ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ), Y ) ), ! hBOOL
% 1.04/1.71 ( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( c_Nat_OSuc, Z )
% 1.04/1.71 ) ) ), Z = c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! Z =
% 1.04/1.71 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ), hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ), Y ) ) }.
% 1.04/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.04/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! Z =
% 1.04/1.71 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ), hBOOL( hAPP(
% 1.04/1.71 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), hAPP( hAPP(
% 1.04/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( c_Nat_OSuc, Z )
% 1.04/1.71 ) ) ) }.
% 1.04/1.71 { ! class_Rings_Oidom( X ),
% 1.04/1.71 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct( X
% 1.04/1.71 ) }.
% 1.04/1.71 { ! class_Rings_Oidom( X ), class_Groups_Ocancel__ab__semigroup__add( X ) }
% 1.04/1.71 .
% 1.04/1.71 { ! class_Rings_Oidom( X ), class_Rings_Oring__1__no__zero__divisors( X ) }
% 1.04/1.71 .
% 1.04/1.71 { ! class_Rings_Oidom( X ), class_Rings_Oring__no__zero__divisors( X ) }.
% 1.04/1.71 { ! class_Rings_Oidom( X ), class_Groups_Ocancel__semigroup__add( X ) }.
% 1.04/1.71 { ! class_Rings_Oidom( X ), class_Groups_Oab__semigroup__mult( X ) }.
% 1.04/1.71 { ! class_Rings_Oidom( X ), class_Groups_Ocomm__monoid__mult( X ) }.
% 1.04/1.71 { ! class_Rings_Oidom( X ), class_Groups_Oab__semigroup__add( X ) }.
% 1.04/1.71 { ! class_Rings_Oidom( X ), class_Rings_Ono__zero__divisors( X ) }.
% 1.04/1.71 { ! class_Rings_Oidom( X ), class_Groups_Ocomm__monoid__add( X ) }.
% 1.04/1.71 { ! class_Rings_Oidom( X ), class_Rings_Ocomm__semiring__1( X ) }.
% 1.04/1.71 { ! class_Rings_Oidom( X ), class_Rings_Ocomm__semiring__0( X ) }.
% 1.04/1.71 { ! class_Rings_Oidom( X ), class_Rings_Ocomm__semiring( X ) }.
% 1.04/1.71 { ! class_Rings_Oidom( X ), class_Groups_Oab__group__add( X ) }.
% 1.04/1.71 { ! class_Rings_Oidom( X ), class_Rings_Ozero__neq__one( X ) }.
% 1.04/1.71 { ! class_Rings_Oidom( X ), class_Groups_Omonoid__mult( X ) }.
% 1.04/1.71 { ! class_Rings_Oidom( X ), class_Rings_Ocomm__ring__1( X ) }.
% 1.04/1.71 { ! class_Rings_Oidom( X ), class_Groups_Omonoid__add( X ) }.
% 1.04/1.71 { ! class_Rings_Oidom( X ), class_Rings_Osemiring__0( X ) }.
% 1.04/1.71 { ! class_Rings_Oidom( X ), class_Groups_Ogroup__add( X ) }.
% 1.04/1.71 { ! class_Rings_Oidom( X ), class_Rings_Omult__zero( X ) }.
% 1.04/1.71 { ! class_Rings_Oidom( X ), class_Rings_Ocomm__ring( X ) }.
% 1.04/1.71 { ! class_Rings_Oidom( X ), class_Rings_Osemiring( X ) }.
% 1.04/1.71 { ! class_Rings_Oidom( X ), class_Groups_Ouminus( X ) }.
% 1.04/1.71 { ! class_Rings_Oidom( X ), class_Rings_Oring__1( X ) }.
% 1.04/1.71 { ! class_Rings_Oidom( X ), class_Groups_Ominus( X ) }.
% 1.04/1.71 { ! class_Rings_Oidom( X ), class_Power_Opower( X ) }.
% 1.04/1.71 { ! class_Rings_Oidom( X ), class_Groups_Ozero( X ) }.
% 1.04/1.71 { ! class_Rings_Oidom( X ), class_Rings_Oring( X ) }.
% 1.04/1.71 { ! class_Rings_Oidom( X ), class_Groups_Oone( X ) }.
% 1.04/1.71 { ! class_Rings_Oidom( X ), class_Rings_Odvd( X ) }.
% 1.04/1.71 { ! class_Rings_Oidom( X ), class_Groups_Ocancel__comm__monoid__add( X ) }
% 1.04/1.71 .
% 1.04/1.71 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 1.04/1.71 class_Groups_Ocancel__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 1.04/1.71 { class_Groups_Ocancel__comm__monoid__add( tc_Nat_Onat ) }.
% 1.04/1.71 { class_Groups_Ocancel__comm__monoid__add( tc_Int_Oint ) }.
% 1.04/1.71 { ! class_Lattices_Oboolean__algebra( X ), class_Lattices_Oboolean__algebra
% 1.04/1.71 ( tc_fun( Y, X ) ) }.
% 1.04/1.71 { ! class_Orderings_Opreorder( X ), class_Orderings_Opreorder( tc_fun( Y, X
% 1.04/1.71 ) ) }.
% 1.04/1.71 { ! class_Orderings_Oorder( X ), class_Orderings_Oorder( tc_fun( Y, X ) ) }
% 1.04/1.71 .
% 1.04/1.71 { ! class_Orderings_Oord( X ), class_Orderings_Oord( tc_fun( Y, X ) ) }.
% 1.04/1.71 { ! class_Groups_Ouminus( X ), class_Groups_Ouminus( tc_fun( Y, X ) ) }.
% 1.04/1.71 { ! class_Groups_Ominus( X ), class_Groups_Ominus( tc_fun( Y, X ) ) }.
% 1.04/1.71 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.04/1.71 tc_Int_Oint ) }.
% 1.04/1.71 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Int_Oint ) }.
% 1.04/1.71 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Int_Oint ) }.
% 1.04/1.71 { class_Rings_Olinordered__comm__semiring__strict( tc_Int_Oint ) }.
% 1.04/1.71 { class_Rings_Olinordered__semiring__1__strict( tc_Int_Oint ) }.
% 1.04/1.71 { class_Rings_Olinordered__semiring__strict( tc_Int_Oint ) }.
% 1.04/1.71 { class_Groups_Oordered__ab__semigroup__add( tc_Int_Oint ) }.
% 1.04/1.71 { class_Groups_Oordered__comm__monoid__add( tc_Int_Oint ) }.
% 1.04/1.71 { class_Groups_Olinordered__ab__group__add( tc_Int_Oint ) }.
% 1.04/1.71 { class_Groups_Ocancel__ab__semigroup__add( tc_Int_Oint ) }.
% 1.04/1.71 { class_Rings_Oring__1__no__zero__divisors( tc_Int_Oint ) }.
% 1.04/1.71 { class_Rings_Oordered__cancel__semiring( tc_Int_Oint ) }.
% 1.04/1.71 { class_Rings_Olinordered__ring__strict( tc_Int_Oint ) }.
% 1.04/1.71 { class_Rings_Oring__no__zero__divisors( tc_Int_Oint ) }.
% 1.04/1.71 { class_Rings_Oordered__comm__semiring( tc_Int_Oint ) }.
% 1.04/1.71 { class_Rings_Olinordered__semiring__1( tc_Int_Oint ) }.
% 1.04/1.71 { class_Groups_Oordered__ab__group__add( tc_Int_Oint ) }.
% 1.04/1.71 { class_Groups_Ocancel__semigroup__add( tc_Int_Oint ) }.
% 1.04/1.71 { class_Rings_Olinordered__semiring( tc_Int_Oint ) }.
% 1.04/1.71 { class_Rings_Olinordered__semidom( tc_Int_Oint ) }.
% 1.04/1.71 { class_Groups_Oab__semigroup__mult( tc_Int_Oint ) }.
% 1.04/1.71 { class_Groups_Ocomm__monoid__mult( tc_Int_Oint ) }.
% 1.04/1.71 { class_Groups_Oab__semigroup__add( tc_Int_Oint ) }.
% 1.04/1.71 { class_Rings_Oordered__semiring( tc_Int_Oint ) }.
% 1.04/1.71 { class_Rings_Ono__zero__divisors( tc_Int_Oint ) }.
% 1.04/1.71 { class_Groups_Ocomm__monoid__add( tc_Int_Oint ) }.
% 1.04/1.71 { class_Rings_Olinordered__ring( tc_Int_Oint ) }.
% 1.04/1.71 { class_Rings_Olinordered__idom( tc_Int_Oint ) }.
% 1.04/1.71 { class_Rings_Ocomm__semiring__1( tc_Int_Oint ) }.
% 1.04/1.71 { class_Rings_Ocomm__semiring__0( tc_Int_Oint ) }.
% 1.04/1.71 { class_Divides_Osemiring__div( tc_Int_Oint ) }.
% 1.04/1.71 { class_Rings_Ocomm__semiring( tc_Int_Oint ) }.
% 1.04/1.71 { class_Groups_Oab__group__add( tc_Int_Oint ) }.
% 1.04/1.71 { class_Rings_Ozero__neq__one( tc_Int_Oint ) }.
% 1.04/1.71 { class_Rings_Oordered__ring( tc_Int_Oint ) }.
% 1.04/1.71 { class_Orderings_Opreorder( tc_Int_Oint ) }.
% 1.04/1.71 { class_Orderings_Olinorder( tc_Int_Oint ) }.
% 1.04/1.71 { class_Groups_Omonoid__mult( tc_Int_Oint ) }.
% 1.04/1.71 { class_Rings_Ocomm__ring__1( tc_Int_Oint ) }.
% 1.04/1.71 { class_Groups_Omonoid__add( tc_Int_Oint ) }.
% 1.04/1.71 { class_Rings_Osemiring__0( tc_Int_Oint ) }.
% 1.04/1.71 { class_Groups_Ogroup__add( tc_Int_Oint ) }.
% 1.04/1.71 { class_Divides_Oring__div( tc_Int_Oint ) }.
% 1.04/1.71 { class_Rings_Omult__zero( tc_Int_Oint ) }.
% 1.04/1.71 { class_Rings_Ocomm__ring( tc_Int_Oint ) }.
% 1.04/1.71 { class_Orderings_Oorder( tc_Int_Oint ) }.
% 1.04/1.71 { class_Int_Oring__char__0( tc_Int_Oint ) }.
% 1.04/1.71 { class_Rings_Osemiring( tc_Int_Oint ) }.
% 1.04/1.71 { class_Orderings_Oord( tc_Int_Oint ) }.
% 1.04/1.71 { class_Groups_Ouminus( tc_Int_Oint ) }.
% 1.04/1.71 { class_Rings_Oring__1( tc_Int_Oint ) }.
% 1.04/1.71 { class_Groups_Ominus( tc_Int_Oint ) }.
% 1.04/1.71 { class_Power_Opower( tc_Int_Oint ) }.
% 1.04/1.71 { class_Groups_Ozero( tc_Int_Oint ) }.
% 1.04/1.71 { class_Rings_Oring( tc_Int_Oint ) }.
% 1.04/1.71 { class_Rings_Oidom( tc_Int_Oint ) }.
% 1.04/1.71 { class_Groups_Oone( tc_Int_Oint ) }.
% 1.04/1.71 { class_Rings_Odvd( tc_Int_Oint ) }.
% 1.04/1.71 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.04/1.71 tc_Nat_Onat ) }.
% 1.04/1.71 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 1.04/1.71 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Nat_Onat ) }.
% 1.04/1.71 { class_Rings_Olinordered__comm__semiring__strict( tc_Nat_Onat ) }.
% 1.04/1.71 { class_Rings_Olinordered__semiring__strict( tc_Nat_Onat ) }.
% 1.04/1.71 { class_Groups_Oordered__ab__semigroup__add( tc_Nat_Onat ) }.
% 1.04/1.71 { class_Groups_Oordered__comm__monoid__add( tc_Nat_Onat ) }.
% 1.04/1.71 { class_Groups_Ocancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 1.04/1.71 { class_Rings_Oordered__cancel__semiring( tc_Nat_Onat ) }.
% 1.04/1.71 { class_Rings_Oordered__comm__semiring( tc_Nat_Onat ) }.
% 1.04/1.71 { class_Groups_Ocancel__semigroup__add( tc_Nat_Onat ) }.
% 1.04/1.71 { class_Rings_Olinordered__semiring( tc_Nat_Onat ) }.
% 1.04/1.71 { class_Rings_Olinordered__semidom( tc_Nat_Onat ) }.
% 1.04/1.71 { class_Groups_Oab__semigroup__mult( tc_Nat_Onat ) }.
% 1.04/1.71 { class_Groups_Ocomm__monoid__mult( tc_Nat_Onat ) }.
% 1.04/1.71 { class_Groups_Oab__semigroup__add( tc_Nat_Onat ) }.
% 1.04/1.71 { class_Rings_Oordered__semiring( tc_Nat_Onat ) }.
% 1.04/1.71 { class_Rings_Ono__zero__divisors( tc_Nat_Onat ) }.
% 1.04/1.71 { class_Groups_Ocomm__monoid__add( tc_Nat_Onat ) }.
% 1.04/1.71 { class_Rings_Ocomm__semiring__1( tc_Nat_Onat ) }.
% 1.04/1.71 { class_Rings_Ocomm__semiring__0( tc_Nat_Onat ) }.
% 1.04/1.71 { class_Divides_Osemiring__div( tc_Nat_Onat ) }.
% 1.04/1.71 { class_Rings_Ocomm__semiring( tc_Nat_Onat ) }.
% 1.04/1.71 { class_Orderings_Owellorder( tc_Nat_Onat ) }.
% 1.04/1.71 { class_Rings_Ozero__neq__one( tc_Nat_Onat ) }.
% 1.04/1.71 { class_Orderings_Opreorder( tc_Nat_Onat ) }.
% 1.04/1.71 { class_Orderings_Olinorder( tc_Nat_Onat ) }.
% 1.04/1.71 { class_Groups_Omonoid__mult( tc_Nat_Onat ) }.
% 1.04/1.71 { class_Groups_Omonoid__add( tc_Nat_Onat ) }.
% 1.04/1.71 { class_Rings_Osemiring__0( tc_Nat_Onat ) }.
% 1.04/1.71 { class_Rings_Omult__zero( tc_Nat_Onat ) }.
% 1.04/1.71 { class_Orderings_Oorder( tc_Nat_Onat ) }.
% 1.04/1.71 { class_Rings_Osemiring( tc_Nat_Onat ) }.
% 1.04/1.71 { class_Orderings_Oord( tc_Nat_Onat ) }.
% 1.04/1.71 { class_Groups_Ominus( tc_Nat_Onat ) }.
% 1.04/1.71 { class_Power_Opower( tc_Nat_Onat ) }.
% 1.04/1.71 { class_Groups_Ozero( tc_Nat_Onat ) }.
% 1.04/1.71 { class_Groups_Oone( tc_Nat_Onat ) }.
% 1.04/1.71 { class_Rings_Odvd( tc_Nat_Onat ) }.
% 1.04/1.71 { class_Lattices_Oboolean__algebra( tc_HOL_Obool ) }.
% 1.04/1.71 { class_Orderings_Opreorder( tc_HOL_Obool ) }.
% 1.04/1.71 { class_Orderings_Oorder( tc_HOL_Obool ) }.
% 1.04/1.71 { class_Orderings_Oord( tc_HOL_Obool ) }.
% 1.04/1.71 { class_Groups_Ouminus( tc_HOL_Obool ) }.
% 1.04/1.71 { class_Groups_Ominus( tc_HOL_Obool ) }.
% 1.04/1.71 { ! class_Rings_Oidom( X ),
% 1.04/1.71 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.04/1.71 tc_Polynomial_Opoly( X ) ) }.
% 1.04/1.72 { ! class_Rings_Olinordered__idom( X ),
% 1.04/1.72 class_Groups_Oordered__cancel__ab__semigroup__add( tc_Polynomial_Opoly( X
% 1.04/1.72 ) ) }.
% 1.04/1.72 { ! class_Rings_Olinordered__idom( X ),
% 1.04/1.72 class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Polynomial_Opoly(
% 1.04/1.72 X ) ) }.
% 1.04/1.72 { ! class_Rings_Olinordered__idom( X ),
% 1.04/1.72 class_Rings_Olinordered__comm__semiring__strict( tc_Polynomial_Opoly( X )
% 1.04/1.72 ) }.
% 1.04/1.72 { ! class_Rings_Olinordered__idom( X ),
% 1.04/1.72 class_Rings_Olinordered__semiring__1__strict( tc_Polynomial_Opoly( X ) )
% 1.04/1.72 }.
% 1.04/1.72 { ! class_Rings_Olinordered__idom( X ),
% 1.04/1.72 class_Rings_Olinordered__semiring__strict( tc_Polynomial_Opoly( X ) ) }.
% 1.04/1.72 { ! class_Rings_Olinordered__idom( X ),
% 1.04/1.72 class_Groups_Oordered__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 1.04/1.72 { ! class_Rings_Olinordered__idom( X ),
% 1.04/1.72 class_Groups_Oordered__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 1.04/1.72 { ! class_Rings_Olinordered__idom( X ),
% 1.04/1.72 class_Groups_Olinordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 1.04/1.72 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 1.04/1.72 class_Groups_Ocancel__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 1.04/1.72 { ! class_Rings_Oidom( X ), class_Rings_Oring__1__no__zero__divisors(
% 1.04/1.72 tc_Polynomial_Opoly( X ) ) }.
% 1.04/1.72 { ! class_Rings_Olinordered__idom( X ),
% 1.04/1.72 class_Rings_Oordered__cancel__semiring( tc_Polynomial_Opoly( X ) ) }.
% 1.04/1.72 { ! class_Rings_Olinordered__idom( X ),
% 1.04/1.72 class_Rings_Olinordered__ring__strict( tc_Polynomial_Opoly( X ) ) }.
% 1.04/1.72 { ! class_Rings_Oidom( X ), class_Rings_Oring__no__zero__divisors(
% 1.04/1.72 tc_Polynomial_Opoly( X ) ) }.
% 1.04/1.72 { ! class_Rings_Olinordered__idom( X ),
% 1.04/1.72 class_Rings_Oordered__comm__semiring( tc_Polynomial_Opoly( X ) ) }.
% 1.04/1.72 { ! class_Rings_Olinordered__idom( X ),
% 1.04/1.72 class_Rings_Olinordered__semiring__1( tc_Polynomial_Opoly( X ) ) }.
% 1.04/1.72 { ! class_Rings_Olinordered__idom( X ),
% 1.04/1.72 class_Groups_Oordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 1.04/1.72 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 1.04/1.72 class_Groups_Ocancel__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 1.04/1.72 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semiring(
% 1.04/1.72 tc_Polynomial_Opoly( X ) ) }.
% 1.04/1.72 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semidom(
% 1.04/1.72 tc_Polynomial_Opoly( X ) ) }.
% 1.04/1.72 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Oab__semigroup__mult
% 1.04/1.72 ( tc_Polynomial_Opoly( X ) ) }.
% 1.04/1.72 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Ocomm__monoid__mult(
% 1.04/1.72 tc_Polynomial_Opoly( X ) ) }.
% 1.04/1.72 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Oab__semigroup__add
% 1.04/1.72 ( tc_Polynomial_Opoly( X ) ) }.
% 1.04/1.72 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__semiring(
% 1.04/1.72 tc_Polynomial_Opoly( X ) ) }.
% 1.04/1.72 { ! class_Rings_Oidom( X ), class_Rings_Ono__zero__divisors(
% 1.04/1.72 tc_Polynomial_Opoly( X ) ) }.
% 1.04/1.72 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Ocomm__monoid__add(
% 1.04/1.72 tc_Polynomial_Opoly( X ) ) }.
% 1.04/1.72 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__ring(
% 1.04/1.72 tc_Polynomial_Opoly( X ) ) }.
% 1.04/1.72 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__idom(
% 1.04/1.72 tc_Polynomial_Opoly( X ) ) }.
% 1.04/1.72 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ocomm__semiring__1(
% 1.04/1.72 tc_Polynomial_Opoly( X ) ) }.
% 1.04/1.72 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring__0(
% 1.04/1.72 tc_Polynomial_Opoly( X ) ) }.
% 1.04/1.72 { ! class_Fields_Ofield( X ), class_Divides_Osemiring__div(
% 1.04/1.72 tc_Polynomial_Opoly( X ) ) }.
% 1.04/1.72 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring(
% 1.04/1.72 tc_Polynomial_Opoly( X ) ) }.
% 1.04/1.72 { ! class_Groups_Oab__group__add( X ), class_Groups_Oab__group__add(
% 1.04/1.72 tc_Polynomial_Opoly( X ) ) }.
% 1.04/1.72 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ozero__neq__one(
% 1.04/1.72 tc_Polynomial_Opoly( X ) ) }.
% 1.04/1.72 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__ring(
% 1.04/1.72 tc_Polynomial_Opoly( X ) ) }.
% 1.04/1.72 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Opreorder(
% 1.04/1.72 tc_Polynomial_Opoly( X ) ) }.
% 1.04/1.72 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Olinorder(
% 1.04/1.72 tc_Polynomial_Opoly( X ) ) }.
% 1.04/1.72 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Omonoid__mult(
% 1.04/1.72 tc_Polynomial_Opoly( X ) ) }.
% 1.04/1.72 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Ocomm__ring__1(
% 1.04/1.72 tc_Polynomial_Opoly( X ) ) }.
% 1.04/1.72 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Omonoid__add(
% 1.04/1.72 tc_Polynomial_Opoly( X ) ) }.
% 1.04/1.72 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring__0(
% 1.04/1.72 tc_Polynomial_Opoly( X ) ) }.
% 1.04/1.72 { ! class_Groups_Oab__group__add( X ), class_Groups_Ogroup__add(
% 1.04/1.72 tc_Polynomial_Opoly( X ) ) }.
% 1.04/1.72 { ! class_Fields_Ofield( X ), class_Divides_Oring__div( tc_Polynomial_Opoly
% 1.04/1.72 ( X ) ) }.
% 1.04/1.72 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Omult__zero(
% 1.04/1.72 tc_Polynomial_Opoly( X ) ) }.
% 1.04/1.72 { ! class_Rings_Ocomm__ring( X ), class_Rings_Ocomm__ring(
% 1.04/1.72 tc_Polynomial_Opoly( X ) ) }.
% 1.04/1.72 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oorder(
% 1.04/1.72 tc_Polynomial_Opoly( X ) ) }.
% 1.04/1.72 { ! class_Rings_Olinordered__idom( X ), class_Int_Oring__char__0(
% 1.04/1.72 tc_Polynomial_Opoly( X ) ) }.
% 1.04/1.72 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring(
% 1.04/1.72 tc_Polynomial_Opoly( X ) ) }.
% 1.04/1.72 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oord(
% 1.04/1.72 tc_Polynomial_Opoly( X ) ) }.
% 1.04/1.72 { ! class_Groups_Oab__group__add( X ), class_Groups_Ouminus(
% 1.04/1.72 tc_Polynomial_Opoly( X ) ) }.
% 1.04/1.72 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Oring__1(
% 1.04/1.72 tc_Polynomial_Opoly( X ) ) }.
% 1.04/1.72 { ! class_Groups_Oab__group__add( X ), class_Groups_Ominus(
% 1.04/1.72 tc_Polynomial_Opoly( X ) ) }.
% 1.04/1.72 { ! class_Rings_Ocomm__semiring__1( X ), class_Power_Opower(
% 1.04/1.72 tc_Polynomial_Opoly( X ) ) }.
% 1.04/1.72 { ! class_Groups_Ozero( X ), class_Groups_Ozero( tc_Polynomial_Opoly( X ) )
% 1.04/1.72 }.
% 1.04/1.72 { ! class_Rings_Ocomm__ring( X ), class_Rings_Oring( tc_Polynomial_Opoly( X
% 1.04/1.72 ) ) }.
% 1.04/1.72 { ! class_Rings_Oidom( X ), class_Rings_Oidom( tc_Polynomial_Opoly( X ) ) }
% 1.04/1.72 .
% 1.04/1.72 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Oone(
% 1.04/1.72 tc_Polynomial_Opoly( X ) ) }.
% 1.04/1.72 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Odvd(
% 1.04/1.72 tc_Polynomial_Opoly( X ) ) }.
% 1.04/1.72 { hAPP( c_COMBI( Y ), X ) = X }.
% 1.04/1.72 { hAPP( hAPP( c_COMBK( T, Z ), Y ), X ) = Y }.
% 1.04/1.72 { hAPP( hAPP( hAPP( c_COMBB( W, U, T ), Z ), Y ), X ) = hAPP( Z, hAPP( Y, X
% 1.04/1.72 ) ) }.
% 1.04/1.72 { hAPP( hAPP( c_COMBC( W, U, T, Z ), Y ), X ) = hAPP( hAPP( Z, X ), Y ) }.
% 1.04/1.72 { hAPP( hAPP( hAPP( c_COMBS( W, U, T ), Z ), Y ), X ) = hAPP( hAPP( Z, X )
% 1.04/1.72 , hAPP( Y, X ) ) }.
% 1.04/1.72 { ! hBOOL( hAPP( c_fequal( Y ), X ) ), Y = X }.
% 1.04/1.72 { ! Y = X, hBOOL( hAPP( c_fequal( Y ), X ) ) }.
% 1.04/1.72 { ! hBOOL( c_fFalse ) }.
% 1.04/1.72 { ! hBOOL( hAPP( c_fNot, X ) ), ! hBOOL( X ) }.
% 1.04/1.72 { hBOOL( X ), hBOOL( hAPP( c_fNot, X ) ) }.
% 1.04/1.72 { ! hBOOL( X ), ! hBOOL( Y ), hBOOL( hAPP( hAPP( c_fconj, X ), Y ) ) }.
% 1.04/1.72 { ! hBOOL( hAPP( hAPP( c_fconj, X ), Y ) ), hBOOL( X ) }.
% 1.04/1.72 { ! hBOOL( hAPP( hAPP( c_fconj, Y ), X ) ), hBOOL( X ) }.
% 1.04/1.72 { ! v_a = c_Groups_Ozero__class_Ozero( t_a ) }.
% 1.04/1.72 { hAPP( c_Nat_OSuc, hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat )
% 1.04/1.72 , c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( t_a, v_q ) ), v_k )
% 1.04/1.72 ) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( t_a, v_cs____ ) }
% 1.04/1.72 .
% 1.04/1.72 { hAPP( c_Polynomial_Opoly( t_a, v_cs____ ), X ) = hAPP( hAPP(
% 1.04/1.72 c_Groups_Otimes__class_Otimes( t_a ), hAPP( hAPP(
% 1.04/1.72 c_Power_Opower__class_Opower( t_a ), X ), v_k ) ), hAPP( hAPP(
% 1.04/1.72 c_Groups_Oplus__class_Oplus( t_a ), v_a ), hAPP( hAPP(
% 1.04/1.72 c_Groups_Otimes__class_Otimes( t_a ), X ), hAPP( c_Polynomial_Opoly( t_a
% 1.04/1.72 , v_q ), X ) ) ) ) }.
% 1.04/1.72 { ! hAPP( c_Nat_OSuc, hAPP( c_Nat_OSuc, hAPP( hAPP(
% 1.04/1.72 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ),
% 1.04/1.72 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( t_a, X ) ), v_k ) ) )
% 1.04/1.72 = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( t_a, hAPP( hAPP(
% 1.04/1.72 c_Polynomial_OpCons( t_a ), v_c____ ), v_cs____ ) ), alpha47( skol30( Y )
% 1.04/1.72 ) }.
% 1.04/1.72 { ! hAPP( c_Nat_OSuc, hAPP( c_Nat_OSuc, hAPP( hAPP(
% 1.04/1.72 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ),
% 1.04/1.72 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( t_a, X ) ), v_k ) ) )
% 1.04/1.72 = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( t_a, hAPP( hAPP(
% 1.04/1.72 c_Polynomial_OpCons( t_a ), v_c____ ), v_cs____ ) ), ! skol30( Y ) =
% 1.04/1.72 c_Groups_Ozero__class_Ozero( t_a ) }.
% 1.04/1.72 { ! hAPP( c_Nat_OSuc, hAPP( c_Nat_OSuc, hAPP( hAPP(
% 1.04/1.72 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ),
% 1.04/1.72 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( t_a, X ) ), v_k ) ) )
% 1.04/1.72 = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( t_a, hAPP( hAPP(
% 1.04/1.72 c_Polynomial_OpCons( t_a ), v_c____ ), v_cs____ ) ), ! hAPP(
% 1.04/1.72 c_Polynomial_Opoly( t_a, v_q ), skol30( X ) ) = hAPP( c_Polynomial_Opoly
% 1.04/1.72 ( t_a, X ), skol30( X ) ) }.
% 1.04/1.72 { ! alpha47( X ), ! X = c_Groups_Ozero__class_Ozero( t_a ) }.
% 1.04/1.72 { ! alpha47( X ), ! X = c_Groups_Ozero__class_Ozero( t_a ), ! hBOOL( hAPP(
% 1.04/1.72 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.04/1.72 tc_Nat_Onat ) ), v_k ) ) }.
% 1.04/1.72 { X = c_Groups_Ozero__class_Ozero( t_a ), X = c_Groups_Ozero__class_Ozero(
% 1.04/1.72 t_a ), alpha47( X ) }.
% 1.04/1.72 { X = c_Groups_Ozero__class_Ozero( t_a ), hBOOL( hAPP(
% 1.04/1.72 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.04/1.72 tc_Nat_Onat ) ), v_k ) ), alpha47( X ) }.
% 1.04/1.72 { class_Rings_Oidom( t_a ) }.
% 1.04/1.72
% 1.04/1.72 *** allocated 15000 integers for clauses
% 1.04/1.72 *** allocated 22500 integers for clauses
% 1.04/1.72 *** allocated 33750 integers for clauses
% 1.04/1.72 *** allocated 50625 integers for clauses
% 1.04/1.72 *** allocated 75937 integers for clauses
% 1.04/1.72 *** allocated 113905 integers for clauses
% 1.04/1.72 percentage equality = 0.260252, percentage horn = 0.907053
% 1.04/1.72 This is a problem with some equality
% 1.04/1.72
% 1.04/1.72
% 1.04/1.72
% 1.04/1.72 Options Used:
% 1.04/1.72
% 1.04/1.72 useres = 1
% 1.04/1.72 useparamod = 1
% 1.04/1.72 useeqrefl = 1
% 1.04/1.72 useeqfact = 1
% 1.04/1.72 usefactor = 1
% 1.04/1.72 usesimpsplitting = 0
% 1.04/1.72 usesimpdemod = 5
% 1.04/1.72 usesimpres = 3
% 1.04/1.72
% 1.04/1.72 resimpinuse = 1000
% 1.04/1.72 resimpclauses = 20000
% 1.04/1.72 substype = eqrewr
% 1.04/1.72 backwardsubs = 1
% 1.04/1.72 selectoldest = 5
% 1.04/1.72
% 1.04/1.72 litorderings [0] = split
% 1.04/1.72 litorderings [1] = extend the termordering, first sorting on arguments
% 1.04/1.72
% 1.04/1.72 termordering = kbo
% 1.04/1.72
% 1.04/1.72 litapriori = 0
% 1.04/1.72 termapriori = 1
% 1.04/1.72 litaposteriori = 0
% 1.04/1.72 termaposteriori = 0
% 1.04/1.72 demodaposteriori = 0
% 1.04/1.72 ordereqreflfact = 0
% 1.04/1.72
% 1.04/1.72 litselect = negord
% 1.04/1.72
% 1.04/1.72 maxweight = 15
% 1.04/1.72 maxdepth = 30000
% 1.04/1.72 maxlength = 115
% 1.04/1.72 maxnrvars = 195
% 1.04/1.72 excuselevel = 1
% 1.04/1.72 increasemaxweight = 1
% 1.04/1.72
% 1.04/1.72 maxselected = 10000000
% 1.04/1.72 maxnrclauses = 10000000
% 1.04/1.72
% 1.04/1.72 showgenerated = 0
% 1.04/1.72 showkept = 0
% 1.04/1.72 showselected = 0
% 1.04/1.72 showdeleted = 0
% 1.04/1.72 showresimp = 1
% 1.04/1.72 showstatus = 2000
% 1.04/1.72
% 1.04/1.72 prologoutput = 0
% 1.04/1.72 nrgoals = 5000000
% 1.04/1.72 totalproof = 1
% 1.04/1.72
% 1.04/1.72 Symbols occurring in the translation:
% 1.04/1.72
% 1.04/1.72 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.04/1.72 . [1, 2] (w:1, o:225, a:1, s:1, b:0),
% 1.04/1.72 ! [4, 1] (w:0, o:128, a:1, s:1, b:0),
% 1.04/1.72 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.04/1.72 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.04/1.72 hAPP [38, 2] (w:1, o:249, a:1, s:1, b:0),
% 1.04/1.72 t_a [39, 0] (w:1, o:19, a:1, s:1, b:0),
% 1.04/1.72 class_Rings_Oidom [40, 1] (w:1, o:133, a:1, s:1, b:0),
% 1.04/1.72 v_p [41, 0] (w:1, o:20, a:1, s:1, b:0),
% 1.04/1.72 c_Polynomial_Opoly [42, 2] (w:1, o:255, a:1, s:1, b:0),
% 1.04/1.72 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant [43, 3] (w:1, o:
% 1.04/1.72 288, a:1, s:1, b:0),
% 1.04/1.72 tc_Nat_Onat [45, 0] (w:1, o:28, a:1, s:1, b:0),
% 1.04/1.72 c_Groups_Ozero__class_Ozero [46, 1] (w:1, o:134, a:1, s:1, b:0),
% 1.04/1.72 c_Orderings_Oord__class_Oless [47, 2] (w:1, o:252, a:1, s:1, b:0),
% 1.04/1.72 c_Nat_OSuc [48, 0] (w:1, o:29, a:1, s:1, b:0),
% 1.04/1.72 hBOOL [49, 1] (w:1, o:135, a:1, s:1, b:0),
% 1.04/1.72 v_cs____ [51, 0] (w:1, o:33, a:1, s:1, b:0),
% 1.04/1.72 class_Rings_Ocomm__semiring__0 [57, 1] (w:1, o:138, a:1, s:1, b:0),
% 1.04/1.72 c_Polynomial_OpCons [58, 1] (w:1, o:139, a:1, s:1, b:0),
% 1.04/1.72 c_Groups_Oplus__class_Oplus [59, 1] (w:1, o:141, a:1, s:1, b:0),
% 1.04/1.72 c_Groups_Otimes__class_Otimes [60, 1] (w:1, o:142, a:1, s:1, b:0),
% 1.04/1.72 class_Rings_Olinordered__ring [62, 1] (w:1, o:143, a:1, s:1, b:0),
% 1.04/1.72 class_Rings_Olinordered__ring__strict [66, 1] (w:1, o:144, a:1, s:1
% 1.04/1.72 , b:0),
% 1.04/1.72 class_Int_Oring__char__0 [74, 1] (w:1, o:145, a:1, s:1, b:0),
% 1.04/1.72 tc_Polynomial_Opoly [75, 1] (w:1, o:156, a:1, s:1, b:0),
% 1.04/1.72 class_Groups_Ozero [79, 1] (w:1, o:158, a:1, s:1, b:0),
% 1.04/1.72 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize [80, 2] (w:1, o:256
% 1.04/1.72 , a:1, s:1, b:0),
% 1.04/1.72 class_Groups_Ocomm__monoid__add [95, 1] (w:1, o:159, a:1, s:1, b:0),
% 1.04/1.72
% 1.04/1.72 class_Rings_Ocomm__semiring__1 [96, 1] (w:1, o:160, a:1, s:1, b:0),
% 1.04/1.72 c_Power_Opower__class_Opower [97, 1] (w:1, o:161, a:1, s:1, b:0),
% 1.04/1.72 v_c____ [100, 0] (w:1, o:87, a:1, s:1, b:0),
% 1.04/1.72 class_Groups_Omonoid__mult [101, 1] (w:1, o:163, a:1, s:1, b:0),
% 1.04/1.72 class_Power_Opower [102, 1] (w:1, o:169, a:1, s:1, b:0),
% 1.04/1.72 class_Rings_Osemiring__0 [103, 1] (w:1, o:174, a:1, s:1, b:0),
% 1.04/1.72 class_Rings_Omult__zero [104, 1] (w:1, o:182, a:1, s:1, b:0),
% 1.04/1.72 class_Rings_Ono__zero__divisors [105, 1] (w:1, o:183, a:1, s:1, b:0)
% 1.04/1.72 ,
% 1.04/1.72 class_Rings_Ozero__neq__one [106, 1] (w:1, o:184, a:1, s:1, b:0),
% 1.04/1.72 class_Rings_Olinordered__semidom [107, 1] (w:1, o:175, a:1, s:1, b:0)
% 1.04/1.72 ,
% 1.04/1.72 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct [
% 1.04/1.72 115, 1] (w:1, o:193, a:1, s:1, b:0),
% 1.04/1.72 class_Rings_Oring__1__no__zero__divisors [120, 1] (w:1, o:170, a:1
% 1.04/1.72 , s:1, b:0),
% 1.04/1.72 class_Groups_Ocomm__monoid__mult [121, 1] (w:1, o:194, a:1, s:1, b:0)
% 1.04/1.72 ,
% 1.04/1.72 c_Polynomial_Opcompose [122, 3] (w:1, o:290, a:1, s:1, b:0),
% 1.04/1.72 class_Groups_Olinordered__ab__group__add [123, 1] (w:1, o:162, a:1
% 1.04/1.72 , s:1, b:0),
% 1.04/1.72 class_Rings_Olinordered__idom [124, 1] (w:1, o:176, a:1, s:1, b:0),
% 1.04/1.72 class_Groups_Oordered__comm__monoid__add [125, 1] (w:1, o:195, a:1
% 1.04/1.72 , s:1, b:0),
% 1.04/1.72 class_Groups_Oab__semigroup__mult [126, 1] (w:1, o:196, a:1, s:1, b:0
% 1.04/1.72 ),
% 1.04/1.72 class_Groups_Ocancel__semigroup__add [127, 1] (w:1, o:197, a:1, s:1
% 1.04/1.72 , b:0),
% 1.04/1.72 class_Groups_Ocancel__ab__semigroup__add [128, 1] (w:1, o:198, a:1
% 1.04/1.72 , s:1, b:0),
% 1.04/1.72 class_Groups_Oab__semigroup__add [129, 1] (w:1, o:199, a:1, s:1, b:0)
% 1.04/1.72 ,
% 1.04/1.72 tc_Int_Oint [130, 0] (w:1, o:95, a:1, s:1, b:0),
% 1.04/1.72 class_Rings_Oring__no__zero__divisors [131, 1] (w:1, o:171, a:1, s:1
% 1.04/1.72 , b:0),
% 1.04/1.72 class_Groups_Omonoid__add [132, 1] (w:1, o:200, a:1, s:1, b:0),
% 1.04/1.72 class_Groups_Oordered__ab__semigroup__add__imp__le [133, 1] (w:1, o:
% 1.04/1.72 201, a:1, s:1, b:0),
% 1.04/1.72 class_Groups_Oordered__cancel__ab__semigroup__add [134, 1] (w:1, o:
% 1.04/1.72 202, a:1, s:1, b:0),
% 1.04/1.72 class_Rings_Osemiring [136, 1] (w:1, o:185, a:1, s:1, b:0),
% 1.04/1.72 class_Rings_Ocomm__semiring [137, 1] (w:1, o:186, a:1, s:1, b:0),
% 1.04/1.72 class_Rings_Olinordered__comm__semiring__strict [139, 1] (w:1, o:177
% 1.04/1.72 , a:1, s:1, b:0),
% 1.04/1.72 class_Rings_Olinordered__semiring__strict [140, 1] (w:1, o:178, a:1
% 1.04/1.72 , s:1, b:0),
% 1.04/1.72 tc_fun [141, 2] (w:1, o:266, a:1, s:1, b:0),
% 1.04/1.72 c_COMBB [142, 3] (w:1, o:291, a:1, s:1, b:0),
% 1.04/1.72 c_COMBK [143, 2] (w:1, o:267, a:1, s:1, b:0),
% 1.04/1.72 c_COMBC [144, 4] (w:1, o:334, a:1, s:1, b:0),
% 1.04/1.72 c_Polynomial_Opoly__rec [145, 5] (w:1, o:348, a:1, s:1, b:0),
% 1.04/1.72 c_Polynomial_Oorder [146, 3] (w:1, o:289, a:1, s:1, b:0),
% 1.04/1.72 c_Groups_Oone__class_Oone [149, 1] (w:1, o:140, a:1, s:1, b:0),
% 1.04/1.72 c_Polynomial_Opos__poly [150, 2] (w:1, o:268, a:1, s:1, b:0),
% 1.04/1.72 class_RealVector_Oreal__normed__algebra [152, 1] (w:1, o:187, a:1, s:
% 1.04/1.72 1, b:0),
% 1.04/1.72 class_Groups_Oone [157, 1] (w:1, o:203, a:1, s:1, b:0),
% 1.04/1.72 c_If [159, 1] (w:1, o:204, a:1, s:1, b:0),
% 1.04/1.72 c_fequal [160, 1] (w:1, o:205, a:1, s:1, b:0),
% 1.04/1.72 c_Power_Opower_Opower [164, 3] (w:1, o:292, a:1, s:1, b:0),
% 1.04/1.72 c_Polynomial_Osmult [165, 1] (w:1, o:206, a:1, s:1, b:0),
% 1.04/1.72 class_Rings_Ocomm__ring__1 [166, 1] (w:1, o:136, a:1, s:1, b:0),
% 1.04/1.72 c_Polynomial_Omonom [167, 3] (w:1, o:293, a:1, s:1, b:0),
% 1.04/1.72 c_Orderings_Oord__class_Oless__eq [168, 2] (w:1, o:253, a:1, s:1, b:0
% 1.04/1.72 ),
% 1.04/1.72 class_Rings_Olinordered__semiring__1__strict [170, 1] (w:1, o:179, a:
% 1.04/1.72 1, s:1, b:0),
% 1.04/1.72 c_Nat_Onat_Onat__size [172, 1] (w:1, o:207, a:1, s:1, b:0),
% 1.04/1.72 c_Polynomial_Ocoeff [173, 2] (w:1, o:269, a:1, s:1, b:0),
% 1.04/1.72 class_Groups_Oordered__ab__semigroup__add [177, 1] (w:1, o:208, a:1
% 1.04/1.72 , s:1, b:0),
% 1.04/1.72 class_Rings_Oordered__cancel__semiring [178, 1] (w:1, o:188, a:1, s:1
% 1.04/1.72 , b:0),
% 1.04/1.72 class_Rings_Oordered__ring [179, 1] (w:1, o:189, a:1, s:1, b:0),
% 1.04/1.72 class_Rings_Oordered__semiring [180, 1] (w:1, o:190, a:1, s:1, b:0),
% 1.04/1.72
% 1.04/1.72 class_Rings_Oordered__comm__semiring [181, 1] (w:1, o:191, a:1, s:1
% 1.04/1.72 , b:0),
% 1.04/1.72 class_Rings_Olinordered__semiring [182, 1] (w:1, o:180, a:1, s:1, b:0
% 1.04/1.72 ),
% 1.04/1.72 class_Rings_Olinordered__semiring__1 [185, 1] (w:1, o:181, a:1, s:1
% 1.04/1.72 , b:0),
% 1.04/1.72 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly [189, 3] (w:
% 1.04/1.72 1, o:294, a:1, s:1, b:0),
% 1.04/1.72 c_COMBS [190, 3] (w:1, o:295, a:1, s:1, b:0),
% 1.04/1.72 class_Orderings_Opreorder [192, 1] (w:1, o:166, a:1, s:1, b:0),
% 1.04/1.72 c_Polynomial_Osynthetic__div [193, 3] (w:1, o:296, a:1, s:1, b:0),
% 1.04/1.72 c_Nat_Osize__class_Osize [194, 2] (w:1, o:250, a:1, s:1, b:0),
% 1.04/1.72 class_Orderings_Olinorder [195, 1] (w:1, o:167, a:1, s:1, b:0),
% 1.04/1.72 class_Orderings_Oord [196, 1] (w:1, o:164, a:1, s:1, b:0),
% 1.04/1.72 class_Orderings_Oorder [197, 1] (w:1, o:165, a:1, s:1, b:0),
% 1.04/1.72 c_Groups_Ouminus__class_Ouminus [198, 1] (w:1, o:209, a:1, s:1, b:0)
% 1.04/1.72 ,
% 1.04/1.72 c_Polynomial_OAbs__poly [201, 2] (w:1, o:270, a:1, s:1, b:0),
% 1.04/1.72 class_Groups_Ogroup__add [202, 1] (w:1, o:210, a:1, s:1, b:0),
% 1.04/1.72 class_Groups_Oordered__ab__group__add [203, 1] (w:1, o:211, a:1, s:1
% 1.04/1.72 , b:0),
% 1.04/1.72 class_Rings_Oring [204, 1] (w:1, o:172, a:1, s:1, b:0),
% 1.04/1.72 class_Groups_Oab__group__add [205, 1] (w:1, o:212, a:1, s:1, b:0),
% 2.76/3.18 class_Rings_Ocomm__ring [206, 1] (w:1, o:137, a:1, s:1, b:0),
% 2.76/3.18 class_Rings_Oring__1 [207, 1] (w:1, o:173, a:1, s:1, b:0),
% 2.76/3.18 tc_HOL_Obool [208, 0] (w:1, o:94, a:1, s:1, b:0),
% 2.76/3.18 c_Rings_Odvd__class_Odvd [209, 1] (w:1, o:213, a:1, s:1, b:0),
% 2.76/3.18 class_Lattices_Oboolean__algebra [210, 1] (w:1, o:215, a:1, s:1, b:0)
% 2.76/3.18 ,
% 2.76/3.18 class_Rings_Odvd [211, 1] (w:1, o:192, a:1, s:1, b:0),
% 2.76/3.18 class_Fields_Ofield [212, 1] (w:1, o:157, a:1, s:1, b:0),
% 2.76/3.18 class_Lattices_Oab__semigroup__idem__mult [213, 1] (w:1, o:214, a:1
% 2.76/3.18 , s:1, b:0),
% 2.76/3.18 class_Groups_Ouminus [215, 1] (w:1, o:216, a:1, s:1, b:0),
% 2.76/3.18 c_fNot [216, 0] (w:1, o:109, a:1, s:1, b:0),
% 2.76/3.18 c_Orderings_Oord__class_OLeast [217, 2] (w:1, o:254, a:1, s:1, b:0),
% 2.76/3.18
% 2.76/3.18 c_Nat_Onat_Onat__case [218, 3] (w:1, o:297, a:1, s:1, b:0),
% 2.76/3.18 class_Orderings_Owellorder [220, 1] (w:1, o:168, a:1, s:1, b:0),
% 2.76/3.18 c_fFalse [224, 0] (w:1, o:110, a:1, s:1, b:0),
% 2.76/3.18 c_fconj [225, 0] (w:1, o:111, a:1, s:1, b:0),
% 2.76/3.18 c_Orderings_Oorder_Ostrict__mono [226, 4] (w:1, o:336, a:1, s:1, b:0)
% 2.76/3.18 ,
% 2.76/3.18 c_Orderings_Oorder_Omono [227, 4] (w:1, o:337, a:1, s:1, b:0),
% 2.76/3.18 c_Groups_Ominus__class_Ominus [228, 1] (w:1, o:217, a:1, s:1, b:0),
% 2.76/3.18 c_Int_Onat [229, 0] (w:1, o:112, a:1, s:1, b:0),
% 2.76/3.18 class_Groups_Ominus [231, 1] (w:1, o:218, a:1, s:1, b:0),
% 2.76/3.18 c_COMBI [236, 1] (w:1, o:219, a:1, s:1, b:0),
% 2.76/3.18 c_Int_Onat__aux [240, 2] (w:1, o:271, a:1, s:1, b:0),
% 2.76/3.18 c_Nat__Transfer_Otransfer__morphism [241, 4] (w:1, o:335, a:1, s:1
% 2.76/3.18 , b:0),
% 2.76/3.18 c_Nat__Transfer_Otsub [242, 2] (w:1, o:251, a:1, s:1, b:0),
% 2.76/3.18 c_Divides_Odiv__class_Odiv [243, 3] (w:1, o:298, a:1, s:1, b:0),
% 2.76/3.18 class_Divides_Osemiring__div [244, 1] (w:1, o:221, a:1, s:1, b:0),
% 2.76/3.18 class_Divides_Oring__div [245, 1] (w:1, o:220, a:1, s:1, b:0),
% 2.76/3.18 c_SMT_Oz3div [249, 2] (w:1, o:272, a:1, s:1, b:0),
% 2.76/3.18 class_Groups_Ocancel__comm__monoid__add [251, 1] (w:1, o:222, a:1, s:
% 2.76/3.18 1, b:0),
% 2.76/3.18 v_a [259, 0] (w:1, o:125, a:1, s:1, b:0),
% 2.76/3.18 v_q [260, 0] (w:1, o:126, a:1, s:1, b:0),
% 2.76/3.18 v_k [261, 0] (w:1, o:127, a:1, s:1, b:0),
% 2.76/3.18 alpha1 [262, 2] (w:1, o:273, a:1, s:1, b:1),
% 2.76/3.18 alpha2 [263, 2] (w:1, o:282, a:1, s:1, b:1),
% 2.76/3.18 alpha3 [264, 2] (w:1, o:284, a:1, s:1, b:1),
% 2.76/3.18 alpha4 [265, 4] (w:1, o:340, a:1, s:1, b:1),
% 2.76/3.18 alpha5 [266, 4] (w:1, o:343, a:1, s:1, b:1),
% 2.76/3.18 alpha6 [267, 3] (w:1, o:299, a:1, s:1, b:1),
% 2.76/3.18 alpha7 [268, 3] (w:1, o:300, a:1, s:1, b:1),
% 2.76/3.18 alpha8 [269, 3] (w:1, o:301, a:1, s:1, b:1),
% 2.76/3.18 alpha9 [270, 3] (w:1, o:302, a:1, s:1, b:1),
% 2.76/3.18 alpha10 [271, 2] (w:1, o:274, a:1, s:1, b:1),
% 2.76/3.18 alpha11 [272, 2] (w:1, o:275, a:1, s:1, b:1),
% 2.76/3.18 alpha12 [273, 3] (w:1, o:303, a:1, s:1, b:1),
% 2.76/3.18 alpha13 [274, 3] (w:1, o:304, a:1, s:1, b:1),
% 2.76/3.18 alpha14 [275, 2] (w:1, o:276, a:1, s:1, b:1),
% 2.76/3.18 alpha15 [276, 2] (w:1, o:277, a:1, s:1, b:1),
% 2.76/3.18 alpha16 [277, 2] (w:1, o:278, a:1, s:1, b:1),
% 2.76/3.18 alpha17 [278, 2] (w:1, o:279, a:1, s:1, b:1),
% 2.76/3.18 alpha18 [279, 2] (w:1, o:280, a:1, s:1, b:1),
% 2.76/3.18 alpha19 [280, 2] (w:1, o:281, a:1, s:1, b:1),
% 2.76/3.18 alpha20 [281, 4] (w:1, o:344, a:1, s:1, b:1),
% 2.76/3.18 alpha21 [282, 4] (w:1, o:345, a:1, s:1, b:1),
% 2.76/3.18 alpha22 [283, 3] (w:1, o:305, a:1, s:1, b:1),
% 2.76/3.18 alpha23 [284, 3] (w:1, o:306, a:1, s:1, b:1),
% 2.76/3.18 alpha24 [285, 4] (w:1, o:346, a:1, s:1, b:1),
% 2.76/3.18 alpha25 [286, 3] (w:1, o:307, a:1, s:1, b:1),
% 2.76/3.18 alpha26 [287, 3] (w:1, o:308, a:1, s:1, b:1),
% 2.76/3.18 alpha27 [288, 2] (w:1, o:283, a:1, s:1, b:1),
% 2.76/3.18 alpha28 [289, 3] (w:1, o:309, a:1, s:1, b:1),
% 2.76/3.18 alpha29 [290, 3] (w:1, o:310, a:1, s:1, b:1),
% 2.76/3.18 alpha30 [291, 3] (w:1, o:311, a:1, s:1, b:1),
% 2.76/3.18 alpha31 [292, 2] (w:1, o:285, a:1, s:1, b:1),
% 2.76/3.18 alpha32 [293, 3] (w:1, o:312, a:1, s:1, b:1),
% 2.76/3.18 alpha33 [294, 3] (w:1, o:313, a:1, s:1, b:1),
% 2.76/3.18 alpha34 [295, 4] (w:1, o:338, a:1, s:1, b:1),
% 2.76/3.18 alpha35 [296, 3] (w:1, o:314, a:1, s:1, b:1),
% 2.76/3.18 alpha36 [297, 3] (w:1, o:315, a:1, s:1, b:1),
% 2.76/3.18 alpha37 [298, 4] (w:1, o:339, a:1, s:1, b:1),
% 2.76/3.18 alpha38 [299, 3] (w:1, o:316, a:1, s:1, b:1),
% 22.16/22.55 alpha39 [300, 3] (w:1, o:317, a:1, s:1, b:1),
% 22.16/22.55 alpha40 [301, 3] (w:1, o:318, a:1, s:1, b:1),
% 22.16/22.55 alpha41 [302, 4] (w:1, o:341, a:1, s:1, b:1),
% 22.16/22.55 alpha42 [303, 4] (w:1, o:342, a:1, s:1, b:1),
% 22.16/22.55 alpha43 [304, 3] (w:1, o:319, a:1, s:1, b:1),
% 22.16/22.55 alpha44 [305, 1] (w:1, o:223, a:1, s:1, b:1),
% 22.16/22.55 alpha45 [306, 2] (w:1, o:286, a:1, s:1, b:1),
% 22.16/22.55 alpha46 [307, 2] (w:1, o:287, a:1, s:1, b:1),
% 22.16/22.55 alpha47 [308, 1] (w:1, o:224, a:1, s:1, b:1),
% 22.16/22.55 alpha48 [309, 3] (w:1, o:320, a:1, s:1, b:1),
% 22.16/22.55 skol1 [310, 2] (w:1, o:257, a:1, s:1, b:1),
% 22.16/22.55 skol2 [311, 0] (w:1, o:14, a:1, s:1, b:1),
% 22.16/22.55 skol3 [312, 0] (w:1, o:15, a:1, s:1, b:1),
% 22.16/22.55 skol4 [313, 2] (w:1, o:259, a:1, s:1, b:1),
% 22.16/22.55 skol5 [314, 1] (w:1, o:146, a:1, s:1, b:1),
% 22.16/22.55 skol6 [315, 2] (w:1, o:260, a:1, s:1, b:1),
% 22.16/22.55 skol7 [316, 1] (w:1, o:147, a:1, s:1, b:1),
% 22.16/22.55 skol8 [317, 0] (w:1, o:16, a:1, s:1, b:1),
% 22.16/22.55 skol9 [318, 1] (w:1, o:148, a:1, s:1, b:1),
% 22.16/22.55 skol10 [319, 0] (w:1, o:13, a:1, s:1, b:1),
% 22.16/22.55 skol11 [320, 3] (w:1, o:321, a:1, s:1, b:1),
% 22.16/22.55 skol12 [321, 2] (w:1, o:261, a:1, s:1, b:1),
% 22.16/22.55 skol13 [322, 3] (w:1, o:322, a:1, s:1, b:1),
% 22.16/22.55 skol14 [323, 2] (w:1, o:262, a:1, s:1, b:1),
% 22.16/22.55 skol15 [324, 2] (w:1, o:263, a:1, s:1, b:1),
% 22.16/22.55 skol16 [325, 3] (w:1, o:323, a:1, s:1, b:1),
% 22.16/22.55 skol17 [326, 2] (w:1, o:264, a:1, s:1, b:1),
% 22.16/22.55 skol18 [327, 2] (w:1, o:265, a:1, s:1, b:1),
% 22.16/22.55 skol19 [328, 1] (w:1, o:149, a:1, s:1, b:1),
% 22.16/22.55 skol20 [329, 1] (w:1, o:150, a:1, s:1, b:1),
% 22.16/22.55 skol21 [330, 3] (w:1, o:324, a:1, s:1, b:1),
% 22.16/22.55 skol22 [331, 3] (w:1, o:325, a:1, s:1, b:1),
% 22.16/22.55 skol23 [332, 3] (w:1, o:326, a:1, s:1, b:1),
% 22.16/22.55 skol24 [333, 3] (w:1, o:327, a:1, s:1, b:1),
% 22.16/22.55 skol25 [334, 3] (w:1, o:328, a:1, s:1, b:1),
% 22.16/22.55 skol26 [335, 3] (w:1, o:329, a:1, s:1, b:1),
% 22.16/22.55 skol27 [336, 3] (w:1, o:330, a:1, s:1, b:1),
% 22.16/22.55 skol28 [337, 4] (w:1, o:347, a:1, s:1, b:1),
% 22.16/22.55 skol29 [338, 3] (w:1, o:331, a:1, s:1, b:1),
% 22.16/22.55 skol30 [339, 1] (w:1, o:151, a:1, s:1, b:1),
% 22.16/22.55 skol31 [340, 1] (w:1, o:152, a:1, s:1, b:1),
% 22.16/22.55 skol32 [341, 1] (w:1, o:153, a:1, s:1, b:1),
% 22.16/22.55 skol33 [342, 0] (w:1, o:17, a:1, s:1, b:1),
% 22.16/22.55 skol34 [343, 3] (w:1, o:332, a:1, s:1, b:1),
% 22.16/22.55 skol35 [344, 2] (w:1, o:258, a:1, s:1, b:1),
% 22.16/22.55 skol36 [345, 1] (w:1, o:154, a:1, s:1, b:1),
% 22.16/22.55 skol37 [346, 1] (w:1, o:155, a:1, s:1, b:1),
% 22.16/22.55 skol38 [347, 3] (w:1, o:333, a:1, s:1, b:1),
% 22.16/22.55 skol39 [348, 0] (w:1, o:18, a:1, s:1, b:1).
% 22.16/22.55
% 22.16/22.55
% 22.16/22.55 Starting Search:
% 22.16/22.55
% 22.16/22.55 *** allocated 170857 integers for clauses
% 22.16/22.55 Resimplifying inuse:
% 22.16/22.55 Done
% 22.16/22.55
% 22.16/22.55
% 22.16/22.55 Intermediate Status:
% 22.16/22.55 Generated: 3084
% 22.16/22.55 Kept: 2073
% 22.16/22.55 Inuse: 64
% 22.16/22.55 Deleted: 7
% 22.16/22.55 Deletedinuse: 0
% 22.16/22.55
% 22.16/22.55 *** allocated 256285 integers for clauses
% 22.16/22.55 Resimplifying inuse:
% 22.16/22.55 Done
% 22.16/22.55
% 22.16/22.55 Resimplifying inuse:
% 22.16/22.55 Done
% 22.16/22.55
% 22.16/22.55 *** allocated 256285 integers for termspace/termends
% 22.16/22.55 *** allocated 384427 integers for clauses
% 22.16/22.55
% 22.16/22.55 Intermediate Status:
% 22.16/22.55 Generated: 14068
% 22.16/22.55 Kept: 4186
% 22.16/22.55 Inuse: 143
% 22.16/22.55 Deleted: 13
% 22.16/22.55 Deletedinuse: 0
% 22.16/22.55
% 22.16/22.55 Resimplifying inuse:
% 22.16/22.55 Done
% 22.16/22.55
% 22.16/22.55 Resimplifying inuse:
% 22.16/22.55 Done
% 22.16/22.55
% 22.16/22.55 *** allocated 384427 integers for termspace/termends
% 22.16/22.55 *** allocated 576640 integers for clauses
% 22.16/22.55
% 22.16/22.55 Intermediate Status:
% 22.16/22.55 Generated: 22633
% 22.16/22.55 Kept: 6666
% 22.16/22.55 Inuse: 260
% 22.16/22.55 Deleted: 21
% 22.16/22.55 Deletedinuse: 0
% 22.16/22.55
% 22.16/22.55 Resimplifying inuse:
% 22.16/22.55 Done
% 22.16/22.55
% 22.16/22.55 Resimplifying inuse:
% 22.16/22.55 Done
% 22.16/22.55
% 22.16/22.55
% 22.16/22.55 Intermediate Status:
% 22.16/22.55 Generated: 28311
% 22.16/22.55 Kept: 8671
% 22.16/22.55 Inuse: 295
% 22.16/22.55 Deleted: 22
% 22.16/22.55 Deletedinuse: 0
% 22.16/22.55
% 22.16/22.55 Resimplifying inuse:
% 22.16/22.55 Done
% 22.16/22.55
% 22.16/22.55
% 22.16/22.55 Intermediate Status:
% 22.16/22.55 Generated: 37228
% 22.16/22.55 Kept: 10706
% 22.16/22.55 Inuse: 339
% 22.16/22.55 Deleted: 26
% 22.16/22.55 Deletedinuse: 4
% 22.16/22.55
% 22.16/22.55 *** allocated 864960 integers for clauses
% 22.16/22.55 Resimplifying inuse:
% 22.16/22.55 Done
% 22.16/22.55
% 22.16/22.55 *** allocated 576640 integers for termspace/termends
% 22.16/22.55 Resimplifying inuse:
% 22.16/22.55 Done
% 22.16/22.55
% 22.16/22.55
% 22.16/22.55 Intermediate Status:
% 22.16/22.55 Generated: 50203
% 22.16/22.55 Kept: 12877
% 22.16/22.55 Inuse: 374
% 22.16/22.55 Deleted: 26
% 22.16/22.55 Deletedinuse: 4
% 22.16/22.55
% 22.16/22.55 Resimplifying inuse:
% 22.16/22.55 Done
% 22.16/22.55
% 22.16/22.55
% 22.16/22.55 Intermediate Status:
% 22.16/22.55 Generated: 57494
% 22.16/22.55 Kept: 14980
% 22.16/22.55 Inuse: 399
% 22.16/22.55 Deleted: 26
% 22.16/22.55 Deletedinuse: 4
% 22.16/22.55
% 22.16/22.55 Resimplifying inuse:
% 22.16/22.55 Done
% 22.16/22.55
% 22.16/22.55 Resimplifying inuse:
% 70.19/70.56 Done
% 70.19/70.56
% 70.19/70.56 *** allocated 1297440 integers for clauses
% 70.19/70.56
% 70.19/70.56 Intermediate Status:
% 70.19/70.56 Generated: 66213
% 70.19/70.56 Kept: 17568
% 70.19/70.56 Inuse: 429
% 70.19/70.56 Deleted: 27
% 70.19/70.56 Deletedinuse: 5
% 70.19/70.56
% 70.19/70.56 Resimplifying inuse:
% 70.19/70.56 Done
% 70.19/70.56
% 70.19/70.56 *** allocated 864960 integers for termspace/termends
% 70.19/70.56 Resimplifying inuse:
% 70.19/70.56 Done
% 70.19/70.56
% 70.19/70.56
% 70.19/70.56 Intermediate Status:
% 70.19/70.56 Generated: 71135
% 70.19/70.56 Kept: 19568
% 70.19/70.56 Inuse: 455
% 70.19/70.56 Deleted: 27
% 70.19/70.56 Deletedinuse: 5
% 70.19/70.56
% 70.19/70.56 Resimplifying inuse:
% 70.19/70.56 Done
% 70.19/70.56
% 70.19/70.56 Resimplifying clauses:
% 70.19/70.56 Done
% 70.19/70.56
% 70.19/70.56
% 70.19/70.56 Intermediate Status:
% 70.19/70.56 Generated: 75791
% 70.19/70.56 Kept: 21820
% 70.19/70.56 Inuse: 464
% 70.19/70.56 Deleted: 469
% 70.19/70.56 Deletedinuse: 5
% 70.19/70.56
% 70.19/70.56 Resimplifying inuse:
% 70.19/70.56 Done
% 70.19/70.56
% 70.19/70.56 Resimplifying inuse:
% 70.19/70.56 Done
% 70.19/70.56
% 70.19/70.56
% 70.19/70.56 Intermediate Status:
% 70.19/70.56 Generated: 83438
% 70.19/70.56 Kept: 24191
% 70.19/70.56 Inuse: 499
% 70.19/70.56 Deleted: 469
% 70.19/70.56 Deletedinuse: 5
% 70.19/70.56
% 70.19/70.56 Resimplifying inuse:
% 70.19/70.56 Done
% 70.19/70.56
% 70.19/70.56 Resimplifying inuse:
% 70.19/70.56 Done
% 70.19/70.56
% 70.19/70.56
% 70.19/70.56 Intermediate Status:
% 70.19/70.56 Generated: 89092
% 70.19/70.56 Kept: 26203
% 70.19/70.56 Inuse: 528
% 70.19/70.56 Deleted: 471
% 70.19/70.56 Deletedinuse: 7
% 70.19/70.56
% 70.19/70.56 Resimplifying inuse:
% 70.19/70.56 Done
% 70.19/70.56
% 70.19/70.56 Resimplifying inuse:
% 70.19/70.56 Done
% 70.19/70.56
% 70.19/70.56 *** allocated 1946160 integers for clauses
% 70.19/70.56
% 70.19/70.56 Intermediate Status:
% 70.19/70.56 Generated: 95304
% 70.19/70.56 Kept: 28407
% 70.19/70.56 Inuse: 544
% 70.19/70.56 Deleted: 471
% 70.19/70.56 Deletedinuse: 7
% 70.19/70.56
% 70.19/70.56 Resimplifying inuse:
% 70.19/70.56 Done
% 70.19/70.56
% 70.19/70.56 *** allocated 1297440 integers for termspace/termends
% 70.19/70.56 Resimplifying inuse:
% 70.19/70.56 Done
% 70.19/70.56
% 70.19/70.56
% 70.19/70.56 Intermediate Status:
% 70.19/70.56 Generated: 104492
% 70.19/70.56 Kept: 31352
% 70.19/70.56 Inuse: 574
% 70.19/70.56 Deleted: 471
% 70.19/70.56 Deletedinuse: 7
% 70.19/70.56
% 70.19/70.56 Resimplifying inuse:
% 70.19/70.56 Done
% 70.19/70.56
% 70.19/70.56 Resimplifying inuse:
% 70.19/70.56 Done
% 70.19/70.56
% 70.19/70.56
% 70.19/70.56 Intermediate Status:
% 70.19/70.56 Generated: 113136
% 70.19/70.56 Kept: 34016
% 70.19/70.56 Inuse: 589
% 70.19/70.56 Deleted: 471
% 70.19/70.56 Deletedinuse: 7
% 70.19/70.56
% 70.19/70.56 Resimplifying inuse:
% 70.19/70.56 Done
% 70.19/70.56
% 70.19/70.56 Resimplifying inuse:
% 70.19/70.56 Done
% 70.19/70.56
% 70.19/70.56
% 70.19/70.56 Intermediate Status:
% 70.19/70.56 Generated: 120244
% 70.19/70.56 Kept: 36017
% 70.19/70.56 Inuse: 624
% 70.19/70.56 Deleted: 471
% 70.19/70.56 Deletedinuse: 7
% 70.19/70.56
% 70.19/70.56 Resimplifying inuse:
% 70.19/70.56 Done
% 70.19/70.56
% 70.19/70.56 Resimplifying inuse:
% 70.19/70.56 Done
% 70.19/70.56
% 70.19/70.56
% 70.19/70.56 Intermediate Status:
% 70.19/70.56 Generated: 125821
% 70.19/70.56 Kept: 39192
% 70.19/70.56 Inuse: 634
% 70.19/70.56 Deleted: 472
% 70.19/70.56 Deletedinuse: 8
% 70.19/70.56
% 70.19/70.56 Resimplifying inuse:
% 70.19/70.56 Done
% 70.19/70.56
% 70.19/70.56 Resimplifying inuse:
% 70.19/70.56 Done
% 70.19/70.56
% 70.19/70.56 Resimplifying clauses:
% 70.19/70.56 Done
% 70.19/70.56
% 70.19/70.56
% 70.19/70.56 Intermediate Status:
% 70.19/70.56 Generated: 131359
% 70.19/70.56 Kept: 42446
% 70.19/70.56 Inuse: 644
% 70.19/70.56 Deleted: 626
% 70.19/70.56 Deletedinuse: 8
% 70.19/70.56
% 70.19/70.56 Resimplifying inuse:
% 70.19/70.56 Done
% 70.19/70.56
% 70.19/70.56 *** allocated 2919240 integers for clauses
% 70.19/70.56 Resimplifying inuse:
% 70.19/70.56 Done
% 70.19/70.56
% 70.19/70.56
% 70.19/70.56 Intermediate Status:
% 70.19/70.56 Generated: 137858
% 70.19/70.56 Kept: 44468
% 70.19/70.56 Inuse: 669
% 70.19/70.56 Deleted: 626
% 70.19/70.56 Deletedinuse: 8
% 70.19/70.56
% 70.19/70.56 Resimplifying inuse:
% 70.19/70.56 Done
% 70.19/70.56
% 70.19/70.56 Resimplifying inuse:
% 70.19/70.56 Done
% 70.19/70.56
% 70.19/70.56 *** allocated 1946160 integers for termspace/termends
% 70.19/70.56
% 70.19/70.56 Intermediate Status:
% 70.19/70.56 Generated: 148047
% 70.19/70.56 Kept: 46845
% 70.19/70.56 Inuse: 679
% 70.19/70.56 Deleted: 626
% 70.19/70.56 Deletedinuse: 8
% 70.19/70.56
% 70.19/70.56 Resimplifying inuse:
% 70.19/70.56 Done
% 70.19/70.56
% 70.19/70.56 Resimplifying inuse:
% 70.19/70.56 Done
% 70.19/70.56
% 70.19/70.56
% 70.19/70.56 Intermediate Status:
% 70.19/70.56 Generated: 154669
% 70.19/70.56 Kept: 48852
% 70.19/70.56 Inuse: 704
% 70.19/70.56 Deleted: 626
% 70.19/70.56 Deletedinuse: 8
% 70.19/70.56
% 70.19/70.56 Resimplifying inuse:
% 70.19/70.56 Done
% 70.19/70.56
% 70.19/70.56 Resimplifying inuse:
% 70.19/70.56 Done
% 70.19/70.56
% 70.19/70.56
% 70.19/70.56 Intermediate Status:
% 70.19/70.56 Generated: 164217
% 70.19/70.56 Kept: 51426
% 70.19/70.56 Inuse: 724
% 70.19/70.56 Deleted: 626
% 70.19/70.56 Deletedinuse: 8
% 70.19/70.56
% 70.19/70.56 Resimplifying inuse:
% 70.19/70.56 Done
% 70.19/70.56
% 70.19/70.56 Resimplifying inuse:
% 70.19/70.56 Done
% 70.19/70.56
% 70.19/70.56
% 70.19/70.56 Intermediate Status:
% 70.19/70.56 Generated: 176118
% 70.19/70.56 Kept: 54419
% 70.19/70.56 Inuse: 746
% 70.19/70.56 Deleted: 629
% 70.19/70.56 Deletedinuse: 10
% 70.19/70.56
% 70.19/70.56 Resimplifying inuse:
% 70.19/70.56 Done
% 70.19/70.56
% 70.19/70.56 Resimplifying inuse:
% 70.19/70.56 Done
% 70.19/70.56
% 70.19/70.56
% 70.19/70.56 Intermediate Status:
% 70.19/70.56 Generated: 188488
% 70.19/70.56 Kept: 56592
% 70.19/70.56 Inuse: 788
% 70.19/70.56 Deleted: 629
% 70.19/70.56 Deletedinuse: 10
% 70.19/70.56
% 70.19/70.56 Resimplifying inuse:
% 70.19/70.56 Done
% 70.19/70.56
% 70.19/70.56
% 70.19/70.56 Intermediate Status:
% 70.19/70.56 Generated: 195329
% 70.19/70.56 Kept: 59107
% 70.19/70.56 Inuse: 813
% 70.19/70.56 Deleted: 629
% 70.19/70.56 Deletedinuse: 10
% 70.19/70.56
% 70.19/70.56 Resimplifying inuse:
% 70.19/70.56 Done
% 70.19/70.56
% 70.19/70.56
% 70.19/70.56 Intermediate Status:
% 70.19/70.56 Generated: 228756
% 70.19/70.56 Kept: 62777
% 70.19/70.56 Inuse: 828
% 70.19/70.56 Deleted: 629
% 70.19/70.56 Deletedinuse: 10
% 70.19/70.56
% 70.19/70.56 Resimplifying inuse:
% 70.19/70.56 Done
% 70.19/70.56
% 70.19/70.56 Resimplifying clauses:
% 70.19/70.56 Done
% 70.19/70.56
% 70.19/70.56 *** allocated 4378860 integers for clauses
% 70.19/70.56 Resimplifying inuse:
% 70.19/70.56 Done
% 70.19/70.56
% 70.19/70.56 *** allocated 2919240 integers for termspace/termends
% 70.19/70.56
% 70.19/70.56 Intermediate Status:
% 70.19/70.56 Generated: 240448
% 70.19/70.56 Kept: 65664
% 70.19/70.56 Inuse: 848
% 70.19/70.56 Deleted: 861
% 70.19/70.56 Deletedinuse: 10
% 70.19/70.56
% 70.19/70.56 Resimplifying inuse:
% 70.19/70.56 Done
% 70.19/70.56
% 70.19/70.56
% 70.19/70.56 Intermediate Status:
% 70.19/70.56 Generated: 271392
% 70.19/70.56 Kept: 68549
% 70.19/70.56 Inuse: 863
% 70.19/70.56 Deleted: 861
% 70.19/70.56 Deletedinuse: 10
% 70.19/70.56
% 70.19/70.56 Resimplifying inuse:
% 70.19/70.56 Done
% 70.19/70.56
% 70.19/70.56 Resimplifying inuse:
% 70.19/70.56 Done
% 70.19/70.56
% 70.19/70.56
% 70.19/70.56 Intermediate Status:
% 70.19/70.56 Generated: 278490
% 70.19/70.56 Kept: 70885
% 70.19/70.56 Inuse: 888
% 70.19/70.56 Deleted: 861
% 70.19/70.56 Deletedinuse: 10
% 70.19/70.56
% 70.19/70.56 Resimplifying inuse:
% 158.79/159.18 Done
% 158.79/159.18
% 158.79/159.18 Resimplifying inuse:
% 158.79/159.18 Done
% 158.79/159.18
% 158.79/159.18
% 158.79/159.18 Intermediate Status:
% 158.79/159.18 Generated: 286613
% 158.79/159.18 Kept: 73321
% 158.79/159.18 Inuse: 913
% 158.79/159.18 Deleted: 861
% 158.79/159.18 Deletedinuse: 10
% 158.79/159.18
% 158.79/159.18 Resimplifying inuse:
% 158.79/159.18 Done
% 158.79/159.18
% 158.79/159.18 Resimplifying inuse:
% 158.79/159.18 Done
% 158.79/159.18
% 158.79/159.18
% 158.79/159.18 Intermediate Status:
% 158.79/159.18 Generated: 297995
% 158.79/159.18 Kept: 75330
% 158.79/159.18 Inuse: 934
% 158.79/159.18 Deleted: 861
% 158.79/159.18 Deletedinuse: 10
% 158.79/159.18
% 158.79/159.18 Resimplifying inuse:
% 158.79/159.18 Done
% 158.79/159.18
% 158.79/159.18
% 158.79/159.18 Intermediate Status:
% 158.79/159.18 Generated: 315566
% 158.79/159.18 Kept: 78011
% 158.79/159.18 Inuse: 943
% 158.79/159.18 Deleted: 861
% 158.79/159.18 Deletedinuse: 10
% 158.79/159.18
% 158.79/159.18 Resimplifying inuse:
% 158.79/159.18 Done
% 158.79/159.18
% 158.79/159.18 Resimplifying inuse:
% 158.79/159.18 Done
% 158.79/159.18
% 158.79/159.18
% 158.79/159.18 Intermediate Status:
% 158.79/159.18 Generated: 328886
% 158.79/159.18 Kept: 80240
% 158.79/159.18 Inuse: 958
% 158.79/159.18 Deleted: 861
% 158.79/159.18 Deletedinuse: 10
% 158.79/159.18
% 158.79/159.18 Resimplifying inuse:
% 158.79/159.18 Done
% 158.79/159.18
% 158.79/159.18 Resimplifying inuse:
% 158.79/159.18 Done
% 158.79/159.18
% 158.79/159.18
% 158.79/159.18 Intermediate Status:
% 158.79/159.18 Generated: 352420
% 158.79/159.18 Kept: 84150
% 158.79/159.18 Inuse: 978
% 158.79/159.18 Deleted: 861
% 158.79/159.18 Deletedinuse: 10
% 158.79/159.18
% 158.79/159.18 Resimplifying inuse:
% 158.79/159.18 Done
% 158.79/159.18
% 158.79/159.18 Resimplifying clauses:
% 158.79/159.18 Done
% 158.79/159.18
% 158.79/159.18
% 158.79/159.18 Intermediate Status:
% 158.79/159.18 Generated: 370820
% 158.79/159.18 Kept: 86660
% 158.79/159.18 Inuse: 983
% 158.79/159.18 Deleted: 899
% 158.79/159.18 Deletedinuse: 10
% 158.79/159.18
% 158.79/159.18 Resimplifying inuse:
% 158.79/159.18 Done
% 158.79/159.18
% 158.79/159.18 Resimplifying inuse:
% 158.79/159.18 Done
% 158.79/159.18
% 158.79/159.18
% 158.79/159.18 Intermediate Status:
% 158.79/159.18 Generated: 383454
% 158.79/159.18 Kept: 89455
% 158.79/159.18 Inuse: 1008
% 158.79/159.18 Deleted: 899
% 158.79/159.18 Deletedinuse: 10
% 158.79/159.18
% 158.79/159.18 Resimplifying inuse:
% 158.79/159.18 Done
% 158.79/159.18
% 158.79/159.18 Resimplifying inuse:
% 158.79/159.18 Done
% 158.79/159.18
% 158.79/159.18
% 158.79/159.18 Intermediate Status:
% 158.79/159.18 Generated: 393695
% 158.79/159.18 Kept: 91510
% 158.79/159.18 Inuse: 1038
% 158.79/159.18 Deleted: 899
% 158.79/159.18 Deletedinuse: 10
% 158.79/159.18
% 158.79/159.18 *** allocated 4378860 integers for termspace/termends
% 158.79/159.18 Resimplifying inuse:
% 158.79/159.18 Done
% 158.79/159.18
% 158.79/159.18
% 158.79/159.18 Intermediate Status:
% 158.79/159.18 Generated: 400506
% 158.79/159.18 Kept: 93548
% 158.79/159.18 Inuse: 1053
% 158.79/159.18 Deleted: 899
% 158.79/159.18 Deletedinuse: 10
% 158.79/159.18
% 158.79/159.18 Resimplifying inuse:
% 158.79/159.18 Done
% 158.79/159.18
% 158.79/159.18 Resimplifying inuse:
% 158.79/159.18 Done
% 158.79/159.18
% 158.79/159.18
% 158.79/159.18 Intermediate Status:
% 158.79/159.18 Generated: 409314
% 158.79/159.18 Kept: 96079
% 158.79/159.18 Inuse: 1073
% 158.79/159.18 Deleted: 899
% 158.79/159.18 Deletedinuse: 10
% 158.79/159.18
% 158.79/159.18 Resimplifying inuse:
% 158.79/159.18 Done
% 158.79/159.18
% 158.79/159.18 Resimplifying inuse:
% 158.79/159.18 Done
% 158.79/159.18
% 158.79/159.18 *** allocated 6568290 integers for clauses
% 158.79/159.18
% 158.79/159.18 Intermediate Status:
% 158.79/159.18 Generated: 417628
% 158.79/159.18 Kept: 98208
% 158.79/159.18 Inuse: 1088
% 158.79/159.18 Deleted: 899
% 158.79/159.18 Deletedinuse: 10
% 158.79/159.18
% 158.79/159.18 Resimplifying inuse:
% 158.79/159.18 Done
% 158.79/159.18
% 158.79/159.18
% 158.79/159.18 Intermediate Status:
% 158.79/159.18 Generated: 426446
% 158.79/159.18 Kept: 100622
% 158.79/159.18 Inuse: 1103
% 158.79/159.18 Deleted: 899
% 158.79/159.18 Deletedinuse: 10
% 158.79/159.18
% 158.79/159.18 Resimplifying inuse:
% 158.79/159.18 Done
% 158.79/159.18
% 158.79/159.18 Resimplifying inuse:
% 158.79/159.18 Done
% 158.79/159.18
% 158.79/159.18
% 158.79/159.18 Intermediate Status:
% 158.79/159.18 Generated: 434333
% 158.79/159.18 Kept: 102809
% 158.79/159.18 Inuse: 1118
% 158.79/159.18 Deleted: 899
% 158.79/159.18 Deletedinuse: 10
% 158.79/159.18
% 158.79/159.18 Resimplifying inuse:
% 158.79/159.18 Done
% 158.79/159.18
% 158.79/159.18 Resimplifying inuse:
% 158.79/159.18 Done
% 158.79/159.18
% 158.79/159.18 Resimplifying clauses:
% 158.79/159.18 Done
% 158.79/159.18
% 158.79/159.18
% 158.79/159.18 Intermediate Status:
% 158.79/159.18 Generated: 442440
% 158.79/159.18 Kept: 104816
% 158.79/159.18 Inuse: 1136
% 158.79/159.18 Deleted: 935
% 158.79/159.18 Deletedinuse: 10
% 158.79/159.18
% 158.79/159.18 Resimplifying inuse:
% 158.79/159.18 Done
% 158.79/159.18
% 158.79/159.18
% 158.79/159.18 Intermediate Status:
% 158.79/159.18 Generated: 450041
% 158.79/159.18 Kept: 106972
% 158.79/159.18 Inuse: 1148
% 158.79/159.18 Deleted: 935
% 158.79/159.18 Deletedinuse: 10
% 158.79/159.18
% 158.79/159.18 Resimplifying inuse:
% 158.79/159.18 Done
% 158.79/159.18
% 158.79/159.18 Resimplifying inuse:
% 158.79/159.18 Done
% 158.79/159.18
% 158.79/159.18
% 158.79/159.18 Intermediate Status:
% 158.79/159.18 Generated: 457496
% 158.79/159.18 Kept: 108985
% 158.79/159.18 Inuse: 1174
% 158.79/159.18 Deleted: 935
% 158.79/159.18 Deletedinuse: 10
% 158.79/159.18
% 158.79/159.18 Resimplifying inuse:
% 158.79/159.18 Done
% 158.79/159.18
% 158.79/159.18 Resimplifying inuse:
% 158.79/159.18 Done
% 158.79/159.18
% 158.79/159.18
% 158.79/159.18 Intermediate Status:
% 158.79/159.18 Generated: 464507
% 158.79/159.18 Kept: 110999
% 158.79/159.18 Inuse: 1200
% 158.79/159.18 Deleted: 935
% 158.79/159.18 Deletedinuse: 10
% 158.79/159.18
% 158.79/159.18 Resimplifying inuse:
% 158.79/159.18 Done
% 158.79/159.18
% 158.79/159.18 Resimplifying inuse:
% 158.79/159.18 Done
% 158.79/159.18
% 158.79/159.18
% 158.79/159.18 Intermediate Status:
% 158.79/159.18 Generated: 471423
% 158.79/159.18 Kept: 113041
% 158.79/159.18 Inuse: 1223
% 158.79/159.18 Deleted: 935
% 158.79/159.18 Deletedinuse: 10
% 158.79/159.18
% 158.79/159.18 Resimplifying inuse:
% 158.79/159.18 Done
% 158.79/159.18
% 158.79/159.18
% 158.79/159.18 Intermediate Status:
% 158.79/159.18 Generated: 483778
% 158.79/159.18 Kept: 115980
% 158.79/159.18 Inuse: 1248
% 158.79/159.18 Deleted: 935
% 158.79/159.18 Deletedinuse: 10
% 158.79/159.18
% 158.79/159.18 Resimplifying inuse:
% 158.79/159.18 Done
% 158.79/159.18
% 158.79/159.18 Resimplifying inuse:
% 158.79/159.18 Done
% 158.79/159.18
% 158.79/159.18
% 158.79/159.18 Intermediate Status:
% 158.79/159.18 Generated: 492017
% 158.79/159.18 Kept: 118158
% 158.79/159.18 Inuse: 1258
% 158.79/159.18 Deleted: 935
% 158.79/159.18 Deletedinuse: 10
% 158.79/159.18
% 158.79/159.18 Resimplifying inuse:
% 158.79/159.18 Done
% 158.79/159.18
% 158.79/159.18
% 158.79/159.18 Intermediate Status:
% 158.79/159.18 Generated: 500033
% 158.79/159.18 Kept: 120314
% 158.79/159.18 Inuse: 1283
% 158.79/159.18 Deleted: 935
% 158.79/159.18 Deletedinuse: 10
% 158.79/159.18
% 158.79/159.18
% 158.79/159.18 Intermediate Status:
% 158.79/159.18 Generated: 507572
% 158.79/159.18 Kept: 124127
% 158.79/159.18 Inuse: 1293
% 158.79/159.18 Deleted: 935
% 158.79/159.18 Deletedinuse: 10
% 158.79/159.18
% 158.79/159.18 Resimplifying inuse:
% 158.79/159.18 Done
% 158.79/159.18
% 158.79/159.18 Resimplifying clauses:
% 158.79/159.18 Done
% 158.79/159.18
% 158.79/159.18 Resimplifying inuse:
% 158.79/159.18 Done
% 158.79/159.18
% 158.79/159.18 *** allocated 6568290 integers for termspace/termends
% 158.79/159.18
% 158.79/159.18 Intermediate Status:
% 158.79/159.18 Generated: 517365
% 158.79/159.18 Kept: 126537
% 158.79/159.18 Inuse: 1318
% 158.79/159.18 Deleted: 1108
% 158.79/159.18 Deletedinuse: 10
% 158.79/159.18
% 158.79/159.18 Resimplifying inuse:
% 158.79/159.18 Done
% 158.79/159.18
% 158.79/159.18 Resimplifying inuse:
% 158.79/159.18 Done
% 158.79/159.18
% 158.79/159.18
% 158.79/159.18 Intermediate Status:
% 158.79/159.18 Generated: 525761
% 158.79/159.18 Kept: 128543
% 158.79/159.18 Inuse: 1336
% 158.79/159.18 Deleted: 1108
% 158.79/159.18 DCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------