TSTP Solution File: SWW241+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWW241+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n018.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 23:21:30 EDT 2022
% Result : Timeout 300.07s 300.52s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SWW241+1 : TPTP v8.1.0. Released v5.2.0.
% 0.12/0.13 % Command : bliksem %s
% 0.12/0.34 % Computer : n018.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % DateTime : Mon Jun 6 09:16:04 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.96/1.59 *** allocated 10000 integers for termspace/termends
% 0.96/1.59 *** allocated 10000 integers for clauses
% 0.96/1.59 *** allocated 10000 integers for justifications
% 0.96/1.59 *** allocated 15000 integers for termspace/termends
% 0.96/1.59 *** allocated 22500 integers for termspace/termends
% 0.96/1.59 *** allocated 33750 integers for termspace/termends
% 0.96/1.59 Bliksem 1.12
% 0.96/1.59
% 0.96/1.59
% 0.96/1.59 Automatic Strategy Selection
% 0.96/1.59
% 0.96/1.59 *** allocated 50625 integers for termspace/termends
% 0.96/1.59 *** allocated 75937 integers for termspace/termends
% 0.96/1.59 *** allocated 113905 integers for termspace/termends
% 0.96/1.59
% 0.96/1.59 Clauses:
% 0.96/1.59
% 0.96/1.59 { ! hAPP( Y, skol1( X, Y ) ) = hAPP( X, skol1( X, Y ) ), Y = X }.
% 0.96/1.59 { ! class_Rings_Oidom( t_a ), v_c____ = c_Groups_Ozero__class_Ozero( t_a )
% 0.96/1.59 }.
% 0.96/1.59 { ! class_Rings_Oidom( t_a ), ! skol2 = c_Groups_Ozero__class_Ozero( t_a )
% 0.96/1.59 }.
% 0.96/1.59 { ! class_Rings_Oidom( t_a ), ! hAPP( c_Polynomial_Opoly( t_a,
% 0.96/1.59 c_Polynomial_OpCons( t_a, v_c____, v_cs____ ) ), skol2 ) =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( t_a ) }.
% 0.96/1.59 { ! class_Rings_Oidom( t_a ), ! skol3 = c_Groups_Ozero__class_Ozero( t_a )
% 0.96/1.59 }.
% 0.96/1.59 { ! class_Rings_Oidom( t_a ), ! hAPP( c_Polynomial_Opoly( t_a, v_p ), skol3
% 0.96/1.59 ) = c_Groups_Ozero__class_Ozero( t_a ) }.
% 0.96/1.59 { ! class_Rings_Oidom( t_a ), X = c_Groups_Ozero__class_Ozero( t_a ), hAPP
% 0.96/1.59 ( c_Polynomial_Opoly( t_a, v_cs____ ), X ) = c_Groups_Ozero__class_Ozero
% 0.96/1.59 ( t_a ), ! skol4 = c_Groups_Ozero__class_Ozero( t_a ) }.
% 0.96/1.59 { ! class_Rings_Oidom( t_a ), X = c_Groups_Ozero__class_Ozero( t_a ), hAPP
% 0.96/1.59 ( c_Polynomial_Opoly( t_a, v_cs____ ), X ) = c_Groups_Ozero__class_Ozero
% 0.96/1.59 ( t_a ), ! v_cs____ = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.96/1.59 t_a ) ), c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_If(
% 0.96/1.59 tc_Nat_Onat, c_fequal( skol26, c_Groups_Ozero__class_Ozero(
% 0.96/1.59 tc_Polynomial_Opoly( t_a ) ) ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 0.96/1.59 ), c_Nat_OSuc( c_Polynomial_Odegree( t_a, skol26 ) ) ), skol22 ) ) =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.59 { ! class_Rings_Oidom( t_a ), X = c_Groups_Ozero__class_Ozero( t_a ), hAPP
% 0.96/1.59 ( c_Polynomial_Opoly( t_a, v_cs____ ), X ) = c_Groups_Ozero__class_Ozero
% 0.96/1.59 ( t_a ), v_cs____ = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( t_a
% 0.96/1.59 ) ), c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_If(
% 0.96/1.59 tc_Nat_Onat, c_fequal( skol26, c_Groups_Ozero__class_Ozero(
% 0.96/1.59 tc_Polynomial_Opoly( t_a ) ) ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 0.96/1.59 ), c_Nat_OSuc( c_Polynomial_Odegree( t_a, skol26 ) ) ), skol22 ) ) =
% 0.96/1.59 c_Nat_OSuc( c_Polynomial_Odegree( t_a, v_cs____ ) ) }.
% 0.96/1.59 { ! class_Rings_Oidom( t_a ), X = c_Groups_Ozero__class_Ozero( t_a ), hAPP
% 0.96/1.59 ( c_Polynomial_Opoly( t_a, v_cs____ ), X ) = c_Groups_Ozero__class_Ozero
% 0.96/1.59 ( t_a ), hAPP( c_Polynomial_Opoly( t_a, v_cs____ ), Y ) = hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( t_a ), hAPP( hAPP(
% 0.96/1.59 c_Power_Opower__class_Opower( t_a ), Y ), skol22 ) ), hAPP(
% 0.96/1.59 c_Polynomial_Opoly( t_a, c_Polynomial_OpCons( t_a, skol4, skol26 ) ), Y )
% 0.96/1.59 ) }.
% 0.96/1.59 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, c_Polynomial_OpCons
% 0.96/1.59 ( X, Y, Z ) ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.59 { ! class_Groups_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, c_Polynomial_OpCons
% 0.96/1.59 ( X, Y, Z ) ) = c_Nat_OSuc( c_Polynomial_Odegree( X, Z ) ) }.
% 0.96/1.59 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, c_Polynomial_OpCons
% 0.96/1.59 ( X, Z, Y ) ) = c_Nat_OSuc( c_Polynomial_Odegree( X, Y ) ) }.
% 0.96/1.59 { ! class_Groups_Ozero( X ), c_Polynomial_Odegree( X, c_Polynomial_OpCons(
% 0.96/1.59 X, Y, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.96/1.59 c_Polynomial_OpCons( X, T, Z ) ), Y ) = c_Groups_Oplus__class_Oplus( X, T
% 0.96/1.59 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), hAPP(
% 0.96/1.59 c_Polynomial_Opoly( X, Z ), Y ) ) ) }.
% 0.96/1.59 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ),
% 0.96/1.59 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.59 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ),
% 0.96/1.59 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) = c_Nat_OSuc(
% 0.96/1.59 c_Polynomial_Odegree( X, Y ) ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.59 { ! class_Groups_Ozero( X ), c_Polynomial_Odegree( X,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.59 { ! class_Groups_Ozero( X ), c_Polynomial_OpCons( X,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.59 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.59 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.59 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.96/1.59 c_Polynomial_OpCons( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.59 { ! c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ), alpha1( X, Y ), alpha23
% 0.96/1.59 ( X, Y ) }.
% 0.96/1.59 { ! alpha1( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.96/1.59 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 0.96/1.59 { ! alpha23( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.96/1.59 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 0.96/1.59 { ! alpha23( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.59 { ! alpha23( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.96/1.59 tc_Nat_Onat ) ) }.
% 0.96/1.59 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha23( X, Y ) }.
% 0.96/1.59 { ! alpha1( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.96/1.59 tc_Nat_Onat ) ) }.
% 0.96/1.59 { ! alpha1( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.59 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha1( X, Y ) }.
% 0.96/1.59 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha2( X, Y ), alpha24( X
% 0.96/1.59 , Y ) }.
% 0.96/1.59 { ! alpha2( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.96/1.59 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.96/1.59 { ! alpha24( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.96/1.59 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.96/1.59 { ! alpha24( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.59 { ! alpha24( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.96/1.59 tc_Nat_Onat ) ) }.
% 0.96/1.59 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha24( X, Y ) }.
% 0.96/1.59 { ! alpha2( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.96/1.59 tc_Nat_Onat ) ) }.
% 0.96/1.59 { ! alpha2( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.59 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha2( X, Y ) }.
% 0.96/1.59 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.96/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z = X
% 0.96/1.59 , Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.59 { ! Z = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.96/1.59 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }
% 0.96/1.59 .
% 0.96/1.59 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.96/1.59 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.96/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Y = X
% 0.96/1.59 , Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.59 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.96/1.59 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.96/1.59 .
% 0.96/1.59 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.96/1.59 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.59 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.59 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.59 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.59 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.59 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z
% 0.96/1.59 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.59 c_Nat_OSuc( Z ) ), X ), Y = X }.
% 0.96/1.59 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.59 c_Nat_OSuc( Z ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.96/1.59 tc_Nat_Onat ), c_Nat_OSuc( Z ) ), X ) }.
% 0.96/1.59 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.96/1.59 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.96/1.59 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.96/1.59 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.96/1.59 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.96/1.59 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ), Y ) = Y }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.59 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.96/1.59 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y = c_Nat_OSuc
% 0.96/1.59 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.96/1.59 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.96/1.59 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X = c_Nat_OSuc
% 0.96/1.59 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.96/1.59 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.96/1.59 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.96/1.59 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Y )
% 0.96/1.59 ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.96/1.59 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), c_Nat_OSuc
% 0.96/1.59 ( X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.96/1.59 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ), Z = c_Groups_Ozero__class_Ozero(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) =
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Polynomial_Odegree( X, Y ),
% 0.96/1.59 c_Polynomial_Odegree( X, Z ) ) }.
% 0.96/1.59 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 0.96/1.59 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 0.96/1.59 { ! Y = X, c_Nat_OSuc( Y ) = c_Nat_OSuc( X ) }.
% 0.96/1.59 { ! c_Nat_OSuc( X ) = X }.
% 0.96/1.59 { ! X = c_Nat_OSuc( X ) }.
% 0.96/1.59 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ), Z = X }.
% 0.96/1.59 { ! Z = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.96/1.59 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ), Y = X }.
% 0.96/1.59 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) }.
% 0.96/1.59 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.96/1.59 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.96/1.59 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, c_Groups_Oplus__class_Oplus
% 0.96/1.59 ( tc_Nat_Onat, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.96/1.59 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.96/1.59 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 0.96/1.59 c_Polynomial_OpCons( X, Z, Y ), U = Z }.
% 0.96/1.59 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 0.96/1.59 c_Polynomial_OpCons( X, Z, Y ), T = Y }.
% 0.96/1.59 { ! class_Groups_Ozero( X ), ! U = Z, ! T = Y, c_Polynomial_OpCons( X, U, T
% 0.96/1.59 ) = c_Polynomial_OpCons( X, Z, Y ) }.
% 0.96/1.59 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 0.96/1.59 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ), Z = Y }.
% 0.96/1.59 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Z = Y,
% 0.96/1.59 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ) }.
% 0.96/1.59 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.59 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.96/1.59 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.59 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.59 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.96/1.59 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.96/1.59 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = Y, X =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.59 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.59 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.59 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.96/1.59 tc_Nat_Onat, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.59 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero
% 0.96/1.59 ( tc_Nat_Onat ) ) = X }.
% 0.96/1.59 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.59 tc_Nat_Onat ), X ) = X }.
% 0.96/1.59 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.96/1.59 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.96/1.59 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.96/1.59 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 0.96/1.59 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.96/1.59 { ! class_Groups_Ozero( X ), !
% 0.96/1.59 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.59 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ),
% 0.96/1.59 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.59 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.96/1.59 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, U, T ),
% 0.96/1.59 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 0.96/1.59 c_Groups_Oplus__class_Oplus( X, U, Z ), c_Groups_Oplus__class_Oplus(
% 0.96/1.59 tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 0.96/1.59 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Z
% 0.96/1.59 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP(
% 0.96/1.59 c_Polynomial_Opoly( X, T ), Y ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 0.96/1.59 ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.96/1.59 c_Groups_Oplus__class_Oplus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 0.96/1.59 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 0.96/1.59 ( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), T ), Z
% 0.96/1.59 ) ), Y ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), hAPP(
% 0.96/1.59 c_Polynomial_Opoly( X, T ), Y ) ), Z ) }.
% 0.96/1.59 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 0.96/1.59 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.59 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Y =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.96/1.59 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.59 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.96/1.59 c_Power_Opower__class_Opower( X ), T ), Y ) ) = hAPP( hAPP(
% 0.96/1.59 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 0.96/1.59 tc_Nat_Onat, Z, Y ) ) }.
% 0.96/1.59 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.96/1.59 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 0.96/1.59 tc_Nat_Onat, Z, Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.96/1.59 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.96/1.59 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.59 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 0.96/1.59 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.96/1.59 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.96/1.59 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 0.96/1.59 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.96/1.59 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.59 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.59 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.96/1.59 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.96/1.59 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.96/1.59 , Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.96/1.59 , Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.96/1.59 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), hAPP( hAPP(
% 0.96/1.59 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.96/1.59 c_Nat_OSuc( Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.59 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.96/1.59 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.96/1.59 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.96/1.59 .
% 0.96/1.59 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.96/1.59 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.96/1.59 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.59 tc_Nat_Onat ) }.
% 0.96/1.59 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.96/1.59 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.96/1.59 , ! Z = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 0.96/1.59 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y )
% 0.96/1.59 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.59 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.96/1.59 ( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! W = U, T = Z, !
% 0.96/1.59 c_Groups_Oplus__class_Oplus( X, W, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) =
% 0.96/1.59 c_Groups_Oplus__class_Oplus( X, U, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.96/1.59 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.59 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.59 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.96/1.59 ) = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X
% 0.96/1.59 ) }.
% 0.96/1.59 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.59 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.59 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.96/1.59 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.96/1.59 ) }.
% 0.96/1.59 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.59 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.59 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ), ! c_Polynomial_Oorder( X, Y, Z ) =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.59 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.59 { ! class_Rings_Oidom( X ), c_Polynomial_Oorder( X, Y, Z ) =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( c_Polynomial_Opoly( X,
% 0.96/1.59 Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.59 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP
% 0.96/1.59 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.96/1.59 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 0.96/1.59 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ), hAPP
% 0.96/1.59 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y
% 0.96/1.59 ) ) }.
% 0.96/1.59 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), c_Nat_OSuc(
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) = c_Nat_OSuc(
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.96/1.59 { ! hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) =
% 0.96/1.59 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = c_Nat_OSuc(
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.96/1.59 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.59 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.96/1.59 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP(
% 0.96/1.59 hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc
% 0.96/1.59 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Z ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), U ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), Y ) ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.96/1.59 , Y ) = c_Groups_Oplus__class_Oplus( X, Y, Z ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.96/1.59 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.96/1.59 ( X, Z, c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.96/1.59 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.96/1.59 ( X, c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.59 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.96/1.59 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.59 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.96/1.59 ( X, c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.59 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.96/1.59 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X
% 0.96/1.59 , U, Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.96/1.59 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.96/1.59 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 0.96/1.59 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.96/1.59 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.59 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.96/1.59 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.96/1.59 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.96/1.59 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.96/1.59 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.96/1.59 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.96/1.59 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.96/1.59 ( X ), ! Z = c_Groups_Oplus__class_Oplus( X, Z, Y ), Y =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.59 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.96/1.59 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.96/1.59 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.59 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.96/1.59 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.96/1.59 ( X ), U = T, Z = Y, ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.96/1.59 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.59 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.96/1.59 ) }.
% 0.96/1.59 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.96/1.59 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.96/1.59 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.59 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.96/1.59 ), ! U = T }.
% 0.96/1.59 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.96/1.59 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.96/1.59 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.59 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.96/1.59 ), ! Z = Y }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.96/1.59 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Y
% 0.96/1.59 ) ), Z ) }.
% 0.96/1.59 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.96/1.59 ( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.96/1.59 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.59 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.96/1.59 ), U = Z, T = Y }.
% 0.96/1.59 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.96/1.59 ( X ), ! U = Z, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.96/1.59 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.59 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.96/1.59 ) }.
% 0.96/1.59 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.96/1.59 ( X ), ! T = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.96/1.59 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.59 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.96/1.59 ) }.
% 0.96/1.59 { ! class_Rings_Oring__1__no__zero__divisors( X ), Y =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.96/1.59 c_Power_Opower__class_Opower( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 0.96/1.59 ( X ) }.
% 0.96/1.59 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.59 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.96/1.59 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.96/1.59 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.96/1.59 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.59 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.96/1.59 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.59 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.59 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.96/1.59 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 0.96/1.59 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus(
% 0.96/1.59 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, T,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 0.96/1.59 c_Polynomial_Opcompose( X, Z, Y ) ) ) }.
% 0.96/1.59 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), T ), Z ),
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), X ) ) =
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus
% 0.96/1.59 ( tc_Nat_Onat, T, Y ) ), Z ), X ) }.
% 0.96/1.59 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.96/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Z =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.96/1.59 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.96/1.59 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.96/1.59 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.96/1.59 .
% 0.96/1.59 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.59 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.96/1.59 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.59 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring( X ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.96/1.59 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.96/1.59 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.96/1.59 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.96/1.59 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.96/1.59 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.96/1.59 { ! class_Rings_Osemiring( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP
% 0.96/1.59 ( c_Groups_Otimes__class_Otimes( X ), U ), T ),
% 0.96/1.59 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.59 ( X ), Z ), T ), Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, U, Z
% 0.96/1.59 ) ), T ), Y ) }.
% 0.96/1.59 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.96/1.59 c_Polynomial_Opcompose( X, T, Z ) ), Y ) = hAPP( c_Polynomial_Opoly( X, T
% 0.96/1.59 ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.96/1.59 { ! class_Groups_Ozero( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y, Y =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.59 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.59 c_Groups_Ozero__class_Ozero( X ) = Y }.
% 0.96/1.59 { ! class_Groups_Oab__semigroup__mult( X ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.96/1.59 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.96/1.59 c_Groups_Oplus__class_Oplus( X, Z, T ) = c_Groups_Oplus__class_Oplus( X,
% 0.96/1.59 Y, T ), Z = Y }.
% 0.96/1.59 { ! class_Groups_Ocancel__ab__semigroup__add( X ), !
% 0.96/1.59 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.96/1.59 T, Y ), Z = Y }.
% 0.96/1.59 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.96/1.59 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.96/1.59 T, Y ), Z = Y }.
% 0.96/1.59 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.96/1.59 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.96/1.59 Y, Z ), T = Y }.
% 0.96/1.59 { ! class_Groups_Ocancel__semigroup__add( X ), ! T = Y,
% 0.96/1.59 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.96/1.59 Y, Z ) }.
% 0.96/1.59 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.96/1.59 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.96/1.59 T, Y ), Z = Y }.
% 0.96/1.59 { ! class_Groups_Ocancel__semigroup__add( X ), ! Z = Y,
% 0.96/1.59 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.96/1.59 T, Y ) }.
% 0.96/1.59 { ! class_Groups_Oab__semigroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.59 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.96/1.59 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.96/1.59 { ! class_Rings_Ono__zero__divisors( X ), ! hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.96/1.59 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.59 { ! class_Rings_Ono__zero__divisors( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.59 X ), Z = c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.59 { ! class_Rings_Oring__no__zero__divisors( X ), ! hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.96/1.59 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.59 { ! class_Rings_Oring__no__zero__divisors( X ), ! Z =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.59 { ! class_Rings_Oring__no__zero__divisors( X ), ! Y =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.59 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.96/1.59 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.59 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.96/1.59 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.59 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.59 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.59 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.96/1.59 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.59 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.96/1.59 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.59 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.59 ( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.59 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.96/1.59 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.96/1.59 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.96/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.96/1.59 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.96/1.59 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero( X ) =
% 0.96/1.59 c_Groups_Oplus__class_Oplus( X, Y, Y ) }.
% 0.96/1.59 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.96/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.96/1.59 c_Groups_Oplus__class_Oplus( X, Y, Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.59 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.96/1.59 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.59 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( W, X, Y,
% 0.96/1.59 Z, c_Polynomial_OpCons( X, U, T ) ) = hAPP( hAPP( hAPP( Z, U ), T ),
% 0.96/1.59 c_Polynomial_Opoly__rec( W, X, Y, Z, T ) ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Osynthetic__div( X
% 0.96/1.59 , Z, Y ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.96/1.59 c_Polynomial_Odegree( X, Z ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.96/1.59 }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Odegree( X, Z ) =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Polynomial_Osynthetic__div
% 0.96/1.59 ( X, Z, Y ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Odegree( X, hAPP(
% 0.96/1.59 hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ),
% 0.96/1.59 c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 0.96/1.59 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ) = Y }.
% 0.96/1.59 { c_Nat_Onat_Onat__size( c_Nat_OSuc( X ) ) = c_Groups_Oplus__class_Oplus(
% 0.96/1.59 tc_Nat_Onat, c_Nat_Onat_Onat__size( X ), c_Nat_OSuc(
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.96/1.59 { ! class_Groups_Ozero( X ), c_Polynomial_Opoly__rec( W, X, U, T,
% 0.96/1.59 c_Polynomial_OpCons( X, Z, Y ) ) = hAPP( hAPP( hAPP( T, Z ), Y ), c_If( W
% 0.96/1.59 , c_fequal( Y, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) )
% 0.96/1.59 , U, c_Polynomial_Opoly__rec( W, X, U, T, Y ) ) ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.96/1.59 c_Polynomial_OpCons( X, T, Z ) ), Y ) = c_Groups_Oplus__class_Oplus(
% 0.96/1.59 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 0.96/1.59 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y ) ) ) }
% 0.96/1.59 .
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ),
% 0.96/1.59 c_Polynomial_OpCons( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus(
% 0.96/1.59 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, Z, T ),
% 0.96/1.59 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ) ) ) }
% 0.96/1.59 .
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__0( X ),
% 0.96/1.59 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X,
% 0.96/1.59 c_Polynomial_OpCons( X, Z, c_Groups_Ozero__class_Ozero(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ) ), Y ) = c_Polynomial_OpCons( X, Z,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.96/1.59 { ! class_Groups_Oone( X ), ! c_Groups_Oone__class_Oone( X ) = Y, Y =
% 0.96/1.59 c_Groups_Oone__class_Oone( X ) }.
% 0.96/1.59 { ! class_Groups_Oone( X ), ! Y = c_Groups_Oone__class_Oone( X ),
% 0.96/1.59 c_Groups_Oone__class_Oone( X ) = Y }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 0.96/1.59 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.96/1.59 c_Groups_Oone__class_Oone( X ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Osmult( X,
% 0.96/1.59 c_Groups_Oone__class_Oone( X ), Y ) = Y }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oone__class_Oone(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ) = c_Polynomial_OpCons( X,
% 0.96/1.59 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ) ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 0.96/1.59 c_Polynomial_Osmult( X, Z, Y ) ) = c_Polynomial_Osmult( X, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 0.96/1.59 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Oone__class_Oone( X ) =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.59 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.96/1.59 c_Groups_Oone__class_Oone( X ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.96/1.59 = Y }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.96/1.59 = Y }.
% 0.96/1.59 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.96/1.59 = Y }.
% 0.96/1.59 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.96/1.59 = Y }.
% 0.96/1.59 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.96/1.59 = Y }.
% 0.96/1.59 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.96/1.59 = Y }.
% 0.96/1.59 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.96/1.59 c_Power_Opower__class_Opower( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.96/1.59 = c_Groups_Oone__class_Oone( X ) }.
% 0.96/1.59 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.96/1.59 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.96/1.59 tc_Nat_Onat ) ) = Y }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.59 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.96/1.59 tc_Nat_Onat ) ) = Y }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, Y,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.59 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.59 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) = X }.
% 0.96/1.59 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), Y =
% 0.96/1.59 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.96/1.59 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X =
% 0.96/1.59 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.96/1.59 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.96/1.59 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Groups_Oone__class_Oone(
% 0.96/1.59 tc_Nat_Onat ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.96/1.59 , Y ), X ) }.
% 0.96/1.59 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.96/1.59 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 0.96/1.59 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.96/1.59 c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y = c_Groups_Oone__class_Oone(
% 0.96/1.59 tc_Nat_Onat ) }.
% 0.96/1.59 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.96/1.59 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X = c_Groups_Oone__class_Oone(
% 0.96/1.59 tc_Nat_Onat ) }.
% 0.96/1.59 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.96/1.59 c_Groups_Oone__class_Oone( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.96/1.59 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Z, Y ) ) =
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ),
% 0.96/1.59 c_Polynomial_Osmult( X, T, Z ), c_Polynomial_Osmult( X, T, Y ) ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ),
% 0.96/1.59 c_Polynomial_Osmult( X, Z, Y ) ) = c_Polynomial_Osmult( X, Z, hAPP( hAPP
% 0.96/1.59 ( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ) ) }
% 0.96/1.59 .
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.96/1.59 c_Polynomial_Osmult( X, T, Z ) ), Y ) = c_Polynomial_Osmult( X, T, hAPP(
% 0.96/1.59 hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y )
% 0.96/1.59 ) }.
% 0.96/1.59 { c_Nat_Onat_Onat__size( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__0( X ),
% 0.96/1.59 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X,
% 0.96/1.59 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus(
% 0.96/1.59 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, Y,
% 0.96/1.59 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) ),
% 0.96/1.59 c_Polynomial_OpCons( X, T,
% 0.96/1.59 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) ) ) }
% 0.96/1.59 .
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.96/1.59 , Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.96/1.59 c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.96/1.59 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.96/1.59 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP
% 0.96/1.59 ( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.96/1.59 c_Groups_Oone__class_Oone( X ) ) ), Z ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = hAPP(
% 0.96/1.59 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X
% 0.96/1.59 , Z, c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.59 { ! class_Rings_Oidom( X ), ! c_Polynomial_Osmult( X, Z, Y ) =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.59 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.59 c_Polynomial_Osmult( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.59 { ! class_Rings_Oidom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ), c_Polynomial_Osmult( X, Z, Y ) =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.59 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.96/1.59 , Y ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.96/1.59 c_Groups_Oone__class_Oone( X ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.59 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ozero__class_Ozero(
% 0.96/1.59 tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__0( X ), c_Groups_Oplus__class_Oplus(
% 0.96/1.59 tc_Polynomial_Opoly( X ), Z, c_Polynomial_Osmult( X, Y,
% 0.96/1.59 c_Polynomial_Osynthetic__div( X, Z, Y ) ) ) = c_Polynomial_OpCons( X,
% 0.96/1.59 hAPP( c_Polynomial_Opoly( X, Z ), Y ), c_Polynomial_Osynthetic__div( X, Z
% 0.96/1.59 , Y ) ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 0.96/1.59 tc_Polynomial_Opoly( X ), U, c_Polynomial_Osmult( X, T, Z ) ) =
% 0.96/1.59 c_Polynomial_OpCons( X, Y, Z ), Y = hAPP( c_Polynomial_Opoly( X, U ), T )
% 0.96/1.59 }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 0.96/1.59 tc_Polynomial_Opoly( X ), U, c_Polynomial_Osmult( X, T, Z ) ) =
% 0.96/1.59 c_Polynomial_OpCons( X, Y, Z ), Z = c_Polynomial_Osynthetic__div( X, U, T
% 0.96/1.59 ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 0.96/1.59 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ), c_Polynomial_Osmult( X, T,
% 0.96/1.59 Y ) ) }.
% 0.96/1.59 { c_Groups_Oone__class_Oone( tc_Nat_Onat ) = c_Nat_OSuc(
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.96/1.59 c_Polynomial_Osmult( X, T, Z ) ), Y ) = hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( c_Polynomial_Opoly( X, Z )
% 0.96/1.59 , Y ) ) }.
% 0.96/1.59 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.96/1.59 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X ) }.
% 0.96/1.59 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.96/1.59 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.96/1.59 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X )
% 0.96/1.59 , X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Odegree( X,
% 0.96/1.59 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ) =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Osmult( X, T, Y ) =
% 0.96/1.59 c_Polynomial_OpCons( X, Z, Y ), Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X,
% 0.96/1.59 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.96/1.59 ( tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 0.96/1.59 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__0( X ),
% 0.96/1.59 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__0( X ), !
% 0.96/1.59 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__0( X ), ! Z = c_Groups_Ozero__class_Ozero
% 0.96/1.59 ( tc_Polynomial_Opoly( X ) ),
% 0.96/1.59 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Odegree( X,
% 0.96/1.59 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) ) =
% 0.96/1.59 c_Polynomial_Odegree( X, Z ) }.
% 0.96/1.59 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), ! Y =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.59 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.96/1.59 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.96/1.59 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), Y =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.59 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.96/1.59 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.59 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.59 c_Polynomial_Odegree( X, c_Polynomial_Osmult( X, Z, Y ) ) =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.59 { ! class_Rings_Oidom( X ), Z = c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.59 c_Polynomial_Odegree( X, c_Polynomial_Osmult( X, Z, Y ) ) =
% 0.96/1.59 c_Polynomial_Odegree( X, Y ) }.
% 0.96/1.59 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ),
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) = hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.96/1.59 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 0.96/1.59 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 0.96/1.59 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 0.96/1.59 c_Polynomial_OpCons( X, Z, Y ) ) = c_Groups_Ozero__class_Ozero(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ), Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.59 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), hAPP( hAPP(
% 0.96/1.59 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 0.96/1.59 ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.96/1.59 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, T, Z ) ), Y
% 0.96/1.59 ) = hAPP( c_Polynomial_Opoly( X, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.96/1.59 , Y ) ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 0.96/1.59 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Polynomial_OpCons( X, hAPP(
% 0.96/1.59 c_Polynomial_Opoly( X, Z ), Y ), c_Polynomial_Osynthetic__div( X, Z, Y )
% 0.96/1.59 ) }.
% 0.96/1.59 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( T, X, Y,
% 0.96/1.59 Z, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.96/1.59 { ! class_Power_Opower( X ), c_Power_Opower__class_Opower( X ) =
% 0.96/1.59 c_Power_Opower_Opower( X, c_Groups_Oone__class_Oone( X ),
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ) ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Oplus__class_Oplus(
% 0.96/1.59 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.96/1.59 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 0.96/1.59 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ) ) ) ), c_Polynomial_Osynthetic__div( X, Y, Z )
% 0.96/1.59 ), c_Polynomial_OpCons( X, hAPP( c_Polynomial_Opoly( X, Y ), Z ),
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) = Y }.
% 0.96/1.59 { c_Nat_Osize__class_Osize( tc_Nat_Onat, c_Nat_OSuc( X ) ) =
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_Osize__class_Osize(
% 0.96/1.59 tc_Nat_Onat, X ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.96/1.59 ) ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__ring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP(
% 0.96/1.59 hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.96/1.59 c_Polynomial_Omonom( X, c_Groups_Oone__class_Oone( X ), T ) ), Z ) ), Y )
% 0.96/1.59 = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.59 c_Power_Opower__class_Opower( X ), Y ), T ) ), hAPP( c_Polynomial_Opoly(
% 0.96/1.59 X, Z ), Y ) ) }.
% 0.96/1.59 { c_HOL_Obool_Obool__size( c_fTrue ) = c_Groups_Ozero__class_Ozero(
% 0.96/1.59 tc_Nat_Onat ) }.
% 0.96/1.59 { c_HOL_Obool_Obool__size( c_fFalse ) = c_Groups_Ozero__class_Ozero(
% 0.96/1.59 tc_Nat_Onat ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Ocoeff( X, hAPP
% 0.96/1.59 ( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ),
% 0.96/1.59 c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 0.96/1.59 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ), Y ) = c_Groups_Oone__class_Oone
% 0.96/1.59 ( X ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Ocoeff( X, hAPP
% 0.96/1.59 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y
% 0.96/1.59 ) ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 0.96/1.59 Z ), c_Polynomial_Odegree( X, Y ) ) ) = hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), hAPP( c_Polynomial_Ocoeff( X, Z ),
% 0.96/1.59 c_Polynomial_Odegree( X, Z ) ) ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.96/1.59 c_Polynomial_Odegree( X, Y ) ) ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X,
% 0.96/1.59 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) =
% 0.96/1.59 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ),
% 0.96/1.59 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 0.96/1.59 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ) ), X ) =
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.96/1.59 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP(
% 0.96/1.59 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.96/1.59 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.96/1.59 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ), X ) =
% 0.96/1.59 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.96/1.59 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) =
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.96/1.59 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) = hAPP
% 0.96/1.59 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) }.
% 0.96/1.59 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 0.96/1.59 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) = X }.
% 0.96/1.59 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.96/1.59 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) = X }.
% 0.96/1.59 { ! class_Groups_Ozero( X ), ! c_Polynomial_Omonom( X, T, Z ) =
% 0.96/1.59 c_Polynomial_Omonom( X, Y, Z ), T = Y }.
% 0.96/1.59 { ! class_Groups_Ozero( X ), ! T = Y, c_Polynomial_Omonom( X, T, Z ) =
% 0.96/1.59 c_Polynomial_Omonom( X, Y, Z ) }.
% 0.96/1.59 { ! class_Groups_Ozero( X ), ! c_Polynomial_Ocoeff( X, Z ) =
% 0.96/1.59 c_Polynomial_Ocoeff( X, Y ), Z = Y }.
% 0.96/1.59 { ! class_Groups_Ozero( X ), ! Z = Y, c_Polynomial_Ocoeff( X, Z ) =
% 0.96/1.59 c_Polynomial_Ocoeff( X, Y ) }.
% 0.96/1.59 { ! class_Groups_Oab__group__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.96/1.59 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ) ), Y ) =
% 0.96/1.59 c_Groups_Ouminus__class_Ouminus( X, hAPP( c_Polynomial_Ocoeff( X, Z ), Y
% 0.96/1.59 ) ) }.
% 0.96/1.59 { ! class_Groups_Ozero( X ), ! Z = Y, hAPP( c_Polynomial_Ocoeff( X, Z ), T
% 0.96/1.59 ) = hAPP( c_Polynomial_Ocoeff( X, Y ), T ) }.
% 0.96/1.59 { ! class_Groups_Ozero( X ), ! hAPP( c_Polynomial_Ocoeff( X, Z ), skol5( X
% 0.96/1.59 , Y, Z ) ) = hAPP( c_Polynomial_Ocoeff( X, Y ), skol5( X, Y, Z ) ), Z = Y
% 0.96/1.59 }.
% 0.96/1.59 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.96/1.59 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, Z, Y ) ) =
% 0.96/1.59 c_Polynomial_Omonom( X, c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 0.96/1.59 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ) ), Y ) =
% 0.96/1.59 c_Groups_Ouminus__class_Ouminus( X, hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 0.96/1.59 ) }.
% 0.96/1.59 { ! class_Groups_Ozero( X ), ! T = Z, hAPP( c_Polynomial_Ocoeff( X,
% 0.96/1.59 c_Polynomial_Omonom( X, Y, T ) ), Z ) = Y }.
% 0.96/1.59 { ! class_Groups_Ozero( X ), T = Z, hAPP( c_Polynomial_Ocoeff( X,
% 0.96/1.59 c_Polynomial_Omonom( X, Y, T ) ), Z ) = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.59 }.
% 0.96/1.59 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.96/1.59 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 0.96/1.59 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.96/1.59 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) }.
% 0.96/1.59 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.96/1.59 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 0.96/1.59 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.96/1.59 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) }.
% 0.96/1.59 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 0.96/1.59 ) = c_Groups_Ouminus__class_Ouminus( X, Y ), Z = Y }.
% 0.96/1.59 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ouminus__class_Ouminus
% 0.96/1.59 ( X, Z ) = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.96/1.59 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 0.96/1.59 ) = Y, c_Groups_Ouminus__class_Ouminus( X, Y ) = Z }.
% 0.96/1.59 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 0.96/1.59 ) = Z, c_Groups_Ouminus__class_Ouminus( X, Z ) = Y }.
% 0.96/1.59 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 0.96/1.59 , Y ), Y = c_Groups_Ouminus__class_Ouminus( X, Z ) }.
% 0.96/1.59 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 0.96/1.59 , Z ), Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.96/1.59 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.96/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 0.96/1.59 { c_Nat_Osize__class_Osize( tc_Nat_Onat, X ) = X }.
% 0.96/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.96/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ) = Y, Y =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.96/1.59 = Y }.
% 0.96/1.59 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 0.96/1.59 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.96/1.59 ) }.
% 0.96/1.59 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.96/1.59 ) }.
% 0.96/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.96/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ), Y = c_Groups_Ozero__class_Ozero
% 0.96/1.59 ( X ) }.
% 0.96/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus( X
% 0.96/1.59 , Y ) }.
% 0.96/1.59 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.96/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Groups_Ozero__class_Ozero( X )
% 0.96/1.59 = Y }.
% 0.96/1.59 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Ouminus__class_Ouminus( X, Y
% 0.96/1.59 ) }.
% 0.96/1.59 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.59 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.96/1.59 ), Z ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 0.96/1.59 Z = Y, Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.96/1.59 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.96/1.59 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.96/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.96/1.59 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.96/1.59 , c_Groups_Ouminus__class_Ouminus( X, Z ) ),
% 0.96/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 0.96/1.59 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.96/1.59 , c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.96/1.59 ( X, Y ) ) }.
% 0.96/1.59 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.96/1.59 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.96/1.59 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.96/1.59 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.96/1.59 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.96/1.59 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.96/1.59 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.96/1.59 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.96/1.59 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 0.96/1.59 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.96/1.59 ) ), Y ) }.
% 0.96/1.59 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 0.96/1.59 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.96/1.59 ( X, Y ) ) }.
% 0.96/1.59 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.59 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.59 Z, Y ) ) = Y }.
% 0.96/1.59 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Z,
% 0.96/1.59 c_Groups_Oplus__class_Oplus( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.96/1.59 Y ) ) = Y }.
% 0.96/1.59 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.96/1.59 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 0.96/1.59 , c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.96/1.59 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.96/1.59 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.96/1.59 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 0.96/1.59 , c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.96/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.96/1.59 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.96/1.59 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.59 { ! class_Groups_Oab__group__add( X ), c_Polynomial_Odegree( X,
% 0.96/1.59 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) =
% 0.96/1.59 c_Polynomial_Odegree( X, Y ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X, Z,
% 0.96/1.59 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) =
% 0.96/1.59 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ),
% 0.96/1.59 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 0.96/1.59 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.96/1.59 = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.96/1.59 Z ) = Y }.
% 0.96/1.59 { ! class_Groups_Oab__group__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.59 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.59 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 0.96/1.59 , Y ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.59 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.96/1.59 = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ouminus__class_Ouminus
% 0.96/1.59 ( X, Y ) }.
% 0.96/1.59 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.96/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Ozero__class_Ozero(
% 0.96/1.59 X ) }.
% 0.96/1.59 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ouminus__class_Ouminus( X, Y
% 0.96/1.59 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.96/1.59 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) ), Y
% 0.96/1.59 ) }.
% 0.96/1.59 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = c_Groups_Oone__class_Oone
% 0.96/1.59 ( X ), Y = c_Groups_Oone__class_Oone( X ), Y =
% 0.96/1.59 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) }.
% 0.96/1.59 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.96/1.59 c_Groups_Oone__class_Oone( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.59 ( X ), Y ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.96/1.59 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.96/1.59 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ),
% 0.96/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) =
% 0.96/1.59 c_Groups_Oone__class_Oone( X ) }.
% 0.96/1.59 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.59 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.96/1.59 c_Polynomial_OpCons( X, Z, Y ) ), c_Groups_Ozero__class_Ozero(
% 0.96/1.59 tc_Nat_Onat ) ) = Z }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.96/1.59 c_Polynomial_Osmult( X, T, Z ) ), Y ) = hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( c_Polynomial_Ocoeff( X, Z
% 0.96/1.59 ), Y ) ) }.
% 0.96/1.59 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.96/1.59 c_Polynomial_OpCons( X, T, Z ) ), c_Nat_OSuc( Y ) ) = hAPP(
% 0.96/1.59 c_Polynomial_Ocoeff( X, Z ), Y ) }.
% 0.96/1.59 { ! class_Groups_Ocomm__monoid__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.96/1.59 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.96/1.59 c_Groups_Oplus__class_Oplus( X, hAPP( c_Polynomial_Ocoeff( X, T ), Y ),
% 0.96/1.59 hAPP( c_Polynomial_Ocoeff( X, Z ), Y ) ) }.
% 0.96/1.59 { ! class_Groups_Ozero( X ), ! c_Polynomial_Omonom( X, Z, Y ) =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.96/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.59 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.59 c_Polynomial_Omonom( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.59 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X,
% 0.96/1.59 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 0.96/1.59 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.59 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.59 c_Polynomial_Odegree( X, c_Polynomial_Omonom( X, Y, Z ) ) = Z }.
% 0.96/1.59 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 0.96/1.59 c_Polynomial_Omonom( X, Z, Y ) ) = c_Polynomial_Omonom( X, hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 0.96/1.59 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.96/1.59 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, T, Z ),
% 0.96/1.59 c_Polynomial_Omonom( X, Y, Z ) ) = c_Polynomial_Omonom( X,
% 0.96/1.59 c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 0.96/1.59 { c_Nat_Osize__class_Osize( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.59 tc_Nat_Onat ) ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.59 { ! class_Rings_Oring__1( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.96/1.59 ), c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 0.96/1.59 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.59 c_Power_Opower__class_Opower( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.96/1.59 c_Groups_Oone__class_Oone( X ) ) ), Y ) ), hAPP( hAPP(
% 0.96/1.59 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! Y = c_Groups_Ozero__class_Ozero
% 0.96/1.60 ( tc_Nat_Onat ), hAPP( c_Polynomial_Ocoeff( X, c_Groups_Oone__class_Oone
% 0.96/1.60 ( tc_Polynomial_Opoly( X ) ) ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__semiring__1( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Nat_Onat ), hAPP( c_Polynomial_Ocoeff( X, c_Groups_Oone__class_Oone(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ) ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.60 { hAPP( hAPP( c_Power_Opower_Opower( T, Z, Y ), X ),
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = Z }.
% 0.96/1.60 { hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), c_Nat_OSuc( X ) ) =
% 0.96/1.60 hAPP( hAPP( Z, Y ), hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), X
% 0.96/1.60 ) ) }.
% 0.96/1.60 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ), ! hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.96/1.60 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.60 { ! class_Groups_Ozero( X ), ! hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.96/1.60 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.60 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.96/1.60 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.60 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X, Z, c_Nat_OSuc( Y ) ) =
% 0.96/1.60 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.60 c_Polynomial_Omonom( X, Z, Y ) ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 0.96/1.60 c_Polynomial_Omonom( X, T, Z ) ), Y ) = hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.96/1.60 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.96/1.60 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X, Y,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = c_Polynomial_OpCons( X, Y
% 0.96/1.60 , c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.96/1.60 c_Polynomial_Omonom( X, U, T ) ), c_Polynomial_Omonom( X, Z, Y ) ) =
% 0.96/1.60 c_Polynomial_Omonom( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U
% 0.96/1.60 ), Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, Y ) ) }.
% 0.96/1.60 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.96/1.60 , Z ), c_Nat_OSuc( c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.96/1.60 ) ) ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc(
% 0.96/1.60 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), Z = Y, Z =
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.96/1.60 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 0.96/1.60 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP(
% 0.96/1.60 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.96/1.60 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.96/1.60 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc(
% 0.96/1.60 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP
% 0.96/1.60 ( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.96/1.60 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.96/1.60 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus
% 0.96/1.60 ( X, Z ) }.
% 0.96/1.60 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 0.96/1.60 , Z ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.60 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.96/1.60 ( X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X )
% 0.96/1.60 ), c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.96/1.60 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ),
% 0.96/1.60 c_Polynomial_Oorder( X, Z, Y ) ), Y ) }.
% 0.96/1.60 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ), ! c_Rings_Odvd__class_Odvd(
% 0.96/1.60 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 0.96/1.60 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ) ) ) ), c_Nat_OSuc( c_Polynomial_Oorder( X, Z,
% 0.96/1.60 Y ) ) ), Y ) }.
% 0.96/1.60 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ), ! c_Rings_Odvd__class_Odvd(
% 0.96/1.60 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 0.96/1.60 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ) ) ) ), c_Nat_OSuc( c_Polynomial_Oorder( X, Z,
% 0.96/1.60 Y ) ) ), Y ) }.
% 0.96/1.60 { ! class_Rings_Oidom( X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly(
% 0.96/1.60 X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) )
% 0.96/1.60 , c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.96/1.60 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ),
% 0.96/1.60 c_Polynomial_Oorder( X, Z, Y ) ), Y ) }.
% 0.96/1.60 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X,
% 0.96/1.60 c_Polynomial_Opoly__gcd( X, Z, Y ) ), c_Polynomial_Odegree( X,
% 0.96/1.60 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.60 }.
% 0.96/1.60 { ! class_Fields_Ofield( X ), Z = c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X,
% 0.96/1.60 c_Polynomial_Opoly__gcd( X, Z, Y ) ), c_Polynomial_Odegree( X,
% 0.96/1.60 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) = c_Groups_Oone__class_Oone( X ) }
% 0.96/1.60 .
% 0.96/1.60 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X,
% 0.96/1.60 c_Polynomial_Opoly__gcd( X, Z, Y ) ), c_Polynomial_Odegree( X,
% 0.96/1.60 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) = c_Groups_Oone__class_Oone( X ) }
% 0.96/1.60 .
% 0.96/1.60 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.96/1.60 ( X ), c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 0.96/1.60 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ) ) ), Y ), hAPP( c_Polynomial_Opoly( X, Y ),
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( X, Z ) ) = c_Groups_Ozero__class_Ozero(
% 0.96/1.60 X ) }.
% 0.96/1.60 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Y ),
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( X, Z ) ) = c_Groups_Ozero__class_Ozero(
% 0.96/1.60 X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ),
% 0.96/1.60 c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 0.96/1.60 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ) ) ), Y ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Y,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.60 { ! class_Fields_Ofield( X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.96/1.60 ( X ), c_Polynomial_Opoly__gcd( X, Z, Y ), Z ) }.
% 0.96/1.60 { ! class_Fields_Ofield( X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.96/1.60 ( X ), c_Polynomial_Opoly__gcd( X, Z, Y ), Y ) }.
% 0.96/1.60 { ! c_Groups_Ozero__class_Ozero( tc_Int_Oint ) = c_Groups_Oone__class_Oone
% 0.96/1.60 ( tc_Int_Oint ) }.
% 0.96/1.60 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.60 ( tc_Int_Oint ) ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.96/1.60 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint,
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) = X }.
% 0.96/1.60 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.96/1.60 ( tc_Int_Oint, X ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.96/1.60 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.96/1.60 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ),
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.96/1.60 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.96/1.60 tc_Int_Oint, c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.96/1.60 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ), Y ) =
% 0.96/1.60 c_Polynomial_Opoly__gcd( X, Z, Y ) }.
% 0.96/1.60 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Z,
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) =
% 0.96/1.60 c_Polynomial_Opoly__gcd( X, Z, Y ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Y, Y
% 0.96/1.60 ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.96/1.60 Y ), ! c_Rings_Odvd__class_Odvd( X, Y, T ), c_Rings_Odvd__class_Odvd( X,
% 0.96/1.60 Z, T ) }.
% 0.96/1.60 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 0.96/1.60 c_Polynomial_Opoly__gcd( X, Y, Z ) }.
% 0.96/1.60 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, T,
% 0.96/1.60 c_Polynomial_Opoly__gcd( X, Z, Y ) ) = c_Polynomial_Opoly__gcd( X, Z,
% 0.96/1.60 c_Polynomial_Opoly__gcd( X, T, Y ) ) }.
% 0.96/1.60 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.96/1.60 tc_Polynomial_Opoly( X ), T, c_Polynomial_Opoly__gcd( X, Z, Y ) ),
% 0.96/1.60 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T, Z ) }.
% 0.96/1.60 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.96/1.60 tc_Polynomial_Opoly( X ), T, c_Polynomial_Opoly__gcd( X, Z, Y ) ),
% 0.96/1.60 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T, Y ) }.
% 0.96/1.60 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.96/1.60 tc_Polynomial_Opoly( X ), T, Z ), ! c_Rings_Odvd__class_Odvd(
% 0.96/1.60 tc_Polynomial_Opoly( X ), T, Y ), c_Rings_Odvd__class_Odvd(
% 0.96/1.60 tc_Polynomial_Opoly( X ), T, c_Polynomial_Opoly__gcd( X, Z, Y ) ) }.
% 0.96/1.60 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 0.96/1.60 c_Polynomial_Opoly__gcd( X, T, Z ), Y ) = c_Polynomial_Opoly__gcd( X, T,
% 0.96/1.60 c_Polynomial_Opoly__gcd( X, Z, Y ) ) }.
% 0.96/1.60 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.96/1.60 tc_Polynomial_Opoly( X ), Z, Y ), ! c_Rings_Odvd__class_Odvd(
% 0.96/1.60 tc_Polynomial_Opoly( X ), Z, T ), c_Rings_Odvd__class_Odvd(
% 0.96/1.60 tc_Polynomial_Opoly( X ), Z, c_Polynomial_Opoly__gcd( X, Y, T ) ) }.
% 0.96/1.60 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Int_Oint ), X ) = X }.
% 0.96/1.60 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero
% 0.96/1.60 ( tc_Int_Oint ) ) = X }.
% 0.96/1.60 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) =
% 0.96/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ) }.
% 0.96/1.60 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus
% 0.96/1.60 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.96/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 0.96/1.60 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.96/1.60 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.96/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), Y ), Y = c_Groups_Ozero__class_Ozero( X
% 0.96/1.60 ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Z,
% 0.96/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Z,
% 0.96/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.96/1.60 Y ), c_Rings_Odvd__class_Odvd( X, Z, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.96/1.60 Y ), c_Rings_Odvd__class_Odvd( X, Z, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.96/1.60 Y ), ! c_Rings_Odvd__class_Odvd( X, U, T ), c_Rings_Odvd__class_Odvd( X,
% 0.96/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.96/1.60 { ! class_Rings_Odvd( X ), ! Z = hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.60 ( X ), Y ), T ), c_Rings_Odvd__class_Odvd( X, Y, Z ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.96/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), Y ),
% 0.96/1.60 c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.96/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ),
% 0.96/1.60 c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.96/1.60 Y ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X,
% 0.96/1.60 Z, c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X,
% 0.96/1.60 c_Groups_Oone__class_Oone( X ), Y ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Rings_Odvd__class_Odvd( X, Z
% 0.96/1.60 , Y ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 0.96/1.60 , c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.96/1.60 ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ), c_Rings_Odvd__class_Odvd( X
% 0.96/1.60 , Z, Y ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 0.96/1.60 , c_Rings_Odvd__class_Odvd( X, c_Groups_Ouminus__class_Ouminus( X, Z ), Y
% 0.96/1.60 ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.96/1.60 Y ), c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 0.96/1.60 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.96/1.60 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd(
% 0.96/1.60 tc_Polynomial_Opoly( X ), Z, Y ), c_Rings_Odvd__class_Odvd(
% 0.96/1.60 tc_Polynomial_Opoly( X ), Z, c_Polynomial_Osmult( X, T, Y ) ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd(
% 0.96/1.60 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ),
% 0.96/1.60 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.96/1.60 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.60 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.60 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.60 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.60 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Z =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, T, Y ) }.
% 0.96/1.60 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.60 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.96/1.60 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) )
% 0.96/1.60 }.
% 0.96/1.60 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, T, Y ),
% 0.96/1.60 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.96/1.60 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) )
% 0.96/1.60 }.
% 0.96/1.60 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), T =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 0.96/1.60 { ! class_Rings_Oidom( X ), ! T = c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.60 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.96/1.60 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) )
% 0.96/1.60 }.
% 0.96/1.60 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y ),
% 0.96/1.60 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.96/1.60 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) )
% 0.96/1.60 }.
% 0.96/1.60 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Y,
% 0.96/1.60 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ) =
% 0.96/1.60 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.60 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 0.96/1.60 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.96/1.60 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.60 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 0.96/1.60 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T,
% 0.96/1.60 c_Polynomial_Osmult( X, Y, Z ) ), c_Rings_Odvd__class_Odvd(
% 0.96/1.60 tc_Polynomial_Opoly( X ), T, Z ) }.
% 0.96/1.60 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 0.96/1.60 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T, Z ),
% 0.96/1.60 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T,
% 0.96/1.60 c_Polynomial_Osmult( X, Y, Z ) ) }.
% 0.96/1.60 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.96/1.60 tc_Polynomial_Opoly( X ), Z, Y ), T = c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.60 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), c_Polynomial_Osmult(
% 0.96/1.60 X, T, Z ), Y ) }.
% 0.96/1.60 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.96/1.60 tc_Polynomial_Opoly( X ), T, c_Polynomial_Osmult( X, Z, Y ) ), Z =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd(
% 0.96/1.60 tc_Polynomial_Opoly( X ), T, Y ) }.
% 0.96/1.60 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Ocoeff( X, Z ),
% 0.96/1.60 c_Polynomial_Odegree( X, Z ) ) = hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.96/1.60 c_Polynomial_Odegree( X, Y ) ), ! c_Rings_Odvd__class_Odvd(
% 0.96/1.60 tc_Polynomial_Opoly( X ), Z, Y ), ! c_Rings_Odvd__class_Odvd(
% 0.96/1.60 tc_Polynomial_Opoly( X ), Y, Z ), Z = Y }.
% 0.96/1.60 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.96/1.60 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ), alpha3( X
% 0.96/1.60 , Y, T ) }.
% 0.96/1.60 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.96/1.60 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ), alpha25( X
% 0.96/1.60 , Y, Z, T ) }.
% 0.96/1.60 { ! class_Fields_Ofield( X ), ! alpha3( X, Y, T ), ! alpha25( X, Y, Z, T )
% 0.96/1.60 , c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), c_Polynomial_Osmult
% 0.96/1.60 ( X, T, Z ), Y ) }.
% 0.96/1.60 { ! alpha25( X, Y, Z, T ), T = c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.60 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.96/1.60 { ! T = c_Groups_Ozero__class_Ozero( X ), alpha25( X, Y, Z, T ) }.
% 0.96/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, Y ), alpha25( X
% 0.96/1.60 , Y, Z, T ) }.
% 0.96/1.60 { ! alpha3( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.60 { Z = c_Groups_Ozero__class_Ozero( X ), alpha3( X, Y, Z ) }.
% 0.96/1.60 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha3( X
% 0.96/1.60 , Y, Z ) }.
% 0.96/1.60 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd(
% 0.96/1.60 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X,
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Polynomial_OpCons( X,
% 0.96/1.60 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ) ) ), Z ) }.
% 0.96/1.60 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.96/1.60 ( X ), c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.96/1.60 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ), Z ), hAPP(
% 0.96/1.60 c_Polynomial_Opoly( X, Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.60 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 0.96/1.60 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ), hBOOL(
% 0.96/1.60 hAPP( Z, skol6( U, W, Z ) ) ) }.
% 0.96/1.60 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 0.96/1.60 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ),
% 0.96/1.60 c_Rings_Odvd__class_Odvd( X, Y, c_Groups_Oplus__class_Oplus( X, skol6( X
% 0.96/1.60 , Y, Z ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.96/1.60 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), !
% 0.96/1.60 c_Rings_Odvd__class_Odvd( X, Y, c_Groups_Oplus__class_Oplus( X, T,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) ) ), ! hBOOL( hAPP( Z, T ) ), hBOOL(
% 0.96/1.60 hAPP( Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), skol23( X,
% 0.96/1.60 Y, Z ) ) ) ) }.
% 0.96/1.60 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.96/1.60 tc_Polynomial_Opoly( X ), Z, Y ), alpha56( X, Y, Z, T ), ! Y =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), ! T =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.96/1.60 c_Polynomial_Opoly__gcd( X, Y, T ) = Z }.
% 0.96/1.60 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.96/1.60 tc_Polynomial_Opoly( X ), Z, Y ), alpha56( X, Y, Z, T ), ! hAPP(
% 0.96/1.60 c_Polynomial_Ocoeff( X, Z ), c_Polynomial_Odegree( X, Z ) ) =
% 0.96/1.60 c_Groups_Oone__class_Oone( X ), c_Polynomial_Opoly__gcd( X, Y, T ) = Z }
% 0.96/1.60 .
% 0.96/1.60 { ! alpha56( X, Y, Z, T ), alpha58( X, Y, Z, T ), alpha53( X, Y, T ) }.
% 0.96/1.60 { ! alpha56( X, Y, Z, T ), alpha58( X, Y, Z, T ), ! hAPP(
% 0.96/1.60 c_Polynomial_Ocoeff( X, Z ), c_Polynomial_Odegree( X, Z ) ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.60 { ! alpha58( X, Y, Z, T ), alpha56( X, Y, Z, T ) }.
% 0.96/1.60 { ! alpha53( X, Y, T ), hAPP( c_Polynomial_Ocoeff( X, Z ),
% 0.96/1.60 c_Polynomial_Odegree( X, Z ) ) = c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.60 alpha56( X, Y, Z, T ) }.
% 0.96/1.60 { ! alpha58( X, Y, Z, T ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.96/1.60 ( X ), Z, T ), alpha59( X, Y, Z, T ) }.
% 0.96/1.60 { c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, T ), alpha58( X, Y
% 0.96/1.60 , Z, T ) }.
% 0.96/1.60 { ! alpha59( X, Y, Z, T ), alpha58( X, Y, Z, T ) }.
% 0.96/1.60 { ! alpha59( X, Y, Z, T ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X
% 0.96/1.60 ), skol7( X, Y, U, W ), Y ) }.
% 0.96/1.60 { ! alpha59( X, Y, Z, T ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X
% 0.96/1.60 ), skol7( X, Y, U, T ), T ) }.
% 0.96/1.60 { ! alpha59( X, Y, Z, T ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.96/1.60 ( X ), skol7( X, Y, Z, T ), Z ) }.
% 0.96/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), U, Y ), !
% 0.96/1.60 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), U, T ),
% 0.96/1.60 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), U, Z ), alpha59( X, Y
% 0.96/1.60 , Z, T ) }.
% 0.96/1.60 { ! alpha53( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.60 { ! alpha53( X, Y, Z ), Z = c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.60 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), ! Z =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha53( X, Y, Z
% 0.96/1.60 ) }.
% 0.96/1.60 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Y,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.96/1.60 c_Polynomial_Osmult( X, c_Rings_Oinverse__class_Oinverse( X, hAPP(
% 0.96/1.60 c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) ), Y ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP
% 0.96/1.60 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), hAPP( hAPP(
% 0.96/1.60 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) ) = hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.96/1.60 Y ) ), c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.96/1.60 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.60 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) =
% 0.96/1.60 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.96/1.60 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.60 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) = hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 0.96/1.60 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ),
% 0.96/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 0.96/1.60 ( tc_Nat_Onat ) ) ) ) }.
% 0.96/1.60 { ! class_Groups_Ozero( X ), c_Polynomial_Ocoeff( X, c_Polynomial_OpCons( X
% 0.96/1.60 , Z, Y ) ) = c_Nat_Onat_Onat__case( X, Z, c_Polynomial_Ocoeff( X, Y ) ) }
% 0.96/1.60 .
% 0.96/1.60 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, c_Nat_OSuc(
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) }.
% 0.96/1.60 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.96/1.60 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd(
% 0.96/1.60 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X
% 0.96/1.60 ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y
% 0.96/1.60 ) ) }.
% 0.96/1.60 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.96/1.60 c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ),
% 0.96/1.60 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 0.96/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), c_Rings_Odvd__class_Odvd
% 0.96/1.60 ( tc_Int_Oint, Y, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.96/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y,
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ),
% 0.96/1.60 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }.
% 0.96/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), c_Rings_Odvd__class_Odvd
% 0.96/1.60 ( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) }.
% 0.96/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.96/1.60 ( tc_Int_Oint, Y ), X ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }
% 0.96/1.60 .
% 0.96/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.96/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ), c_Rings_Odvd__class_Odvd(
% 0.96/1.60 tc_Nat_Onat, Y, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) }.
% 0.96/1.60 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.60 , Z = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ominus__class_Ominus( X
% 0.96/1.60 , c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.96/1.60 c_Rings_Oinverse__class_Oinverse( X, Z ) ) = hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 0.96/1.60 Y ) ), c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ),
% 0.96/1.60 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X,
% 0.96/1.60 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 0.96/1.60 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ),
% 0.96/1.60 c_Polynomial_Osmult( X, T, Y ), c_Polynomial_Osmult( X, Z, Y ) ) }.
% 0.96/1.60 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.96/1.60 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.96/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ), Y ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 0.96/1.60 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.96/1.60 c_Groups_Ominus__class_Ominus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 0.96/1.60 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.96/1.60 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 0.96/1.60 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, U, T ),
% 0.96/1.60 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 0.96/1.60 c_Groups_Ominus__class_Ominus( X, U, Z ), c_Groups_Ominus__class_Ominus(
% 0.96/1.60 tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 0.96/1.60 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.96/1.60 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! U = T, Z = Y }.
% 0.96/1.60 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.96/1.60 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! Z = Y, U = T }.
% 0.96/1.60 { ! class_Rings_Odivision__ring__inverse__zero( X ), !
% 0.96/1.60 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 0.96/1.60 c_Rings_Oinverse__class_Oinverse( X, Y ), Z = Y }.
% 0.96/1.60 { ! class_Rings_Odivision__ring__inverse__zero( X ), !
% 0.96/1.60 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 0.96/1.60 c_Rings_Oinverse__class_Oinverse( X, Y ), Z = Y }.
% 0.96/1.60 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Z = Y,
% 0.96/1.60 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 0.96/1.60 c_Rings_Oinverse__class_Oinverse( X, Y ) }.
% 0.96/1.60 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 0.96/1.60 c_Rings_Oinverse__class_Oinverse( X, c_Rings_Oinverse__class_Oinverse( X
% 0.96/1.60 , Y ) ) = Y }.
% 0.96/1.60 { ! class_Groups_Oab__group__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.96/1.60 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.96/1.60 c_Groups_Ominus__class_Ominus( X, hAPP( c_Polynomial_Ocoeff( X, T ), Y )
% 0.96/1.60 , hAPP( c_Polynomial_Ocoeff( X, Z ), Y ) ) }.
% 0.96/1.60 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 0.96/1.60 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, T, Z ),
% 0.96/1.60 c_Polynomial_Omonom( X, Y, Z ) ) = c_Polynomial_Omonom( X,
% 0.96/1.60 c_Groups_Ominus__class_Ominus( X, T, Y ), Z ) }.
% 0.96/1.60 { ! class_Rings_Odivision__ring( X ), ! c_Rings_Oinverse__class_Oinverse( X
% 0.96/1.60 , Z ) = c_Rings_Oinverse__class_Oinverse( X, Y ), Z =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z
% 0.96/1.60 = Y }.
% 0.96/1.60 { ! class_Rings_Odivision__ring( X ), ! c_Rings_Oinverse__class_Oinverse( X
% 0.96/1.60 , Y ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 0.96/1.60 ( X ) }.
% 0.96/1.60 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.60 , c_Rings_Oinverse__class_Oinverse( X, c_Rings_Oinverse__class_Oinverse(
% 0.96/1.60 X, Y ) ) = Y }.
% 0.96/1.60 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.60 , ! c_Rings_Oinverse__class_Oinverse( X, Y ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.60 { ! class_Rings_Odivision__ring__inverse__zero( X ), !
% 0.96/1.60 c_Rings_Oinverse__class_Oinverse( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.96/1.60 ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.60 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Y =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X, Y
% 0.96/1.60 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.60 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 0.96/1.60 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.60 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Oinverse( X,
% 0.96/1.60 c_Groups_Oone__class_Oone( X ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.96/1.60 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.96/1.60 ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.96/1.60 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ominus__class_Ominus(
% 0.96/1.60 X, Z, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.60 { ! class_Groups_Oab__group__add( X ), ! Z = Y,
% 0.96/1.60 c_Groups_Ominus__class_Ominus( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.96/1.60 ) }.
% 0.96/1.60 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.96/1.60 Z, Y ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.96/1.60 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y, Y )
% 0.96/1.60 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.60 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.96/1.60 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 0.96/1.60 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ouminus__class_Ouminus( X,
% 0.96/1.60 Y ) ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.96/1.60 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.96/1.60 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 0.96/1.60 c_Rings_Oinverse__class_Oinverse( X, hAPP( hAPP(
% 0.96/1.60 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.96/1.60 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Oinverse( X, Z
% 0.96/1.60 ) ), Y ) }.
% 0.96/1.60 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 0.96/1.60 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.96/1.60 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 0.96/1.60 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.96/1.60 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 0.96/1.60 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.96/1.60 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 0.96/1.60 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.96/1.60 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.96/1.60 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = Z }.
% 0.96/1.60 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.60 c_Groups_Ominus__class_Ominus( X, Z, Y ), Y ) = Z }.
% 0.96/1.60 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.96/1.60 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) =
% 0.96/1.60 c_Groups_Ominus__class_Ominus( X, Y, Z ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 0.96/1.60 , ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X, Z,
% 0.96/1.60 c_Groups_Ominus__class_Ominus( X, Y, T ) ) }.
% 0.96/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), Z =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Rings_Odvd__class_Odvd(
% 0.96/1.60 tc_Int_Oint, Y, X ) }.
% 0.96/1.60 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.96/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.96/1.60 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, X ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.60 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = X }.
% 0.96/1.60 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Nat_Onat ), X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.60 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.96/1.60 ( tc_Nat_Onat, c_Nat_OSuc( Z ), Y ), c_Nat_OSuc( X ) ) =
% 0.96/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.96/1.60 ( tc_Nat_Onat, Z, Y ), X ) }.
% 0.96/1.60 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.96/1.60 X ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 0.96/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, c_Groups_Oplus__class_Oplus(
% 0.96/1.60 tc_Nat_Onat, X, Y ) ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.96/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.96/1.60 ( tc_Nat_Onat, Y, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.96/1.60 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.96/1.60 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) =
% 0.96/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ) }.
% 0.96/1.60 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.96/1.60 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) =
% 0.96/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 0.96/1.60 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.96/1.60 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.96/1.60 Z, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.96/1.60 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.96/1.60 tc_Nat_Onat, Y, X ), Y ) = X }.
% 0.96/1.60 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.96/1.60 tc_Nat_Onat, Y, X ), X ) = Y }.
% 0.96/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.96/1.60 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ), X ) =
% 0.96/1.60 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.96/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.96/1.60 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) ) =
% 0.96/1.60 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.96/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.96/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.96/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.96/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) =
% 0.96/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.96/1.60 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 0.96/1.60 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.96/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Groups_Oone__class_Oone(
% 0.96/1.60 tc_Nat_Onat ) ), X = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.96/1.60 { ! X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd
% 0.96/1.60 ( tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X, T,
% 0.96/1.60 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Z, Y ) ) =
% 0.96/1.60 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ),
% 0.96/1.60 c_Polynomial_Osmult( X, T, Z ), c_Polynomial_Osmult( X, T, Y ) ) }.
% 0.96/1.60 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.60 , Z = c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse
% 0.96/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP(
% 0.96/1.60 hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.96/1.60 c_Rings_Oinverse__class_Oinverse( X, Z ) ),
% 0.96/1.60 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.96/1.60 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.60 , c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ouminus__class_Ouminus( X
% 0.96/1.60 , Y ) ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.96/1.60 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.96/1.60 { ! class_Rings_Odivision__ring( X ), ! hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = c_Groups_Oone__class_Oone
% 0.96/1.60 ( X ), c_Rings_Oinverse__class_Oinverse( X, Z ) = Y }.
% 0.96/1.60 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.60 , c_Rings_Oinverse__class_Oinverse( X, hAPP( hAPP(
% 0.96/1.60 c_Power_Opower__class_Opower( X ), Y ), Z ) ) = hAPP( hAPP(
% 0.96/1.60 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Oinverse( X, Y
% 0.96/1.60 ) ), Z ) }.
% 0.96/1.60 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.96/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.60 ( X ), Z ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.96/1.60 Z ) ), U ), T ) = Y }.
% 0.96/1.60 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.96/1.60 Z ) ), U ), T ) = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.96/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.60 ( X ), Z ), U ), Y ) }.
% 0.96/1.60 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.96/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.60 ( X ), Z ), U ), Y ), T = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.96/1.60 W ) ), U ), Y ) }.
% 0.96/1.60 { ! class_Rings_Oring( X ), ! T = c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.96/1.60 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.96/1.60 X, Z, W ) ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.96/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.60 ( X ), Z ), U ), Y ) }.
% 0.96/1.60 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.96/1.60 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.96/1.60 c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.96/1.60 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.96/1.60 X, U, Z ) ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 0.96/1.60 Z ) ), Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 0.96/1.60 c_Groups_Ominus__class_Ominus( X, T, Y ) ) ) }.
% 0.96/1.60 { ! class_Rings_Oring( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.96/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.60 ( X ), U ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 0.96/1.60 Z ) ), Y ) ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 0.96/1.60 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.96/1.60 c_Groups_Oplus__class_Oplus( X, U, T ) ), c_Rings_Odvd__class_Odvd( X, Z
% 0.96/1.60 , c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U,
% 0.96/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 0.96/1.60 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.96/1.60 c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U, hAPP
% 0.96/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ),
% 0.96/1.60 c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oplus__class_Oplus( X, U, T ) )
% 0.96/1.60 }.
% 0.96/1.60 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 0.96/1.60 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.96/1.60 c_Groups_Oplus__class_Oplus( X, U, T ) ), c_Rings_Odvd__class_Odvd( X, Z
% 0.96/1.60 , c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U,
% 0.96/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 0.96/1.60 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.96/1.60 c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U, hAPP
% 0.96/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ),
% 0.96/1.60 c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oplus__class_Oplus( X, U, T ) )
% 0.96/1.60 }.
% 0.96/1.60 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.96/1.60 X, Y ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.96/1.60 ) = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus(
% 0.96/1.60 X, Y ) ) }.
% 0.96/1.60 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Oplus__class_Oplus(
% 0.96/1.60 X, Z, Y ) }.
% 0.96/1.60 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X, Z
% 0.96/1.60 , Y ) = c_Groups_Oplus__class_Oplus( X, Z,
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.96/1.60 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z, Y )
% 0.96/1.60 = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus( X
% 0.96/1.60 , Y ) ) }.
% 0.96/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 0.96/1.60 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 0.96/1.60 tc_Int_Oint, U, T ) ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y,
% 0.96/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.96/1.60 tc_Int_Oint, U, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 0.96/1.60 , Z ), X ) ), T ) ) }.
% 0.96/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 0.96/1.60 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 0.96/1.60 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), T ) ),
% 0.96/1.60 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 0.96/1.60 tc_Int_Oint, U, T ) ) }.
% 0.96/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus(
% 0.96/1.60 tc_Int_Oint, Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 0.96/1.60 , Z ), X ) ) ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 0.96/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd
% 0.96/1.60 ( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP( hAPP
% 0.96/1.60 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ) }.
% 0.96/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X = c_Nat_OSuc(
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.96/1.60 { ! X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 0.96/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.96/1.60 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y,
% 0.96/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), Z =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 0.96/1.60 tc_Nat_Onat, Y, X ) }.
% 0.96/1.60 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.96/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.96/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.96/1.60 ( tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.60 Z ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.96/1.60 X ) ) }.
% 0.96/1.60 { hAPP( c_Nat_Onat_Onat__case( Z, Y, X ), c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Nat_Onat ) ) = Y }.
% 0.96/1.60 { hAPP( c_Nat_Onat_Onat__case( T, Z, Y ), c_Nat_OSuc( X ) ) = hAPP( Y, X )
% 0.96/1.60 }.
% 0.96/1.60 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 0.96/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.96/1.60 ( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) }.
% 0.96/1.60 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 0.96/1.60 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 0.96/1.60 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) =
% 0.96/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.96/1.60 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.96/1.60 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) }.
% 0.96/1.60 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 0.96/1.60 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.96/1.60 tc_Polynomial_Opoly( X ), Y ) }.
% 0.96/1.60 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.60 , Z = c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.60 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.96/1.60 c_Rings_Oinverse__class_Oinverse( X, Z ) ) = hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 0.96/1.60 Y ) ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) ),
% 0.96/1.60 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.96/1.60 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.60 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.96/1.60 c_Rings_Oinverse__class_Oinverse( X, Y ) ), Y ) =
% 0.96/1.60 c_Groups_Oone__class_Oone( X ) }.
% 0.96/1.60 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.60 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ),
% 0.96/1.60 c_Rings_Oinverse__class_Oinverse( X, Y ) ) = c_Groups_Oone__class_Oone( X
% 0.96/1.60 ) }.
% 0.96/1.60 { ! class_Rings_Oring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP
% 0.96/1.60 ( c_Groups_Otimes__class_Otimes( X ), Y ), Y ), c_Groups_Oone__class_Oone
% 0.96/1.60 ( X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.96/1.60 c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) ) ),
% 0.96/1.60 c_Groups_Ominus__class_Ominus( X, Y, c_Groups_Oone__class_Oone( X ) ) ) }
% 0.96/1.60 .
% 0.96/1.60 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Odegree( X,
% 0.96/1.60 c_Polynomial_Osynthetic__div( X, Z, Y ) ) = c_Groups_Ominus__class_Ominus
% 0.96/1.60 ( tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Groups_Oone__class_Oone(
% 0.96/1.60 tc_Nat_Onat ) ) }.
% 0.96/1.60 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.96/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = X }.
% 0.96/1.60 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.96/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.96/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.96/1.60 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) ) }.
% 0.96/1.60 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.60 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.96/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 0.96/1.60 ( tc_Nat_Onat ) ) ), X ) ) }.
% 0.96/1.60 { ! class_Power_Opower( X ), ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 0.96/1.60 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) =
% 0.96/1.60 c_Groups_Oone__class_Oone( X ) }.
% 0.96/1.60 { ! class_Power_Opower( X ), Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.96/1.60 , hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) = hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.96/1.60 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ominus__class_Ominus(
% 0.96/1.60 tc_Nat_Onat, Z, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 0.96/1.60 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.60 , Z = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ominus__class_Ominus( X
% 0.96/1.60 , c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.96/1.60 c_Rings_Oinverse__class_Oinverse( X, Z ) ) =
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 0.96/1.60 Y ) ), c_Groups_Ominus__class_Ominus( X, Y, Z ) ) ),
% 0.96/1.60 c_Rings_Oinverse__class_Oinverse( X, Z ) ) ) }.
% 0.96/1.60 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP(
% 0.96/1.60 hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.96/1.60 c_Rings_Oinverse__class_Oinverse( X, Y ) ), Y ) =
% 0.96/1.60 c_Groups_Oone__class_Oone( X ) }.
% 0.96/1.60 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.60 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.96/1.60 c_Rings_Oinverse__class_Oinverse( X, Z ) ) = hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.96/1.60 ) ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) ),
% 0.96/1.60 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.96/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.60 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.96/1.60 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ), Y =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 0.96/1.60 tc_Nat_Onat, Z, X ) }.
% 0.96/1.60 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, X ) }.
% 0.96/1.60 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.96/1.60 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.96/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.96/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 0.96/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), alpha4( X, Y ), Y = X }
% 0.96/1.60 .
% 0.96/1.60 { ! alpha4( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.96/1.60 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.96/1.60 { ! alpha4( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.96/1.60 { ! alpha4( X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.96/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.96/1.60 ( tc_Nat_Onat, X, Y ), alpha4( X, Y ) }.
% 0.96/1.60 { ! alpha5( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.96/1.60 { ! alpha5( X, Y ), ! Y = X }.
% 0.96/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X, alpha5( X, Y ) }
% 0.96/1.60 .
% 0.96/1.60 { ! alpha5( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.96/1.60 { ! alpha5( X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.96/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.96/1.60 ( tc_Nat_Onat, X, Y ), alpha5( X, Y ) }.
% 0.96/1.60 { Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ),
% 0.96/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.96/1.60 { Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.96/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.96/1.60 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.96/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.96/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), X = Y }.
% 0.96/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), ! X = Y,
% 0.96/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.96/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.96/1.60 ( tc_Nat_Onat, Y, X ), Y = X }.
% 0.96/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.96/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 0.96/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X,
% 0.96/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.96/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X, !
% 0.96/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.96/1.60 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.96/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 0.96/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), ! X = Z,
% 0.96/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 0.96/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.96/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 0.96/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.96/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 0.96/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.96/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 0.96/1.60 tc_Nat_Onat, Y, Z ) }.
% 0.96/1.60 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.96/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd(
% 0.96/1.60 tc_Nat_Onat, Y, Z ) }.
% 0.96/1.60 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.96/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd
% 0.96/1.60 ( tc_Nat_Onat, Z, Y ) }.
% 0.96/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.96/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 0.96/1.60 tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 0.96/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.96/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 0.96/1.60 tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.96/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.96/1.60 ( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.96/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.96/1.60 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 0.96/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.96/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.96/1.60 ( tc_Nat_Onat, X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.96/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.96/1.60 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 0.96/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.96/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.96/1.60 ( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.96/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.96/1.60 ( tc_Nat_Onat, X, Y ), ! X = Y }.
% 0.96/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.96/1.60 ( tc_Nat_Onat, X, Y ), ! X = Z, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 0.96/1.60 , Z ) }.
% 0.96/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.96/1.60 ( tc_Nat_Onat, X, Y ), ! X = Z, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat,
% 0.96/1.60 Z, Y ) }.
% 0.96/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.96/1.60 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.96/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 0.96/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.96/1.60 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), !
% 0.96/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.96/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.96/1.60 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 0.96/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.96/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.96/1.60 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.96/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd(
% 0.96/1.60 tc_Nat_Onat, Y, Z ) }.
% 0.96/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.96/1.60 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.96/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd
% 0.96/1.60 ( tc_Nat_Onat, Z, Y ) }.
% 0.96/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.96/1.60 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 0.96/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.96/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, c_Groups_Ominus__class_Ominus
% 0.96/1.60 ( tc_Int_Oint, Y, X ) ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, X )
% 0.96/1.60 , c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 0.96/1.60 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Nat_Onat ) ) }.
% 0.96/1.60 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 0.96/1.60 tc_Nat_Onat ), X ) }.
% 0.96/1.60 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.96/1.60 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.96/1.60 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus(
% 0.96/1.60 X, U, Z ), c_Groups_Ominus__class_Ominus( X, T, Y ) ) }.
% 0.96/1.60 { ! class_Fields_Ofield__inverse__zero( X ),
% 0.96/1.60 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.60 { ! class_Fields_Ofield__inverse__zero( X ),
% 0.96/1.60 c_Rings_Oinverse__class_Oinverse( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 0.96/1.60 Z ) ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.96/1.60 { ! class_Fields_Ofield__inverse__zero( X ), !
% 0.96/1.60 c_Rings_Oinverse__class_Oinverse( X, Y ) = c_Groups_Oone__class_Oone( X )
% 0.96/1.60 , Y = c_Groups_Oone__class_Oone( X ) }.
% 0.96/1.60 { ! class_Fields_Ofield__inverse__zero( X ), ! Y =
% 0.96/1.60 c_Groups_Oone__class_Oone( X ), c_Rings_Oinverse__class_Oinverse( X, Y )
% 0.96/1.60 = c_Groups_Oone__class_Oone( X ) }.
% 0.96/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.60 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.96/1.60 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ), Y =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 0.96/1.60 tc_Int_Oint, Z, X ) }.
% 0.96/1.60 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.96/1.60 c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.60 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.96/1.60 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ) ),
% 0.96/1.60 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 0.96/1.60 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.96/1.60 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd(
% 0.96/1.60 tc_Int_Oint, hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z )
% 0.96/1.60 , X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X )
% 0.96/1.60 ) }.
% 0.96/1.60 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.96/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.60 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.96/1.60 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ),
% 0.96/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.96/1.60 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.96/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ), c_Rings_Odvd__class_Odvd(
% 0.96/1.60 tc_Nat_Onat, hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Z )
% 0.96/1.60 , X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X )
% 0.96/1.60 ) }.
% 0.96/1.60 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Ouminus__class_Ouminus
% 0.96/1.60 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.96/1.60 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) }.
% 0.96/1.60 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Y, Z ) =
% 0.96/1.60 c_Polynomial_Osmult( X, c_Rings_Oinverse__class_Oinverse( X, hAPP(
% 0.96/1.60 c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) ), Y ) }.
% 0.96/1.60 { ! class_Fields_Ofield( X ), Z = c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Y, Z ) =
% 0.96/1.60 c_Polynomial_Opoly__gcd( X, Z, c_Divides_Odiv__class_Omod(
% 0.96/1.60 tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 0.96/1.60 { ! class_Groups_Ozero( X ), c_Polynomial_OpCons( X, Z, Y ) =
% 0.96/1.60 c_Polynomial_OAbs__poly( X, c_Nat_Onat_Onat__case( X, Z,
% 0.96/1.60 c_Polynomial_Ocoeff( X, Y ) ) ) }.
% 0.96/1.60 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless(
% 0.96/1.60 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), hAPP( hAPP
% 0.96/1.60 ( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.60 c_Power_Opower__class_Opower( X ), Z ), c_Groups_Ominus__class_Ominus(
% 0.96/1.60 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ), Z ) =
% 0.96/1.60 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.96/1.60 X ) ) }.
% 0.96/1.60 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( X ) ) }.
% 0.96/1.60 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Nat_Onat ), c_Nat_OSuc( X ) ) }.
% 0.96/1.60 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.96/1.60 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ), c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, T, Y ) }.
% 0.96/1.60 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, T, Y ), c_Orderings_Oord__class_Oless(
% 0.96/1.60 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.96/1.60 , Y, Z ) ) }.
% 0.96/1.60 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.96/1.60 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, Z, Y ) }.
% 0.96/1.60 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.96/1.60 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.96/1.60 , T, Y ) ) }.
% 0.96/1.60 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.96/1.60 X, c_Groups_Oplus__class_Oplus( X, Z, T ), c_Groups_Oplus__class_Oplus( X
% 0.96/1.60 , Y, T ) ) }.
% 0.96/1.60 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.96/1.60 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.96/1.60 , T, Y ) ) }.
% 0.96/1.60 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, U, T ), c_Orderings_Oord__class_Oless( X,
% 0.96/1.60 c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X, Y
% 0.96/1.60 , T ) ) }.
% 0.96/1.60 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, T )
% 0.96/1.60 , c_Groups_Oplus__class_Oplus( X, Y, T ) ), c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, Z, Y ) }.
% 0.96/1.60 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.96/1.60 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, Z, Y ) }.
% 0.96/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.60 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.96/1.60 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, U, T ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.96/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.60 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.96/1.60 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, U, T ) }.
% 0.96/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ouminus__class_Ouminus( X,
% 0.96/1.60 Y ) ), c_Orderings_Oord__class_Oless( X, Y,
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.96/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ouminus__class_Ouminus( X,
% 0.96/1.60 Z ) ), c_Orderings_Oord__class_Oless( X, Z,
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.96/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.96/1.60 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 0.96/1.60 ( X, Y ), Z ) }.
% 0.96/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.96/1.60 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 0.96/1.60 ( X, Z ), Y ) }.
% 0.96/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.96/1.60 , c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.96/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, Y, Z ), c_Orderings_Oord__class_Oless(
% 0.96/1.60 X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.96/1.60 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Omod(
% 0.96/1.60 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ) =
% 0.96/1.60 c_Polynomial_Osmult( X, T, c_Divides_Odiv__class_Omod(
% 0.96/1.60 tc_Polynomial_Opoly( X ), Z, Y ) ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.96/1.60 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Nat_Onat ), X ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.60 ( tc_Nat_Onat ), X ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 0.96/1.60 .
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.60 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Nat_Onat ), X ) }.
% 0.96/1.60 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.96/1.60 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) )
% 0.96/1.60 }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 0.96/1.60 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.96/1.60 X ) ) }.
% 0.96/1.60 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y = X }
% 0.96/1.60 .
% 0.96/1.60 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X,
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.96/1.60 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), X = Y }
% 0.96/1.60 .
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) = X
% 0.96/1.60 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 0.96/1.60 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.96/1.60 ( tc_Nat_Onat, Y, X ), Y ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.96/1.60 ( tc_Nat_Onat, Y, X ), X ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.96/1.60 ( tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) )
% 0.96/1.60 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.96/1.60 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }
% 0.96/1.60 .
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.96/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.96/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.96/1.60 tc_Nat_Onat, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.96/1.60 .
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.96/1.60 tc_Nat_Onat, Y, T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.96/1.60 .
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.96/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, X ) =
% 0.96/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.96/1.60 ( tc_Nat_Onat, Y, Z ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y
% 0.96/1.60 , X ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.96/1.60 ( tc_Nat_Onat, Y, Z ), X ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.96/1.60 ( tc_Nat_Onat, Z, X ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.96/1.60 ) }.
% 0.96/1.60 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Omod(
% 0.96/1.60 tc_Polynomial_Opoly( X ), c_Groups_Ouminus__class_Ouminus(
% 0.96/1.60 tc_Polynomial_Opoly( X ), Z ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.96/1.60 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly
% 0.96/1.60 ( X ), Z, Y ) ) }.
% 0.96/1.60 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Omod(
% 0.96/1.60 tc_Polynomial_Opoly( X ), Z, c_Groups_Ouminus__class_Ouminus(
% 0.96/1.60 tc_Polynomial_Opoly( X ), Y ) ) = c_Divides_Odiv__class_Omod(
% 0.96/1.60 tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.96/1.60 { alpha54( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 0.96/1.60 hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.96/1.60 { alpha54( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP
% 0.96/1.60 ( X, Y ), Z ) ) }.
% 0.96/1.60 { ! alpha54( X, Y, Z ), alpha57( X, Y, Z ), Z = Y }.
% 0.96/1.60 { ! alpha54( X, Y, Z ), alpha57( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z
% 0.96/1.60 ) ) }.
% 0.96/1.60 { ! alpha57( X, Y, Z ), alpha54( X, Y, Z ) }.
% 0.96/1.60 { ! Z = Y, hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha54( X, Y, Z ) }.
% 0.96/1.60 { ! alpha57( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y )
% 0.96/1.60 }.
% 0.96/1.60 { ! alpha57( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ), hBOOL( hAPP( hAPP(
% 0.96/1.60 X, Y ), Z ) ), alpha57( X, Y, Z ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X = Y }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.96/1.60 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.96/1.60 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.96/1.60 { ! class_Fields_Ofield( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 0.96/1.60 , c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) ),
% 0.96/1.60 c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), Z, Y ) = Z }.
% 0.96/1.60 { ! class_Rings_Olinordered__idom( X ), Z = Y,
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.96/1.60 X, Y, Z ) }.
% 0.96/1.60 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ), c_Divides_Odiv__class_Omod(
% 0.96/1.60 tc_Polynomial_Opoly( X ), Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.60 c_Polynomial_Odegree( X, c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly
% 0.96/1.60 ( X ), Z, Y ) ), c_Polynomial_Odegree( X, Y ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.60 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.96/1.60 c_Groups_Oone__class_Oone( X ), T ), c_Orderings_Oord__class_Oless( X,
% 0.96/1.60 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.60 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.96/1.60 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.96/1.60 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.96/1.60 ( tc_Nat_Onat, T, Z ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.60 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.96/1.60 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.60 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 0.96/1.60 , T, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.96/1.60 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.96/1.60 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.96/1.60 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), hAPP(
% 0.96/1.60 hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.96/1.60 { ! class_Groups_Ozero( X ), c_Polynomial_OAbs__poly( X,
% 0.96/1.60 c_Polynomial_Ocoeff( X, Y ) ) = Y }.
% 0.96/1.60 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.60 c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), T,
% 0.96/1.60 c_Polynomial_Osmult( X, Y, Z ) ) = c_Divides_Odiv__class_Omod(
% 0.96/1.60 tc_Polynomial_Opoly( X ), T, Z ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP
% 0.96/1.60 ( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.96/1.60 ( c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__comm__semiring__strict( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.96/1.60 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.96/1.60 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP
% 0.96/1.60 ( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.96/1.60 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.60 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.96/1.60 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.96/1.60 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.96/1.60 ( X ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.96/1.60 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.96/1.60 ! c_Orderings_Oord__class_Oless( X, Z, T ), c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.96/1.60 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.96/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ) }
% 0.96/1.60 .
% 0.96/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.96/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.96/1.60 .
% 0.96/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.96/1.60 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.60 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.96/1.60 ( X ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.96/1.60 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.60 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.96/1.60 ( X ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.96/1.60 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.96/1.60 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.96/1.60 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.96/1.60 ! c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.96/1.60 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha6( X, Y, Z, T ),
% 0.96/1.60 alpha26( X, Y, Z, T ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha6( X, Y, Z, T ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha26( X, Y, Z, T ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.96/1.60 { ! alpha26( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.60 { ! alpha26( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( X, T, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.60 , ! c_Orderings_Oord__class_Oless( X, Y, Z ), alpha26( X, Y, Z, T ) }.
% 0.96/1.60 { ! alpha6( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), T ) }.
% 0.96/1.60 { ! alpha6( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T )
% 0.96/1.60 , ! c_Orderings_Oord__class_Oless( X, Z, Y ), alpha6( X, Y, Z, T ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha7( X, Y, Z, T ),
% 0.96/1.60 alpha27( X, Y, Z, T ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha7( X, Y, Z, T ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha27( X, Y, Z, T ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.96/1.60 { ! alpha27( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.60 { ! alpha27( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, T ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.60 , ! c_Orderings_Oord__class_Oless( X, Y, T ), alpha27( X, Y, Z, T ) }.
% 0.96/1.60 { ! alpha7( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.96/1.60 { ! alpha7( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.96/1.60 , ! c_Orderings_Oord__class_Oless( X, T, Y ), alpha7( X, Y, Z, T ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.96/1.60 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.60 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.96/1.60 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.60 , c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.96/1.60 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless(
% 0.96/1.60 X, T, c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.96/1.60 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.96/1.60 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.96/1.60 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.60 c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.96/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.96/1.60 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Y
% 0.96/1.60 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.96/1.60 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.60 c_Groups_Oplus__class_Oplus( X, Y, Y ) ), c_Orderings_Oord__class_Oless(
% 0.96/1.60 X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.96/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.60 c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.96/1.60 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.96/1.60 ) ), c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 0.96/1.60 ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.96/1.60 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.96/1.60 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.96/1.60 ) ) }.
% 0.96/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.96/1.60 X, c_Groups_Ominus__class_Ominus( X, Z, Y ), c_Groups_Ozero__class_Ozero
% 0.96/1.60 ( X ) ) }.
% 0.96/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.96/1.60 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.96/1.60 , Z, Y ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero( X ) ) }
% 0.96/1.60 .
% 0.96/1.60 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.96/1.60 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.96/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.96/1.60 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.96/1.60 .
% 0.96/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.96/1.60 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.96/1.60 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.96/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.96/1.60 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.96/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.96/1.60 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.96/1.60 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.96/1.60 , Y ) }.
% 0.96/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.96/1.60 , Y ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, c_Groups_Oone__class_Oone( X ), Z ), c_Orderings_Oord__class_Oless(
% 0.96/1.60 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.96/1.60 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.96/1.60 , Y, c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) )
% 0.96/1.60 ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! hAPP( hAPP(
% 0.96/1.60 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 0.96/1.60 c_Power_Opower__class_Opower( X ), Y ), Z ), T = Z }.
% 0.96/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! T = Z, hAPP( hAPP(
% 0.96/1.60 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 0.96/1.60 c_Power_Opower__class_Opower( X ), Y ), Z ) }.
% 0.96/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.96/1.60 X, c_Rings_Oinverse__class_Oinverse( X, Z ),
% 0.96/1.60 c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.96/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.96/1.60 X, c_Rings_Oinverse__class_Oinverse( X, Z ),
% 0.96/1.60 c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.96/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.96/1.60 X, c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Ozero__class_Ozero
% 0.96/1.60 ( X ) ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.96/1.60 .
% 0.96/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.96/1.60 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.96/1.60 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.96/1.60 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.96/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.96/1.60 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless( X,
% 0.96/1.60 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.96/1.60 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.96/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.96/1.60 X, Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless(
% 0.96/1.60 X, c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Ozero__class_Ozero
% 0.96/1.60 ( X ) ) }.
% 0.96/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.96/1.60 X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X
% 0.96/1.60 , Y ) ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.96/1.60 .
% 0.96/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.96/1.60 X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.96/1.60 X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X
% 0.96/1.60 , Y ) ) }.
% 0.96/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 0.96/1.60 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.96/1.60 , Y, c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 0.96/1.60 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.60 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.96/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.60 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha8( X, Y ) }.
% 0.96/1.60 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.96/1.60 { ! alpha8( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.96/1.60 c_Nat_OSuc( X ) ) }.
% 0.96/1.60 { ! alpha8( X, Y ), Y = c_Nat_OSuc( skol8( Z, Y ) ) }.
% 0.96/1.60 { ! alpha8( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol8( X, Y
% 0.96/1.60 ), X ) }.
% 0.96/1.60 { ! Y = c_Nat_OSuc( Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.96/1.60 ), alpha8( X, Y ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.60 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.60 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( skol9( X ) ) }.
% 0.96/1.60 { ! X = c_Nat_OSuc( Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.60 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y
% 0.96/1.60 ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.60 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Nat_Onat ), Y ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.60 ( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.60 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.96/1.60 tc_Nat_Onat, Y, X ) ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.60 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.96/1.60 tc_Nat_Onat, Y, X ) ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), X = c_Nat_OSuc(
% 0.96/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol10( X, Y ) ) ) }.
% 0.96/1.60 { ! X = c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.96/1.60 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 0.96/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) ) }.
% 0.96/1.60 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 0.96/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.60 ( tc_Nat_Onat ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.96/1.60 tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.96/1.60 tc_Nat_Onat ), X ), Y ), Z = Y }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.60 ( tc_Nat_Onat ), X ), ! Z = Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.60 ( tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.96/1.60 tc_Nat_Onat ), X ), Y ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.60 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 0.96/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP(
% 0.96/1.60 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.60 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 0.96/1.60 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.60 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.96/1.60 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.60 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.96/1.60 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.60 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.60 Y ), X ) ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Nat_Onat ), Z ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.60 ( tc_Nat_Onat ), Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 0.96/1.60 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Nat_Onat ), Y ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.60 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.96/1.60 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.96/1.60 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP
% 0.96/1.60 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.96/1.60 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP
% 0.96/1.60 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.96/1.60 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 0.96/1.60 c_Polynomial_Opoly__gcd( X, Y, c_Divides_Odiv__class_Omod(
% 0.96/1.60 tc_Polynomial_Opoly( X ), Z, Y ) ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.60 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.96/1.60 ( tc_Nat_Onat, Y, X ), Y ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.60 ( tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.96/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.96/1.60 ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.96/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.96/1.60 ), X ) ) }.
% 0.96/1.60 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.96/1.60 ( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z,
% 0.96/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.96/1.60 tc_Nat_Onat, Z, X ), Y ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.96/1.60 ( tc_Nat_Onat, Z, X ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z
% 0.96/1.60 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 0.96/1.60 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.96/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) = Y }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.60 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 0.96/1.60 ( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Z ), hAPP( hAPP
% 0.96/1.60 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.60 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.96/1.60 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), X =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.60 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.60 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.96/1.60 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 0.96/1.60 ), X ) ) }.
% 0.96/1.60 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 0.96/1.60 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, T )
% 0.96/1.60 , Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree(
% 0.96/1.60 X, c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Z, T ) ), Y ) }
% 0.96/1.60 .
% 0.96/1.60 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 0.96/1.60 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) )
% 0.96/1.60 , c_Polynomial_Odegree( X, c_Groups_Oplus__class_Oplus(
% 0.96/1.60 tc_Polynomial_Opoly( X ), Z, Y ) ) = c_Polynomial_Odegree( X, Y ) }.
% 0.96/1.60 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 0.96/1.60 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) )
% 0.96/1.60 , c_Polynomial_Odegree( X, c_Groups_Oplus__class_Oplus(
% 0.96/1.60 tc_Polynomial_Opoly( X ), Y, Z ) ) = c_Polynomial_Odegree( X, Y ) }.
% 0.96/1.60 { ! class_Groups_Oab__group__add( X ), ! c_Orderings_Oord__class_Oless(
% 0.96/1.60 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, T )
% 0.96/1.60 , Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree(
% 0.96/1.60 X, c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Z, T ) ), Y )
% 0.96/1.60 }.
% 0.96/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.60 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.96/1.60 ) ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__ring__strict( X ), Z =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.96/1.60 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__ring__strict( X ), Y =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.96/1.60 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.96/1.60 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.96/1.60 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.60 c_Groups_Oone__class_Oone( X ), c_Groups_Oone__class_Oone( X ) ) ) }.
% 0.96/1.60 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.96/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.60 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, hAPP
% 0.96/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus
% 0.96/1.60 ( X, Z, W ) ), U ), Y ) ) }.
% 0.96/1.60 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X, T
% 0.96/1.60 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.96/1.60 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless( X,
% 0.96/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.60 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.96/1.60 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.96/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.60 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.96/1.60 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.96/1.60 X, W, Z ) ), U ), T ), Y ) }.
% 0.96/1.60 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.96/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.60 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.96/1.60 hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.96/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.60 ( X ), Z ), U ), Y ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.96/1.60 X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.96/1.60 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.96/1.60 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.96/1.60 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.96/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 0.96/1.60 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.96/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 0.96/1.60 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, Y, c_Groups_Oone__class_Oone( X ) ) }.
% 0.96/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.96/1.60 ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 0.96/1.60 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.96/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.96/1.60 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, Y, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless(
% 0.96/1.60 X, c_Groups_Oone__class_Oone( X ), c_Rings_Oinverse__class_Oinverse( X, Y
% 0.96/1.60 ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.96/1.60 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.96/1.60 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ) ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.60 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.60 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.96/1.60 tc_Nat_Onat, X, c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) )
% 0.96/1.60 ) ) = X }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.60 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 0.96/1.60 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.96/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.60 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ),
% 0.96/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.96/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Nat_Onat ), Z ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.96/1.60 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.96/1.60 , alpha9( X, Y, Z ) }.
% 0.96/1.60 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.96/1.60 , alpha28( X, Y, Z ) }.
% 0.96/1.60 { ! alpha9( X, Y, Z ), ! alpha28( X, Y, Z ), hBOOL( hAPP( Z,
% 0.96/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.96/1.60 { ! alpha28( X, Y, Z ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.96/1.60 T ), hBOOL( hAPP( Z, T ) ) }.
% 0.96/1.60 { ! hBOOL( hAPP( Z, skol11( T, U, Z ) ) ), alpha28( X, Y, Z ) }.
% 0.96/1.60 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, skol11( X, Y, Z ) ),
% 0.96/1.60 alpha28( X, Y, Z ) }.
% 0.96/1.60 { ! alpha9( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 0.96/1.60 , hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.96/1.60 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), alpha9( X, Y, Z ) }.
% 0.96/1.60 { ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha9
% 0.96/1.60 ( X, Y, Z ) }.
% 0.96/1.60 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.96/1.60 , ! alpha10( X, Y, Z ) }.
% 0.96/1.60 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.96/1.60 , ! alpha29( X, Y, Z ) }.
% 0.96/1.60 { alpha10( X, Y, Z ), alpha29( X, Y, Z ), hBOOL( hAPP( Z,
% 0.96/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.96/1.60 { ! alpha29( X, Y, Z ), ! hBOOL( hAPP( Z, skol12( T, U, Z ) ) ) }.
% 0.96/1.60 { ! alpha29( X, Y, Z ), Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.96/1.60 skol12( X, Y, Z ) ) }.
% 0.96/1.60 { ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, T ), hBOOL( hAPP( Z, T
% 0.96/1.60 ) ), alpha29( X, Y, Z ) }.
% 0.96/1.60 { ! alpha10( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 0.96/1.60 }.
% 0.96/1.60 { ! alpha10( X, Y, Z ), ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Nat_Onat ) ) ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), hBOOL( hAPP( Z,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha10( X, Y, Z ) }.
% 0.96/1.60 { ! class_Groups_Ozero( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.60 c_Polynomial_Odegree( X, Z ), Y ), hAPP( c_Polynomial_Ocoeff( X, Z ), Y )
% 0.96/1.60 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.96/1.60 c_Power_Opower__class_Opower( X ), Y ), Z ) ), hAPP( hAPP(
% 0.96/1.60 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.60 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ),
% 0.96/1.60 c_Groups_Oone__class_Oone( X ) ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Orderings_Oord__class_Oless(
% 0.96/1.60 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 0.96/1.60 c_Rings_Odvd__class_Odvd( X, Y, hAPP( hAPP( c_Power_Opower__class_Opower
% 0.96/1.60 ( X ), Y ), Z ) ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! Y = c_Groups_Oone__class_Oone( X
% 0.96/1.60 ), c_Rings_Odvd__class_Odvd( X, Y, hAPP( hAPP(
% 0.96/1.60 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.60 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.96/1.60 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) = X }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.60 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.96/1.60 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.60 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 0.96/1.60 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ), Y =
% 0.96/1.60 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.60 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 0.96/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.60 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 0.96/1.60 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ), Y =
% 0.96/1.60 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.60 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 0.96/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.60 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.96/1.60 , Y ), X ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Nat_Onat ), Y ) }.
% 0.96/1.60 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 0.96/1.60 ), X ) ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.60 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.60 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( c_Nat_OSuc(
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), X =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X = c_Nat_OSuc(
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.96/1.60 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.96/1.60 ), c_Divides_Odiv__class_Omod( X, Y, Z ) = c_Groups_Ozero__class_Ozero(
% 0.96/1.60 X ) }.
% 0.96/1.60 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, Y,
% 0.96/1.60 Z ) = c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.96/1.60 ) }.
% 0.96/1.60 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.96/1.60 ), c_Divides_Odiv__class_Omod( X, Y, Z ) = c_Groups_Ozero__class_Ozero(
% 0.96/1.60 X ) }.
% 0.96/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, c_Divides_Odiv__class_Omod(
% 0.96/1.60 tc_Int_Oint, Y, X ) ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, X ),
% 0.96/1.60 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 0.96/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 0.96/1.60 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, Z ), c_Rings_Odvd__class_Odvd(
% 0.96/1.60 tc_Int_Oint, Y, c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Z ) ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.60 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) = Y }.
% 0.96/1.60 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.60 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 0.96/1.60 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.96/1.60 tc_Nat_Onat, Y, X ), X ) }.
% 0.96/1.60 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ominus__class_Ominus(
% 0.96/1.60 tc_Int_Oint, Z, c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) =
% 0.96/1.60 c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ominus__class_Ominus(
% 0.96/1.60 tc_Int_Oint, Z, Y ), X ) }.
% 0.96/1.60 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ominus__class_Ominus(
% 0.96/1.60 tc_Int_Oint, c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, Y ), X ), Y ) =
% 0.96/1.60 c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ominus__class_Ominus(
% 0.96/1.60 tc_Int_Oint, Z, X ), Y ) }.
% 0.96/1.60 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.60 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 0.96/1.60 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.96/1.60 tc_Nat_Onat, Y, X ), X ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.96/1.60 tc_Int_Oint, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 0.96/1.60 .
% 0.96/1.60 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.60 { ! c_Nat_OSuc( c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) = X,
% 0.96/1.60 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.60 { c_Nat_OSuc( c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) = X,
% 0.96/1.60 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.96/1.60 c_Nat_OSuc( c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) }.
% 0.96/1.60 { ! c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol13( X, Y ) ) }.
% 0.96/1.60 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z )
% 0.96/1.60 , c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.60 { ! c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y = hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), skol14( X, Y ) ) }.
% 0.96/1.60 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z )
% 0.96/1.60 , c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.96/1.60 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.96/1.60 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z
% 0.96/1.60 ), Y ), X ), Y ) = c_Divides_Odiv__class_Omod( tc_Nat_Onat, X, Y ) }.
% 0.96/1.60 { c_Divides_Odiv__class_Omod( tc_Int_Oint, Y,
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), ! c_Divides_Odiv__class_Omod
% 0.96/1.60 ( tc_Int_Oint, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.96/1.60 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.96/1.60 ( tc_Int_Oint, Y ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.96/1.60 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.96/1.60 { c_Divides_Odiv__class_Omod( tc_Int_Oint, Y,
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Divides_Odiv__class_Omod
% 0.96/1.60 ( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) ) }
% 0.96/1.60 .
% 0.96/1.60 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.96/1.60 ( tc_Int_Oint, Y ), c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Divides_Odiv__class_Omod
% 0.96/1.60 ( tc_Int_Oint, Y, X ) ) }.
% 0.96/1.60 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.96/1.60 ( tc_Int_Oint, c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) =
% 0.96/1.60 c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.96/1.60 ( tc_Int_Oint, Y ), X ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.60 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) = Y }.
% 0.96/1.60 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.96/1.60 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc(
% 0.96/1.60 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ), X ) }.
% 0.96/1.60 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.60 c_Power_Opower__class_Opower( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.96/1.60 tc_Int_Oint, Z, Y ) ), X ), Y ) = c_Divides_Odiv__class_Omod( tc_Int_Oint
% 0.96/1.60 , hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ), Y )
% 0.96/1.60 }.
% 0.96/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.60 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.96/1.60 c_Divides_Odiv__class_Omod( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.96/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.96/1.60 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) =
% 0.96/1.60 c_Divides_Odiv__class_Omod( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.96/1.60 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.96/1.60 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) =
% 0.96/1.60 c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ) }.
% 0.96/1.60 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ) =
% 0.96/1.60 c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.96/1.60 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) }.
% 0.96/1.60 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Int_Oint ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.96/1.60 { c_Divides_Odiv__class_Omod( tc_Int_Oint, X, X ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.60 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.96/1.60 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ), X ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.60 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.60 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ), X ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Divides_Odiv__class_Omod
% 0.96/1.60 ( tc_Int_Oint, Y, X ) ) }.
% 0.96/1.60 { ! c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, Y ) =
% 0.96/1.60 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ), c_Rings_Odvd__class_Odvd
% 0.96/1.60 ( tc_Int_Oint, Y, c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, X ) ) }
% 0.96/1.60 .
% 0.96/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Ominus__class_Ominus
% 0.96/1.60 ( tc_Int_Oint, Z, X ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, Y )
% 0.96/1.60 = c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ) }.
% 0.96/1.60 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc(
% 0.96/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), X ) ), Y ) =
% 0.96/1.60 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) }.
% 0.96/1.60 { ! c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.96/1.60 tc_Int_Oint, Y, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.96/1.60 { c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.96/1.60 tc_Int_Oint, Y, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.96/1.60 c_Groups_Ominus__class_Ominus( tc_Int_Oint, c_Divides_Odiv__class_Omod(
% 0.96/1.60 tc_Int_Oint, Y, X ), X ) }.
% 0.96/1.60 { ! c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.96/1.60 tc_Int_Oint, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.96/1.60 { c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.96/1.60 tc_Int_Oint, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) =
% 0.96/1.60 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Divides_Odiv__class_Omod
% 0.96/1.60 ( tc_Int_Oint, Y, X ) ) }.
% 0.96/1.60 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Int_Oint ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 0.96/1.60 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP
% 0.96/1.60 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.96/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.96/1.60 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y
% 0.96/1.60 = X }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.96/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.96/1.60 tc_Int_Oint ) ) ) }.
% 0.96/1.60 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.96/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.96/1.60 tc_Int_Oint ) ) ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ominus__class_Ominus
% 0.96/1.60 ( tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.96/1.60 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ),
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.60 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y
% 0.96/1.60 ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.60 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 0.96/1.60 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ),
% 0.96/1.60 c_Divides_Odiv__class_Omod( tc_Nat_Onat, T, X ) ), Z ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.96/1.60 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) ),
% 0.96/1.60 alpha11( X, Y, Z ) }.
% 0.96/1.60 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) ),
% 0.96/1.60 alpha30( X, Y, Z ) }.
% 0.96/1.60 { ! alpha11( X, Y, Z ), ! alpha30( X, Y, Z ), hBOOL( hAPP( Z,
% 0.96/1.60 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) ) }.
% 0.96/1.60 { ! alpha30( X, Y, Z ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.96/1.60 alpha41( X, Y, Z ) }.
% 0.96/1.60 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha30( X, Y, Z ) }.
% 0.96/1.60 { ! alpha41( X, Y, Z ), alpha30( X, Y, Z ) }.
% 0.96/1.60 { ! alpha41( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, X
% 0.96/1.60 ), alpha47( X, Y, Z, T ) }.
% 0.96/1.60 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol15( X, T, U ), X ),
% 0.96/1.60 alpha41( X, Y, Z ) }.
% 0.96/1.60 { ! alpha47( X, Y, Z, skol15( X, Y, Z ) ), alpha41( X, Y, Z ) }.
% 0.96/1.60 { ! alpha47( X, Y, Z, T ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.96/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 0.96/1.60 hBOOL( hAPP( Z, T ) ) }.
% 0.96/1.60 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol16( X, Y, T ) ), T
% 0.96/1.60 ), alpha47( X, Y, Z, T ) }.
% 0.96/1.60 { ! hBOOL( hAPP( Z, T ) ), alpha47( X, Y, Z, T ) }.
% 0.96/1.60 { ! alpha11( X, Y, Z ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.96/1.60 hBOOL( hAPP( Z, Y ) ) }.
% 0.96/1.60 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha11( X, Y, Z ) }.
% 0.96/1.60 { ! hBOOL( hAPP( Z, Y ) ), alpha11( X, Y, Z ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 0.96/1.60 tc_Nat_Onat ), X ), c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc(
% 0.96/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), X )
% 0.96/1.60 = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.96/1.60 ( tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.96/1.60 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.96/1.60 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.96/1.60 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.60 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.96/1.60 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), X =
% 0.96/1.60 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.60 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.96/1.60 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), Y =
% 0.96/1.60 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.60 ( tc_Int_Oint ), X ), ! X = c_Groups_Oone__class_Oone( tc_Int_Oint ), ! Y
% 0.96/1.60 = c_Groups_Oone__class_Oone( tc_Int_Oint ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 0.96/1.60 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.96/1.60 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.96/1.60 c_Divides_Odiv__class_Omod( X, Z, Y ), Y ) = c_Divides_Odiv__class_Omod(
% 0.96/1.60 X, Z, Y ) }.
% 0.96/1.60 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.60 }.
% 0.96/1.60 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.96/1.60 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y, Y
% 0.96/1.60 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.60 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.96/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 0.96/1.60 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.60 ( X ), T ), c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 0.96/1.60 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.96/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 0.96/1.60 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.60 ( X ), c_Divides_Odiv__class_Omod( X, T, Y ) ), Z ), Y ) }.
% 0.96/1.60 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.96/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 0.96/1.60 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.60 ( X ), c_Divides_Odiv__class_Omod( X, T, Y ) ),
% 0.96/1.60 c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 0.96/1.60 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.96/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) = hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), T ), c_Divides_Odiv__class_Omod( X, Z
% 0.96/1.60 , Y ) ) }.
% 0.96/1.60 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.96/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Omod( X, T, Y )
% 0.96/1.60 ), Z ) }.
% 0.96/1.60 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.96/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Omod( X
% 0.96/1.60 , T, Z ) ), Y ), Z ) = c_Divides_Odiv__class_Omod( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.96/1.60 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, T,
% 0.96/1.60 Z ) = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod
% 0.96/1.60 ( X, W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 0.96/1.60 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.60 ( X ), T ), W ), Z ) = c_Divides_Odiv__class_Omod( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), U ), Z ) }.
% 0.96/1.60 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.96/1.60 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = c_Divides_Odiv__class_Omod
% 0.96/1.60 ( X, Z, Y ) }.
% 0.96/1.60 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.96/1.60 c_Groups_Oplus__class_Oplus( X, Z, Y ), Z ) = c_Divides_Odiv__class_Omod
% 0.96/1.60 ( X, Y, Z ) }.
% 0.96/1.60 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.96/1.60 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 0.96/1.60 ( X, c_Groups_Oplus__class_Oplus( X, T, c_Divides_Odiv__class_Omod( X, Z
% 0.96/1.60 , Y ) ), Y ) }.
% 0.96/1.60 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.96/1.60 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 0.96/1.60 ( X, c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Omod( X, T, Y
% 0.96/1.60 ), Z ), Y ) }.
% 0.96/1.60 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.96/1.60 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 0.96/1.60 ( X, c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Omod( X, T, Y
% 0.96/1.60 ), c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 0.96/1.60 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.96/1.60 c_Groups_Oplus__class_Oplus( X, T, c_Divides_Odiv__class_Omod( X, Z, Y )
% 0.96/1.60 ), Y ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X,
% 0.96/1.60 T, Z ), Y ) }.
% 0.96/1.60 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.96/1.60 c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Omod( X, T, Z ), Y
% 0.96/1.60 ), Z ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X,
% 0.96/1.60 T, Y ), Z ) }.
% 0.96/1.60 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, T,
% 0.96/1.60 Z ) = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod
% 0.96/1.60 ( X, W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 0.96/1.60 c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X, T, W ), Z
% 0.96/1.60 ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X, Y, U
% 0.96/1.60 ), Z ) }.
% 0.96/1.60 { ! class_Divides_Oring__div( X ), ! c_Divides_Odiv__class_Omod( X, T, Z )
% 0.96/1.60 = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod( X
% 0.96/1.60 , W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 0.96/1.60 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, T, W ),
% 0.96/1.60 Z ) = c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, Y
% 0.96/1.60 , U ), Z ) }.
% 0.96/1.60 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.96/1.60 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 0.96/1.60 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X,
% 0.96/1.60 c_Divides_Odiv__class_Omod( X, T, Y ), c_Divides_Odiv__class_Omod( X, Z,
% 0.96/1.60 Y ) ), Y ) }.
% 0.96/1.60 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.96/1.60 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 0.96/1.60 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X,
% 0.96/1.60 c_Divides_Odiv__class_Omod( X, T, Y ), Z ), Y ) }.
% 0.96/1.60 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.96/1.60 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 0.96/1.60 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, T,
% 0.96/1.60 c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 0.96/1.60 { ! class_Divides_Oring__div( X ), ! c_Divides_Odiv__class_Omod( X, T, Z )
% 0.96/1.60 = c_Divides_Odiv__class_Omod( X, Y, Z ), c_Divides_Odiv__class_Omod( X,
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( X, T ), Z ) = c_Divides_Odiv__class_Omod
% 0.96/1.60 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ), Z ) }.
% 0.96/1.60 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) = c_Divides_Odiv__class_Omod
% 0.96/1.60 ( X, c_Groups_Ouminus__class_Ouminus( X, c_Divides_Odiv__class_Omod( X, Z
% 0.96/1.60 , Y ) ), Y ) }.
% 0.96/1.60 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.96/1.60 ), ! c_Rings_Odvd__class_Odvd( X, Z, c_Divides_Odiv__class_Omod( X, T, Y
% 0.96/1.60 ) ), c_Rings_Odvd__class_Odvd( X, Z, T ) }.
% 0.96/1.60 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.96/1.60 ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X, Z
% 0.96/1.60 , c_Divides_Odiv__class_Omod( X, T, Y ) ) }.
% 0.96/1.60 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.96/1.60 ), c_Divides_Odiv__class_Omod( X, c_Divides_Odiv__class_Omod( X, T, Y )
% 0.96/1.60 , Z ) = c_Divides_Odiv__class_Omod( X, T, Z ) }.
% 0.96/1.60 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.96/1.60 ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X, Z
% 0.96/1.60 , c_Divides_Odiv__class_Omod( X, Y, T ) ) }.
% 0.96/1.60 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, T,
% 0.96/1.60 c_Divides_Odiv__class_Omod( X, Z, Y ) ), ! c_Rings_Odvd__class_Odvd( X, T
% 0.96/1.60 , Y ), c_Rings_Odvd__class_Odvd( X, T, Z ) }.
% 0.96/1.60 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.96/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Z ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.60 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.96/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.60 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y,
% 0.96/1.60 c_Groups_Oone__class_Oone( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.60 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.96/1.60 c_Groups_Oplus__class_Oplus( X, T, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) =
% 0.96/1.60 c_Divides_Odiv__class_Omod( X, T, Y ) }.
% 0.96/1.60 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.96/1.60 c_Groups_Oplus__class_Oplus( X, T, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Z ) =
% 0.96/1.60 c_Divides_Odiv__class_Omod( X, T, Z ) }.
% 0.96/1.60 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ), c_Divides_Odiv__class_Omod(
% 0.96/1.60 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, T, Z ), Y ) =
% 0.96/1.60 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ),
% 0.96/1.60 c_Polynomial_OpCons( X, T, c_Divides_Odiv__class_Omod(
% 0.96/1.60 tc_Polynomial_Opoly( X ), Z, Y ) ), c_Polynomial_Osmult( X,
% 0.96/1.60 c_Rings_Oinverse__class_Odivide( X, hAPP( c_Polynomial_Ocoeff( X,
% 0.96/1.60 c_Polynomial_OpCons( X, T, c_Divides_Odiv__class_Omod(
% 0.96/1.60 tc_Polynomial_Opoly( X ), Z, Y ) ) ), c_Polynomial_Odegree( X, Y ) ),
% 0.96/1.60 hAPP( c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) ), Y )
% 0.96/1.60 ) }.
% 0.96/1.60 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.96/1.60 , U = c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), T ), Y )
% 0.96/1.60 }.
% 0.96/1.60 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.96/1.60 , alpha42( X, Y, Z, T ) }.
% 0.96/1.60 { ! class_Fields_Ofield( X ), ! U = c_Groups_Oplus__class_Oplus(
% 0.96/1.60 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ), Z ), T ), Y ), ! alpha42( X, Y, Z, T ),
% 0.96/1.60 c_Polynomial_Opdivmod__rel( X, U, T, Z, Y ) }.
% 0.96/1.60 { ! alpha42( X, Y, Z, T ), alpha12( X, Z, T ) }.
% 0.96/1.60 { ! alpha42( X, Y, Z, T ), alpha31( X, Y, T ) }.
% 0.96/1.60 { ! alpha12( X, Z, T ), ! alpha31( X, Y, T ), alpha42( X, Y, Z, T ) }.
% 0.96/1.60 { ! alpha31( X, Y, Z ), Z = c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ), alpha43( X, Y, Z ) }.
% 0.96/1.60 { ! Z = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha31( X
% 0.96/1.60 , Y, Z ) }.
% 0.96/1.60 { ! alpha43( X, Y, Z ), alpha31( X, Y, Z ) }.
% 0.96/1.60 { ! alpha43( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.60 c_Polynomial_Odegree( X, Y ), c_Polynomial_Odegree( X, Z ) ) }.
% 0.96/1.60 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha43( X
% 0.96/1.60 , Y, Z ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, Y
% 0.96/1.60 ), c_Polynomial_Odegree( X, Z ) ), alpha43( X, Y, Z ) }.
% 0.96/1.60 { ! alpha12( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ), Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.60 { Z = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha12( X,
% 0.96/1.60 Y, Z ) }.
% 0.96/1.60 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha12( X
% 0.96/1.60 , Y, Z ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.96/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.96/1.60 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y = X,
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.96/1.60 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ), Z =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.60 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ), Y =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.60 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opdivmod__rel( X,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ) }.
% 0.96/1.60 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ), Z =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.60 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ), Y = T }
% 0.96/1.60 .
% 0.96/1.60 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ), ! Y = T, c_Polynomial_Opdivmod__rel( X, T,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ) }.
% 0.96/1.60 { ! class_Fields_Ofield( X ), c_Polynomial_Opdivmod__rel( X,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.96/1.60 { ! class_Fields_Ofield( X ), c_Polynomial_Opdivmod__rel( X, Y,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) }.
% 0.96/1.60 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.96/1.60 , c_Polynomial_Opdivmod__rel( X, c_Polynomial_Osmult( X, W, U ), T,
% 0.96/1.60 c_Polynomial_Osmult( X, W, Z ), c_Polynomial_Osmult( X, W, Y ) ) }.
% 0.96/1.60 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, U, Y )
% 0.96/1.60 , c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), T, Z ) = Y }.
% 0.96/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.60 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ), alpha13( X, Y, Z ), alpha32
% 0.96/1.60 ( X, Y, Z ) }.
% 0.96/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha13( X, Y, Z
% 0.96/1.60 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.60 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.96/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha32( X, Y, Z
% 0.96/1.60 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.60 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.96/1.60 { ! alpha32( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.60 { ! alpha32( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.60 , ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.96/1.60 ), alpha32( X, Y, Z ) }.
% 0.96/1.60 { ! alpha13( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.96/1.60 { ! alpha13( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.96/1.60 , ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.96/1.60 ), alpha13( X, Y, Z ) }.
% 0.96/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, Z,
% 0.96/1.60 Y ), c_Groups_Ozero__class_Ozero( X ) ), alpha14( X, Y, Z ), alpha33( X,
% 0.96/1.60 Y, Z ) }.
% 0.96/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha14( X, Y, Z
% 0.96/1.60 ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X
% 0.96/1.60 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha33( X, Y, Z
% 0.96/1.60 ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X
% 0.96/1.60 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.60 { ! alpha33( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.60 { ! alpha33( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.60 , ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.96/1.60 ), alpha33( X, Y, Z ) }.
% 0.96/1.60 { ! alpha14( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.96/1.60 { ! alpha14( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.96/1.60 , ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.96/1.60 ), alpha14( X, Y, Z ) }.
% 0.96/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.96/1.60 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X
% 0.96/1.60 , Y, Z ) ) }.
% 0.96/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.96/1.60 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, Z, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, c_Rings_Oinverse__class_Odivide( X, Y, Z ),
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.96/1.60 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, c_Rings_Oinverse__class_Odivide( X, Y, Z ),
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.96/1.60 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, Z, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X
% 0.96/1.60 , Y, Z ) ) }.
% 0.96/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.96/1.60 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless( X,
% 0.96/1.60 c_Rings_Oinverse__class_Odivide( X, Z, T ),
% 0.96/1.60 c_Rings_Oinverse__class_Odivide( X, Y, T ) ) }.
% 0.96/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.96/1.60 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, T,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.96/1.60 c_Rings_Oinverse__class_Odivide( X, Y, T ),
% 0.96/1.60 c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 0.96/1.60 { ! class_Fields_Ofield__inverse__zero( X ), ! T =
% 0.96/1.60 c_Rings_Oinverse__class_Odivide( X, Z, Y ), alpha34( X, Y, Z, T ) }.
% 0.96/1.60 { ! class_Fields_Ofield__inverse__zero( X ), ! T =
% 0.96/1.60 c_Rings_Oinverse__class_Odivide( X, Z, Y ), alpha15( X, Y, T ) }.
% 0.96/1.60 { ! class_Fields_Ofield__inverse__zero( X ), ! alpha34( X, Y, Z, T ), !
% 0.96/1.60 alpha15( X, Y, T ), T = c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.96/1.60 { ! alpha34( X, Y, Z, T ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP
% 0.96/1.60 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z }.
% 0.96/1.60 { ! Y = c_Groups_Ozero__class_Ozero( X ), alpha34( X, Y, Z, T ) }.
% 0.96/1.60 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, alpha34(
% 0.96/1.60 X, Y, Z, T ) }.
% 0.96/1.60 { ! alpha15( X, Y, Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.60 { Y = c_Groups_Ozero__class_Ozero( X ), alpha15( X, Y, Z ) }.
% 0.96/1.60 { ! Z = c_Groups_Ozero__class_Ozero( X ), alpha15( X, Y, Z ) }.
% 0.96/1.60 { ! class_Fields_Ofield__inverse__zero( X ), !
% 0.96/1.60 c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y, alpha35( X, Y, Z, T ) }.
% 0.96/1.60 { ! class_Fields_Ofield__inverse__zero( X ), !
% 0.96/1.60 c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y, alpha16( X, Y, Z ) }.
% 0.96/1.60 { ! class_Fields_Ofield__inverse__zero( X ), ! alpha35( X, Y, Z, T ), !
% 0.96/1.60 alpha16( X, Y, Z ), c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y }.
% 0.96/1.60 { ! alpha35( X, Y, Z, T ), Z = c_Groups_Ozero__class_Ozero( X ), T = hAPP(
% 0.96/1.60 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 0.96/1.60 { ! Z = c_Groups_Ozero__class_Ozero( X ), alpha35( X, Y, Z, T ) }.
% 0.96/1.60 { ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), alpha35(
% 0.96/1.60 X, Y, Z, T ) }.
% 0.96/1.60 { ! alpha16( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.60 { Z = c_Groups_Ozero__class_Ozero( X ), alpha16( X, Y, Z ) }.
% 0.96/1.60 { ! Y = c_Groups_Ozero__class_Ozero( X ), alpha16( X, Y, Z ) }.
% 0.96/1.60 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.96/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.96/1.60 c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 0.96/1.60 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.96/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) =
% 0.96/1.60 c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 0.96/1.60 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), ! c_Rings_Oinverse__class_Odivide( X, U
% 0.96/1.60 , Y ) = c_Rings_Oinverse__class_Odivide( X, T, Z ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), U ), Z ) = hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) }.
% 0.96/1.60 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), U ), Z ) = hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ),
% 0.96/1.60 c_Rings_Oinverse__class_Odivide( X, U, Y ) =
% 0.96/1.60 c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 0.96/1.60 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.60 , ! T = c_Rings_Oinverse__class_Odivide( X, Z, Y ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z }.
% 0.96/1.60 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.60 , ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, T =
% 0.96/1.60 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.96/1.60 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.60 , ! c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z, T = hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 0.96/1.60 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.60 , ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.96/1.60 c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z }.
% 0.96/1.60 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.60 , ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.96/1.60 c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z }.
% 0.96/1.60 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.60 , ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, T =
% 0.96/1.60 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.96/1.60 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.60 , ! c_Rings_Oinverse__class_Odivide( X, Z, Y ) =
% 0.96/1.60 c_Groups_Oone__class_Oone( X ), Z = Y }.
% 0.96/1.60 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.60 , ! Z = Y, c_Rings_Oinverse__class_Odivide( X, Z, Y ) =
% 0.96/1.60 c_Groups_Oone__class_Oone( X ) }.
% 0.96/1.60 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.60 , c_Rings_Oinverse__class_Odivide( X, Y, Y ) = c_Groups_Oone__class_Oone
% 0.96/1.60 ( X ) }.
% 0.96/1.60 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Y =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X, Y,
% 0.96/1.60 Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.60 { ! class_Rings_Odivision__ring__inverse__zero( X ), Y =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X, Y,
% 0.96/1.60 Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.96/1.60 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.60 , c_Rings_Oinverse__class_Odivide( X, c_Groups_Ouminus__class_Ouminus( X
% 0.96/1.60 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 0.96/1.60 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.96/1.60 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.60 , c_Groups_Ouminus__class_Ouminus( X, c_Rings_Oinverse__class_Odivide( X
% 0.96/1.60 , Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X, Z,
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.96/1.60 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP(
% 0.96/1.60 hAPP( c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Odivide
% 0.96/1.60 ( X, T, Y ) ), Z ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 0.96/1.60 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.60 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.96/1.60 { ! class_Fields_Ofield__inverse__zero( X ),
% 0.96/1.60 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oone__class_Oone( X ), hAPP
% 0.96/1.60 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.96/1.60 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.96/1.60 c_Groups_Oone__class_Oone( X ), Z ) ), Y ) }.
% 0.96/1.60 { ! class_Fields_Ofield__inverse__zero( X ),
% 0.96/1.60 c_Rings_Oinverse__class_Oinverse( X, c_Rings_Oinverse__class_Odivide( X,
% 0.96/1.60 Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X, Y, Z ) }.
% 0.96/1.60 { ! class_Fields_Ofield__inverse__zero( X ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Odivide( X, U
% 0.96/1.60 , T ) ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 0.96/1.60 c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.96/1.60 { ! class_Fields_Ofield__inverse__zero( X ),
% 0.96/1.60 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ouminus__class_Ouminus( X, Z
% 0.96/1.60 ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 0.96/1.60 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.96/1.60 { ! class_Fields_Ofield__inverse__zero( X ),
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( X, c_Rings_Oinverse__class_Odivide( X, Z
% 0.96/1.60 , Y ) ) = c_Rings_Oinverse__class_Odivide( X, Z,
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.96/1.60 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.96/1.60 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 0.96/1.60 c_Groups_Ominus__class_Ominus( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.96/1.60 Y ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.96/1.60 { ! class_RealVector_Oreal__normed__field( X ),
% 0.96/1.60 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ominus__class_Ominus( X, T,
% 0.96/1.60 Z ), Y ) = c_Groups_Ominus__class_Ominus( X,
% 0.96/1.60 c_Rings_Oinverse__class_Odivide( X, T, Y ),
% 0.96/1.60 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.96/1.60 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X, Y
% 0.96/1.60 , c_Groups_Oone__class_Oone( X ) ) = Y }.
% 0.96/1.60 { ! class_Rings_Odivision__ring( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.96/1.60 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 0.96/1.60 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ouminus__class_Ouminus( X, Z
% 0.96/1.60 ), Y ) }.
% 0.96/1.60 { ! class_RealVector_Oreal__normed__field( X ),
% 0.96/1.60 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ouminus__class_Ouminus( X, Z
% 0.96/1.60 ), Y ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.96/1.60 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.96/1.60 { ! class_Fields_Ofield__inverse__zero( X ), hAPP( hAPP(
% 0.96/1.60 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Odivide( X, T
% 0.96/1.60 , Z ) ), Y ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 0.96/1.60 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.96/1.60 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.96/1.60 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.96/1.60 , ! c_Polynomial_Opdivmod__rel( X, U, T, V0, W ), Z = V0 }.
% 0.96/1.60 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.96/1.60 , ! c_Polynomial_Opdivmod__rel( X, U, T, V0, W ), Y = W }.
% 0.96/1.60 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, U, Y )
% 0.96/1.60 , ! c_Polynomial_Opdivmod__rel( X, T, Z, V0, W ), Y = W }.
% 0.96/1.60 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, Y, U )
% 0.96/1.60 , ! c_Polynomial_Opdivmod__rel( X, T, Z, W, V0 ), Y = W }.
% 0.96/1.60 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.96/1.60 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.96/1.60 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ),
% 0.96/1.60 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.96/1.60 { ! class_RealVector_Oreal__normed__field( X ),
% 0.96/1.60 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, T, Z
% 0.96/1.60 ), Y ) = c_Groups_Oplus__class_Oplus( X, c_Rings_Oinverse__class_Odivide
% 0.96/1.60 ( X, T, Y ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.96/1.60 { ! class_Rings_Odivision__ring( X ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), T ), c_Rings_Oinverse__class_Odivide
% 0.96/1.60 ( X, Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 0.96/1.60 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.60 }.
% 0.96/1.60 { ! class_RealVector_Oreal__normed__field( X ),
% 0.96/1.60 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.96/1.60 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.60 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 0.96/1.60 c_Rings_Oinverse__class_Odivide( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.60 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.60 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X, Z
% 0.96/1.60 , Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 0.96/1.60 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.96/1.60 { ! class_Fields_Ofield( X ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) =
% 0.96/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 0.96/1.60 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.96/1.60 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Oinverse( X,
% 0.96/1.60 Y ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oone__class_Oone( X )
% 0.96/1.60 , Y ) }.
% 0.96/1.60 { ! class_Fields_Ofield( X ), c_Rings_Oinverse__class_Oinverse( X, Y ) =
% 0.96/1.60 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oone__class_Oone( X ), Y ) }
% 0.96/1.60 .
% 0.96/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.96/1.60 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, T,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless( X,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.96/1.60 Z ), c_Rings_Oinverse__class_Odivide( X, T, Y ) ) }.
% 0.96/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.96/1.60 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 0.96/1.60 , c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.96/1.60 Y ), c_Rings_Oinverse__class_Odivide( X, T, Z ) ) }.
% 0.96/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.96/1.60 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ) }.
% 0.96/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.96/1.60 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.96/1.60 Y ), Z ) }.
% 0.96/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.96/1.60 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, T, c_Rings_Oinverse__class_Odivide( X, Z, Y ) ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, Z, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.96/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.96/1.60 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.96/1.60 Z, Y ) ) }.
% 0.96/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.96/1.60 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.96/1.60 Z, Y ) ) }.
% 0.96/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.96/1.60 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.96/1.60 Y ), Z ) }.
% 0.96/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.96/1.60 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.96/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.96/1.60 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.96/1.60 Y ), Z ) }.
% 0.96/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.96/1.60 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, T, c_Rings_Oinverse__class_Odivide( X, Z, Y ) ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.96/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.96/1.60 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.96/1.60 Z, Y ) ) }.
% 0.96/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.96/1.60 Z ), Y ), alpha36( X, Y, Z, T ) }.
% 0.96/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.96/1.60 Z ), Y ), alpha44( X, Y, Z, T ) }.
% 0.96/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha36( X, Y, Z
% 0.96/1.60 , T ), ! alpha44( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.96/1.60 c_Rings_Oinverse__class_Odivide( X, T, Z ), Y ) }.
% 0.96/1.60 { ! alpha44( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), Z ), alpha48( X, Y, Z, T ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.96/1.60 , alpha44( X, Y, Z, T ) }.
% 0.96/1.60 { ! alpha48( X, Y, Z, T ), alpha44( X, Y, Z, T ) }.
% 0.96/1.60 { ! alpha48( X, Y, Z, T ), alpha51( X, Y, Z, T ) }.
% 0.96/1.60 { ! alpha48( X, Y, Z, T ), alpha17( X, Y, Z ) }.
% 0.96/1.60 { ! alpha51( X, Y, Z, T ), ! alpha17( X, Y, Z ), alpha48( X, Y, Z, T ) }.
% 0.96/1.60 { ! alpha51( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.96/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ) }.
% 0.96/1.60 { c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) ),
% 0.96/1.60 alpha51( X, Y, Z, T ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ), alpha51( X, Y, Z, T )
% 0.96/1.60 }.
% 0.96/1.60 { ! alpha36( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless( X,
% 0.96/1.60 T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.96/1.60 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.96/1.60 alpha36( X, Y, Z, T ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha36( X, Y, Z, T ) }.
% 0.96/1.60 { ! alpha17( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.60 , alpha17( X, Y, Z ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.96/1.60 , alpha17( X, Y, Z ) }.
% 0.96/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.96/1.60 Z, Y ) ), alpha37( X, Y, Z, T ) }.
% 0.96/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.96/1.60 Z, Y ) ), alpha45( X, Y, Z, T ) }.
% 0.96/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha37( X, Y, Z
% 0.96/1.60 , T ), ! alpha45( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 0.96/1.60 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.96/1.60 { ! alpha45( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), Y ), alpha49( X, Y, Z, T ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.96/1.60 , alpha45( X, Y, Z, T ) }.
% 0.96/1.60 { ! alpha49( X, Y, Z, T ), alpha45( X, Y, Z, T ) }.
% 0.96/1.60 { ! alpha49( X, Y, Z, T ), alpha52( X, Y, Z, T ) }.
% 0.96/1.60 { ! alpha49( X, Y, Z, T ), alpha18( X, Y, T ) }.
% 0.96/1.60 { ! alpha52( X, Y, Z, T ), ! alpha18( X, Y, T ), alpha49( X, Y, Z, T ) }.
% 0.96/1.60 { ! alpha52( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Z,
% 0.96/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.96/1.60 { c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.96/1.60 alpha52( X, Y, Z, T ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( X, Z, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha52( X, Y, Z, T ) }.
% 0.96/1.60 { ! alpha37( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless( X,
% 0.96/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.96/1.60 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.96/1.60 alpha37( X, Y, Z, T ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ), alpha37( X, Y, Z, T )
% 0.96/1.60 }.
% 0.96/1.60 { ! alpha18( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Z,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.60 , alpha18( X, Y, Z ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.60 , alpha18( X, Y, Z ) }.
% 0.96/1.60 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.60 c_Rings_Oinverse__class_Odivide( X, U, Y ),
% 0.96/1.60 c_Rings_Oinverse__class_Odivide( X, T, Z ) ) =
% 0.96/1.60 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, hAPP
% 0.96/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.96/1.60 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.60 c_Groups_Oplus__class_Oplus( X, c_Rings_Oinverse__class_Odivide( X, T, Y
% 0.96/1.60 ), Z ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus
% 0.96/1.60 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) }
% 0.96/1.60 .
% 0.96/1.60 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.60 c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ) =
% 0.96/1.60 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.96/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) }.
% 0.96/1.60 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.60 c_Groups_Oplus__class_Oplus( X, T, c_Rings_Oinverse__class_Odivide( X, Z
% 0.96/1.60 , Y ) ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus
% 0.96/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), Z ), Y ) }
% 0.96/1.60 .
% 0.96/1.60 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, T,
% 0.96/1.60 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 0.96/1.60 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.96/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Y ) }.
% 0.96/1.60 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ominus__class_Ominus( X,
% 0.96/1.60 c_Rings_Oinverse__class_Odivide( X, U, Y ),
% 0.96/1.60 c_Rings_Oinverse__class_Odivide( X, T, Z ) ) =
% 0.96/1.60 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ominus__class_Ominus( X,
% 0.96/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.96/1.60 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.60 c_Groups_Ominus__class_Ominus( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.96/1.60 Y ), Z ) = c_Rings_Oinverse__class_Odivide( X,
% 0.96/1.60 c_Groups_Ominus__class_Ominus( X, T, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) }.
% 0.96/1.60 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.60 c_Groups_Ominus__class_Ominus( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.96/1.60 Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X,
% 0.96/1.60 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ), Z ), Y ) }.
% 0.96/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.96/1.60 X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z,
% 0.96/1.60 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.96/1.60 ), c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.96/1.60 c_Groups_Oone__class_Oone( X ) ) ) ) }.
% 0.96/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.96/1.60 X, Z, Y ), c_Orderings_Oord__class_Oless( X,
% 0.96/1.60 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.96/1.60 ), c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.96/1.60 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.96/1.60 { ! class_RealVector_Oreal__field( X ), c_Rings_Oinverse__class_Odivide( X
% 0.96/1.60 , c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), W ), U ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) =
% 0.96/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.60 ( X ), W ), c_Rings_Oinverse__class_Odivide( X,
% 0.96/1.60 c_Groups_Ominus__class_Ominus( X, U, Z ), Y ) ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.96/1.60 c_Groups_Ominus__class_Ominus( X, W, T ), Y ) ), Z ) ) }.
% 0.96/1.60 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.60 , c_Rings_Oinverse__class_Oinverse( X, Y ) =
% 0.96/1.60 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oone__class_Oone( X ), Y ) }
% 0.96/1.60 .
% 0.96/1.60 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.96/1.60 , ! c_Polynomial_Opdivmod__rel( X, Z, V1, V0, W ),
% 0.96/1.60 c_Polynomial_Opdivmod__rel( X, U, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), V1 ), V0
% 0.96/1.60 , c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), W ), Y )
% 0.96/1.60 ) }.
% 0.96/1.60 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.96/1.60 , T = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), ! V0 =
% 0.96/1.60 c_Rings_Oinverse__class_Odivide( X, hAPP( c_Polynomial_Ocoeff( X,
% 0.96/1.60 c_Polynomial_OpCons( X, W, Y ) ), c_Polynomial_Odegree( X, T ) ), hAPP(
% 0.96/1.60 c_Polynomial_Ocoeff( X, T ), c_Polynomial_Odegree( X, T ) ) ),
% 0.96/1.60 c_Polynomial_Opdivmod__rel( X, c_Polynomial_OpCons( X, W, U ), T,
% 0.96/1.60 c_Polynomial_OpCons( X, V0, Z ), c_Groups_Ominus__class_Ominus(
% 0.96/1.60 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, W, Y ),
% 0.96/1.60 c_Polynomial_Osmult( X, V0, T ) ) ) }.
% 0.96/1.60 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 0.96/1.60 c_Polynomial_Opdivmod__rel( X, W, U, T, Z ), c_Polynomial_Opdivmod__rel(
% 0.96/1.60 X, W, c_Polynomial_Osmult( X, Y, U ), c_Polynomial_Osmult( X,
% 0.96/1.60 c_Rings_Oinverse__class_Oinverse( X, Y ), T ), Z ) }.
% 0.96/1.60 { ! class_RealVector_Oreal__normed__field( X ), Y =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.60 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ominus__class_Ominus( X,
% 0.96/1.60 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.96/1.60 c_Rings_Oinverse__class_Oinverse( X, Z ) ), T ) =
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 0.96/1.60 Y ) ), c_Rings_Oinverse__class_Odivide( X, c_Groups_Ominus__class_Ominus
% 0.96/1.60 ( X, Y, Z ), T ) ) ), c_Rings_Oinverse__class_Oinverse( X, Z ) ) ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.96/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.96/1.60 ( c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.96/1.60 , c_Groups_Ozero__class_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.96/1.60 c_Polynomial_Odegree( X, Y ) ) ), c_Polynomial_Opos__poly( X, Y ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.96/1.60 c_Polynomial_OpCons( X, Z, Y ) ), c_Polynomial_Opos__poly( X, Y ),
% 0.96/1.60 alpha19( X, Y, Z ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.96/1.60 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__idom( X ), ! alpha19( X, Y, Z ),
% 0.96/1.60 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ) }.
% 0.96/1.60 { ! alpha19( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.60 { ! alpha19( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.96/1.60 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.96/1.60 alpha19( X, Y, Z ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.96/1.60 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X,
% 0.96/1.60 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.96/1.60 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X, hAPP( hAPP
% 0.96/1.60 ( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) }
% 0.96/1.60 .
% 0.96/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless(
% 0.96/1.60 tc_Polynomial_Opoly( X ), Z, Y ), c_Polynomial_Opos__poly( X,
% 0.96/1.60 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.96/1.60 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opos__poly( X, Y ),
% 0.96/1.60 c_Polynomial_Opos__poly( X, c_Groups_Ouminus__class_Ouminus(
% 0.96/1.60 tc_Polynomial_Opoly( X ), Y ) ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.60 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.96/1.60 c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.60 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ), Y ) = hAPP( hAPP(
% 0.96/1.60 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ),
% 0.96/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.60 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Z,
% 0.96/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), c_Groups_Oplus__class_Oplus
% 0.96/1.60 ( tc_Int_Oint, c_Groups_Oabs__class_Oabs( tc_Int_Oint,
% 0.96/1.60 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, Z ) ),
% 0.96/1.60 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ), X ) ) ) }.
% 0.96/1.60 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.60 }.
% 0.96/1.60 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X, Y,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.60 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Int_Oint ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.96/1.60 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.96/1.60 ( tc_Int_Oint, Y ), c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.96/1.60 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) }.
% 0.96/1.60 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y,
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.96/1.60 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.96/1.60 ( tc_Int_Oint, Y ), X ) }.
% 0.96/1.60 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X, Y,
% 0.96/1.60 c_Groups_Oone__class_Oone( X ) ) = Y }.
% 0.96/1.60 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.96/1.60 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, X ) =
% 0.96/1.60 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.96/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ),
% 0.96/1.60 c_Groups_Oabs__class_Oabs( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.96/1.60 tc_Int_Oint, X, Y ) ) = c_Divides_Odiv__class_Odiv( tc_Int_Oint,
% 0.96/1.60 c_Groups_Oabs__class_Oabs( tc_Int_Oint, X ), c_Groups_Oabs__class_Oabs(
% 0.96/1.60 tc_Int_Oint, Y ) ) }.
% 0.96/1.60 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.96/1.60 ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), ! c_Rings_Odvd__class_Odvd( X
% 0.96/1.60 , c_Divides_Odiv__class_Odiv( X, Y, Z ), c_Divides_Odiv__class_Odiv( X, T
% 0.96/1.60 , Z ) ), c_Rings_Odvd__class_Odvd( X, Y, T ) }.
% 0.96/1.60 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.96/1.60 ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), ! c_Rings_Odvd__class_Odvd( X
% 0.96/1.60 , Y, T ), c_Rings_Odvd__class_Odvd( X, c_Divides_Odiv__class_Odiv( X, Y,
% 0.96/1.60 Z ), c_Divides_Odiv__class_Odiv( X, T, Z ) ) }.
% 0.96/1.60 { ! class_Fields_Olinordered__field( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.60 X ), c_Groups_Oabs__class_Oabs( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 0.96/1.60 ) ) = c_Rings_Oinverse__class_Oinverse( X, c_Groups_Oabs__class_Oabs( X
% 0.96/1.60 , Y ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X, hAPP
% 0.96/1.60 ( hAPP( c_Power_Opower__class_Opower( X ),
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) ) =
% 0.96/1.60 c_Groups_Oabs__class_Oabs( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.96/1.60 ), Z ), Y ) ) }.
% 0.96/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 0.96/1.60 c_Rings_Odvd__class_Odvd( tc_Int_Oint, X, Y ), c_Groups_Oabs__class_Oabs
% 0.96/1.60 ( tc_Int_Oint, Y ) = c_Groups_Oabs__class_Oabs( tc_Int_Oint, X ) }.
% 0.96/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ),
% 0.96/1.60 c_Groups_Oabs__class_Oabs( X, c_Rings_Oinverse__class_Oinverse( X, Y ) )
% 0.96/1.60 = c_Rings_Oinverse__class_Oinverse( X, c_Groups_Oabs__class_Oabs( X, Y )
% 0.96/1.60 ) }.
% 0.96/1.60 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.96/1.60 c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Z, Y ) )
% 0.96/1.60 = c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Y, Z )
% 0.96/1.60 ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Oabs__class_Oabs( X, Z )
% 0.96/1.60 = c_Groups_Oabs__class_Oabs( X, Y ), c_Rings_Odvd__class_Odvd( X, Z, Y )
% 0.96/1.60 }.
% 0.96/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.96/1.60 c_Groups_Oabs__class_Oabs( X, Z ), Y ), c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.96/1.60 ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.96/1.60 ), c_Rings_Odvd__class_Odvd( X, c_Groups_Oabs__class_Oabs( X, Z ), Y ) }
% 0.96/1.60 .
% 0.96/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.96/1.60 c_Groups_Oabs__class_Oabs( X, Y ) ), c_Rings_Odvd__class_Odvd( X, Z, Y )
% 0.96/1.60 }.
% 0.96/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.96/1.60 ), c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oabs__class_Oabs( X, Y ) ) }
% 0.96/1.60 .
% 0.96/1.60 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.96/1.60 c_Groups_Oabs__class_Oabs( X, c_Groups_Oabs__class_Oabs( X, Y ) ) =
% 0.96/1.60 c_Groups_Oabs__class_Oabs( X, Y ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X, hAPP
% 0.96/1.60 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.96/1.60 c_Power_Opower__class_Opower( X ), c_Groups_Oabs__class_Oabs( X, Z ) ), Y
% 0.96/1.60 ) }.
% 0.96/1.60 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.96/1.60 c_Groups_Oabs__class_Oabs( X, c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 0.96/1.60 c_Groups_Oabs__class_Oabs( X, Y ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X,
% 0.96/1.60 c_Groups_Oone__class_Oone( X ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.96/1.60 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.96/1.61 c_Groups_Oabs__class_Oabs( X, c_Groups_Oplus__class_Oplus( X,
% 0.96/1.61 c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ) )
% 0.96/1.61 = c_Groups_Oplus__class_Oplus( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.96/1.61 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X, hAPP
% 0.96/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 0.96/1.61 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__idom( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Y ) ),
% 0.96/1.61 c_Groups_Oabs__class_Oabs( X, Y ) ) = hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.96/1.61 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.96/1.61 c_Groups_Oabs__class_Oabs( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.61 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.96/1.61 c_Groups_Oabs__class_Oabs( X, Y ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.61 { ! class_Groups_Oordered__ab__group__add__abs( X ), ! Y =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oabs__class_Oabs( X, Y ) =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.61 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.96/1.61 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ),
% 0.96/1.61 c_Divides_Odiv__class_Odiv( X, Y, Z ) ), T ) = c_Divides_Odiv__class_Odiv
% 0.96/1.61 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.96/1.61 ( c_Power_Opower__class_Opower( X ), Z ), T ) ) }.
% 0.96/1.61 { ! class_Divides_Oring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y ),
% 0.96/1.61 c_Divides_Odiv__class_Odiv( X, c_Groups_Ouminus__class_Ouminus( X, Y ), Z
% 0.96/1.61 ) = c_Groups_Ouminus__class_Ouminus( X, c_Divides_Odiv__class_Odiv( X, Y
% 0.96/1.61 , Z ) ) }.
% 0.96/1.61 { ! class_Divides_Oring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y ),
% 0.96/1.61 c_Divides_Odiv__class_Odiv( X, Y, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.96/1.61 ) = c_Groups_Ouminus__class_Ouminus( X, c_Divides_Odiv__class_Odiv( X, Y
% 0.96/1.61 , Z ) ) }.
% 0.96/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X,
% 0.96/1.61 c_Divides_Odiv__class_Omod( X, Z, Y ), Y ) = c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( X ) }.
% 0.96/1.61 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.96/1.61 ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Divides_Odiv__class_Odiv( X
% 0.96/1.61 , c_Groups_Oplus__class_Oplus( X, Y, T ), Z ) =
% 0.96/1.61 c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Odiv( X, Y, Z ),
% 0.96/1.61 c_Divides_Odiv__class_Odiv( X, T, Z ) ) }.
% 0.96/1.61 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.96/1.61 ), ! c_Rings_Odvd__class_Odvd( X, U, T ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Odiv( X, Y, Z )
% 0.96/1.61 ), c_Divides_Odiv__class_Odiv( X, T, U ) ) = c_Divides_Odiv__class_Odiv
% 0.96/1.61 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.96/1.61 ( c_Groups_Otimes__class_Otimes( X ), Z ), U ) ) }.
% 0.96/1.61 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.96/1.61 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.96/1.61 c_Divides_Odiv__class_Odiv( X, Y, Z ) ), T ) = c_Divides_Odiv__class_Odiv
% 0.96/1.61 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), Z ) }.
% 0.96/1.61 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.96/1.61 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.96/1.61 c_Divides_Odiv__class_Odiv( X, Y, Z ) ), Z ) = Y }.
% 0.96/1.61 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.96/1.61 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ),
% 0.96/1.61 c_Divides_Odiv__class_Odiv( X, Y, Z ) ) = c_Divides_Odiv__class_Odiv( X,
% 0.96/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.96/1.61 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.96/1.61 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 0.96/1.61 c_Divides_Odiv__class_Odiv( X, Y, Z ) ) = Y }.
% 0.96/1.61 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.61 , c_Divides_Odiv__class_Odiv( X, Y, Y ) = c_Groups_Oone__class_Oone( X )
% 0.96/1.61 }.
% 0.96/1.61 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.61 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) =
% 0.96/1.61 c_Divides_Odiv__class_Odiv( X, T, Z ) }.
% 0.96/1.61 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.61 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.96/1.61 c_Divides_Odiv__class_Odiv( X, T, Z ) }.
% 0.96/1.61 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.61 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) = Z }.
% 0.96/1.61 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.61 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = Z }.
% 0.96/1.61 { ! class_Divides_Osemiring__div( X ), ! T = c_Groups_Ozero__class_Ozero( X
% 0.96/1.61 ), c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.61 { ! class_Divides_Osemiring__div( X ), T = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.61 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.96/1.61 c_Divides_Odiv__class_Odiv( X, Z, Y ) }.
% 0.96/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.96/1.61 tc_Int_Oint ) ), c_Groups_Oabs__class_Oabs( tc_Int_Oint, X ) =
% 0.96/1.61 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.96/1.61 { ! c_Groups_Oabs__class_Oabs( tc_Int_Oint, X ) = c_Groups_Oone__class_Oone
% 0.96/1.61 ( tc_Int_Oint ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, X,
% 0.96/1.61 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.96/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ),
% 0.96/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) = X }.
% 0.96/1.61 { ! c_Groups_Oabs__class_Oabs( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) =
% 0.96/1.61 c_Groups_Oone__class_Oone( tc_Int_Oint ), c_Groups_Oabs__class_Oabs(
% 0.96/1.61 tc_Int_Oint, X ) = c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.96/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ),
% 0.96/1.61 c_Groups_Oabs__class_Oabs( X, c_Rings_Oinverse__class_Odivide( X, Z, Y )
% 0.96/1.61 ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oabs__class_Oabs( X, Z
% 0.96/1.61 ), c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.96/1.61 { ! class_Fields_Olinordered__field( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.61 X ), c_Groups_Oabs__class_Oabs( X, c_Rings_Oinverse__class_Odivide( X, Z
% 0.96/1.61 , Y ) ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oabs__class_Oabs(
% 0.96/1.61 X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.96/1.61 , c_Groups_Oabs__class_Oabs( X, Z ), Y ), c_Orderings_Oord__class_Oless(
% 0.96/1.61 X, Z, Y ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.96/1.61 , c_Groups_Oabs__class_Oabs( X, Z ), Y ), c_Orderings_Oord__class_Oless(
% 0.96/1.61 X, c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.96/1.61 , Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.96/1.61 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Oabs__class_Oabs( X, Z ), Y )
% 0.96/1.61 }.
% 0.96/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.96/1.61 , c_Groups_Oabs__class_Oabs( X, Z ), Y ), ! c_Orderings_Oord__class_Oless
% 0.96/1.61 ( X, c_Groups_Oabs__class_Oabs( X, U ), T ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 0.96/1.61 c_Groups_Oabs__class_Oabs( X, U ) ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.96/1.61 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.96/1.61 c_Groups_Oabs__class_Oabs( X, Y ) = Y }.
% 0.96/1.61 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.61 c_Groups_Oabs__class_Oabs( X, Y ) ), ! Y = c_Groups_Ozero__class_Ozero( X
% 0.96/1.61 ) }.
% 0.96/1.61 { ! class_Groups_Oordered__ab__group__add__abs( X ), Y =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.96/1.61 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Oabs__class_Oabs( X, Y ),
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.96/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.96/1.61 tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Int_Oint ), Y ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.96/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ),
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.96/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ),
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.96/1.61 tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.96/1.61 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Divides_Odiv__class_Omod(
% 0.96/1.61 tc_Int_Oint, Y, X ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.96/1.61 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Int_Oint ) ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.96/1.61 { c_Divides_Odiv__class_Omod( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Int_Oint ) ) = X }.
% 0.96/1.61 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.96/1.61 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.96/1.61 tc_Int_Oint, Z, X ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 0.96/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.96/1.61 tc_Int_Oint, c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, X ),
% 0.96/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) ) }.
% 0.96/1.61 { ! class_Groups_Oabs__if( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Oabs__class_Oabs( X, Y ) =
% 0.96/1.61 c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.96/1.61 { ! class_Groups_Oabs__if( X ), c_Orderings_Oord__class_Oless( X, Y,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Oabs__class_Oabs( X, Y ) = Y
% 0.96/1.61 }.
% 0.96/1.61 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.96/1.61 c_Groups_Oabs__class_Oabs( X, Y ) = c_Groups_Ouminus__class_Ouminus( X, Y
% 0.96/1.61 ) }.
% 0.96/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.96/1.61 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oabs__class_Oabs( X, Z ), Y
% 0.96/1.61 ) = c_Groups_Oabs__class_Oabs( X, c_Rings_Oinverse__class_Odivide( X, Z
% 0.96/1.61 , Y ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.96/1.61 c_Groups_Oone__class_Oone( tc_Int_Oint ), Y ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.96/1.61 tc_Int_Oint, X, Y ), X ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Int_Oint ), X ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Z, hAPP(
% 0.96/1.61 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) =
% 0.96/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.96/1.61 tc_Int_Oint, Z, Y ), X ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oabs__class_Oabs(
% 0.96/1.61 tc_Int_Oint, X ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.96/1.61 { ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oabs__class_Oabs(
% 0.96/1.61 tc_Int_Oint, X ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Groups_Oabs__class_Oabs(
% 0.96/1.61 tc_Int_Oint, X ) = c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) }.
% 0.96/1.61 { c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Groups_Oabs__class_Oabs(
% 0.96/1.61 tc_Int_Oint, X ) = X }.
% 0.96/1.61 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.96/1.61 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.96/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Z, Y ) ), Y ),
% 0.96/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, Y ) ), X ) =
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) }.
% 0.96/1.61 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.96/1.61 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.96/1.61 ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, Z ) ),
% 0.96/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, Z ) ), X ) =
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) }.
% 0.96/1.61 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ) =
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.96/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 0.96/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.96/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) ) }.
% 0.96/1.61 { Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 0.96/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 0.96/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) }.
% 0.96/1.61 { c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.96/1.61 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), c_Divides_Odiv__class_Odiv
% 0.96/1.61 ( tc_Int_Oint, Y, X ) ), X ) ) }.
% 0.96/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ),
% 0.96/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) =
% 0.96/1.61 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Divides_Odiv__class_Omod
% 0.96/1.61 ( tc_Int_Oint, X, Y ) ) }.
% 0.96/1.61 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.61 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, T, hAPP
% 0.96/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) =
% 0.96/1.61 c_Groups_Oplus__class_Oplus( X, Z, c_Divides_Odiv__class_Odiv( X, T, Y )
% 0.96/1.61 ) }.
% 0.96/1.61 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.61 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, T, hAPP
% 0.96/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) =
% 0.96/1.61 c_Groups_Oplus__class_Oplus( X, Z, c_Divides_Odiv__class_Odiv( X, T, Y )
% 0.96/1.61 ) }.
% 0.96/1.61 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.61 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, Y, Z ),
% 0.96/1.61 Y ) = c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Odiv( X, Z, Y
% 0.96/1.61 ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.96/1.61 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.61 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, Z, Y ),
% 0.96/1.61 Y ) = c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Odiv( X, Z, Y
% 0.96/1.61 ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.96/1.61 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.61 , ! c_Rings_Odvd__class_Odvd( X, Y, Z ), ! c_Divides_Odiv__class_Odiv( X
% 0.96/1.61 , Z, Y ) = T, Z = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y
% 0.96/1.61 ) }.
% 0.96/1.61 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.61 , ! c_Rings_Odvd__class_Odvd( X, Y, Z ), ! Z = hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ), c_Divides_Odiv__class_Odiv
% 0.96/1.61 ( X, Z, Y ) = T }.
% 0.96/1.61 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.61 , Z = c_Groups_Ozero__class_Ozero( X ), ! c_Rings_Odvd__class_Odvd( X, Y
% 0.96/1.61 , T ), ! c_Rings_Odvd__class_Odvd( X, Z, U ), !
% 0.96/1.61 c_Divides_Odiv__class_Odiv( X, T, Y ) = c_Divides_Odiv__class_Odiv( X, U
% 0.96/1.61 , Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ) = hAPP(
% 0.96/1.61 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), U ) }.
% 0.96/1.61 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.61 , Z = c_Groups_Ozero__class_Ozero( X ), ! c_Rings_Odvd__class_Odvd( X, Y
% 0.96/1.61 , T ), ! c_Rings_Odvd__class_Odvd( X, Z, U ), ! hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ) = hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), U ), c_Divides_Odiv__class_Odiv
% 0.96/1.61 ( X, T, Y ) = c_Divides_Odiv__class_Odiv( X, U, Z ) }.
% 0.96/1.61 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.61 c_Divides_Odiv__class_Omod( X, Z, Y ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Odiv( X, Z, Y )
% 0.96/1.61 ), Y ) ) = Z }.
% 0.96/1.61 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 0.96/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 0.96/1.61 c_Divides_Odiv__class_Odiv( X, Y, Z ) ), c_Divides_Odiv__class_Omod( X, Y
% 0.96/1.61 , Z ) ) = Y }.
% 0.96/1.61 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 0.96/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Odiv( X
% 0.96/1.61 , Z, Y ) ), Y ), c_Divides_Odiv__class_Omod( X, Z, Y ) ) = Z }.
% 0.96/1.61 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.61 ( X ), T ), c_Divides_Odiv__class_Odiv( X, Z, T ) ),
% 0.96/1.61 c_Divides_Odiv__class_Omod( X, Z, T ) ), Y ) =
% 0.96/1.61 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 0.96/1.61 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.61 ( X ), c_Divides_Odiv__class_Odiv( X, T, Z ) ), Z ),
% 0.96/1.61 c_Divides_Odiv__class_Omod( X, T, Z ) ), Y ) =
% 0.96/1.61 c_Groups_Oplus__class_Oplus( X, T, Y ) }.
% 0.96/1.61 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.96/1.61 c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ), X ),
% 0.96/1.61 c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) = c_Groups_Oone__class_Oone(
% 0.96/1.61 tc_Int_Oint ) }.
% 0.96/1.61 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.96/1.61 c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) = c_Groups_Oone__class_Oone(
% 0.96/1.61 tc_Int_Oint ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ), X ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Int_Oint ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint )
% 0.96/1.61 , c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) ), X ) ), ! Y =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.61 { Y = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Int_Oint ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ),
% 0.96/1.61 c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) ), X ) ) }.
% 0.96/1.61 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Int_Oint ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ),
% 0.96/1.61 c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) ), X ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Int_Oint ), X ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, hAPP(
% 0.96/1.61 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) =
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ),
% 0.96/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.96/1.61 tc_Int_Oint, Z, Y ), X ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, Y
% 0.96/1.61 ) ) }.
% 0.96/1.61 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.96/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.96/1.61 tc_Int_Oint, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) =
% 0.96/1.61 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Divides_Odiv__class_Odiv
% 0.96/1.61 ( tc_Int_Oint, Y, X ) ) }.
% 0.96/1.61 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.96/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.96/1.61 tc_Int_Oint, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) =
% 0.96/1.61 c_Groups_Ominus__class_Ominus( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Divides_Odiv__class_Odiv
% 0.96/1.61 ( tc_Int_Oint, Y, X ) ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.96/1.61 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.96/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.96/1.61 tc_Int_Oint, Y, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.96/1.61 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Divides_Odiv__class_Odiv
% 0.96/1.61 ( tc_Int_Oint, Y, X ) ) }.
% 0.96/1.61 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.96/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.96/1.61 tc_Int_Oint, Y, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.96/1.61 c_Groups_Ominus__class_Ominus( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Divides_Odiv__class_Odiv
% 0.96/1.61 ( tc_Int_Oint, Y, X ) ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), c_Groups_Oplus__class_Oplus
% 0.96/1.61 ( tc_Int_Oint, c_Groups_Oabs__class_Oabs( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ),
% 0.96/1.61 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ), X ) ), Y ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.96/1.61 , c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, T, Z )
% 0.96/1.61 ), Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus
% 0.96/1.61 ( X, Z, Y ), T ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.96/1.61 , c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, T, Z )
% 0.96/1.61 ), Y ), c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus
% 0.96/1.61 ( X, Z, Y ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.96/1.61 , c_Groups_Ominus__class_Ominus( X, Z, Y ), T ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.96/1.61 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oabs__class_Oabs( X,
% 0.96/1.61 c_Groups_Ominus__class_Ominus( X, T, Z ) ), Y ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__idom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Polynomial_Opoly( X ) ), c_Groups_Osgn__class_Osgn(
% 0.96/1.61 tc_Polynomial_Opoly( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Polynomial_Opoly( X ) ), ! c_Orderings_Oord__class_Oless(
% 0.96/1.61 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Polynomial_Opoly( X ) ), Y ), c_Groups_Osgn__class_Osgn(
% 0.96/1.61 tc_Polynomial_Opoly( X ), Y ) = c_Groups_Oone__class_Oone(
% 0.96/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless(
% 0.96/1.61 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Polynomial_Opoly( X ) ), Y ), c_Groups_Osgn__class_Osgn(
% 0.96/1.61 tc_Polynomial_Opoly( X ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.96/1.61 tc_Polynomial_Opoly( X ), c_Groups_Oone__class_Oone( tc_Polynomial_Opoly
% 0.96/1.61 ( X ) ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.96/1.61 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.96/1.61 .
% 0.96/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.96/1.61 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless( X
% 0.96/1.61 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) ) }
% 0.96/1.61 .
% 0.96/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.96/1.61 , c_Groups_Osgn__class_Osgn( X, Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.96/1.61 .
% 0.96/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.96/1.61 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.96/1.61 , c_Groups_Osgn__class_Osgn( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }
% 0.96/1.61 .
% 0.96/1.61 { ! class_Fields_Ofield( X ), c_Polynomial_Opdivmod__rel( X, Z, Y,
% 0.96/1.61 c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly( X ), Z, Y ),
% 0.96/1.61 c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), Z, Y ) ) }.
% 0.96/1.61 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) =
% 0.96/1.61 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 0.96/1.61 tc_Nat_Onat, Z, Y ), X ) }.
% 0.96/1.61 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) = X }.
% 0.96/1.61 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.96/1.61 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.61 { Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.96/1.61 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) =
% 0.96/1.61 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) }.
% 0.96/1.61 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Odiv(
% 0.96/1.61 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ) =
% 0.96/1.61 c_Polynomial_Osmult( X, T, c_Divides_Odiv__class_Odiv(
% 0.96/1.61 tc_Polynomial_Opoly( X ), Z, Y ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X, Y ) =
% 0.96/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ),
% 0.96/1.61 c_Groups_Osgn__class_Osgn( X, Y ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__idom( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Osgn__class_Osgn( X, Y ) ),
% 0.96/1.61 c_Groups_Oabs__class_Oabs( X, Y ) ) = Y }.
% 0.96/1.61 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Odiv(
% 0.96/1.61 tc_Polynomial_Opoly( X ), c_Groups_Ouminus__class_Ouminus(
% 0.96/1.61 tc_Polynomial_Opoly( X ), Z ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.96/1.61 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly
% 0.96/1.61 ( X ), Z, Y ) ) }.
% 0.96/1.61 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Odiv(
% 0.96/1.61 tc_Polynomial_Opoly( X ), Z, c_Groups_Ouminus__class_Ouminus(
% 0.96/1.61 tc_Polynomial_Opoly( X ), Y ) ) = c_Groups_Ouminus__class_Ouminus(
% 0.96/1.61 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly
% 0.96/1.61 ( X ), Z, Y ) ) }.
% 0.96/1.61 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Odiv(
% 0.96/1.61 tc_Polynomial_Opoly( X ), T, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.96/1.61 tc_Polynomial_Opoly( X ) ), Z ), Y ) ) = c_Divides_Odiv__class_Odiv(
% 0.96/1.61 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly
% 0.96/1.61 ( X ), T, Z ), Y ) }.
% 0.96/1.61 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, Y, U )
% 0.96/1.61 , c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly( X ), T, Z ) = Y }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.61 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.61 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.96/1.61 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 0.96/1.61 tc_Nat_Onat, Z, X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ),
% 0.96/1.61 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.96/1.61 tc_Nat_Onat, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, X ),
% 0.96/1.61 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ), X ) ) }.
% 0.96/1.61 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.96/1.61 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.61 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 0.96/1.61 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.61 }.
% 0.96/1.61 { ! class_Rings_Olinordered__idom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.61 X ), c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.61 }.
% 0.96/1.61 { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Osgn__class_Osgn
% 0.96/1.61 ( X, c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X
% 0.96/1.61 ) }.
% 0.96/1.61 { ! class_Groups_Osgn__if( X ), c_Groups_Osgn__class_Osgn( X,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.61 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 0.96/1.61 c_Groups_Osgn__class_Osgn( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.96/1.61 X ), Z ), Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.96/1.61 c_Groups_Osgn__class_Osgn( X, Z ) ), c_Groups_Osgn__class_Osgn( X, Y ) )
% 0.96/1.61 }.
% 0.96/1.61 { ! class_Rings_Olinordered__idom( X ), c_Groups_Osgn__class_Osgn( X, hAPP
% 0.96/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Osgn__class_Osgn( X, Z ) ),
% 0.96/1.61 c_Groups_Osgn__class_Osgn( X, Y ) ) }.
% 0.96/1.61 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 0.96/1.61 c_Groups_Osgn__class_Osgn( X, c_Groups_Oone__class_Oone( X ) ) =
% 0.96/1.61 c_Groups_Oone__class_Oone( X ) }.
% 0.96/1.61 { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Osgn__class_Osgn
% 0.96/1.61 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 0.96/1.61 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Osgn__class_Osgn( X, Y ) ) }
% 0.96/1.61 .
% 0.96/1.61 { ! class_Rings_Olinordered__idom( X ), c_Groups_Osgn__class_Osgn( X,
% 0.96/1.61 c_Groups_Osgn__class_Osgn( X, Y ) ) = c_Groups_Osgn__class_Osgn( X, Y ) }
% 0.96/1.61 .
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 0.96/1.61 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ) = Y }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 0.96/1.61 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ) = Y }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 0.96/1.61 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) =
% 0.96/1.61 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, Y ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 0.96/1.61 tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 0.96/1.61 tc_Nat_Onat, Y, X ), Y ) }.
% 0.96/1.61 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) =
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ),
% 0.96/1.61 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 0.96/1.61 tc_Nat_Onat, Z, Y ), X ) ), c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, Y
% 0.96/1.61 ) ) }.
% 0.96/1.61 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), X ) =
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.96/1.61 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ),
% 0.96/1.61 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.96/1.61 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ), X ) ) }.
% 0.96/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.61 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ), X ) =
% 0.96/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Divides_Odiv__class_Omod
% 0.96/1.61 ( tc_Nat_Onat, Y, X ) ) }.
% 0.96/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ),
% 0.96/1.61 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, X, Y ) ) =
% 0.96/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Divides_Odiv__class_Omod
% 0.96/1.61 ( tc_Nat_Onat, X, Y ) ) }.
% 0.96/1.61 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 0.96/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Divides_Odiv__class_Odiv
% 0.96/1.61 ( tc_Nat_Onat, Y, X ) ), X ) ) }.
% 0.96/1.61 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.61 c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly( X ), T,
% 0.96/1.61 c_Polynomial_Osmult( X, Y, Z ) ) = c_Polynomial_Osmult( X,
% 0.96/1.61 c_Rings_Oinverse__class_Oinverse( X, Y ), c_Divides_Odiv__class_Odiv(
% 0.96/1.61 tc_Polynomial_Opoly( X ), T, Z ) ) }.
% 0.96/1.61 { ! class_Fields_Ofield( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 0.96/1.61 , c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) ),
% 0.96/1.61 c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly( X ), Z, Y ) =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 0.96/1.61 = c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless( X,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.96/1.61 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Groups_Osgn__class_Osgn( X, Y
% 0.96/1.61 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.96/1.61 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Groups_Osgn__class_Osgn( X, Y
% 0.96/1.61 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.96/1.61 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Omod(
% 0.96/1.61 tc_Polynomial_Opoly( X ), T, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.96/1.61 tc_Polynomial_Opoly( X ) ), Z ), Y ) ) = c_Groups_Oplus__class_Oplus(
% 0.96/1.61 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.96/1.61 tc_Polynomial_Opoly( X ) ), Z ), c_Divides_Odiv__class_Omod(
% 0.96/1.61 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly
% 0.96/1.61 ( X ), T, Z ), Y ) ), c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X
% 0.96/1.61 ), T, Z ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 0.96/1.61 , c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.96/1.61 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.96/1.61 tc_Nat_Onat, Y, X ), X ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 0.96/1.61 ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 0.96/1.61 , c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.96/1.61 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.96/1.61 tc_Nat_Onat, Y, X ), X ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ),
% 0.96/1.61 alpha20( X, Z ) }.
% 0.96/1.61 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ),
% 0.96/1.61 alpha38( X, Y, Z ) }.
% 0.96/1.61 { ! alpha20( X, Z ), ! alpha38( X, Y, Z ), hBOOL( hAPP( Z,
% 0.96/1.61 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ) }.
% 0.96/1.61 { ! alpha38( X, Y, Z ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.96/1.61 alpha46( X, Y, Z ) }.
% 0.96/1.61 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha38( X, Y, Z ) }.
% 0.96/1.61 { ! alpha46( X, Y, Z ), alpha38( X, Y, Z ) }.
% 0.96/1.61 { ! alpha46( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, X
% 0.96/1.61 ), alpha50( X, Y, Z, T ) }.
% 0.96/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol17( X, T, U ), X ),
% 0.96/1.61 alpha46( X, Y, Z ) }.
% 0.96/1.61 { ! alpha50( X, Y, Z, skol17( X, Y, Z ) ), alpha46( X, Y, Z ) }.
% 0.96/1.61 { ! alpha50( X, Y, Z, T ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.96/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 0.96/1.61 hBOOL( hAPP( Z, U ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( Z, skol18( U, W, Z, V0 ) ) ), alpha50( X, Y, Z, T ) }.
% 0.96/1.61 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol18( X, Y, Z, T ) )
% 0.96/1.61 , T ), alpha50( X, Y, Z, T ) }.
% 0.96/1.61 { ! alpha20( X, Y ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.96/1.61 hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.96/1.61 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha20( X, Y ) }.
% 0.96/1.61 { ! hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha20
% 0.96/1.61 ( X, Y ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless(
% 0.96/1.61 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Polynomial_Opoly( X ) ) ), c_Groups_Oabs__class_Oabs(
% 0.96/1.61 tc_Polynomial_Opoly( X ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.96/1.61 tc_Polynomial_Opoly( X ), Y ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__idom( X ), c_Orderings_Oord__class_Oless(
% 0.96/1.61 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Polynomial_Opoly( X ) ) ), c_Groups_Oabs__class_Oabs(
% 0.96/1.61 tc_Polynomial_Opoly( X ), Y ) = Y }.
% 0.96/1.61 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.96/1.61 tc_Nat_Onat, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ),
% 0.96/1.61 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Nat_OSuc(
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ),
% 0.96/1.61 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.96/1.61 tc_Nat_Onat, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ),
% 0.96/1.61 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc(
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), X ) ) }.
% 0.96/1.61 { ! class_Groups_Osgn__if( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.61 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.61 { ! class_Groups_Osgn__if( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.96/1.61 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.96/1.61 { ! class_Groups_Osgn__if( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.96/1.61 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.96/1.61 c_Groups_Oone__class_Oone( X ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 0.96/1.61 = c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.96/1.61 .
% 0.96/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.96/1.61 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Osgn__class_Osgn( X, Y
% 0.96/1.61 ) = c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) )
% 0.96/1.61 }.
% 0.96/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.96/1.61 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Osgn__class_Osgn( X, Y
% 0.96/1.61 ) = c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) )
% 0.96/1.61 }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! hBOOL( hAPP( hAPP( Z,
% 0.96/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 0.96/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ), ! alpha21( X, Y, T,
% 0.96/1.61 U ), hBOOL( hAPP( hAPP( Z, T ), U ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha21( X, Y, skol19( X, Y
% 0.96/1.61 , Z ), skol24( X, Y, Z ) ), hBOOL( hAPP( hAPP( Z,
% 0.96/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 0.96/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! hBOOL( hAPP( hAPP( Z,
% 0.96/1.61 skol19( X, Y, Z ) ), skol24( X, Y, Z ) ) ), hBOOL( hAPP( hAPP( Z,
% 0.96/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 0.96/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 0.96/1.61 { ! alpha21( X, Y, Z, T ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, T
% 0.96/1.61 ) }.
% 0.96/1.61 { ! alpha21( X, Y, Z, T ), alpha39( X, Y, Z, T ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, T ), ! alpha39( X, Y, Z
% 0.96/1.61 , T ), alpha21( X, Y, Z, T ) }.
% 0.96/1.61 { ! alpha39( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 T, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.96/1.61 { ! alpha39( X, Y, Z, T ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.96/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ) }
% 0.96/1.61 .
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! Y =
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ), alpha39( X,
% 0.96/1.61 Y, Z, T ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( hAPP( Z, c_Divides_Odiv__class_Odiv
% 0.96/1.61 ( tc_Int_Oint, Y, X ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X )
% 0.96/1.61 ) ), ! alpha22( X, Y, T, U ), hBOOL( hAPP( hAPP( Z, T ), U ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Int_Oint ), X ), alpha22( X, Y, skol20( X, Y, Z ), skol25( X, Y, Z )
% 0.96/1.61 ), hBOOL( hAPP( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X )
% 0.96/1.61 ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( hAPP( Z, skol20( X, Y, Z ) ), skol25
% 0.96/1.61 ( X, Y, Z ) ) ), hBOOL( hAPP( hAPP( Z, c_Divides_Odiv__class_Odiv(
% 0.96/1.61 tc_Int_Oint, Y, X ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) )
% 0.96/1.61 ) }.
% 0.96/1.61 { ! alpha22( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ) }.
% 0.96/1.61 { ! alpha22( X, Y, Z, T ), alpha40( X, Y, Z, T ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! alpha40( X, Y, Z, T )
% 0.96/1.61 , alpha22( X, Y, Z, T ) }.
% 0.96/1.61 { ! alpha40( X, Y, Z, T ), c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X
% 0.96/1.61 ) }.
% 0.96/1.61 { ! alpha40( X, Y, Z, T ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.96/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ) }
% 0.96/1.61 .
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X ), ! Y =
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ), alpha40( X,
% 0.96/1.61 Y, Z, T ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.96/1.61 tc_Int_Oint, X, Y ) ) }.
% 0.96/1.61 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X,
% 0.96/1.61 c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ),
% 0.96/1.61 c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Y, Z ) )
% 0.96/1.61 ) }.
% 0.96/1.61 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X,
% 0.96/1.61 c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ),
% 0.96/1.61 c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Z, Y ) )
% 0.96/1.61 ) }.
% 0.96/1.61 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 0.96/1.61 c_Groups_Ominus__class_Ominus( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.96/1.61 c_Groups_Oabs__class_Oabs( X, Y ) ) ), c_Groups_Oabs__class_Oabs( X,
% 0.96/1.61 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ) }.
% 0.96/1.61 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.96/1.61 Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.61 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.96/1.61 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.96/1.61 , Z ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.61 c_Groups_Oabs__class_Oabs( X, Z ), Y ) }.
% 0.96/1.61 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.96/1.61 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.96/1.61 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.96/1.61 Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.61 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.96/1.61 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.96/1.61 , Z ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.61 c_Groups_Oabs__class_Oabs( X, Z ), Y ) }.
% 0.96/1.61 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.96/1.61 , Y ), c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.96/1.61 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( X, Z, Y ) ), c_Groups_Oplus__class_Oplus( X
% 0.96/1.61 , c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) )
% 0.96/1.61 ) }.
% 0.96/1.61 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.96/1.61 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.96/1.61 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oabs__class_Oabs( X, Y
% 0.96/1.61 ) ) }.
% 0.96/1.61 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.96/1.61 ), c_Groups_Oabs__class_Oabs( X, Y ) = Y }.
% 0.96/1.61 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Y ),
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.61 }.
% 0.96/1.61 { ! class_Groups_Oordered__ab__group__add__abs( X ), ! Y =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.61 c_Groups_Oabs__class_Oabs( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.61 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.61 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.96/1.61 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.96/1.61 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.96/1.61 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.96/1.61 ! c_Orderings_Oord__class_Oless__eq( X, Z, T ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.96/1.61 ( X, U, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.96/1.61 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.96/1.61 ( X, U, T ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.96/1.61 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.96/1.61 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.96/1.61 , U ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, U, T ), ! c_Orderings_Oord__class_Oless
% 0.96/1.61 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.96/1.61 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.61 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.96/1.61 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.96/1.61 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.96/1.61 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.61 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.96/1.61 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.96/1.61 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.96/1.61 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.96/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.96/1.61 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.96/1.61 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.96/1.61 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.96/1.61 ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.96/1.61 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.96/1.61 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.96/1.61 ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.96/1.61 ) ) }.
% 0.96/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.96/1.61 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.96/1.61 ) ) }.
% 0.96/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.96/1.61 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.96/1.61 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.96/1.61 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.96/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.96/1.61 ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.96/1.61 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.96/1.61 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 0.96/1.61 X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 0.96/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.96/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ) ), Z = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.61 }.
% 0.96/1.61 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.96/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.61 }.
% 0.96/1.61 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.61 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.96/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.61 { ! class_Rings_Oidom( X ),
% 0.96/1.61 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct( X
% 0.96/1.61 ) }.
% 0.96/1.61 { ! class_Rings_Oidom( X ), class_Groups_Ocancel__ab__semigroup__add( X ) }
% 0.96/1.61 .
% 0.96/1.61 { ! class_Rings_Oidom( X ), class_Rings_Oring__1__no__zero__divisors( X ) }
% 0.96/1.61 .
% 0.96/1.61 { ! class_Rings_Oidom( X ), class_Rings_Oring__no__zero__divisors( X ) }.
% 0.96/1.61 { ! class_Rings_Oidom( X ), class_Groups_Ocancel__semigroup__add( X ) }.
% 0.96/1.61 { ! class_Rings_Oidom( X ), class_Groups_Oab__semigroup__mult( X ) }.
% 0.96/1.61 { ! class_Rings_Oidom( X ), class_Groups_Ocomm__monoid__mult( X ) }.
% 0.96/1.61 { ! class_Rings_Oidom( X ), class_Groups_Oab__semigroup__add( X ) }.
% 0.96/1.61 { ! class_Rings_Oidom( X ), class_Rings_Ono__zero__divisors( X ) }.
% 0.96/1.61 { ! class_Rings_Oidom( X ), class_Groups_Ocomm__monoid__add( X ) }.
% 0.96/1.61 { ! class_Rings_Oidom( X ), class_Rings_Ocomm__semiring__1( X ) }.
% 0.96/1.61 { ! class_Rings_Oidom( X ), class_Rings_Ocomm__semiring__0( X ) }.
% 0.96/1.61 { ! class_Rings_Oidom( X ), class_Rings_Ocomm__semiring( X ) }.
% 0.96/1.61 { ! class_Rings_Oidom( X ), class_Groups_Oab__group__add( X ) }.
% 0.96/1.61 { ! class_Rings_Oidom( X ), class_Rings_Ozero__neq__one( X ) }.
% 0.96/1.61 { ! class_Rings_Oidom( X ), class_Groups_Omonoid__mult( X ) }.
% 0.96/1.61 { ! class_Rings_Oidom( X ), class_Rings_Ocomm__ring__1( X ) }.
% 0.96/1.61 { ! class_Rings_Oidom( X ), class_Groups_Omonoid__add( X ) }.
% 0.96/1.61 { ! class_Rings_Oidom( X ), class_Rings_Osemiring__0( X ) }.
% 0.96/1.61 { ! class_Rings_Oidom( X ), class_Groups_Ogroup__add( X ) }.
% 0.96/1.61 { ! class_Rings_Oidom( X ), class_Rings_Omult__zero( X ) }.
% 0.96/1.61 { ! class_Rings_Oidom( X ), class_Rings_Ocomm__ring( X ) }.
% 0.96/1.61 { ! class_Rings_Oidom( X ), class_Rings_Osemiring( X ) }.
% 0.96/1.61 { ! class_Rings_Oidom( X ), class_Rings_Oring__1( X ) }.
% 0.96/1.61 { ! class_Rings_Oidom( X ), class_Power_Opower( X ) }.
% 0.96/1.61 { ! class_Rings_Oidom( X ), class_Groups_Ozero( X ) }.
% 0.96/1.61 { ! class_Rings_Oidom( X ), class_Rings_Oring( X ) }.
% 0.96/1.61 { ! class_Rings_Oidom( X ), class_Groups_Oone( X ) }.
% 0.96/1.61 { ! class_Rings_Oidom( X ), class_Rings_Odvd( X ) }.
% 0.96/1.61 { ! class_Rings_Oidom( X ), class_Groups_Ocancel__comm__monoid__add( X ) }
% 0.96/1.61 .
% 0.96/1.61 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.96/1.61 class_Groups_Ocancel__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.61 { class_Groups_Ocancel__comm__monoid__add( tc_Nat_Onat ) }.
% 0.96/1.61 { class_Groups_Ocancel__comm__monoid__add( tc_Int_Oint ) }.
% 0.96/1.61 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.96/1.61 tc_Int_Oint ) }.
% 0.96/1.61 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.96/1.61 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Int_Oint ) }.
% 0.96/1.61 { class_Rings_Olinordered__comm__semiring__strict( tc_Int_Oint ) }.
% 0.96/1.61 { class_Rings_Olinordered__semiring__strict( tc_Int_Oint ) }.
% 0.96/1.61 { class_Groups_Oordered__ab__group__add__abs( tc_Int_Oint ) }.
% 0.96/1.61 { class_Groups_Oordered__comm__monoid__add( tc_Int_Oint ) }.
% 0.96/1.61 { class_Groups_Olinordered__ab__group__add( tc_Int_Oint ) }.
% 0.96/1.61 { class_Groups_Ocancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.96/1.61 { class_Rings_Oring__1__no__zero__divisors( tc_Int_Oint ) }.
% 0.96/1.61 { class_Rings_Olinordered__ring__strict( tc_Int_Oint ) }.
% 0.96/1.61 { class_Rings_Oring__no__zero__divisors( tc_Int_Oint ) }.
% 0.96/1.61 { class_Groups_Oordered__ab__group__add( tc_Int_Oint ) }.
% 0.96/1.61 { class_Groups_Ocancel__semigroup__add( tc_Int_Oint ) }.
% 0.96/1.61 { class_Rings_Olinordered__semiring( tc_Int_Oint ) }.
% 0.96/1.61 { class_Rings_Olinordered__semidom( tc_Int_Oint ) }.
% 0.96/1.61 { class_Groups_Oab__semigroup__mult( tc_Int_Oint ) }.
% 0.96/1.61 { class_Groups_Ocomm__monoid__mult( tc_Int_Oint ) }.
% 0.96/1.61 { class_Groups_Oab__semigroup__add( tc_Int_Oint ) }.
% 0.96/1.61 { class_Rings_Ono__zero__divisors( tc_Int_Oint ) }.
% 0.96/1.61 { class_Groups_Ocomm__monoid__add( tc_Int_Oint ) }.
% 0.96/1.61 { class_Rings_Olinordered__ring( tc_Int_Oint ) }.
% 0.96/1.61 { class_Rings_Olinordered__idom( tc_Int_Oint ) }.
% 0.96/1.61 { class_Rings_Ocomm__semiring__1( tc_Int_Oint ) }.
% 0.96/1.61 { class_Rings_Ocomm__semiring__0( tc_Int_Oint ) }.
% 0.96/1.61 { class_Divides_Osemiring__div( tc_Int_Oint ) }.
% 0.96/1.61 { class_Rings_Ocomm__semiring( tc_Int_Oint ) }.
% 0.96/1.61 { class_Groups_Oab__group__add( tc_Int_Oint ) }.
% 0.96/1.61 { class_Rings_Ozero__neq__one( tc_Int_Oint ) }.
% 0.96/1.61 { class_Rings_Oordered__ring( tc_Int_Oint ) }.
% 0.96/1.61 { class_Groups_Omonoid__mult( tc_Int_Oint ) }.
% 0.96/1.61 { class_Rings_Ocomm__ring__1( tc_Int_Oint ) }.
% 0.96/1.61 { class_Groups_Omonoid__add( tc_Int_Oint ) }.
% 0.96/1.61 { class_Rings_Osemiring__0( tc_Int_Oint ) }.
% 0.96/1.61 { class_Groups_Ogroup__add( tc_Int_Oint ) }.
% 0.96/1.61 { class_Divides_Oring__div( tc_Int_Oint ) }.
% 0.96/1.61 { class_Rings_Omult__zero( tc_Int_Oint ) }.
% 0.96/1.61 { class_Rings_Ocomm__ring( tc_Int_Oint ) }.
% 0.96/1.61 { class_Int_Oring__char__0( tc_Int_Oint ) }.
% 0.96/1.61 { class_Rings_Osemiring( tc_Int_Oint ) }.
% 0.96/1.61 { class_Groups_Osgn__if( tc_Int_Oint ) }.
% 0.96/1.61 { class_Groups_Oabs__if( tc_Int_Oint ) }.
% 0.96/1.61 { class_Rings_Oring__1( tc_Int_Oint ) }.
% 0.96/1.61 { class_Power_Opower( tc_Int_Oint ) }.
% 0.96/1.61 { class_Groups_Ozero( tc_Int_Oint ) }.
% 0.96/1.61 { class_Rings_Oring( tc_Int_Oint ) }.
% 0.96/1.61 { class_Rings_Oidom( tc_Int_Oint ) }.
% 0.96/1.61 { class_Groups_Oone( tc_Int_Oint ) }.
% 0.96/1.61 { class_Rings_Odvd( tc_Int_Oint ) }.
% 0.96/1.61 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.96/1.61 tc_Nat_Onat ) }.
% 0.96/1.61 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.96/1.61 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Nat_Onat ) }.
% 0.96/1.61 { class_Rings_Olinordered__comm__semiring__strict( tc_Nat_Onat ) }.
% 0.96/1.61 { class_Rings_Olinordered__semiring__strict( tc_Nat_Onat ) }.
% 0.96/1.61 { class_Groups_Oordered__comm__monoid__add( tc_Nat_Onat ) }.
% 0.96/1.61 { class_Groups_Ocancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.96/1.61 { class_Groups_Ocancel__semigroup__add( tc_Nat_Onat ) }.
% 0.96/1.61 { class_Rings_Olinordered__semiring( tc_Nat_Onat ) }.
% 0.96/1.61 { class_Rings_Olinordered__semidom( tc_Nat_Onat ) }.
% 0.96/1.61 { class_Groups_Oab__semigroup__mult( tc_Nat_Onat ) }.
% 0.96/1.61 { class_Groups_Ocomm__monoid__mult( tc_Nat_Onat ) }.
% 0.96/1.61 { class_Groups_Oab__semigroup__add( tc_Nat_Onat ) }.
% 0.96/1.61 { class_Rings_Ono__zero__divisors( tc_Nat_Onat ) }.
% 0.96/1.61 { class_Groups_Ocomm__monoid__add( tc_Nat_Onat ) }.
% 0.96/1.61 { class_Rings_Ocomm__semiring__1( tc_Nat_Onat ) }.
% 0.96/1.61 { class_Rings_Ocomm__semiring__0( tc_Nat_Onat ) }.
% 0.96/1.61 { class_Divides_Osemiring__div( tc_Nat_Onat ) }.
% 0.96/1.61 { class_Rings_Ocomm__semiring( tc_Nat_Onat ) }.
% 0.96/1.61 { class_Rings_Ozero__neq__one( tc_Nat_Onat ) }.
% 0.96/1.61 { class_Groups_Omonoid__mult( tc_Nat_Onat ) }.
% 0.96/1.61 { class_Groups_Omonoid__add( tc_Nat_Onat ) }.
% 0.96/1.61 { class_Rings_Osemiring__0( tc_Nat_Onat ) }.
% 0.96/1.61 { class_Rings_Omult__zero( tc_Nat_Onat ) }.
% 0.96/1.61 { class_Rings_Osemiring( tc_Nat_Onat ) }.
% 0.96/1.61 { class_Power_Opower( tc_Nat_Onat ) }.
% 0.96/1.61 { class_Groups_Ozero( tc_Nat_Onat ) }.
% 0.96/1.61 { class_Groups_Oone( tc_Nat_Onat ) }.
% 0.96/1.61 { class_Rings_Odvd( tc_Nat_Onat ) }.
% 0.96/1.61 { ! class_Rings_Oidom( X ),
% 0.96/1.61 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.96/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.96/1.61 class_Groups_Oordered__cancel__ab__semigroup__add( tc_Polynomial_Opoly( X
% 0.96/1.61 ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.96/1.61 class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Polynomial_Opoly(
% 0.96/1.61 X ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.96/1.61 class_Rings_Olinordered__comm__semiring__strict( tc_Polynomial_Opoly( X )
% 0.96/1.61 ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.96/1.61 class_Rings_Olinordered__semiring__strict( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.96/1.61 class_Groups_Oordered__ab__group__add__abs( tc_Polynomial_Opoly( X ) ) }
% 0.96/1.61 .
% 0.96/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.96/1.61 class_Groups_Oordered__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.96/1.61 class_Groups_Olinordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.61 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.96/1.61 class_Groups_Ocancel__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.61 { ! class_Rings_Oidom( X ), class_Rings_Oring__1__no__zero__divisors(
% 0.96/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.96/1.61 class_Rings_Olinordered__ring__strict( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.61 { ! class_Rings_Oidom( X ), class_Rings_Oring__no__zero__divisors(
% 0.96/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.96/1.61 class_Groups_Oordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.61 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.96/1.61 class_Groups_Ocancel__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semiring(
% 0.96/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semidom(
% 0.96/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Oab__semigroup__mult
% 0.96/1.61 ( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Ocomm__monoid__mult(
% 0.96/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.61 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Oab__semigroup__add
% 0.96/1.61 ( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.61 { ! class_Rings_Oidom( X ), class_Rings_Ono__zero__divisors(
% 0.96/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.61 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Ocomm__monoid__add(
% 0.96/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__ring(
% 0.96/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__idom(
% 0.96/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ocomm__semiring__1(
% 0.96/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring__0(
% 0.96/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.61 { ! class_Fields_Ofield( X ), class_Divides_Osemiring__div(
% 0.96/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring(
% 0.96/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.61 { ! class_Groups_Oab__group__add( X ), class_Groups_Oab__group__add(
% 0.96/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ozero__neq__one(
% 0.96/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__ring(
% 0.96/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Omonoid__mult(
% 0.96/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Ocomm__ring__1(
% 0.96/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.61 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Omonoid__add(
% 0.96/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring__0(
% 0.96/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.61 { ! class_Groups_Oab__group__add( X ), class_Groups_Ogroup__add(
% 0.96/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.61 { ! class_Fields_Ofield( X ), class_Divides_Oring__div( tc_Polynomial_Opoly
% 0.96/1.61 ( X ) ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Omult__zero(
% 0.96/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__ring( X ), class_Rings_Ocomm__ring(
% 0.96/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__idom( X ), class_Int_Oring__char__0(
% 0.96/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring(
% 0.96/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__idom( X ), class_Groups_Osgn__if(
% 0.96/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__idom( X ), class_Groups_Oabs__if(
% 0.96/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Oring__1(
% 0.96/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__1( X ), class_Power_Opower(
% 0.96/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.61 { ! class_Groups_Ozero( X ), class_Groups_Ozero( tc_Polynomial_Opoly( X ) )
% 0.96/1.61 }.
% 0.96/1.61 { ! class_Rings_Ocomm__ring( X ), class_Rings_Oring( tc_Polynomial_Opoly( X
% 0.96/1.61 ) ) }.
% 0.96/1.61 { ! class_Rings_Oidom( X ), class_Rings_Oidom( tc_Polynomial_Opoly( X ) ) }
% 0.96/1.61 .
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Oone(
% 0.96/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Odvd(
% 0.96/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.61 { ! hBOOL( c_fequal( Y, X ) ), Y = X }.
% 0.96/1.61 { ! Y = X, hBOOL( c_fequal( Y, X ) ) }.
% 0.96/1.61 { ! hBOOL( c_fFalse ) }.
% 0.96/1.61 { hBOOL( c_fTrue ) }.
% 0.96/1.61 { X = c_Groups_Ozero__class_Ozero( t_a ), alpha55( Y, Z ), !
% 0.96/1.61 c_Polynomial_OpCons( t_a, v_c____, v_cs____ ) =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( t_a ) ), ! hAPP(
% 0.96/1.61 c_Polynomial_Opoly( t_a, c_Polynomial_OpCons( t_a, v_c____, v_cs____ ) )
% 0.96/1.61 , skol21( X, Y, Z ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( t_a )
% 0.96/1.61 , hAPP( hAPP( c_Power_Opower__class_Opower( t_a ), skol21( X, Y, Z ) ), Y
% 0.96/1.61 ) ), hAPP( c_Polynomial_Opoly( t_a, c_Polynomial_OpCons( t_a, X, Z ) ),
% 0.96/1.61 skol21( X, Y, Z ) ) ) }.
% 0.96/1.61 { X = c_Groups_Ozero__class_Ozero( t_a ), alpha55( Y, Z ), ! c_Nat_OSuc(
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_If( tc_Nat_Onat, c_fequal( Z
% 0.96/1.61 , c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( t_a ) ) ),
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Nat_OSuc(
% 0.96/1.61 c_Polynomial_Odegree( t_a, Z ) ) ), Y ) ) = c_Nat_OSuc(
% 0.96/1.61 c_Polynomial_Odegree( t_a, c_Polynomial_OpCons( t_a, v_c____, v_cs____ )
% 0.96/1.61 ) ), ! hAPP( c_Polynomial_Opoly( t_a, c_Polynomial_OpCons( t_a, v_c____
% 0.96/1.61 , v_cs____ ) ), skol21( X, Y, Z ) ) = hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( t_a ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( t_a ), skol21( X, Y, Z ) ), Y ) ), hAPP(
% 0.96/1.61 c_Polynomial_Opoly( t_a, c_Polynomial_OpCons( t_a, X, Z ) ), skol21( X, Y
% 0.96/1.61 , Z ) ) ) }.
% 0.96/1.61 { ! alpha55( X, Y ), c_Polynomial_OpCons( t_a, v_c____, v_cs____ ) =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( t_a ) ) }.
% 0.96/1.61 { ! alpha55( X, Y ), ! c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat
% 0.96/1.61 , c_If( tc_Nat_Onat, c_fequal( Y, c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Polynomial_Opoly( t_a ) ) ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 0.96/1.61 ), c_Nat_OSuc( c_Polynomial_Odegree( t_a, Y ) ) ), X ) ) =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.61 { ! c_Polynomial_OpCons( t_a, v_c____, v_cs____ ) =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( t_a ) ), c_Nat_OSuc(
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_If( tc_Nat_Onat, c_fequal( Y
% 0.96/1.61 , c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( t_a ) ) ),
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Nat_OSuc(
% 0.96/1.61 c_Polynomial_Odegree( t_a, Y ) ) ), X ) ) = c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Nat_Onat ), alpha55( X, Y ) }.
% 0.96/1.61 { class_Rings_Oidom( t_a ) }.
% 0.96/1.61
% 0.96/1.61 *** allocated 15000 integers for clauses
% 0.96/1.61 *** allocated 22500 integers for clauses
% 0.96/1.61 *** allocated 33750 integers for clauses
% 0.96/1.61 *** allocated 50625 integers for clauses
% 0.96/1.61 *** allocated 75937 integers for clauses
% 0.96/1.61 *** allocated 113905 integers for clauses
% 0.96/1.61 percentage equality = 0.346983, percentage horn = 0.867850
% 0.96/1.61 This is a problem with some equality
% 0.96/1.61
% 0.96/1.61
% 0.96/1.61
% 0.96/1.61 Options Used:
% 0.96/1.61
% 0.96/1.61 useres = 1
% 0.96/1.61 useparamod = 1
% 0.96/1.61 useeqrefl = 1
% 0.96/1.61 useeqfact = 1
% 0.96/1.61 usefactor = 1
% 0.96/1.61 usesimpsplitting = 0
% 0.96/1.61 usesimpdemod = 5
% 0.96/1.61 usesimpres = 3
% 0.96/1.61
% 0.96/1.61 resimpinuse = 1000
% 0.96/1.61 resimpclauses = 20000
% 0.96/1.61 substype = eqrewr
% 0.96/1.61 backwardsubs = 1
% 0.96/1.61 selectoldest = 5
% 0.96/1.61
% 0.96/1.61 litorderings [0] = split
% 0.96/1.61 litorderings [1] = extend the termordering, first sorting on arguments
% 0.96/1.61
% 0.96/1.61 termordering = kbo
% 0.96/1.61
% 0.96/1.61 litapriori = 0
% 0.96/1.61 termapriori = 1
% 0.96/1.61 litaposteriori = 0
% 0.96/1.61 termaposteriori = 0
% 0.96/1.61 demodaposteriori = 0
% 0.96/1.61 ordereqreflfact = 0
% 0.96/1.61
% 0.96/1.61 litselect = negord
% 0.96/1.61
% 0.96/1.61 maxweight = 15
% 0.96/1.61 maxdepth = 30000
% 0.96/1.61 maxlength = 115
% 0.96/1.61 maxnrvars = 195
% 0.96/1.61 excuselevel = 1
% 0.96/1.61 increasemaxweight = 1
% 0.96/1.61
% 0.96/1.61 maxselected = 10000000
% 0.96/1.61 maxnrclauses = 10000000
% 0.96/1.61
% 0.96/1.61 showgenerated = 0
% 0.96/1.61 showkept = 0
% 0.96/1.61 showselected = 0
% 0.96/1.61 showdeleted = 0
% 0.96/1.61 showresimp = 1
% 0.96/1.61 showstatus = 2000
% 0.96/1.61
% 0.96/1.61 prologoutput = 0
% 0.96/1.61 nrgoals = 5000000
% 0.96/1.61 totalproof = 1
% 0.96/1.61
% 0.96/1.61 Symbols occurring in the translation:
% 0.96/1.61
% 0.96/1.61 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.96/1.61 . [1, 2] (w:1, o:185, a:1, s:1, b:0),
% 0.96/1.61 ! [4, 1] (w:0, o:108, a:1, s:1, b:0),
% 0.96/1.61 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.96/1.61 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.96/1.61 hAPP [38, 2] (w:1, o:209, a:1, s:1, b:0),
% 0.96/1.61 t_a [39, 0] (w:1, o:19, a:1, s:1, b:0),
% 0.96/1.61 class_Rings_Oidom [40, 1] (w:1, o:113, a:1, s:1, b:0),
% 0.96/1.61 v_c____ [41, 0] (w:1, o:20, a:1, s:1, b:0),
% 0.96/1.61 c_Groups_Ozero__class_Ozero [42, 1] (w:1, o:114, a:1, s:1, b:0),
% 0.96/1.61 v_cs____ [44, 0] (w:1, o:22, a:1, s:1, b:0),
% 0.96/1.61 c_Polynomial_OpCons [45, 3] (w:1, o:239, a:1, s:1, b:0),
% 0.96/1.61 c_Polynomial_Opoly [46, 2] (w:1, o:210, a:1, s:1, b:0),
% 0.96/1.61 v_p [47, 0] (w:1, o:23, a:1, s:1, b:0),
% 0.96/1.61 tc_Polynomial_Opoly [51, 1] (w:1, o:116, a:1, s:1, b:0),
% 0.96/1.61 tc_Nat_Onat [52, 0] (w:1, o:29, a:1, s:1, b:0),
% 0.96/1.61 c_fequal [53, 2] (w:1, o:211, a:1, s:1, b:0),
% 0.96/1.61 c_Polynomial_Odegree [54, 2] (w:1, o:213, a:1, s:1, b:0),
% 0.96/1.61 c_Nat_OSuc [55, 1] (w:1, o:117, a:1, s:1, b:0),
% 0.96/1.61 c_If [56, 4] (w:1, o:292, a:1, s:1, b:0),
% 0.96/1.61 c_Groups_Oplus__class_Oplus [57, 3] (w:1, o:241, a:1, s:1, b:0),
% 0.96/1.61 c_Groups_Otimes__class_Otimes [58, 1] (w:1, o:118, a:1, s:1, b:0),
% 0.96/1.61 c_Power_Opower__class_Opower [59, 1] (w:1, o:119, a:1, s:1, b:0),
% 0.96/1.61 class_Groups_Ozero [63, 1] (w:1, o:124, a:1, s:1, b:0),
% 0.96/1.61 class_Rings_Ocomm__semiring__0 [65, 1] (w:1, o:127, a:1, s:1, b:0),
% 0.96/1.61 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize [66, 2] (w:1, o:214
% 0.96/1.61 , a:1, s:1, b:0),
% 0.96/1.61 class_Groups_Ocomm__monoid__add [76, 1] (w:1, o:128, a:1, s:1, b:0),
% 0.96/1.61
% 0.96/1.61 class_Int_Oring__char__0 [84, 1] (w:1, o:129, a:1, s:1, b:0),
% 0.96/1.61 class_Rings_Ocomm__semiring__1 [88, 1] (w:1, o:130, a:1, s:1, b:0),
% 0.96/1.61 class_Groups_Omonoid__mult [89, 1] (w:1, o:132, a:1, s:1, b:0),
% 0.96/1.61 class_Power_Opower [90, 1] (w:1, o:133, a:1, s:1, b:0),
% 0.96/1.61 class_Rings_Osemiring__0 [91, 1] (w:1, o:138, a:1, s:1, b:0),
% 0.96/1.61 class_Rings_Omult__zero [92, 1] (w:1, o:146, a:1, s:1, b:0),
% 0.96/1.61 class_Rings_Ono__zero__divisors [93, 1] (w:1, o:147, a:1, s:1, b:0),
% 0.96/1.61
% 0.96/1.61 class_Rings_Ozero__neq__one [94, 1] (w:1, o:148, a:1, s:1, b:0),
% 0.96/1.61 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct [98
% 0.96/1.61 , 1] (w:1, o:161, a:1, s:1, b:0),
% 0.96/1.61 class_Rings_Olinordered__ring__strict [101, 1] (w:1, o:139, a:1, s:1
% 0.96/1.61 , b:0),
% 0.96/1.61 c_Polynomial_Oorder [102, 3] (w:1, o:238, a:1, s:1, b:0),
% 0.96/1.61 class_Rings_Oring__1__no__zero__divisors [111, 1] (w:1, o:134, a:1
% 0.96/1.61 , s:1, b:0),
% 0.96/1.61 class_Groups_Ocomm__monoid__mult [112, 1] (w:1, o:162, a:1, s:1, b:0)
% 0.96/1.61 ,
% 0.96/1.61 c_Polynomial_Opcompose [113, 3] (w:1, o:242, a:1, s:1, b:0),
% 0.96/1.61 class_RealVector_Oreal__normed__algebra [118, 1] (w:1, o:149, a:1, s:
% 0.96/1.61 1, b:0),
% 0.96/1.61 class_Rings_Ocomm__semiring [120, 1] (w:1, o:150, a:1, s:1, b:0),
% 0.96/1.61 class_Rings_Osemiring [124, 1] (w:1, o:151, a:1, s:1, b:0),
% 0.96/1.61 class_Groups_Omonoid__add [125, 1] (w:1, o:163, a:1, s:1, b:0),
% 0.96/1.61 class_Groups_Oab__semigroup__mult [126, 1] (w:1, o:164, a:1, s:1, b:0
% 0.96/1.61 ),
% 0.96/1.61 class_Groups_Ocancel__semigroup__add [127, 1] (w:1, o:165, a:1, s:1
% 0.96/1.61 , b:0),
% 0.96/1.61 class_Groups_Ocancel__ab__semigroup__add [128, 1] (w:1, o:166, a:1
% 0.96/1.61 , s:1, b:0),
% 0.96/1.61 class_Groups_Oab__semigroup__add [129, 1] (w:1, o:167, a:1, s:1, b:0)
% 0.96/1.61 ,
% 0.96/1.61 class_Rings_Oring__no__zero__divisors [130, 1] (w:1, o:135, a:1, s:1
% 0.96/1.61 , b:0),
% 0.96/1.61 class_Groups_Olinordered__ab__group__add [131, 1] (w:1, o:131, a:1
% 0.96/1.61 , s:1, b:0),
% 0.96/1.61 c_Polynomial_Opoly__rec [133, 5] (w:1, o:320, a:1, s:1, b:0),
% 0.96/1.61 c_Polynomial_Osynthetic__div [134, 3] (w:1, o:243, a:1, s:1, b:0),
% 0.96/1.61 c_Groups_Oone__class_Oone [135, 1] (w:1, o:168, a:1, s:1, b:0),
% 0.96/1.61 c_Nat_Onat_Onat__size [137, 1] (w:1, o:169, a:1, s:1, b:0),
% 0.96/1.61 c_Polynomial_Osmult [138, 3] (w:1, o:244, a:1, s:1, b:0),
% 0.96/1.61 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly [140, 3] (w:
% 0.96/1.61 1, o:240, a:1, s:1, b:0),
% 0.96/1.61 class_Groups_Oone [141, 1] (w:1, o:170, a:1, s:1, b:0),
% 0.96/1.61 tc_Int_Oint [143, 0] (w:1, o:94, a:1, s:1, b:0),
% 0.96/1.61 c_Power_Opower_Opower [144, 3] (w:1, o:245, a:1, s:1, b:0),
% 0.96/1.61 class_Rings_Ocomm__ring__1 [145, 1] (w:1, o:125, a:1, s:1, b:0),
% 0.96/1.61 c_Groups_Ouminus__class_Ouminus [146, 2] (w:1, o:215, a:1, s:1, b:0)
% 0.96/1.61 ,
% 0.96/1.61 c_Nat_Osize__class_Osize [147, 2] (w:1, o:216, a:1, s:1, b:0),
% 0.96/1.61 c_Polynomial_Omonom [148, 3] (w:1, o:246, a:1, s:1, b:0),
% 0.96/1.61 c_fTrue [149, 0] (w:1, o:95, a:1, s:1, b:0),
% 0.96/1.61 c_HOL_Obool_Obool__size [150, 1] (w:1, o:171, a:1, s:1, b:0),
% 0.96/1.61 c_fFalse [151, 0] (w:1, o:96, a:1, s:1, b:0),
% 0.96/1.61 c_Polynomial_Ocoeff [152, 2] (w:1, o:212, a:1, s:1, b:0),
% 0.96/1.61 class_Rings_Ocomm__ring [153, 1] (w:1, o:126, a:1, s:1, b:0),
% 0.96/1.61 class_Groups_Oab__group__add [158, 1] (w:1, o:172, a:1, s:1, b:0),
% 0.96/1.61 class_Groups_Ogroup__add [160, 1] (w:1, o:173, a:1, s:1, b:0),
% 0.96/1.61 class_Rings_Oring [161, 1] (w:1, o:136, a:1, s:1, b:0),
% 0.96/1.61 class_Rings_Oring__1 [162, 1] (w:1, o:137, a:1, s:1, b:0),
% 0.96/1.61 c_Rings_Odvd__class_Odvd [165, 3] (w:1, o:247, a:1, s:1, b:0),
% 0.96/1.61 class_Fields_Ofield [166, 1] (w:1, o:120, a:1, s:1, b:0),
% 0.96/1.61 c_Polynomial_Opoly__gcd [167, 3] (w:1, o:248, a:1, s:1, b:0),
% 0.96/1.61 class_Rings_Odvd [168, 1] (w:1, o:152, a:1, s:1, b:0),
% 0.96/1.61 hBOOL [171, 1] (w:1, o:174, a:1, s:1, b:0),
% 0.96/1.61 c_Rings_Oinverse__class_Oinverse [172, 2] (w:1, o:217, a:1, s:1, b:0)
% 0.96/1.61 ,
% 0.96/1.61 c_Groups_Ominus__class_Ominus [173, 3] (w:1, o:249, a:1, s:1, b:0),
% 0.96/1.61 c_Nat_Onat_Onat__case [174, 3] (w:1, o:250, a:1, s:1, b:0),
% 0.96/1.61 class_Rings_Odivision__ring [176, 1] (w:1, o:153, a:1, s:1, b:0),
% 0.96/1.61 class_Rings_Odivision__ring__inverse__zero [177, 1] (w:1, o:154, a:1
% 0.96/1.61 , s:1, b:0),
% 0.96/1.61 class_Fields_Ofield__inverse__zero [182, 1] (w:1, o:121, a:1, s:1, b:
% 0.96/1.61 0),
% 0.96/1.61 c_Divides_Odiv__class_Omod [183, 3] (w:1, o:251, a:1, s:1, b:0),
% 0.96/1.61 c_Polynomial_OAbs__poly [184, 2] (w:1, o:218, a:1, s:1, b:0),
% 0.96/1.61 c_Orderings_Oord__class_Oless [185, 3] (w:1, o:236, a:1, s:1, b:0),
% 0.96/1.61 class_Groups_Oordered__ab__semigroup__add__imp__le [186, 1] (w:1, o:
% 0.96/1.61 175, a:1, s:1, b:0),
% 0.96/1.61 class_Groups_Oordered__cancel__ab__semigroup__add [187, 1] (w:1, o:
% 0.96/1.61 176, a:1, s:1, b:0),
% 0.96/1.61 class_Groups_Oordered__ab__group__add [188, 1] (w:1, o:177, a:1, s:1
% 0.96/1.61 , b:0),
% 0.96/1.61 class_Rings_Olinordered__idom [192, 1] (w:1, o:140, a:1, s:1, b:0),
% 0.96/1.61 class_Rings_Olinordered__semidom [194, 1] (w:1, o:142, a:1, s:1, b:0)
% 0.96/1.61 ,
% 0.96/1.61 class_Rings_Olinordered__comm__semiring__strict [195, 1] (w:1, o:143
% 0.96/1.61 , a:1, s:1, b:0),
% 0.96/1.61 class_Rings_Olinordered__semiring__strict [196, 1] (w:1, o:144, a:1
% 0.96/1.61 , s:1, b:0),
% 0.96/1.61 class_Rings_Olinordered__ring [197, 1] (w:1, o:141, a:1, s:1, b:0),
% 0.96/1.61 class_Groups_Oordered__comm__monoid__add [198, 1] (w:1, o:178, a:1
% 2.76/3.11 , s:1, b:0),
% 2.76/3.11 class_Fields_Olinordered__field [199, 1] (w:1, o:122, a:1, s:1, b:0)
% 2.76/3.11 ,
% 2.76/3.11 class_Fields_Olinordered__field__inverse__zero [200, 1] (w:1, o:123
% 2.76/3.11 , a:1, s:1, b:0),
% 2.76/3.11 class_Rings_Oordered__ring [205, 1] (w:1, o:155, a:1, s:1, b:0),
% 2.76/3.11 class_Divides_Osemiring__div [207, 1] (w:1, o:180, a:1, s:1, b:0),
% 2.76/3.11 class_Divides_Oring__div [210, 1] (w:1, o:179, a:1, s:1, b:0),
% 2.76/3.11 c_Rings_Oinverse__class_Odivide [211, 3] (w:1, o:252, a:1, s:1, b:0)
% 2.76/3.11 ,
% 2.76/3.11 c_Polynomial_Opdivmod__rel [213, 5] (w:1, o:321, a:1, s:1, b:0),
% 2.76/3.11 class_RealVector_Oreal__normed__field [214, 1] (w:1, o:156, a:1, s:1
% 2.76/3.11 , b:0),
% 2.76/3.11 class_RealVector_Oreal__field [219, 1] (w:1, o:157, a:1, s:1, b:0),
% 2.76/3.11 c_Polynomial_Opos__poly [222, 2] (w:1, o:219, a:1, s:1, b:0),
% 2.76/3.11 c_Divides_Odiv__class_Odiv [223, 3] (w:1, o:253, a:1, s:1, b:0),
% 2.76/3.11 c_Groups_Oabs__class_Oabs [224, 2] (w:1, o:220, a:1, s:1, b:0),
% 2.76/3.11 class_Groups_Oordered__ab__group__add__abs [225, 1] (w:1, o:181, a:1
% 2.76/3.11 , s:1, b:0),
% 2.76/3.11 class_Groups_Oabs__if [226, 1] (w:1, o:182, a:1, s:1, b:0),
% 2.76/3.11 c_Groups_Osgn__class_Osgn [227, 2] (w:1, o:221, a:1, s:1, b:0),
% 2.76/3.11 class_RealVector_Oreal__normed__vector [228, 1] (w:1, o:158, a:1, s:1
% 2.76/3.11 , b:0),
% 2.76/3.11 class_Groups_Osgn__if [229, 1] (w:1, o:183, a:1, s:1, b:0),
% 2.76/3.11 class_RealVector_Oreal__normed__div__algebra [230, 1] (w:1, o:159, a:
% 2.76/3.11 1, s:1, b:0),
% 2.76/3.11 class_RealVector_Oreal__normed__algebra__1 [231, 1] (w:1, o:160, a:1
% 2.76/3.11 , s:1, b:0),
% 2.76/3.11 c_Orderings_Oord__class_Oless__eq [232, 3] (w:1, o:237, a:1, s:1, b:0
% 2.76/3.11 ),
% 2.76/3.11 class_Rings_Olinordered__semiring [233, 1] (w:1, o:145, a:1, s:1, b:0
% 2.76/3.11 ),
% 2.76/3.11 class_Groups_Ocancel__comm__monoid__add [235, 1] (w:1, o:184, a:1, s:
% 2.76/3.11 1, b:0),
% 2.76/3.11 alpha1 [237, 2] (w:1, o:222, a:1, s:1, b:1),
% 2.76/3.11 alpha2 [238, 2] (w:1, o:223, a:1, s:1, b:1),
% 2.76/3.11 alpha3 [239, 3] (w:1, o:256, a:1, s:1, b:1),
% 2.76/3.11 alpha4 [240, 2] (w:1, o:224, a:1, s:1, b:1),
% 2.76/3.11 alpha5 [241, 2] (w:1, o:225, a:1, s:1, b:1),
% 2.76/3.11 alpha6 [242, 4] (w:1, o:299, a:1, s:1, b:1),
% 2.76/3.11 alpha7 [243, 4] (w:1, o:300, a:1, s:1, b:1),
% 2.76/3.11 alpha8 [244, 2] (w:1, o:226, a:1, s:1, b:1),
% 2.76/3.11 alpha9 [245, 3] (w:1, o:257, a:1, s:1, b:1),
% 2.76/3.11 alpha10 [246, 3] (w:1, o:258, a:1, s:1, b:1),
% 2.76/3.11 alpha11 [247, 3] (w:1, o:259, a:1, s:1, b:1),
% 2.76/3.11 alpha12 [248, 3] (w:1, o:260, a:1, s:1, b:1),
% 2.76/3.11 alpha13 [249, 3] (w:1, o:261, a:1, s:1, b:1),
% 2.76/3.11 alpha14 [250, 3] (w:1, o:262, a:1, s:1, b:1),
% 2.76/3.11 alpha15 [251, 3] (w:1, o:263, a:1, s:1, b:1),
% 2.76/3.11 alpha16 [252, 3] (w:1, o:264, a:1, s:1, b:1),
% 2.76/3.11 alpha17 [253, 3] (w:1, o:265, a:1, s:1, b:1),
% 2.76/3.11 alpha18 [254, 3] (w:1, o:266, a:1, s:1, b:1),
% 2.76/3.11 alpha19 [255, 3] (w:1, o:267, a:1, s:1, b:1),
% 2.76/3.11 alpha20 [256, 2] (w:1, o:227, a:1, s:1, b:1),
% 2.76/3.11 alpha21 [257, 4] (w:1, o:301, a:1, s:1, b:1),
% 2.76/3.11 alpha22 [258, 4] (w:1, o:302, a:1, s:1, b:1),
% 2.76/3.11 alpha23 [259, 2] (w:1, o:228, a:1, s:1, b:1),
% 2.76/3.11 alpha24 [260, 2] (w:1, o:229, a:1, s:1, b:1),
% 2.76/3.11 alpha25 [261, 4] (w:1, o:303, a:1, s:1, b:1),
% 2.76/3.11 alpha26 [262, 4] (w:1, o:304, a:1, s:1, b:1),
% 2.76/3.11 alpha27 [263, 4] (w:1, o:305, a:1, s:1, b:1),
% 2.76/3.11 alpha28 [264, 3] (w:1, o:254, a:1, s:1, b:1),
% 2.76/3.11 alpha29 [265, 3] (w:1, o:255, a:1, s:1, b:1),
% 2.76/3.11 alpha30 [266, 3] (w:1, o:268, a:1, s:1, b:1),
% 2.76/3.11 alpha31 [267, 3] (w:1, o:269, a:1, s:1, b:1),
% 2.76/3.11 alpha32 [268, 3] (w:1, o:270, a:1, s:1, b:1),
% 2.76/3.11 alpha33 [269, 3] (w:1, o:271, a:1, s:1, b:1),
% 2.76/3.11 alpha34 [270, 4] (w:1, o:306, a:1, s:1, b:1),
% 2.76/3.11 alpha35 [271, 4] (w:1, o:307, a:1, s:1, b:1),
% 2.76/3.11 alpha36 [272, 4] (w:1, o:308, a:1, s:1, b:1),
% 2.76/3.11 alpha37 [273, 4] (w:1, o:309, a:1, s:1, b:1),
% 2.76/3.11 alpha38 [274, 3] (w:1, o:272, a:1, s:1, b:1),
% 2.76/3.11 alpha39 [275, 4] (w:1, o:310, a:1, s:1, b:1),
% 2.76/3.11 alpha40 [276, 4] (w:1, o:311, a:1, s:1, b:1),
% 2.76/3.11 alpha41 [277, 3] (w:1, o:273, a:1, s:1, b:1),
% 2.76/3.11 alpha42 [278, 4] (w:1, o:312, a:1, s:1, b:1),
% 2.76/3.11 alpha43 [279, 3] (w:1, o:274, a:1, s:1, b:1),
% 2.76/3.11 alpha44 [280, 4] (w:1, o:313, a:1, s:1, b:1),
% 23.36/23.71 alpha45 [281, 4] (w:1, o:314, a:1, s:1, b:1),
% 23.36/23.71 alpha46 [282, 3] (w:1, o:275, a:1, s:1, b:1),
% 23.36/23.71 alpha47 [283, 4] (w:1, o:315, a:1, s:1, b:1),
% 23.36/23.71 alpha48 [284, 4] (w:1, o:316, a:1, s:1, b:1),
% 23.36/23.71 alpha49 [285, 4] (w:1, o:317, a:1, s:1, b:1),
% 23.36/23.71 alpha50 [286, 4] (w:1, o:293, a:1, s:1, b:1),
% 23.36/23.71 alpha51 [287, 4] (w:1, o:294, a:1, s:1, b:1),
% 23.36/23.71 alpha52 [288, 4] (w:1, o:295, a:1, s:1, b:1),
% 23.36/23.71 alpha53 [289, 3] (w:1, o:276, a:1, s:1, b:1),
% 23.36/23.71 alpha54 [290, 3] (w:1, o:277, a:1, s:1, b:1),
% 23.36/23.71 alpha55 [291, 2] (w:1, o:230, a:1, s:1, b:1),
% 23.36/23.71 alpha56 [292, 4] (w:1, o:296, a:1, s:1, b:1),
% 23.36/23.71 alpha57 [293, 3] (w:1, o:278, a:1, s:1, b:1),
% 23.36/23.71 alpha58 [294, 4] (w:1, o:297, a:1, s:1, b:1),
% 23.36/23.71 alpha59 [295, 4] (w:1, o:298, a:1, s:1, b:1),
% 23.36/23.71 skol1 [296, 2] (w:1, o:231, a:1, s:1, b:1),
% 23.36/23.71 skol2 [297, 0] (w:1, o:14, a:1, s:1, b:1),
% 23.36/23.71 skol3 [298, 0] (w:1, o:17, a:1, s:1, b:1),
% 23.36/23.71 skol4 [299, 0] (w:1, o:18, a:1, s:1, b:1),
% 23.36/23.71 skol5 [300, 3] (w:1, o:279, a:1, s:1, b:1),
% 23.36/23.71 skol6 [301, 3] (w:1, o:280, a:1, s:1, b:1),
% 23.36/23.71 skol7 [302, 4] (w:1, o:318, a:1, s:1, b:1),
% 23.36/23.71 skol8 [303, 2] (w:1, o:232, a:1, s:1, b:1),
% 23.36/23.71 skol9 [304, 1] (w:1, o:115, a:1, s:1, b:1),
% 23.36/23.71 skol10 [305, 2] (w:1, o:233, a:1, s:1, b:1),
% 23.36/23.71 skol11 [306, 3] (w:1, o:281, a:1, s:1, b:1),
% 23.36/23.71 skol12 [307, 3] (w:1, o:282, a:1, s:1, b:1),
% 23.36/23.71 skol13 [308, 2] (w:1, o:234, a:1, s:1, b:1),
% 23.36/23.71 skol14 [309, 2] (w:1, o:235, a:1, s:1, b:1),
% 23.36/23.71 skol15 [310, 3] (w:1, o:283, a:1, s:1, b:1),
% 23.36/23.71 skol16 [311, 3] (w:1, o:284, a:1, s:1, b:1),
% 23.36/23.71 skol17 [312, 3] (w:1, o:285, a:1, s:1, b:1),
% 23.36/23.71 skol18 [313, 4] (w:1, o:319, a:1, s:1, b:1),
% 23.36/23.71 skol19 [314, 3] (w:1, o:286, a:1, s:1, b:1),
% 23.36/23.71 skol20 [315, 3] (w:1, o:287, a:1, s:1, b:1),
% 23.36/23.71 skol21 [316, 3] (w:1, o:288, a:1, s:1, b:1),
% 23.36/23.71 skol22 [317, 0] (w:1, o:15, a:1, s:1, b:1),
% 23.36/23.71 skol23 [318, 3] (w:1, o:289, a:1, s:1, b:1),
% 23.36/23.71 skol24 [319, 3] (w:1, o:290, a:1, s:1, b:1),
% 23.36/23.71 skol25 [320, 3] (w:1, o:291, a:1, s:1, b:1),
% 23.36/23.71 skol26 [321, 0] (w:1, o:16, a:1, s:1, b:1).
% 23.36/23.71
% 23.36/23.71
% 23.36/23.71 Starting Search:
% 23.36/23.71
% 23.36/23.71 *** allocated 170857 integers for clauses
% 23.36/23.71 Resimplifying inuse:
% 23.36/23.71 Done
% 23.36/23.71
% 23.36/23.71
% 23.36/23.71 Intermediate Status:
% 23.36/23.71 Generated: 2925
% 23.36/23.71 Kept: 2000
% 23.36/23.71 Inuse: 68
% 23.36/23.71 Deleted: 12
% 23.36/23.71 Deletedinuse: 0
% 23.36/23.71
% 23.36/23.71 *** allocated 256285 integers for clauses
% 23.36/23.71 Resimplifying inuse:
% 23.36/23.71 Done
% 23.36/23.71
% 23.36/23.71 *** allocated 170857 integers for termspace/termends
% 23.36/23.71 Resimplifying inuse:
% 23.36/23.71 Done
% 23.36/23.71
% 23.36/23.71 *** allocated 384427 integers for clauses
% 23.36/23.71
% 23.36/23.71 Intermediate Status:
% 23.36/23.71 Generated: 10909
% 23.36/23.71 Kept: 4283
% 23.36/23.71 Inuse: 193
% 23.36/23.71 Deleted: 28
% 23.36/23.71 Deletedinuse: 0
% 23.36/23.71
% 23.36/23.71 Resimplifying inuse:
% 23.36/23.71 Done
% 23.36/23.71
% 23.36/23.71 *** allocated 256285 integers for termspace/termends
% 23.36/23.71 Resimplifying inuse:
% 23.36/23.71 Done
% 23.36/23.71
% 23.36/23.71
% 23.36/23.71 Intermediate Status:
% 23.36/23.71 Generated: 19555
% 23.36/23.71 Kept: 6311
% 23.36/23.71 Inuse: 252
% 23.36/23.71 Deleted: 29
% 23.36/23.71 Deletedinuse: 0
% 23.36/23.71
% 23.36/23.71 *** allocated 576640 integers for clauses
% 23.36/23.71 Resimplifying inuse:
% 23.36/23.71 Done
% 23.36/23.71
% 23.36/23.71 Resimplifying inuse:
% 23.36/23.71 Done
% 23.36/23.71
% 23.36/23.71
% 23.36/23.71 Intermediate Status:
% 23.36/23.71 Generated: 29818
% 23.36/23.71 Kept: 8346
% 23.36/23.71 Inuse: 299
% 23.36/23.71 Deleted: 32
% 23.36/23.71 Deletedinuse: 0
% 23.36/23.71
% 23.36/23.71 Resimplifying inuse:
% 23.36/23.71 Done
% 23.36/23.71
% 23.36/23.71 Resimplifying inuse:
% 23.36/23.71 Done
% 23.36/23.71
% 23.36/23.71 *** allocated 384427 integers for termspace/termends
% 23.36/23.71
% 23.36/23.71 Intermediate Status:
% 23.36/23.71 Generated: 38262
% 23.36/23.71 Kept: 10395
% 23.36/23.71 Inuse: 334
% 23.36/23.71 Deleted: 32
% 23.36/23.71 Deletedinuse: 0
% 23.36/23.71
% 23.36/23.71 *** allocated 864960 integers for clauses
% 23.36/23.71 Resimplifying inuse:
% 23.36/23.71 Done
% 23.36/23.71
% 23.36/23.71
% 23.36/23.71 Intermediate Status:
% 23.36/23.71 Generated: 47857
% 23.36/23.71 Kept: 12832
% 23.36/23.71 Inuse: 354
% 23.36/23.71 Deleted: 32
% 23.36/23.71 Deletedinuse: 0
% 23.36/23.71
% 23.36/23.71 Resimplifying inuse:
% 23.36/23.71 Done
% 23.36/23.71
% 23.36/23.71 Resimplifying inuse:
% 23.36/23.71 Done
% 23.36/23.71
% 23.36/23.71
% 23.36/23.71 Intermediate Status:
% 23.36/23.71 Generated: 52925
% 23.36/23.71 Kept: 15131
% 23.36/23.71 Inuse: 374
% 23.36/23.71 Deleted: 32
% 23.36/23.71 Deletedinuse: 0
% 23.36/23.71
% 23.36/23.71 Resimplifying inuse:
% 23.36/23.71 Done
% 23.36/23.71
% 23.36/23.71 Resimplifying inuse:
% 23.36/23.71 Done
% 23.36/23.71
% 23.36/23.71
% 23.36/23.71 Intermediate Status:
% 23.36/23.71 Generated: 57763
% 23.36/23.71 Kept: 17134
% 23.36/23.71 Inuse: 415
% 23.36/23.71 Deleted: 35
% 23.36/23.71 Deletedinuse: 0
% 23.36/23.71
% 23.36/23.71 *** allocated 576640 integers for termspace/termends
% 23.36/23.71 Resimplifying inuse:
% 23.36/23.71 Done
% 23.36/23.71
% 23.36/23.71 *** allocated 1297440 integers for clauses
% 23.36/23.71 Resimplifying inuse:
% 23.36/23.71 Done
% 23.36/23.71
% 23.36/23.71
% 23.36/23.71 Intermediate Status:
% 23.36/23.71 Generated: 63683
% 23.36/23.71 Kept: 19225
% 23.36/23.71 Inuse: 449
% 23.36/23.71 Deleted: 37
% 23.36/23.71 Deletedinuse: 0
% 79.79/80.17
% 79.79/80.17 Resimplifying inuse:
% 79.79/80.17 Done
% 79.79/80.17
% 79.79/80.17 Resimplifying clauses:
% 79.79/80.17 Done
% 79.79/80.17
% 79.79/80.17
% 79.79/80.17 Intermediate Status:
% 79.79/80.17 Generated: 85234
% 79.79/80.17 Kept: 22074
% 79.79/80.17 Inuse: 469
% 79.79/80.17 Deleted: 229
% 79.79/80.17 Deletedinuse: 0
% 79.79/80.17
% 79.79/80.17 Resimplifying inuse:
% 79.79/80.17 Done
% 79.79/80.17
% 79.79/80.17 *** allocated 864960 integers for termspace/termends
% 79.79/80.17 Resimplifying inuse:
% 79.79/80.17 Done
% 79.79/80.17
% 79.79/80.17
% 79.79/80.17 Intermediate Status:
% 79.79/80.17 Generated: 93837
% 79.79/80.17 Kept: 24133
% 79.79/80.17 Inuse: 484
% 79.79/80.17 Deleted: 229
% 79.79/80.17 Deletedinuse: 0
% 79.79/80.17
% 79.79/80.17 Resimplifying inuse:
% 79.79/80.17 Done
% 79.79/80.17
% 79.79/80.17 Resimplifying inuse:
% 79.79/80.17 Done
% 79.79/80.17
% 79.79/80.17
% 79.79/80.17 Intermediate Status:
% 79.79/80.17 Generated: 100939
% 79.79/80.17 Kept: 26166
% 79.79/80.17 Inuse: 512
% 79.79/80.17 Deleted: 229
% 79.79/80.17 Deletedinuse: 0
% 79.79/80.17
% 79.79/80.17 Resimplifying inuse:
% 79.79/80.17 Done
% 79.79/80.17
% 79.79/80.17 *** allocated 1946160 integers for clauses
% 79.79/80.17 Resimplifying inuse:
% 79.79/80.17 Done
% 79.79/80.17
% 79.79/80.17
% 79.79/80.17 Intermediate Status:
% 79.79/80.17 Generated: 111284
% 79.79/80.17 Kept: 28205
% 79.79/80.17 Inuse: 548
% 79.79/80.17 Deleted: 229
% 79.79/80.17 Deletedinuse: 0
% 79.79/80.17
% 79.79/80.17 Resimplifying inuse:
% 79.79/80.17 Done
% 79.79/80.17
% 79.79/80.17
% 79.79/80.17 Intermediate Status:
% 79.79/80.17 Generated: 119995
% 79.79/80.17 Kept: 30241
% 79.79/80.17 Inuse: 576
% 79.79/80.17 Deleted: 229
% 79.79/80.17 Deletedinuse: 0
% 79.79/80.17
% 79.79/80.17 Resimplifying inuse:
% 79.79/80.17 Done
% 79.79/80.17
% 79.79/80.17
% 79.79/80.17 Intermediate Status:
% 79.79/80.17 Generated: 126069
% 79.79/80.17 Kept: 32446
% 79.79/80.17 Inuse: 594
% 79.79/80.17 Deleted: 229
% 79.79/80.17 Deletedinuse: 0
% 79.79/80.17
% 79.79/80.17 Resimplifying inuse:
% 79.79/80.17 Done
% 79.79/80.17
% 79.79/80.17 *** allocated 1297440 integers for termspace/termends
% 79.79/80.17
% 79.79/80.17 Intermediate Status:
% 79.79/80.17 Generated: 151906
% 79.79/80.17 Kept: 34982
% 79.79/80.17 Inuse: 609
% 79.79/80.17 Deleted: 229
% 79.79/80.17 Deletedinuse: 0
% 79.79/80.17
% 79.79/80.17 Resimplifying inuse:
% 79.79/80.17 Done
% 79.79/80.17
% 79.79/80.17 Resimplifying inuse:
% 79.79/80.17 Done
% 79.79/80.17
% 79.79/80.17
% 79.79/80.17 Intermediate Status:
% 79.79/80.17 Generated: 163772
% 79.79/80.17 Kept: 37600
% 79.79/80.17 Inuse: 629
% 79.79/80.17 Deleted: 229
% 79.79/80.17 Deletedinuse: 0
% 79.79/80.17
% 79.79/80.17 Resimplifying inuse:
% 79.79/80.17 Done
% 79.79/80.17
% 79.79/80.17 Resimplifying inuse:
% 79.79/80.17 Done
% 79.79/80.17
% 79.79/80.17
% 79.79/80.17 Intermediate Status:
% 79.79/80.17 Generated: 176084
% 79.79/80.17 Kept: 40461
% 79.79/80.17 Inuse: 652
% 79.79/80.17 Deleted: 229
% 79.79/80.17 Deletedinuse: 0
% 79.79/80.17
% 79.79/80.17 Resimplifying inuse:
% 79.79/80.17 Done
% 79.79/80.17
% 79.79/80.17 Resimplifying clauses:
% 79.79/80.17 Done
% 79.79/80.17
% 79.79/80.17 Resimplifying inuse:
% 79.79/80.17 Done
% 79.79/80.17
% 79.79/80.17 *** allocated 2919240 integers for clauses
% 79.79/80.17
% 79.79/80.17 Intermediate Status:
% 79.79/80.17 Generated: 189508
% 79.79/80.17 Kept: 43199
% 79.79/80.17 Inuse: 689
% 79.79/80.17 Deleted: 350
% 79.79/80.17 Deletedinuse: 0
% 79.79/80.17
% 79.79/80.17 Resimplifying inuse:
% 79.79/80.17 Done
% 79.79/80.17
% 79.79/80.17 Resimplifying inuse:
% 79.79/80.17 Done
% 79.79/80.17
% 79.79/80.17
% 79.79/80.17 Intermediate Status:
% 79.79/80.17 Generated: 201756
% 79.79/80.17 Kept: 45640
% 79.79/80.17 Inuse: 699
% 79.79/80.17 Deleted: 350
% 79.79/80.17 Deletedinuse: 0
% 79.79/80.17
% 79.79/80.17 Resimplifying inuse:
% 79.79/80.17 Done
% 79.79/80.17
% 79.79/80.17 Resimplifying inuse:
% 79.79/80.17 Done
% 79.79/80.17
% 79.79/80.17
% 79.79/80.17 Intermediate Status:
% 79.79/80.17 Generated: 219208
% 79.79/80.17 Kept: 47642
% 79.79/80.17 Inuse: 723
% 79.79/80.17 Deleted: 350
% 79.79/80.17 Deletedinuse: 0
% 79.79/80.17
% 79.79/80.17 Resimplifying inuse:
% 79.79/80.17 Done
% 79.79/80.17
% 79.79/80.17 *** allocated 1946160 integers for termspace/termends
% 79.79/80.17
% 79.79/80.17 Intermediate Status:
% 79.79/80.17 Generated: 237017
% 79.79/80.17 Kept: 49745
% 79.79/80.17 Inuse: 739
% 79.79/80.17 Deleted: 350
% 79.79/80.17 Deletedinuse: 0
% 79.79/80.17
% 79.79/80.17 Resimplifying inuse:
% 79.79/80.17 Done
% 79.79/80.17
% 79.79/80.17
% 79.79/80.17 Intermediate Status:
% 79.79/80.17 Generated: 245705
% 79.79/80.17 Kept: 52069
% 79.79/80.17 Inuse: 769
% 79.79/80.17 Deleted: 350
% 79.79/80.17 Deletedinuse: 0
% 79.79/80.17
% 79.79/80.17 Resimplifying inuse:
% 79.79/80.17 Done
% 79.79/80.17
% 79.79/80.17 Resimplifying inuse:
% 79.79/80.17 Done
% 79.79/80.17
% 79.79/80.17
% 79.79/80.17 Intermediate Status:
% 79.79/80.17 Generated: 254720
% 79.79/80.17 Kept: 54119
% 79.79/80.17 Inuse: 804
% 79.79/80.17 Deleted: 350
% 79.79/80.17 Deletedinuse: 0
% 79.79/80.17
% 79.79/80.17 Resimplifying inuse:
% 79.79/80.17 Done
% 79.79/80.17
% 79.79/80.17 Resimplifying inuse:
% 79.79/80.17 Done
% 79.79/80.17
% 79.79/80.17
% 79.79/80.17 Intermediate Status:
% 79.79/80.17 Generated: 263608
% 79.79/80.17 Kept: 56262
% 79.79/80.17 Inuse: 834
% 79.79/80.17 Deleted: 350
% 79.79/80.17 Deletedinuse: 0
% 79.79/80.17
% 79.79/80.17 Resimplifying inuse:
% 79.79/80.17 Done
% 79.79/80.17
% 79.79/80.17 Resimplifying inuse:
% 79.79/80.17 Done
% 79.79/80.17
% 79.79/80.17
% 79.79/80.17 Intermediate Status:
% 79.79/80.17 Generated: 274221
% 79.79/80.17 Kept: 58332
% 79.79/80.17 Inuse: 874
% 79.79/80.17 Deleted: 350
% 79.79/80.17 Deletedinuse: 0
% 79.79/80.17
% 79.79/80.17 Resimplifying inuse:
% 79.79/80.17 Done
% 79.79/80.17
% 79.79/80.17 Resimplifying inuse:
% 79.79/80.17 Done
% 79.79/80.17
% 79.79/80.17
% 79.79/80.17 Intermediate Status:
% 79.79/80.17 Generated: 285834
% 79.79/80.17 Kept: 61750
% 79.79/80.17 Inuse: 904
% 79.79/80.17 Deleted: 350
% 79.79/80.17 Deletedinuse: 0
% 79.79/80.17
% 79.79/80.17 Resimplifying inuse:
% 79.79/80.17 Done
% 79.79/80.17
% 79.79/80.17 Resimplifying clauses:
% 79.79/80.17 Done
% 79.79/80.17
% 79.79/80.17
% 79.79/80.17 Intermediate Status:
% 79.79/80.17 Generated: 290785
% 79.79/80.17 Kept: 63804
% 79.79/80.17 Inuse: 909
% 79.79/80.17 Deleted: 444
% 79.79/80.17 Deletedinuse: 0
% 79.79/80.17
% 79.79/80.17 Resimplifying inuse:
% 79.79/80.17 Done
% 79.79/80.17
% 79.79/80.17 *** allocated 4378860 integers for clauses
% 79.79/80.17 Resimplifying inuse:
% 79.79/80.17 Done
% 79.79/80.17
% 79.79/80.17
% 79.79/80.17 Intermediate Status:
% 79.79/80.17 Generated: 302733
% 79.79/80.17 Kept: 66066
% 79.79/80.17 Inuse: 944
% 79.79/80.17 Deleted: 444
% 79.79/80.17 Deletedinuse: 0
% 79.79/80.17
% 79.79/80.17 Resimplifying inuse:
% 79.79/80.17 Done
% 79.79/80.17
% 79.79/80.17
% 79.79/80.17 Intermediate Status:
% 79.79/80.17 Generated: 323672
% 79.79/80.17 Kept: 68710
% 79.79/80.17 Inuse: 959
% 79.79/80.17 Deleted: 444
% 79.79/80.17 Deletedinuse: 0
% 79.79/80.17
% 79.79/80.17 Resimplifying inuse:
% 79.79/80.17 Done
% 79.79/80.17
% 79.79/80.17 Resimplifying inuse:
% 79.79/80.17 Done
% 79.79/80.17
% 79.79/80.17
% 79.79/80.17 Intermediate Status:
% 79.79/80.17 Generated: 336680
% 79.79/80.17 Kept: 71309
% 79.79/80.17 Inuse: 989
% 79.79/80.17 Deleted: 444
% 79.79/80.17 Deletedinuse: 0
% 79.79/80.17
% 79.79/80.17 Resimplifying inuse:
% 79.79/80.17 Done
% 79.79/80.17
% 79.79/80.17 *** allocated 2919240 integers for termspace/termends
% 79.79/80.17 Resimplifying inuse:
% 79.79/80.17 Done
% 79.79/80.17
% 79.79/80.17
% 79.79/80.17 Intermediate Status:
% 79.79/80.17 Generated: 346546
% 79.79/80.17 Kept: 73368
% 79.79/80.17 Inuse: 1009
% 79.79/80.17 Deleted: 444
% 183.38/183.88 Deletedinuse: 0
% 183.38/183.88
% 183.38/183.88 Resimplifying inuse:
% 183.38/183.88 Done
% 183.38/183.88
% 183.38/183.88
% 183.38/183.88 Intermediate Status:
% 183.38/183.88 Generated: 366112
% 183.38/183.88 Kept: 75699
% 183.38/183.88 Inuse: 1024
% 183.38/183.88 Deleted: 444
% 183.38/183.88 Deletedinuse: 0
% 183.38/183.88
% 183.38/183.88 Resimplifying inuse:
% 183.38/183.88 Done
% 183.38/183.88
% 183.38/183.88 Resimplifying inuse:
% 183.38/183.88 Done
% 183.38/183.88
% 183.38/183.88
% 183.38/183.88 Intermediate Status:
% 183.38/183.88 Generated: 375752
% 183.38/183.88 Kept: 77704
% 183.38/183.88 Inuse: 1044
% 183.38/183.88 Deleted: 444
% 183.38/183.88 Deletedinuse: 0
% 183.38/183.88
% 183.38/183.88 Resimplifying inuse:
% 183.38/183.88 Done
% 183.38/183.88
% 183.38/183.88
% 183.38/183.88 Intermediate Status:
% 183.38/183.88 Generated: 385239
% 183.38/183.88 Kept: 79769
% 183.38/183.88 Inuse: 1064
% 183.38/183.88 Deleted: 444
% 183.38/183.88 Deletedinuse: 0
% 183.38/183.88
% 183.38/183.88 Resimplifying inuse:
% 183.38/183.88 Done
% 183.38/183.88
% 183.38/183.88
% 183.38/183.88 Intermediate Status:
% 183.38/183.88 Generated: 398218
% 183.38/183.88 Kept: 82113
% 183.38/183.88 Inuse: 1074
% 183.38/183.88 Deleted: 444
% 183.38/183.88 Deletedinuse: 0
% 183.38/183.88
% 183.38/183.88 Resimplifying inuse:
% 183.38/183.88 Done
% 183.38/183.88
% 183.38/183.88 Resimplifying clauses:
% 183.38/183.88 Done
% 183.38/183.88
% 183.38/183.88 Resimplifying inuse:
% 183.38/183.88 Done
% 183.38/183.88
% 183.38/183.88
% 183.38/183.88 Intermediate Status:
% 183.38/183.88 Generated: 409109
% 183.38/183.88 Kept: 84533
% 183.38/183.88 Inuse: 1089
% 183.38/183.88 Deleted: 599
% 183.38/183.88 Deletedinuse: 0
% 183.38/183.88
% 183.38/183.88 Resimplifying inuse:
% 183.38/183.88 Done
% 183.38/183.88
% 183.38/183.88
% 183.38/183.88 Intermediate Status:
% 183.38/183.88 Generated: 419448
% 183.38/183.88 Kept: 87123
% 183.38/183.88 Inuse: 1114
% 183.38/183.88 Deleted: 599
% 183.38/183.88 Deletedinuse: 0
% 183.38/183.88
% 183.38/183.88 Resimplifying inuse:
% 183.38/183.88 Done
% 183.38/183.88
% 183.38/183.88 Resimplifying inuse:
% 183.38/183.88 Done
% 183.38/183.88
% 183.38/183.88
% 183.38/183.88 Intermediate Status:
% 183.38/183.88 Generated: 428860
% 183.38/183.88 Kept: 89132
% 183.38/183.88 Inuse: 1134
% 183.38/183.88 Deleted: 599
% 183.38/183.88 Deletedinuse: 0
% 183.38/183.88
% 183.38/183.88 Resimplifying inuse:
% 183.38/183.88 Done
% 183.38/183.88
% 183.38/183.88 Resimplifying inuse:
% 183.38/183.88 Done
% 183.38/183.88
% 183.38/183.88
% 183.38/183.88 Intermediate Status:
% 183.38/183.88 Generated: 439040
% 183.38/183.88 Kept: 91143
% 183.38/183.88 Inuse: 1160
% 183.38/183.88 Deleted: 599
% 183.38/183.88 Deletedinuse: 0
% 183.38/183.88
% 183.38/183.88 Resimplifying inuse:
% 183.38/183.88 Done
% 183.38/183.88
% 183.38/183.88
% 183.38/183.88 Intermediate Status:
% 183.38/183.88 Generated: 450476
% 183.38/183.88 Kept: 93153
% 183.38/183.88 Inuse: 1170
% 183.38/183.88 Deleted: 599
% 183.38/183.88 Deletedinuse: 0
% 183.38/183.88
% 183.38/183.88 *** allocated 6568290 integers for clauses
% 183.38/183.88
% 183.38/183.88 Intermediate Status:
% 183.38/183.88 Generated: 463372
% 183.38/183.88 Kept: 96211
% 183.38/183.88 Inuse: 1179
% 183.38/183.88 Deleted: 599
% 183.38/183.88 Deletedinuse: 0
% 183.38/183.88
% 183.38/183.88 Resimplifying inuse:
% 183.38/183.88 Done
% 183.38/183.88
% 183.38/183.88 Resimplifying inuse:
% 183.38/183.88 Done
% 183.38/183.88
% 183.38/183.88
% 183.38/183.88 Intermediate Status:
% 183.38/183.88 Generated: 480921
% 183.38/183.88 Kept: 99435
% 183.38/183.88 Inuse: 1199
% 183.38/183.88 Deleted: 599
% 183.38/183.88 Deletedinuse: 0
% 183.38/183.88
% 183.38/183.88 Resimplifying inuse:
% 183.38/183.88 Done
% 183.38/183.88
% 183.38/183.88 Resimplifying inuse:
% 183.38/183.88 Done
% 183.38/183.88
% 183.38/183.88
% 183.38/183.88 Intermediate Status:
% 183.38/183.88 Generated: 496878
% 183.38/183.88 Kept: 102484
% 183.38/183.88 Inuse: 1219
% 183.38/183.88 Deleted: 599
% 183.38/183.88 Deletedinuse: 0
% 183.38/183.88
% 183.38/183.88 Resimplifying inuse:
% 183.38/183.88 Done
% 183.38/183.88
% 183.38/183.88 Resimplifying clauses:
% 183.38/183.88 Done
% 183.38/183.88
% 183.38/183.88 *** allocated 4378860 integers for termspace/termends
% 183.38/183.88
% 183.38/183.88 Intermediate Status:
% 183.38/183.88 Generated: 510362
% 183.38/183.88 Kept: 105745
% 183.38/183.88 Inuse: 1229
% 183.38/183.88 Deleted: 743
% 183.38/183.88 Deletedinuse: 0
% 183.38/183.88
% 183.38/183.88 Resimplifying inuse:
% 183.38/183.88 Done
% 183.38/183.88
% 183.38/183.88
% 183.38/183.88 Intermediate Status:
% 183.38/183.88 Generated: 521242
% 183.38/183.88 Kept: 109099
% 183.38/183.88 Inuse: 1239
% 183.38/183.88 Deleted: 743
% 183.38/183.88 Deletedinuse: 0
% 183.38/183.88
% 183.38/183.88 Resimplifying inuse:
% 183.38/183.88 Done
% 183.38/183.88
% 183.38/183.88
% 183.38/183.88 Intermediate Status:
% 183.38/183.88 Generated: 528840
% 183.38/183.88 Kept: 112400
% 183.38/183.88 Inuse: 1249
% 183.38/183.88 Deleted: 743
% 183.38/183.88 Deletedinuse: 0
% 183.38/183.88
% 183.38/183.88 Resimplifying inuse:
% 183.38/183.88 Done
% 183.38/183.88
% 183.38/183.88
% 183.38/183.88 Intermediate Status:
% 183.38/183.88 Generated: 536966
% 183.38/183.88 Kept: 116042
% 183.38/183.88 Inuse: 1259
% 183.38/183.88 Deleted: 743
% 183.38/183.88 Deletedinuse: 0
% 183.38/183.88
% 183.38/183.88 Resimplifying inuse:
% 183.38/183.88 Done
% 183.38/183.88
% 183.38/183.88
% 183.38/183.88 Intermediate Status:
% 183.38/183.88 Generated: 568755
% 183.38/183.88 Kept: 120067
% 183.38/183.88 Inuse: 1274
% 183.38/183.88 Deleted: 743
% 183.38/183.88 Deletedinuse: 0
% 183.38/183.88
% 183.38/183.88 Resimplifying inuse:
% 183.38/183.88 Done
% 183.38/183.88
% 183.38/183.88 Resimplifying inuse:
% 183.38/183.88 Done
% 183.38/183.88
% 183.38/183.88
% 183.38/183.88 Intermediate Status:
% 183.38/183.88 Generated: 579444
% 183.38/183.88 Kept: 122244
% 183.38/183.88 Inuse: 1294
% 183.38/183.88 Deleted: 743
% 183.38/183.88 Deletedinuse: 0
% 183.38/183.88
% 183.38/183.88 Resimplifying inuse:
% 183.38/183.88 Done
% 183.38/183.88
% 183.38/183.88 Resimplifying clauses:
% 183.38/183.88 Done
% 183.38/183.88
% 183.38/183.88 Resimplifying inuse:
% 183.38/183.88 Done
% 183.38/183.88
% 183.38/183.88
% 183.38/183.88 Intermediate Status:
% 183.38/183.88 Generated: 588724
% 183.38/183.88 Kept: 124265
% 183.38/183.88 Inuse: 1324
% 183.38/183.88 Deleted: 839
% 183.38/183.88 Deletedinuse: 0
% 183.38/183.88
% 183.38/183.88 Resimplifying inuse:
% 183.38/183.88 Done
% 183.38/183.88
% 183.38/183.88
% 183.38/183.88 Intermediate Status:
% 183.38/183.88 Generated: 595957
% 183.38/183.88 Kept: 126274
% 183.38/183.88 Inuse: 1337
% 183.38/183.88 Deleted: 839
% 183.38/183.88 Deletedinuse: 0
% 183.38/183.88
% 183.38/183.88
% 183.38/183.88 Intermediate Status:
% 183.38/183.88 Generated: 610484
% 183.38/183.88 Kept: 128525
% 183.38/183.88 Inuse: 1354
% 183.38/183.88 Deleted: 839
% 183.38/183.88 Deletedinuse: 0
% 183.38/183.88
% 183.38/183.88 Resimplifying inuse:
% 183.38/183.88 Done
% 183.38/183.88
% 183.38/183.88
% 183.38/183.88 Intermediate Status:
% 183.38/183.88 Generated: 627951
% 183.38/183.88 Kept: 131379
% 183.38/183.88 Inuse: 1363
% 183.38/183.88 Deleted: 841
% 183.38/183.88 Deletedinuse: 1
% 183.38/183.88
% 183.38/183.88 Resimplifying inuse:
% 183.38/183.88 Done
% 183.38/183.88
% 183.38/183.88 Resimplifying inuse:
% 183.38/183.88 Done
% 183.38/183.88
% 183.38/183.88
% 183.38/183.88 Intermediate Status:
% 183.38/183.88 Generated: 639478
% 183.38/183.88 Kept: 133763
% 183.38/183.88 Inuse: 1387
% 183.38/183.88 Deleted: 842
% 183.38/183.88 Deletedinuse: 1
% 183.38/183.88
% 183.38/183.88 Resimplifying inuse:
% 183.38/183.88 Done
% 183.38/183.88
% 183.38/183.88
% 183.38/183.88 Intermediate Status:
% 183.38/183.88 Generated: 650055
% 183.38/183.88 Kept: 136829
% 183.38/183.88 Inuse: 1402
% 183.38/183.88 Deleted: 842
% 183.38/183.88 Deletedinuse: 1
% 183.38/183.88
% 183.38/183.88 Resimplifying inuse:
% 183.38/183.88 Done
% 183.38/183.88
% 183.38/183.88
% 183.38/183.88 Intermediate Status:
% 183.38/183.88 Generated: 661240
% 183.38/183.88 Kept: 139624
% 183.38/183.88 Inuse: 1417
% 183.38/183.88 Deleted: 842
% 183.38/183.88 Deletedinuse: 1
% 183.38/183.88
% 183.38/183.88 Resimplifying inuse:
% 183.38/183.88 Done
% 183.38/183.88
% 183.38/183.88 Resimplifying inuse:
% 183.38/183.88 Done
% 183.38/183.88
% 183.38/183.88
% 183.38/183.88 Intermediate Status:
% 183.38/183.88 GCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------