TSTP Solution File: SWW268+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWW268+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n025.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 23:21:42 EDT 2022
% Result : Timeout 300.03s 300.48s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWW268+1 : TPTP v8.1.0. Released v5.2.0.
% 0.03/0.13 % Command : bliksem %s
% 0.12/0.34 % Computer : n025.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % DateTime : Sat Jun 4 19:18:31 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.95/1.60 *** allocated 10000 integers for termspace/termends
% 0.95/1.60 *** allocated 10000 integers for clauses
% 0.95/1.60 *** allocated 10000 integers for justifications
% 0.95/1.60 *** allocated 15000 integers for termspace/termends
% 0.95/1.60 *** allocated 22500 integers for termspace/termends
% 0.95/1.60 *** allocated 33750 integers for termspace/termends
% 0.95/1.60 Bliksem 1.12
% 0.95/1.60
% 0.95/1.60
% 0.95/1.60 Automatic Strategy Selection
% 0.95/1.60
% 0.95/1.60 *** allocated 50625 integers for termspace/termends
% 0.95/1.60 *** allocated 75937 integers for termspace/termends
% 0.95/1.60 *** allocated 113905 integers for termspace/termends
% 0.95/1.60
% 0.95/1.60 Clauses:
% 0.95/1.60
% 0.95/1.60 { ! hAPP( Y, skol1( X, Y ) ) = hAPP( X, skol1( X, Y ) ), Y = X }.
% 0.95/1.60 { ! v_c____ = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.95/1.60 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_OpCons(
% 0.95/1.60 tc_Complex_Ocomplex, v_c____, v_cs____ ) ), c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Complex_Ocomplex ) ) = hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 0.95/1.60 c_Polynomial_OpCons( tc_Complex_Ocomplex, v_c____, v_cs____ ) ), X ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.60 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 0.95/1.60 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ), Z = Y }.
% 0.95/1.60 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Z = Y,
% 0.95/1.60 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ) }.
% 0.95/1.60 { c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( tc_Complex_Ocomplex
% 0.95/1.60 , tc_Complex_Ocomplex, c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 0.95/1.60 c_Polynomial_OpCons( tc_Complex_Ocomplex, v_c____, v_cs____ ) ) ) }.
% 0.95/1.60 { ! class_Groups_Ozero( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y, Y =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.60 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ) = Y }.
% 0.95/1.60 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Polynomial_Opoly( X ) ), ! c_Polynomial_Oorder( X, Y, Z ) =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.60 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.60 { ! class_Rings_Oidom( X ), c_Polynomial_Oorder( X, Y, Z ) =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( c_Polynomial_Opoly( X,
% 0.95/1.60 Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.60 { ! v_c____ = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), hAPP(
% 0.95/1.60 c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_OpCons(
% 0.95/1.60 tc_Complex_Ocomplex, v_c____, v_cs____ ) ), skol2 ) =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.95/1.60 { c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( tc_Complex_Ocomplex
% 0.95/1.60 , tc_Complex_Ocomplex, c_Polynomial_Opoly( tc_Complex_Ocomplex, X ) ),
% 0.95/1.60 hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, X ), skol3( X ) ) =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.95/1.60 { X = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), !
% 0.95/1.60 c_Polynomial_OpCons( tc_Complex_Ocomplex, v_c____, v_cs____ ) =
% 0.95/1.60 c_Polynomial_OpCons( tc_Complex_Ocomplex, X, c_Groups_Ozero__class_Ozero
% 0.95/1.60 ( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ) ) }.
% 0.95/1.60 { ! skol4 = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), hAPP(
% 0.95/1.60 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_cs____ ), skol25 ) =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.95/1.60 { v_cs____ = c_Polynomial_OpCons( tc_Complex_Ocomplex, skol4,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) )
% 0.95/1.60 ), hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_cs____ ), skol25 ) =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.95/1.60 c_Polynomial_Opcompose( X, T, Z ) ), Y ) = hAPP( c_Polynomial_Opoly( X, T
% 0.95/1.60 ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.95/1.60 { X = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), ! v_p =
% 0.95/1.60 c_Polynomial_OpCons( tc_Complex_Ocomplex, X, c_Groups_Ozero__class_Ozero
% 0.95/1.60 ( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ) ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.60 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 0.95/1.60 c_Polynomial_OpCons( X, Z, Y ), U = Z }.
% 0.95/1.60 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 0.95/1.60 c_Polynomial_OpCons( X, Z, Y ), T = Y }.
% 0.95/1.60 { ! class_Groups_Ozero( X ), ! U = Z, ! T = Y, c_Polynomial_OpCons( X, U, T
% 0.95/1.60 ) = c_Polynomial_OpCons( X, Z, Y ) }.
% 0.95/1.60 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.60 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.60 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.95/1.60 c_Polynomial_OpCons( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.60 { ! class_Groups_Ozero( X ), c_Polynomial_OpCons( X,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.60 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 0.95/1.60 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.60 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Y =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.95/1.60 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.95/1.60 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( Z, Y, X ), hAPP(
% 0.95/1.60 X, T ) = hAPP( X, U ) }.
% 0.95/1.60 { ! hAPP( X, skol5( X ) ) = hAPP( X, skol26( X ) ),
% 0.95/1.60 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( Z, Y, X ) }.
% 0.95/1.60 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( W, X, Y,
% 0.95/1.60 Z, c_Polynomial_OpCons( X, U, T ) ) = hAPP( hAPP( hAPP( Z, U ), T ),
% 0.95/1.60 c_Polynomial_Opoly__rec( W, X, Y, Z, T ) ) }.
% 0.95/1.60 { ! class_Groups_Ozero( X ), !
% 0.95/1.60 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.60 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Polynomial_Opoly( X ) ),
% 0.95/1.60 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.60 { ! class_Groups_Ozero( X ), c_Polynomial_Opoly__rec( W, X, U, T,
% 0.95/1.60 c_Polynomial_OpCons( X, Z, Y ) ) = hAPP( hAPP( hAPP( T, Z ), Y ), c_If( W
% 0.95/1.60 , hAPP( hAPP( c_fequal, Y ), c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Polynomial_Opoly( X ) ) ), U, c_Polynomial_Opoly__rec( W, X, U, T, Y )
% 0.95/1.60 ) ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__0( X ),
% 0.95/1.60 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X,
% 0.95/1.60 c_Polynomial_OpCons( X, Z, c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Polynomial_Opoly( X ) ) ), Y ) = c_Polynomial_OpCons( X, Z,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.95/1.60 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( T, X, Y,
% 0.95/1.60 Z, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 0.95/1.60 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Polynomial_OpCons( X, hAPP(
% 0.95/1.60 c_Polynomial_Opoly( X, Z ), Y ), c_Polynomial_Osynthetic__div( X, Z, Y )
% 0.95/1.60 ) }.
% 0.95/1.60 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X, Y,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = c_Polynomial_OpCons( X, Y
% 0.95/1.60 , c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.95/1.60 { ! class_Groups_Ozero( X ), c_Polynomial_Odegree( X, c_Polynomial_OpCons(
% 0.95/1.60 X, Y, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.60 { ! class_Groups_Ozero( X ), ! hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero
% 0.95/1.60 ( tc_Polynomial_Opoly( X ) ) ) ), hBOOL( hAPP( Y, skol6( Z, Y ) ) ),
% 0.95/1.60 hBOOL( hAPP( Y, T ) ) }.
% 0.95/1.60 { ! class_Groups_Ozero( X ), ! hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero
% 0.95/1.60 ( tc_Polynomial_Opoly( X ) ) ) ), ! hBOOL( hAPP( Y, c_Polynomial_OpCons(
% 0.95/1.60 X, skol27( X, Y ), skol6( X, Y ) ) ) ), hBOOL( hAPP( Y, Z ) ) }.
% 0.95/1.60 { ! class_Groups_Ozero( X ), ! c_Polynomial_Omonom( X, Z, Y ) =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.60 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.60 c_Polynomial_Omonom( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.60 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.60 { ! class_Groups_Ozero( X ), ! class_HOL_Oequal( X ), ! hBOOL( hAPP( hAPP(
% 0.95/1.60 c_HOL_Oequal__class_Oequal( tc_Polynomial_Opoly( X ) ),
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ),
% 0.95/1.60 c_Polynomial_OpCons( X, Z, Y ) ) ), hBOOL( hAPP( hAPP(
% 0.95/1.60 c_HOL_Oequal__class_Oequal( X ), c_Groups_Ozero__class_Ozero( X ) ), Z )
% 0.95/1.60 ) }.
% 0.95/1.60 { ! class_Groups_Ozero( X ), ! class_HOL_Oequal( X ), ! hBOOL( hAPP( hAPP(
% 0.95/1.60 c_HOL_Oequal__class_Oequal( tc_Polynomial_Opoly( X ) ),
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ),
% 0.95/1.60 c_Polynomial_OpCons( X, Z, Y ) ) ), hBOOL( hAPP( hAPP(
% 0.95/1.60 c_HOL_Oequal__class_Oequal( tc_Polynomial_Opoly( X ) ),
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) ) }.
% 0.95/1.60 { ! class_Groups_Ozero( X ), ! class_HOL_Oequal( X ), ! hBOOL( hAPP( hAPP(
% 0.95/1.60 c_HOL_Oequal__class_Oequal( X ), c_Groups_Ozero__class_Ozero( X ) ), Z )
% 0.95/1.60 ), ! hBOOL( hAPP( hAPP( c_HOL_Oequal__class_Oequal( tc_Polynomial_Opoly
% 0.95/1.60 ( X ) ), c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) )
% 0.95/1.60 , hBOOL( hAPP( hAPP( c_HOL_Oequal__class_Oequal( tc_Polynomial_Opoly( X )
% 0.95/1.60 ), c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ),
% 0.95/1.60 c_Polynomial_OpCons( X, Z, Y ) ) ) }.
% 0.95/1.60 { ! class_Groups_Ozero( X ), ! class_HOL_Oequal( X ), ! hBOOL( hAPP( hAPP(
% 0.95/1.60 c_HOL_Oequal__class_Oequal( tc_Polynomial_Opoly( X ) ), Z ), Y ) ), Z = Y
% 0.95/1.60 }.
% 0.95/1.60 { ! class_Groups_Ozero( X ), ! class_HOL_Oequal( X ), ! Z = Y, hBOOL( hAPP
% 0.95/1.60 ( hAPP( c_HOL_Oequal__class_Oequal( tc_Polynomial_Opoly( X ) ), Z ), Y )
% 0.95/1.60 ) }.
% 0.95/1.60 { ! class_Groups_Ozero( X ), ! c_Polynomial_Omonom( X, T, Z ) =
% 0.95/1.60 c_Polynomial_Omonom( X, Y, Z ), T = Y }.
% 0.95/1.60 { ! class_Groups_Ozero( X ), ! T = Y, c_Polynomial_Omonom( X, T, Z ) =
% 0.95/1.60 c_Polynomial_Omonom( X, Y, Z ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Odegree( X,
% 0.95/1.60 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) ) =
% 0.95/1.60 c_Polynomial_Odegree( X, Z ) }.
% 0.95/1.60 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.60 c_Polynomial_Odegree( X, c_Polynomial_Omonom( X, Y, Z ) ) = Z }.
% 0.95/1.60 { ! class_Groups_Ozero( X ), ! class_HOL_Oequal( X ), ! hBOOL( hAPP( hAPP(
% 0.95/1.60 c_HOL_Oequal__class_Oequal( tc_Polynomial_Opoly( X ) ),
% 0.95/1.60 c_Polynomial_OpCons( X, U, T ) ), c_Polynomial_OpCons( X, Z, Y ) ) ),
% 0.95/1.60 hBOOL( hAPP( hAPP( c_HOL_Oequal__class_Oequal( X ), U ), Z ) ) }.
% 0.95/1.60 { ! class_Groups_Ozero( X ), ! class_HOL_Oequal( X ), ! hBOOL( hAPP( hAPP(
% 0.95/1.60 c_HOL_Oequal__class_Oequal( tc_Polynomial_Opoly( X ) ),
% 0.95/1.60 c_Polynomial_OpCons( X, U, T ) ), c_Polynomial_OpCons( X, Z, Y ) ) ),
% 0.95/1.60 hBOOL( hAPP( hAPP( c_HOL_Oequal__class_Oequal( tc_Polynomial_Opoly( X ) )
% 0.95/1.60 , T ), Y ) ) }.
% 0.95/1.60 { ! class_Groups_Ozero( X ), ! class_HOL_Oequal( X ), ! hBOOL( hAPP( hAPP(
% 0.95/1.60 c_HOL_Oequal__class_Oequal( X ), U ), Z ) ), ! hBOOL( hAPP( hAPP(
% 0.95/1.60 c_HOL_Oequal__class_Oequal( tc_Polynomial_Opoly( X ) ), T ), Y ) ), hBOOL
% 0.95/1.60 ( hAPP( hAPP( c_HOL_Oequal__class_Oequal( tc_Polynomial_Opoly( X ) ),
% 0.95/1.60 c_Polynomial_OpCons( X, U, T ) ), c_Polynomial_OpCons( X, Z, Y ) ) ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Osynthetic__div( X
% 0.95/1.60 , Z, Y ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.95/1.60 c_Polynomial_Odegree( X, Z ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.95/1.60 }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Odegree( X, Z ) =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Polynomial_Osynthetic__div
% 0.95/1.60 ( X, Z, Y ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.60 { ! class_Groups_Ozero( X ), ! class_HOL_Oequal( X ), hBOOL( hAPP( hAPP(
% 0.95/1.60 c_HOL_Oequal__class_Oequal( tc_Polynomial_Opoly( X ) ),
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ),
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) }.
% 0.95/1.60 { ! class_Groups_Ozero( X ), c_Polynomial_Odegree( X,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__0( X ), !
% 0.95/1.60 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__0( X ), ! Z = c_Groups_Ozero__class_Ozero
% 0.95/1.60 ( tc_Polynomial_Opoly( X ) ),
% 0.95/1.60 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__0( X ),
% 0.95/1.60 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.60 { ! class_Groups_Ozero( X ), ! class_HOL_Oequal( X ), ! hBOOL( hAPP( hAPP(
% 0.95/1.60 c_HOL_Oequal__class_Oequal( tc_Polynomial_Opoly( X ) ),
% 0.95/1.60 c_Polynomial_OpCons( X, Z, Y ) ), c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Polynomial_Opoly( X ) ) ) ), hBOOL( hAPP( hAPP(
% 0.95/1.60 c_HOL_Oequal__class_Oequal( X ), Z ), c_Groups_Ozero__class_Ozero( X ) )
% 0.95/1.60 ) }.
% 0.95/1.60 { ! class_Groups_Ozero( X ), ! class_HOL_Oequal( X ), ! hBOOL( hAPP( hAPP(
% 0.95/1.60 c_HOL_Oequal__class_Oequal( tc_Polynomial_Opoly( X ) ),
% 0.95/1.60 c_Polynomial_OpCons( X, Z, Y ) ), c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Polynomial_Opoly( X ) ) ) ), hBOOL( hAPP( hAPP(
% 0.95/1.60 c_HOL_Oequal__class_Oequal( tc_Polynomial_Opoly( X ) ), Y ),
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) }.
% 0.95/1.60 { ! class_Groups_Ozero( X ), ! class_HOL_Oequal( X ), ! hBOOL( hAPP( hAPP(
% 0.95/1.60 c_HOL_Oequal__class_Oequal( X ), Z ), c_Groups_Ozero__class_Ozero( X ) )
% 0.95/1.60 ), ! hBOOL( hAPP( hAPP( c_HOL_Oequal__class_Oequal( tc_Polynomial_Opoly
% 0.95/1.60 ( X ) ), Y ), c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) )
% 0.95/1.60 , hBOOL( hAPP( hAPP( c_HOL_Oequal__class_Oequal( tc_Polynomial_Opoly( X )
% 0.95/1.60 ), c_Polynomial_OpCons( X, Z, Y ) ), c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Polynomial_Opoly( X ) ) ) ) }.
% 0.95/1.60 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Polynomial_Opoly( X ) ),
% 0.95/1.60 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.60 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Polynomial_Opoly( X ) ),
% 0.95/1.60 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) = c_Nat_OSuc(
% 0.95/1.60 c_Polynomial_Odegree( X, Y ) ) }.
% 0.95/1.60 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, c_Polynomial_OpCons
% 0.95/1.60 ( X, Y, Z ) ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.60 { ! class_Groups_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, c_Polynomial_OpCons
% 0.95/1.60 ( X, Y, Z ) ) = c_Nat_OSuc( c_Polynomial_Odegree( X, Z ) ) }.
% 0.95/1.60 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless__eq(
% 0.95/1.60 tc_Nat_Onat, c_Polynomial_Oorder( X, Z, Y ), c_Polynomial_Odegree( X, Y )
% 0.95/1.60 ) }.
% 0.95/1.60 { ! class_HOL_Oequal( X ), c_fequal = c_HOL_Oequal__class_Oequal( X ) }.
% 0.95/1.60 { ! class_HOL_Oequal( X ), ! hBOOL( hAPP( hAPP( c_HOL_Oequal__class_Oequal
% 0.95/1.60 ( X ), Z ), Y ) ), Z = Y }.
% 0.95/1.60 { ! class_HOL_Oequal( X ), ! Z = Y, hBOOL( hAPP( hAPP(
% 0.95/1.60 c_HOL_Oequal__class_Oequal( X ), Z ), Y ) ) }.
% 0.95/1.60 { ! class_HOL_Oequal( X ), hBOOL( hAPP( hAPP( c_HOL_Oequal__class_Oequal( X
% 0.95/1.60 ), Y ), Y ) ) }.
% 0.95/1.60 { ! class_HOL_Oequal( X ), c_HOL_Oequal__class_Oequal( X ) = c_fequal }.
% 0.95/1.60 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X, Z, c_Nat_OSuc( Y ) ) =
% 0.95/1.60 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.60 c_Polynomial_Omonom( X, Z, Y ) ) }.
% 0.95/1.60 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, c_Polynomial_OpCons
% 0.95/1.60 ( X, Z, Y ) ) = c_Nat_OSuc( c_Polynomial_Odegree( X, Y ) ) }.
% 0.95/1.60 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Polynomial_Opoly( X ) ), ! hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.95/1.60 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.60 { ! class_Groups_Ozero( X ), ! hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.95/1.60 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.60 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.95/1.60 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.60 { ! class_Groups_Ozero( X ), ! c_Polynomial_Ocoeff( X, Z ) =
% 0.95/1.60 c_Polynomial_Ocoeff( X, Y ), Z = Y }.
% 0.95/1.60 { ! class_Groups_Ozero( X ), ! Z = Y, c_Polynomial_Ocoeff( X, Z ) =
% 0.95/1.60 c_Polynomial_Ocoeff( X, Y ) }.
% 0.95/1.60 { ! class_Groups_Ozero( X ), ! Z = Y, hAPP( c_Polynomial_Ocoeff( X, Z ), T
% 0.95/1.60 ) = hAPP( c_Polynomial_Ocoeff( X, Y ), T ) }.
% 0.95/1.60 { ! class_Groups_Ozero( X ), ! hAPP( c_Polynomial_Ocoeff( X, Z ), skol7( X
% 0.95/1.60 , Y, Z ) ) = hAPP( c_Polynomial_Ocoeff( X, Y ), skol7( X, Y, Z ) ), Z = Y
% 0.95/1.60 }.
% 0.95/1.60 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.95/1.60 c_Polynomial_OpCons( X, T, Z ) ), c_Nat_OSuc( Y ) ) = hAPP(
% 0.95/1.60 c_Polynomial_Ocoeff( X, Z ), Y ) }.
% 0.95/1.60 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X, Z ), Y ) =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless__eq(
% 0.95/1.60 tc_Nat_Onat, Y, c_Polynomial_Odegree( X, Z ) ) }.
% 0.95/1.60 { ! class_Groups_Ozero( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat
% 0.95/1.60 , c_Polynomial_Odegree( X, c_Polynomial_OpCons( X, Z, Y ) ), c_Nat_OSuc(
% 0.95/1.60 c_Polynomial_Odegree( X, Y ) ) ) }.
% 0.95/1.60 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.60 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.95/1.60 c_Polynomial_OpCons( X, Z, Y ) ), c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Nat_Onat ) ) = Z }.
% 0.95/1.60 { ! class_Groups_Ozero( X ), ! T = Z, hAPP( c_Polynomial_Ocoeff( X,
% 0.95/1.60 c_Polynomial_Omonom( X, Y, T ) ), Z ) = Y }.
% 0.95/1.60 { ! class_Groups_Ozero( X ), T = Z, hAPP( c_Polynomial_Ocoeff( X,
% 0.95/1.60 c_Polynomial_Omonom( X, Y, T ) ), Z ) = c_Groups_Ozero__class_Ozero( X )
% 0.95/1.60 }.
% 0.95/1.60 { ! class_Groups_Ozero( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat
% 0.95/1.60 , c_Polynomial_Odegree( X, c_Polynomial_Omonom( X, Z, Y ) ), Y ) }.
% 0.95/1.60 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.95/1.60 { ! class_Orderings_Opreorder( X ), c_Orderings_Oord__class_Oless__eq( X, Y
% 0.95/1.60 , Y ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), X ) }
% 0.95/1.60 .
% 0.95/1.60 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 0.95/1.60 ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.95/1.60 { ! Y = c_Nat_OSuc( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 0.95/1.60 , c_Nat_OSuc( X ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 0.95/1.60 c_Nat_OSuc( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X )
% 0.95/1.60 }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 0.95/1.60 c_Nat_OSuc( X ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 0.95/1.60 ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.60 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.95/1.60 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.60 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.95/1.60 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.95/1.60 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.95/1.60 hAPP( Y, U ) ) }.
% 0.95/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.60 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.95/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.60 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 0.95/1.60 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.60 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.95/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.60 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 0.95/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.60 , Y ), ! Z = T, c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.95/1.60 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y
% 0.95/1.60 ), ! Y = T, c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.95/1.60 { ! class_Orderings_Oorder( X ), ! Z = Y, !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 0.95/1.60 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.95/1.60 ( X, Y, T ), c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.95/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.60 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 0.95/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.60 , Y ), ! Y = Z, c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.95/1.60 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.95/1.60 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.95/1.60 hAPP( Y, U ) ) }.
% 0.95/1.60 { ! class_Orderings_Opreorder( X ), ! Z = Y,
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.95/1.60 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.95/1.60 ( X, Z, Y ) }.
% 0.95/1.60 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.95/1.60 ( X, Y, Z ) }.
% 0.95/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.60 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 0.95/1.60 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.60 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.95/1.60 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.95/1.60 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.95/1.60 hAPP( Y, U ) ) }.
% 0.95/1.60 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, hAPP
% 0.95/1.60 ( Z, skol8( X, Y, Z ) ), hAPP( Y, skol8( X, Y, Z ) ) ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }.
% 0.95/1.60 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 0.95/1.60 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 0.95/1.60 { ! Y = X, c_Nat_OSuc( Y ) = c_Nat_OSuc( X ) }.
% 0.95/1.60 { ! c_Nat_OSuc( X ) = X }.
% 0.95/1.60 { ! X = c_Nat_OSuc( X ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ), Y = X }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ) }.
% 0.95/1.60 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.60 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ) }.
% 0.95/1.60 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, X ) }.
% 0.95/1.60 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.60 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.95/1.60 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.60 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.60 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.95/1.60 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.60 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.95/1.60 { ! class_Groups_Ozero( X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.95/1.60 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), ! hAPP(
% 0.95/1.60 c_Polynomial_Ocoeff( X, Z ), Y ) = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, Z )
% 0.95/1.60 , Y ) }.
% 0.95/1.60 { ! class_Groups_Ozero( X ), c_Polynomial_Ocoeff( X, c_Polynomial_OpCons( X
% 0.95/1.60 , Z, Y ) ) = c_Nat_Onat_Onat__case( X, Z, c_Polynomial_Ocoeff( X, Y ) ) }
% 0.95/1.60 .
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__0( X ), c_Orderings_Oord__class_Oless__eq
% 0.95/1.60 ( tc_Nat_Onat, c_Polynomial_Odegree( X, c_Polynomial_Opcompose( X, Z, Y )
% 0.95/1.60 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.60 c_Polynomial_Odegree( X, Z ) ), c_Polynomial_Odegree( X, Y ) ) ) }.
% 0.95/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.60 hAPP( Y, skol9( X, Y ) ), hAPP( Y, c_Nat_OSuc( skol9( X, Y ) ) ) ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, T ), hAPP( Y, Z ) ) }.
% 0.95/1.60 { ! class_Groups_Ozero( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.60 c_Polynomial_Odegree( X, Z ), Y ), hAPP( c_Polynomial_Ocoeff( X, Z ), Y )
% 0.95/1.60 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.95/1.60 { ! class_Rings_Osemiring__1( X ), c_Nat_Osemiring__1__class_Oof__nat__aux
% 0.95/1.60 ( X, T, c_Nat_OSuc( Z ), Y ) = c_Nat_Osemiring__1__class_Oof__nat__aux( X
% 0.95/1.60 , T, Z, hAPP( T, Y ) ) }.
% 0.95/1.60 { ! class_Rings_Osemiring__1( X ), c_Nat_Osemiring__1__class_Oof__nat__aux
% 0.95/1.60 ( X, Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) = Y }.
% 0.95/1.60 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.60 c_Polynomial_Odegree( X, c_Polynomial_Osmult( X, Z, Y ) ) =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.60 { ! class_Rings_Oidom( X ), Z = c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.60 c_Polynomial_Odegree( X, c_Polynomial_Osmult( X, Z, Y ) ) =
% 0.95/1.60 c_Polynomial_Odegree( X, Y ) }.
% 0.95/1.60 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.95/1.60 tc_Polynomial_Opoly( X ) ), Z ), Y ) ), Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless__eq(
% 0.95/1.60 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) )
% 0.95/1.60 }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.95/1.60 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( X ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.95/1.60 X ) ) }.
% 0.95/1.60 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Nat_Onat ), c_Nat_OSuc( X ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.60 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.95/1.60 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.60 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.95/1.60 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.60 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.60 Y ), X ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Nat_Onat ), Z ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.60 ( tc_Nat_Onat ), Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 0.95/1.60 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Nat_Onat ), Y ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.60 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.95/1.60 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.95/1.60 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP
% 0.95/1.60 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.95/1.60 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP
% 0.95/1.60 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.95/1.60 { alpha23( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 0.95/1.60 hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.95/1.60 { alpha23( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP
% 0.95/1.60 ( X, Y ), Z ) ) }.
% 0.95/1.60 { ! alpha23( X, Y, Z ), alpha25( X, Y, Z ), Z = Y }.
% 0.95/1.60 { ! alpha23( X, Y, Z ), alpha25( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z
% 0.95/1.60 ) ) }.
% 0.95/1.60 { ! alpha25( X, Y, Z ), alpha23( X, Y, Z ) }.
% 0.95/1.60 { ! Z = Y, hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha23( X, Y, Z ) }.
% 0.95/1.60 { ! alpha25( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y )
% 0.95/1.60 }.
% 0.95/1.60 { ! alpha25( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ), hBOOL( hAPP( hAPP(
% 0.95/1.60 X, Y ), Z ) ), alpha25( X, Y, Z ) }.
% 0.95/1.60 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.95/1.60 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.60 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.95/1.60 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.95/1.60 , ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.95/1.60 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.95/1.60 Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.95/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.95/1.60 , ! Z = T, c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.95/1.60 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 0.95/1.60 ! Y = T, c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.95/1.60 { ! class_Orderings_Oorder( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless(
% 0.95/1.60 X, T, Y ), c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.95/1.60 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X
% 0.95/1.60 , Y, T ), c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.95/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.95/1.60 , ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.60 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.95/1.60 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.95/1.60 , ! Y = Z }.
% 0.95/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.95/1.60 , ! Z = Y }.
% 0.95/1.60 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.95/1.60 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.60 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.95/1.60 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.95/1.60 , ! Z = Y }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X = Y }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.95/1.60 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.95/1.60 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 0.95/1.60 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.60 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.95/1.60 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Y = Z }.
% 0.95/1.60 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.95/1.60 ), ! Y = Z, ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 0.95/1.60 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.95/1.60 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.95/1.60 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP
% 0.95/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.95/1.60 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.95/1.60 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Z = Y }.
% 0.95/1.60 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.95/1.60 Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.95/1.60 { ! class_Orderings_Olinorder( X ), ! Z = Y, !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.95/1.60 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 0.95/1.60 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.60 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.95/1.60 Y ), ! Z = Y }.
% 0.95/1.60 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.95/1.60 Z ), ! Z = Y }.
% 0.95/1.60 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.95/1.60 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.95/1.60 Y ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.95/1.60 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), c_Polynomial_Osmult
% 0.95/1.60 ( X, T, Z ) ), Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.95/1.60 tc_Polynomial_Opoly( X ) ), Z ), Y ) ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.95/1.60 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Z ), Y ) ), hBOOL(
% 0.95/1.60 hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Z ),
% 0.95/1.60 c_Polynomial_Osmult( X, T, Y ) ) ) }.
% 0.95/1.60 { ! class_Groups_Oab__semigroup__mult( X ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 0.95/1.60 c_Polynomial_Osmult( X, Z, Y ) ) = c_Polynomial_Osmult( X, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 0.95/1.60 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 0.95/1.60 ( tc_Polynomial_Opoly( X ) ), T ), c_Polynomial_Osmult( X, Z, Y ) ) ), Z
% 0.95/1.60 = c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP( hAPP(
% 0.95/1.60 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), T ), Y ) ) }.
% 0.95/1.60 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 0.95/1.60 ( tc_Polynomial_Opoly( X ) ), Z ), Y ) ), T = c_Groups_Ozero__class_Ozero
% 0.95/1.60 ( X ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly(
% 0.95/1.60 X ) ), c_Polynomial_Osmult( X, T, Z ) ), Y ) ) }.
% 0.95/1.60 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! hBOOL
% 0.95/1.60 ( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), T ),
% 0.95/1.60 c_Polynomial_Osmult( X, Y, Z ) ) ), hBOOL( hAPP( hAPP(
% 0.95/1.60 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), T ), Z ) ) }.
% 0.95/1.60 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! hBOOL
% 0.95/1.60 ( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), T ),
% 0.95/1.60 Z ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly(
% 0.95/1.60 X ) ), T ), c_Polynomial_Osmult( X, Y, Z ) ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.95/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.95/1.60 ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.95/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.95/1.60 ), X ) ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 0.95/1.60 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), c_Polynomial_Osmult( X, T,
% 0.95/1.60 Y ) ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.95/1.60 c_Polynomial_Osmult( X, T, Z ) ), Y ) = hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( c_Polynomial_Ocoeff( X, Z
% 0.95/1.60 ), Y ) ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.95/1.60 c_Polynomial_Osmult( X, T, Z ) ), Y ) = hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( c_Polynomial_Opoly( X, Z )
% 0.95/1.60 , Y ) ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 0.95/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Z
% 0.95/1.60 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP(
% 0.95/1.60 c_Polynomial_Opoly( X, T ), Y ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 0.95/1.60 ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 0.95/1.60 c_Polynomial_Omonom( X, Z, Y ) ) = c_Polynomial_Omonom( X, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 0.95/1.60 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 0.95/1.60 ( tc_Polynomial_Opoly( X ) ), c_Polynomial_Osmult( X, T, Z ) ), Y ) ),
% 0.95/1.60 alpha1( X, Y, T ) }.
% 0.95/1.60 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 0.95/1.60 ( tc_Polynomial_Opoly( X ) ), c_Polynomial_Osmult( X, T, Z ) ), Y ) ),
% 0.95/1.60 alpha13( X, Y, Z, T ) }.
% 0.95/1.60 { ! class_Fields_Ofield( X ), ! alpha1( X, Y, T ), ! alpha13( X, Y, Z, T )
% 0.95/1.60 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) )
% 0.95/1.60 , c_Polynomial_Osmult( X, T, Z ) ), Y ) ) }.
% 0.95/1.60 { ! alpha13( X, Y, Z, T ), T = c_Groups_Ozero__class_Ozero( X ), hBOOL(
% 0.95/1.60 hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Z ), Y
% 0.95/1.60 ) ) }.
% 0.95/1.60 { ! T = c_Groups_Ozero__class_Ozero( X ), alpha13( X, Y, Z, T ) }.
% 0.95/1.60 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) )
% 0.95/1.60 , Z ), Y ) ), alpha13( X, Y, Z, T ) }.
% 0.95/1.60 { ! alpha1( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.60 { Z = c_Groups_Ozero__class_Ozero( X ), alpha1( X, Y, Z ) }.
% 0.95/1.60 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha1( X
% 0.95/1.60 , Y, Z ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X
% 0.95/1.60 ) }.
% 0.95/1.60 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 0.95/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 0.95/1.60 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 0.95/1.60 ) }.
% 0.95/1.60 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 0.95/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 0.95/1.60 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.95/1.60 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.95/1.60 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.95/1.60 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.60 , Y, Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.95/1.60 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.60 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.60 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.95/1.60 Z ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.95/1.60 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.60 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.95/1.60 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.95/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.95/1.60 , ! Z = Y }.
% 0.95/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.60 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.95/1.60 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.95/1.60 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.95/1.60 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.95/1.60 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.95/1.60 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.60 , Z, Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.95/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.60 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.95/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.95/1.60 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.95/1.60 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.95/1.60 ( X, Z, Y ) }.
% 0.95/1.60 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.95/1.60 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.95/1.60 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.60 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.60 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.95/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ), Z = Y }.
% 0.95/1.60 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.95/1.60 ), ! Z = Y, c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.95/1.60 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.95/1.60 ( X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.95/1.60 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.95/1.60 ( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.60 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.60 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.60 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.95/1.60 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.95/1.60 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.60 , Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.95/1.60 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.60 , Z, Y ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.95/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.60 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.95/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.60 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.95/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.60 , Y ), Y = Z, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.95/1.60 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.95/1.60 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.95/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.95/1.60 , ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.95/1.60 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.60 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.95/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.60 , Y ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.95/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.60 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.60 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.60 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.60 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.95/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Y = X
% 0.95/1.60 , Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.60 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.95/1.60 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.95/1.60 .
% 0.95/1.60 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.95/1.60 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.95/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z = X
% 0.95/1.60 , Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.60 { ! Z = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.95/1.60 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }
% 0.95/1.60 .
% 0.95/1.60 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.95/1.60 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Nat_Onat ), X ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.60 ( tc_Nat_Onat ), X ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 0.95/1.60 .
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.60 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Nat_Onat ), X ) }.
% 0.95/1.60 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z
% 0.95/1.60 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.60 c_Nat_OSuc( Z ) ), X ), Y = X }.
% 0.95/1.60 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.60 c_Nat_OSuc( Z ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.95/1.60 tc_Nat_Onat ), c_Nat_OSuc( Z ) ), X ) }.
% 0.95/1.60 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.95/1.60 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) )
% 0.95/1.60 }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 0.95/1.60 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.95/1.60 X ) ) }.
% 0.95/1.60 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y = X }
% 0.95/1.60 .
% 0.95/1.60 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X,
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.95/1.60 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), X = Y }
% 0.95/1.60 .
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) = X
% 0.95/1.60 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 0.95/1.60 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.95/1.60 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) }.
% 0.95/1.60 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), T ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.60 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.60 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, Y,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.60 { hAPP( c_Nat_Onat_Onat__case( Z, Y, X ), c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Nat_Onat ) ) = Y }.
% 0.95/1.60 { ! class_Rings_Oidom( X ), ! c_Polynomial_Osmult( X, Z, Y ) =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.60 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.60 c_Polynomial_Osmult( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.60 { ! class_Rings_Oidom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Polynomial_Opoly( X ) ), c_Polynomial_Osmult( X, Z, Y ) =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.60 { hAPP( c_Nat_Onat_Onat__case( T, Z, Y ), c_Nat_OSuc( X ) ) = hAPP( Y, X )
% 0.95/1.60 }.
% 0.95/1.60 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.95/1.60 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y = c_Nat_OSuc
% 0.95/1.60 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.95/1.60 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.95/1.60 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X = c_Nat_OSuc
% 0.95/1.60 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.95/1.60 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.95/1.60 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.95/1.60 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Ocoeff( X, Z ),
% 0.95/1.60 c_Polynomial_Odegree( X, Z ) ) = hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.95/1.60 c_Polynomial_Odegree( X, Y ) ), ! hBOOL( hAPP( hAPP(
% 0.95/1.60 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Z ), Y ) ), ! hBOOL
% 0.95/1.60 ( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Y ),
% 0.95/1.60 Z ) ), Z = Y }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha2( X, Y ) }.
% 0.95/1.60 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.95/1.60 { ! alpha2( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.95/1.60 c_Nat_OSuc( X ) ) }.
% 0.95/1.60 { ! alpha2( X, Y ), Y = c_Nat_OSuc( skol10( Z, Y ) ) }.
% 0.95/1.60 { ! alpha2( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol10( X,
% 0.95/1.60 Y ), X ) }.
% 0.95/1.60 { ! Y = c_Nat_OSuc( Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.95/1.60 ), alpha2( X, Y ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.60 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.60 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( skol11( X ) ) }.
% 0.95/1.60 { ! X = c_Nat_OSuc( Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.95/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.95/1.60 ), X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.95/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.95/1.60 ), X ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X = Y }
% 0.95/1.60 .
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X = Y,
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__0( X ), c_Orderings_Oord__class_Oless__eq
% 0.95/1.60 ( tc_Nat_Onat, c_Polynomial_Odegree( X, c_Polynomial_Osmult( X, Z, Y ) )
% 0.95/1.60 , c_Polynomial_Odegree( X, Y ) ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Osmult( X, T, Y ) =
% 0.95/1.60 c_Polynomial_OpCons( X, Z, Y ), Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hBOOL( hAPP( hAPP(
% 0.95/1.60 c_Rings_Odvd__class_Odvd( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) )
% 0.95/1.60 }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.60 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP
% 0.95/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.60 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z
% 0.95/1.60 , Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.95/1.60 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.95/1.60 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.95/1.60 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.95/1.60 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.95/1.60 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.95/1.60 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, U, T ), ! c_Orderings_Oord__class_Oless
% 0.95/1.60 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.95/1.60 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.95/1.60 { hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), c_Nat_OSuc(
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) ) }.
% 0.95/1.60 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 0.95/1.60 X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }
% 0.95/1.60 .
% 0.95/1.60 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 0.95/1.60 X ), Z, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z )
% 0.95/1.60 }.
% 0.95/1.60 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.95/1.60 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z
% 0.95/1.60 ), c_Orderings_Oord__class_Oless( tc_fun( T, X ), Z, Y ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ),
% 0.95/1.60 c_Polynomial_Osmult( X, Z, Y ) ) = c_Polynomial_Osmult( X, Z, hAPP( hAPP
% 0.95/1.60 ( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ) ) }
% 0.95/1.60 .
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.95/1.60 c_Polynomial_Osmult( X, T, Z ) ), Y ) = c_Polynomial_Osmult( X, T, hAPP(
% 0.95/1.60 hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y )
% 0.95/1.60 ) }.
% 0.95/1.60 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP
% 0.95/1.60 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ), Z =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 0.95/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ) }.
% 0.95/1.60 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 0.95/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ) }.
% 0.95/1.60 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.95/1.60 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP
% 0.95/1.60 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ) }.
% 0.95/1.60 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ),
% 0.95/1.60 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), X =
% 0.95/1.60 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.95/1.60 { ! X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hBOOL(
% 0.95/1.60 hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), c_Nat_OSuc(
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.60 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y
% 0.95/1.60 ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X
% 0.95/1.60 ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.60 ( tc_Nat_Onat ), X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.95/1.60 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.60 X ), Z ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X )
% 0.95/1.60 , Y ) ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z
% 0.95/1.60 ), Y ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.60 ( tc_Nat_Onat ), X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.95/1.60 tc_Nat_Onat ), Z ), Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.95/1.60 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.60 X ), Z ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X )
% 0.95/1.60 , Y ) ) ) }.
% 0.95/1.60 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.95/1.60 , ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.60 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP
% 0.95/1.60 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Nat_Onat ), Z ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.95/1.60 tc_Nat_Onat ), Y ), X ) ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__idom( X ), Z = Y,
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.95/1.60 X, Y, Z ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.95/1.60 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 0.95/1.60 c_Rings_Odvd__class_Odvd( X ), Y ), T ) ), hBOOL( hAPP( hAPP(
% 0.95/1.60 c_Rings_Odvd__class_Odvd( X ), Z ), T ) ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hBOOL( hAPP( hAPP(
% 0.95/1.60 c_Rings_Odvd__class_Odvd( X ), Y ), Y ) ) }.
% 0.95/1.60 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.60 ( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.60 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.60 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.60 { ! class_Rings_Oring__no__zero__divisors( X ), ! hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.60 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.60 { ! class_Rings_Oring__no__zero__divisors( X ), ! Z =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.60 { ! class_Rings_Oring__no__zero__divisors( X ), ! Y =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.60 { ! class_Rings_Ono__zero__divisors( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.60 X ), Z = c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.60 { ! class_Rings_Ono__zero__divisors( X ), ! hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.60 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.95/1.60 c_Rings_Odvd__class_Odvd( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) )
% 0.95/1.60 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.95/1.60 c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.60 ( X ), T ), Z ) ), Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X
% 0.95/1.60 ), Z ), Y ) ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.95/1.60 c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.60 ( X ), Z ), T ) ), Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X
% 0.95/1.60 ), Z ), Y ) ) }.
% 0.95/1.60 { ! class_Rings_Odvd( X ), ! Z = hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.60 ( X ), Y ), T ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Y ), Z
% 0.95/1.60 ) ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.95/1.60 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 0.95/1.60 c_Rings_Odvd__class_Odvd( X ), U ), T ) ), hBOOL( hAPP( hAPP(
% 0.95/1.60 c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.60 ( X ), Z ), U ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T
% 0.95/1.60 ) ) ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.95/1.60 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 0.95/1.60 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.95/1.60 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 0.95/1.60 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hBOOL( hAPP( hAPP(
% 0.95/1.60 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hBOOL( hAPP( hAPP(
% 0.95/1.60 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 0.95/1.60 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.95/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Z =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.95/1.60 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.95/1.60 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.95/1.60 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.95/1.60 .
% 0.95/1.60 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 0.95/1.60 X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), alpha3( X, Y
% 0.95/1.60 , Z ), alpha14( X, Y, Z ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha3( X, Y, Z ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha14( X, Y, Z ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.95/1.60 { ! alpha14( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.60 { ! alpha14( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.95/1.60 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ) ), alpha14( X, Y, Z ) }.
% 0.95/1.60 { ! alpha3( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.95/1.60 { ! alpha3( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.60 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ), Y ), alpha3( X, Y, Z ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.95/1.60 ( X ) ), alpha4( X, Y, Z ), alpha15( X, Y, Z ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha4( X, Y, Z ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.95/1.60 ( X ) ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha15( X, Y, Z ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.95/1.60 ( X ) ) }.
% 0.95/1.60 { ! alpha15( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.60 { ! alpha15( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.95/1.60 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 0.95/1.60 ( X ), Y ), alpha15( X, Y, Z ) }.
% 0.95/1.60 { ! alpha4( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.95/1.60 { ! alpha4( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.60 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ) ), alpha4( X, Y, Z ) }.
% 0.95/1.60 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.95/1.60 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.95/1.60 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.60 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ),
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.60 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.60 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.60 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.95/1.60 X ), Z ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.95/1.60 ( X ) ) }.
% 0.95/1.60 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.60 , Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.60 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.95/1.60 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.95/1.60 { ! class_Rings_Oordered__semiring( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.95/1.60 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.95/1.60 { ! class_Rings_Oordered__semiring( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.95/1.60 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.95/1.60 { ! class_Rings_Oordered__comm__semiring( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.95/1.60 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.95/1.60 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.60 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.60 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.95/1.60 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.60 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.60 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 0.95/1.60 { ! class_Rings_Oordered__semiring( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.95/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.95/1.60 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.95/1.60 { ! class_Rings_Oordered__semiring( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.95/1.60 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.95/1.60 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.60 , c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.60 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.95/1.60 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.95/1.60 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.60 , Z, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.60 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.95/1.60 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.95/1.60 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.95/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.60 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.60 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.95/1.60 X ), Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.95/1.60 ( X ) ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.95/1.60 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha5( X, Y, Z, T ),
% 0.95/1.60 alpha16( X, Y, Z, T ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha5( X, Y, Z, T ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha16( X, Y, Z, T ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.95/1.60 { ! alpha16( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.60 { ! alpha16( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, T ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.95/1.60 , ! c_Orderings_Oord__class_Oless( X, Y, T ), alpha16( X, Y, Z, T ) }.
% 0.95/1.60 { ! alpha5( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.95/1.60 { ! alpha5( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.95/1.60 , ! c_Orderings_Oord__class_Oless( X, T, Y ), alpha5( X, Y, Z, T ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha6( X, Y, Z, T ),
% 0.95/1.60 alpha17( X, Y, Z, T ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha6( X, Y, Z, T ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha17( X, Y, Z, T ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.95/1.60 { ! alpha17( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.60 { ! alpha17( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( X, T, c_Groups_Ozero__class_Ozero( X ) )
% 0.95/1.60 , ! c_Orderings_Oord__class_Oless( X, Y, Z ), alpha17( X, Y, Z, T ) }.
% 0.95/1.60 { ! alpha6( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ), T ) }.
% 0.95/1.60 { ! alpha6( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T )
% 0.95/1.60 , ! c_Orderings_Oord__class_Oless( X, Z, Y ), alpha6( X, Y, Z, T ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.95/1.60 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.95/1.60 ! c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless
% 0.95/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.95/1.60 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.95/1.60 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.95/1.60 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.95/1.60 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.95/1.60 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.95/1.60 ( X ) ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.95/1.60 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.95/1.60 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.95/1.60 ( X ) ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.95/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.95/1.60 .
% 0.95/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.95/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ) }
% 0.95/1.60 .
% 0.95/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.60 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.60 ! c_Orderings_Oord__class_Oless( X, Z, T ), c_Orderings_Oord__class_Oless
% 0.95/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.95/1.60 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.60 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.95/1.60 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.95/1.60 ( X ) ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.60 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.95/1.60 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.95/1.60 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.95/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP
% 0.95/1.60 ( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.95/1.60 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.95/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.95/1.60 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__comm__semiring__strict( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.95/1.60 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.95/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.95/1.60 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.95/1.60 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.95/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.95/1.60 ( c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.95/1.60 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.95/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP
% 0.95/1.60 ( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 0.95/1.60 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.95/1.60 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP(
% 0.95/1.60 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), Z =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP( hAPP(
% 0.95/1.60 c_Rings_Odvd__class_Odvd( X ), T ), Y ) ) }.
% 0.95/1.60 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ), hBOOL(
% 0.95/1.60 hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 0.95/1.60 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.95/1.60 X ), T ), Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), hAPP(
% 0.95/1.60 hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 0.95/1.60 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.95/1.60 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP(
% 0.95/1.60 hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ), T =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP( hAPP(
% 0.95/1.60 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ) }.
% 0.95/1.60 { ! class_Rings_Oidom( X ), ! T = c_Groups_Ozero__class_Ozero( X ), hBOOL(
% 0.95/1.60 hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 0.95/1.60 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.95/1.60 X ), Z ), Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), hAPP(
% 0.95/1.60 hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.60 ( tc_Nat_Onat ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.95/1.60 tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.95/1.60 tc_Nat_Onat ), X ), Y ), Z = Y }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.60 ( tc_Nat_Onat ), X ), ! Z = Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.60 ( tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.95/1.60 tc_Nat_Onat ), X ), Y ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.60 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 0.95/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP(
% 0.95/1.60 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.60 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 0.95/1.60 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.95/1.60 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.95/1.60 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.60 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.60 ! c_Orderings_Oord__class_Oless__eq( X, Z, T ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.95/1.60 ( X, U, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.95/1.60 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.95/1.60 ( X, U, T ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.95/1.60 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.95/1.60 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.60 , U ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( c_Nat_OSuc(
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), X =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X = c_Nat_OSuc(
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.95/1.60 ( c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.95/1.60 , c_Groups_Ozero__class_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.95/1.60 c_Polynomial_Odegree( X, Y ) ) ), c_Polynomial_Opos__poly( X, Y ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.60 ( tc_Nat_Onat ), X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.95/1.60 tc_Nat_Onat ), Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.95/1.60 c_Polynomial_OpCons( X, Z, Y ) ), c_Polynomial_Opos__poly( X, Y ), alpha7
% 0.95/1.60 ( X, Y, Z ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.95/1.60 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__idom( X ), ! alpha7( X, Y, Z ),
% 0.95/1.60 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ) }.
% 0.95/1.60 { ! alpha7( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly
% 0.95/1.60 ( X ) ) }.
% 0.95/1.60 { ! alpha7( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.95/1.60 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.95/1.60 alpha7( X, Y, Z ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.95/1.60 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.60 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.95/1.60 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.60 { hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), X ) ) }
% 0.95/1.60 .
% 0.95/1.60 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.95/1.60 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.95/1.60 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 0.95/1.60 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X )
% 0.95/1.60 ) }.
% 0.95/1.60 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.95/1.60 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.95/1.60 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 0.95/1.60 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X )
% 0.95/1.60 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), Z )
% 0.95/1.60 ) }.
% 0.95/1.60 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.95/1.60 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.95/1.60 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 0.95/1.60 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X )
% 0.95/1.60 ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y
% 0.95/1.60 ) ) }.
% 0.95/1.60 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.95/1.60 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.95/1.60 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 0.95/1.60 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X )
% 0.95/1.60 ) }.
% 0.95/1.60 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.95/1.60 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.95/1.60 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 0.95/1.60 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), Z )
% 0.95/1.60 ) }.
% 0.95/1.60 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.95/1.60 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.95/1.60 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 0.95/1.60 ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y
% 0.95/1.60 ) ) }.
% 0.95/1.60 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.95/1.60 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.95/1.60 , ! X = Z, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y
% 0.95/1.60 ), Z ) ) }.
% 0.95/1.60 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.95/1.60 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.95/1.60 , ! X = Z, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ),
% 0.95/1.60 Z ), Y ) ) }.
% 0.95/1.60 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.95/1.60 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.95/1.60 , ! X = Y }.
% 0.95/1.60 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.95/1.60 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.95/1.60 , ! Y = X }.
% 0.95/1.60 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.95/1.60 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.95/1.60 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 0.95/1.60 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X )
% 0.95/1.60 ) }.
% 0.95/1.60 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.95/1.60 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.95/1.60 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.95/1.60 }.
% 0.95/1.60 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.95/1.60 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.95/1.60 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 0.95/1.60 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X )
% 0.95/1.60 ) }.
% 0.95/1.60 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.95/1.60 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.95/1.60 , ! Y = X }.
% 0.95/1.60 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.95/1.60 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 0.95/1.60 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X )
% 0.95/1.60 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), Z )
% 0.95/1.60 ) }.
% 0.95/1.60 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.95/1.60 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 0.95/1.60 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X )
% 0.95/1.60 ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y
% 0.95/1.60 ) ) }.
% 0.95/1.60 { ! Y = X, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X
% 0.95/1.60 ), Z ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z
% 0.95/1.60 ), X ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y
% 0.95/1.60 ), Z ) ) }.
% 0.95/1.60 { ! Y = X, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X
% 0.95/1.60 ), Z ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z
% 0.95/1.60 ), X ) ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ),
% 0.95/1.60 Z ), Y ) ) }.
% 0.95/1.60 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.95/1.60 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 0.95/1.60 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), Z )
% 0.95/1.60 ) }.
% 0.95/1.60 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.95/1.60 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 0.95/1.60 ), Y = X }.
% 0.95/1.60 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.95/1.60 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 0.95/1.60 ), Y = X }.
% 0.95/1.60 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.95/1.60 , ! X = Z, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y
% 0.95/1.60 ), Z ) ) }.
% 0.95/1.60 { ! Y = X, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X
% 0.95/1.60 ), Z ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y
% 0.95/1.60 ), Z ) ) }.
% 0.95/1.60 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.95/1.60 , Y = X, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 0.95/1.60 , X ) ) }.
% 0.95/1.60 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.95/1.60 , Y = X, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X
% 0.95/1.60 ), Y ) ) }.
% 0.95/1.60 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.95/1.60 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.95/1.60 , Y = X }.
% 0.95/1.60 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.95/1.60 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 0.95/1.60 ), Y = X }.
% 0.95/1.60 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.95/1.60 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 0.95/1.60 ), X = Y }.
% 0.95/1.60 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.95/1.60 , ! X = Y, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X
% 0.95/1.60 ), Y ) ) }.
% 0.95/1.60 { ! Y = X, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 0.95/1.60 , X ) ) }.
% 0.95/1.60 { Y = X, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 0.95/1.60 , X ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 0.95/1.60 , X ) ) }.
% 0.95/1.60 { Y = X, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 0.95/1.60 , X ) ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X
% 0.95/1.60 ), Y ) ) }.
% 0.95/1.60 { ! alpha8( X, Y ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.95/1.60 tc_Nat_Onat ), Y ), X ) ) }.
% 0.95/1.60 { ! alpha8( X, Y ), ! Y = X }.
% 0.95/1.60 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.95/1.60 , Y = X, alpha8( X, Y ) }.
% 0.95/1.60 { ! alpha8( X, Y ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.95/1.60 tc_Nat_Onat ), Y ), X ) ) }.
% 0.95/1.60 { ! alpha8( X, Y ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.95/1.60 tc_Nat_Onat ), X ), Y ) ) }.
% 0.95/1.60 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.95/1.60 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.95/1.60 , alpha8( X, Y ) }.
% 0.95/1.60 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.95/1.60 , alpha9( X, Y ), Y = X }.
% 0.95/1.60 { ! alpha9( X, Y ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.95/1.60 tc_Nat_Onat ), Y ), X ) ) }.
% 0.95/1.60 { ! Y = X, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 0.95/1.60 , X ) ) }.
% 0.95/1.60 { ! alpha9( X, Y ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.95/1.60 tc_Nat_Onat ), Y ), X ) ) }.
% 0.95/1.60 { ! alpha9( X, Y ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.95/1.60 tc_Nat_Onat ), X ), Y ) ) }.
% 0.95/1.60 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.95/1.60 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.95/1.60 , alpha9( X, Y ) }.
% 0.95/1.60 { ! Y = X, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 0.95/1.60 , X ) ) }.
% 0.95/1.60 { ! Y = X, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X )
% 0.95/1.60 , Y ) ) }.
% 0.95/1.60 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.95/1.60 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 0.95/1.60 ), Y = X }.
% 0.95/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.95/1.60 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X, hAPP( hAPP
% 0.95/1.60 ( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) }
% 0.95/1.60 .
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Z ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), U ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), Y ) ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.95/1.60 { hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ),
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.95/1.60 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.95/1.60 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.60 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.95/1.60 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.95/1.60 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.60 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.95/1.60 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.60 { ! class_Groups_Ozero( X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z
% 0.95/1.60 , skol12( T, U, Z ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.60 c_Polynomial_Odegree( X, Y ), Z ) }.
% 0.95/1.60 { ! class_Groups_Ozero( X ), ! hAPP( c_Polynomial_Ocoeff( X, Y ), skol12( X
% 0.95/1.60 , Y, Z ) ) = c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 0.95/1.60 Y ), Z ) }.
% 0.95/1.60 { ! class_Groups_Ozero( X ), c_Polynomial_OpCons( X, Z, Y ) =
% 0.95/1.60 c_Polynomial_OAbs__poly( X, c_Nat_Onat_Onat__case( X, Z,
% 0.95/1.60 c_Polynomial_Ocoeff( X, Y ) ) ) }.
% 0.95/1.60 { ! class_Groups_Ozero( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.60 Z, c_Polynomial_Odegree( X, Y ) ), c_Orderings_Oord__class_Oless(
% 0.95/1.60 tc_Nat_Onat, Z, skol13( T, U, Z ) ) }.
% 0.95/1.60 { ! class_Groups_Ozero( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.60 Z, c_Polynomial_Odegree( X, Y ) ), ! hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.95/1.60 skol13( X, Y, Z ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oorder_Omono( tc_Nat_Onat, X
% 0.95/1.60 , c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), ! hBOOL( hAPP( hAPP(
% 0.95/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), T ), Z ) ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, T ), hAPP( Y, Z ) ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 0.95/1.60 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus(
% 0.95/1.60 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, T,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 0.95/1.60 c_Polynomial_Opcompose( X, Z, Y ) ) ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__0( X ), c_Groups_Oplus__class_Oplus(
% 0.95/1.60 tc_Polynomial_Opoly( X ), Z, c_Polynomial_Osmult( X, Y,
% 0.95/1.60 c_Polynomial_Osynthetic__div( X, Z, Y ) ) ) = c_Polynomial_OpCons( X,
% 0.95/1.60 hAPP( c_Polynomial_Opoly( X, Z ), Y ), c_Polynomial_Osynthetic__div( X, Z
% 0.95/1.60 , Y ) ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.95/1.60 , Y ) = c_Groups_Oplus__class_Oplus( X, Y, Z ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.95/1.60 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.95/1.60 ( X, Z, c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.95/1.60 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.95/1.60 ( X, c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.60 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.95/1.60 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.60 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.95/1.60 ( X, c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.60 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.95/1.60 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X
% 0.95/1.60 , U, Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X,
% 0.95/1.60 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.95/1.60 ( tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 0.95/1.60 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 0.95/1.60 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.95/1.60 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, U, T ),
% 0.95/1.60 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 0.95/1.60 c_Groups_Oplus__class_Oplus( X, U, Z ), c_Groups_Oplus__class_Oplus(
% 0.95/1.60 tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 0.95/1.60 { ! class_Groups_Ocomm__monoid__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.95/1.60 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.95/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( c_Polynomial_Ocoeff( X, T ), Y ),
% 0.95/1.60 hAPP( c_Polynomial_Ocoeff( X, Z ), Y ) ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.95/1.60 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.95/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 0.95/1.60 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.95/1.60 { ! class_Groups_Oab__semigroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.60 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.95/1.60 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.95/1.60 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.95/1.60 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.95/1.60 T, Y ), Z = Y }.
% 0.95/1.60 { ! class_Groups_Ocancel__semigroup__add( X ), ! Z = Y,
% 0.95/1.60 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.95/1.60 T, Y ) }.
% 0.95/1.60 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.95/1.60 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.95/1.60 Y, Z ), T = Y }.
% 0.95/1.60 { ! class_Groups_Ocancel__semigroup__add( X ), ! T = Y,
% 0.95/1.60 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.95/1.60 Y, Z ) }.
% 0.95/1.60 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.95/1.60 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.95/1.60 T, Y ), Z = Y }.
% 0.95/1.60 { ! class_Groups_Ocancel__ab__semigroup__add( X ), !
% 0.95/1.60 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.95/1.60 T, Y ), Z = Y }.
% 0.95/1.60 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.95/1.60 c_Groups_Oplus__class_Oplus( X, Z, T ) = c_Groups_Oplus__class_Oplus( X,
% 0.95/1.60 Y, T ), Z = Y }.
% 0.95/1.60 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.95/1.60 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, T, Z ),
% 0.95/1.61 c_Polynomial_Omonom( X, Y, Z ) ) = c_Polynomial_Omonom( X,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 0.95/1.61 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.95/1.61 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.95/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.95/1.61 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero( X ) =
% 0.95/1.61 c_Groups_Oplus__class_Oplus( X, Y, Y ) }.
% 0.95/1.61 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.95/1.61 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.95/1.61 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.95/1.61 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.95/1.61 ( X ), ! Z = c_Groups_Oplus__class_Oplus( X, Z, Y ), Y =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.61 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.95/1.61 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.95/1.61 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.95/1.61 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.95/1.61 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.95/1.61 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.95/1.61 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.95/1.61 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.95/1.61 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.95/1.61 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.95/1.61 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.95/1.61 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.95/1.61 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.95/1.61 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.95/1.61 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.95/1.61 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.95/1.61 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.95/1.61 U ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.95/1.61 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.95/1.61 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.95/1.61 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.95/1.61 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.95/1.61 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.95/1.61 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ), c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, T, Y ) }.
% 0.95/1.61 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, T, Y ), c_Orderings_Oord__class_Oless(
% 0.95/1.61 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.95/1.61 , Y, Z ) ) }.
% 0.95/1.61 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.95/1.61 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, Z, Y ) }.
% 0.95/1.61 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.95/1.61 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.95/1.61 , T, Y ) ) }.
% 0.95/1.61 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.95/1.61 X, c_Groups_Oplus__class_Oplus( X, Z, T ), c_Groups_Oplus__class_Oplus( X
% 0.95/1.61 , Y, T ) ) }.
% 0.95/1.61 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.95/1.61 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.95/1.61 , T, Y ) ) }.
% 0.95/1.61 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, U, T ), c_Orderings_Oord__class_Oless( X,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X, Y
% 0.95/1.61 , T ) ) }.
% 0.95/1.61 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, T )
% 0.95/1.61 , c_Groups_Oplus__class_Oplus( X, Y, T ) ), c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, Z, Y ) }.
% 0.95/1.61 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.95/1.61 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, Z, Y ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.95/1.61 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.95/1.61 { ! class_Rings_Osemiring( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP
% 0.95/1.61 ( c_Groups_Otimes__class_Otimes( X ), U ), T ),
% 0.95/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.61 ( X ), Z ), T ), Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, U, Z
% 0.95/1.61 ) ), T ), Y ) }.
% 0.95/1.61 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.95/1.61 ( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.95/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.61 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.95/1.61 ), U = Z, T = Y }.
% 0.95/1.61 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.95/1.61 ( X ), ! U = Z, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.95/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.61 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.95/1.61 ) }.
% 0.95/1.61 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.95/1.61 ( X ), ! T = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.95/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.61 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.95/1.61 ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Y
% 0.95/1.61 ) ), Z ) }.
% 0.95/1.61 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.95/1.61 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.95/1.61 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.95/1.61 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.95/1.61 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.95/1.61 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.95/1.61 ( X ), U = T, Z = Y, ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.95/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.61 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.95/1.61 ) }.
% 0.95/1.61 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.95/1.61 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.95/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.61 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.95/1.61 ), ! U = T }.
% 0.95/1.61 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.95/1.61 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.95/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.61 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.95/1.61 ), ! Z = Y }.
% 0.95/1.61 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.61 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.61 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.95/1.61 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.61 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.95/1.61 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 0.95/1.61 c_Rings_Odvd__class_Odvd( X ), Z ), T ) ), hBOOL( hAPP( hAPP(
% 0.95/1.61 c_Rings_Odvd__class_Odvd( X ), Z ), c_Groups_Oplus__class_Oplus( X, Y, T
% 0.95/1.61 ) ) ) }.
% 0.95/1.61 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.95/1.61 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.95/1.61 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.95/1.61 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ), Y ) = Y }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Z, Y ) ) =
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ),
% 0.95/1.61 c_Polynomial_Osmult( X, T, Z ), c_Polynomial_Osmult( X, T, Y ) ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ), hAPP
% 0.95/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y
% 0.95/1.61 ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.95/1.61 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 0.95/1.61 { ! class_Groups_Ozero( X ), c_Polynomial_OAbs__poly( X,
% 0.95/1.61 c_Polynomial_Ocoeff( X, Y ) ) = Y }.
% 0.95/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.61 , c_Groups_Oplus__class_Oplus( X, Y, Z ), c_Groups_Ozero__class_Ozero( X
% 0.95/1.61 ) ) }.
% 0.95/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 0.95/1.61 Z, Y ) ) }.
% 0.95/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 0.95/1.61 Y, Z ) ) }.
% 0.95/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.95/1.61 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 0.95/1.61 .
% 0.95/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.95/1.61 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.95/1.61 .
% 0.95/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.95/1.61 X ), Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), ! Z =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.95/1.61 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.95/1.61 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.95/1.61 ) }.
% 0.95/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Y,
% 0.95/1.61 Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.61 ) }.
% 0.95/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.61 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X
% 0.95/1.61 , Y, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.61 c_Groups_Oplus__class_Oplus( X, Y, Y ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.61 ) }.
% 0.95/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.61 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.95/1.61 ), c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless(
% 0.95/1.61 X, T, c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.95/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.61 c_Groups_Oplus__class_Oplus( X, Y, Y ) ), c_Orderings_Oord__class_Oless(
% 0.95/1.61 X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.95/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.61 c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.95/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.95/1.61 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Y
% 0.95/1.61 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.95/1.61 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.95/1.61 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.95/1.61 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.61 c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.95/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.61 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.95/1.61 , c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.95/1.61 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.61 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, U, T ), c_Orderings_Oord__class_Oless(
% 0.95/1.61 X, c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X
% 0.95/1.61 , Y, T ) ) }.
% 0.95/1.61 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, U )
% 0.95/1.61 , c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.61 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.95/1.61 ) = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X
% 0.95/1.61 ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.61 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.95/1.61 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.95/1.61 ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.95/1.61 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.61 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.95/1.61 ( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! W = U, T = Z, !
% 0.95/1.61 c_Groups_Oplus__class_Oplus( X, W, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) =
% 0.95/1.61 c_Groups_Oplus__class_Oplus( X, U, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.95/1.61 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 0.95/1.61 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, T )
% 0.95/1.61 , Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree(
% 0.95/1.61 X, c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Z, T ) ), Y ) }
% 0.95/1.61 .
% 0.95/1.61 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 0.95/1.61 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) )
% 0.95/1.61 , c_Polynomial_Odegree( X, c_Groups_Oplus__class_Oplus(
% 0.95/1.61 tc_Polynomial_Opoly( X ), Z, Y ) ) = c_Polynomial_Odegree( X, Y ) }.
% 0.95/1.61 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 0.95/1.61 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) )
% 0.95/1.61 , c_Polynomial_Odegree( X, c_Groups_Oplus__class_Oplus(
% 0.95/1.61 tc_Polynomial_Opoly( X ), Y, Z ) ) = c_Polynomial_Odegree( X, Y ) }.
% 0.95/1.61 { ! class_Groups_Ocomm__monoid__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 0.95/1.61 Z ), Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.61 c_Polynomial_Odegree( X, T ), Y ), c_Orderings_Oord__class_Oless__eq(
% 0.95/1.61 tc_Nat_Onat, c_Polynomial_Odegree( X, c_Groups_Oplus__class_Oplus(
% 0.95/1.61 tc_Polynomial_Opoly( X ), Z, T ) ), Y ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.95/1.61 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, T, Z ) ), Y
% 0.95/1.61 ) = hAPP( c_Polynomial_Opoly( X, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.95/1.61 , Y ) ) }.
% 0.95/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.95/1.61 ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.61 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.61 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.95/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.61 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.61 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.61 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.95/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.95/1.61 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.95/1.61 ) ) }.
% 0.95/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.61 ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.95/1.61 ) ) }.
% 0.95/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.61 ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.95/1.61 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.95/1.61 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.61 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.95/1.61 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.95/1.61 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 0.95/1.61 X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 0.95/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.95/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) ), Z = c_Groups_Ozero__class_Ozero( X )
% 0.95/1.61 }.
% 0.95/1.61 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.95/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.95/1.61 }.
% 0.95/1.61 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.95/1.61 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.95/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.61 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.95/1.61 ) ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__ring__strict( X ), Z =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.95/1.61 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__ring__strict( X ), Y =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.95/1.61 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.95/1.61 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.95/1.61 c_Polynomial_OpCons( X, T, Z ) ), Y ) = c_Groups_Oplus__class_Oplus( X, T
% 0.95/1.61 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), hAPP(
% 0.95/1.61 c_Polynomial_Opoly( X, Z ), Y ) ) ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 0.95/1.61 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 0.95/1.61 c_Polynomial_OpCons( X, Z, Y ) ) = c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ), Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__0( X ),
% 0.95/1.61 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X,
% 0.95/1.61 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus(
% 0.95/1.61 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, Y,
% 0.95/1.61 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) ),
% 0.95/1.61 c_Polynomial_OpCons( X, T,
% 0.95/1.61 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) ) ) }
% 0.95/1.61 .
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.95/1.61 c_Polynomial_OpCons( X, T, Z ) ), Y ) = c_Groups_Oplus__class_Oplus(
% 0.95/1.61 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 0.95/1.61 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y ) ) ) }
% 0.95/1.61 .
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ),
% 0.95/1.61 c_Polynomial_OpCons( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus(
% 0.95/1.61 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, Z, T ),
% 0.95/1.61 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ) ) ) }
% 0.95/1.61 .
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 0.95/1.61 tc_Polynomial_Opoly( X ), U, c_Polynomial_Osmult( X, T, Z ) ) =
% 0.95/1.61 c_Polynomial_OpCons( X, Y, Z ), Y = hAPP( c_Polynomial_Opoly( X, U ), T )
% 0.95/1.61 }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 0.95/1.61 tc_Polynomial_Opoly( X ), U, c_Polynomial_Osmult( X, T, Z ) ) =
% 0.95/1.61 c_Polynomial_OpCons( X, Y, Z ), Z = c_Polynomial_Osynthetic__div( X, U, T
% 0.95/1.61 ) }.
% 0.95/1.61 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 0.95/1.61 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ), hBOOL(
% 0.95/1.61 hAPP( Z, skol14( U, W, Z ) ) ) }.
% 0.95/1.61 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 0.95/1.61 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ), hBOOL(
% 0.95/1.61 hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Y ),
% 0.95/1.61 c_Groups_Oplus__class_Oplus( X, skol14( X, Y, Z ),
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) ) ) ) }.
% 0.95/1.61 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 0.95/1.61 hAPP( c_Rings_Odvd__class_Odvd( X ), Y ), c_Groups_Oplus__class_Oplus( X
% 0.95/1.61 , T, c_Groups_Ozero__class_Ozero( X ) ) ) ), ! hBOOL( hAPP( Z, T ) ),
% 0.95/1.61 hBOOL( hAPP( Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ),
% 0.95/1.61 skol28( X, Y, Z ) ) ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.95/1.61 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.95/1.61 ) ), c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 0.95/1.61 ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.95/1.61 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.95/1.61 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.95/1.61 ) ) }.
% 0.95/1.61 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.95/1.61 , U = c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), T ), Y )
% 0.95/1.61 }.
% 0.95/1.61 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.95/1.61 , alpha21( X, Y, Z, T ) }.
% 0.95/1.61 { ! class_Fields_Ofield( X ), ! U = c_Groups_Oplus__class_Oplus(
% 0.95/1.61 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ), Z ), T ), Y ), ! alpha21( X, Y, Z, T ),
% 0.95/1.61 c_Polynomial_Opdivmod__rel( X, U, T, Z, Y ) }.
% 0.95/1.61 { ! alpha21( X, Y, Z, T ), alpha10( X, Z, T ) }.
% 0.95/1.61 { ! alpha21( X, Y, Z, T ), alpha18( X, Y, T ) }.
% 0.95/1.61 { ! alpha10( X, Z, T ), ! alpha18( X, Y, T ), alpha21( X, Y, Z, T ) }.
% 0.95/1.61 { ! alpha18( X, Y, Z ), Z = c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ), alpha22( X, Y, Z ) }.
% 0.95/1.61 { ! Z = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha18( X
% 0.95/1.61 , Y, Z ) }.
% 0.95/1.61 { ! alpha22( X, Y, Z ), alpha18( X, Y, Z ) }.
% 0.95/1.61 { ! alpha22( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.61 c_Polynomial_Odegree( X, Y ), c_Polynomial_Odegree( X, Z ) ) }.
% 0.95/1.61 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha22( X
% 0.95/1.61 , Y, Z ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, Y
% 0.95/1.61 ), c_Polynomial_Odegree( X, Z ) ), alpha22( X, Y, Z ) }.
% 0.95/1.61 { ! alpha10( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ), Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.61 { Z = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha10( X,
% 0.95/1.61 Y, Z ) }.
% 0.95/1.61 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha10( X
% 0.95/1.61 , Y, Z ) }.
% 0.95/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.95/1.61 c_Groups_Oplus__class_Oplus( X, Y, Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.95/1.61 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.95/1.61 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__semiring__1__strict( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, T, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), U ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), W
% 0.95/1.61 ), ! c_Groups_Oplus__class_Oplus( X, U, W ) = c_Groups_Oone__class_Oone
% 0.95/1.61 ( X ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X,
% 0.95/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), W ), T ) ), Y ) }.
% 0.95/1.61 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.95/1.61 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.95/1.61 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.95/1.61 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oone__class_Oone(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ) = c_Polynomial_OpCons( X,
% 0.95/1.61 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ) ) }.
% 0.95/1.61 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.95/1.61 c_Groups_Oone__class_Oone( X ) }.
% 0.95/1.61 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Oone__class_Oone( X ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.61 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.95/1.61 = Y }.
% 0.95/1.61 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.95/1.61 = Y }.
% 0.95/1.61 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.95/1.61 = Y }.
% 0.95/1.61 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.95/1.61 = Y }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.95/1.61 = Y }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.95/1.61 = Y }.
% 0.95/1.61 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = Y, X =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.61 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.61 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.61 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.95/1.61 tc_Nat_Onat, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.61 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( tc_Nat_Onat ) ) = X }.
% 0.95/1.61 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Nat_Onat ), X ) = X }.
% 0.95/1.61 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.95/1.61 , ! c_Polynomial_Opdivmod__rel( X, U, T, V0, W ), Z = V0 }.
% 0.95/1.61 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.95/1.61 , ! c_Polynomial_Opdivmod__rel( X, U, T, V0, W ), Y = W }.
% 0.95/1.61 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, U, Y )
% 0.95/1.61 , ! c_Polynomial_Opdivmod__rel( X, T, Z, V0, W ), Y = W }.
% 0.95/1.61 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, Y, U )
% 0.95/1.61 , ! c_Polynomial_Opdivmod__rel( X, T, Z, W, V0 ), Y = W }.
% 0.95/1.61 { ! class_Groups_Oone( X ), ! c_Groups_Oone__class_Oone( X ) = Y, Y =
% 0.95/1.61 c_Groups_Oone__class_Oone( X ) }.
% 0.95/1.61 { ! class_Groups_Oone( X ), ! Y = c_Groups_Oone__class_Oone( X ),
% 0.95/1.61 c_Groups_Oone__class_Oone( X ) = Y }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 0.95/1.61 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.95/1.61 c_Groups_Oone__class_Oone( X ) }.
% 0.95/1.61 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 0.95/1.61 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.95/1.61 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.95/1.61 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.95/1.61 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hBOOL( hAPP( hAPP(
% 0.95/1.61 c_Rings_Odvd__class_Odvd( X ), c_Groups_Oone__class_Oone( X ) ), Y ) ) }
% 0.95/1.61 .
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.95/1.61 ( tc_Nat_Onat, Y, Z ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y
% 0.95/1.61 , X ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, X ) =
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.95/1.61 tc_Nat_Onat, Y, T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.95/1.61 .
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.95/1.61 tc_Nat_Onat, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.95/1.61 .
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.95/1.61 ( tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) )
% 0.95/1.61 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.95/1.61 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }
% 0.95/1.61 .
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.95/1.61 ( tc_Nat_Onat, Y, X ), X ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.95/1.61 ( tc_Nat_Onat, Y, X ), Y ) }.
% 0.95/1.61 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ),
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) ), hBOOL( hAPP( hAPP(
% 0.95/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ) }.
% 0.95/1.61 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.95/1.61 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ),
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.95/1.61 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.95/1.61 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol15( X, Y ) ) }.
% 0.95/1.61 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, T ),
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ), X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.95/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.95/1.61 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), T ), Z ),
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), X ) ) =
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus
% 0.95/1.61 ( tc_Nat_Onat, T, Y ) ), Z ), X ) }.
% 0.95/1.61 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ),
% 0.95/1.61 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ), X =
% 0.95/1.61 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.95/1.61 { ! X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 0.95/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), c_Groups_Oone__class_Oone(
% 0.95/1.61 tc_Nat_Onat ) ) ) }.
% 0.95/1.61 { hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ),
% 0.95/1.61 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) ) }.
% 0.95/1.61 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.95/1.61 c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y = c_Groups_Oone__class_Oone(
% 0.95/1.61 tc_Nat_Onat ) }.
% 0.95/1.61 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.95/1.61 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X = c_Groups_Oone__class_Oone(
% 0.95/1.61 tc_Nat_Onat ) }.
% 0.95/1.61 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.95/1.61 c_Groups_Oone__class_Oone( tc_Nat_Onat ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.95/1.61 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.95/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.95/1.61 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 0.95/1.61 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), Y =
% 0.95/1.61 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.95/1.61 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X =
% 0.95/1.61 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.95/1.61 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.95/1.61 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Groups_Oone__class_Oone(
% 0.95/1.61 tc_Nat_Onat ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.95/1.61 , Y ), X ) }.
% 0.95/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.61 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) = X }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Osmult( X,
% 0.95/1.61 c_Groups_Oone__class_Oone( X ), Y ) = Y }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__1( X ), ! Y = c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( tc_Nat_Onat ), hAPP( c_Polynomial_Ocoeff( X, c_Groups_Oone__class_Oone
% 0.95/1.61 ( tc_Polynomial_Opoly( X ) ) ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__1( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Nat_Onat ), hAPP( c_Polynomial_Ocoeff( X, c_Groups_Oone__class_Oone(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ) ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.61 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ), Z =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.61 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ), Y =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.61 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opdivmod__rel( X,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ) }.
% 0.95/1.61 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ), Z =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.61 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ), Y = T }
% 0.95/1.61 .
% 0.95/1.61 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ), ! Y = T, c_Polynomial_Opdivmod__rel( X, T,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ) }.
% 0.95/1.61 { ! class_Fields_Ofield( X ), c_Polynomial_Opdivmod__rel( X,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.95/1.61 { ! class_Fields_Ofield( X ), c_Polynomial_Opdivmod__rel( X, Y,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) }.
% 0.95/1.61 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.95/1.61 , c_Polynomial_Opdivmod__rel( X, c_Polynomial_Osmult( X, W, U ), T,
% 0.95/1.61 c_Polynomial_Osmult( X, W, Z ), c_Polynomial_Osmult( X, W, Y ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__semidom( X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.61 c_Groups_Oone__class_Oone( X ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__semidom( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.95/1.61 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero( X ) ) }
% 0.95/1.61 .
% 0.95/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, c_Groups_Oone__class_Oone( X ), Z ), c_Orderings_Oord__class_Oless(
% 0.95/1.61 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.95/1.61 , Y, c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) )
% 0.95/1.61 ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = hAPP(
% 0.95/1.61 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X
% 0.95/1.61 , Z, c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.95/1.61 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP
% 0.95/1.61 ( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.95/1.61 c_Groups_Oone__class_Oone( X ) ) ), Z ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.95/1.61 , Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.95/1.61 c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.95/1.61 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.95/1.61 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha11( X, Y ), alpha19( X
% 0.95/1.61 , Y ) }.
% 0.95/1.61 { ! alpha11( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.95/1.61 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.95/1.61 { ! alpha19( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.95/1.61 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.95/1.61 { ! alpha19( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.61 { ! alpha19( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Nat_Onat ) ) }.
% 0.95/1.61 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha19( X, Y ) }.
% 0.95/1.61 { ! alpha11( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Nat_Onat ) ) }.
% 0.95/1.61 { ! alpha11( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.61 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha11( X, Y ) }.
% 0.95/1.61 { ! c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ), alpha12( X, Y ),
% 0.95/1.61 alpha20( X, Y ) }.
% 0.95/1.61 { ! alpha12( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.95/1.61 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 0.95/1.61 { ! alpha20( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.95/1.61 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 0.95/1.61 { ! alpha20( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.61 { ! alpha20( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Nat_Onat ) ) }.
% 0.95/1.61 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha20( X, Y ) }.
% 0.95/1.61 { ! alpha12( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Nat_Onat ) ) }.
% 0.95/1.61 { ! alpha12( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.61 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha12( X, Y ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.95/1.61 tc_Nat_Onat, Y, X ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.95/1.61 tc_Nat_Onat, Y, X ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), X = c_Nat_OSuc(
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol16( X, Y ) ) ) }.
% 0.95/1.61 { ! X = c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.95/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) ) }.
% 0.95/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.95/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Y )
% 0.95/1.61 ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.95/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), c_Nat_OSuc
% 0.95/1.61 ( X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.95/1.61 { c_Groups_Oone__class_Oone( tc_Nat_Onat ) = c_Nat_OSuc(
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.95/1.61 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X )
% 0.95/1.61 , X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Odegree( X,
% 0.95/1.61 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.95/1.61 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.95/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 0.95/1.61 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.95/1.61 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.95/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 0.95/1.61 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.95/1.61 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.61 c_Groups_Oone__class_Oone( X ), c_Groups_Oone__class_Oone( X ) ) ) }.
% 0.95/1.61 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.95/1.61 , ! c_Polynomial_Opdivmod__rel( X, Z, V1, V0, W ),
% 0.95/1.61 c_Polynomial_Opdivmod__rel( X, U, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), V1 ), V0
% 0.95/1.61 , c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), W ), Y )
% 0.95/1.61 ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__0( X ), c_Orderings_Oord__class_Oless__eq
% 0.95/1.61 ( tc_Nat_Onat, c_Polynomial_Odegree( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y ) ),
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Polynomial_Odegree( X, Z ),
% 0.95/1.61 c_Polynomial_Odegree( X, Y ) ) ) }.
% 0.95/1.61 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ), Z = c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) =
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Polynomial_Odegree( X, Y ),
% 0.95/1.61 c_Polynomial_Odegree( X, Z ) ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.95/1.61 c_Polynomial_Omonom( X, U, T ) ), c_Polynomial_Omonom( X, Z, Y ) ) =
% 0.95/1.61 c_Polynomial_Omonom( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U
% 0.95/1.61 ), Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, Y ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__semiring__1( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, T, Y ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.95/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.95/1.61 X ), W ), ! c_Groups_Oplus__class_Oplus( X, U, W ) =
% 0.95/1.61 c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.61 ( X ), U ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), T )
% 0.95/1.61 ), Y ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( tc_Nat_Onat ), X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.95/1.61 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.61 X ), Y ) ), X ) ), Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 0.95/1.61 hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), X ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( tc_Nat_Onat ), X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.95/1.61 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.61 Y ), X ) ), X ) ), Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 0.95/1.61 hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ), X ) ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Ocoeff( X, hAPP
% 0.95/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y
% 0.95/1.61 ) ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 0.95/1.61 Z ), c_Polynomial_Odegree( X, Y ) ) ) = hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( c_Polynomial_Ocoeff( X, Z ),
% 0.95/1.61 c_Polynomial_Odegree( X, Z ) ) ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.95/1.61 c_Polynomial_Odegree( X, Y ) ) ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Oplus__class_Oplus(
% 0.95/1.61 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 0.95/1.61 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ) ) ) ), c_Polynomial_Osynthetic__div( X, Y, Z )
% 0.95/1.61 ), c_Polynomial_OpCons( X, hAPP( c_Polynomial_Opoly( X, Y ), Z ),
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) = Y }.
% 0.95/1.61 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X,
% 0.95/1.61 c_Polynomial_Opoly__gcd( X, Z, Y ) ), c_Polynomial_Odegree( X,
% 0.95/1.61 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) = c_Groups_Ozero__class_Ozero( X )
% 0.95/1.61 }.
% 0.95/1.61 { ! class_Fields_Ofield( X ), Z = c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X,
% 0.95/1.61 c_Polynomial_Opoly__gcd( X, Z, Y ) ), c_Polynomial_Odegree( X,
% 0.95/1.61 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) = c_Groups_Oone__class_Oone( X ) }
% 0.95/1.61 .
% 0.95/1.61 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X,
% 0.95/1.61 c_Polynomial_Opoly__gcd( X, Z, Y ) ), c_Polynomial_Odegree( X,
% 0.95/1.61 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) = c_Groups_Oone__class_Oone( X ) }
% 0.95/1.61 .
% 0.95/1.61 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP( hAPP(
% 0.95/1.61 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons
% 0.95/1.61 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ), c_Polynomial_OpCons( X,
% 0.95/1.61 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ) ) ) ), Z ) ) }.
% 0.95/1.61 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Polynomial_OpCons( X,
% 0.95/1.61 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ) ) ) ), Z ) ), hAPP( c_Polynomial_Opoly( X, Z )
% 0.95/1.61 , Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.61 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X, Z,
% 0.95/1.61 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ),
% 0.95/1.61 hAPP( c_Polynomial_Opoly( X, Y ), c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.95/1.61 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.61 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Y ),
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( X, Z ) ) = c_Groups_Ozero__class_Ozero(
% 0.95/1.61 X ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X
% 0.95/1.61 ) ), c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 0.95/1.61 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ) }.
% 0.95/1.61 { ! class_Fields_Ofield( X ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Z, Y ) ), Z ) ) }
% 0.95/1.61 .
% 0.95/1.61 { ! class_Fields_Ofield( X ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Z, Y ) ), Y ) ) }
% 0.95/1.61 .
% 0.95/1.61 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 0.95/1.61 , c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.95/1.61 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 0.95/1.61 , c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.95/1.61 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Z,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.95/1.61 Y ) ) = Y }.
% 0.95/1.61 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.61 Z, Y ) ) = Y }.
% 0.95/1.61 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.95/1.61 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, c_Groups_Oplus__class_Oplus
% 0.95/1.61 ( tc_Nat_Onat, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.95/1.61 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.95/1.61 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.95/1.61 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ), Y = X }.
% 0.95/1.61 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) }.
% 0.95/1.61 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ), Z = X }.
% 0.95/1.61 { ! Z = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.95/1.61 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Y,
% 0.95/1.61 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ) =
% 0.95/1.61 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.61 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 0.95/1.61 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.95/1.61 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.61 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.95/1.61 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.61 { ! class_Groups_Oab__group__add( X ), c_Polynomial_Odegree( X,
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) =
% 0.95/1.61 c_Polynomial_Odegree( X, Y ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X, Z,
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) =
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ),
% 0.95/1.61 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X,
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) =
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ),
% 0.95/1.61 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 0.95/1.61 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.95/1.61 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 0.95/1.61 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) }.
% 0.95/1.61 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.95/1.61 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 0.95/1.61 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) }.
% 0.95/1.61 { ! class_Groups_Oab__group__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ) ), Y ) =
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( X, hAPP( c_Polynomial_Ocoeff( X, Z ), Y
% 0.95/1.61 ) ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ) ), Y ) =
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( X, hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 0.95/1.61 ) }.
% 0.95/1.61 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.95/1.61 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, Z, Y ) ) =
% 0.95/1.61 c_Polynomial_Omonom( X, c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.95/1.61 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 0.95/1.61 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 0.95/1.61 c_Polynomial_Opoly__gcd( X, Y, Z ) }.
% 0.95/1.61 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Z,
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) =
% 0.95/1.61 c_Polynomial_Opoly__gcd( X, Z, Y ) }.
% 0.95/1.61 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 0.95/1.61 , Y ), Y = c_Groups_Ouminus__class_Ouminus( X, Z ) }.
% 0.95/1.61 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 0.95/1.61 , Z ), Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.95/1.61 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, T,
% 0.95/1.61 c_Polynomial_Opoly__gcd( X, Z, Y ) ) = c_Polynomial_Opoly__gcd( X, Z,
% 0.95/1.61 c_Polynomial_Opoly__gcd( X, T, Y ) ) }.
% 0.95/1.61 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ), Y ) =
% 0.95/1.61 c_Polynomial_Opoly__gcd( X, Z, Y ) }.
% 0.95/1.61 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 0.95/1.61 ) = Y, c_Groups_Ouminus__class_Ouminus( X, Y ) = Z }.
% 0.95/1.61 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 0.95/1.61 ) = Z, c_Groups_Ouminus__class_Ouminus( X, Z ) = Y }.
% 0.95/1.61 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 0.95/1.61 ) = c_Groups_Ouminus__class_Ouminus( X, Y ), Z = Y }.
% 0.95/1.61 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ouminus__class_Ouminus
% 0.95/1.61 ( X, Z ) = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.95/1.61 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 0.95/1.61 c_Polynomial_Opoly__gcd( X, T, Z ), Y ) = c_Polynomial_Opoly__gcd( X, T,
% 0.95/1.61 c_Polynomial_Opoly__gcd( X, Z, Y ) ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__ring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.95/1.61 c_Rings_Odvd__class_Odvd( X ), c_Groups_Ouminus__class_Ouminus( X, Z ) )
% 0.95/1.61 , Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__ring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.95/1.61 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 0.95/1.61 c_Rings_Odvd__class_Odvd( X ), c_Groups_Ouminus__class_Ouminus( X, Z ) )
% 0.95/1.61 , Y ) ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__ring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.95/1.61 c_Rings_Odvd__class_Odvd( X ), Z ), c_Groups_Ouminus__class_Ouminus( X, Y
% 0.95/1.61 ) ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__ring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.95/1.61 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 0.95/1.61 c_Rings_Odvd__class_Odvd( X ), Z ), c_Groups_Ouminus__class_Ouminus( X, Y
% 0.95/1.61 ) ) ) }.
% 0.95/1.61 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.95/1.61 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.95/1.61 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.95/1.61 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.95/1.61 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.95/1.61 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.95/1.61 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.95/1.61 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.95/1.61 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.95/1.61 ), Z ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 0.95/1.61 Z = Y, Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.95/1.61 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.95/1.61 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.95/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.95/1.61 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.95/1.61 , c_Groups_Ouminus__class_Ouminus( X, Z ) ),
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 0.95/1.61 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.95/1.61 , c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.95/1.61 ( X, Y ) ) }.
% 0.95/1.61 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 0.95/1.61 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.95/1.61 ) ), Y ) }.
% 0.95/1.61 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 0.95/1.61 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.95/1.61 ( X, Y ) ) }.
% 0.95/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.95/1.61 , c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, Y, Z ), c_Orderings_Oord__class_Oless(
% 0.95/1.61 X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.95/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.95/1.61 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 0.95/1.61 ( X, Y ), Z ) }.
% 0.95/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.95/1.61 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 0.95/1.61 ( X, Z ), Y ) }.
% 0.95/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ouminus__class_Ouminus( X,
% 0.95/1.61 Y ) ), c_Orderings_Oord__class_Oless( X, Y,
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.95/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ouminus__class_Ouminus( X,
% 0.95/1.61 Z ) ), c_Orderings_Oord__class_Oless( X, Z,
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.95/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.95/1.61 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.95/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.95/1.61 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.95/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.95/1.61 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.95/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.95/1.61 , Z ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( X, Y ), Z ) }.
% 0.95/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.95/1.61 , Y ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.95/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ouminus__class_Ouminus
% 0.95/1.61 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.95/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 0.95/1.61 ( X, Z ) ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.95/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( X, Y ) = Y, Y =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.95/1.61 = Y }.
% 0.95/1.61 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 0.95/1.61 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.95/1.61 ) }.
% 0.95/1.61 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.95/1.61 ) }.
% 0.95/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( X, Y ), Y = c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( X ) }.
% 0.95/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus( X
% 0.95/1.61 , Y ) }.
% 0.95/1.61 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Groups_Ozero__class_Ozero( X )
% 0.95/1.61 = Y }.
% 0.95/1.61 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Ouminus__class_Ouminus( X, Y
% 0.95/1.61 ) }.
% 0.95/1.61 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.61 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.61 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.61 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.61 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.61 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 0.95/1.61 ( tc_Polynomial_Opoly( X ) ), T ), c_Polynomial_Opoly__gcd( X, Z, Y ) ) )
% 0.95/1.61 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) )
% 0.95/1.61 , T ), Z ) ) }.
% 0.95/1.61 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 0.95/1.61 ( tc_Polynomial_Opoly( X ) ), T ), c_Polynomial_Opoly__gcd( X, Z, Y ) ) )
% 0.95/1.61 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) )
% 0.95/1.61 , T ), Y ) ) }.
% 0.95/1.61 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 0.95/1.61 ( tc_Polynomial_Opoly( X ) ), T ), Z ) ), ! hBOOL( hAPP( hAPP(
% 0.95/1.61 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), T ), Y ) ), hBOOL(
% 0.95/1.61 hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), T ),
% 0.95/1.61 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) }.
% 0.95/1.61 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 0.95/1.61 ( tc_Polynomial_Opoly( X ) ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 0.95/1.61 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Z ), T ) ), hBOOL(
% 0.95/1.61 hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Z ),
% 0.95/1.61 c_Polynomial_Opoly__gcd( X, Y, T ) ) ) }.
% 0.95/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.95/1.61 , Y ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.95/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.61 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 0.95/1.61 ( X, Y ), Y ) }.
% 0.95/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.95/1.61 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.61 ) }.
% 0.95/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.61 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 0.95/1.61 ( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 0.95/1.61 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.61 ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.95/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.61 ) }.
% 0.95/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.61 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.95/1.61 ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.95/1.61 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.95/1.61 .
% 0.95/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.95/1.61 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.95/1.61 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.95/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.95/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.95/1.61 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.95/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.95/1.61 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.95/1.61 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.61 , Y ) }.
% 0.95/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.95/1.61 , Y ) }.
% 0.95/1.61 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Ozero__class_Ozero(
% 0.95/1.61 X ) }.
% 0.95/1.61 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 0.95/1.61 , Y ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.61 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.95/1.61 = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ouminus__class_Ouminus
% 0.95/1.61 ( X, Y ) }.
% 0.95/1.61 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.61 { ! class_Groups_Oab__group__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.61 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.95/1.61 = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.95/1.61 Z ) = Y }.
% 0.95/1.61 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ouminus__class_Ouminus( X, Y
% 0.95/1.61 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) ), Y
% 0.95/1.61 ) }.
% 0.95/1.61 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = c_Groups_Oone__class_Oone
% 0.95/1.61 ( X ), Y = c_Groups_Oone__class_Oone( X ), Y =
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) }.
% 0.95/1.61 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.95/1.61 c_Groups_Oone__class_Oone( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.61 ( X ), Y ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.95/1.61 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ),
% 0.95/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) =
% 0.95/1.61 c_Groups_Oone__class_Oone( X ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opos__poly( X, Y ),
% 0.95/1.61 c_Polynomial_Opos__poly( X, c_Groups_Ouminus__class_Ouminus(
% 0.95/1.61 tc_Polynomial_Opoly( X ), Y ) ) }.
% 0.95/1.61 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.95/1.61 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus
% 0.95/1.61 ( X, Z ) }.
% 0.95/1.61 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 0.95/1.61 , Z ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.61 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 0.95/1.61 ( tc_Polynomial_Opoly( X ) ), Z ), Y ) ), alpha26( X, Y, Z, T ), ! Y =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), ! T =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.95/1.61 c_Polynomial_Opoly__gcd( X, Y, T ) = Z }.
% 0.95/1.61 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 0.95/1.61 ( tc_Polynomial_Opoly( X ) ), Z ), Y ) ), alpha26( X, Y, Z, T ), ! hAPP(
% 0.95/1.61 c_Polynomial_Ocoeff( X, Z ), c_Polynomial_Odegree( X, Z ) ) =
% 0.95/1.61 c_Groups_Oone__class_Oone( X ), c_Polynomial_Opoly__gcd( X, Y, T ) = Z }
% 0.95/1.61 .
% 0.95/1.61 { ! alpha26( X, Y, Z, T ), alpha27( X, Y, Z, T ), alpha24( X, Y, T ) }.
% 0.95/1.61 { ! alpha26( X, Y, Z, T ), alpha27( X, Y, Z, T ), ! hAPP(
% 0.95/1.61 c_Polynomial_Ocoeff( X, Z ), c_Polynomial_Odegree( X, Z ) ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.61 { ! alpha27( X, Y, Z, T ), alpha26( X, Y, Z, T ) }.
% 0.95/1.61 { ! alpha24( X, Y, T ), hAPP( c_Polynomial_Ocoeff( X, Z ),
% 0.95/1.61 c_Polynomial_Odegree( X, Z ) ) = c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.61 alpha26( X, Y, Z, T ) }.
% 0.95/1.61 { ! alpha27( X, Y, Z, T ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ), Z ), T ) ), alpha28( X, Y, Z, T ) }.
% 0.95/1.61 { hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ),
% 0.95/1.61 Z ), T ) ), alpha27( X, Y, Z, T ) }.
% 0.95/1.61 { ! alpha28( X, Y, Z, T ), alpha27( X, Y, Z, T ) }.
% 0.95/1.61 { ! alpha28( X, Y, Z, T ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ), skol17( X, Y, U, W ) ), Y ) ) }.
% 0.95/1.61 { ! alpha28( X, Y, Z, T ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ), skol17( X, Y, U, T ) ), T ) ) }.
% 0.95/1.61 { ! alpha28( X, Y, Z, T ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ), skol17( X, Y, Z, T ) ), Z ) ) }.
% 0.95/1.61 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) )
% 0.95/1.61 , U ), Y ) ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ), U ), T ) ), hBOOL( hAPP( hAPP(
% 0.95/1.61 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), U ), Z ) ), alpha28
% 0.95/1.61 ( X, Y, Z, T ) }.
% 0.95/1.61 { ! alpha24( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.61 { ! alpha24( X, Y, Z ), Z = c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.61 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), ! Z =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha24( X, Y, Z
% 0.95/1.61 ) }.
% 0.95/1.61 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 0.95/1.61 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ) ) ) ), c_Polynomial_Oorder( X, Z, Y ) ) ), Y )
% 0.95/1.61 ) }.
% 0.95/1.61 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 0.95/1.61 ( tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 0.95/1.61 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ) ) ) ), c_Nat_OSuc( c_Polynomial_Oorder( X, Z,
% 0.95/1.61 Y ) ) ) ), Y ) ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.95/1.61 tc_Nat_Onat ) ) = Y }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 0.95/1.61 ( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), T ), Z
% 0.95/1.61 ) ), Y ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), hAPP(
% 0.95/1.61 c_Polynomial_Opoly( X, T ), Y ) ), Z ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.95/1.61 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.95/1.61 , Z ), c_Nat_OSuc( c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.95/1.61 ) ) ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc(
% 0.95/1.61 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), Z = Y, Z =
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.95/1.61 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.95/1.61 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.95/1.61 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc(
% 0.95/1.61 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP
% 0.95/1.61 ( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), T ), Y ) ) = hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 0.95/1.61 tc_Nat_Onat, Z, Y ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__semidom( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone
% 0.95/1.61 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ), Y ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Orderings_Oord__class_Oless__eq
% 0.95/1.61 ( tc_Nat_Onat, c_Polynomial_Odegree( X, hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), Z ), Y ) ),
% 0.95/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.61 c_Polynomial_Odegree( X, Z ) ), Y ) ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 0.95/1.61 c_Polynomial_Omonom( X, T, Z ) ), Y ) = hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Odegree( X, hAPP(
% 0.95/1.61 hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ),
% 0.95/1.61 c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 0.95/1.61 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ) = Y }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Ocoeff( X, hAPP
% 0.95/1.61 ( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ),
% 0.95/1.61 c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 0.95/1.61 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ), Y ) = c_Groups_Oone__class_Oone
% 0.95/1.61 ( X ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__ring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP(
% 0.95/1.61 hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.95/1.61 c_Polynomial_Omonom( X, c_Groups_Oone__class_Oone( X ), T ) ), Z ) ), Y )
% 0.95/1.61 = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Y ), T ) ), hAPP( c_Polynomial_Opoly(
% 0.95/1.61 X, Z ), Y ) ) }.
% 0.95/1.61 { ! class_Rings_Oidom( X ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 0.95/1.61 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ) ) ) ), c_Polynomial_Oorder( X, Z, Y ) ) ), Y )
% 0.95/1.61 ) }.
% 0.95/1.61 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 0.95/1.61 ( tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 0.95/1.61 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ) ) ) ), c_Nat_OSuc( c_Polynomial_Oorder( X, Z,
% 0.95/1.61 Y ) ) ) ), Y ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), Z ), ! c_Orderings_Oord__class_Oless(
% 0.95/1.61 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), T ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Orderings_Oord__class_Oless(
% 0.95/1.61 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ), hBOOL( hAPP
% 0.95/1.61 ( hAPP( c_Rings_Odvd__class_Odvd( X ), Y ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__1( X ), ! Y = c_Groups_Oone__class_Oone( X
% 0.95/1.61 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Y ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.95/1.61 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), hAPP(
% 0.95/1.61 hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.95/1.61 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ),
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) = hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ) }.
% 0.95/1.61 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! hBOOL( hAPP( hAPP(
% 0.95/1.61 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ) ) ), hBOOL( hAPP(
% 0.95/1.61 hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ) }.
% 0.95/1.61 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! hBOOL( hAPP( hAPP(
% 0.95/1.61 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 0.95/1.61 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ) ) ) }.
% 0.95/1.61 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP( hAPP
% 0.95/1.61 ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) ), Y =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 0.95/1.61 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), X ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.95/1.61 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), X =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.95/1.61 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 0.95/1.61 ), X ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 0.95/1.61 ( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Z ), hAPP( hAPP
% 0.95/1.61 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.95/1.61 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), c_Nat_OSuc(
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) = c_Nat_OSuc(
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.95/1.61 { ! hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) =
% 0.95/1.61 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = c_Nat_OSuc(
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.95/1.61 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.95/1.61 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP(
% 0.95/1.61 hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc
% 0.95/1.61 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.95/1.61 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 0.95/1.61 ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.95/1.61 , Y ), X ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Nat_Onat ), Y ) }.
% 0.95/1.61 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 0.95/1.61 ), X ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.95/1.61 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! hBOOL( hAPP( hAPP(
% 0.95/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ) ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) ), hBOOL( hAPP(
% 0.95/1.61 hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y ) ) }.
% 0.95/1.61 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! hBOOL( hAPP( hAPP(
% 0.95/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 0.95/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ) ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) ) }.
% 0.95/1.61 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP
% 0.95/1.61 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ) ), Y =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 0.95/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X ) ) }.
% 0.95/1.61 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP
% 0.95/1.61 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ) ) ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 0.95/1.61 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 0.95/1.61 ) }.
% 0.95/1.61 { ! class_Rings_Oring__1__no__zero__divisors( X ), Y =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( X ) }.
% 0.95/1.61 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.95/1.61 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.95/1.61 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.95/1.61 = c_Groups_Oone__class_Oone( X ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.95/1.61 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 0.95/1.61 c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.95/1.61 X ), Z ), T ) ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T )
% 0.95/1.61 ) ) }.
% 0.95/1.61 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) }.
% 0.95/1.61 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.95/1.61 tc_Nat_Onat ) ) = Y }.
% 0.95/1.61 { ! class_Rings_Olinordered__semidom( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.95/1.61 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__semidom( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.61 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.95/1.61 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__semidom( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), Y )
% 0.95/1.61 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.95/1.61 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.95/1.61 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.95/1.61 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.95/1.61 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.95/1.61 .
% 0.95/1.61 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.95/1.61 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.95/1.61 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Nat_Onat ) }.
% 0.95/1.61 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.95/1.61 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.95/1.61 , ! Z = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y )
% 0.95/1.61 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ), T = Z }.
% 0.95/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! T = Z, hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) }.
% 0.95/1.61 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.61 c_Nat_OSuc( Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.61 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) }.
% 0.95/1.61 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.95/1.61 , Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.95/1.61 , Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.95/1.61 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.95/1.61 , Y ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.95/1.61 c_Groups_Oone__class_Oone( X ) }.
% 0.95/1.61 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 0.95/1.61 tc_Nat_Onat, Z, Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.95/1.61 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__1( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), hBOOL( hAPP( hAPP
% 0.95/1.61 ( c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Power_Opower__class_Opower
% 0.95/1.61 ( X ), T ), Z ) ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y
% 0.95/1.61 ) ) ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.95/1.61 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, U, T ), hBOOL( hAPP( hAPP
% 0.95/1.61 ( c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Power_Opower__class_Opower
% 0.95/1.61 ( X ), Z ), U ) ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T
% 0.95/1.61 ) ) ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.95/1.61 c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.95/1.61 X ), T ), Z ) ), Y ) ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat
% 0.95/1.61 , U, Z ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), T ), U ) ), Y ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP
% 0.95/1.61 ( c_Power_Opower__class_Opower( X ), Y ), T ) ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.61 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__semidom( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ) ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.61 ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ) = hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.95/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.95/1.61 X ), Y ), Z = Y }.
% 0.95/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.95/1.61 X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.95/1.61 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.95/1.61 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), ! Y =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.95/1.61 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.95/1.61 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), Y =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.95/1.61 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.95/1.61 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ) ) }.
% 0.95/1.61 { ! class_Rings_Oring__1( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.95/1.61 ), c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.95/1.61 c_Groups_Oone__class_Oone( X ) ) ), Y ) ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.61 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.95/1.61 c_Groups_Oone__class_Oone( X ), T ), c_Orderings_Oord__class_Oless( X,
% 0.95/1.61 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.95/1.61 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.95/1.61 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.95/1.61 ( tc_Nat_Onat, T, Z ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__semidom( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), T )
% 0.95/1.61 , c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ),
% 0.95/1.61 c_Groups_Oone__class_Oone( X ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.61 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 0.95/1.61 , T, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.95/1.61 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), T ), Z ) = hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.95/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.95/1.61 X ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ), T = Y }.
% 0.95/1.61 { ! class_Rings_Olinordered__semidom( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.95/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oone__class_Oone
% 0.95/1.61 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 0.95/1.61 { ! class_Power_Opower( X ), c_Power_Opower__class_Opower( X ) =
% 0.95/1.61 c_Power_Opower_Opower( X, c_Groups_Oone__class_Oone( X ),
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol18( X, Y ) ) }.
% 0.95/1.61 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.61 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.95/1.61 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.95/1.61 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.95/1.61 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.95/1.61 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ),
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ) ), hBOOL( hAPP
% 0.95/1.61 ( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ) }.
% 0.95/1.61 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) )
% 0.95/1.61 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ),
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ) ) }.
% 0.95/1.61 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) )
% 0.95/1.61 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ),
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, T ) ) ), hBOOL( hAPP( hAPP(
% 0.95/1.61 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), c_Groups_Oplus__class_Oplus
% 0.95/1.61 ( tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), T ) ) ) }.
% 0.95/1.61 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) )
% 0.95/1.61 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ),
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.95/1.61 tc_Int_Oint, U, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 0.95/1.61 , Z ), X ) ), T ) ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.95/1.61 tc_Int_Oint ), Y ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, T ) ) )
% 0.95/1.61 }.
% 0.95/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ) ), X ) =
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.95/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) =
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.95/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.95/1.61 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) = X }.
% 0.95/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 0.95/1.61 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) = X }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.95/1.61 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), X =
% 0.95/1.61 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.95/1.61 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), Y =
% 0.95/1.61 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( tc_Int_Oint ), X ), ! X = c_Groups_Oone__class_Oone( tc_Int_Oint ), ! Y
% 0.95/1.61 = c_Groups_Oone__class_Oone( tc_Int_Oint ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 0.95/1.61 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.95/1.61 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) )
% 0.95/1.61 , ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), ! hBOOL( hAPP( hAPP(
% 0.95/1.61 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), X ), Y ) ), ! hBOOL( hAPP( hAPP
% 0.95/1.61 ( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) ), X = Y }.
% 0.95/1.61 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP( hAPP
% 0.95/1.61 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ), Z =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hBOOL( hAPP( hAPP(
% 0.95/1.61 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 0.95/1.61 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP
% 0.95/1.61 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y
% 0.95/1.61 ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X
% 0.95/1.61 ) ) }.
% 0.95/1.61 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), ! hBOOL( hAPP( hAPP(
% 0.95/1.61 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 0.95/1.61 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ) ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) ) }.
% 0.95/1.61 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), ! hBOOL( hAPP( hAPP(
% 0.95/1.61 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ) ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) ), hBOOL( hAPP(
% 0.95/1.61 hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ) }.
% 0.95/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP(
% 0.95/1.61 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.95/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) = hAPP
% 0.95/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) }.
% 0.95/1.61 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) )
% 0.95/1.61 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ),
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) ) }.
% 0.95/1.61 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ),
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) ), hBOOL( hAPP( hAPP
% 0.95/1.61 ( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) ) }.
% 0.95/1.61 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) )
% 0.95/1.61 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ),
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ), X ) ) }.
% 0.95/1.61 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ),
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ), X ) ), hBOOL( hAPP(
% 0.95/1.61 hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) ) }.
% 0.95/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ), X ) =
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.95/1.61 { hAPP( hAPP( c_Power_Opower_Opower( T, Z, Y ), X ),
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = Z }.
% 0.95/1.61 { hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), c_Nat_OSuc( X ) ) =
% 0.95/1.61 hAPP( hAPP( Z, Y ), hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), X
% 0.95/1.61 ) ) }.
% 0.95/1.61 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 0.95/1.61 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 0.95/1.61 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 0.95/1.61 { ! class_Lattices_Oboolean__algebra( X ), c_Groups_Ouminus__class_Ouminus
% 0.95/1.61 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 0.95/1.61 { ! class_Groups_Ouminus( X ), hAPP( c_Groups_Ouminus__class_Ouminus(
% 0.95/1.61 tc_fun( T, X ), Z ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( Z, Y
% 0.95/1.61 ) ) }.
% 0.95/1.61 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( X, Z ) = c_Groups_Ouminus__class_Ouminus
% 0.95/1.61 ( X, Y ), Z = Y }.
% 0.95/1.61 { ! class_Lattices_Oboolean__algebra( X ), ! Z = Y,
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( X, Z ) = c_Groups_Ouminus__class_Ouminus
% 0.95/1.61 ( X, Y ) }.
% 0.95/1.61 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.95/1.61 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.95/1.61 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.95/1.61 hAPP( X, Y ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol19( Z, Y
% 0.95/1.61 ), Y ) }.
% 0.95/1.61 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.95/1.61 hAPP( X, Y ) ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.95/1.61 skol19( X, Y ) ), ! hBOOL( hAPP( X, Z ) ) }.
% 0.95/1.61 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.95/1.61 hAPP( X, Y ) ), hBOOL( hAPP( X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat
% 0.95/1.61 , skol19( X, Y ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 0.95/1.61 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Y,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.95/1.61 c_Polynomial_Osmult( X, c_Rings_Oinverse__class_Oinverse( X, hAPP(
% 0.95/1.61 c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) ), Y ) }.
% 0.95/1.61 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 0.95/1.61 c_Rings_Oinverse__class_Oinverse( X, hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Oinverse( X, Z
% 0.95/1.61 ) ), Y ) }.
% 0.95/1.61 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.95/1.61 , c_Rings_Oinverse__class_Oinverse( X, hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) ) = hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Oinverse( X, Y
% 0.95/1.61 ) ), Z ) }.
% 0.95/1.61 { ! class_Rings_Odivision__ring( X ), ! hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = c_Groups_Oone__class_Oone
% 0.95/1.61 ( X ), c_Rings_Oinverse__class_Oinverse( X, Z ) = Y }.
% 0.95/1.61 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.95/1.61 , Z = c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse
% 0.95/1.61 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP(
% 0.95/1.61 hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.95/1.61 c_Rings_Oinverse__class_Oinverse( X, Z ) ),
% 0.95/1.61 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.95/1.61 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.95/1.61 ( tc_Int_Oint, X ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.95/1.61 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.95/1.61 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ),
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.95/1.61 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint,
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) = X }.
% 0.95/1.61 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( tc_Int_Oint ) ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.95/1.61 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 0.95/1.61 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ouminus__class_Ouminus( X,
% 0.95/1.61 Y ) ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.95/1.61 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.95/1.61 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.95/1.61 , c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ouminus__class_Ouminus( X
% 0.95/1.61 , Y ) ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.95/1.61 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ), Y = X }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Z ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, Z ) }.
% 0.95/1.61 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ) }.
% 0.95/1.61 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, X ) }.
% 0.95/1.61 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y = X,
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), ! Y = X }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), Y = X,
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.95/1.61 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 0.95/1.61 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.61 { ! class_Rings_Odivision__ring__inverse__zero( X ), !
% 0.95/1.61 c_Rings_Oinverse__class_Oinverse( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.95/1.61 ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.61 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Y =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X, Y
% 0.95/1.61 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.61 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.95/1.61 , ! c_Rings_Oinverse__class_Oinverse( X, Y ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.61 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.95/1.61 , c_Rings_Oinverse__class_Oinverse( X, c_Rings_Oinverse__class_Oinverse(
% 0.95/1.61 X, Y ) ) = Y }.
% 0.95/1.61 { ! class_Rings_Odivision__ring( X ), ! c_Rings_Oinverse__class_Oinverse( X
% 0.95/1.61 , Y ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( X ) }.
% 0.95/1.61 { ! class_Rings_Odivision__ring( X ), ! c_Rings_Oinverse__class_Oinverse( X
% 0.95/1.61 , Z ) = c_Rings_Oinverse__class_Oinverse( X, Y ), Z =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z
% 0.95/1.61 = Y }.
% 0.95/1.61 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 0.95/1.61 c_Rings_Oinverse__class_Oinverse( X, c_Rings_Oinverse__class_Oinverse( X
% 0.95/1.61 , Y ) ) = Y }.
% 0.95/1.61 { ! class_Rings_Odivision__ring__inverse__zero( X ), !
% 0.95/1.61 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 0.95/1.61 c_Rings_Oinverse__class_Oinverse( X, Y ), Z = Y }.
% 0.95/1.61 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Z = Y,
% 0.95/1.61 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 0.95/1.61 c_Rings_Oinverse__class_Oinverse( X, Y ) }.
% 0.95/1.61 { ! class_Rings_Odivision__ring__inverse__zero( X ), !
% 0.95/1.61 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 0.95/1.61 c_Rings_Oinverse__class_Oinverse( X, Y ), Z = Y }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.61 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Int_Oint ), X ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.61 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) }.
% 0.95/1.61 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Int_Oint ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.95/1.61 { ! c_Groups_Ozero__class_Ozero( tc_Int_Oint ) = c_Groups_Oone__class_Oone
% 0.95/1.61 ( tc_Int_Oint ) }.
% 0.95/1.61 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Oinverse( X,
% 0.95/1.61 c_Groups_Oone__class_Oone( X ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.95/1.61 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) =
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ) }.
% 0.95/1.61 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus
% 0.95/1.61 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 0.95/1.61 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.95/1.61 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 0.95/1.61 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( tc_Int_Oint ) ) = X }.
% 0.95/1.61 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Int_Oint ), X ) = X }.
% 0.95/1.61 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.95/1.61 tc_Int_Oint, c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ),
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.95/1.61 ( tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.95/1.61 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.95/1.61 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.95/1.61 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.95/1.61 tc_Int_Oint, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 0.95/1.61 .
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.95/1.61 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y
% 0.95/1.61 = X }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.95/1.61 tc_Int_Oint ) ) ) }.
% 0.95/1.61 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.95/1.61 tc_Int_Oint ) ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Int_Oint ), c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.95/1.61 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Z ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.95/1.61 tc_Int_Oint, Y, T ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 0.95/1.61 .
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.95/1.61 tc_Int_Oint ) ), X ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.95/1.61 tc_Int_Oint ) ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X )
% 0.95/1.61 }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.95/1.61 tc_Int_Oint ) ), X ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.95/1.61 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X )
% 0.95/1.61 }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.95/1.61 tc_Int_Oint ) ) ) }.
% 0.95/1.61 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.95/1.61 , Z = c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.61 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.95/1.61 c_Rings_Oinverse__class_Oinverse( X, Z ) ) = hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 0.95/1.61 Y ) ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) ),
% 0.95/1.61 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.95/1.61 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.95/1.61 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.95/1.61 c_Rings_Oinverse__class_Oinverse( X, Y ) ), Y ) =
% 0.95/1.61 c_Groups_Oone__class_Oone( X ) }.
% 0.95/1.61 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.95/1.61 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ),
% 0.95/1.61 c_Rings_Oinverse__class_Oinverse( X, Y ) ) = c_Groups_Oone__class_Oone( X
% 0.95/1.61 ) }.
% 0.95/1.61 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 0.95/1.61 c_Polynomial_Opdivmod__rel( X, W, U, T, Z ), c_Polynomial_Opdivmod__rel(
% 0.95/1.61 X, W, c_Polynomial_Osmult( X, Y, U ), c_Polynomial_Osmult( X,
% 0.95/1.61 c_Rings_Oinverse__class_Oinverse( X, Y ), T ), Z ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.95/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.95/1.61 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.95/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oone__class_Oone
% 0.95/1.61 ( tc_Int_Oint ), Y ) }.
% 0.95/1.61 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.95/1.61 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.95/1.61 ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, T, W ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.95/1.61 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, U ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, Z ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, T ) }.
% 0.95/1.61 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.95/1.61 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.95/1.61 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.95/1.61 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, U, Y ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, U ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, U ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Y ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.95/1.61 ( tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.95/1.61 Z ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.95/1.61 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.95/1.61 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.95/1.61 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.95/1.61 c_Rings_Oinverse__class_Oinverse( X, Y ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone( X ) )
% 0.95/1.61 }.
% 0.95/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.95/1.61 ! c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone( X )
% 0.95/1.61 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X )
% 0.95/1.61 , c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 0.95/1.61 ), c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless__eq(
% 0.95/1.61 X, Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless(
% 0.95/1.61 X, c_Groups_Oone__class_Oone( X ), Y ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.61 ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X
% 0.95/1.61 , Y ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), Y ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 0.95/1.61 ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.95/1.61 { ! class_Fields_Ofield__inverse__zero( X ),
% 0.95/1.61 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.61 { ! class_Fields_Ofield__inverse__zero( X ),
% 0.95/1.61 c_Rings_Oinverse__class_Oinverse( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 0.95/1.61 Z ) ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.95/1.61 { ! class_Fields_Ofield__inverse__zero( X ), !
% 0.95/1.61 c_Rings_Oinverse__class_Oinverse( X, Y ) = c_Groups_Oone__class_Oone( X )
% 0.95/1.61 , Y = c_Groups_Oone__class_Oone( X ) }.
% 0.95/1.61 { ! class_Fields_Ofield__inverse__zero( X ), ! Y =
% 0.95/1.61 c_Groups_Oone__class_Oone( X ), c_Rings_Oinverse__class_Oinverse( X, Y )
% 0.95/1.61 = c_Groups_Oone__class_Oone( X ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 0.95/1.61 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.61 ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.61 ), c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.61 c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Ozero__class_Ozero( X
% 0.95/1.61 ) ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.61 c_Rings_Oinverse__class_Oinverse( X, Y ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.61 ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.61 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.95/1.61 ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.95/1.61 X, c_Rings_Oinverse__class_Oinverse( X, Z ),
% 0.95/1.61 c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.95/1.61 X, c_Rings_Oinverse__class_Oinverse( X, Z ),
% 0.95/1.61 c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.95/1.61 X, c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( X ) ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.95/1.61 .
% 0.95/1.61 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.95/1.61 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.95/1.61 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.95/1.61 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.95/1.61 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless( X,
% 0.95/1.61 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.95/1.61 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.95/1.61 X, Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless(
% 0.95/1.61 X, c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( X ) ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.95/1.61 X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X
% 0.95/1.61 , Y ) ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.95/1.61 .
% 0.95/1.61 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.95/1.61 X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.95/1.61 X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X
% 0.95/1.61 , Y ) ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 0.95/1.61 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.95/1.61 , Y, c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 0.95/1.61 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.61 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.61 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 0.95/1.61 , Z ), c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 0.95/1.61 , Z ), c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 0.95/1.61 , Y ), c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 0.95/1.61 , Y ), c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 0.95/1.61 , Y ), c_Groups_Oone__class_Oone( X ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.61 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X )
% 0.95/1.61 , Y ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.61 ), c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.61 c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Oone__class_Oone( X )
% 0.95/1.61 ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), Y )
% 0.95/1.61 , c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse
% 0.95/1.61 ( X, Y ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.95/1.61 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.61 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.95/1.61 c_Rings_Oinverse__class_Oinverse( X, Z ) ) = hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.95/1.61 ) ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) ),
% 0.95/1.61 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.95/1.61 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, Y, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless(
% 0.95/1.61 X, c_Groups_Oone__class_Oone( X ), c_Rings_Oinverse__class_Oinverse( X, Y
% 0.95/1.61 ) ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 0.95/1.61 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 0.95/1.61 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, Y, c_Groups_Oone__class_Oone( X ) ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.95/1.61 ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 0.95/1.61 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.95/1.61 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP(
% 0.95/1.61 hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.95/1.61 c_Rings_Oinverse__class_Oinverse( X, Y ) ), Y ) =
% 0.95/1.61 c_Groups_Oone__class_Oone( X ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.95/1.61 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone( X ) )
% 0.95/1.61 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.95/1.61 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) }.
% 0.95/1.61 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Int_Oint ) ) }.
% 0.95/1.61 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 0.95/1.61 tc_Int_Oint ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.95/1.61 tc_Int_Oint, X, Y ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( tc_Int_Oint ), X ), hBOOL( hAPP( Y, skol20( Z, Y ) ) ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! hBOOL( hAPP( Y, U ) )
% 0.95/1.61 , hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, hAPP( hAPP
% 0.95/1.61 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), T ), X ) ) ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus(
% 0.95/1.61 tc_Int_Oint, skol20( X, Y ), X ) ) ), ! c_Orderings_Oord__class_Oless__eq
% 0.95/1.61 ( tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), ! hBOOL(
% 0.95/1.61 hAPP( Y, T ) ), hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus( tc_Int_Oint
% 0.95/1.61 , T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) )
% 0.95/1.61 ) ) }.
% 0.95/1.61 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Y, Z ) =
% 0.95/1.61 c_Polynomial_Osmult( X, c_Rings_Oinverse__class_Oinverse( X, hAPP(
% 0.95/1.61 c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) ), Y ) }.
% 0.95/1.61 { ! class_Fields_Ofield( X ), Z = c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Y, Z ) =
% 0.95/1.61 c_Polynomial_Opoly__gcd( X, Z, c_Divides_Odiv__class_Omod(
% 0.95/1.61 tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 0.95/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( X, T, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Z ) =
% 0.95/1.61 c_Divides_Odiv__class_Omod( X, T, Z ) }.
% 0.95/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( X, T, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) =
% 0.95/1.61 c_Divides_Odiv__class_Omod( X, T, Y ) }.
% 0.95/1.61 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 0.95/1.61 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), c_Divides_Odiv__class_Omod( X
% 0.95/1.61 , Y, Z ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.61 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, Y,
% 0.95/1.61 Z ) = c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP( hAPP(
% 0.95/1.61 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ) }.
% 0.95/1.61 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 0.95/1.61 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), c_Divides_Odiv__class_Omod( X
% 0.95/1.61 , Y, Z ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.95/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.95/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Z ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.61 { ! class_Divides_Oring__div( X ), ! c_Divides_Odiv__class_Omod( X, T, Z )
% 0.95/1.61 = c_Divides_Odiv__class_Omod( X, Y, Z ), c_Divides_Odiv__class_Omod( X,
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( X, T ), Z ) = c_Divides_Odiv__class_Omod
% 0.95/1.61 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ), Z ) }.
% 0.95/1.61 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) = c_Divides_Odiv__class_Omod
% 0.95/1.61 ( X, c_Groups_Ouminus__class_Ouminus( X, c_Divides_Odiv__class_Omod( X, Z
% 0.95/1.61 , Y ) ), Y ) }.
% 0.95/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y, Y
% 0.95/1.61 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.95/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.95/1.61 }.
% 0.95/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y,
% 0.95/1.61 c_Groups_Oone__class_Oone( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = c_Divides_Odiv__class_Omod
% 0.95/1.61 ( X, Z, Y ) }.
% 0.95/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( X, Z, Y ), Z ) = c_Divides_Odiv__class_Omod
% 0.95/1.61 ( X, Y, Z ) }.
% 0.95/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 0.95/1.61 ( X, c_Groups_Oplus__class_Oplus( X, T, c_Divides_Odiv__class_Omod( X, Z
% 0.95/1.61 , Y ) ), Y ) }.
% 0.95/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 0.95/1.61 ( X, c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Omod( X, T, Y
% 0.95/1.61 ), Z ), Y ) }.
% 0.95/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 0.95/1.61 ( X, c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Omod( X, T, Y
% 0.95/1.61 ), c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 0.95/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( X, T, c_Divides_Odiv__class_Omod( X, Z, Y )
% 0.95/1.61 ), Y ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X,
% 0.95/1.61 T, Z ), Y ) }.
% 0.95/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Omod( X, T, Z ), Y
% 0.95/1.61 ), Z ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X,
% 0.95/1.61 T, Y ), Z ) }.
% 0.95/1.61 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, T,
% 0.95/1.61 Z ) = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod
% 0.95/1.61 ( X, W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 0.95/1.61 c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X, T, W ), Z
% 0.95/1.61 ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X, Y, U
% 0.95/1.61 ), Z ) }.
% 0.95/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.95/1.61 c_Divides_Odiv__class_Omod( X, Z, Y ), Y ) = c_Divides_Odiv__class_Omod(
% 0.95/1.61 X, Z, Y ) }.
% 0.95/1.61 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 0.95/1.61 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 0.95/1.61 c_Rings_Odvd__class_Odvd( X ), Z ), c_Divides_Odiv__class_Omod( X, T, Y )
% 0.95/1.61 ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), T ) ) }.
% 0.95/1.61 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 0.95/1.61 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 0.95/1.61 c_Rings_Odvd__class_Odvd( X ), Z ), T ) ), hBOOL( hAPP( hAPP(
% 0.95/1.61 c_Rings_Odvd__class_Odvd( X ), Z ), c_Divides_Odiv__class_Omod( X, T, Y )
% 0.95/1.61 ) ) }.
% 0.95/1.61 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 0.95/1.61 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), c_Divides_Odiv__class_Omod( X
% 0.95/1.61 , c_Divides_Odiv__class_Omod( X, T, Y ), Z ) = c_Divides_Odiv__class_Omod
% 0.95/1.61 ( X, T, Z ) }.
% 0.95/1.61 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 0.95/1.61 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 0.95/1.61 c_Rings_Odvd__class_Odvd( X ), Z ), T ) ), hBOOL( hAPP( hAPP(
% 0.95/1.61 c_Rings_Odvd__class_Odvd( X ), Z ), c_Divides_Odiv__class_Omod( X, Y, T )
% 0.95/1.61 ) ) }.
% 0.95/1.61 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 0.95/1.61 c_Rings_Odvd__class_Odvd( X ), T ), c_Divides_Odiv__class_Omod( X, Z, Y )
% 0.95/1.61 ) ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), T ), Y ) ),
% 0.95/1.61 hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), T ), Z ) ) }.
% 0.95/1.61 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, T,
% 0.95/1.61 Z ) = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod
% 0.95/1.61 ( X, W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 0.95/1.61 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.61 ( X ), T ), W ), Z ) = c_Divides_Odiv__class_Omod( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), U ), Z ) }.
% 0.95/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.95/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Omod( X
% 0.95/1.61 , T, Z ) ), Y ), Z ) = c_Divides_Odiv__class_Omod( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.95/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.95/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Omod( X, T, Y )
% 0.95/1.61 ), Z ) }.
% 0.95/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.95/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) = hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), c_Divides_Odiv__class_Omod( X, Z
% 0.95/1.61 , Y ) ) }.
% 0.95/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.95/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 0.95/1.61 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.61 ( X ), c_Divides_Odiv__class_Omod( X, T, Y ) ),
% 0.95/1.61 c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 0.95/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.95/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 0.95/1.61 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.61 ( X ), c_Divides_Odiv__class_Omod( X, T, Y ) ), Z ), Y ) }.
% 0.95/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.95/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 0.95/1.61 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.61 ( X ), T ), c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 0.95/1.61 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, U, Y )
% 0.95/1.61 , c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), T, Z ) = Y }.
% 0.95/1.61 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Omod(
% 0.95/1.61 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ) =
% 0.95/1.61 c_Polynomial_Osmult( X, T, c_Divides_Odiv__class_Omod(
% 0.95/1.61 tc_Polynomial_Opoly( X ), Z, Y ) ) }.
% 0.95/1.61 { ! class_Fields_Ofield( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 0.95/1.61 , c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) ),
% 0.95/1.61 c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), Z, Y ) = Z }.
% 0.95/1.61 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.61 c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), T,
% 0.95/1.61 c_Polynomial_Osmult( X, Y, Z ) ) = c_Divides_Odiv__class_Omod(
% 0.95/1.61 tc_Polynomial_Opoly( X ), T, Z ) }.
% 0.95/1.61 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Omod(
% 0.95/1.61 tc_Polynomial_Opoly( X ), c_Groups_Ouminus__class_Ouminus(
% 0.95/1.61 tc_Polynomial_Opoly( X ), Z ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.95/1.61 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly
% 0.95/1.61 ( X ), Z, Y ) ) }.
% 0.95/1.61 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Omod(
% 0.95/1.61 tc_Polynomial_Opoly( X ), Z, c_Groups_Ouminus__class_Ouminus(
% 0.95/1.61 tc_Polynomial_Opoly( X ), Y ) ) = c_Divides_Odiv__class_Omod(
% 0.95/1.61 tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.95/1.61 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 0.95/1.61 c_Polynomial_Opoly__gcd( X, Y, c_Divides_Odiv__class_Omod(
% 0.95/1.61 tc_Polynomial_Opoly( X ), Z, Y ) ) }.
% 0.95/1.61 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ), c_Divides_Odiv__class_Omod(
% 0.95/1.61 tc_Polynomial_Opoly( X ), Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.61 c_Polynomial_Odegree( X, c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly
% 0.95/1.61 ( X ), Z, Y ) ), c_Polynomial_Odegree( X, Y ) ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.61 skol21( X, T, U ) ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, skol21( X, T, U ),
% 0.95/1.61 c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.61 , Y ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), skol21( X, Y, Z ) ), Z ), Y ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.95/1.61 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless(
% 0.95/1.61 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), hAPP( hAPP
% 0.95/1.61 ( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Z ), c_Groups_Ominus__class_Ominus(
% 0.95/1.61 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ), Z ) =
% 0.95/1.61 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) }.
% 0.95/1.61 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.95/1.61 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z
% 0.95/1.61 ), Y ), X ), Y ) = c_Divides_Odiv__class_Omod( tc_Nat_Onat, X, Y ) }.
% 0.95/1.61 { ! c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y = hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), skol22( X, Y ) ) }.
% 0.95/1.61 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z )
% 0.95/1.61 , c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.95/1.61 { ! c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol23( X, Y ) ) }.
% 0.95/1.61 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z )
% 0.95/1.61 , c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.61 { c_Divides_Odiv__class_Omod( tc_Int_Oint, Y,
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), ! c_Divides_Odiv__class_Omod
% 0.95/1.61 ( tc_Int_Oint, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.95/1.61 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.95/1.61 ( tc_Int_Oint, Y ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.95/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.95/1.61 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.95/1.61 ( tc_Int_Oint, c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) =
% 0.95/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.95/1.61 ( tc_Int_Oint, Y ), X ) }.
% 0.95/1.61 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.95/1.61 ( tc_Int_Oint, Y ), c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Divides_Odiv__class_Omod
% 0.95/1.61 ( tc_Int_Oint, Y, X ) ) }.
% 0.95/1.61 { c_Divides_Odiv__class_Omod( tc_Int_Oint, Y,
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Divides_Odiv__class_Omod
% 0.95/1.61 ( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) ) }
% 0.95/1.61 .
% 0.95/1.61 { ! c_Nat_OSuc( c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) = X,
% 0.95/1.61 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.61 { c_Nat_OSuc( c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) = X,
% 0.95/1.61 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.95/1.61 c_Nat_OSuc( c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) }.
% 0.95/1.61 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.61 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ), X ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.61 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) = Y }.
% 0.95/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.61 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 0.95/1.61 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.95/1.61 tc_Nat_Onat, Y, X ), X ) }.
% 0.95/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.61 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 0.95/1.61 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.95/1.61 tc_Nat_Onat, Y, X ), X ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.61 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) = Y }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Divides_Odiv__class_Omod
% 0.95/1.61 ( tc_Int_Oint, Y, X ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.95/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ), X ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.61 c_Divides_Odiv__class_Omod( tc_Nat_Onat, X, Y ) =
% 0.95/1.61 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.95/1.61 tc_Nat_Onat, X, Y ), Y ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.95/1.61 tc_Int_Oint, X, Y ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ), X ) }.
% 0.95/1.61 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.61 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ), Y ) }.
% 0.95/1.61 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Int_Oint ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.95/1.61 { c_Divides_Odiv__class_Omod( tc_Int_Oint, X, X ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.95/1.61 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.95/1.61 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 0.95/1.61 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, T,
% 0.95/1.61 c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 0.95/1.61 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.95/1.61 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 0.95/1.61 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X,
% 0.95/1.61 c_Divides_Odiv__class_Omod( X, T, Y ), Z ), Y ) }.
% 0.95/1.61 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.95/1.61 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 0.95/1.61 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X,
% 0.95/1.61 c_Divides_Odiv__class_Omod( X, T, Y ), c_Divides_Odiv__class_Omod( X, Z,
% 0.95/1.61 Y ) ), Y ) }.
% 0.95/1.61 { ! class_Divides_Oring__div( X ), ! c_Divides_Odiv__class_Omod( X, T, Z )
% 0.95/1.61 = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod( X
% 0.95/1.61 , W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 0.95/1.61 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, T, W ),
% 0.95/1.61 Z ) = c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, Y
% 0.95/1.61 , U ), Z ) }.
% 0.95/1.61 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.95/1.61 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc(
% 0.95/1.61 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ), X ) }.
% 0.95/1.61 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) )
% 0.95/1.61 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), Z )
% 0.95/1.61 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ),
% 0.95/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Z ) ) ) }.
% 0.95/1.61 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ),
% 0.95/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ), ! hBOOL( hAPP( hAPP
% 0.95/1.61 ( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), X ) ), hBOOL( hAPP( hAPP
% 0.95/1.61 ( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ) }.
% 0.95/1.61 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.95/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) =
% 0.95/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ) }.
% 0.95/1.61 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ) =
% 0.95/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.95/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) }.
% 0.95/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.61 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.95/1.61 c_Divides_Odiv__class_Omod( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.95/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.95/1.61 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) =
% 0.95/1.61 c_Divides_Odiv__class_Omod( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.95/1.61 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.95/1.61 tc_Int_Oint, Z, Y ) ), X ), Y ) = c_Divides_Odiv__class_Omod( tc_Int_Oint
% 0.95/1.61 , hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ), Y )
% 0.95/1.61 }.
% 0.95/1.61 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.61 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.95/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.61 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X, T,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.61 ( X ), c_Groups_Ominus__class_Ominus( X, Z, W ) ), U ), Y ) ) }.
% 0.95/1.61 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.61 , T, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.95/1.61 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.61 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.95/1.61 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.61 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.95/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.61 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.61 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ) }.
% 0.95/1.61 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.61 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.95/1.61 Z ) ), U ), T ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.61 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.95/1.61 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.61 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, hAPP
% 0.95/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus
% 0.95/1.61 ( X, Z, W ) ), U ), Y ) ) }.
% 0.95/1.61 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X, T
% 0.95/1.61 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.95/1.61 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless( X,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.61 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.95/1.61 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.61 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.95/1.61 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.95/1.61 X, W, Z ) ), U ), T ), Y ) }.
% 0.95/1.61 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.61 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.95/1.61 hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.95/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.61 ( X ), Z ), U ), Y ) ) }.
% 0.95/1.61 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.95/1.61 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.95/1.62 c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.95/1.62 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.95/1.62 X, U, Z ) ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 0.95/1.62 Z ) ), Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 0.95/1.62 c_Groups_Ominus__class_Ominus( X, T, Y ) ) ) }.
% 0.95/1.62 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.95/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.62 ( X ), Z ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.95/1.62 Z ) ), U ), T ) = Y }.
% 0.95/1.62 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.95/1.62 Z ) ), U ), T ) = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.95/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.62 ( X ), Z ), U ), Y ) }.
% 0.95/1.62 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.95/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.62 ( X ), Z ), U ), Y ), T = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.95/1.62 W ) ), U ), Y ) }.
% 0.95/1.62 { ! class_Rings_Oring( X ), ! T = c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.95/1.62 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.95/1.62 X, Z, W ) ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.95/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.62 ( X ), Z ), U ), Y ) }.
% 0.95/1.62 { ! class_Rings_Oring( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.95/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.62 ( X ), U ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 0.95/1.62 Z ) ), Y ) ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.95/1.62 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.95/1.62 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 0.95/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.95/1.62 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.95/1.62 ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ),
% 0.95/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.95/1.62 ( tc_Nat_Onat, Y, Z ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z )
% 0.95/1.62 ) }.
% 0.95/1.62 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ),
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ), ! hBOOL( hAPP(
% 0.95/1.62 hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X ) ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ), hBOOL( hAPP( hAPP
% 0.95/1.62 ( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y ) ) }.
% 0.95/1.62 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ),
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ), ! hBOOL( hAPP(
% 0.95/1.62 hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y ) ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ), hBOOL( hAPP( hAPP
% 0.95/1.62 ( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X ) ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z,
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.95/1.62 tc_Nat_Onat, Z, Y ), X ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.95/1.62 tc_Nat_Onat, X, Z ), Y ) ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = X }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.95/1.62 tc_Nat_Onat, Z, X ), Y ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.95/1.62 tc_Nat_Onat, X, Y ), Y ) = X }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z, X =
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X =
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.95/1.62 tc_Nat_Onat, Z, X ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.95/1.62 tc_Nat_Onat, X, Y ), Z ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ), Y ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.95/1.62 tc_Nat_Onat, X, Z ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), Z ) }.
% 0.95/1.62 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 0.95/1.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 0.95/1.62 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.95/1.62 ( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) }.
% 0.95/1.62 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.95/1.62 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) =
% 0.95/1.62 c_Groups_Ominus__class_Ominus( X, Y, Z ) }.
% 0.95/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 0.95/1.62 , Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 0.95/1.62 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.95/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.95/1.62 X, c_Groups_Ominus__class_Ominus( X, Z, Y ), c_Groups_Ozero__class_Ozero
% 0.95/1.62 ( X ) ) }.
% 0.95/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.95/1.62 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.95/1.62 , Z, Y ) }.
% 0.95/1.62 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.95/1.62 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.95/1.62 X, Y ) }.
% 0.95/1.62 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.95/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Oplus__class_Oplus(
% 0.95/1.62 X, Z, Y ) }.
% 0.95/1.62 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X, Z
% 0.95/1.62 , Y ) = c_Groups_Oplus__class_Oplus( X, Z,
% 0.95/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.95/1.62 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z, Y )
% 0.95/1.62 = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus( X
% 0.95/1.62 , Y ) ) }.
% 0.95/1.62 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.95/1.62 ) = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus(
% 0.95/1.62 X, Y ) ) }.
% 0.95/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ), Y ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ),
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, Z ),
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = Y }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X = Z }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), ! X = Z,
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ),
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.95/1.62 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.95/1.62 ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 0.95/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.95/1.62 ( tc_Nat_Onat, Z, X ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.95/1.62 ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.95/1.62 ( tc_Nat_Onat, Y, Z ), X ) }.
% 0.95/1.62 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.62 tc_Nat_Onat ), X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.62 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = X }.
% 0.95/1.62 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, X ) =
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.62 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.95/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.62 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.95/1.62 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, U, T ),
% 0.95/1.62 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.95/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.62 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.95/1.62 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 0.95/1.62 c_Orderings_Oord__class_Oless( X, U, T ) }.
% 0.95/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.62 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.95/1.62 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.95/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.62 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.95/1.62 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, U, T ) }.
% 0.95/1.62 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.95/1.62 ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.95/1.62 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ominus__class_Ominus(
% 0.95/1.62 X, Z, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.62 { ! class_Groups_Oab__group__add( X ), ! Z = Y,
% 0.95/1.62 c_Groups_Ominus__class_Ominus( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.95/1.62 ) }.
% 0.95/1.62 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.95/1.62 Z, Y ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.95/1.62 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y, Y )
% 0.95/1.62 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.62 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y,
% 0.95/1.62 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.95/1.62 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.95/1.62 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) =
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ) }.
% 0.95/1.62 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.95/1.62 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) =
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 0.95/1.62 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.95/1.62 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.95/1.62 Z, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.95/1.62 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.95/1.62 tc_Nat_Onat, Y, X ), Y ) = X }.
% 0.95/1.62 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.95/1.62 tc_Nat_Onat, Y, X ), X ) = Y }.
% 0.95/1.62 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = Z }.
% 0.95/1.62 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.62 c_Groups_Ominus__class_Ominus( X, Z, Y ), Y ) = Z }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z,
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 0.95/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.95/1.62 tc_Nat_Onat, Z, X ), Y ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.95/1.62 ( tc_Nat_Onat, Z, X ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z
% 0.95/1.62 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 0.95/1.62 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) = Y }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) =
% 0.95/1.62 c_Nat_OSuc( c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.62 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.95/1.62 class_Groups_Ocancel__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { class_Groups_Ocancel__comm__monoid__add( tc_Complex_Ocomplex ) }.
% 0.95/1.62 { class_Enum_Oenum( tc_HOL_Obool ) }.
% 0.95/1.62 { class_Groups_Ocancel__comm__monoid__add( tc_Nat_Onat ) }.
% 0.95/1.62 { class_Groups_Ocancel__comm__monoid__add( tc_Int_Oint ) }.
% 0.95/1.62 { ! class_Enum_Oenum( Y ), ! class_Enum_Oenum( X ), class_Enum_Oenum(
% 0.95/1.62 tc_fun( Y, X ) ) }.
% 0.95/1.62 { ! class_Lattices_Oboolean__algebra( X ), class_Lattices_Oboolean__algebra
% 0.95/1.62 ( tc_fun( Y, X ) ) }.
% 0.95/1.62 { ! class_Orderings_Opreorder( X ), class_Orderings_Opreorder( tc_fun( Y, X
% 0.95/1.62 ) ) }.
% 0.95/1.62 { ! class_Orderings_Oorder( X ), class_Orderings_Oorder( tc_fun( Y, X ) ) }
% 0.95/1.62 .
% 0.95/1.62 { ! class_Orderings_Oord( X ), class_Orderings_Oord( tc_fun( Y, X ) ) }.
% 0.95/1.62 { ! class_Groups_Ouminus( X ), class_Groups_Ouminus( tc_fun( Y, X ) ) }.
% 0.95/1.62 { ! class_Enum_Oenum( Y ), ! class_HOL_Oequal( X ), class_HOL_Oequal(
% 0.95/1.62 tc_fun( Y, X ) ) }.
% 0.95/1.62 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.95/1.62 tc_Int_Oint ) }.
% 0.95/1.62 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.95/1.62 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Int_Oint ) }.
% 0.95/1.62 { class_Rings_Olinordered__comm__semiring__strict( tc_Int_Oint ) }.
% 0.95/1.62 { class_Rings_Olinordered__semiring__1__strict( tc_Int_Oint ) }.
% 0.95/1.62 { class_Rings_Olinordered__semiring__strict( tc_Int_Oint ) }.
% 0.95/1.62 { class_Groups_Oordered__ab__semigroup__add( tc_Int_Oint ) }.
% 0.95/1.62 { class_Groups_Oordered__comm__monoid__add( tc_Int_Oint ) }.
% 0.95/1.62 { class_Groups_Olinordered__ab__group__add( tc_Int_Oint ) }.
% 0.95/1.62 { class_Groups_Ocancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.95/1.62 { class_Rings_Oring__1__no__zero__divisors( tc_Int_Oint ) }.
% 0.95/1.62 { class_Rings_Oordered__cancel__semiring( tc_Int_Oint ) }.
% 0.95/1.62 { class_Rings_Olinordered__ring__strict( tc_Int_Oint ) }.
% 0.95/1.62 { class_Rings_Oring__no__zero__divisors( tc_Int_Oint ) }.
% 0.95/1.62 { class_Rings_Oordered__comm__semiring( tc_Int_Oint ) }.
% 0.95/1.62 { class_Rings_Olinordered__semiring__1( tc_Int_Oint ) }.
% 0.95/1.62 { class_Groups_Oordered__ab__group__add( tc_Int_Oint ) }.
% 0.95/1.62 { class_Groups_Ocancel__semigroup__add( tc_Int_Oint ) }.
% 0.95/1.62 { class_Rings_Olinordered__semiring( tc_Int_Oint ) }.
% 0.95/1.62 { class_Rings_Olinordered__semidom( tc_Int_Oint ) }.
% 0.95/1.62 { class_Groups_Oab__semigroup__mult( tc_Int_Oint ) }.
% 0.95/1.62 { class_Groups_Ocomm__monoid__mult( tc_Int_Oint ) }.
% 0.95/1.62 { class_Groups_Oab__semigroup__add( tc_Int_Oint ) }.
% 0.95/1.62 { class_Rings_Oordered__semiring( tc_Int_Oint ) }.
% 0.95/1.62 { class_Rings_Ono__zero__divisors( tc_Int_Oint ) }.
% 0.95/1.62 { class_Groups_Ocomm__monoid__add( tc_Int_Oint ) }.
% 0.95/1.62 { class_Rings_Olinordered__ring( tc_Int_Oint ) }.
% 0.95/1.62 { class_Rings_Olinordered__idom( tc_Int_Oint ) }.
% 0.95/1.62 { class_Rings_Ocomm__semiring__1( tc_Int_Oint ) }.
% 0.95/1.62 { class_Rings_Ocomm__semiring__0( tc_Int_Oint ) }.
% 0.95/1.62 { class_Divides_Osemiring__div( tc_Int_Oint ) }.
% 0.95/1.62 { class_Rings_Ocomm__semiring( tc_Int_Oint ) }.
% 0.95/1.62 { class_Groups_Oab__group__add( tc_Int_Oint ) }.
% 0.95/1.62 { class_Rings_Ozero__neq__one( tc_Int_Oint ) }.
% 0.95/1.62 { class_Rings_Oordered__ring( tc_Int_Oint ) }.
% 0.95/1.62 { class_Orderings_Opreorder( tc_Int_Oint ) }.
% 0.95/1.62 { class_Orderings_Olinorder( tc_Int_Oint ) }.
% 0.95/1.62 { class_Groups_Omonoid__mult( tc_Int_Oint ) }.
% 0.95/1.62 { class_Rings_Ocomm__ring__1( tc_Int_Oint ) }.
% 0.95/1.62 { class_Groups_Omonoid__add( tc_Int_Oint ) }.
% 0.95/1.62 { class_Rings_Osemiring__1( tc_Int_Oint ) }.
% 0.95/1.62 { class_Rings_Osemiring__0( tc_Int_Oint ) }.
% 0.95/1.62 { class_Groups_Ogroup__add( tc_Int_Oint ) }.
% 0.95/1.62 { class_Divides_Oring__div( tc_Int_Oint ) }.
% 0.95/1.62 { class_Rings_Omult__zero( tc_Int_Oint ) }.
% 0.95/1.62 { class_Rings_Ocomm__ring( tc_Int_Oint ) }.
% 0.95/1.62 { class_Orderings_Oorder( tc_Int_Oint ) }.
% 0.95/1.62 { class_Int_Oring__char__0( tc_Int_Oint ) }.
% 0.95/1.62 { class_Rings_Osemiring( tc_Int_Oint ) }.
% 0.95/1.62 { class_Orderings_Oord( tc_Int_Oint ) }.
% 0.95/1.62 { class_Groups_Ouminus( tc_Int_Oint ) }.
% 0.95/1.62 { class_Rings_Oring__1( tc_Int_Oint ) }.
% 0.95/1.62 { class_Power_Opower( tc_Int_Oint ) }.
% 0.95/1.62 { class_Groups_Ozero( tc_Int_Oint ) }.
% 0.95/1.62 { class_Rings_Oring( tc_Int_Oint ) }.
% 0.95/1.62 { class_Rings_Oidom( tc_Int_Oint ) }.
% 0.95/1.62 { class_Groups_Oone( tc_Int_Oint ) }.
% 0.95/1.62 { class_Rings_Odvd( tc_Int_Oint ) }.
% 0.95/1.62 { class_HOL_Oequal( tc_Int_Oint ) }.
% 0.95/1.62 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.95/1.62 tc_Nat_Onat ) }.
% 0.95/1.62 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.95/1.62 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Nat_Onat ) }.
% 0.95/1.62 { class_Rings_Olinordered__comm__semiring__strict( tc_Nat_Onat ) }.
% 0.95/1.62 { class_Rings_Olinordered__semiring__strict( tc_Nat_Onat ) }.
% 0.95/1.62 { class_Groups_Oordered__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.95/1.62 { class_Groups_Oordered__comm__monoid__add( tc_Nat_Onat ) }.
% 0.95/1.62 { class_Groups_Ocancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.95/1.62 { class_Rings_Oordered__cancel__semiring( tc_Nat_Onat ) }.
% 0.95/1.62 { class_Rings_Oordered__comm__semiring( tc_Nat_Onat ) }.
% 0.95/1.62 { class_Groups_Ocancel__semigroup__add( tc_Nat_Onat ) }.
% 0.95/1.62 { class_Rings_Olinordered__semiring( tc_Nat_Onat ) }.
% 0.95/1.62 { class_Rings_Olinordered__semidom( tc_Nat_Onat ) }.
% 0.95/1.62 { class_Groups_Oab__semigroup__mult( tc_Nat_Onat ) }.
% 0.95/1.62 { class_Groups_Ocomm__monoid__mult( tc_Nat_Onat ) }.
% 0.95/1.62 { class_Groups_Oab__semigroup__add( tc_Nat_Onat ) }.
% 0.95/1.62 { class_Rings_Oordered__semiring( tc_Nat_Onat ) }.
% 0.95/1.62 { class_Rings_Ono__zero__divisors( tc_Nat_Onat ) }.
% 0.95/1.62 { class_Groups_Ocomm__monoid__add( tc_Nat_Onat ) }.
% 0.95/1.62 { class_Rings_Ocomm__semiring__1( tc_Nat_Onat ) }.
% 0.95/1.62 { class_Rings_Ocomm__semiring__0( tc_Nat_Onat ) }.
% 0.95/1.62 { class_Divides_Osemiring__div( tc_Nat_Onat ) }.
% 0.95/1.62 { class_Rings_Ocomm__semiring( tc_Nat_Onat ) }.
% 0.95/1.62 { class_Rings_Ozero__neq__one( tc_Nat_Onat ) }.
% 0.95/1.62 { class_Orderings_Opreorder( tc_Nat_Onat ) }.
% 0.95/1.62 { class_Orderings_Olinorder( tc_Nat_Onat ) }.
% 0.95/1.62 { class_Groups_Omonoid__mult( tc_Nat_Onat ) }.
% 0.95/1.62 { class_Groups_Omonoid__add( tc_Nat_Onat ) }.
% 0.95/1.62 { class_Rings_Osemiring__1( tc_Nat_Onat ) }.
% 0.95/1.62 { class_Rings_Osemiring__0( tc_Nat_Onat ) }.
% 0.95/1.62 { class_Rings_Omult__zero( tc_Nat_Onat ) }.
% 0.95/1.62 { class_Orderings_Oorder( tc_Nat_Onat ) }.
% 0.95/1.62 { class_Rings_Osemiring( tc_Nat_Onat ) }.
% 0.95/1.62 { class_Orderings_Oord( tc_Nat_Onat ) }.
% 0.95/1.62 { class_Power_Opower( tc_Nat_Onat ) }.
% 0.95/1.62 { class_Groups_Ozero( tc_Nat_Onat ) }.
% 0.95/1.62 { class_Groups_Oone( tc_Nat_Onat ) }.
% 0.95/1.62 { class_Rings_Odvd( tc_Nat_Onat ) }.
% 0.95/1.62 { class_HOL_Oequal( tc_Nat_Onat ) }.
% 0.95/1.62 { class_Lattices_Oboolean__algebra( tc_HOL_Obool ) }.
% 0.95/1.62 { class_Orderings_Opreorder( tc_HOL_Obool ) }.
% 0.95/1.62 { class_Orderings_Oorder( tc_HOL_Obool ) }.
% 0.95/1.62 { class_Orderings_Oord( tc_HOL_Obool ) }.
% 0.95/1.62 { class_Groups_Ouminus( tc_HOL_Obool ) }.
% 0.95/1.62 { class_HOL_Oequal( tc_HOL_Obool ) }.
% 0.95/1.62 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.95/1.62 tc_Complex_Ocomplex ) }.
% 0.95/1.62 { class_Rings_Odivision__ring__inverse__zero( tc_Complex_Ocomplex ) }.
% 0.95/1.62 { class_RealVector_Oreal__normed__algebra( tc_Complex_Ocomplex ) }.
% 0.95/1.62 { class_Groups_Ocancel__ab__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.95/1.62 { class_Rings_Oring__1__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.95/1.62 { class_Rings_Oring__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.95/1.62 { class_Groups_Ocancel__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.95/1.62 { class_Fields_Ofield__inverse__zero( tc_Complex_Ocomplex ) }.
% 0.95/1.62 { class_Groups_Oab__semigroup__mult( tc_Complex_Ocomplex ) }.
% 0.95/1.62 { class_Groups_Ocomm__monoid__mult( tc_Complex_Ocomplex ) }.
% 0.95/1.62 { class_Groups_Oab__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.95/1.62 { class_Rings_Ono__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.95/1.62 { class_Groups_Ocomm__monoid__add( tc_Complex_Ocomplex ) }.
% 0.95/1.62 { class_Rings_Ocomm__semiring__1( tc_Complex_Ocomplex ) }.
% 0.95/1.62 { class_Rings_Ocomm__semiring__0( tc_Complex_Ocomplex ) }.
% 0.95/1.62 { class_Rings_Odivision__ring( tc_Complex_Ocomplex ) }.
% 0.95/1.62 { class_Rings_Ocomm__semiring( tc_Complex_Ocomplex ) }.
% 0.95/1.62 { class_Groups_Oab__group__add( tc_Complex_Ocomplex ) }.
% 0.95/1.62 { class_Rings_Ozero__neq__one( tc_Complex_Ocomplex ) }.
% 0.95/1.62 { class_Groups_Omonoid__mult( tc_Complex_Ocomplex ) }.
% 0.95/1.62 { class_Rings_Ocomm__ring__1( tc_Complex_Ocomplex ) }.
% 0.95/1.62 { class_Groups_Omonoid__add( tc_Complex_Ocomplex ) }.
% 0.95/1.62 { class_Rings_Osemiring__1( tc_Complex_Ocomplex ) }.
% 0.95/1.62 { class_Rings_Osemiring__0( tc_Complex_Ocomplex ) }.
% 0.95/1.62 { class_Groups_Ogroup__add( tc_Complex_Ocomplex ) }.
% 0.95/1.62 { class_Rings_Omult__zero( tc_Complex_Ocomplex ) }.
% 0.95/1.62 { class_Rings_Ocomm__ring( tc_Complex_Ocomplex ) }.
% 0.95/1.62 { class_Int_Oring__char__0( tc_Complex_Ocomplex ) }.
% 0.95/1.62 { class_Rings_Osemiring( tc_Complex_Ocomplex ) }.
% 0.95/1.62 { class_Groups_Ouminus( tc_Complex_Ocomplex ) }.
% 0.95/1.62 { class_Rings_Oring__1( tc_Complex_Ocomplex ) }.
% 0.95/1.62 { class_Fields_Ofield( tc_Complex_Ocomplex ) }.
% 0.95/1.62 { class_Power_Opower( tc_Complex_Ocomplex ) }.
% 0.95/1.62 { class_Groups_Ozero( tc_Complex_Ocomplex ) }.
% 0.95/1.62 { class_Rings_Oring( tc_Complex_Ocomplex ) }.
% 0.95/1.62 { class_Rings_Oidom( tc_Complex_Ocomplex ) }.
% 0.95/1.62 { class_Groups_Oone( tc_Complex_Ocomplex ) }.
% 0.95/1.62 { class_Rings_Odvd( tc_Complex_Ocomplex ) }.
% 0.95/1.62 { class_HOL_Oequal( tc_Complex_Ocomplex ) }.
% 0.95/1.62 { ! class_Rings_Oidom( X ),
% 0.95/1.62 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__idom( X ),
% 0.95/1.62 class_Groups_Oordered__cancel__ab__semigroup__add( tc_Polynomial_Opoly( X
% 0.95/1.62 ) ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__idom( X ),
% 0.95/1.62 class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Polynomial_Opoly(
% 0.95/1.62 X ) ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__idom( X ),
% 0.95/1.62 class_Rings_Olinordered__comm__semiring__strict( tc_Polynomial_Opoly( X )
% 0.95/1.62 ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__idom( X ),
% 0.95/1.62 class_Rings_Olinordered__semiring__1__strict( tc_Polynomial_Opoly( X ) )
% 0.95/1.62 }.
% 0.95/1.62 { ! class_Rings_Olinordered__idom( X ),
% 0.95/1.62 class_Rings_Olinordered__semiring__strict( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__idom( X ),
% 0.95/1.62 class_Groups_Oordered__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__idom( X ),
% 0.95/1.62 class_Groups_Oordered__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__idom( X ),
% 0.95/1.62 class_Groups_Olinordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.95/1.62 class_Groups_Ocancel__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Rings_Oidom( X ), class_Rings_Oring__1__no__zero__divisors(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__idom( X ),
% 0.95/1.62 class_Rings_Oordered__cancel__semiring( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__idom( X ),
% 0.95/1.62 class_Rings_Olinordered__ring__strict( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Rings_Oidom( X ), class_Rings_Oring__no__zero__divisors(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__idom( X ),
% 0.95/1.62 class_Rings_Oordered__comm__semiring( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__idom( X ),
% 0.95/1.62 class_Rings_Olinordered__semiring__1( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__idom( X ),
% 0.95/1.62 class_Groups_Oordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.95/1.62 class_Groups_Ocancel__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semiring(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semidom(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Oab__semigroup__mult
% 0.95/1.62 ( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Ocomm__monoid__mult(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Oab__semigroup__add
% 0.95/1.62 ( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__semiring(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Rings_Oidom( X ), class_Rings_Ono__zero__divisors(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Ocomm__monoid__add(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__ring(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__idom(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ocomm__semiring__1(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring__0(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Fields_Ofield( X ), class_Divides_Osemiring__div(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Groups_Oab__group__add( X ), class_Groups_Oab__group__add(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ozero__neq__one(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__ring(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Opreorder(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Olinorder(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Omonoid__mult(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Ocomm__ring__1(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Omonoid__add(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Osemiring__1(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring__0(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Groups_Oab__group__add( X ), class_Groups_Ogroup__add(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Fields_Ofield( X ), class_Divides_Oring__div( tc_Polynomial_Opoly
% 0.95/1.62 ( X ) ) }.
% 0.95/1.62 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Omult__zero(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Rings_Ocomm__ring( X ), class_Rings_Ocomm__ring(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oorder(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__idom( X ), class_Int_Oring__char__0(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oord(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Groups_Oab__group__add( X ), class_Groups_Ouminus(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Oring__1(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Rings_Ocomm__semiring__1( X ), class_Power_Opower(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Groups_Ozero( X ), class_Groups_Ozero( tc_Polynomial_Opoly( X ) )
% 0.95/1.62 }.
% 0.95/1.62 { ! class_Rings_Ocomm__ring( X ), class_Rings_Oring( tc_Polynomial_Opoly( X
% 0.95/1.62 ) ) }.
% 0.95/1.62 { ! class_Rings_Oidom( X ), class_Rings_Oidom( tc_Polynomial_Opoly( X ) ) }
% 0.95/1.62 .
% 0.95/1.62 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Oone(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Odvd(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Groups_Ozero( X ), ! class_HOL_Oequal( X ), class_HOL_Oequal(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! hBOOL( hAPP( hAPP( c_fequal, Y ), X ) ), Y = X }.
% 0.95/1.62 { ! Y = X, hBOOL( hAPP( hAPP( c_fequal, Y ), X ) ) }.
% 0.95/1.62 { ! skol24 = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.95/1.62 { ! hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_cs____ ), skol24 ) =
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.95/1.62
% 0.95/1.62 *** allocated 15000 integers for clauses
% 0.95/1.62 *** allocated 22500 integers for clauses
% 0.95/1.62 *** allocated 33750 integers for clauses
% 0.95/1.62 *** allocated 50625 integers for clauses
% 0.95/1.62 *** allocated 75937 integers for clauses
% 0.95/1.62 percentage equality = 0.270799, percentage horn = 0.905647
% 0.95/1.62 This is a problem with some equality
% 0.95/1.62
% 0.95/1.62
% 0.95/1.62
% 0.95/1.62 Options Used:
% 0.95/1.62
% 0.95/1.62 useres = 1
% 0.95/1.62 useparamod = 1
% 0.95/1.62 useeqrefl = 1
% 0.95/1.62 useeqfact = 1
% 0.95/1.62 usefactor = 1
% 0.95/1.62 usesimpsplitting = 0
% 0.95/1.62 usesimpdemod = 5
% 0.95/1.62 usesimpres = 3
% 0.95/1.62
% 0.95/1.62 resimpinuse = 1000
% 0.95/1.62 resimpclauses = 20000
% 0.95/1.62 substype = eqrewr
% 0.95/1.62 backwardsubs = 1
% 0.95/1.62 selectoldest = 5
% 0.95/1.62
% 0.95/1.62 litorderings [0] = split
% 0.95/1.62 litorderings [1] = extend the termordering, first sorting on arguments
% 0.95/1.62
% 0.95/1.62 termordering = kbo
% 0.95/1.62
% 0.95/1.62 litapriori = 0
% 0.95/1.62 termapriori = 1
% 0.95/1.62 litaposteriori = 0
% 0.95/1.62 termaposteriori = 0
% 0.95/1.62 demodaposteriori = 0
% 0.95/1.62 ordereqreflfact = 0
% 0.95/1.62
% 0.95/1.62 litselect = negord
% 0.95/1.62
% 0.95/1.62 maxweight = 15
% 0.95/1.62 maxdepth = 30000
% 0.95/1.62 maxlength = 115
% 0.95/1.62 maxnrvars = 195
% 0.95/1.62 excuselevel = 1
% 0.95/1.62 increasemaxweight = 1
% 0.95/1.62
% 0.95/1.62 maxselected = 10000000
% 0.95/1.62 maxnrclauses = 10000000
% 0.95/1.62
% 0.95/1.62 showgenerated = 0
% 0.95/1.62 showkept = 0
% 0.95/1.62 showselected = 0
% 0.95/1.62 showdeleted = 0
% 0.95/1.62 showresimp = 1
% 0.95/1.62 showstatus = 2000
% 0.95/1.62
% 0.95/1.62 prologoutput = 0
% 0.95/1.62 nrgoals = 5000000
% 0.95/1.62 totalproof = 1
% 0.95/1.62
% 0.95/1.62 Symbols occurring in the translation:
% 0.95/1.62
% 0.95/1.62 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.95/1.62 . [1, 2] (w:1, o:200, a:1, s:1, b:0),
% 0.95/1.62 ! [4, 1] (w:0, o:112, a:1, s:1, b:0),
% 0.95/1.62 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.95/1.62 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.95/1.62 hAPP [38, 2] (w:1, o:224, a:1, s:1, b:0),
% 0.95/1.62 v_c____ [39, 0] (w:1, o:16, a:1, s:1, b:0),
% 0.95/1.62 tc_Complex_Ocomplex [40, 0] (w:1, o:21, a:1, s:1, b:0),
% 0.95/1.62 c_Groups_Ozero__class_Ozero [41, 1] (w:1, o:117, a:1, s:1, b:0),
% 0.95/1.62 v_cs____ [43, 0] (w:1, o:30, a:1, s:1, b:0),
% 0.95/1.62 c_Polynomial_OpCons [44, 3] (w:1, o:257, a:1, s:1, b:0),
% 0.95/1.62 c_Polynomial_Opoly [45, 2] (w:1, o:225, a:1, s:1, b:0),
% 0.95/1.62 class_Rings_Ocomm__semiring__0 [48, 1] (w:1, o:120, a:1, s:1, b:0),
% 0.95/1.62 tc_Polynomial_Opoly [49, 1] (w:1, o:125, a:1, s:1, b:0),
% 0.95/1.62 class_Int_Oring__char__0 [52, 1] (w:1, o:151, a:1, s:1, b:0),
% 0.95/1.62 class_Rings_Oidom [53, 1] (w:1, o:152, a:1, s:1, b:0),
% 0.95/1.62 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant [54, 3] (w:1, o:
% 0.95/1.62 258, a:1, s:1, b:0),
% 0.95/1.62 class_Groups_Ozero [56, 1] (w:1, o:153, a:1, s:1, b:0),
% 0.95/1.62 c_Polynomial_Oorder [58, 3] (w:1, o:256, a:1, s:1, b:0),
% 0.95/1.62 tc_Nat_Onat [59, 0] (w:1, o:37, a:1, s:1, b:0),
% 0.95/1.62 c_Polynomial_Opcompose [64, 3] (w:1, o:259, a:1, s:1, b:0),
% 0.95/1.62 v_p [65, 0] (w:1, o:42, a:1, s:1, b:0),
% 0.95/1.62 c_Polynomial_Opoly__rec [70, 5] (w:1, o:301, a:1, s:1, b:0),
% 0.95/1.62 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize [71, 2] (w:1, o:226
% 0.95/1.62 , a:1, s:1, b:0),
% 0.95/1.62 c_fequal [72, 0] (w:1, o:50, a:1, s:1, b:0),
% 0.95/1.62 c_If [73, 4] (w:1, o:288, a:1, s:1, b:0),
% 0.95/1.62 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly [76, 3] (w:1
% 0.95/1.62 , o:260, a:1, s:1, b:0),
% 0.95/1.62 c_Polynomial_Osynthetic__div [78, 3] (w:1, o:261, a:1, s:1, b:0),
% 0.95/1.62 c_Polynomial_Omonom [79, 3] (w:1, o:262, a:1, s:1, b:0),
% 0.95/1.62 c_Polynomial_Odegree [80, 2] (w:1, o:228, a:1, s:1, b:0),
% 0.95/1.62 hBOOL [82, 1] (w:1, o:154, a:1, s:1, b:0),
% 0.95/1.62 class_HOL_Oequal [86, 1] (w:1, o:150, a:1, s:1, b:0),
% 0.95/1.62 c_HOL_Oequal__class_Oequal [87, 1] (w:1, o:157, a:1, s:1, b:0),
% 0.95/1.62 c_Nat_OSuc [90, 1] (w:1, o:158, a:1, s:1, b:0),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq [91, 3] (w:1, o:254, a:1, s:1, b:0)
% 0.95/1.62 ,
% 0.95/1.62 c_Polynomial_Ocoeff [93, 2] (w:1, o:227, a:1, s:1, b:0),
% 0.95/1.62 class_Orderings_Opreorder [96, 1] (w:1, o:161, a:1, s:1, b:0),
% 0.95/1.62 class_Orderings_Olinorder [98, 1] (w:1, o:162, a:1, s:1, b:0),
% 0.95/1.62 class_Orderings_Oord [99, 1] (w:1, o:159, a:1, s:1, b:0),
% 0.95/1.62 tc_fun [100, 2] (w:1, o:241, a:1, s:1, b:0),
% 0.95/1.62 class_Orderings_Oorder [102, 1] (w:1, o:160, a:1, s:1, b:0),
% 0.95/1.62 c_Orderings_Oord__class_Oless [111, 3] (w:1, o:255, a:1, s:1, b:0),
% 0.95/1.62 c_Nat_Onat_Onat__case [112, 3] (w:1, o:253, a:1, s:1, b:0),
% 0.95/1.62 c_Groups_Otimes__class_Otimes [113, 1] (w:1, o:155, a:1, s:1, b:0),
% 0.95/1.62 class_Rings_Osemiring__1 [117, 1] (w:1, o:168, a:1, s:1, b:0),
% 0.95/1.62 c_Nat_Osemiring__1__class_Oof__nat__aux [118, 4] (w:1, o:289, a:1, s:
% 0.95/1.62 1, b:0),
% 0.95/1.62 c_Polynomial_Osmult [119, 3] (w:1, o:263, a:1, s:1, b:0),
% 0.95/1.62 c_Rings_Odvd__class_Odvd [120, 1] (w:1, o:169, a:1, s:1, b:0),
% 0.95/1.62 class_Rings_Ocomm__semiring__1 [124, 1] (w:1, o:170, a:1, s:1, b:0),
% 0.95/1.62
% 0.95/1.62 class_Groups_Oab__semigroup__mult [125, 1] (w:1, o:131, a:1, s:1, b:0
% 0.95/1.62 ),
% 0.95/1.62 class_Fields_Ofield [126, 1] (w:1, o:127, a:1, s:1, b:0),
% 0.95/1.62 class_Rings_Olinordered__semiring__strict [132, 1] (w:1, o:173, a:1
% 0.95/1.62 , s:1, b:0),
% 0.95/1.62 class_Rings_Olinordered__semiring [133, 1] (w:1, o:174, a:1, s:1, b:0
% 0.95/1.62 ),
% 0.95/1.62 class_Rings_Olinordered__idom [135, 1] (w:1, o:175, a:1, s:1, b:0),
% 0.95/1.62 class_Rings_Omult__zero [136, 1] (w:1, o:180, a:1, s:1, b:0),
% 0.95/1.62 class_Rings_Oring__no__zero__divisors [137, 1] (w:1, o:163, a:1, s:1
% 0.95/1.62 , b:0),
% 0.95/1.62 class_Rings_Ono__zero__divisors [138, 1] (w:1, o:181, a:1, s:1, b:0)
% 0.95/1.62 ,
% 0.95/1.62 class_Rings_Odvd [139, 1] (w:1, o:183, a:1, s:1, b:0),
% 0.95/1.62 class_Rings_Olinordered__ring [140, 1] (w:1, o:171, a:1, s:1, b:0),
% 0.95/1.62 class_Rings_Olinordered__ring__strict [141, 1] (w:1, o:172, a:1, s:1
% 0.95/1.62 , b:0),
% 1.27/1.67 class_Rings_Oordered__cancel__semiring [142, 1] (w:1, o:184, a:1, s:1
% 1.27/1.67 , b:0),
% 1.27/1.67 class_Rings_Oordered__ring [143, 1] (w:1, o:185, a:1, s:1, b:0),
% 1.27/1.67 class_Rings_Oordered__semiring [144, 1] (w:1, o:186, a:1, s:1, b:0),
% 1.27/1.67
% 1.27/1.67 class_Rings_Oordered__comm__semiring [145, 1] (w:1, o:187, a:1, s:1
% 1.27/1.67 , b:0),
% 1.27/1.67 class_Rings_Olinordered__comm__semiring__strict [146, 1] (w:1, o:176
% 1.27/1.67 , a:1, s:1, b:0),
% 1.27/1.67 c_Polynomial_Opos__poly [147, 2] (w:1, o:242, a:1, s:1, b:0),
% 1.27/1.67 class_RealVector_Oreal__normed__algebra [148, 1] (w:1, o:188, a:1, s:
% 1.27/1.67 1, b:0),
% 1.27/1.67 c_Polynomial_OAbs__poly [154, 2] (w:1, o:243, a:1, s:1, b:0),
% 1.27/1.67 c_Orderings_Oorder_Omono [155, 4] (w:1, o:290, a:1, s:1, b:0),
% 1.27/1.67 c_Groups_Oplus__class_Oplus [156, 3] (w:1, o:264, a:1, s:1, b:0),
% 1.27/1.67 class_Groups_Ocomm__monoid__add [157, 1] (w:1, o:132, a:1, s:1, b:0)
% 1.27/1.67 ,
% 1.27/1.67 class_Groups_Oab__semigroup__add [158, 1] (w:1, o:133, a:1, s:1, b:0)
% 1.27/1.67 ,
% 1.27/1.67 class_Groups_Ocancel__semigroup__add [159, 1] (w:1, o:134, a:1, s:1
% 1.27/1.67 , b:0),
% 1.27/1.67 class_Groups_Ocancel__ab__semigroup__add [160, 1] (w:1, o:135, a:1
% 1.27/1.67 , s:1, b:0),
% 1.27/1.67 class_Groups_Omonoid__add [161, 1] (w:1, o:137, a:1, s:1, b:0),
% 1.27/1.67 class_Groups_Olinordered__ab__group__add [162, 1] (w:1, o:136, a:1
% 1.27/1.67 , s:1, b:0),
% 1.27/1.67 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct [
% 1.27/1.67 163, 1] (w:1, o:193, a:1, s:1, b:0),
% 1.27/1.67 class_Groups_Oordered__ab__semigroup__add__imp__le [164, 1] (w:1, o:
% 1.27/1.67 138, a:1, s:1, b:0),
% 1.27/1.67 class_Groups_Oordered__ab__semigroup__add [165, 1] (w:1, o:139, a:1
% 1.27/1.67 , s:1, b:0),
% 1.27/1.67 class_Groups_Oordered__cancel__ab__semigroup__add [166, 1] (w:1, o:
% 1.27/1.67 140, a:1, s:1, b:0),
% 1.27/1.67 class_Rings_Ocomm__semiring [167, 1] (w:1, o:182, a:1, s:1, b:0),
% 1.27/1.67 class_Rings_Osemiring [169, 1] (w:1, o:189, a:1, s:1, b:0),
% 1.27/1.67 class_Groups_Oordered__comm__monoid__add [177, 1] (w:1, o:141, a:1
% 1.27/1.67 , s:1, b:0),
% 1.27/1.67 class_Rings_Olinordered__semidom [178, 1] (w:1, o:177, a:1, s:1, b:0)
% 1.27/1.67 ,
% 1.27/1.67 class_Rings_Osemiring__0 [180, 1] (w:1, o:167, a:1, s:1, b:0),
% 1.27/1.67 c_Polynomial_Opdivmod__rel [182, 5] (w:1, o:302, a:1, s:1, b:0),
% 1.27/1.67 class_Rings_Olinordered__semiring__1__strict [185, 1] (w:1, o:178, a:
% 1.27/1.67 1, s:1, b:0),
% 1.27/1.67 c_Groups_Oone__class_Oone [186, 1] (w:1, o:156, a:1, s:1, b:0),
% 1.27/1.67 class_Rings_Ozero__neq__one [187, 1] (w:1, o:190, a:1, s:1, b:0),
% 1.27/1.67 class_Groups_Omonoid__mult [188, 1] (w:1, o:142, a:1, s:1, b:0),
% 1.27/1.67 class_Groups_Ocomm__monoid__mult [189, 1] (w:1, o:143, a:1, s:1, b:0)
% 1.27/1.67 ,
% 1.27/1.67 class_Groups_Oone [194, 1] (w:1, o:144, a:1, s:1, b:0),
% 1.27/1.67 class_Rings_Olinordered__semiring__1 [198, 1] (w:1, o:179, a:1, s:1
% 1.27/1.67 , b:0),
% 1.27/1.67 class_Rings_Ocomm__ring__1 [199, 1] (w:1, o:118, a:1, s:1, b:0),
% 1.27/1.67 c_Groups_Ouminus__class_Ouminus [200, 2] (w:1, o:244, a:1, s:1, b:0)
% 1.27/1.67 ,
% 1.27/1.67 c_Polynomial_Opoly__gcd [201, 3] (w:1, o:265, a:1, s:1, b:0),
% 1.27/1.67 class_Groups_Oab__group__add [202, 1] (w:1, o:145, a:1, s:1, b:0),
% 1.27/1.67 class_Groups_Ogroup__add [203, 1] (w:1, o:146, a:1, s:1, b:0),
% 1.27/1.67 class_Rings_Ocomm__ring [204, 1] (w:1, o:119, a:1, s:1, b:0),
% 1.27/1.67 class_Rings_Oring [205, 1] (w:1, o:164, a:1, s:1, b:0),
% 1.27/1.67 class_Groups_Oordered__ab__group__add [206, 1] (w:1, o:147, a:1, s:1
% 1.27/1.67 , b:0),
% 1.27/1.67 class_Rings_Oring__1__no__zero__divisors [207, 1] (w:1, o:165, a:1
% 1.27/1.67 , s:1, b:0),
% 1.27/1.67 c_Power_Opower__class_Opower [208, 1] (w:1, o:194, a:1, s:1, b:0),
% 1.27/1.67 tc_Int_Oint [209, 0] (w:1, o:102, a:1, s:1, b:0),
% 1.27/1.67 class_Power_Opower [210, 1] (w:1, o:195, a:1, s:1, b:0),
% 1.27/1.67 class_Rings_Oring__1 [211, 1] (w:1, o:166, a:1, s:1, b:0),
% 1.27/1.67 c_Power_Opower_Opower [213, 3] (w:1, o:266, a:1, s:1, b:0),
% 1.27/1.67 class_Lattices_Oboolean__algebra [214, 1] (w:1, o:197, a:1, s:1, b:0)
% 1.27/1.67 ,
% 1.27/1.67 class_Lattices_Oab__semigroup__idem__mult [222, 1] (w:1, o:196, a:1
% 1.27/1.67 , s:1, b:0),
% 1.27/1.67 class_Groups_Ouminus [224, 1] (w:1, o:148, a:1, s:1, b:0),
% 1.27/1.67 c_Rings_Oinverse__class_Oinverse [225, 2] (w:1, o:245, a:1, s:1, b:0)
% 1.27/1.67 ,
% 1.27/1.67 class_Rings_Odivision__ring__inverse__zero [226, 1] (w:1, o:191, a:1
% 1.27/1.67 , s:1, b:0),
% 1.27/1.67 class_Rings_Odivision__ring [227, 1] (w:1, o:192, a:1, s:1, b:0),
% 5.33/5.70 class_Fields_Olinordered__field__inverse__zero [230, 1] (w:1, o:128
% 5.33/5.70 , a:1, s:1, b:0),
% 5.33/5.70 class_Fields_Ofield__inverse__zero [231, 1] (w:1, o:129, a:1, s:1, b:
% 5.33/5.70 0),
% 5.33/5.70 class_Fields_Olinordered__field [232, 1] (w:1, o:130, a:1, s:1, b:0)
% 5.33/5.70 ,
% 5.33/5.70 c_Divides_Odiv__class_Omod [233, 3] (w:1, o:267, a:1, s:1, b:0),
% 5.33/5.70 class_Divides_Osemiring__div [234, 1] (w:1, o:199, a:1, s:1, b:0),
% 5.33/5.70 class_Divides_Oring__div [235, 1] (w:1, o:198, a:1, s:1, b:0),
% 5.33/5.70 c_Groups_Ominus__class_Ominus [236, 3] (w:1, o:268, a:1, s:1, b:0),
% 5.33/5.70 class_Groups_Ocancel__comm__monoid__add [242, 1] (w:1, o:149, a:1, s:
% 5.33/5.70 1, b:0),
% 5.33/5.70 tc_HOL_Obool [243, 0] (w:1, o:101, a:1, s:1, b:0),
% 5.33/5.70 class_Enum_Oenum [244, 1] (w:1, o:126, a:1, s:1, b:0),
% 5.33/5.70 alpha1 [247, 3] (w:1, o:269, a:1, s:1, b:1),
% 5.33/5.70 alpha2 [248, 2] (w:1, o:249, a:1, s:1, b:1),
% 5.33/5.70 alpha3 [249, 3] (w:1, o:274, a:1, s:1, b:1),
% 5.33/5.70 alpha4 [250, 3] (w:1, o:275, a:1, s:1, b:1),
% 5.33/5.70 alpha5 [251, 4] (w:1, o:291, a:1, s:1, b:1),
% 5.33/5.70 alpha6 [252, 4] (w:1, o:292, a:1, s:1, b:1),
% 5.33/5.70 alpha7 [253, 3] (w:1, o:276, a:1, s:1, b:1),
% 5.33/5.70 alpha8 [254, 2] (w:1, o:250, a:1, s:1, b:1),
% 5.33/5.70 alpha9 [255, 2] (w:1, o:251, a:1, s:1, b:1),
% 5.33/5.70 alpha10 [256, 3] (w:1, o:277, a:1, s:1, b:1),
% 5.33/5.70 alpha11 [257, 2] (w:1, o:246, a:1, s:1, b:1),
% 5.33/5.70 alpha12 [258, 2] (w:1, o:247, a:1, s:1, b:1),
% 5.33/5.70 alpha13 [259, 4] (w:1, o:293, a:1, s:1, b:1),
% 5.33/5.70 alpha14 [260, 3] (w:1, o:278, a:1, s:1, b:1),
% 5.33/5.70 alpha15 [261, 3] (w:1, o:279, a:1, s:1, b:1),
% 5.33/5.70 alpha16 [262, 4] (w:1, o:294, a:1, s:1, b:1),
% 5.33/5.70 alpha17 [263, 4] (w:1, o:295, a:1, s:1, b:1),
% 5.33/5.70 alpha18 [264, 3] (w:1, o:280, a:1, s:1, b:1),
% 5.33/5.70 alpha19 [265, 2] (w:1, o:248, a:1, s:1, b:1),
% 5.33/5.70 alpha20 [266, 2] (w:1, o:252, a:1, s:1, b:1),
% 5.33/5.70 alpha21 [267, 4] (w:1, o:296, a:1, s:1, b:1),
% 5.33/5.70 alpha22 [268, 3] (w:1, o:270, a:1, s:1, b:1),
% 5.33/5.70 alpha23 [269, 3] (w:1, o:271, a:1, s:1, b:1),
% 5.33/5.70 alpha24 [270, 3] (w:1, o:272, a:1, s:1, b:1),
% 5.33/5.70 alpha25 [271, 3] (w:1, o:273, a:1, s:1, b:1),
% 5.33/5.70 alpha26 [272, 4] (w:1, o:297, a:1, s:1, b:1),
% 5.33/5.70 alpha27 [273, 4] (w:1, o:298, a:1, s:1, b:1),
% 5.33/5.70 alpha28 [274, 4] (w:1, o:299, a:1, s:1, b:1),
% 5.33/5.70 skol1 [275, 2] (w:1, o:229, a:1, s:1, b:1),
% 5.33/5.70 skol2 [276, 0] (w:1, o:17, a:1, s:1, b:1),
% 5.33/5.70 skol3 [277, 1] (w:1, o:122, a:1, s:1, b:1),
% 5.33/5.70 skol4 [278, 0] (w:1, o:18, a:1, s:1, b:1),
% 5.33/5.70 skol5 [279, 1] (w:1, o:123, a:1, s:1, b:1),
% 5.33/5.70 skol6 [280, 2] (w:1, o:230, a:1, s:1, b:1),
% 5.33/5.70 skol7 [281, 3] (w:1, o:281, a:1, s:1, b:1),
% 5.33/5.70 skol8 [282, 3] (w:1, o:282, a:1, s:1, b:1),
% 5.33/5.70 skol9 [283, 2] (w:1, o:231, a:1, s:1, b:1),
% 5.33/5.70 skol10 [284, 2] (w:1, o:232, a:1, s:1, b:1),
% 5.33/5.70 skol11 [285, 1] (w:1, o:124, a:1, s:1, b:1),
% 5.33/5.70 skol12 [286, 3] (w:1, o:283, a:1, s:1, b:1),
% 5.33/5.70 skol13 [287, 3] (w:1, o:284, a:1, s:1, b:1),
% 5.33/5.70 skol14 [288, 3] (w:1, o:285, a:1, s:1, b:1),
% 5.33/5.70 skol15 [289, 2] (w:1, o:233, a:1, s:1, b:1),
% 5.33/5.70 skol16 [290, 2] (w:1, o:234, a:1, s:1, b:1),
% 5.33/5.70 skol17 [291, 4] (w:1, o:300, a:1, s:1, b:1),
% 5.33/5.70 skol18 [292, 2] (w:1, o:235, a:1, s:1, b:1),
% 5.33/5.70 skol19 [293, 2] (w:1, o:236, a:1, s:1, b:1),
% 5.33/5.70 skol20 [294, 2] (w:1, o:237, a:1, s:1, b:1),
% 5.33/5.70 skol21 [295, 3] (w:1, o:286, a:1, s:1, b:1),
% 5.33/5.70 skol22 [296, 2] (w:1, o:238, a:1, s:1, b:1),
% 5.33/5.70 skol23 [297, 2] (w:1, o:239, a:1, s:1, b:1),
% 5.33/5.70 skol24 [298, 0] (w:1, o:19, a:1, s:1, b:1),
% 5.33/5.70 skol25 [299, 0] (w:1, o:20, a:1, s:1, b:1),
% 5.33/5.70 skol26 [300, 1] (w:1, o:121, a:1, s:1, b:1),
% 5.33/5.70 skol27 [301, 2] (w:1, o:240, a:1, s:1, b:1),
% 5.33/5.70 skol28 [302, 3] (w:1, o:287, a:1, s:1, b:1).
% 5.33/5.70
% 5.33/5.70
% 5.33/5.70 Starting Search:
% 5.33/5.70
% 5.33/5.70 *** allocated 113905 integers for clauses
% 5.33/5.70 *** allocated 170857 integers for clauses
% 5.33/5.70 Resimplifying inuse:
% 5.33/5.70 Done
% 5.33/5.70
% 5.33/5.70
% 5.33/5.70 Intermediate Status:
% 5.33/5.70 Generated: 3299
% 5.33/5.70 Kept: 2044
% 5.33/5.70 Inuse: 46
% 5.33/5.70 Deleted: 0
% 5.33/5.70 Deletedinuse: 0
% 5.33/5.70
% 5.33/5.70 *** allocated 256285 integers for clauses
% 5.33/5.70 Resimplifying inuse:
% 5.33/5.70 Done
% 5.33/5.70
% 5.33/5.70 *** allocated 170857 integers for termspace/termends
% 50.08/50.46 Resimplifying inuse:
% 50.08/50.46 Done
% 50.08/50.46
% 50.08/50.46 *** allocated 384427 integers for clauses
% 50.08/50.46
% 50.08/50.46 Intermediate Status:
% 50.08/50.46 Generated: 8147
% 50.08/50.46 Kept: 4181
% 50.08/50.46 Inuse: 140
% 50.08/50.46 Deleted: 2
% 50.08/50.46 Deletedinuse: 1
% 50.08/50.46
% 50.08/50.46 Resimplifying inuse:
% 50.08/50.46 Done
% 50.08/50.46
% 50.08/50.46 *** allocated 256285 integers for termspace/termends
% 50.08/50.46 Resimplifying inuse:
% 50.08/50.46 Done
% 50.08/50.46
% 50.08/50.46
% 50.08/50.46 Intermediate Status:
% 50.08/50.46 Generated: 12129
% 50.08/50.46 Kept: 6201
% 50.08/50.46 Inuse: 212
% 50.08/50.46 Deleted: 7
% 50.08/50.46 Deletedinuse: 4
% 50.08/50.46
% 50.08/50.46 *** allocated 576640 integers for clauses
% 50.08/50.46 Resimplifying inuse:
% 50.08/50.46 Done
% 50.08/50.46
% 50.08/50.46 Resimplifying inuse:
% 50.08/50.46 Done
% 50.08/50.46
% 50.08/50.46
% 50.08/50.46 Intermediate Status:
% 50.08/50.46 Generated: 17684
% 50.08/50.46 Kept: 8642
% 50.08/50.46 Inuse: 247
% 50.08/50.46 Deleted: 8
% 50.08/50.46 Deletedinuse: 4
% 50.08/50.46
% 50.08/50.46 *** allocated 384427 integers for termspace/termends
% 50.08/50.46 Resimplifying inuse:
% 50.08/50.46 Done
% 50.08/50.46
% 50.08/50.46 Resimplifying inuse:
% 50.08/50.46 Done
% 50.08/50.46
% 50.08/50.46
% 50.08/50.46 Intermediate Status:
% 50.08/50.46 Generated: 21578
% 50.08/50.46 Kept: 10648
% 50.08/50.46 Inuse: 299
% 50.08/50.46 Deleted: 11
% 50.08/50.46 Deletedinuse: 4
% 50.08/50.46
% 50.08/50.46 *** allocated 864960 integers for clauses
% 50.08/50.46 Resimplifying inuse:
% 50.08/50.46 Done
% 50.08/50.46
% 50.08/50.46
% 50.08/50.46 Intermediate Status:
% 50.08/50.46 Generated: 26577
% 50.08/50.46 Kept: 12656
% 50.08/50.46 Inuse: 332
% 50.08/50.46 Deleted: 13
% 50.08/50.46 Deletedinuse: 4
% 50.08/50.46
% 50.08/50.46 Resimplifying inuse:
% 50.08/50.46 Done
% 50.08/50.46
% 50.08/50.46 Resimplifying inuse:
% 50.08/50.46 Done
% 50.08/50.46
% 50.08/50.46 *** allocated 576640 integers for termspace/termends
% 50.08/50.46
% 50.08/50.46 Intermediate Status:
% 50.08/50.46 Generated: 32883
% 50.08/50.46 Kept: 14847
% 50.08/50.46 Inuse: 368
% 50.08/50.46 Deleted: 17
% 50.08/50.46 Deletedinuse: 4
% 50.08/50.46
% 50.08/50.46 Resimplifying inuse:
% 50.08/50.46 Done
% 50.08/50.46
% 50.08/50.46 Resimplifying inuse:
% 50.08/50.46 Done
% 50.08/50.46
% 50.08/50.46 *** allocated 1297440 integers for clauses
% 50.08/50.46
% 50.08/50.46 Intermediate Status:
% 50.08/50.46 Generated: 39522
% 50.08/50.46 Kept: 16934
% 50.08/50.46 Inuse: 398
% 50.08/50.46 Deleted: 18
% 50.08/50.46 Deletedinuse: 5
% 50.08/50.46
% 50.08/50.46 Resimplifying inuse:
% 50.08/50.46 Done
% 50.08/50.46
% 50.08/50.46 Resimplifying inuse:
% 50.08/50.46 Done
% 50.08/50.46
% 50.08/50.46
% 50.08/50.46 Intermediate Status:
% 50.08/50.46 Generated: 45293
% 50.08/50.46 Kept: 18954
% 50.08/50.46 Inuse: 430
% 50.08/50.46 Deleted: 18
% 50.08/50.46 Deletedinuse: 5
% 50.08/50.46
% 50.08/50.46 Resimplifying inuse:
% 50.08/50.46 Done
% 50.08/50.46
% 50.08/50.46 Resimplifying clauses:
% 50.08/50.46 Done
% 50.08/50.46
% 50.08/50.46
% 50.08/50.46 Intermediate Status:
% 50.08/50.46 Generated: 49707
% 50.08/50.46 Kept: 21032
% 50.08/50.46 Inuse: 458
% 50.08/50.46 Deleted: 832
% 50.08/50.46 Deletedinuse: 5
% 50.08/50.46
% 50.08/50.46 Resimplifying inuse:
% 50.08/50.46 Done
% 50.08/50.46
% 50.08/50.46 Resimplifying inuse:
% 50.08/50.46 Done
% 50.08/50.46
% 50.08/50.46
% 50.08/50.46 Intermediate Status:
% 50.08/50.46 Generated: 55567
% 50.08/50.46 Kept: 23057
% 50.08/50.46 Inuse: 494
% 50.08/50.46 Deleted: 832
% 50.08/50.46 Deletedinuse: 5
% 50.08/50.46
% 50.08/50.46 *** allocated 864960 integers for termspace/termends
% 50.08/50.46 Resimplifying inuse:
% 50.08/50.46 Done
% 50.08/50.46
% 50.08/50.46
% 50.08/50.46 Intermediate Status:
% 50.08/50.46 Generated: 61958
% 50.08/50.46 Kept: 25318
% 50.08/50.46 Inuse: 528
% 50.08/50.46 Deleted: 832
% 50.08/50.46 Deletedinuse: 5
% 50.08/50.46
% 50.08/50.46 Resimplifying inuse:
% 50.08/50.46 Done
% 50.08/50.46
% 50.08/50.46 *** allocated 1946160 integers for clauses
% 50.08/50.46 Resimplifying inuse:
% 50.08/50.46 Done
% 50.08/50.46
% 50.08/50.46
% 50.08/50.46 Intermediate Status:
% 50.08/50.46 Generated: 68569
% 50.08/50.46 Kept: 27345
% 50.08/50.46 Inuse: 554
% 50.08/50.46 Deleted: 832
% 50.08/50.46 Deletedinuse: 5
% 50.08/50.46
% 50.08/50.46 Resimplifying inuse:
% 50.08/50.46 Done
% 50.08/50.46
% 50.08/50.46
% 50.08/50.46 Intermediate Status:
% 50.08/50.46 Generated: 73497
% 50.08/50.46 Kept: 29353
% 50.08/50.46 Inuse: 564
% 50.08/50.46 Deleted: 832
% 50.08/50.46 Deletedinuse: 5
% 50.08/50.46
% 50.08/50.46 Resimplifying inuse:
% 50.08/50.46 Done
% 50.08/50.46
% 50.08/50.46 Resimplifying inuse:
% 50.08/50.46 Done
% 50.08/50.46
% 50.08/50.46
% 50.08/50.46 Intermediate Status:
% 50.08/50.46 Generated: 82030
% 50.08/50.46 Kept: 31375
% 50.08/50.46 Inuse: 598
% 50.08/50.46 Deleted: 832
% 50.08/50.46 Deletedinuse: 5
% 50.08/50.46
% 50.08/50.46 Resimplifying inuse:
% 50.08/50.46 Done
% 50.08/50.46
% 50.08/50.46
% 50.08/50.46 Intermediate Status:
% 50.08/50.46 Generated: 90545
% 50.08/50.46 Kept: 33425
% 50.08/50.46 Inuse: 628
% 50.08/50.46 Deleted: 832
% 50.08/50.46 Deletedinuse: 5
% 50.08/50.46
% 50.08/50.46 Resimplifying inuse:
% 50.08/50.46 Done
% 50.08/50.46
% 50.08/50.46 Resimplifying inuse:
% 50.08/50.46 Done
% 50.08/50.46
% 50.08/50.46 *** allocated 1297440 integers for termspace/termends
% 50.08/50.46
% 50.08/50.46 Intermediate Status:
% 50.08/50.46 Generated: 99832
% 50.08/50.46 Kept: 35430
% 50.08/50.46 Inuse: 665
% 50.08/50.46 Deleted: 832
% 50.08/50.46 Deletedinuse: 5
% 50.08/50.46
% 50.08/50.46
% 50.08/50.46 Intermediate Status:
% 50.08/50.46 Generated: 103807
% 50.08/50.46 Kept: 38325
% 50.08/50.46 Inuse: 668
% 50.08/50.46 Deleted: 832
% 50.08/50.46 Deletedinuse: 5
% 50.08/50.46
% 50.08/50.46 Resimplifying inuse:
% 50.08/50.46 Done
% 50.08/50.46
% 50.08/50.46 Resimplifying inuse:
% 50.08/50.46 Done
% 50.08/50.46
% 50.08/50.46
% 50.08/50.46 Intermediate Status:
% 50.08/50.46 Generated: 113383
% 50.08/50.46 Kept: 40628
% 50.08/50.46 Inuse: 697
% 50.08/50.46 Deleted: 832
% 50.08/50.46 Deletedinuse: 5
% 50.08/50.46
% 50.08/50.46 Resimplifying inuse:
% 50.08/50.46 Done
% 50.08/50.46
% 50.08/50.46 Resimplifying clauses:
% 50.08/50.46 Done
% 50.08/50.46
% 50.08/50.46 *** allocated 2919240 integers for clauses
% 50.08/50.46 Resimplifying inuse:
% 50.08/50.46 Done
% 50.08/50.46
% 50.08/50.46
% 50.08/50.46 Intermediate Status:
% 50.08/50.46 Generated: 122437
% 50.08/50.46 Kept: 42629
% 50.08/50.46 Inuse: 745
% 50.08/50.46 Deleted: 1433
% 50.08/50.46 Deletedinuse: 5
% 50.08/50.46
% 50.08/50.46 Resimplifying inuse:
% 50.08/50.46 Done
% 50.08/50.46
% 50.08/50.46
% 50.08/50.46 Intermediate Status:
% 50.08/50.46 Generated: 129672
% 50.08/50.46 Kept: 44632
% 50.08/50.46 Inuse: 758
% 50.08/50.46 Deleted: 1433
% 50.08/50.46 Deletedinuse: 5
% 50.08/50.46
% 50.08/50.46 Resimplifying inuse:
% 50.08/50.46 Done
% 50.08/50.46
% 50.08/50.46
% 50.08/50.46 Intermediate Status:
% 50.08/50.46 Generated: 138318
% 50.08/50.46 Kept: 47072
% 50.08/50.46 Inuse: 803
% 50.08/50.46 Deleted: 1433
% 50.08/50.46 Deletedinuse: 5
% 50.08/50.46
% 50.08/50.46 Resimplifying inuse:
% 50.08/50.46 Done
% 50.08/50.46
% 50.08/50.46 Resimplifying inuse:
% 50.08/50.46 Done
% 50.08/50.46
% 50.08/50.46
% 50.08/50.46 Intermediate Status:
% 50.08/50.46 Generated: 144999
% 50.08/50.46 Kept: 49153
% 50.08/50.46 Inuse: 813
% 50.08/50.46 Deleted: 1433
% 50.08/50.46 Deletedinuse: 5
% 50.08/50.46
% 50.08/50.46 Resimplifying inuse:
% 50.08/50.46 Done
% 50.08/50.46
% 50.08/50.46 Resimplifying inuse:
% 50.08/50.46 Done
% 50.08/50.46
% 50.08/50.46
% 50.08/50.46 Intermediate Status:
% 125.40/125.84 Generated: 152014
% 125.40/125.84 Kept: 51215
% 125.40/125.84 Inuse: 858
% 125.40/125.84 Deleted: 1433
% 125.40/125.84 Deletedinuse: 5
% 125.40/125.84
% 125.40/125.84 Resimplifying inuse:
% 125.40/125.84 Done
% 125.40/125.84
% 125.40/125.84 Resimplifying inuse:
% 125.40/125.84 Done
% 125.40/125.84
% 125.40/125.84 *** allocated 1946160 integers for termspace/termends
% 125.40/125.84
% 125.40/125.84 Intermediate Status:
% 125.40/125.84 Generated: 161765
% 125.40/125.84 Kept: 56176
% 125.40/125.84 Inuse: 878
% 125.40/125.84 Deleted: 1433
% 125.40/125.84 Deletedinuse: 5
% 125.40/125.84
% 125.40/125.84 Resimplifying inuse:
% 125.40/125.84 Done
% 125.40/125.84
% 125.40/125.84
% 125.40/125.84 Intermediate Status:
% 125.40/125.84 Generated: 164707
% 125.40/125.84 Kept: 58234
% 125.40/125.84 Inuse: 883
% 125.40/125.84 Deleted: 1433
% 125.40/125.84 Deletedinuse: 5
% 125.40/125.84
% 125.40/125.84 Resimplifying inuse:
% 125.40/125.84 Done
% 125.40/125.84
% 125.40/125.84 Resimplifying inuse:
% 125.40/125.84 Done
% 125.40/125.84
% 125.40/125.84
% 125.40/125.84 Intermediate Status:
% 125.40/125.84 Generated: 171233
% 125.40/125.84 Kept: 60273
% 125.40/125.84 Inuse: 913
% 125.40/125.84 Deleted: 1433
% 125.40/125.84 Deletedinuse: 5
% 125.40/125.84
% 125.40/125.84 Resimplifying inuse:
% 125.40/125.84 Done
% 125.40/125.84
% 125.40/125.84 Resimplifying clauses:
% 125.40/125.84 Done
% 125.40/125.84
% 125.40/125.84
% 125.40/125.84 Intermediate Status:
% 125.40/125.84 Generated: 181207
% 125.40/125.84 Kept: 64334
% 125.40/125.84 Inuse: 938
% 125.40/125.84 Deleted: 1778
% 125.40/125.84 Deletedinuse: 5
% 125.40/125.84
% 125.40/125.84 Resimplifying inuse:
% 125.40/125.84 Done
% 125.40/125.84
% 125.40/125.84 *** allocated 4378860 integers for clauses
% 125.40/125.84
% 125.40/125.84 Intermediate Status:
% 125.40/125.84 Generated: 189224
% 125.40/125.84 Kept: 67980
% 125.40/125.84 Inuse: 958
% 125.40/125.84 Deleted: 1784
% 125.40/125.84 Deletedinuse: 11
% 125.40/125.84
% 125.40/125.84 Resimplifying inuse:
% 125.40/125.84 Done
% 125.40/125.84
% 125.40/125.84 Resimplifying inuse:
% 125.40/125.84 Done
% 125.40/125.84
% 125.40/125.84
% 125.40/125.84 Intermediate Status:
% 125.40/125.84 Generated: 206914
% 125.40/125.84 Kept: 70859
% 125.40/125.84 Inuse: 998
% 125.40/125.84 Deleted: 1784
% 125.40/125.84 Deletedinuse: 11
% 125.40/125.84
% 125.40/125.84 Resimplifying inuse:
% 125.40/125.84 Done
% 125.40/125.84
% 125.40/125.84
% 125.40/125.84 Intermediate Status:
% 125.40/125.84 Generated: 227073
% 125.40/125.84 Kept: 73289
% 125.40/125.84 Inuse: 1013
% 125.40/125.84 Deleted: 1784
% 125.40/125.84 Deletedinuse: 11
% 125.40/125.84
% 125.40/125.84 Resimplifying inuse:
% 125.40/125.84 Done
% 125.40/125.84
% 125.40/125.84
% 125.40/125.84 Intermediate Status:
% 125.40/125.84 Generated: 247035
% 125.40/125.84 Kept: 75482
% 125.40/125.84 Inuse: 1023
% 125.40/125.84 Deleted: 1784
% 125.40/125.84 Deletedinuse: 11
% 125.40/125.84
% 125.40/125.84 Resimplifying inuse:
% 125.40/125.84 Done
% 125.40/125.84
% 125.40/125.84
% 125.40/125.84 Intermediate Status:
% 125.40/125.84 Generated: 253367
% 125.40/125.84 Kept: 78133
% 125.40/125.84 Inuse: 1033
% 125.40/125.84 Deleted: 1784
% 125.40/125.84 Deletedinuse: 11
% 125.40/125.84
% 125.40/125.84 Resimplifying inuse:
% 125.40/125.84 Done
% 125.40/125.84
% 125.40/125.84 Resimplifying inuse:
% 125.40/125.84 Done
% 125.40/125.84
% 125.40/125.84 *** allocated 2919240 integers for termspace/termends
% 125.40/125.84
% 125.40/125.84 Intermediate Status:
% 125.40/125.84 Generated: 272568
% 125.40/125.84 Kept: 83736
% 125.40/125.84 Inuse: 1058
% 125.40/125.84 Deleted: 1785
% 125.40/125.84 Deletedinuse: 12
% 125.40/125.84
% 125.40/125.84 Resimplifying inuse:
% 125.40/125.84 Done
% 125.40/125.84
% 125.40/125.84 Resimplifying clauses:
% 125.40/125.84 Done
% 125.40/125.84
% 125.40/125.84
% 125.40/125.84 Intermediate Status:
% 125.40/125.84 Generated: 281195
% 125.40/125.84 Kept: 86214
% 125.40/125.84 Inuse: 1078
% 125.40/125.84 Deleted: 2288
% 125.40/125.84 Deletedinuse: 12
% 125.40/125.84
% 125.40/125.84 Resimplifying inuse:
% 125.40/125.84 Done
% 125.40/125.84
% 125.40/125.84 Resimplifying inuse:
% 125.40/125.84 Done
% 125.40/125.84
% 125.40/125.84
% 125.40/125.84 Intermediate Status:
% 125.40/125.84 Generated: 298288
% 125.40/125.84 Kept: 92082
% 125.40/125.84 Inuse: 1113
% 125.40/125.84 Deleted: 2288
% 125.40/125.84 Deletedinuse: 12
% 125.40/125.84
% 125.40/125.84 Resimplifying inuse:
% 125.40/125.84 Done
% 125.40/125.84
% 125.40/125.84
% 125.40/125.84 Intermediate Status:
% 125.40/125.84 Generated: 315572
% 125.40/125.84 Kept: 94761
% 125.40/125.84 Inuse: 1128
% 125.40/125.84 Deleted: 2288
% 125.40/125.84 Deletedinuse: 12
% 125.40/125.84
% 125.40/125.84 Resimplifying inuse:
% 125.40/125.84 Done
% 125.40/125.84
% 125.40/125.84 Resimplifying inuse:
% 125.40/125.84 Done
% 125.40/125.84
% 125.40/125.84
% 125.40/125.84 Intermediate Status:
% 125.40/125.84 Generated: 332212
% 125.40/125.84 Kept: 97162
% 125.40/125.84 Inuse: 1153
% 125.40/125.84 Deleted: 2289
% 125.40/125.84 Deletedinuse: 13
% 125.40/125.84
% 125.40/125.84 Resimplifying inuse:
% 125.40/125.84 Done
% 125.40/125.84
% 125.40/125.84
% 125.40/125.84 Intermediate Status:
% 125.40/125.84 Generated: 337076
% 125.40/125.84 Kept: 99391
% 125.40/125.84 Inuse: 1158
% 125.40/125.84 Deleted: 2289
% 125.40/125.84 Deletedinuse: 13
% 125.40/125.84
% 125.40/125.84 Resimplifying inuse:
% 125.40/125.84 Done
% 125.40/125.84
% 125.40/125.84 Resimplifying inuse:
% 125.40/125.84 Done
% 125.40/125.84
% 125.40/125.84
% 125.40/125.84 Intermediate Status:
% 125.40/125.84 Generated: 346989
% 125.40/125.84 Kept: 101737
% 125.40/125.84 Inuse: 1198
% 125.40/125.84 Deleted: 2289
% 125.40/125.84 Deletedinuse: 13
% 125.40/125.84
% 125.40/125.84 Resimplifying inuse:
% 125.40/125.84 Done
% 125.40/125.84
% 125.40/125.84 *** allocated 6568290 integers for clauses
% 125.40/125.84 Resimplifying inuse:
% 125.40/125.84 Done
% 125.40/125.84
% 125.40/125.84
% 125.40/125.84 Intermediate Status:
% 125.40/125.84 Generated: 361141
% 125.40/125.84 Kept: 106948
% 125.40/125.84 Inuse: 1223
% 125.40/125.84 Deleted: 2289
% 125.40/125.84 Deletedinuse: 13
% 125.40/125.84
% 125.40/125.84 Resimplifying inuse:
% 125.40/125.84 Done
% 125.40/125.84
% 125.40/125.84 Resimplifying clauses:
% 125.40/125.84 Done
% 125.40/125.84
% 125.40/125.84 Resimplifying inuse:
% 125.40/125.84 Done
% 125.40/125.84
% 125.40/125.84
% 125.40/125.84 Intermediate Status:
% 125.40/125.84 Generated: 369452
% 125.40/125.84 Kept: 109145
% 125.40/125.84 Inuse: 1238
% 125.40/125.84 Deleted: 2627
% 125.40/125.84 Deletedinuse: 14
% 125.40/125.84
% 125.40/125.84 Resimplifying inuse:
% 125.40/125.84 Done
% 125.40/125.84
% 125.40/125.84 Resimplifying inuse:
% 125.40/125.84 Done
% 125.40/125.84
% 125.40/125.84
% 125.40/125.84 Intermediate Status:
% 125.40/125.84 Generated: 377076
% 125.40/125.84 Kept: 111324
% 125.40/125.84 Inuse: 1258
% 125.40/125.84 Deleted: 2627
% 125.40/125.84 Deletedinuse: 14
% 125.40/125.84
% 125.40/125.84 Resimplifying inuse:
% 125.40/125.84 Done
% 125.40/125.84
% 125.40/125.84 Resimplifying inuse:
% 125.40/125.84 Done
% 125.40/125.84
% 125.40/125.84
% 125.40/125.84 Intermediate Status:
% 125.40/125.84 Generated: 385348
% 125.40/125.84 Kept: 113374
% 125.40/125.84 Inuse: 1278
% 125.40/125.84 Deleted: 2627
% 125.40/125.84 Deletedinuse: 14
% 125.40/125.84
% 125.40/125.84 Resimplifying inuse:
% 125.40/125.84 Done
% 125.40/125.84
% 125.40/125.84
% 125.40/125.84 Intermediate Status:
% 125.40/125.84 Generated: 399305
% 125.40/125.84 Kept: 116492
% 125.40/125.84 Inuse: 1308
% 125.40/125.84 Deleted: 2627
% 125.40/125.84 Deletedinuse: 14
% 125.40/125.84
% 125.40/125.84 Resimplifying inuse:
% 125.40/125.84 Done
% 125.40/125.84
% 125.40/125.84 *** allocated 4378860 integers for termspace/termends
% 125.40/125.84 Resimplifying inuse:
% 125.40/125.84 Done
% 125.40/125.84
% 125.40/125.84
% 125.40/125.84 Intermediate Status:
% 125.40/125.84 Generated: 416192
% 125.40/125.84 Kept: 120138
% 125.40/125.84 Inuse: 1332
% 125.40/125.84 Deleted: 2628
% 125.40/125.84 Deletedinuse: 14
% 125.40/125.84
% 125.40/125.84 Resimplifying inuse:
% 125.40/125.84 Done
% 125.40/125.84
% 125.40/125.84 Resimplifying inuse:
% 125.40/125.84 Done
% 125.40/125.84
% 125.40/125.84
% 125.40/125.84 Intermediate Status:
% 125.40/125.84 Generated: 440464
% 125.40/125.84 Kept: 124186
% 125.40/125.84 Inuse: 1357
% 285.53/286.04 Deleted: 2628
% 285.53/286.04 Deletedinuse: 14
% 285.53/286.04
% 285.53/286.04 Resimplifying inuse:
% 285.53/286.04 Done
% 285.53/286.04
% 285.53/286.04
% 285.53/286.04 Intermediate Status:
% 285.53/286.04 Generated: 463346
% 285.53/286.04 Kept: 127526
% 285.53/286.04 Inuse: 1372
% 285.53/286.04 Deleted: 2628
% 285.53/286.04 Deletedinuse: 14
% 285.53/286.04
% 285.53/286.04 Resimplifying inuse:
% 285.53/286.04 Done
% 285.53/286.04
% 285.53/286.04 Resimplifying clauses:
% 285.53/286.04 Done
% 285.53/286.04
% 285.53/286.04
% 285.53/286.04 Intermediate Status:
% 285.53/286.04 Generated: 469916
% 285.53/286.04 Kept: 129697
% 285.53/286.04 Inuse: 1377
% 285.53/286.04 Deleted: 2925
% 285.53/286.04 Deletedinuse: 14
% 285.53/286.04
% 285.53/286.04 Resimplifying inuse:
% 285.53/286.04 Done
% 285.53/286.04
% 285.53/286.04 Resimplifying inuse:
% 285.53/286.04 Done
% 285.53/286.04
% 285.53/286.04
% 285.53/286.04 Intermediate Status:
% 285.53/286.04 Generated: 479329
% 285.53/286.04 Kept: 132006
% 285.53/286.04 Inuse: 1392
% 285.53/286.04 Deleted: 2927
% 285.53/286.04 Deletedinuse: 16
% 285.53/286.04
% 285.53/286.04 Resimplifying inuse:
% 285.53/286.04 Done
% 285.53/286.04
% 285.53/286.04
% 285.53/286.04 Intermediate Status:
% 285.53/286.04 Generated: 488348
% 285.53/286.04 Kept: 134010
% 285.53/286.04 Inuse: 1405
% 285.53/286.04 Deleted: 2927
% 285.53/286.04 Deletedinuse: 16
% 285.53/286.04
% 285.53/286.04 Resimplifying inuse:
% 285.53/286.04 Done
% 285.53/286.04
% 285.53/286.04 Resimplifying inuse:
% 285.53/286.04 Done
% 285.53/286.04
% 285.53/286.04
% 285.53/286.04 Intermediate Status:
% 285.53/286.04 Generated: 496720
% 285.53/286.04 Kept: 136047
% 285.53/286.04 Inuse: 1420
% 285.53/286.04 Deleted: 2927
% 285.53/286.04 Deletedinuse: 16
% 285.53/286.04
% 285.53/286.04 Resimplifying inuse:
% 285.53/286.04 Done
% 285.53/286.04
% 285.53/286.04
% 285.53/286.04 Intermediate Status:
% 285.53/286.04 Generated: 505167
% 285.53/286.04 Kept: 138069
% 285.53/286.04 Inuse: 1437
% 285.53/286.04 Deleted: 2927
% 285.53/286.04 Deletedinuse: 16
% 285.53/286.04
% 285.53/286.04 Resimplifying inuse:
% 285.53/286.04 Done
% 285.53/286.04
% 285.53/286.04 Resimplifying inuse:
% 285.53/286.04 Done
% 285.53/286.04
% 285.53/286.04
% 285.53/286.04 Intermediate Status:
% 285.53/286.04 Generated: 514846
% 285.53/286.04 Kept: 140145
% 285.53/286.04 Inuse: 1467
% 285.53/286.04 Deleted: 2932
% 285.53/286.04 Deletedinuse: 16
% 285.53/286.04
% 285.53/286.04 Resimplifying inuse:
% 285.53/286.04 Done
% 285.53/286.04
% 285.53/286.04 Resimplifying inuse:
% 285.53/286.04 Done
% 285.53/286.04
% 285.53/286.04
% 285.53/286.04 Intermediate Status:
% 285.53/286.04 Generated: 524722
% 285.53/286.04 Kept: 142219
% 285.53/286.04 Inuse: 1493
% 285.53/286.04 Deleted: 2936
% 285.53/286.04 Deletedinuse: 16
% 285.53/286.04
% 285.53/286.04 Resimplifying inuse:
% 285.53/286.04 Done
% 285.53/286.04
% 285.53/286.04 Resimplifying inuse:
% 285.53/286.04 Done
% 285.53/286.04
% 285.53/286.04
% 285.53/286.04 Intermediate Status:
% 285.53/286.04 Generated: 536932
% 285.53/286.04 Kept: 144574
% 285.53/286.04 Inuse: 1517
% 285.53/286.04 Deleted: 2937
% 285.53/286.04 Deletedinuse: 16
% 285.53/286.04
% 285.53/286.04 Resimplifying inuse:
% 285.53/286.04 Done
% 285.53/286.04
% 285.53/286.04 Resimplifying inuse:
% 285.53/286.04 Done
% 285.53/286.04
% 285.53/286.04
% 285.53/286.04 Intermediate Status:
% 285.53/286.04 Generated: 547362
% 285.53/286.04 Kept: 146637
% 285.53/286.04 Inuse: 1532
% 285.53/286.04 Deleted: 2937
% 285.53/286.04 Deletedinuse: 16
% 285.53/286.04
% 285.53/286.04 Resimplifying inuse:
% 285.53/286.04 Done
% 285.53/286.04
% 285.53/286.04 Resimplifying clauses:
% 285.53/286.04 Done
% 285.53/286.04
% 285.53/286.04
% 285.53/286.04 Intermediate Status:
% 285.53/286.04 Generated: 555455
% 285.53/286.04 Kept: 148640
% 285.53/286.04 Inuse: 1547
% 285.53/286.04 Deleted: 3072
% 285.53/286.04 Deletedinuse: 16
% 285.53/286.04
% 285.53/286.04 Resimplifying inuse:
% 285.53/286.04 Done
% 285.53/286.04
% 285.53/286.04 Resimplifying inuse:
% 285.53/286.04 Done
% 285.53/286.04
% 285.53/286.04
% 285.53/286.04 Intermediate Status:
% 285.53/286.04 Generated: 570865
% 285.53/286.04 Kept: 150864
% 285.53/286.04 Inuse: 1562
% 285.53/286.04 Deleted: 3072
% 285.53/286.04 Deletedinuse: 16
% 285.53/286.04
% 285.53/286.04 Resimplifying inuse:
% 285.53/286.04 Done
% 285.53/286.04
% 285.53/286.04 Resimplifying inuse:
% 285.53/286.04 Done
% 285.53/286.04
% 285.53/286.04
% 285.53/286.04 Intermediate Status:
% 285.53/286.04 Generated: 576374
% 285.53/286.04 Kept: 152916
% 285.53/286.04 Inuse: 1577
% 285.53/286.04 Deleted: 3072
% 285.53/286.04 Deletedinuse: 16
% 285.53/286.04
% 285.53/286.04 Resimplifying inuse:
% 285.53/286.04 Done
% 285.53/286.04
% 285.53/286.04 Resimplifying inuse:
% 285.53/286.04 Done
% 285.53/286.04
% 285.53/286.04
% 285.53/286.04 Intermediate Status:
% 285.53/286.04 Generated: 580847
% 285.53/286.04 Kept: 154920
% 285.53/286.04 Inuse: 1621
% 285.53/286.04 Deleted: 3076
% 285.53/286.04 Deletedinuse: 20
% 285.53/286.04
% 285.53/286.04 Resimplifying inuse:
% 285.53/286.04 Done
% 285.53/286.04
% 285.53/286.04 *** allocated 9852435 integers for clauses
% 285.53/286.04
% 285.53/286.04 Intermediate Status:
% 285.53/286.04 Generated: 585868
% 285.53/286.04 Kept: 157128
% 285.53/286.04 Inuse: 1662
% 285.53/286.04 Deleted: 3076
% 285.53/286.04 Deletedinuse: 20
% 285.53/286.04
% 285.53/286.04 Resimplifying inuse:
% 285.53/286.04 Done
% 285.53/286.04
% 285.53/286.04 Resimplifying inuse:
% 285.53/286.04 Done
% 285.53/286.04
% 285.53/286.04
% 285.53/286.04 Intermediate Status:
% 285.53/286.04 Generated: 594589
% 285.53/286.04 Kept: 159262
% 285.53/286.04 Inuse: 1682
% 285.53/286.04 Deleted: 3080
% 285.53/286.04 Deletedinuse: 24
% 285.53/286.04
% 285.53/286.04 Resimplifying inuse:
% 285.53/286.04 Done
% 285.53/286.04
% 285.53/286.04 Resimplifying inuse:
% 285.53/286.04 Done
% 285.53/286.04
% 285.53/286.04
% 285.53/286.04 Intermediate Status:
% 285.53/286.04 Generated: 601692
% 285.53/286.04 Kept: 161465
% 285.53/286.04 Inuse: 1702
% 285.53/286.04 Deleted: 3080
% 285.53/286.04 Deletedinuse: 24
% 285.53/286.04
% 285.53/286.04 Resimplifying inuse:
% 285.53/286.04 Done
% 285.53/286.04
% 285.53/286.04 Resimplifying inuse:
% 285.53/286.04 Done
% 285.53/286.04
% 285.53/286.04
% 285.53/286.04 Intermediate Status:
% 285.53/286.04 Generated: 612160
% 285.53/286.04 Kept: 163770
% 285.53/286.04 Inuse: 1722
% 285.53/286.04 Deleted: 3080
% 285.53/286.04 Deletedinuse: 24
% 285.53/286.04
% 285.53/286.04 Resimplifying inuse:
% 285.53/286.04 Done
% 285.53/286.04
% 285.53/286.04 *** allocated 6568290 integers for termspace/termends
% 285.53/286.04
% 285.53/286.04 Intermediate Status:
% 285.53/286.04 Generated: 624375
% 285.53/286.04 Kept: 166768
% 285.53/286.04 Inuse: 1732
% 285.53/286.04 Deleted: 3080
% 285.53/286.04 Deletedinuse: 24
% 285.53/286.04
% 285.53/286.04 Resimplifying inuse:
% 285.53/286.04 Done
% 285.53/286.04
% 285.53/286.04 Resimplifying inuse:
% 285.53/286.04 Done
% 285.53/286.04
% 285.53/286.04 Resimplifying clauses:
% 285.53/286.04 Done
% 285.53/286.04
% 285.53/286.04
% 285.53/286.04 Intermediate Status:
% 285.53/286.04 Generated: 638358
% 285.53/286.04 Kept: 170681
% 285.53/286.04 Inuse: 1747
% 285.53/286.04 Deleted: 3356
% 285.53/286.04 Deletedinuse: 24
% 285.53/286.04
% 285.53/286.04 Resimplifying inuse:
% 285.53/286.04 Done
% 285.53/286.04
% 285.53/286.04 Resimplifying inuse:
% 285.53/286.04 Done
% 285.53/286.04
% 285.53/286.04
% 285.53/286.04 Intermediate Status:
% 285.53/286.04 Generated: 644913
% 285.53/286.04 Kept: 172766
% 285.53/286.04 Inuse: 1762
% 285.53/286.04 Deleted: 3356
% 285.53/286.04 Deletedinuse: 24
% 285.53/286.04
% 285.53/286.04 Resimplifying inuse:
% 285.53/286.04 Done
% 285.53/286.04
% 285.53/286.04 Resimplifying inuse:
% 285.53/286.04 Done
% 285.53/286.04
% 285.53/286.04
% 285.53/286.04 Intermediate Status:
% 285.53/286.04 Generated: 654859
% 285.53/286.04 Kept: 175325
% 285.53/286.04 Inuse: 1782
% 285.53/286.04 Deleted: 3356
% 285.53/286.04 Deletedinuse: 24
% 285.53/286.04
% 285.53/286.04 Resimplifying inuse:
% 285.53/286.04 Done
% 285.53/286.04
% 285.53/286.04
% 285.53/286.04 Intermediate Status:
% 285.53/286.04 Generated: 663829
% 285.53/286.04 Kept: 177447
% 285.53/286.04 Inuse: 1797
% 285.53/286.04 Deleted: 3356
% 285.53/286.04 Deletedinuse: 24
% 285.53/286.04
% 285.53/286.04 Resimplifying inuse:
% 285.53/286.04 Done
% 285.53/286.04
% 285.53/286.04 Resimplifying inuse:
% 285.53/286.04 Done
% 285.53/286.04
% 285.53/286.04
% 285.53/286.04 Intermediate StatCputime limit exceeded (core dumped)
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