TSTP Solution File: SWW255+1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWW255+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Wed Jul 20 23:21:36 EDT 2022
% Result : Timeout 300.02s 300.50s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWW255+1 : TPTP v8.1.0. Released v5.2.0.
% 0.11/0.12 % Command : bliksem %s
% 0.12/0.34 % Computer : n025.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % DateTime : Sun Jun 5 06:52:47 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.99/1.49 *** allocated 10000 integers for termspace/termends
% 0.99/1.49 *** allocated 10000 integers for clauses
% 0.99/1.49 *** allocated 10000 integers for justifications
% 0.99/1.49 *** allocated 15000 integers for termspace/termends
% 0.99/1.49 *** allocated 22500 integers for termspace/termends
% 0.99/1.49 *** allocated 33750 integers for termspace/termends
% 0.99/1.49 Bliksem 1.12
% 0.99/1.49
% 0.99/1.49
% 0.99/1.49 Automatic Strategy Selection
% 0.99/1.49
% 0.99/1.49 *** allocated 50625 integers for termspace/termends
% 0.99/1.49 *** allocated 75937 integers for termspace/termends
% 0.99/1.49 *** allocated 113905 integers for termspace/termends
% 0.99/1.49
% 0.99/1.49 Clauses:
% 0.99/1.49
% 0.99/1.49 { ! hAPP( Y, skol1( X, Y ) ) = hAPP( X, skol1( X, Y ) ), Y = X }.
% 0.99/1.49 { v_s____ = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.99/1.49 tc_Complex_Ocomplex ) ) }.
% 0.99/1.49 { ! v_a____ = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.99/1.49 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(
% 0.99/1.49 tc_Complex_Ocomplex, tc_Complex_Ocomplex, c_Polynomial_Opoly(
% 0.99/1.49 tc_Complex_Ocomplex, v_p ) ) }.
% 0.99/1.49 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 0.99/1.49 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 0.99/1.49 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 0.99/1.49 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 0.99/1.49 v_q____ ) ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) =
% 0.99/1.49 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) }.
% 0.99/1.49 { ! hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 0.99/1.49 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) =
% 0.99/1.49 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.99/1.49 { ! v_k____ = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.49 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ), X ) = hAPP(
% 0.99/1.49 hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP(
% 0.99/1.49 c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 0.99/1.49 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 0.99/1.49 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 0.99/1.49 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 0.99/1.49 v_q____ ) ), X ) ), hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 0.99/1.49 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ) }.
% 0.99/1.49 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 0.99/1.49 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) = hAPP( hAPP(
% 0.99/1.49 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP(
% 0.99/1.49 c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 0.99/1.49 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 0.99/1.49 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 0.99/1.49 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 0.99/1.49 v_q____ ) ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ), hAPP
% 0.99/1.49 ( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 0.99/1.49 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ) }.
% 0.99/1.49 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(
% 0.99/1.49 tc_Complex_Ocomplex, tc_Complex_Ocomplex, c_Polynomial_Opoly(
% 0.99/1.49 tc_Complex_Ocomplex, v_q____ ) ) }.
% 0.99/1.49 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(
% 0.99/1.49 tc_Complex_Ocomplex, tc_Complex_Ocomplex, c_Polynomial_Opoly(
% 0.99/1.49 tc_Complex_Ocomplex, v_q____ ) ) }.
% 0.99/1.49 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(
% 0.99/1.49 tc_Complex_Ocomplex, tc_Complex_Ocomplex, c_Polynomial_Opoly(
% 0.99/1.49 tc_Complex_Ocomplex, c_Polynomial_Osmult( tc_Complex_Ocomplex,
% 0.99/1.49 c_Rings_Oinverse__class_Oinverse( tc_Complex_Ocomplex, hAPP(
% 0.99/1.49 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 0.99/1.49 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ), v_q____ ) ) ) }.
% 0.99/1.49 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 0.99/1.49 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 0.99/1.49 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 0.99/1.49 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 0.99/1.49 v_q____ ) ), v_w____ ) = c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex
% 0.99/1.49 , hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 0.99/1.49 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 0.99/1.49 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 0.99/1.49 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 0.99/1.49 v_q____ ) ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ), hAPP(
% 0.99/1.49 hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP( hAPP(
% 0.99/1.49 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), v_w____ ), v_k____ )
% 0.99/1.49 ), hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_OpCons(
% 0.99/1.49 tc_Complex_Ocomplex, v_a____, v_s____ ) ), v_w____ ) ) ) }.
% 0.99/1.49 { c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex,
% 0.99/1.49 v_q____ ) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(
% 0.99/1.49 tc_Complex_Ocomplex, c_Polynomial_Osmult( tc_Complex_Ocomplex,
% 0.99/1.49 c_Rings_Oinverse__class_Oinverse( tc_Complex_Ocomplex, hAPP(
% 0.99/1.49 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 0.99/1.49 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ), v_q____ ) ) }.
% 0.99/1.49 { c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex,
% 0.99/1.49 c_Polynomial_Osmult( tc_Complex_Ocomplex,
% 0.99/1.49 c_Rings_Oinverse__class_Oinverse( tc_Complex_Ocomplex, hAPP(
% 0.99/1.49 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 0.99/1.49 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ), v_q____ ) ) =
% 0.99/1.49 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex,
% 0.99/1.49 v_q____ ) }.
% 0.99/1.49 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 0.99/1.49 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 0.99/1.49 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 0.99/1.49 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 0.99/1.49 v_q____ ) ), X ) = c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, hAPP
% 0.99/1.49 ( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 0.99/1.49 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 0.99/1.49 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 0.99/1.49 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 0.99/1.49 v_q____ ) ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ), hAPP(
% 0.99/1.49 hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP( hAPP(
% 0.99/1.49 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), X ), v_k____ ) ),
% 0.99/1.49 hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_OpCons(
% 0.99/1.49 tc_Complex_Ocomplex, v_a____, v_s____ ) ), X ) ) ) }.
% 0.99/1.49 { ! hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 0.99/1.49 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 0.99/1.49 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 0.99/1.49 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 0.99/1.49 v_q____ ) ), skol2 ) = hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 0.99/1.49 c_Polynomial_Osmult( tc_Complex_Ocomplex,
% 0.99/1.49 c_Rings_Oinverse__class_Oinverse( tc_Complex_Ocomplex, hAPP(
% 0.99/1.49 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 0.99/1.49 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ), v_q____ ) ),
% 0.99/1.49 skol50 ) }.
% 0.99/1.49 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.99/1.49 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ),
% 0.99/1.49 c_Rings_Oinverse__class_Oinverse( X, Y ) ) = c_Groups_Oone__class_Oone( X
% 0.99/1.49 ) }.
% 0.99/1.49 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP(
% 0.99/1.49 hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.99/1.49 c_Rings_Oinverse__class_Oinverse( X, Y ) ), Y ) =
% 0.99/1.49 c_Groups_Oone__class_Oone( X ) }.
% 0.99/1.49 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.99/1.49 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.99/1.49 c_Rings_Oinverse__class_Oinverse( X, Y ) ), Y ) =
% 0.99/1.49 c_Groups_Oone__class_Oone( X ) }.
% 0.99/1.49 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.99/1.49 , Z = c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.99/1.49 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.99/1.49 c_Rings_Oinverse__class_Oinverse( X, Z ) ) = hAPP( hAPP(
% 0.99/1.49 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.49 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 0.99/1.49 Y ) ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) ),
% 0.99/1.49 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.99/1.49 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.99/1.49 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.99/1.49 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.99/1.49 c_Rings_Oinverse__class_Oinverse( X, Z ) ) = hAPP( hAPP(
% 0.99/1.49 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.49 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.99/1.49 ) ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) ),
% 0.99/1.49 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.99/1.49 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.99/1.49 c_Polynomial_Osmult( X, T, Z ) ), Y ) = hAPP( hAPP(
% 0.99/1.49 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( c_Polynomial_Opoly( X, Z )
% 0.99/1.49 , Y ) ) }.
% 0.99/1.49 { ! class_RealVector_Oreal__normed__div__algebra( X ), Y =
% 0.99/1.49 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X,
% 0.99/1.49 c_Rings_Oinverse__class_Oinverse( X, Y ) ) =
% 0.99/1.49 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal,
% 0.99/1.49 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 0.99/1.49 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.99/1.49 , c_Rings_Oinverse__class_Oinverse( X, hAPP( hAPP(
% 0.99/1.49 c_Power_Opower__class_Opower( X ), Y ), Z ) ) = hAPP( hAPP(
% 0.99/1.49 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Oinverse( X, Y
% 0.99/1.49 ) ), Z ) }.
% 0.99/1.49 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.49 tc_Nat_Onat, c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(
% 0.99/1.49 tc_Complex_Ocomplex, v_s____ ), v_k____ ), c_Groups_Oone__class_Oone(
% 0.99/1.49 tc_Nat_Onat ) ) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(
% 0.99/1.49 tc_Complex_Ocomplex, c_Polynomial_Osmult( tc_Complex_Ocomplex,
% 0.99/1.49 c_Rings_Oinverse__class_Oinverse( tc_Complex_Ocomplex, hAPP(
% 0.99/1.49 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 0.99/1.49 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ), v_q____ ) ) }.
% 0.99/1.49 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(
% 0.99/1.49 tc_Complex_Ocomplex, tc_Complex_Ocomplex, c_Polynomial_Opoly(
% 0.99/1.49 tc_Complex_Ocomplex, v_pa____ ) ) }.
% 0.99/1.49 { c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex,
% 0.99/1.49 v_q____ ) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(
% 0.99/1.49 tc_Complex_Ocomplex, v_pa____ ) }.
% 0.99/1.49 { c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex,
% 0.99/1.49 v_pa____ ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, v_k____,
% 0.99/1.49 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.99/1.49 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oone__class_Oone(
% 0.99/1.49 tc_Polynomial_Opoly( X ) ) = c_Polynomial_OpCons( X,
% 0.99/1.49 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.99/1.49 tc_Polynomial_Opoly( X ) ) ) }.
% 0.99/1.49 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.99/1.49 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.99/1.49 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.99/1.49 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.49 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.99/1.49 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.99/1.49 tc_Polynomial_Opoly( X ) ), Y ) = Y }.
% 0.99/1.49 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.99/1.49 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 0.99/1.49 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.99/1.49 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.49 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.99/1.49 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 0.99/1.49 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.99/1.49 { ! class_Groups_Ozero( X ), !
% 0.99/1.49 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.99/1.49 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.99/1.49 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.49 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.99/1.49 tc_Polynomial_Opoly( X ) ),
% 0.99/1.49 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.99/1.49 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.49 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 0.99/1.49 c_Polynomial_OpCons( X, Z, Y ), U = Z }.
% 0.99/1.49 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 0.99/1.49 c_Polynomial_OpCons( X, Z, Y ), T = Y }.
% 0.99/1.49 { ! class_Groups_Ozero( X ), ! U = Z, ! T = Y, c_Polynomial_OpCons( X, U, T
% 0.99/1.49 ) = c_Polynomial_OpCons( X, Z, Y ) }.
% 0.99/1.49 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Osmult( X, T, Y ) =
% 0.99/1.49 c_Polynomial_OpCons( X, Z, Y ), Y = c_Groups_Ozero__class_Ozero(
% 0.99/1.49 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.49 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 0.99/1.49 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 0.99/1.49 c_Polynomial_OpCons( X, Z, Y ) ) = c_Groups_Ozero__class_Ozero(
% 0.99/1.49 tc_Polynomial_Opoly( X ) ), Y = c_Groups_Ozero__class_Ozero(
% 0.99/1.49 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.49 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.99/1.49 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.99/1.49 c_Polynomial_OpCons( X, T, Z ) ), Y ) = c_Groups_Oplus__class_Oplus(
% 0.99/1.49 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 0.99/1.49 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.99/1.49 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y ) ) ) }
% 0.99/1.49 .
% 0.99/1.49 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.99/1.49 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ),
% 0.99/1.49 c_Polynomial_OpCons( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus(
% 0.99/1.49 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, Z, T ),
% 0.99/1.49 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.99/1.49 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ) ) ) }
% 0.99/1.49 .
% 0.99/1.49 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 0.99/1.49 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.99/1.49 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.49 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 0.99/1.49 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y =
% 0.99/1.49 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.49 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 0.99/1.49 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.99/1.49 c_Polynomial_OpCons( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.99/1.49 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.49 { ! class_Groups_Ozero( X ), c_Polynomial_OpCons( X,
% 0.99/1.49 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero(
% 0.99/1.49 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 0.99/1.49 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.49 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.99/1.49 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, U, T ),
% 0.99/1.49 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 0.99/1.49 c_Groups_Oplus__class_Oplus( X, U, Z ), c_Groups_Oplus__class_Oplus(
% 0.99/1.49 tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 0.99/1.49 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.99/1.49 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.99/1.49 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.49 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.99/1.49 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) }.
% 0.99/1.49 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.99/1.49 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.99/1.49 tc_Nat_Onat ) ) = Y }.
% 0.99/1.49 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 0.99/1.49 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Z, Y ) ) =
% 0.99/1.49 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ),
% 0.99/1.49 c_Polynomial_Osmult( X, T, Z ), c_Polynomial_Osmult( X, T, Y ) ) }.
% 0.99/1.49 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.99/1.49 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.99/1.49 c_Polynomial_Osmult( X, T, Z ) ), Y ) = c_Polynomial_Osmult( X, T, hAPP(
% 0.99/1.49 hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y )
% 0.99/1.49 ) }.
% 0.99/1.49 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.99/1.49 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ),
% 0.99/1.49 c_Polynomial_Osmult( X, Z, Y ) ) = c_Polynomial_Osmult( X, Z, hAPP( hAPP
% 0.99/1.49 ( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ) ) }
% 0.99/1.49 .
% 0.99/1.49 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 0.99/1.49 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 0.99/1.49 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y =
% 0.99/1.49 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.49 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Y =
% 0.99/1.49 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.99/1.49 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 0.99/1.49 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.99/1.49 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, Y,
% 0.99/1.49 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.99/1.49 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.49 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( Z, Y, X ), hAPP(
% 0.99/1.49 X, T ) = hAPP( X, U ) }.
% 0.99/1.49 { ! hAPP( X, skol3( X ) ) = hAPP( X, skol51( X ) ),
% 0.99/1.49 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( Z, Y, X ) }.
% 0.99/1.49 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 0.99/1.49 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X, hAPP( hAPP(
% 0.99/1.49 c_Groups_Otimes__class_Otimes( X ), T ), Z ), c_Polynomial_Osmult( X, T,
% 0.99/1.49 Y ) ) }.
% 0.99/1.49 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.99/1.49 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 0.99/1.49 tc_Nat_Onat, Z, Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.99/1.49 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.99/1.49 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.99/1.49 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.99/1.49 , Y ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.99/1.49 c_Groups_Oone__class_Oone( X ) }.
% 0.99/1.49 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.99/1.49 c_Polynomial_OpCons( X, T, Z ) ), Y ) = c_Groups_Oplus__class_Oplus( X, T
% 0.99/1.49 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), hAPP(
% 0.99/1.49 c_Polynomial_Opoly( X, Z ), Y ) ) ) }.
% 0.99/1.49 { ! class_Rings_Odivision__ring__inverse__zero( X ), !
% 0.99/1.49 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 0.99/1.49 c_Rings_Oinverse__class_Oinverse( X, Y ), Z = Y }.
% 0.99/1.49 { ! class_Rings_Odivision__ring__inverse__zero( X ), !
% 0.99/1.49 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 0.99/1.49 c_Rings_Oinverse__class_Oinverse( X, Y ), Z = Y }.
% 0.99/1.49 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Z = Y,
% 0.99/1.49 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 0.99/1.49 c_Rings_Oinverse__class_Oinverse( X, Y ) }.
% 0.99/1.49 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 0.99/1.49 c_Rings_Oinverse__class_Oinverse( X, c_Rings_Oinverse__class_Oinverse( X
% 0.99/1.49 , Y ) ) = Y }.
% 0.99/1.49 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 0.99/1.49 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ), Z = Y }.
% 0.99/1.49 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Z = Y,
% 0.99/1.49 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ) }.
% 0.99/1.49 { ! class_Rings_Ono__zero__divisors( X ), ! hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.50 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.50 { ! class_Rings_Ono__zero__divisors( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.99/1.50 X ), Z = c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.50 { ! class_Rings_Oring__no__zero__divisors( X ), ! hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.50 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.50 { ! class_Rings_Oring__no__zero__divisors( X ), ! Z =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.50 { ! class_Rings_Oring__no__zero__divisors( X ), ! Y =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.50 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.99/1.50 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.50 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.99/1.50 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.50 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.50 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.50 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.99/1.50 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.50 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.99/1.50 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.50 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.50 ( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.50 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.99/1.50 c_Groups_Oone__class_Oone( X ) }.
% 0.99/1.50 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Oone__class_Oone( X ) =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.50 { ! class_Rings_Osemiring( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP
% 0.99/1.50 ( c_Groups_Otimes__class_Otimes( X ), U ), T ),
% 0.99/1.50 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.50 ( X ), Z ), T ), Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, U, Z
% 0.99/1.50 ) ), T ), Y ) }.
% 0.99/1.50 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.99/1.50 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.50 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.99/1.50 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.50 { ! class_Rings_Ocomm__semiring( X ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.99/1.50 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.50 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.99/1.50 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.99/1.50 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.99/1.50 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.99/1.50 { ! class_Rings_Oring__1__no__zero__divisors( X ), Y =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.99/1.50 c_Power_Opower__class_Opower( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 0.99/1.50 ( X ) }.
% 0.99/1.50 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.99/1.50 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.99/1.50 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.99/1.50 .
% 0.99/1.50 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.99/1.50 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.99/1.50 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.99/1.50 tc_Nat_Onat ) }.
% 0.99/1.50 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.99/1.50 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.99/1.50 , ! Z = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 0.99/1.50 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y )
% 0.99/1.50 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.50 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.99/1.50 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.50 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.99/1.50 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.99/1.50 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.50 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.99/1.50 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.99/1.50 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.99/1.50 c_Power_Opower__class_Opower( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.99/1.50 = c_Groups_Oone__class_Oone( X ) }.
% 0.99/1.50 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.99/1.50 c_RealVector_Onorm__class_Onorm( X, Y ) = c_Groups_Ozero__class_Ozero(
% 0.99/1.50 tc_RealDef_Oreal ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.50 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X, Y )
% 0.99/1.50 = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.99/1.50 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.99/1.50 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.99/1.50 { ! class_Rings_Odivision__ring( X ), ! c_Rings_Oinverse__class_Oinverse( X
% 0.99/1.50 , Z ) = c_Rings_Oinverse__class_Oinverse( X, Y ), Z =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z
% 0.99/1.50 = Y }.
% 0.99/1.50 { ! class_Rings_Odivision__ring( X ), ! c_Rings_Oinverse__class_Oinverse( X
% 0.99/1.50 , Y ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 0.99/1.50 ( X ) }.
% 0.99/1.50 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.99/1.50 , c_Rings_Oinverse__class_Oinverse( X, c_Rings_Oinverse__class_Oinverse(
% 0.99/1.50 X, Y ) ) = Y }.
% 0.99/1.50 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.99/1.50 , ! c_Rings_Oinverse__class_Oinverse( X, Y ) =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.50 { ! class_Rings_Odivision__ring__inverse__zero( X ), !
% 0.99/1.50 c_Rings_Oinverse__class_Oinverse( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.99/1.50 ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.50 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Y =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X, Y
% 0.99/1.50 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.50 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 0.99/1.50 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.50 { ! class_Fields_Ofield__inverse__zero( X ),
% 0.99/1.50 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.50 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 0.99/1.50 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.99/1.50 c_RealVector_Onorm__class_Onorm( X, Z ) ),
% 0.99/1.50 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 0.99/1.50 { ! class_Fields_Ofield__inverse__zero( X ),
% 0.99/1.50 c_Rings_Oinverse__class_Oinverse( X, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 0.99/1.50 Z ) ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.99/1.50 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 0.99/1.50 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oone__class_Oone( X ) ) =
% 0.99/1.50 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.99/1.50 { ! class_Fields_Ofield__inverse__zero( X ), !
% 0.99/1.50 c_Rings_Oinverse__class_Oinverse( X, Y ) = c_Groups_Oone__class_Oone( X )
% 0.99/1.50 , Y = c_Groups_Oone__class_Oone( X ) }.
% 0.99/1.50 { ! class_Fields_Ofield__inverse__zero( X ), ! Y =
% 0.99/1.50 c_Groups_Oone__class_Oone( X ), c_Rings_Oinverse__class_Oinverse( X, Y )
% 0.99/1.50 = c_Groups_Oone__class_Oone( X ) }.
% 0.99/1.50 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Oinverse( X,
% 0.99/1.50 c_Groups_Oone__class_Oone( X ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.99/1.50 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 0.99/1.50 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.99/1.50 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.50 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.99/1.50 c_RealVector_Onorm__class_Onorm( X, Z ) ), Y ) }.
% 0.99/1.50 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.50 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 0.99/1.50 c_Rings_Oinverse__class_Oinverse( X, hAPP( hAPP(
% 0.99/1.50 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.50 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Oinverse( X, Z
% 0.99/1.50 ) ), Y ) }.
% 0.99/1.50 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 0.99/1.50 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Z
% 0.99/1.50 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP(
% 0.99/1.50 c_Polynomial_Opoly( X, T ), Y ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 0.99/1.50 ) }.
% 0.99/1.50 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.99/1.50 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.99/1.50 c_Groups_Oplus__class_Oplus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 0.99/1.50 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.99/1.50 { ! class_Rings_Oidom( X ), ! c_Polynomial_Osmult( X, Z, Y ) =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.99/1.50 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.50 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.50 c_Polynomial_Osmult( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.99/1.50 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.50 { ! class_Rings_Oidom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.99/1.50 tc_Polynomial_Opoly( X ) ), c_Polynomial_Osmult( X, Z, Y ) =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.50 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 0.99/1.50 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.50 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 0.99/1.50 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.99/1.50 c_Groups_Oone__class_Oone( X ) }.
% 0.99/1.50 { ! class_RealVector_Oreal__normed__div__algebra( X ), !
% 0.99/1.50 class_Rings_Odivision__ring__inverse__zero( X ),
% 0.99/1.50 c_RealVector_Onorm__class_Onorm( X, c_Rings_Oinverse__class_Oinverse( X,
% 0.99/1.50 Y ) ) = c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal,
% 0.99/1.50 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 0.99/1.50 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 0.99/1.50 c_Polynomial_Osmult( X, Z, Y ) ) = c_Polynomial_Osmult( X, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 0.99/1.50 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 0.99/1.50 ( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), T ), Z
% 0.99/1.50 ) ), Y ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), hAPP(
% 0.99/1.50 c_Polynomial_Opoly( X, T ), Y ) ), Z ) }.
% 0.99/1.50 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X,
% 0.99/1.50 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.99/1.50 ( tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 0.99/1.50 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 0.99/1.50 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Osmult( X,
% 0.99/1.50 c_Groups_Oone__class_Oone( X ), Y ) = Y }.
% 0.99/1.50 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), ! Y =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.50 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.99/1.50 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.99/1.50 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), Y =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.50 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.99/1.50 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.50 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.99/1.50 , Z = c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse
% 0.99/1.50 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP(
% 0.99/1.50 hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.99/1.50 c_Rings_Oinverse__class_Oinverse( X, Z ) ),
% 0.99/1.50 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.99/1.50 { ! class_Rings_Odivision__ring( X ), ! hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = c_Groups_Oone__class_Oone
% 0.99/1.50 ( X ), c_Rings_Oinverse__class_Oinverse( X, Z ) = Y }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.50 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.99/1.50 c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 0.99/1.50 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 0.99/1.50 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 0.99/1.50 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 0.99/1.50 v_q____ ) ), X ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.99/1.50 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.50 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.99/1.50 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ), X ) ),
% 0.99/1.50 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.99/1.50 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ) ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.50 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.99/1.50 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ), X ) ),
% 0.99/1.50 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.99/1.50 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ) ),
% 0.99/1.50 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.50 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.99/1.50 c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 0.99/1.50 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 0.99/1.50 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 0.99/1.50 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 0.99/1.50 v_q____ ) ), X ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.99/1.50 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.50 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ozero__class_Ozero(
% 0.99/1.50 tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.99/1.50 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.99/1.50 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = hAPP(
% 0.99/1.50 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X
% 0.99/1.50 , Z, c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.99/1.50 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.99/1.50 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP
% 0.99/1.50 ( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.99/1.50 c_Groups_Oone__class_Oone( X ) ) ), Z ) }.
% 0.99/1.50 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.99/1.50 , Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.99/1.50 c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.99/1.50 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.99/1.50 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.99/1.50 ( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! W = U, T = Z, !
% 0.99/1.50 c_Groups_Oplus__class_Oplus( X, W, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) =
% 0.99/1.50 c_Groups_Oplus__class_Oplus( X, U, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.99/1.50 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.50 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.99/1.50 ) = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X
% 0.99/1.50 ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.99/1.50 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.50 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.99/1.50 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.99/1.50 ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.99/1.50 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.50 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 0.99/1.50 tc_Polynomial_Opoly( X ) ), ! c_Polynomial_Oorder( X, Y, Z ) =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.50 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.99/1.50 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.50 { ! class_Rings_Oidom( X ), c_Polynomial_Oorder( X, Y, Z ) =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( c_Polynomial_Opoly( X,
% 0.99/1.50 Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.50 { ! class_Power_Opower( X ), c_Power_Opower__class_Opower( X ) =
% 0.99/1.50 c_Power_Opower_Opower( X, c_Groups_Oone__class_Oone( X ),
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ) ) }.
% 0.99/1.50 { ! skol4 = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.99/1.50 { ! skol52 = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.50 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.50 tc_Nat_Onat, c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(
% 0.99/1.50 tc_Complex_Ocomplex, skol63 ), skol52 ), c_Groups_Oone__class_Oone(
% 0.99/1.50 tc_Nat_Onat ) ) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(
% 0.99/1.50 tc_Complex_Ocomplex, c_Polynomial_Osmult( tc_Complex_Ocomplex,
% 0.99/1.50 c_Rings_Oinverse__class_Oinverse( tc_Complex_Ocomplex, hAPP(
% 0.99/1.50 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ), v_q____ ) ) }.
% 0.99/1.50 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 0.99/1.50 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 0.99/1.50 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 0.99/1.50 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 0.99/1.50 v_q____ ) ), X ) = c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, hAPP
% 0.99/1.50 ( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 0.99/1.50 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 0.99/1.50 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 0.99/1.50 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 0.99/1.50 v_q____ ) ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ), hAPP(
% 0.99/1.50 hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP( hAPP(
% 0.99/1.50 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), X ), skol52 ) ),
% 0.99/1.50 hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_OpCons(
% 0.99/1.50 tc_Complex_Ocomplex, skol4, skol63 ) ), X ) ) ) }.
% 0.99/1.50 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ), X ) = hAPP(
% 0.99/1.50 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ),
% 0.99/1.50 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, v_c____, X ) ) }.
% 0.99/1.50 { ! hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), v_c____ ) =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.99/1.50 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), v_c____ ) =
% 0.99/1.50 hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) }.
% 0.99/1.50 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.50 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.99/1.50 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), v_c____ ) ),
% 0.99/1.50 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.99/1.50 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), X ) ) ) }.
% 0.99/1.50 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.99/1.50 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.99/1.50 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ), hAPP
% 0.99/1.50 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y
% 0.99/1.50 ) ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__idom( X ), Z = Y,
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.99/1.50 X, Y, Z ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.50 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.99/1.50 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.99/1.50 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.99/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.50 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.99/1.50 ( tc_Nat_Onat, T, Z ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.50 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.99/1.50 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.50 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.99/1.50 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.99/1.50 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.99/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.50 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.99/1.50 c_Groups_Oone__class_Oone( X ), T ), c_Orderings_Oord__class_Oless( X,
% 0.99/1.50 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.50 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.99/1.50 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.50 c_RealVector_Onorm__class_Onorm( X, Y ), c_Groups_Ozero__class_Ozero(
% 0.99/1.50 tc_RealDef_Oreal ) ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.50 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 0.99/1.50 , T, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.99/1.50 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.99/1.50 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.50 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.99/1.50 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), hAPP(
% 0.99/1.50 hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.99/1.50 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.50 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.50 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.99/1.50 ) ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__ring__strict( X ), Z =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.99/1.50 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__ring__strict( X ), Y =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.99/1.50 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.99/1.50 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha1( X, Y, Z, T ),
% 0.99/1.50 alpha12( X, Y, Z, T ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha1( X, Y, Z, T ),
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha12( X, Y, Z, T ),
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.99/1.50 { ! alpha12( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.50 { ! alpha12( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, T ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.50 , ! c_Orderings_Oord__class_Oless( X, Y, T ), alpha12( X, Y, Z, T ) }.
% 0.99/1.50 { ! alpha1( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.99/1.50 { ! alpha1( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.99/1.50 , ! c_Orderings_Oord__class_Oless( X, T, Y ), alpha1( X, Y, Z, T ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha2( X, Y, Z, T ),
% 0.99/1.50 alpha13( X, Y, Z, T ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha2( X, Y, Z, T ),
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha13( X, Y, Z, T ),
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.99/1.50 { ! alpha13( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.50 { ! alpha13( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( X, T, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.50 , ! c_Orderings_Oord__class_Oless( X, Y, Z ), alpha13( X, Y, Z, T ) }.
% 0.99/1.50 { ! alpha2( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ), T ) }.
% 0.99/1.50 { ! alpha2( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T )
% 0.99/1.50 , ! c_Orderings_Oord__class_Oless( X, Z, Y ), alpha2( X, Y, Z, T ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.99/1.50 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.99/1.50 ! c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless
% 0.99/1.50 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.99/1.50 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.99/1.50 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.99/1.50 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.50 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.99/1.50 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.50 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.99/1.50 ( X ) ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.99/1.50 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.50 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.99/1.50 ( X ) ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.99/1.50 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.99/1.50 .
% 0.99/1.50 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.99/1.50 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ) }
% 0.99/1.50 .
% 0.99/1.50 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.50 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.50 ! c_Orderings_Oord__class_Oless( X, Z, T ), c_Orderings_Oord__class_Oless
% 0.99/1.50 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.99/1.50 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.50 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.99/1.50 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.99/1.50 ( X ) ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.50 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.50 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.50 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.99/1.50 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.99/1.50 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP
% 0.99/1.50 ( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.99/1.50 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.99/1.50 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.99/1.50 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__comm__semiring__strict( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.99/1.50 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.99/1.50 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.99/1.50 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.99/1.50 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.99/1.50 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.99/1.50 ( c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.99/1.50 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.99/1.50 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP
% 0.99/1.50 ( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.50 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless(
% 0.99/1.50 X, T, c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.50 ( X, c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero( X ) ) }
% 0.99/1.50 .
% 0.99/1.50 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.99/1.50 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.50 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.99/1.50 ( X, c_Groups_Oone__class_Oone( X ), Z ), c_Orderings_Oord__class_Oless(
% 0.99/1.50 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.50 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless
% 0.99/1.50 ( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.99/1.50 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.99/1.50 , Y, c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) )
% 0.99/1.50 ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.50 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! hAPP( hAPP(
% 0.99/1.50 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 0.99/1.50 c_Power_Opower__class_Opower( X ), Y ), Z ), T = Z }.
% 0.99/1.50 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.50 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! T = Z, hAPP( hAPP(
% 0.99/1.50 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 0.99/1.50 c_Power_Opower__class_Opower( X ), Y ), Z ) }.
% 0.99/1.50 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.50 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.99/1.50 ( X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.99/1.50 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.50 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.99/1.50 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 0.99/1.50 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.99/1.50 , Y, c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.50 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 0.99/1.50 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.50 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.99/1.50 X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.99/1.50 X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X
% 0.99/1.50 , Y ) ) }.
% 0.99/1.50 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.99/1.50 X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X
% 0.99/1.50 , Y ) ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.99/1.50 .
% 0.99/1.50 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.99/1.50 X, Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless(
% 0.99/1.50 X, c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Ozero__class_Ozero
% 0.99/1.50 ( X ) ) }.
% 0.99/1.50 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.99/1.50 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless( X,
% 0.99/1.50 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.99/1.50 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.99/1.50 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.99/1.50 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.99/1.50 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.99/1.50 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.99/1.50 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.99/1.50 X, c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Ozero__class_Ozero
% 0.99/1.50 ( X ) ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.99/1.50 .
% 0.99/1.50 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.99/1.50 X, c_Rings_Oinverse__class_Oinverse( X, Z ),
% 0.99/1.50 c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.99/1.50 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.99/1.50 X, c_Rings_Oinverse__class_Oinverse( X, Z ),
% 0.99/1.50 c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.99/1.50 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.99/1.50 c_RealVector_Onorm__class_Onorm( X, Y ) ), ! Y =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.50 { ! class_RealVector_Oreal__normed__vector( X ), Y =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless(
% 0.99/1.50 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.99/1.50 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 0.99/1.50 { ! class_RealVector_Oreal__normed__algebra( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.50 c_RealVector_Onorm__class_Onorm( X, Z ), Y ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.50 c_RealVector_Onorm__class_Onorm( X, U ), T ),
% 0.99/1.50 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.50 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), T ) ) }.
% 0.99/1.50 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.50 c_RealVector_Onorm__class_Onorm( X, Z ), Y ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.50 c_RealVector_Onorm__class_Onorm( X, U ), T ),
% 0.99/1.50 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.50 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, Z, U
% 0.99/1.50 ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, T ) ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.99/1.50 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.99/1.50 c_Groups_Oone__class_Oone( X ), c_Groups_Oone__class_Oone( X ) ) ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.50 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.99/1.50 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.99/1.50 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.50 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.99/1.50 X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.99/1.50 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.99/1.50 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 0.99/1.50 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.99/1.50 ( X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.99/1.50 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 0.99/1.50 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.99/1.50 ( X, Y, c_Groups_Oone__class_Oone( X ) ) }.
% 0.99/1.50 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.99/1.50 ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 0.99/1.50 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.99/1.50 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.99/1.50 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.99/1.50 ( X, Y, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless(
% 0.99/1.50 X, c_Groups_Oone__class_Oone( X ), c_Rings_Oinverse__class_Oinverse( X, Y
% 0.99/1.50 ) ) }.
% 0.99/1.50 { hAPP( hAPP( c_Power_Opower_Opower( T, Z, Y ), X ),
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = Z }.
% 0.99/1.50 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 0.99/1.50 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.99/1.50 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) }.
% 0.99/1.50 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.50 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Z ) }.
% 0.99/1.50 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), U ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 0.99/1.50 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), Y ) ) }.
% 0.99/1.50 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.99/1.50 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.99/1.50 , Y ) = c_Groups_Oplus__class_Oplus( X, Y, Z ) }.
% 0.99/1.50 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.99/1.50 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.99/1.50 ( X, Z, c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.99/1.50 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.99/1.50 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.99/1.50 ( X, c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) }.
% 0.99/1.50 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.99/1.50 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.99/1.50 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.99/1.50 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.99/1.50 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.99/1.50 ( X, c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 0.99/1.50 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.99/1.50 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.99/1.50 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X
% 0.99/1.50 , U, Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.99/1.50 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.50 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.99/1.50 tc_Nat_Onat ) ) = Y }.
% 0.99/1.50 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.50 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.99/1.50 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.99/1.50 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.50 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.99/1.50 c_Power_Opower__class_Opower( X ), Y ), Z ) ), hAPP( hAPP(
% 0.99/1.50 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.99/1.50 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.99/1.50 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.50 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.99/1.50 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.50 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.99/1.50 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.99/1.50 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.99/1.50 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.99/1.50 ( X ), ! Z = c_Groups_Oplus__class_Oplus( X, Z, Y ), Y =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.50 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.99/1.50 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.99/1.50 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 0.99/1.50 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.99/1.50 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.99/1.50 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.99/1.50 ( X ), U = T, Z = Y, ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.99/1.50 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.50 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.99/1.50 ) }.
% 0.99/1.50 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.99/1.50 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.99/1.50 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.50 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.99/1.50 ), ! U = T }.
% 0.99/1.50 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.99/1.50 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.99/1.50 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.50 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.99/1.50 ), ! Z = Y }.
% 0.99/1.50 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.99/1.50 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.50 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.99/1.50 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Y
% 0.99/1.50 ) ), Z ) }.
% 0.99/1.50 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.99/1.50 ( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.99/1.50 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.50 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.99/1.50 ), U = Z, T = Y }.
% 0.99/1.50 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.99/1.50 ( X ), ! U = Z, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.99/1.50 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.50 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.99/1.50 ) }.
% 0.99/1.50 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.99/1.50 ( X ), ! T = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.99/1.50 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.50 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.99/1.50 ) }.
% 0.99/1.50 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.99/1.50 = Y }.
% 0.99/1.50 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.99/1.50 = Y }.
% 0.99/1.50 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.50 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.50 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.99/1.50 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.99/1.50 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.50 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.99/1.50 c_Power_Opower__class_Opower( X ), T ), Y ) ) = hAPP( hAPP(
% 0.99/1.50 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 0.99/1.50 tc_Nat_Onat, Z, Y ) ) }.
% 0.99/1.50 { c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex,
% 0.99/1.50 skol5 ) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(
% 0.99/1.50 tc_Complex_Ocomplex, v_pa____ ) }.
% 0.99/1.50 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, skol5 ), X ) = hAPP(
% 0.99/1.50 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ),
% 0.99/1.50 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, v_c____, X ) ) }.
% 0.99/1.50 { ! hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), v_c____ ) =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), hAPP(
% 0.99/1.50 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), skol6 ) =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.99/1.50 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.50 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.99/1.50 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 0.99/1.50 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.99/1.50 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), X ) ) ) }.
% 0.99/1.50 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.99/1.50 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, X ) ), X ) =
% 0.99/1.50 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), T ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) ),
% 0.99/1.50 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.99/1.50 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, X ) ), T ), hAPP(
% 0.99/1.50 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.99/1.50 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, Y ) ), Z ) ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), T ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) ),
% 0.99/1.50 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), T ),
% 0.99/1.50 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, X ) ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ),
% 0.99/1.50 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, Y ) ) ) }.
% 0.99/1.50 { X = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), Y =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Orderings_Oord__class_Oless
% 0.99/1.50 ( tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex
% 0.99/1.50 , c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex,
% 0.99/1.50 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), X ), hAPP( hAPP(
% 0.99/1.50 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), skol7( X, Y ) ), Y )
% 0.99/1.50 ) ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.99/1.50 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X )
% 0.99/1.50 , X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.50 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ), X =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.99/1.50 { ! X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.50 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ),
% 0.99/1.50 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, X ) ) }.
% 0.99/1.50 { alpha19( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 0.99/1.50 hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.99/1.50 { alpha19( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP
% 0.99/1.50 ( X, Y ), Z ) ) }.
% 0.99/1.50 { ! alpha19( X, Y, Z ), alpha20( X, Y, Z ), Z = Y }.
% 0.99/1.50 { ! alpha19( X, Y, Z ), alpha20( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z
% 0.99/1.50 ) ) }.
% 0.99/1.50 { ! alpha20( X, Y, Z ), alpha19( X, Y, Z ) }.
% 0.99/1.50 { ! Z = Y, hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha19( X, Y, Z ) }.
% 0.99/1.50 { ! alpha20( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y )
% 0.99/1.50 }.
% 0.99/1.50 { ! alpha20( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ), hBOOL( hAPP( hAPP(
% 0.99/1.50 X, Y ), Z ) ), alpha20( X, Y, Z ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X = Y }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.99/1.50 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.99/1.50 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.99/1.50 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, X ) }.
% 0.99/1.50 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Z ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, Z ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ), Y = X }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.99/1.50 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.99/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.50 tc_Nat_Onat ), X ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.50 ( tc_Nat_Onat ), X ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 0.99/1.50 .
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.50 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.99/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.50 tc_Nat_Onat ), X ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), ! Y = X }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), Y = X,
% 0.99/1.50 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.99/1.50 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), Y = X }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.99/1.50 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.99/1.50 ( tc_Nat_Onat, Y, Z ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y
% 0.99/1.50 , X ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.99/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, X ) =
% 0.99/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.99/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ),
% 0.99/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.50 tc_Nat_Onat, Y, T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.99/1.50 .
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.50 tc_Nat_Onat, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.99/1.50 .
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.99/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.99/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.99/1.50 ( tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) )
% 0.99/1.50 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.50 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }
% 0.99/1.50 .
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.99/1.50 ( tc_Nat_Onat, Y, X ), X ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.99/1.50 ( tc_Nat_Onat, Y, X ), Y ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__semidom( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), T )
% 0.99/1.50 , c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.50 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.50 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.50 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.99/1.50 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), X =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.50 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.50 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.99/1.50 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.99/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.50 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 0.99/1.50 ), X ) ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.50 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 0.99/1.50 ( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Z ), hAPP( hAPP
% 0.99/1.50 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ),
% 0.99/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.50 ( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ),
% 0.99/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.50 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.50 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.99/1.50 tc_Nat_Onat, Y, X ) ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.50 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.99/1.50 tc_Nat_Onat, Y, X ) ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.50 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.99/1.50 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.50 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.99/1.50 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.50 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 0.99/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.50 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.50 Y ), X ) ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 0.99/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.50 tc_Nat_Onat ), Z ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 0.99/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.50 ( tc_Nat_Onat ), Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 0.99/1.50 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.99/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.50 tc_Nat_Onat ), Y ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.99/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.50 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.99/1.50 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.50 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.99/1.50 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP
% 0.99/1.50 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.50 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.99/1.50 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP
% 0.99/1.50 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__semidom( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.99/1.50 ), ! c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oone__class_Oone
% 0.99/1.50 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.50 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.99/1.50 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 0.99/1.50 c_Power_Opower__class_Opower( X ), T ), Z ) = hAPP( hAPP(
% 0.99/1.50 c_Power_Opower__class_Opower( X ), Y ), Z ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.99/1.50 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.99/1.50 X ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ), T = Y }.
% 0.99/1.50 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.50 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.50 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.99/1.50 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.50 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.50 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.99/1.50 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.50 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.50 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.99/1.50 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.99/1.50 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.99/1.50 ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.50 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.50 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.50 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.99/1.50 X ), Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.99/1.50 ( X ) ) }.
% 0.99/1.50 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.50 , c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.50 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.99/1.50 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.50 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.50 , Z, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.50 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.99/1.50 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.50 { ! class_Rings_Oordered__semiring( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.50 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.99/1.50 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.99/1.50 { ! class_Rings_Oordered__semiring( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.99/1.50 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.99/1.50 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.99/1.50 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.50 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.50 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 0.99/1.50 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.50 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.50 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.99/1.50 { ! class_Rings_Oordered__comm__semiring( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.99/1.50 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.99/1.50 { ! class_Rings_Oordered__semiring( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.99/1.50 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.99/1.50 { ! class_Rings_Oordered__semiring( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.99/1.50 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.99/1.50 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.50 , Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.50 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.99/1.50 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.99/1.50 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.50 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.99/1.50 X ), Z ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.99/1.50 ( X ) ) }.
% 0.99/1.50 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.50 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.50 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.50 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.50 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.50 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ),
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.50 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.50 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.99/1.50 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.99/1.50 ( X ) ), alpha3( X, Y, Z ), alpha14( X, Y, Z ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha3( X, Y, Z ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.99/1.50 ( X ) ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha14( X, Y, Z ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.99/1.50 ( X ) ) }.
% 0.99/1.50 { ! alpha14( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.50 { ! alpha14( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.99/1.50 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 0.99/1.50 ( X ), Y ), alpha14( X, Y, Z ) }.
% 0.99/1.50 { ! alpha3( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.99/1.50 { ! alpha3( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.50 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ) ), alpha3( X, Y, Z ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.50 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), alpha4( X, Y
% 0.99/1.50 , Z ), alpha15( X, Y, Z ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha4( X, Y, Z ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.50 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha15( X, Y, Z ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.50 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.50 { ! alpha15( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.50 { ! alpha15( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.99/1.50 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ) ), alpha15( X, Y, Z ) }.
% 0.99/1.50 { ! alpha4( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.99/1.50 { ! alpha4( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.50 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ), Y ), alpha4( X, Y, Z ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 0.99/1.50 X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__semidom( X ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.50 c_Groups_Oone__class_Oone( X ) ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__semidom( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__semidom( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.99/1.50 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.50 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.99/1.50 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__semidom( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.50 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.99/1.50 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__semidom( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), Y )
% 0.99/1.50 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.99/1.50 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.99/1.50 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 0.99/1.50 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.50 ) }.
% 0.99/1.50 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.50 ), c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.50 c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Ozero__class_Ozero( X
% 0.99/1.50 ) ) }.
% 0.99/1.50 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.50 c_Rings_Oinverse__class_Oinverse( X, Y ) ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.50 ) }.
% 0.99/1.50 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.50 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.99/1.50 ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.99/1.50 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.50 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.99/1.50 ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.99/1.50 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.99/1.50 ( X, Y ) ) ) }.
% 0.99/1.50 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.99/1.50 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 0.99/1.50 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.50 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Y ),
% 0.99/1.50 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.99/1.50 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.99/1.50 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X ) ),
% 0.99/1.50 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.99/1.50 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.50 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.99/1.50 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.99/1.50 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.99/1.50 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.50 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.99/1.50 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.99/1.50 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, U, T ), ! c_Orderings_Oord__class_Oless
% 0.99/1.50 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.99/1.50 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.99/1.50 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.50 , U ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.99/1.50 ( X, U, T ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.99/1.50 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.99/1.50 ( X, U, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.99/1.50 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.50 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.50 ! c_Orderings_Oord__class_Oless__eq( X, Z, T ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.99/1.50 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.99/1.50 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.99/1.50 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ) ), Z = c_Groups_Ozero__class_Ozero( X )
% 0.99/1.50 }.
% 0.99/1.50 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.99/1.50 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.99/1.50 }.
% 0.99/1.50 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.99/1.50 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.99/1.50 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 0.99/1.50 X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 0.99/1.50 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.99/1.50 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.99/1.50 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 0.99/1.50 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.99/1.50 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.99/1.50 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 0.99/1.50 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.50 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP
% 0.99/1.50 ( c_Power_Opower__class_Opower( X ), Y ), T ) ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.50 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.99/1.50 { ! class_Fields_Olinordered__field( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 0.99/1.50 , Z ), c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.99/1.50 { ! class_Fields_Olinordered__field( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 0.99/1.50 , Z ), c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.99/1.50 { ! class_Fields_Olinordered__field( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 0.99/1.50 , Y ), c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.99/1.50 { ! class_Fields_Olinordered__field( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 0.99/1.50 , Y ), c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.99/1.50 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 0.99/1.50 , Y ), c_Groups_Oone__class_Oone( X ) ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.50 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X )
% 0.99/1.50 , Y ) }.
% 0.99/1.50 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.50 ), c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.50 c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Oone__class_Oone( X )
% 0.99/1.50 ) }.
% 0.99/1.50 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), Y )
% 0.99/1.50 , c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse
% 0.99/1.50 ( X, Y ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.99/1.50 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.50 c_RealVector_Onorm__class_Onorm( X, Y ), c_Groups_Ozero__class_Ozero(
% 0.99/1.50 tc_RealDef_Oreal ) ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.50 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless__eq(
% 0.99/1.50 tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( X, Y ),
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.99/1.50 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.50 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.99/1.50 c_RealVector_Onorm__class_Onorm( X, Z ) ),
% 0.99/1.50 c_RealVector_Onorm__class_Onorm( X, Y ) ) ) }.
% 0.99/1.50 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.50 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.99/1.50 c_Power_Opower__class_Opower( X ), Z ), Y ) ), hAPP( hAPP(
% 0.99/1.50 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.99/1.50 c_RealVector_Onorm__class_Onorm( X, Z ) ), Y ) ) }.
% 0.99/1.50 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.99/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ), Z = X }.
% 0.99/1.50 { ! Z = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.99/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.99/1.50 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.99/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ), Y = X }.
% 0.99/1.50 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.99/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) }.
% 0.99/1.50 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.50 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.99/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.99/1.50 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, c_Groups_Oplus__class_Oplus
% 0.99/1.50 ( tc_Nat_Onat, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 0.99/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.99/1.50 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.99/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.99/1.50 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.99/1.50 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ) ), X ) =
% 0.99/1.50 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.99/1.50 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP
% 0.99/1.50 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), Y ) ), X ) =
% 0.99/1.50 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), hAPP
% 0.99/1.50 ( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.99/1.50 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) =
% 0.99/1.50 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y )
% 0.99/1.50 }.
% 0.99/1.50 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 0.99/1.50 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.99/1.50 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP
% 0.99/1.50 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__semiring__1( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, T, Y ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.99/1.50 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.99/1.50 X ), W ), ! c_Groups_Oplus__class_Oplus( X, U, W ) =
% 0.99/1.50 c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.50 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.50 ( X ), U ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), T )
% 0.99/1.50 ), Y ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.50 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ), Z ), ! c_Orderings_Oord__class_Oless(
% 0.99/1.50 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), T ),
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.50 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.99/1.50 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.99/1.50 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.99/1.50 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone( X ) )
% 0.99/1.50 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.99/1.50 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.99/1.50 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 0.99/1.50 ), c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless__eq(
% 0.99/1.50 X, Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless(
% 0.99/1.50 X, c_Groups_Oone__class_Oone( X ), Y ) }.
% 0.99/1.50 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.50 ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X
% 0.99/1.50 , Y ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.99/1.50 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), Y ),
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 0.99/1.50 ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.99/1.50 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.99/1.50 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.99/1.50 ( X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.99/1.50 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.99/1.50 c_Rings_Oinverse__class_Oinverse( X, Y ) ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone( X ) )
% 0.99/1.50 }.
% 0.99/1.50 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.99/1.50 ! c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone( X )
% 0.99/1.50 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X )
% 0.99/1.50 , c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__semiring__1__strict( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.99/1.50 ( X, T, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ), U ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), W
% 0.99/1.50 ), ! c_Groups_Oplus__class_Oplus( X, U, W ) = c_Groups_Oone__class_Oone
% 0.99/1.50 ( X ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X,
% 0.99/1.50 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), W ), T ) ), Y ) }.
% 0.99/1.50 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.50 tc_Nat_Onat ), X ) = X }.
% 0.99/1.50 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero
% 0.99/1.50 ( tc_Nat_Onat ) ) = X }.
% 0.99/1.50 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.50 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.50 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.99/1.50 tc_Nat_Onat, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.50 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = Y, X =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.50 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.50 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.50 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.50 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.50 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.50 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.99/1.50 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Y = X
% 0.99/1.50 , Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.50 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.99/1.50 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.99/1.50 .
% 0.99/1.50 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.99/1.50 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.99/1.50 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z = X
% 0.99/1.50 , Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.50 { ! Z = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.99/1.50 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }
% 0.99/1.50 .
% 0.99/1.50 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.99/1.50 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) = hAPP( hAPP
% 0.99/1.50 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ), Z = Y }.
% 0.99/1.50 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y, hAPP( hAPP
% 0.99/1.50 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) = hAPP(
% 0.99/1.50 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) }.
% 0.99/1.50 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) = hAPP( hAPP
% 0.99/1.50 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ), Z = Y }.
% 0.99/1.50 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y, hAPP( hAPP
% 0.99/1.50 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) = hAPP(
% 0.99/1.50 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) }.
% 0.99/1.50 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.99/1.50 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.99/1.50 { ! Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! X =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.99/1.50 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.99/1.50 { ! c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) =
% 0.99/1.50 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.99/1.50 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.99/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.99/1.50 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.99/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 0.99/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.99/1.50 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.99/1.50 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) = X }.
% 0.99/1.50 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.99/1.50 c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y = c_Groups_Oone__class_Oone(
% 0.99/1.50 tc_Nat_Onat ) }.
% 0.99/1.50 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.99/1.50 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X = c_Groups_Oone__class_Oone(
% 0.99/1.50 tc_Nat_Onat ) }.
% 0.99/1.50 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.99/1.50 c_Groups_Oone__class_Oone( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.99/1.50 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.99/1.50 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.99/1.50 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 0.99/1.50 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), Y =
% 0.99/1.50 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.99/1.50 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X =
% 0.99/1.50 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.99/1.50 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.99/1.50 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Groups_Oone__class_Oone(
% 0.99/1.50 tc_Nat_Onat ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.99/1.50 , Y ), X ) }.
% 0.99/1.50 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.50 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) = X }.
% 0.99/1.50 { c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ),
% 0.99/1.50 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.99/1.50 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ),
% 0.99/1.50 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ),
% 0.99/1.50 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.50 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex, X
% 0.99/1.50 ), c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(
% 0.99/1.50 tc_Complex_Ocomplex, v_pa____ ) ),
% 0.99/1.50 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( tc_Complex_Ocomplex
% 0.99/1.50 , tc_Complex_Ocomplex, c_Polynomial_Opoly( tc_Complex_Ocomplex, X ) ),
% 0.99/1.50 hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, X ), skol8( X ) ) =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.99/1.50 { ! class_RealVector_Oreal__normed__div__algebra( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z,
% 0.99/1.50 c_RealVector_Onorm__class_Onorm( X, Y ) ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.50 c_RealVector_Onorm__class_Onorm( X, c_Rings_Oinverse__class_Oinverse( X,
% 0.99/1.50 Y ) ), c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, Z ) ) }.
% 0.99/1.50 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.50 c_RealVector_Onorm__class_Onorm( X, Z ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ),
% 0.99/1.50 c_RealVector_Onorm__class_Onorm( X, T ) ) ), Z =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.50 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.50 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.99/1.50 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.99/1.50 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.50 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.50 ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.99/1.50 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.99/1.50 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.50 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.50 ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.99/1.50 ) ) }.
% 0.99/1.50 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.99/1.50 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.99/1.50 ) ) }.
% 0.99/1.50 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.99/1.50 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, X ) }.
% 0.99/1.50 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ) }.
% 0.99/1.50 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ), Y = X }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 0.99/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol9( X, Y ) ) }.
% 0.99/1.50 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.50 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.99/1.50 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 0.99/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.99/1.50 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 0.99/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.99/1.50 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.99/1.50 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.99/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.99/1.50 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.99/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 0.99/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol10( X, Y ) ) }.
% 0.99/1.50 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.99/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.99/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.99/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.99/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.99/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, T ),
% 0.99/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ), X ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.99/1.50 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) }.
% 0.99/1.50 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), T ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.99/1.50 { ! class_Groups_Ozero( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y, Y =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.50 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ) = Y }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.50 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 0.99/1.50 ) }.
% 0.99/1.50 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.50 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 0.99/1.50 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 0.99/1.50 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.50 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X
% 0.99/1.50 ) }.
% 0.99/1.50 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.50 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 0.99/1.50 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 0.99/1.50 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.99/1.50 { ! class_Groups_Oab__semigroup__mult( X ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.50 { ! class_Groups_Oab__semigroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.99/1.50 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.99/1.50 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.99/1.50 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.99/1.50 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.99/1.50 T, Y ), Z = Y }.
% 0.99/1.50 { ! class_Groups_Ocancel__semigroup__add( X ), ! Z = Y,
% 0.99/1.50 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.99/1.50 T, Y ) }.
% 0.99/1.50 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.99/1.50 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.99/1.50 Y, Z ), T = Y }.
% 0.99/1.50 { ! class_Groups_Ocancel__semigroup__add( X ), ! T = Y,
% 0.99/1.50 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.99/1.50 Y, Z ) }.
% 0.99/1.50 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.99/1.50 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.99/1.50 T, Y ), Z = Y }.
% 0.99/1.50 { ! class_Groups_Ocancel__ab__semigroup__add( X ), !
% 0.99/1.50 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.99/1.50 T, Y ), Z = Y }.
% 0.99/1.50 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.99/1.50 c_Groups_Oplus__class_Oplus( X, Z, T ) = c_Groups_Oplus__class_Oplus( X,
% 0.99/1.50 Y, T ), Z = Y }.
% 0.99/1.50 { ! class_Groups_Oone( X ), ! c_Groups_Oone__class_Oone( X ) = Y, Y =
% 0.99/1.50 c_Groups_Oone__class_Oone( X ) }.
% 0.99/1.50 { ! class_Groups_Oone( X ), ! Y = c_Groups_Oone__class_Oone( X ),
% 0.99/1.50 c_Groups_Oone__class_Oone( X ) = Y }.
% 0.99/1.50 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.99/1.50 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.99/1.50 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.99/1.50 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.50 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero( X ) =
% 0.99/1.50 c_Groups_Oplus__class_Oplus( X, Y, Y ) }.
% 0.99/1.50 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.99/1.50 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.99/1.50 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.99/1.50 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.99/1.50 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.99/1.50 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.99/1.50 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.99/1.50 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.99/1.50 U ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.99/1.50 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.99/1.50 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.99/1.50 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.99/1.50 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.99/1.50 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.99/1.50 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.99/1.50 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.99/1.50 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.99/1.50 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.99/1.50 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.99/1.50 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.99/1.50 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.99/1.50 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.99/1.50 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ), c_Orderings_Oord__class_Oless
% 0.99/1.50 ( X, T, Y ) }.
% 0.99/1.50 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, T, Y ), c_Orderings_Oord__class_Oless(
% 0.99/1.50 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.99/1.50 , Y, Z ) ) }.
% 0.99/1.50 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.99/1.50 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.99/1.50 ( X, Z, Y ) }.
% 0.99/1.50 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.99/1.50 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.99/1.50 , T, Y ) ) }.
% 0.99/1.50 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.99/1.50 X, c_Groups_Oplus__class_Oplus( X, Z, T ), c_Groups_Oplus__class_Oplus( X
% 0.99/1.50 , Y, T ) ) }.
% 0.99/1.50 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.99/1.50 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.99/1.50 , T, Y ) ) }.
% 0.99/1.50 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.99/1.50 ( X, U, T ), c_Orderings_Oord__class_Oless( X,
% 0.99/1.50 c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X, Y
% 0.99/1.50 , T ) ) }.
% 0.99/1.50 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, T )
% 0.99/1.50 , c_Groups_Oplus__class_Oplus( X, Y, T ) ), c_Orderings_Oord__class_Oless
% 0.99/1.50 ( X, Z, Y ) }.
% 0.99/1.50 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.99/1.50 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.99/1.50 ( X, Z, Y ) }.
% 0.99/1.50 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.99/1.50 = Y }.
% 0.99/1.50 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.99/1.50 = Y }.
% 0.99/1.50 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.99/1.50 = Y }.
% 0.99/1.50 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.99/1.50 = Y }.
% 0.99/1.50 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.50 c_Groups_Oplus__class_Oplus( X, Y, Y ) ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.50 ) }.
% 0.99/1.50 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.50 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.99/1.50 ), c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.99/1.50 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Y,
% 0.99/1.50 Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.50 ) }.
% 0.99/1.50 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.50 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X
% 0.99/1.50 , Y, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.50 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.50 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.99/1.50 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.99/1.50 ) }.
% 0.99/1.50 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.50 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.99/1.50 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 0.99/1.50 .
% 0.99/1.50 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.50 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.99/1.50 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.99/1.50 .
% 0.99/1.50 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.50 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.99/1.50 X ), Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), ! Z =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.99/1.50 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.50 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.50 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 0.99/1.50 Y, Z ) ) }.
% 0.99/1.50 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.50 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 0.99/1.50 Z, Y ) ) }.
% 0.99/1.50 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.50 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.50 , c_Groups_Oplus__class_Oplus( X, Y, Z ), c_Groups_Ozero__class_Ozero( X
% 0.99/1.50 ) ) }.
% 0.99/1.50 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.50 c_Groups_Oplus__class_Oplus( X, Y, Y ) ), c_Orderings_Oord__class_Oless(
% 0.99/1.50 X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.99/1.50 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.50 c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.99/1.50 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.99/1.50 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Y
% 0.99/1.50 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.50 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.99/1.50 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.50 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.99/1.50 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.99/1.50 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.50 c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.99/1.50 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.50 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.50 , c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.99/1.50 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.50 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, U )
% 0.99/1.50 , c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.99/1.50 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, U, T ), c_Orderings_Oord__class_Oless(
% 0.99/1.50 X, c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X
% 0.99/1.50 , Y, T ) ) }.
% 0.99/1.50 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.99/1.50 ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.50 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.50 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.99/1.50 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.50 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.50 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.50 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.50 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.50 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP
% 0.99/1.50 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.50 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z
% 0.99/1.50 , Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.50 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.99/1.50 , Y ), X ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.99/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.50 tc_Nat_Onat ), Y ) }.
% 0.99/1.50 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.99/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.50 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 0.99/1.50 ), X ) ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.50 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.50 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.50 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 0.99/1.50 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP(
% 0.99/1.50 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.99/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.50 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 0.99/1.50 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.50 ( tc_Nat_Onat ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.99/1.50 tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.99/1.50 tc_Nat_Onat ), X ), Y ), Z = Y }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.50 ( tc_Nat_Onat ), X ), ! Z = Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.50 ( tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.99/1.50 tc_Nat_Onat ), X ), Y ) }.
% 0.99/1.50 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 0.99/1.50 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus(
% 0.99/1.50 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, T,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 0.99/1.50 c_Polynomial_Opcompose( X, Z, Y ) ) ) }.
% 0.99/1.50 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.50 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.99/1.50 c_Polynomial_Opcompose( X, T, Z ) ), Y ) = hAPP( c_Polynomial_Opoly( X, T
% 0.99/1.50 ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.99/1.50 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.99/1.50 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Z =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.99/1.50 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.99/1.50 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.99/1.50 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.99/1.50 .
% 0.99/1.50 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), T ), Z ),
% 0.99/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), X ) ) =
% 0.99/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus
% 0.99/1.50 ( tc_Nat_Onat, T, Y ) ), Z ), X ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.99/1.50 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.99/1.50 ) ), c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 0.99/1.50 ) ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.99/1.50 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.99/1.50 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.99/1.50 ) ) }.
% 0.99/1.50 { X = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( tc_Complex_Ocomplex
% 0.99/1.50 ) ), ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, skol11( X, Y
% 0.99/1.50 , Z ), c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, T ) ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z,
% 0.99/1.50 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.99/1.50 c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_OpCons(
% 0.99/1.50 tc_Complex_Ocomplex, Y, X ) ), T ) ) ) }.
% 0.99/1.50 { ! class_Orderings_Opreorder( X ), c_Orderings_Oord__class_Oless__eq( X, Y
% 0.99/1.50 , Y ) }.
% 0.99/1.50 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 0.99/1.50 tc_Polynomial_Opoly( X ), U, c_Polynomial_Osmult( X, T, Z ) ) =
% 0.99/1.50 c_Polynomial_OpCons( X, Y, Z ), Y = hAPP( c_Polynomial_Opoly( X, U ), T )
% 0.99/1.50 }.
% 0.99/1.50 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 0.99/1.50 tc_Polynomial_Opoly( X ), U, c_Polynomial_Osmult( X, T, Z ) ) =
% 0.99/1.50 c_Polynomial_OpCons( X, Y, Z ), Z = c_Polynomial_Osynthetic__div( X, U, T
% 0.99/1.50 ) }.
% 0.99/1.50 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.50 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.99/1.50 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.99/1.50 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.99/1.50 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.99/1.50 hAPP( Y, U ) ) }.
% 0.99/1.50 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.99/1.50 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.99/1.50 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.99/1.50 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 0.99/1.50 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.50 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.99/1.50 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.99/1.50 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 0.99/1.50 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.99/1.50 , Y ), ! Z = T, c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.99/1.50 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y
% 0.99/1.50 ), ! Y = T, c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.99/1.50 { ! class_Orderings_Oorder( X ), ! Z = Y, !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 0.99/1.50 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.99/1.50 ( X, Y, T ), c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.99/1.50 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.99/1.50 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 0.99/1.50 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.99/1.50 , Y ), ! Y = Z, c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.99/1.50 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.99/1.50 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.99/1.50 hAPP( Y, U ) ) }.
% 0.99/1.50 { ! class_Orderings_Opreorder( X ), ! Z = Y,
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.99/1.50 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.99/1.50 ( X, Z, Y ) }.
% 0.99/1.50 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.99/1.50 ( X, Y, Z ) }.
% 0.99/1.50 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.99/1.50 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 0.99/1.50 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.99/1.50 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.99/1.50 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.99/1.50 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.99/1.50 hAPP( Y, U ) ) }.
% 0.99/1.50 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, hAPP
% 0.99/1.50 ( Z, skol12( X, Y, Z ) ), hAPP( Y, skol12( X, Y, Z ) ) ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }.
% 0.99/1.50 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.99/1.50 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.99/1.50 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.99/1.50 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.99/1.50 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.99/1.50 , ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.99/1.50 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.99/1.50 Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.99/1.50 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.99/1.50 , ! Z = T, c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.99/1.50 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 0.99/1.50 ! Y = T, c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.99/1.50 { ! class_Orderings_Oorder( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless(
% 0.99/1.50 X, T, Y ), c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.99/1.50 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X
% 0.99/1.50 , Y, T ), c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.99/1.50 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.99/1.50 , ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.99/1.50 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.99/1.50 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.99/1.50 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.99/1.50 , ! Y = Z }.
% 0.99/1.50 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.99/1.50 , ! Z = Y }.
% 0.99/1.50 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.99/1.50 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.99/1.50 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.99/1.50 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.99/1.50 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.99/1.50 , ! Z = Y }.
% 0.99/1.50 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 0.99/1.50 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.99/1.50 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.99/1.50 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Y = Z }.
% 0.99/1.50 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.99/1.50 ), ! Y = Z, ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.99/1.50 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.99/1.50 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.99/1.50 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.99/1.50 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Z = Y }.
% 0.99/1.50 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.99/1.50 Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.99/1.50 { ! class_Orderings_Olinorder( X ), ! Z = Y, !
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.99/1.50 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 0.99/1.50 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.99/1.50 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.99/1.50 Y ), ! Z = Y }.
% 0.99/1.50 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.99/1.50 Z ), ! Z = Y }.
% 0.99/1.50 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.99/1.50 Y ) }.
% 0.99/1.50 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ),
% 0.99/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) = hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.99/1.50 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 0.99/1.50 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ) }.
% 0.99/1.50 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), hAPP( hAPP(
% 0.99/1.50 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 0.99/1.50 ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.99/1.50 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 0.99/1.50 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Polynomial_OpCons( X, hAPP(
% 0.99/1.50 c_Polynomial_Opoly( X, Z ), Y ), c_Polynomial_Osynthetic__div( X, Z, Y )
% 0.99/1.50 ) }.
% 0.99/1.50 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.99/1.50 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.99/1.50 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.50 , Y, Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.99/1.50 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.99/1.50 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.99/1.50 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.99/1.50 Z ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.99/1.50 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.99/1.50 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.99/1.50 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.99/1.50 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.99/1.50 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.99/1.50 , ! Z = Y }.
% 0.99/1.50 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.99/1.50 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.99/1.50 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.99/1.50 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.99/1.50 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.99/1.50 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.99/1.50 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.50 , Z, Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.99/1.50 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.99/1.50 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.99/1.50 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.99/1.50 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.99/1.50 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.99/1.50 ( X, Z, Y ) }.
% 0.99/1.50 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.99/1.50 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.99/1.50 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.99/1.50 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.99/1.50 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.99/1.50 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ), Z = Y }.
% 0.99/1.50 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.99/1.50 ), ! Z = Y, c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.99/1.50 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.99/1.50 ( X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.99/1.50 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.99/1.50 ( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.99/1.50 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.50 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.99/1.50 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.99/1.50 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.99/1.50 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.50 , Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.99/1.50 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.50 , Z, Y ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.99/1.50 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.99/1.50 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.99/1.50 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.99/1.50 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.99/1.50 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.99/1.50 , Y ), Y = Z, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.99/1.50 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.99/1.50 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.99/1.50 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.99/1.50 , ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.99/1.50 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.50 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.99/1.50 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.99/1.50 , Y ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.99/1.50 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.99/1.50 c_Groups_Oplus__class_Oplus( X, Y, Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.99/1.50 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.50 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.99/1.50 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.50 { ! class_Rings_Ocomm__semiring__0( X ), c_Groups_Oplus__class_Oplus(
% 0.99/1.50 tc_Polynomial_Opoly( X ), Z, c_Polynomial_Osmult( X, Y,
% 0.99/1.50 c_Polynomial_Osynthetic__div( X, Z, Y ) ) ) = c_Polynomial_OpCons( X,
% 0.99/1.50 hAPP( c_Polynomial_Opoly( X, Z ), Y ), c_Polynomial_Osynthetic__div( X, Z
% 0.99/1.50 , Y ) ) }.
% 0.99/1.50 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Oplus__class_Oplus(
% 0.99/1.50 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.99/1.50 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.99/1.50 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 0.99/1.50 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.99/1.50 tc_Polynomial_Opoly( X ) ) ) ) ), c_Polynomial_Osynthetic__div( X, Y, Z )
% 0.99/1.50 ), c_Polynomial_OpCons( X, hAPP( c_Polynomial_Opoly( X, Y ), Z ),
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) = Y }.
% 0.99/1.50 { c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex,
% 0.99/1.50 skol13 ) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(
% 0.99/1.50 tc_Complex_Ocomplex, v_pa____ ) }.
% 0.99/1.50 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, skol13 ), X ) = hAPP(
% 0.99/1.50 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ),
% 0.99/1.50 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, v_c____, X ) ) }.
% 0.99/1.50 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.99/1.50 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol14( Z, T ) ) }.
% 0.99/1.50 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.50 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.99/1.50 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol14( X, Y ) ) ) }.
% 0.99/1.50 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.99/1.50 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol15( Z, T ) ) }.
% 0.99/1.50 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.50 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.99/1.50 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol15( X, Y ) ) ) }.
% 0.99/1.50 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.99/1.50 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) =
% 0.99/1.50 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.99/1.50 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.99/1.50 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ) ), X ) =
% 0.99/1.50 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.99/1.50 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.99/1.50 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), X =
% 0.99/1.50 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.99/1.50 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.99/1.50 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), Y =
% 0.99/1.50 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.99/1.50 ( tc_Int_Oint ), X ), ! X = c_Groups_Oone__class_Oone( tc_Int_Oint ), ! Y
% 0.99/1.50 = c_Groups_Oone__class_Oone( tc_Int_Oint ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 0.99/1.50 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.50 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 0.99/1.50 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP
% 0.99/1.50 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.99/1.50 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP(
% 0.99/1.50 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.99/1.50 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.99/1.50 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ), X ) =
% 0.99/1.50 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.99/1.50 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) = hAPP
% 0.99/1.50 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) }.
% 0.99/1.50 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 0.99/1.50 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) = X }.
% 0.99/1.50 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.99/1.50 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) = X }.
% 0.99/1.50 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 0.99/1.50 X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }
% 0.99/1.50 .
% 0.99/1.50 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 0.99/1.50 X ), Z, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z )
% 0.99/1.50 }.
% 0.99/1.50 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.99/1.50 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z
% 0.99/1.50 ), c_Orderings_Oord__class_Oless( tc_fun( T, X ), Z, Y ) }.
% 0.99/1.50 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.99/1.50 , c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.99/1.50 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, Y, Z ), c_Orderings_Oord__class_Oless(
% 0.99/1.50 X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.99/1.50 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.99/1.50 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.99/1.50 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 0.99/1.50 ( X, Y ), Z ) }.
% 0.99/1.50 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.99/1.50 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 0.99/1.50 ( X, Z ), Y ) }.
% 0.99/1.50 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ouminus__class_Ouminus( X,
% 0.99/1.50 Y ) ), c_Orderings_Oord__class_Oless( X, Y,
% 0.99/1.50 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.99/1.50 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ouminus__class_Ouminus( X,
% 0.99/1.50 Z ) ), c_Orderings_Oord__class_Oless( X, Z,
% 0.99/1.50 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.99/1.50 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.99/1.50 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 0.99/1.50 , c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.99/1.50 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.99/1.50 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.99/1.50 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 0.99/1.50 , c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.99/1.50 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.99/1.50 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Z,
% 0.99/1.50 c_Groups_Oplus__class_Oplus( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.99/1.50 Y ) ) = Y }.
% 0.99/1.50 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.99/1.50 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Oplus__class_Oplus( X,
% 0.99/1.50 Z, Y ) ) = Y }.
% 0.99/1.50 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ouminus__class_Ouminus
% 0.99/1.50 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.99/1.50 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.99/1.50 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 0.99/1.50 ( X, Z ) ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.99/1.50 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.99/1.50 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.99/1.50 , Z ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.50 c_Groups_Ouminus__class_Ouminus( X, Y ), Z ) }.
% 0.99/1.50 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.99/1.50 , Y ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.50 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.99/1.50 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.99/1.50 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.99/1.50 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.99/1.50 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.99/1.50 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.99/1.50 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.99/1.50 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 0.99/1.50 ) = c_Groups_Ouminus__class_Ouminus( X, Y ), Z = Y }.
% 0.99/1.50 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ouminus__class_Ouminus
% 0.99/1.50 ( X, Z ) = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.99/1.50 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 0.99/1.50 ) = Y, c_Groups_Ouminus__class_Ouminus( X, Y ) = Z }.
% 0.99/1.50 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 0.99/1.50 ) = Z, c_Groups_Ouminus__class_Ouminus( X, Z ) = Y }.
% 0.99/1.50 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 0.99/1.50 , Y ), Y = c_Groups_Ouminus__class_Ouminus( X, Z ) }.
% 0.99/1.50 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 0.99/1.50 , Z ), Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.99/1.50 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.99/1.50 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 0.99/1.50 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.99/1.50 c_Groups_Ouminus__class_Ouminus( X, Y ) = Y, Y =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.50 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.99/1.50 = Y }.
% 0.99/1.50 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 0.99/1.50 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.99/1.50 ) }.
% 0.99/1.50 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.50 c_Groups_Ouminus__class_Ouminus( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.99/1.50 ) }.
% 0.99/1.50 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.99/1.50 c_Groups_Ouminus__class_Ouminus( X, Y ), Y = c_Groups_Ozero__class_Ozero
% 0.99/1.50 ( X ) }.
% 0.99/1.50 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus( X
% 0.99/1.50 , Y ) }.
% 0.99/1.50 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.99/1.50 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Groups_Ozero__class_Ozero( X )
% 0.99/1.50 = Y }.
% 0.99/1.50 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Ouminus__class_Ouminus( X, Y
% 0.99/1.50 ) }.
% 0.99/1.50 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.50 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 0.99/1.50 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.99/1.50 ( X, Y ) ) }.
% 0.99/1.50 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 0.99/1.50 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.99/1.50 ) ), Y ) }.
% 0.99/1.50 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.99/1.50 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.50 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.99/1.50 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.50 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.99/1.50 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.50 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.99/1.50 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.50 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.99/1.50 , c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.99/1.50 ( X, Y ) ) }.
% 0.99/1.50 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.99/1.50 , c_Groups_Ouminus__class_Ouminus( X, Z ) ),
% 0.99/1.50 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 0.99/1.50 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.99/1.50 ), Z ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 0.99/1.50 Z = Y, Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.99/1.50 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.99/1.50 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.99/1.50 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.99/1.50 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 0.99/1.50 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ) ), Y ) =
% 0.99/1.50 c_Groups_Ouminus__class_Ouminus( X, hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 0.99/1.50 ) }.
% 0.99/1.50 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.99/1.50 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 0.99/1.50 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.99/1.50 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) }.
% 0.99/1.50 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.99/1.50 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 0.99/1.50 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.99/1.50 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) }.
% 0.99/1.50 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X,
% 0.99/1.50 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) =
% 0.99/1.50 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ),
% 0.99/1.50 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 0.99/1.50 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X, Z,
% 0.99/1.50 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) =
% 0.99/1.50 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ),
% 0.99/1.50 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 0.99/1.50 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.99/1.50 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.99/1.50 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 0.99/1.50 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.50 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 0.99/1.50 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ouminus__class_Ouminus( X,
% 0.99/1.50 Y ) ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.99/1.50 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.99/1.50 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.99/1.50 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ouminus__class_Ouminus( X, Y
% 0.99/1.50 ) ) = c_RealVector_Onorm__class_Onorm( X, Y ) }.
% 0.99/1.50 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.50 c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.50 ) }.
% 0.99/1.50 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.50 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.99/1.50 ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.99/1.50 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 0.99/1.50 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.50 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.50 ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.99/1.50 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.99/1.50 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.99/1.50 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.50 ) }.
% 0.99/1.50 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.50 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 0.99/1.50 ( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.50 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.99/1.50 , Y ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.99/1.50 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.50 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 0.99/1.50 ( X, Y ), Y ) }.
% 0.99/1.50 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.99/1.50 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.99/1.50 .
% 0.99/1.50 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.99/1.50 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.99/1.50 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.99/1.50 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.99/1.50 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.50 , Y ) }.
% 0.99/1.50 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.99/1.50 , Y ) }.
% 0.99/1.50 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.99/1.50 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.99/1.50 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.99/1.50 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.50 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.50 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.99/1.50 ( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.50 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.50 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.99/1.50 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.99/1.50 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus
% 0.99/1.50 ( X, Z ) }.
% 0.99/1.50 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 0.99/1.50 , Z ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.50 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.99/1.50 = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.99/1.50 Z ) = Y }.
% 0.99/1.50 { ! class_Groups_Oab__group__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.99/1.50 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.50 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.99/1.50 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.50 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 0.99/1.50 , Y ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.50 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.99/1.50 = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ouminus__class_Ouminus
% 0.99/1.50 ( X, Y ) }.
% 0.99/1.50 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.99/1.50 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Ozero__class_Ozero(
% 0.99/1.50 X ) }.
% 0.99/1.50 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = c_Groups_Oone__class_Oone
% 0.99/1.50 ( X ), Y = c_Groups_Oone__class_Oone( X ), Y =
% 0.99/1.50 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) }.
% 0.99/1.50 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.99/1.50 c_Groups_Oone__class_Oone( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.50 ( X ), Y ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.99/1.50 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.99/1.50 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ),
% 0.99/1.50 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) =
% 0.99/1.50 c_Groups_Oone__class_Oone( X ) }.
% 0.99/1.50 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ouminus__class_Ouminus( X, Y
% 0.99/1.50 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.99/1.50 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) ), Y
% 0.99/1.50 ) }.
% 0.99/1.50 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.99/1.50 , c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ouminus__class_Ouminus( X
% 0.99/1.50 , Y ) ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.99/1.50 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.99/1.50 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.50 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ) ), hAPP( hAPP
% 0.99/1.50 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) }.
% 0.99/1.50 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X =
% 0.99/1.50 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) }.
% 0.99/1.50 { ! X = c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ),
% 0.99/1.50 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.99/1.50 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 0.99/1.50 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y = X }.
% 0.99/1.50 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 0.99/1.50 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) =
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.99/1.50 { ! class_Rings_Oring__1( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.99/1.50 ), c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.50 c_Power_Opower__class_Opower( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.99/1.50 c_Groups_Oone__class_Oone( X ) ) ), Y ) ), hAPP( hAPP(
% 0.99/1.50 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.99/1.50 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.50 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.50 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.99/1.50 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.50 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.99/1.50 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.99/1.50 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.50 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.50 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.99/1.50 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.99/1.50 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.99/1.50 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ),
% 0.99/1.50 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.50 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.99/1.50 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ),
% 0.99/1.50 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.50 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.50 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ),
% 0.99/1.50 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.99/1.50 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ) }.
% 0.99/1.50 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.99/1.50 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol16( Y ) ) }.
% 0.99/1.50 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.50 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.99/1.50 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.99/1.50 c_RealVector_Onorm__class_Onorm( X, Y ) ),
% 0.99/1.50 c_RealVector_Onorm__class_Onorm( X, Z ) ) ), skol16( X ) ) ) }.
% 0.99/1.50 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.50 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal,
% 0.99/1.50 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ),
% 0.99/1.50 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.99/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.99/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.99/1.50 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.99/1.50 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.99/1.50 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ),
% 0.99/1.50 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.99/1.50 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.99/1.50 ( tc_Int_Oint, X ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.99/1.50 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint,
% 0.99/1.50 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) = X }.
% 0.99/1.50 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.99/1.50 ( tc_Int_Oint ) ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), ! Y = X }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), Y = X,
% 0.99/1.50 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Z ),
% 0.99/1.50 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.99/1.50 tc_Int_Oint, Y, T ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 0.99/1.50 .
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.50 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ),
% 0.99/1.50 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.50 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.99/1.50 tc_Int_Oint ) ), X ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.99/1.50 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.50 tc_Int_Oint ), c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.99/1.50 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.50 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.99/1.50 tc_Int_Oint ) ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X )
% 0.99/1.50 }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.99/1.50 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.50 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.99/1.50 tc_Int_Oint ) ), X ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.99/1.50 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.99/1.50 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X )
% 0.99/1.50 }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.99/1.50 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.99/1.50 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.99/1.50 tc_Int_Oint ) ) ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.50 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ),
% 0.99/1.50 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.50 tc_Int_Oint ), X ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.99/1.50 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.50 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) }.
% 0.99/1.50 { ! c_Groups_Ozero__class_Ozero( tc_Int_Oint ) = c_Groups_Oone__class_Oone
% 0.99/1.50 ( tc_Int_Oint ) }.
% 0.99/1.50 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y = X,
% 0.99/1.50 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.99/1.50 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.99/1.50 tc_Int_Oint, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 0.99/1.50 .
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.99/1.50 ( tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.99/1.50 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.99/1.50 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.99/1.50 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.99/1.50 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.99/1.50 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 0.99/1.50 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.99/1.50 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.99/1.50 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.99/1.50 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 0.99/1.50 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus
% 0.99/1.50 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.99/1.50 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.99/1.50 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.99/1.50 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y
% 0.99/1.50 = X }.
% 0.99/1.50 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.99/1.50 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.99/1.50 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.99/1.50 tc_Int_Oint ) ) ) }.
% 0.99/1.50 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.99/1.50 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.99/1.50 tc_Int_Oint ) ) ) }.
% 0.99/1.50 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) =
% 0.99/1.50 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ) }.
% 0.99/1.50 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero
% 0.99/1.50 ( tc_Int_Oint ) ) = X }.
% 0.99/1.50 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.50 tc_Int_Oint ), X ) = X }.
% 0.99/1.50 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.51 tc_Int_Oint ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.99/1.51 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.99/1.51 tc_Int_Oint, c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ) =
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.99/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.99/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.99/1.51 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.99/1.51 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ),
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oone__class_Oone
% 0.99/1.51 ( tc_Int_Oint ), Y ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.99/1.51 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.99/1.51 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ),
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.99/1.51 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.99/1.51 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 0.99/1.51 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.99/1.51 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.99/1.51 ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_Int_Oint, T, W ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.51 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.99/1.51 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, U ) }.
% 0.99/1.51 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, X ) }.
% 0.99/1.51 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Z ),
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, Z ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ), Y = X }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.99/1.51 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.99/1.51 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.51 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.99/1.51 ( tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.99/1.51 Z ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.51 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.51 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 0.99/1.51 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, U ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, U ),
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Y ) }.
% 0.99/1.51 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 0.99/1.51 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.99/1.51 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.99/1.51 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.51 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.99/1.51 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, U, Y ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.51 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 0.99/1.51 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, X ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, Z ),
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, T ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 0.99/1.51 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.99/1.51 tc_Int_Oint, X, Y ) ) }.
% 0.99/1.51 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Ozero__class_Ozero(
% 0.99/1.51 tc_Int_Oint ) ) }.
% 0.99/1.51 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 0.99/1.51 tc_Int_Oint ) ) }.
% 0.99/1.51 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.99/1.51 c_Polynomial_OpCons( X, Z, Y ) ), c_Polynomial_Opos__poly( X, Y ), alpha5
% 0.99/1.51 ( X, Y, Z ) }.
% 0.99/1.51 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.99/1.51 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ) }.
% 0.99/1.51 { ! class_Rings_Olinordered__idom( X ), ! alpha5( X, Y, Z ),
% 0.99/1.51 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ) }.
% 0.99/1.51 { ! alpha5( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly
% 0.99/1.51 ( X ) ) }.
% 0.99/1.51 { ! alpha5( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.99/1.51 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.99/1.51 alpha5( X, Y, Z ) }.
% 0.99/1.51 { ! class_Orderings_Oorder( X ), ! c_SEQ_Odecseq( X, Y ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, T ),
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, T ), hAPP( Y, Z ) ) }.
% 0.99/1.51 { ! class_Orderings_Oorder( X ), c_Orderings_Oord__class_Oless__eq(
% 0.99/1.51 tc_Nat_Onat, skol17( X, Y ), skol53( X, Y ) ), c_SEQ_Odecseq( X, Y ) }.
% 0.99/1.51 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.51 hAPP( Y, skol53( X, Y ) ), hAPP( Y, skol17( X, Y ) ) ), c_SEQ_Odecseq( X
% 0.99/1.51 , Y ) }.
% 0.99/1.51 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.99/1.51 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.99/1.51 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.99/1.51 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.99/1.51 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X,
% 0.99/1.51 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 0.99/1.51 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.99/1.51 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X, hAPP( hAPP
% 0.99/1.51 ( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) }
% 0.99/1.51 .
% 0.99/1.51 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 0.99/1.51 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 0.99/1.51 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 0.99/1.51 { ! class_Lattices_Oboolean__algebra( X ), c_Groups_Ouminus__class_Ouminus
% 0.99/1.51 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 0.99/1.51 { ! class_Groups_Ouminus( X ), hAPP( c_Groups_Ouminus__class_Ouminus(
% 0.99/1.51 tc_fun( T, X ), Z ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( Z, Y
% 0.99/1.51 ) ) }.
% 0.99/1.51 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.99/1.51 c_Groups_Ouminus__class_Ouminus( X, Z ) = c_Groups_Ouminus__class_Ouminus
% 0.99/1.51 ( X, Y ), Z = Y }.
% 0.99/1.51 { ! class_Lattices_Oboolean__algebra( X ), ! Z = Y,
% 0.99/1.51 c_Groups_Ouminus__class_Ouminus( X, Z ) = c_Groups_Ouminus__class_Ouminus
% 0.99/1.51 ( X, Y ) }.
% 0.99/1.51 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.99/1.51 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opos__poly( X, Y ),
% 0.99/1.51 c_Polynomial_Opos__poly( X, c_Groups_Ouminus__class_Ouminus(
% 0.99/1.51 tc_Polynomial_Opoly( X ), Y ) ) }.
% 0.99/1.51 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.99/1.51 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.99/1.51 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.99/1.51 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.99/1.51 { ! class_Rings_Ocomm__ring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP(
% 0.99/1.51 hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.99/1.51 c_Polynomial_Omonom( X, c_Groups_Oone__class_Oone( X ), T ) ), Z ) ), Y )
% 0.99/1.51 = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.51 c_Power_Opower__class_Opower( X ), Y ), T ) ), hAPP( c_Polynomial_Opoly(
% 0.99/1.51 X, Z ), Y ) ) }.
% 0.99/1.51 { ! class_Rings_Oidom( X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly(
% 0.99/1.51 X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) )
% 0.99/1.51 , c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.99/1.51 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ),
% 0.99/1.51 c_Polynomial_Oorder( X, Z, Y ) ), Y ) }.
% 0.99/1.51 { ! class_Rings_Ocomm__semiring__0( X ),
% 0.99/1.51 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X,
% 0.99/1.51 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus(
% 0.99/1.51 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, Y,
% 0.99/1.51 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) ),
% 0.99/1.51 c_Polynomial_OpCons( X, T,
% 0.99/1.51 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) ) ) }
% 0.99/1.51 .
% 0.99/1.51 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Y,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.51 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), T =
% 0.99/1.51 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 0.99/1.51 { ! class_Rings_Oidom( X ), ! T = c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.51 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.99/1.51 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) )
% 0.99/1.51 }.
% 0.99/1.51 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y ),
% 0.99/1.51 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.99/1.51 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) )
% 0.99/1.51 }.
% 0.99/1.51 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Z =
% 0.99/1.51 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, T, Y ) }.
% 0.99/1.51 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.51 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.99/1.51 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) )
% 0.99/1.51 }.
% 0.99/1.51 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, T, Y ),
% 0.99/1.51 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.99/1.51 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) )
% 0.99/1.51 }.
% 0.99/1.51 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Z,
% 0.99/1.51 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.51 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Z,
% 0.99/1.51 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.99/1.51 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.99/1.51 Y ), c_Rings_Odvd__class_Odvd( X, Z, hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.99/1.51 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.99/1.51 Y ), c_Rings_Odvd__class_Odvd( X, Z, hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.99/1.51 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.99/1.51 Y ), ! c_Rings_Odvd__class_Odvd( X, U, T ), c_Rings_Odvd__class_Odvd( X,
% 0.99/1.51 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.99/1.51 { ! class_Rings_Odvd( X ), ! Z = hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.51 ( X ), Y ), T ), c_Rings_Odvd__class_Odvd( X, Y, Z ) }.
% 0.99/1.51 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.99/1.51 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), Y ),
% 0.99/1.51 c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 0.99/1.51 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.99/1.51 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ),
% 0.99/1.51 c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 0.99/1.51 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.99/1.51 Y ), c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 0.99/1.51 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.99/1.51 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.99/1.51 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd(
% 0.99/1.51 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ),
% 0.99/1.51 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.99/1.51 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd(
% 0.99/1.51 tc_Polynomial_Opoly( X ), Z, Y ), c_Rings_Odvd__class_Odvd(
% 0.99/1.51 tc_Polynomial_Opoly( X ), Z, c_Polynomial_Osmult( X, T, Y ) ) }.
% 0.99/1.51 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Y, Y
% 0.99/1.51 ) }.
% 0.99/1.51 { ! class_Groups_Ozero( X ), ! c_Polynomial_Omonom( X, T, Z ) =
% 0.99/1.51 c_Polynomial_Omonom( X, Y, Z ), T = Y }.
% 0.99/1.51 { ! class_Groups_Ozero( X ), ! T = Y, c_Polynomial_Omonom( X, T, Z ) =
% 0.99/1.51 c_Polynomial_Omonom( X, Y, Z ) }.
% 0.99/1.51 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.99/1.51 Y ), ! c_Rings_Odvd__class_Odvd( X, Y, T ), c_Rings_Odvd__class_Odvd( X,
% 0.99/1.51 Z, T ) }.
% 0.99/1.51 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( X ), Y ), Y = c_Groups_Ozero__class_Ozero( X
% 0.99/1.51 ) }.
% 0.99/1.51 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.99/1.51 Y ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X,
% 0.99/1.51 Z, c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.99/1.51 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X,
% 0.99/1.51 c_Groups_Oone__class_Oone( X ), Y ) }.
% 0.99/1.51 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.99/1.51 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Rings_Odvd__class_Odvd( X, Z
% 0.99/1.51 , Y ) }.
% 0.99/1.51 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 0.99/1.51 , c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.99/1.51 ) }.
% 0.99/1.51 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.99/1.51 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ), c_Rings_Odvd__class_Odvd( X
% 0.99/1.51 , Z, Y ) }.
% 0.99/1.51 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 0.99/1.51 , c_Rings_Odvd__class_Odvd( X, c_Groups_Ouminus__class_Ouminus( X, Z ), Y
% 0.99/1.51 ) }.
% 0.99/1.51 { ! class_Rings_Ocomm__semiring__1( X ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ),
% 0.99/1.51 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.99/1.51 ), T ), Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ) ) }
% 0.99/1.51 .
% 0.99/1.51 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.99/1.51 Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, U, T ),
% 0.99/1.51 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.99/1.51 ), Z ), U ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ) ) }
% 0.99/1.51 .
% 0.99/1.51 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.99/1.51 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), Y ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, U, Z ),
% 0.99/1.51 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.99/1.51 ), T ), U ), Y ) }.
% 0.99/1.51 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 0.99/1.51 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T,
% 0.99/1.51 c_Polynomial_Osmult( X, Y, Z ) ), c_Rings_Odvd__class_Odvd(
% 0.99/1.51 tc_Polynomial_Opoly( X ), T, Z ) }.
% 0.99/1.51 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 0.99/1.51 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T, Z ),
% 0.99/1.51 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T,
% 0.99/1.51 c_Polynomial_Osmult( X, Y, Z ) ) }.
% 0.99/1.51 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.99/1.51 tc_Polynomial_Opoly( X ), Z, Y ), T = c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.51 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), c_Polynomial_Osmult(
% 0.99/1.51 X, T, Z ), Y ) }.
% 0.99/1.51 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.99/1.51 tc_Polynomial_Opoly( X ), T, c_Polynomial_Osmult( X, Z, Y ) ), Z =
% 0.99/1.51 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd(
% 0.99/1.51 tc_Polynomial_Opoly( X ), T, Y ) }.
% 0.99/1.51 { ! class_Rings_Ocomm__semiring__0( X ), !
% 0.99/1.51 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) =
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.51 { ! class_Rings_Ocomm__semiring__0( X ), ! Z = c_Groups_Ozero__class_Ozero
% 0.99/1.51 ( tc_Polynomial_Opoly( X ) ),
% 0.99/1.51 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) =
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.51 { ! class_Rings_Ocomm__semiring__0( X ),
% 0.99/1.51 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.51 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 0.99/1.51 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.51 { ! class_Groups_Ozero( X ), ! c_Polynomial_Omonom( X, Z, Y ) =
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.99/1.51 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.51 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.51 c_Polynomial_Omonom( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.99/1.51 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.51 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 0.99/1.51 c_Polynomial_Omonom( X, Z, Y ) ) = c_Polynomial_Omonom( X, hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 0.99/1.51 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.99/1.51 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, T, Z ),
% 0.99/1.51 c_Polynomial_Omonom( X, Y, Z ) ) = c_Polynomial_Omonom( X,
% 0.99/1.51 c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 0.99/1.51 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.99/1.51 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, Z, Y ) ) =
% 0.99/1.51 c_Polynomial_Omonom( X, c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.99/1.51 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.99/1.51 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ), alpha6( X
% 0.99/1.51 , Y, T ) }.
% 0.99/1.51 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.99/1.51 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ), alpha16( X
% 0.99/1.51 , Y, Z, T ) }.
% 0.99/1.51 { ! class_Fields_Ofield( X ), ! alpha6( X, Y, T ), ! alpha16( X, Y, Z, T )
% 0.99/1.51 , c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), c_Polynomial_Osmult
% 0.99/1.51 ( X, T, Z ), Y ) }.
% 0.99/1.51 { ! alpha16( X, Y, Z, T ), T = c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.51 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.99/1.51 { ! T = c_Groups_Ozero__class_Ozero( X ), alpha16( X, Y, Z, T ) }.
% 0.99/1.51 { ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, Y ), alpha16( X
% 0.99/1.51 , Y, Z, T ) }.
% 0.99/1.51 { ! alpha6( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.51 { Z = c_Groups_Ozero__class_Ozero( X ), alpha6( X, Y, Z ) }.
% 0.99/1.51 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha6( X
% 0.99/1.51 , Y, Z ) }.
% 0.99/1.51 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Orderings_Oord__class_Oless(
% 0.99/1.51 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 0.99/1.51 c_Rings_Odvd__class_Odvd( X, Y, hAPP( hAPP( c_Power_Opower__class_Opower
% 0.99/1.51 ( X ), Y ), Z ) ) }.
% 0.99/1.51 { ! class_Rings_Ocomm__semiring__1( X ), ! Y = c_Groups_Oone__class_Oone( X
% 0.99/1.51 ), c_Rings_Odvd__class_Odvd( X, Y, hAPP( hAPP(
% 0.99/1.51 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.99/1.51 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 0.99/1.51 c_Polynomial_Omonom( X, T, Z ) ), Y ) = hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.99/1.51 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.99/1.51 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X, Y,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = c_Polynomial_OpCons( X, Y
% 0.99/1.51 , c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.99/1.51 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.99/1.51 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, T, Z ) ), Y
% 0.99/1.51 ) = hAPP( c_Polynomial_Opoly( X, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.99/1.51 , Y ) ) }.
% 0.99/1.51 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.99/1.51 c_Polynomial_Omonom( X, U, T ) ), c_Polynomial_Omonom( X, Z, Y ) ) =
% 0.99/1.51 c_Polynomial_Omonom( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U
% 0.99/1.51 ), Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, Y ) ) }.
% 0.99/1.51 { ! class_Rings_Ocomm__semiring__0( X ),
% 0.99/1.51 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X,
% 0.99/1.51 c_Polynomial_OpCons( X, Z, c_Groups_Ozero__class_Ozero(
% 0.99/1.51 tc_Polynomial_Opoly( X ) ) ), Y ) = c_Polynomial_OpCons( X, Z,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.99/1.51 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.99/1.51 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd(
% 0.99/1.51 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X,
% 0.99/1.51 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Polynomial_OpCons( X,
% 0.99/1.51 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.99/1.51 tc_Polynomial_Opoly( X ) ) ) ), Z ) }.
% 0.99/1.51 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.99/1.51 ( X ), c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.99/1.51 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ), Z ), hAPP(
% 0.99/1.51 c_Polynomial_Opoly( X, Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.51 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.99/1.51 ( X ), c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 0.99/1.51 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.99/1.51 tc_Polynomial_Opoly( X ) ) ) ), Y ), hAPP( c_Polynomial_Opoly( X, Y ),
% 0.99/1.51 c_Groups_Ouminus__class_Ouminus( X, Z ) ) = c_Groups_Ozero__class_Ozero(
% 0.99/1.51 X ) }.
% 0.99/1.51 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Y ),
% 0.99/1.51 c_Groups_Ouminus__class_Ouminus( X, Z ) ) = c_Groups_Ozero__class_Ozero(
% 0.99/1.51 X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ),
% 0.99/1.51 c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 0.99/1.51 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.99/1.51 tc_Polynomial_Opoly( X ) ) ) ), Y ) }.
% 0.99/1.51 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 0.99/1.51 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ), hBOOL(
% 0.99/1.51 hAPP( Z, skol18( U, W, Z ) ) ) }.
% 0.99/1.51 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 0.99/1.51 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ),
% 0.99/1.51 c_Rings_Odvd__class_Odvd( X, Y, c_Groups_Oplus__class_Oplus( X, skol18( X
% 0.99/1.51 , Y, Z ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.99/1.51 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), !
% 0.99/1.51 c_Rings_Odvd__class_Odvd( X, Y, c_Groups_Oplus__class_Oplus( X, T,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( X ) ) ), ! hBOOL( hAPP( Z, T ) ), hBOOL(
% 0.99/1.51 hAPP( Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), skol54( X,
% 0.99/1.51 Y, Z ) ) ) ) }.
% 0.99/1.51 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.99/1.51 tc_Polynomial_Opoly( X ) ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.99/1.51 ( X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X )
% 0.99/1.51 ), c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.99/1.51 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ),
% 0.99/1.51 c_Polynomial_Oorder( X, Z, Y ) ), Y ) }.
% 0.99/1.51 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.99/1.51 tc_Polynomial_Opoly( X ) ), ! c_Rings_Odvd__class_Odvd(
% 0.99/1.51 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.99/1.51 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.99/1.51 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 0.99/1.51 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.99/1.51 tc_Polynomial_Opoly( X ) ) ) ) ), c_Nat_OSuc( c_Polynomial_Oorder( X, Z,
% 0.99/1.51 Y ) ) ), Y ) }.
% 0.99/1.51 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.99/1.51 tc_Polynomial_Opoly( X ) ), ! c_Rings_Odvd__class_Odvd(
% 0.99/1.51 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.99/1.51 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.99/1.51 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 0.99/1.51 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.99/1.51 tc_Polynomial_Opoly( X ) ) ) ) ), c_Nat_OSuc( c_Polynomial_Oorder( X, Z,
% 0.99/1.51 Y ) ) ), Y ) }.
% 0.99/1.51 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, c_Nat_OSuc(
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.99/1.51 X ) ) }.
% 0.99/1.51 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( X ) ) }.
% 0.99/1.51 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.51 tc_Nat_Onat ), c_Nat_OSuc( X ) ) }.
% 0.99/1.51 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X = c_Nat_OSuc(
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.99/1.51 { ! X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 0.99/1.51 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.99/1.51 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Groups_Oone__class_Oone(
% 0.99/1.51 tc_Nat_Onat ) ), X = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.99/1.51 { ! X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd
% 0.99/1.51 ( tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.99/1.51 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, c_Groups_Oplus__class_Oplus(
% 0.99/1.51 tc_Nat_Onat, X, Y ) ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.99/1.51 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.99/1.51 ( tc_Nat_Onat, Y, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.99/1.51 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), c_Rings_Odvd__class_Odvd
% 0.99/1.51 ( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) }.
% 0.99/1.51 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.99/1.51 ( tc_Int_Oint, Y ), X ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }
% 0.99/1.51 .
% 0.99/1.51 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), c_Rings_Odvd__class_Odvd
% 0.99/1.51 ( tc_Int_Oint, Y, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.99/1.51 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y,
% 0.99/1.51 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ),
% 0.99/1.51 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }.
% 0.99/1.51 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.99/1.51 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd(
% 0.99/1.51 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X
% 0.99/1.51 ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y
% 0.99/1.51 ) ) }.
% 0.99/1.51 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.99/1.51 c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ),
% 0.99/1.51 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 0.99/1.51 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.51 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.99/1.51 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.51 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.51 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.99/1.51 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 0.99/1.51 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) = X
% 0.99/1.51 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.99/1.51 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), X = Y }
% 0.99/1.51 .
% 0.99/1.51 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y = X }
% 0.99/1.51 .
% 0.99/1.51 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X,
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 0.99/1.51 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.99/1.51 X ) ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.99/1.51 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) )
% 0.99/1.51 }.
% 0.99/1.51 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.99/1.51 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.99/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.99/1.51 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.99/1.51 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.99/1.51 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 0.99/1.51 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.99/1.51 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 0.99/1.51 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 0.99/1.51 { ! Y = X, c_Nat_OSuc( Y ) = c_Nat_OSuc( X ) }.
% 0.99/1.51 { ! c_Nat_OSuc( X ) = X }.
% 0.99/1.51 { ! X = c_Nat_OSuc( X ) }.
% 0.99/1.51 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z
% 0.99/1.51 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.51 c_Nat_OSuc( Z ) ), X ), Y = X }.
% 0.99/1.51 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.51 c_Nat_OSuc( Z ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.99/1.51 tc_Nat_Onat ), c_Nat_OSuc( Z ) ), X ) }.
% 0.99/1.51 { hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), c_Nat_OSuc( X ) ) =
% 0.99/1.51 hAPP( hAPP( Z, Y ), hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), X
% 0.99/1.51 ) ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), X ) }
% 0.99/1.51 .
% 0.99/1.51 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 0.99/1.51 ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.99/1.51 { ! Y = c_Nat_OSuc( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 0.99/1.51 , c_Nat_OSuc( X ) ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 0.99/1.51 c_Nat_OSuc( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X )
% 0.99/1.51 }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 0.99/1.51 c_Nat_OSuc( X ) ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 0.99/1.51 ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), !
% 0.99/1.51 c_Rings_Odvd__class_Odvd( tc_Int_Oint, X, Y ), ! c_Rings_Odvd__class_Odvd
% 0.99/1.51 ( tc_Int_Oint, Y, X ), X = Y }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.99/1.51 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y
% 0.99/1.51 ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }.
% 0.99/1.51 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), Z =
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Rings_Odvd__class_Odvd(
% 0.99/1.51 tc_Int_Oint, Y, X ) }.
% 0.99/1.51 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), hAPP( hAPP(
% 0.99/1.51 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.51 c_Nat_OSuc( Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.51 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 0.99/1.51 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 0.99/1.51 tc_Int_Oint, U, T ) ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y,
% 0.99/1.51 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.99/1.51 tc_Int_Oint, U, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 0.99/1.51 , Z ), X ) ), T ) ) }.
% 0.99/1.51 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 0.99/1.51 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 0.99/1.51 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), T ) ),
% 0.99/1.51 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 0.99/1.51 tc_Int_Oint, U, T ) ) }.
% 0.99/1.51 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus(
% 0.99/1.51 tc_Int_Oint, Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 0.99/1.51 , Z ), X ) ) ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 0.99/1.51 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd
% 0.99/1.51 ( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP( hAPP
% 0.99/1.51 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ) }.
% 0.99/1.51 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.99/1.51 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.51 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) }.
% 0.99/1.51 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.99/1.51 , Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.99/1.51 , Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.99/1.51 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.51 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 0.99/1.51 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 0.99/1.51 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.99/1.51 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.51 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 0.99/1.51 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.51 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.99/1.51 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.51 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y
% 0.99/1.51 ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( c_Nat_OSuc(
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), X =
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X = c_Nat_OSuc(
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.51 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( skol19( X ) ) }.
% 0.99/1.51 { ! X = c_Nat_OSuc( Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X =
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.51 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y =
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha7( X, Y ) }.
% 0.99/1.51 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.99/1.51 { ! alpha7( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.99/1.51 c_Nat_OSuc( X ) ) }.
% 0.99/1.51 { ! alpha7( X, Y ), Y = c_Nat_OSuc( skol20( Z, Y ) ) }.
% 0.99/1.51 { ! alpha7( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol20( X,
% 0.99/1.51 Y ), X ) }.
% 0.99/1.51 { ! Y = c_Nat_OSuc( Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.99/1.51 ), alpha7( X, Y ) }.
% 0.99/1.51 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), Z =
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 0.99/1.51 tc_Nat_Onat, Y, X ) }.
% 0.99/1.51 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.99/1.51 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.99/1.51 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.99/1.51 ( tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.51 Z ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.99/1.51 X ) ) }.
% 0.99/1.51 { ! c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.99/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ), alpha8( X, Y ), alpha17
% 0.99/1.51 ( X, Y ) }.
% 0.99/1.51 { ! alpha8( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.99/1.51 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 0.99/1.51 { ! alpha17( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.99/1.51 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 0.99/1.51 { ! alpha17( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.51 { ! alpha17( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.99/1.51 tc_Nat_Onat ) ) }.
% 0.99/1.51 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha17( X, Y ) }.
% 0.99/1.51 { ! alpha8( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.99/1.51 tc_Nat_Onat ) ) }.
% 0.99/1.51 { ! alpha8( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.51 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha8( X, Y ) }.
% 0.99/1.51 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha9( X, Y ), alpha18( X
% 0.99/1.51 , Y ) }.
% 0.99/1.51 { ! alpha9( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.99/1.51 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.99/1.51 { ! alpha18( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.99/1.51 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.99/1.51 { ! alpha18( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.51 { ! alpha18( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.99/1.51 tc_Nat_Onat ) ) }.
% 0.99/1.51 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha18( X, Y ) }.
% 0.99/1.51 { ! alpha9( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.99/1.51 tc_Nat_Onat ) ) }.
% 0.99/1.51 { ! alpha9( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.51 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha9( X, Y ) }.
% 0.99/1.51 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.99/1.51 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y = c_Nat_OSuc
% 0.99/1.51 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.99/1.51 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.99/1.51 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X = c_Nat_OSuc
% 0.99/1.51 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.99/1.51 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.99/1.51 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.99/1.51 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 0.99/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.99/1.51 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 0.99/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), X = c_Nat_OSuc(
% 0.99/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol21( X, Y ) ) ) }.
% 0.99/1.51 { ! X = c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ),
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X = Y }
% 0.99/1.51 .
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X = Y,
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.99/1.51 { c_Groups_Oone__class_Oone( tc_Nat_Onat ) = c_Nat_OSuc(
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.99/1.51 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.99/1.51 ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.99/1.51 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.99/1.51 ), X ) ) }.
% 0.99/1.51 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Y )
% 0.99/1.51 ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.99/1.51 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), c_Nat_OSuc
% 0.99/1.51 ( X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.99/1.51 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.99/1.51 ), X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.99/1.51 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.99/1.51 ), X ) ) }.
% 0.99/1.51 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.99/1.51 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.99/1.51 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.99/1.51 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X ) }.
% 0.99/1.51 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), c_Nat_OSuc(
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) = c_Nat_OSuc(
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.99/1.51 { ! hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) =
% 0.99/1.51 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = c_Nat_OSuc(
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.99/1.51 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.51 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.99/1.51 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP(
% 0.99/1.51 hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc
% 0.99/1.51 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.99/1.51 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.51 tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 0.99/1.51 ) }.
% 0.99/1.51 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 0.99/1.51 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ) = hAPP( hAPP(
% 0.99/1.51 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.99/1.51 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.99/1.51 X ), Y ), Z = Y }.
% 0.99/1.51 { ! class_Rings_Olinordered__semidom( X ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.51 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ), hAPP( hAPP(
% 0.99/1.51 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ) ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.51 ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.99/1.51 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.51 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.99/1.51 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.99/1.51 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ) ) }.
% 0.99/1.51 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.99/1.51 , Z ), c_Nat_OSuc( c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.99/1.51 ) ) ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc(
% 0.99/1.51 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), Z = Y, Z =
% 0.99/1.51 c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.99/1.51 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 0.99/1.51 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP(
% 0.99/1.51 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.99/1.51 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.99/1.51 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc(
% 0.99/1.51 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP
% 0.99/1.51 ( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.99/1.51 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.51 tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 0.99/1.51 ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.51 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 0.99/1.51 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.99/1.51 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.51 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ),
% 0.99/1.51 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.99/1.51 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.51 tc_Nat_Onat ), Z ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.99/1.51 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ) }.
% 0.99/1.51 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X, Z, c_Nat_OSuc( Y ) ) =
% 0.99/1.51 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.51 c_Polynomial_Omonom( X, Z, Y ) ) }.
% 0.99/1.51 { ! class_Rings_Olinordered__semidom( X ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.51 ), ! c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone
% 0.99/1.51 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.51 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ), Y ) }.
% 0.99/1.51 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.51 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.99/1.51 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.51 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ),
% 0.99/1.51 c_Groups_Oone__class_Oone( X ) ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.51 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 0.99/1.51 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ), Y =
% 0.99/1.51 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.51 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 0.99/1.51 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.51 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 0.99/1.51 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ), Y =
% 0.99/1.51 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.51 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 0.99/1.51 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ) }.
% 0.99/1.51 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.51 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.99/1.51 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ) ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 0.99/1.51 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 0.99/1.51 ) }.
% 0.99/1.51 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.99/1.51 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.51 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.99/1.51 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ),
% 0.99/1.51 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.99/1.51 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.99/1.51 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ), c_Rings_Odvd__class_Odvd(
% 0.99/1.51 tc_Nat_Onat, hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Z )
% 0.99/1.51 , X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X )
% 0.99/1.51 ) }.
% 0.99/1.51 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.51 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.99/1.51 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ), Y =
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 0.99/1.51 tc_Nat_Onat, Z, X ) }.
% 0.99/1.51 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.51 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.99/1.51 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ), Y =
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 0.99/1.51 tc_Int_Oint, Z, X ) }.
% 0.99/1.51 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, X ) }.
% 0.99/1.51 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.99/1.51 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.99/1.51 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.99/1.51 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 0.99/1.51 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), alpha10( X, Y ), Y = X }
% 0.99/1.51 .
% 0.99/1.51 { ! alpha10( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.99/1.51 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.99/1.51 { ! alpha10( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.99/1.51 { ! alpha10( X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.99/1.51 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.99/1.51 ( tc_Nat_Onat, X, Y ), alpha10( X, Y ) }.
% 0.99/1.51 { ! alpha11( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.99/1.51 { ! alpha11( X, Y ), ! Y = X }.
% 0.99/1.51 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X, alpha11( X, Y ) }
% 0.99/1.51 .
% 0.99/1.51 { ! alpha11( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.99/1.51 { ! alpha11( X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.99/1.51 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.99/1.51 ( tc_Nat_Onat, X, Y ), alpha11( X, Y ) }.
% 0.99/1.51 { Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ),
% 0.99/1.51 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.99/1.51 { Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.99/1.51 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.99/1.51 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.99/1.51 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.99/1.51 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), X = Y }.
% 0.99/1.51 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), ! X = Y,
% 0.99/1.51 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.99/1.51 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.99/1.51 ( tc_Nat_Onat, Y, X ), Y = X }.
% 0.99/1.51 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.99/1.51 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 0.99/1.51 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X,
% 0.99/1.51 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.99/1.51 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X, !
% 0.99/1.51 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.99/1.51 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.99/1.51 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 0.99/1.51 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), ! X = Z,
% 0.99/1.51 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 0.99/1.51 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.99/1.51 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 0.99/1.51 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.99/1.51 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 0.99/1.51 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.99/1.51 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 0.99/1.51 tc_Nat_Onat, Y, Z ) }.
% 0.99/1.51 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.99/1.51 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd(
% 0.99/1.51 tc_Nat_Onat, Y, Z ) }.
% 0.99/1.51 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.99/1.51 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd
% 0.99/1.51 ( tc_Nat_Onat, Z, Y ) }.
% 0.99/1.51 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.99/1.51 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 0.99/1.51 tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 0.99/1.51 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.99/1.51 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 0.99/1.51 tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.99/1.51 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.99/1.51 ( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.99/1.51 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.99/1.51 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 0.99/1.51 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.99/1.51 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.99/1.51 ( tc_Nat_Onat, X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.99/1.51 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.99/1.51 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 0.99/1.51 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.99/1.51 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.99/1.51 ( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.99/1.51 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.99/1.51 ( tc_Nat_Onat, X, Y ), ! X = Y }.
% 0.99/1.51 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.99/1.51 ( tc_Nat_Onat, X, Y ), ! X = Z, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 0.99/1.51 , Z ) }.
% 0.99/1.51 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.99/1.51 ( tc_Nat_Onat, X, Y ), ! X = Z, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat,
% 0.99/1.51 Z, Y ) }.
% 0.99/1.51 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.99/1.51 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.99/1.51 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 0.99/1.51 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.99/1.51 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), !
% 0.99/1.51 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.99/1.51 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.99/1.51 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 0.99/1.51 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.99/1.51 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.99/1.51 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.99/1.51 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd(
% 0.99/1.51 tc_Nat_Onat, Y, Z ) }.
% 0.99/1.51 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.99/1.51 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.99/1.51 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd
% 0.99/1.51 ( tc_Nat_Onat, Z, Y ) }.
% 0.99/1.51 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.99/1.51 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 0.99/1.51 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.99/1.51 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero(
% 0.99/1.51 tc_Nat_Onat ) ) }.
% 0.99/1.51 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 0.99/1.51 tc_Nat_Onat ), X ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.51 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ),
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.51 tc_Nat_Onat ), Y ) }.
% 0.99/1.51 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.99/1.51 c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.51 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.99/1.51 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ) ),
% 0.99/1.51 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 0.99/1.51 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.99/1.51 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd(
% 0.99/1.51 tc_Int_Oint, hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z )
% 0.99/1.51 , X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X )
% 0.99/1.51 ) }.
% 0.99/1.51 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol22( Z, T ) ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.51 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Z ), Y ),
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.51 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.99/1.51 c_Polynomial_Opoly( tc_Complex_Ocomplex, X ), Z ) ), skol22( X, Y ) ) }.
% 0.99/1.51 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 0.99/1.51 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( W, X, Y,
% 0.99/1.51 Z, c_Polynomial_OpCons( X, U, T ) ) = hAPP( hAPP( hAPP( Z, U ), T ),
% 0.99/1.51 c_Polynomial_Opoly__rec( W, X, Y, Z, T ) ) }.
% 0.99/1.51 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 0.99/1.51 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( T, X, Y,
% 0.99/1.51 Z, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.99/1.51 { ! class_Groups_Ozero( X ), c_Polynomial_Opoly__rec( W, X, U, T,
% 0.99/1.51 c_Polynomial_OpCons( X, Z, Y ) ) = hAPP( hAPP( hAPP( T, Z ), Y ), c_If( W
% 0.99/1.51 , c_fequal( Y, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) )
% 0.99/1.51 , U, c_Polynomial_Opoly__rec( W, X, U, T, Y ) ) ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.99/1.51 ( tc_Int_Oint ), X ), hBOOL( hAPP( Y, skol23( Z, Y ) ) ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! hBOOL( hAPP( Y, U ) )
% 0.99/1.51 , hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, hAPP( hAPP
% 0.99/1.51 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), T ), X ) ) ) ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.99/1.51 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus(
% 0.99/1.51 tc_Int_Oint, skol23( X, Y ), X ) ) ), ! c_Orderings_Oord__class_Oless__eq
% 0.99/1.51 ( tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), ! hBOOL(
% 0.99/1.51 hAPP( Y, T ) ), hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus( tc_Int_Oint
% 0.99/1.51 , T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) )
% 0.99/1.51 ) ) }.
% 0.99/1.51 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.99/1.51 hAPP( X, Y ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol24( Z, Y
% 0.99/1.51 ), Y ) }.
% 0.99/1.51 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.99/1.51 hAPP( X, Y ) ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.99/1.51 skol24( X, Y ) ), ! hBOOL( hAPP( X, Z ) ) }.
% 0.99/1.51 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.99/1.51 hAPP( X, Y ) ), hBOOL( hAPP( X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat
% 0.99/1.51 , skol24( X, Y ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.51 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol25( Z, T ) ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.51 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), hAPP( hAPP(
% 0.99/1.51 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), skol25( X, Y ) ), X ) =
% 0.99/1.51 Y }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.51 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol26( Z, T ) ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.51 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), hAPP( hAPP(
% 0.99/1.51 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), skol26( X, Y ) ), X ) =
% 0.99/1.51 Y }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.51 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), ! hAPP( hAPP(
% 0.99/1.51 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Z ), X ) = Y, Z =
% 0.99/1.51 skol26( X, Y ) }.
% 0.99/1.51 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol27( Z, T ) ) }.
% 0.99/1.51 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.51 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.99/1.51 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol27( X, Y ) ) ) }.
% 0.99/1.51 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol28( Z, T ) ) }.
% 0.99/1.51 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.51 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.99/1.51 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol28( X, Y ) ) ) }.
% 0.99/1.51 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol29( Y ) ) }.
% 0.99/1.51 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.51 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.99/1.51 c_RealVector_Onorm__class_Onorm( X, Y ) ),
% 0.99/1.51 c_RealVector_Onorm__class_Onorm( X, Z ) ) ), skol29( X ) ) ) }.
% 0.99/1.51 { ! class_Fields_Olinordered__field__inverse__zero( X ),
% 0.99/1.51 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.51 skol30( X, T, U ) ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.99/1.51 { ! class_Fields_Olinordered__field__inverse__zero( X ),
% 0.99/1.51 c_Orderings_Oord__class_Oless( X, skol30( X, T, U ),
% 0.99/1.51 c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.99/1.51 , Y ) }.
% 0.99/1.51 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( X ), skol30( X, Y, Z ) ), Z ), Y ),
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.99/1.51 tc_Nat_Onat, Y ) ), X ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 0.99/1.51 , hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.99/1.51 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 0.99/1.51 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ), Y ) ) }.
% 0.99/1.51 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol31( Z, T ) ) }.
% 0.99/1.51 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.51 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, Z ) ), skol31( X, Y ) ) }.
% 0.99/1.51 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.51 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol55( X, Y, Z ) ) ), Z ),
% 0.99/1.51 c_SEQ_OBseq( X, Y ) }.
% 0.99/1.51 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.99/1.51 tc_Nat_Onat, X ) ) }.
% 0.99/1.51 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.51 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, Z ) ), c_RealDef_Oreal(
% 0.99/1.51 tc_Nat_Onat, c_Nat_OSuc( skol32( X, Y ) ) ) ) }.
% 0.99/1.51 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.51 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol56( X, Y, Z ) ) ),
% 0.99/1.51 c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Z ) ) ), c_SEQ_OBseq( X, Y ) }
% 0.99/1.51 .
% 0.99/1.51 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.51 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, Z ) ), c_RealDef_Oreal(
% 0.99/1.51 tc_Nat_Onat, c_Nat_OSuc( skol33( X, Y ) ) ) ) }.
% 0.99/1.51 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.51 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol57( X, Y, Z ) ) ),
% 0.99/1.51 c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Z ) ) ), c_SEQ_OBseq( X, Y ) }
% 0.99/1.51 .
% 0.99/1.51 { c_RealDef_Oreal( tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.99/1.51 tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.99/1.51 tc_RealDef_Oreal ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ), c_RealDef_Oreal
% 0.99/1.51 ( tc_Nat_Onat, X ) ) }.
% 0.99/1.51 { c_RealDef_Oreal( tc_Nat_Onat, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y
% 0.99/1.51 , X ) ) = c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal
% 0.99/1.51 ( tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 0.99/1.51 { c_RealDef_Oreal( tc_Nat_Onat, c_Groups_Oone__class_Oone( tc_Nat_Onat ) )
% 0.99/1.51 = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.99/1.51 { c_RealDef_Oreal( tc_Nat_Onat, hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.99/1.51 tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.99/1.51 tc_RealDef_Oreal ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ), X ) }.
% 0.99/1.51 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.99/1.51 c_RealDef_Oreal( tc_Nat_Onat, Y ) ), X ) = c_RealDef_Oreal( tc_Nat_Onat,
% 0.99/1.51 hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.99/1.51 { ! c_RealDef_Oreal( tc_Nat_Onat, Y ) = c_RealDef_Oreal( tc_Nat_Onat, X ),
% 0.99/1.51 Y = X }.
% 0.99/1.51 { ! Y = X, c_RealDef_Oreal( tc_Nat_Onat, Y ) = c_RealDef_Oreal( tc_Nat_Onat
% 0.99/1.51 , X ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.99/1.51 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ),
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.99/1.51 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.99/1.51 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ),
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.99/1.51 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.99/1.51 tc_Nat_Onat, X ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.99/1.51 { c_RealDef_Oreal( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.99/1.51 ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.99/1.51 { ! c_RealDef_Oreal( tc_Nat_Onat, X ) = c_Groups_Ozero__class_Ozero(
% 0.99/1.51 tc_RealDef_Oreal ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.51 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_RealDef_Oreal(
% 0.99/1.51 tc_Nat_Onat, X ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.99/1.51 tc_Nat_Onat, X ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X =
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.51 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.99/1.51 tc_Nat_Onat, X ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.99/1.51 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.99/1.51 tc_Nat_Onat, c_Nat_OSuc( X ) ) ) }.
% 0.99/1.51 { c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.99/1.51 tc_Nat_Onat ) ) ) = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.99/1.51 { c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( X ) ) =
% 0.99/1.51 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.99/1.51 tc_Nat_Onat, X ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.99/1.51 tc_Nat_Onat, X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.51 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.99/1.51 tc_Nat_Onat, X ) ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.99/1.51 tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.99/1.51 c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.99/1.51 tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.99/1.51 c_RealDef_Oreal( tc_Nat_Onat, X ) ), c_Orderings_Oord__class_Oless(
% 0.99/1.51 tc_Nat_Onat, Y, X ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.99/1.51 tc_Nat_Onat, Y ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.99/1.51 c_RealDef_Oreal( tc_Nat_Onat, X ), c_Groups_Oone__class_Oone(
% 0.99/1.51 tc_RealDef_Oreal ) ) ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.99/1.51 tc_Nat_Onat, Y ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.99/1.51 c_RealDef_Oreal( tc_Nat_Onat, X ), c_Groups_Oone__class_Oone(
% 0.99/1.51 tc_RealDef_Oreal ) ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 0.99/1.51 , X ) }.
% 0.99/1.51 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.51 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol34( X, Y, Z ) ) ), Z ),
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.51 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, T ) ), c_RealDef_Oreal(
% 0.99/1.51 tc_Nat_Onat, c_Nat_OSuc( skol58( X, Y ) ) ) ) }.
% 0.99/1.51 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.51 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol64( X, Y, Z ) ) ),
% 0.99/1.51 c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Z ) ) ),
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol68( T, U ) ) }.
% 0.99/1.51 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.51 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol64( X, Y, Z ) ) ),
% 0.99/1.51 c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Z ) ) ),
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.51 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, T ) ), skol68( X, Y ) ) }.
% 0.99/1.51 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.51 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol35( X, Y, Z ) ) ), Z ),
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.51 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, T ) ), c_RealDef_Oreal(
% 0.99/1.51 tc_Nat_Onat, c_Nat_OSuc( skol59( X, Y ) ) ) ) }.
% 0.99/1.51 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.51 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol65( X, Y, Z ) ) ),
% 0.99/1.51 c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Z ) ) ),
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol69( T, U ) ) }.
% 0.99/1.51 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.51 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol65( X, Y, Z ) ) ),
% 0.99/1.51 c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Z ) ) ),
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.51 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, T ) ), skol69( X, Y ) ) }.
% 0.99/1.51 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol36( Z, T ) ) }.
% 0.99/1.51 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.51 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, hAPP
% 0.99/1.51 ( Y, Z ), c_Groups_Ouminus__class_Ouminus( X, skol60( X, Y ) ) ) ),
% 0.99/1.51 skol36( X, Y ) ) }.
% 0.99/1.51 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.51 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, hAPP
% 0.99/1.51 ( Y, skol66( X, Y, Z, T ) ), c_Groups_Ouminus__class_Ouminus( X, T ) ) )
% 0.99/1.51 , Z ), c_SEQ_OBseq( X, Y ) }.
% 0.99/1.51 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol37( Z, T ) ) }.
% 0.99/1.51 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.51 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, hAPP
% 0.99/1.51 ( Y, Z ), c_Groups_Ouminus__class_Ouminus( X, hAPP( Y, skol61( X, Y ) ) )
% 0.99/1.51 ) ), skol37( X, Y ) ) }.
% 0.99/1.51 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.51 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, hAPP
% 0.99/1.51 ( Y, skol67( X, Y, Z, T ) ), c_Groups_Ouminus__class_Ouminus( X, hAPP( Y
% 0.99/1.51 , T ) ) ) ), Z ), c_SEQ_OBseq( X, Y ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.99/1.51 tc_Nat_Onat, skol38( X, Y ) ) ), X ), Y ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.99/1.51 tc_Nat_Onat, c_Nat_OSuc( skol38( X, Y ) ) ) ), X ) ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.99/1.51 tc_Nat_Onat, Y ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.99/1.51 tc_RealDef_Oreal, X, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.99/1.51 c_RealDef_Oreal( tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone(
% 0.99/1.51 tc_RealDef_Oreal ) ) ), c_RComplete_Onatceiling( X ) =
% 0.99/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone(
% 0.99/1.51 tc_Nat_Onat ) ) }.
% 0.99/1.51 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_RComplete_Onatceiling( X )
% 0.99/1.51 ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 0.99/1.51 Y ), c_RComplete_Onatceiling( X ) ) }.
% 0.99/1.51 { c_RComplete_Onatceiling( c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 0.99/1.51 = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.99/1.51 { c_RComplete_Onatceiling( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal )
% 0.99/1.51 ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.99/1.51 c_RComplete_Onatceiling( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.99/1.51 }.
% 0.99/1.51 { c_RComplete_Onatceiling( c_RealDef_Oreal( tc_Nat_Onat, X ) ) = X }.
% 0.99/1.51 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.99/1.51 tc_Nat_Onat, c_RComplete_Onatceiling( X ) ) ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, c_RealDef_Oreal
% 0.99/1.51 ( tc_Nat_Onat, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.51 c_RComplete_Onatceiling( Y ), X ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 0.99/1.51 X ), Y ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.99/1.51 c_RealDef_Oreal( tc_Nat_Onat, Y ) ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.99/1.51 tc_Nat_Onat, Y ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.51 c_RComplete_Onatceiling( X ), Y ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling
% 0.99/1.51 ( X ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ),
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.99/1.51 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.99/1.51 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 0.99/1.51 X ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.99/1.51 c_RComplete_Onatceiling( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X
% 0.99/1.51 , c_RealDef_Oreal( tc_Nat_Onat, Y ) ) ) = c_Groups_Oplus__class_Oplus(
% 0.99/1.51 tc_Nat_Onat, c_RComplete_Onatceiling( X ), Y ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.99/1.51 c_RComplete_Onatceiling( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X
% 0.99/1.51 , c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) =
% 0.99/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_RComplete_Onatceiling( X ),
% 0.99/1.51 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.99/1.51 c_RComplete_Onatfloor( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 0.99/1.51 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) =
% 0.99/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_RComplete_Onatfloor( X ),
% 0.99/1.51 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.99/1.51 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ),
% 0.99/1.51 c_Complex_Orcis( Z, Y ) ), X ) = c_Complex_Orcis( hAPP( hAPP(
% 0.99/1.51 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.99/1.51 tc_Nat_Onat, X ) ), Y ) ) }.
% 0.99/1.51 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) )
% 0.99/1.51 }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatfloor( Y
% 0.99/1.51 ), c_RComplete_Onatfloor( X ) ) }.
% 0.99/1.51 { c_RComplete_Onatfloor( c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) =
% 0.99/1.51 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.99/1.51 { c_RComplete_Onatfloor( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) )
% 0.99/1.51 = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.51 { c_RComplete_Onatfloor( c_RealDef_Oreal( tc_Nat_Onat, X ) ) = X }.
% 0.99/1.51 { c_Complex_Orcis( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ) =
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), c_RComplete_Onatfloor
% 0.99/1.51 ( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.99/1.51 tc_Nat_Onat, c_RComplete_Onatfloor( X ) ), X ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.99/1.51 tc_Nat_Onat, Y ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 0.99/1.51 , c_RComplete_Onatfloor( X ) ) }.
% 0.99/1.51 { ! X = c_RealDef_Oreal( tc_Nat_Onat, c_RComplete_Onatfloor( X ) ),
% 0.99/1.51 c_RComplete_Onatfloor( hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.99/1.51 tc_RealDef_Oreal ), X ), Y ) ) = hAPP( hAPP( c_Power_Opower__class_Opower
% 0.99/1.51 ( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ), Y ) }.
% 0.99/1.51 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.99/1.51 c_Complex_Orcis( T, Z ) ), c_Complex_Orcis( Y, X ) ) = c_Complex_Orcis(
% 0.99/1.51 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), T ), Y ),
% 0.99/1.51 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, X ) ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_RComplete_Onatfloor
% 0.99/1.51 ( X ) ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.51 c_RealDef_Oreal( tc_Nat_Onat, Y ), X ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.99/1.51 tc_Nat_Onat, Y ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 0.99/1.51 , c_RComplete_Onatfloor( X ) ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.51 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ),
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Groups_Oone__class_Oone
% 0.99/1.51 ( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ) }.
% 0.99/1.51 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.99/1.51 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.99/1.51 tc_Nat_Onat, c_RComplete_Onatfloor( X ) ), c_Groups_Oone__class_Oone(
% 0.99/1.51 tc_RealDef_Oreal ) ) ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.99/1.51 tc_Nat_Onat, Y ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.51 c_RComplete_Onatfloor( X ), Y ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_RComplete_Onatfloor( X )
% 0.99/1.51 ), c_RComplete_Onatfloor( Y ) ), c_RComplete_Onatfloor( hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.99/1.51 c_RComplete_Onatfloor( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 0.99/1.51 c_RealDef_Oreal( tc_Nat_Onat, Y ) ) ) = c_Groups_Oplus__class_Oplus(
% 0.99/1.51 tc_Nat_Onat, c_RComplete_Onatfloor( X ), Y ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_RComplete_Onatfloor( Y ),
% 0.99/1.51 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ),
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, c_RealDef_Oreal(
% 0.99/1.51 tc_Nat_Onat, X ) ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.99/1.51 tc_Nat_Onat, Y ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal
% 0.99/1.51 , X, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.99/1.51 tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ),
% 0.99/1.51 c_RComplete_Onatfloor( X ) = Y }.
% 0.99/1.51 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol39( Z, T ) ) }.
% 0.99/1.51 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.51 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, Z ) ), skol39( X, Y ) ) }.
% 0.99/1.51 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.51 c_RealVector_Onorm__class_Onorm( X, hAPP( Z, skol40( X, Y, Z ) ) ), Y ),
% 0.99/1.51 c_SEQ_OBseq( X, Z ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.51 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.99/1.51 tc_Nat_Onat, c_Nat_OSuc( skol41( X ) ) ) ), X ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.99/1.51 tc_Nat_Onat, skol42( X ) ), X ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.99/1.51 tc_Nat_Onat, c_Nat_OSuc( skol42( X ) ) ) ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.99/1.51 c_Transcendental_Oln( hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.99/1.51 tc_RealDef_Oreal ), X ), Y ) ) = hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.99/1.51 tc_Nat_Onat, Y ) ), c_Transcendental_Oln( X ) ) }.
% 0.99/1.51 { ! class_Orderings_Oorder( X ), ! c_SEQ_Oincseq( X, Y ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, T ),
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, Z ), hAPP( Y, T ) ) }.
% 0.99/1.51 { ! class_Orderings_Oorder( X ), c_Orderings_Oord__class_Oless__eq(
% 0.99/1.51 tc_Nat_Onat, skol43( X, Y ), skol62( X, Y ) ), c_SEQ_Oincseq( X, Y ) }.
% 0.99/1.51 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.51 hAPP( Y, skol43( X, Y ) ), hAPP( Y, skol62( X, Y ) ) ), c_SEQ_Oincseq( X
% 0.99/1.51 , Y ) }.
% 0.99/1.51 { c_Transcendental_Oln( c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) =
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 0.99/1.51 ), c_Transcendental_Oln( Y ) ), c_Orderings_Oord__class_Oless(
% 0.99/1.51 tc_RealDef_Oreal, X, Y ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, Y ),
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 0.99/1.51 ), c_Transcendental_Oln( Y ) ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.99/1.51 c_Transcendental_Oln( X ) = c_Transcendental_Oln( Y ), X = Y }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), ! X = Y,
% 0.99/1.51 c_Transcendental_Oln( X ) = c_Transcendental_Oln( Y ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 0.99/1.51 ), X ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_Transcendental_Oln
% 0.99/1.51 ( X ), c_Transcendental_Oln( Y ) ), c_Orderings_Oord__class_Oless__eq(
% 0.99/1.51 tc_RealDef_Oreal, X, Y ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ),
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_Transcendental_Oln
% 0.99/1.51 ( X ), c_Transcendental_Oln( Y ) ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 0.99/1.51 ) ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 0.99/1.51 ) ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 0.99/1.51 ) ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 0.99/1.51 ) ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.99/1.51 c_Transcendental_Oln( X ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal
% 0.99/1.51 ), X = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), ! X =
% 0.99/1.51 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_Transcendental_Oln( X )
% 0.99/1.51 = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 0.99/1.51 ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.99/1.51 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.99/1.51 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 0.99/1.51 ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.99/1.51 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 0.99/1.51 ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 0.99/1.51 ) ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 0.99/1.51 ) ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 0.99/1.51 ) ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 0.99/1.51 ) ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.99/1.51 c_Transcendental_Oln( hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.99/1.51 tc_RealDef_Oreal ), X ), Y ) ) = c_Groups_Oplus__class_Oplus(
% 0.99/1.51 tc_RealDef_Oreal, c_Transcendental_Oln( X ), c_Transcendental_Oln( Y ) )
% 0.99/1.51 }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_Transcendental_Oln
% 0.99/1.51 ( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) ), X ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.99/1.51 c_Transcendental_Oln( c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal
% 0.99/1.51 , X ) ) = c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal,
% 0.99/1.51 c_Transcendental_Oln( X ) ) }.
% 0.99/1.51 { c_Complex_Ocis( hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.99/1.51 tc_RealDef_Oreal ), c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Y ) ) ), X
% 0.99/1.51 ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.99/1.51 c_Complex_Ocis( X ) ), c_Complex_Ocis( hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.99/1.51 tc_Nat_Onat, Y ) ), X ) ) ) }.
% 0.99/1.51 { c_Complex_Oexpi( c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) =
% 0.99/1.51 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) }.
% 0.99/1.51 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.99/1.51 c_Complex_Ocis( Y ) ), c_Complex_Ocis( X ) ) = c_Complex_Ocis(
% 0.99/1.51 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ) }.
% 0.99/1.51 { c_Rings_Oinverse__class_Oinverse( tc_Complex_Ocomplex, c_Complex_Ocis( X
% 0.99/1.51 ) ) = c_Complex_Ocis( c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal
% 0.99/1.51 , X ) ) }.
% 0.99/1.51 { c_Complex_Ocis( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) =
% 0.99/1.51 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) }.
% 0.99/1.51 { c_Complex_Ocis( X ) = c_Complex_Orcis( c_Groups_Oone__class_Oone(
% 0.99/1.51 tc_RealDef_Oreal ), X ) }.
% 0.99/1.51 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ),
% 0.99/1.51 c_Complex_Ocis( Y ) ), X ) = c_Complex_Ocis( hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.99/1.51 tc_Nat_Onat, X ) ), Y ) ) }.
% 0.99/1.51 { c_Complex_Oexpi( c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X )
% 0.99/1.51 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.99/1.51 c_Complex_Oexpi( Y ) ), c_Complex_Oexpi( X ) ) }.
% 0.99/1.51 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, skol44( U, W, V0, T )
% 0.99/1.51 ), c_SEQ_OBseq( X, Y ) }.
% 0.99/1.51 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.51 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol44( X, Y, Z, T ) ) ), Z
% 0.99/1.51 ), c_SEQ_OBseq( X, Y ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.99/1.51 tc_Nat_Onat, skol45( X, Y ) ) ), X ) ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol46( Z, T ) ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), hAPP( hAPP(
% 0.99/1.51 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), skol46( X, Y ) ),
% 0.99/1.51 c_Nat_OSuc( Y ) ) = X }.
% 0.99/1.51 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.51 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.99/1.51 c_RealVector_Onorm__class_Onorm( X, Y ) ),
% 0.99/1.51 c_RealVector_Onorm__class_Onorm( X, Z ) ) ), skol47( X ) ) ) }.
% 0.99/1.51 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.51 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.99/1.51 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol48( X, Y ) ) ) }.
% 0.99/1.51 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.51 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.99/1.51 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol49( X, Y ) ) ) }.
% 0.99/1.51 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless(
% 0.99/1.51 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), hAPP( hAPP
% 0.99/1.51 ( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.51 c_Power_Opower__class_Opower( X ), Z ), c_Groups_Ominus__class_Ominus(
% 0.99/1.51 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ), Z ) =
% 0.99/1.51 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) }.
% 0.99/1.51 { ! class_Power_Opower( X ), ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 0.99/1.51 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) =
% 0.99/1.51 c_Groups_Oone__class_Oone( X ) }.
% 0.99/1.51 { ! class_Power_Opower( X ), Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.99/1.51 , hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) = hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.99/1.51 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ominus__class_Ominus(
% 0.99/1.51 tc_Nat_Onat, Z, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, c_Nat_OSuc(
% 0.99/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) ) =
% 0.99/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.51 tc_Nat_Onat, Z, Y ), c_Nat_OSuc( X ) ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc(
% 0.99/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), Z ) =
% 0.99/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 0.99/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 0.99/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ),
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ),
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 0.99/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.51 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 0.99/1.51 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) =
% 0.99/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.51 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ) =
% 0.99/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ),
% 0.99/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ) = Z }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ) = Z,
% 0.99/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ) =
% 0.99/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ),
% 0.99/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ),
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T,
% 0.99/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T,
% 0.99/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ),
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ),
% 0.99/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.51 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 0.99/1.51 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) =
% 0.99/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, T,
% 0.99/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ) =
% 0.99/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ), T =
% 0.99/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! T =
% 0.99/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ),
% 0.99/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ) =
% 0.99/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) }.
% 0.99/1.51 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.51 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.99/1.51 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.51 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X, T,
% 0.99/1.51 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.51 ( X ), c_Groups_Ominus__class_Ominus( X, Z, W ) ), U ), Y ) ) }.
% 0.99/1.51 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.51 , T, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.99/1.51 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.51 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.51 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.99/1.51 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.51 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.99/1.51 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.51 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.51 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.51 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ) }.
% 0.99/1.51 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.51 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.99/1.51 Z ) ), U ), T ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.51 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.51 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.99/1.51 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, c_Groups_Ominus__class_Ominus
% 0.99/1.51 ( tc_Nat_Onat, Y, X ) ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X )
% 0.99/1.51 , ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ),
% 0.99/1.51 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.99/1.51 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, c_Groups_Ominus__class_Ominus
% 0.99/1.51 ( tc_Nat_Onat, Y, X ) ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y )
% 0.99/1.51 , ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ),
% 0.99/1.51 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ) }.
% 0.99/1.51 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.99/1.51 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ), c_Rings_Odvd__class_Odvd(
% 0.99/1.51 tc_Nat_Onat, Y, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) }.
% 0.99/1.51 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 0.99/1.51 , ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X, Z,
% 0.99/1.51 c_Groups_Ominus__class_Ominus( X, Y, T ) ) }.
% 0.99/1.51 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 0.99/1.51 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, T, Z ),
% 0.99/1.51 c_Polynomial_Omonom( X, Y, Z ) ) = c_Polynomial_Omonom( X,
% 0.99/1.51 c_Groups_Ominus__class_Ominus( X, T, Y ), Z ) }.
% 0.99/1.51 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.99/1.51 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) =
% 0.99/1.51 c_Groups_Ominus__class_Ominus( X, Y, Z ) }.
% 0.99/1.51 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.99/1.51 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.99/1.51 c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.99/1.51 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.99/1.51 X, U, Z ) ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 0.99/1.51 Z ) ), Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 0.99/1.51 c_Groups_Ominus__class_Ominus( X, T, Y ) ) ) }.
% 0.99/1.51 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.99/1.51 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.51 ( X ), Z ), U ), Y ), T = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.99/1.51 W ) ), U ), Y ) }.
% 0.99/1.51 { ! class_Rings_Oring( X ), ! T = c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.99/1.51 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.99/1.51 X, Z, W ) ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.99/1.51 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.51 ( X ), Z ), U ), Y ) }.
% 0.99/1.51 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.99/1.51 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.51 ( X ), Z ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.99/1.51 Z ) ), U ), T ) = Y }.
% 0.99/1.51 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.99/1.51 Z ) ), U ), T ) = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.99/1.51 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.51 ( X ), Z ), U ), Y ) }.
% 0.99/1.51 { ! class_Rings_Oring( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.99/1.51 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.51 ( X ), U ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 0.99/1.51 Z ) ), Y ) ) }.
% 0.99/1.51 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.99/1.51 X, Y ) }.
% 0.99/1.51 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.99/1.51 ) = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus(
% 0.99/1.51 X, Y ) ) }.
% 0.99/1.51 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.99/1.51 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Oplus__class_Oplus(
% 0.99/1.51 X, Z, Y ) }.
% 0.99/1.51 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X, Z
% 0.99/1.51 , Y ) = c_Groups_Oplus__class_Oplus( X, Z,
% 0.99/1.51 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.99/1.51 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z, Y )
% 0.99/1.51 = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus( X
% 0.99/1.51 , Y ) ) }.
% 0.99/1.51 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 0.99/1.51 , Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.51 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 0.99/1.51 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.99/1.51 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.99/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.99/1.51 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, X ) =
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.51 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = X }.
% 0.99/1.51 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.51 tc_Nat_Onat ), X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.99/1.51 ( tc_Nat_Onat, Z, X ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.99/1.51 ) }.
% 0.99/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.99/1.51 ( tc_Nat_Onat, Y, Z ), X ) }.
% 0.99/1.51 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.51 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) =
% 0.99/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ) }.
% 0.99/1.51 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.51 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) =
% 0.99/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 0.99/1.51 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.99/1.51 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.99/1.51 Z, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.99/1.51 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.51 tc_Nat_Onat, Y, X ), Y ) = X }.
% 0.99/1.51 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.51 tc_Nat_Onat, Y, X ), X ) = Y }.
% 0.99/1.51 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y,
% 0.99/1.51 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.99/1.51 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y, Y )
% 0.99/1.51 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.51 { ! class_Groups_Oab__group__add( X ), ! Z = Y,
% 0.99/1.51 c_Groups_Ominus__class_Ominus( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.99/1.51 ) }.
% 0.99/1.51 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.99/1.51 Z, Y ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.99/1.51 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.99/1.51 ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.99/1.51 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ominus__class_Ominus(
% 0.99/1.51 X, Z, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.51 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.99/1.51 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = Z }.
% 0.99/1.51 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.99/1.51 class_Groups_Ocancel__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.51 { class_Groups_Ocancel__comm__monoid__add( tc_Complex_Ocomplex ) }.
% 0.99/1.51 { class_Groups_Ocancel__comm__monoid__add( tc_RealDef_Oreal ) }.
% 0.99/1.51 { class_Groups_Ocancel__comm__monoid__add( tc_Nat_Onat ) }.
% 0.99/1.51 { class_Groups_Ocancel__comm__monoid__add( tc_Int_Oint ) }.
% 0.99/1.51 { ! class_Lattices_Oboolean__algebra( X ), class_Lattices_Oboolean__algebra
% 0.99/1.51 ( tc_fun( Y, X ) ) }.
% 0.99/1.51 { ! class_Orderings_Opreorder( X ), class_Orderings_Opreorder( tc_fun( Y, X
% 0.99/1.51 ) ) }.
% 0.99/1.51 { ! class_Orderings_Oorder( X ), class_Orderings_Oorder( tc_fun( Y, X ) ) }
% 0.99/1.51 .
% 0.99/1.51 { ! class_Orderings_Oord( X ), class_Orderings_Oord( tc_fun( Y, X ) ) }.
% 0.99/1.51 { ! class_Groups_Ouminus( X ), class_Groups_Ouminus( tc_fun( Y, X ) ) }.
% 0.99/1.51 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.99/1.51 tc_Int_Oint ) }.
% 0.99/1.51 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.99/1.51 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Int_Oint ) }.
% 0.99/1.51 { class_Rings_Olinordered__comm__semiring__strict( tc_Int_Oint ) }.
% 0.99/1.51 { class_Rings_Olinordered__semiring__1__strict( tc_Int_Oint ) }.
% 0.99/1.51 { class_Rings_Olinordered__semiring__strict( tc_Int_Oint ) }.
% 0.99/1.51 { class_Groups_Oordered__ab__semigroup__add( tc_Int_Oint ) }.
% 0.99/1.51 { class_Groups_Oordered__comm__monoid__add( tc_Int_Oint ) }.
% 0.99/1.51 { class_Groups_Olinordered__ab__group__add( tc_Int_Oint ) }.
% 0.99/1.51 { class_Groups_Ocancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.99/1.51 { class_Rings_Oring__1__no__zero__divisors( tc_Int_Oint ) }.
% 0.99/1.51 { class_Rings_Oordered__cancel__semiring( tc_Int_Oint ) }.
% 0.99/1.51 { class_Rings_Olinordered__ring__strict( tc_Int_Oint ) }.
% 0.99/1.51 { class_Rings_Oring__no__zero__divisors( tc_Int_Oint ) }.
% 0.99/1.51 { class_Rings_Oordered__comm__semiring( tc_Int_Oint ) }.
% 0.99/1.51 { class_Rings_Olinordered__semiring__1( tc_Int_Oint ) }.
% 0.99/1.51 { class_Groups_Oordered__ab__group__add( tc_Int_Oint ) }.
% 0.99/1.51 { class_Groups_Ocancel__semigroup__add( tc_Int_Oint ) }.
% 0.99/1.51 { class_Rings_Olinordered__semiring( tc_Int_Oint ) }.
% 0.99/1.51 { class_Rings_Olinordered__semidom( tc_Int_Oint ) }.
% 0.99/1.51 { class_Groups_Oab__semigroup__mult( tc_Int_Oint ) }.
% 0.99/1.51 { class_Groups_Ocomm__monoid__mult( tc_Int_Oint ) }.
% 0.99/1.51 { class_Groups_Oab__semigroup__add( tc_Int_Oint ) }.
% 0.99/1.51 { class_Rings_Oordered__semiring( tc_Int_Oint ) }.
% 0.99/1.51 { class_Rings_Ono__zero__divisors( tc_Int_Oint ) }.
% 0.99/1.51 { class_Groups_Ocomm__monoid__add( tc_Int_Oint ) }.
% 0.99/1.51 { class_Rings_Olinordered__ring( tc_Int_Oint ) }.
% 0.99/1.51 { class_Rings_Olinordered__idom( tc_Int_Oint ) }.
% 0.99/1.51 { class_Rings_Ocomm__semiring__1( tc_Int_Oint ) }.
% 0.99/1.51 { class_Rings_Ocomm__semiring__0( tc_Int_Oint ) }.
% 0.99/1.51 { class_Rings_Ocomm__semiring( tc_Int_Oint ) }.
% 0.99/1.51 { class_Groups_Oab__group__add( tc_Int_Oint ) }.
% 0.99/1.51 { class_Rings_Ozero__neq__one( tc_Int_Oint ) }.
% 0.99/1.51 { class_Rings_Oordered__ring( tc_Int_Oint ) }.
% 0.99/1.51 { class_Orderings_Opreorder( tc_Int_Oint ) }.
% 0.99/1.51 { class_Orderings_Olinorder( tc_Int_Oint ) }.
% 0.99/1.51 { class_Groups_Omonoid__mult( tc_Int_Oint ) }.
% 0.99/1.51 { class_Rings_Ocomm__ring__1( tc_Int_Oint ) }.
% 0.99/1.51 { class_Groups_Omonoid__add( tc_Int_Oint ) }.
% 0.99/1.51 { class_Rings_Osemiring__0( tc_Int_Oint ) }.
% 0.99/1.51 { class_Groups_Ogroup__add( tc_Int_Oint ) }.
% 0.99/1.51 { class_Rings_Omult__zero( tc_Int_Oint ) }.
% 0.99/1.51 { class_Rings_Ocomm__ring( tc_Int_Oint ) }.
% 0.99/1.51 { class_Orderings_Oorder( tc_Int_Oint ) }.
% 0.99/1.51 { class_Int_Oring__char__0( tc_Int_Oint ) }.
% 0.99/1.51 { class_Rings_Osemiring( tc_Int_Oint ) }.
% 0.99/1.51 { class_Orderings_Oord( tc_Int_Oint ) }.
% 0.99/1.51 { class_Groups_Ouminus( tc_Int_Oint ) }.
% 0.99/1.51 { class_Rings_Oring__1( tc_Int_Oint ) }.
% 0.99/1.51 { class_Power_Opower( tc_Int_Oint ) }.
% 0.99/1.51 { class_Groups_Ozero( tc_Int_Oint ) }.
% 0.99/1.51 { class_Rings_Oring( tc_Int_Oint ) }.
% 0.99/1.51 { class_Rings_Oidom( tc_Int_Oint ) }.
% 0.99/1.51 { class_Groups_Oone( tc_Int_Oint ) }.
% 0.99/1.51 { class_Rings_Odvd( tc_Int_Oint ) }.
% 0.99/1.51 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.99/1.51 tc_Nat_Onat ) }.
% 0.99/1.51 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.99/1.51 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Nat_Onat ) }.
% 0.99/1.51 { class_Rings_Olinordered__comm__semiring__strict( tc_Nat_Onat ) }.
% 0.99/1.51 { class_Rings_Olinordered__semiring__strict( tc_Nat_Onat ) }.
% 0.99/1.51 { class_Groups_Oordered__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.99/1.51 { class_Groups_Oordered__comm__monoid__add( tc_Nat_Onat ) }.
% 0.99/1.51 { class_Groups_Ocancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.99/1.51 { class_Rings_Oordered__cancel__semiring( tc_Nat_Onat ) }.
% 0.99/1.51 { class_Rings_Oordered__comm__semiring( tc_Nat_Onat ) }.
% 0.99/1.51 { class_Groups_Ocancel__semigroup__add( tc_Nat_Onat ) }.
% 0.99/1.51 { class_Rings_Olinordered__semiring( tc_Nat_Onat ) }.
% 0.99/1.51 { class_Rings_Olinordered__semidom( tc_Nat_Onat ) }.
% 0.99/1.51 { class_Groups_Oab__semigroup__mult( tc_Nat_Onat ) }.
% 0.99/1.51 { class_Groups_Ocomm__monoid__mult( tc_Nat_Onat ) }.
% 0.99/1.51 { class_Groups_Oab__semigroup__add( tc_Nat_Onat ) }.
% 0.99/1.51 { class_Rings_Oordered__semiring( tc_Nat_Onat ) }.
% 0.99/1.51 { class_Rings_Ono__zero__divisors( tc_Nat_Onat ) }.
% 0.99/1.51 { class_Groups_Ocomm__monoid__add( tc_Nat_Onat ) }.
% 0.99/1.51 { class_Rings_Ocomm__semiring__1( tc_Nat_Onat ) }.
% 0.99/1.51 { class_Rings_Ocomm__semiring__0( tc_Nat_Onat ) }.
% 0.99/1.51 { class_Rings_Ocomm__semiring( tc_Nat_Onat ) }.
% 0.99/1.51 { class_Rings_Ozero__neq__one( tc_Nat_Onat ) }.
% 0.99/1.51 { class_Orderings_Opreorder( tc_Nat_Onat ) }.
% 0.99/1.51 { class_Orderings_Olinorder( tc_Nat_Onat ) }.
% 0.99/1.51 { class_Groups_Omonoid__mult( tc_Nat_Onat ) }.
% 0.99/1.51 { class_Groups_Omonoid__add( tc_Nat_Onat ) }.
% 0.99/1.51 { class_Rings_Osemiring__0( tc_Nat_Onat ) }.
% 0.99/1.51 { class_Rings_Omult__zero( tc_Nat_Onat ) }.
% 0.99/1.51 { class_Orderings_Oorder( tc_Nat_Onat ) }.
% 0.99/1.51 { class_Rings_Osemiring( tc_Nat_Onat ) }.
% 0.99/1.51 { class_Orderings_Oord( tc_Nat_Onat ) }.
% 0.99/1.51 { class_Power_Opower( tc_Nat_Onat ) }.
% 0.99/1.51 { class_Groups_Ozero( tc_Nat_Onat ) }.
% 0.99/1.51 { class_Groups_Oone( tc_Nat_Onat ) }.
% 0.99/1.51 { class_Rings_Odvd( tc_Nat_Onat ) }.
% 0.99/1.51 { class_Lattices_Oboolean__algebra( tc_HOL_Obool ) }.
% 0.99/1.51 { class_Orderings_Opreorder( tc_HOL_Obool ) }.
% 0.99/1.51 { class_Orderings_Oorder( tc_HOL_Obool ) }.
% 0.99/1.51 { class_Orderings_Oord( tc_HOL_Obool ) }.
% 0.99/1.51 { class_Groups_Ouminus( tc_HOL_Obool ) }.
% 0.99/1.51 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.99/1.51 tc_RealDef_Oreal ) }.
% 0.99/1.51 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.99/1.51 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_RealDef_Oreal ) }
% 0.99/1.51 .
% 0.99/1.51 { class_Rings_Olinordered__comm__semiring__strict( tc_RealDef_Oreal ) }.
% 0.99/1.51 { class_Fields_Olinordered__field__inverse__zero( tc_RealDef_Oreal ) }.
% 0.99/1.51 { class_Rings_Olinordered__semiring__1__strict( tc_RealDef_Oreal ) }.
% 0.99/1.51 { class_RealVector_Oreal__normed__div__algebra( tc_RealDef_Oreal ) }.
% 0.99/1.51 { class_Rings_Olinordered__semiring__strict( tc_RealDef_Oreal ) }.
% 0.99/1.51 { class_Rings_Odivision__ring__inverse__zero( tc_RealDef_Oreal ) }.
% 0.99/1.51 { class_RealVector_Oreal__normed__algebra__1( tc_RealDef_Oreal ) }.
% 0.99/1.51 { class_Groups_Oordered__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.99/1.51 { class_RealVector_Oreal__normed__algebra( tc_RealDef_Oreal ) }.
% 0.99/1.51 { class_Groups_Oordered__comm__monoid__add( tc_RealDef_Oreal ) }.
% 0.99/1.51 { class_Groups_Olinordered__ab__group__add( tc_RealDef_Oreal ) }.
% 0.99/1.51 { class_Groups_Ocancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.99/1.51 { class_Rings_Oring__1__no__zero__divisors( tc_RealDef_Oreal ) }.
% 0.99/1.51 { class_Rings_Oordered__cancel__semiring( tc_RealDef_Oreal ) }.
% 0.99/1.51 { class_RealVector_Oreal__normed__vector( tc_RealDef_Oreal ) }.
% 0.99/1.51 { class_Rings_Olinordered__ring__strict( tc_RealDef_Oreal ) }.
% 0.99/1.51 { class_Rings_Oring__no__zero__divisors( tc_RealDef_Oreal ) }.
% 0.99/1.51 { class_Rings_Oordered__comm__semiring( tc_RealDef_Oreal ) }.
% 0.99/1.51 { class_Rings_Olinordered__semiring__1( tc_RealDef_Oreal ) }.
% 0.99/1.51 { class_Groups_Oordered__ab__group__add( tc_RealDef_Oreal ) }.
% 0.99/1.51 { class_Groups_Ocancel__semigroup__add( tc_RealDef_Oreal ) }.
% 0.99/1.51 { class_Rings_Olinordered__semiring( tc_RealDef_Oreal ) }.
% 0.99/1.51 { class_Fields_Ofield__inverse__zero( tc_RealDef_Oreal ) }.
% 0.99/1.51 { class_Rings_Olinordered__semidom( tc_RealDef_Oreal ) }.
% 0.99/1.51 { class_Groups_Oab__semigroup__mult( tc_RealDef_Oreal ) }.
% 0.99/1.51 { class_Groups_Ocomm__monoid__mult( tc_RealDef_Oreal ) }.
% 0.99/1.51 { class_Groups_Oab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.99/1.51 { class_Fields_Olinordered__field( tc_RealDef_Oreal ) }.
% 0.99/1.51 { class_Rings_Oordered__semiring( tc_RealDef_Oreal ) }.
% 0.99/1.51 { class_Rings_Ono__zero__divisors( tc_RealDef_Oreal ) }.
% 0.99/1.51 { class_Groups_Ocomm__monoid__add( tc_RealDef_Oreal ) }.
% 0.99/1.51 { class_Rings_Olinordered__ring( tc_RealDef_Oreal ) }.
% 0.99/1.51 { class_Rings_Olinordered__idom( tc_RealDef_Oreal ) }.
% 0.99/1.51 { class_Rings_Ocomm__semiring__1( tc_RealDef_Oreal ) }.
% 0.99/1.51 { class_Rings_Ocomm__semiring__0( tc_RealDef_Oreal ) }.
% 0.99/1.51 { class_Rings_Odivision__ring( tc_RealDef_Oreal ) }.
% 0.99/1.51 { class_Rings_Ocomm__semiring( tc_RealDef_Oreal ) }.
% 0.99/1.51 { class_Groups_Oab__group__add( tc_RealDef_Oreal ) }.
% 0.99/1.51 { class_Rings_Ozero__neq__one( tc_RealDef_Oreal ) }.
% 0.99/1.51 { class_Rings_Oordered__ring( tc_RealDef_Oreal ) }.
% 0.99/1.51 { class_Orderings_Opreorder( tc_RealDef_Oreal ) }.
% 0.99/1.51 { class_Orderings_Olinorder( tc_RealDef_Oreal ) }.
% 0.99/1.51 { class_Groups_Omonoid__mult( tc_RealDef_Oreal ) }.
% 0.99/1.51 { class_Rings_Ocomm__ring__1( tc_RealDef_Oreal ) }.
% 0.99/1.51 { class_Groups_Omonoid__add( tc_RealDef_Oreal ) }.
% 0.99/1.51 { class_Rings_Osemiring__0( tc_RealDef_Oreal ) }.
% 0.99/1.51 { class_Groups_Ogroup__add( tc_RealDef_Oreal ) }.
% 0.99/1.51 { class_Rings_Omult__zero( tc_RealDef_Oreal ) }.
% 0.99/1.51 { class_Rings_Ocomm__ring( tc_RealDef_Oreal ) }.
% 0.99/1.51 { class_Orderings_Oorder( tc_RealDef_Oreal ) }.
% 0.99/1.51 { class_Int_Oring__char__0( tc_RealDef_Oreal ) }.
% 0.99/1.51 { class_Rings_Osemiring( tc_RealDef_Oreal ) }.
% 0.99/1.51 { class_Orderings_Oord( tc_RealDef_Oreal ) }.
% 0.99/1.51 { class_Groups_Ouminus( tc_RealDef_Oreal ) }.
% 0.99/1.51 { class_Rings_Oring__1( tc_RealDef_Oreal ) }.
% 0.99/1.51 { class_Fields_Ofield( tc_RealDef_Oreal ) }.
% 0.99/1.51 { class_Power_Opower( tc_RealDef_Oreal ) }.
% 0.99/1.51 { class_Groups_Ozero( tc_RealDef_Oreal ) }.
% 0.99/1.51 { class_Rings_Oring( tc_RealDef_Oreal ) }.
% 0.99/1.51 { class_Rings_Oidom( tc_RealDef_Oreal ) }.
% 0.99/1.51 { class_Groups_Oone( tc_RealDef_Oreal ) }.
% 0.99/1.51 { class_Rings_Odvd( tc_RealDef_Oreal ) }.
% 0.99/1.51 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.99/1.51 tc_Complex_Ocomplex ) }.
% 0.99/1.51 { class_RealVector_Oreal__normed__div__algebra( tc_Complex_Ocomplex ) }.
% 0.99/1.51 { class_Rings_Odivision__ring__inverse__zero( tc_Complex_Ocomplex ) }.
% 0.99/1.51 { class_RealVector_Oreal__normed__algebra__1( tc_Complex_Ocomplex ) }.
% 0.99/1.51 { class_RealVector_Oreal__normed__algebra( tc_Complex_Ocomplex ) }.
% 0.99/1.51 { class_Groups_Ocancel__ab__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.99/1.51 { class_Rings_Oring__1__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.99/1.51 { class_RealVector_Oreal__normed__vector( tc_Complex_Ocomplex ) }.
% 0.99/1.51 { class_Rings_Oring__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.99/1.51 { class_Groups_Ocancel__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.99/1.51 { class_Fields_Ofield__inverse__zero( tc_Complex_Ocomplex ) }.
% 0.99/1.51 { class_Groups_Oab__semigroup__mult( tc_Complex_Ocomplex ) }.
% 0.99/1.51 { class_Groups_Ocomm__monoid__mult( tc_Complex_Ocomplex ) }.
% 0.99/1.51 { class_Groups_Oab__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.99/1.51 { class_Rings_Ono__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.99/1.51 { class_Groups_Ocomm__monoid__add( tc_Complex_Ocomplex ) }.
% 0.99/1.51 { class_Rings_Ocomm__semiring__1( tc_Complex_Ocomplex ) }.
% 0.99/1.51 { class_Rings_Ocomm__semiring__0( tc_Complex_Ocomplex ) }.
% 0.99/1.51 { class_Rings_Odivision__ring( tc_Complex_Ocomplex ) }.
% 0.99/1.51 { class_Rings_Ocomm__semiring( tc_Complex_Ocomplex ) }.
% 0.99/1.51 { class_Groups_Oab__group__add( tc_Complex_Ocomplex ) }.
% 0.99/1.51 { class_Rings_Ozero__neq__one( tc_Complex_Ocomplex ) }.
% 0.99/1.51 { class_Groups_Omonoid__mult( tc_Complex_Ocomplex ) }.
% 0.99/1.51 { class_Rings_Ocomm__ring__1( tc_Complex_Ocomplex ) }.
% 0.99/1.51 { class_Groups_Omonoid__add( tc_Complex_Ocomplex ) }.
% 0.99/1.51 { class_Rings_Osemiring__0( tc_Complex_Ocomplex ) }.
% 0.99/1.51 { class_Groups_Ogroup__add( tc_Complex_Ocomplex ) }.
% 0.99/1.51 { class_Rings_Omult__zero( tc_Complex_Ocomplex ) }.
% 0.99/1.51 { class_Rings_Ocomm__ring( tc_Complex_Ocomplex ) }.
% 0.99/1.51 { class_Int_Oring__char__0( tc_Complex_Ocomplex ) }.
% 0.99/1.51 { class_Rings_Osemiring( tc_Complex_Ocomplex ) }.
% 0.99/1.51 { class_Groups_Ouminus( tc_Complex_Ocomplex ) }.
% 0.99/1.51 { class_Rings_Oring__1( tc_Complex_Ocomplex ) }.
% 0.99/1.51 { class_Fields_Ofield( tc_Complex_Ocomplex ) }.
% 0.99/1.51 { class_Power_Opower( tc_Complex_Ocomplex ) }.
% 0.99/1.51 { class_Groups_Ozero( tc_Complex_Ocomplex ) }.
% 0.99/1.51 { class_Rings_Oring( tc_Complex_Ocomplex ) }.
% 0.99/1.51 { class_Rings_Oidom( tc_Complex_Ocomplex ) }.
% 0.99/1.51 { class_Groups_Oone( tc_Complex_Ocomplex ) }.
% 0.99/1.51 { class_Rings_Odvd( tc_Complex_Ocomplex ) }.
% 0.99/1.51 { ! class_Rings_Oidom( X ),
% 0.99/1.51 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.99/1.51 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.51 { ! class_Rings_Olinordered__idom( X ),
% 0.99/1.51 class_Groups_Oordered__cancel__ab__semigroup__add( tc_Polynomial_Opoly( X
% 0.99/1.51 ) ) }.
% 0.99/1.51 { ! class_Rings_Olinordered__idom( X ),
% 0.99/1.51 class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Polynomial_Opoly(
% 0.99/1.51 X ) ) }.
% 0.99/1.51 { ! class_Rings_Olinordered__idom( X ),
% 0.99/1.51 class_Rings_Olinordered__comm__semiring__strict( tc_Polynomial_Opoly( X )
% 0.99/1.51 ) }.
% 0.99/1.51 { ! class_Rings_Olinordered__idom( X ),
% 0.99/1.51 class_Rings_Olinordered__semiring__1__strict( tc_Polynomial_Opoly( X ) )
% 0.99/1.51 }.
% 0.99/1.51 { ! class_Rings_Olinordered__idom( X ),
% 0.99/1.51 class_Rings_Olinordered__semiring__strict( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.51 { ! class_Rings_Olinordered__idom( X ),
% 0.99/1.51 class_Groups_Oordered__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.51 { ! class_Rings_Olinordered__idom( X ),
% 0.99/1.51 class_Groups_Oordered__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.51 { ! class_Rings_Olinordered__idom( X ),
% 0.99/1.51 class_Groups_Olinordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.51 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.99/1.51 class_Groups_Ocancel__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.51 { ! class_Rings_Oidom( X ), class_Rings_Oring__1__no__zero__divisors(
% 0.99/1.51 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.51 { ! class_Rings_Olinordered__idom( X ),
% 0.99/1.51 class_Rings_Oordered__cancel__semiring( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.51 { ! class_Rings_Olinordered__idom( X ),
% 0.99/1.51 class_Rings_Olinordered__ring__strict( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.51 { ! class_Rings_Oidom( X ), class_Rings_Oring__no__zero__divisors(
% 0.99/1.51 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.51 { ! class_Rings_Olinordered__idom( X ),
% 0.99/1.51 class_Rings_Oordered__comm__semiring( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.51 { ! class_Rings_Olinordered__idom( X ),
% 0.99/1.51 class_Rings_Olinordered__semiring__1( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.51 { ! class_Rings_Olinordered__idom( X ),
% 0.99/1.51 class_Groups_Oordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.51 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.99/1.51 class_Groups_Ocancel__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.51 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semiring(
% 0.99/1.51 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.51 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semidom(
% 0.99/1.51 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.51 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Oab__semigroup__mult
% 0.99/1.51 ( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.51 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Ocomm__monoid__mult(
% 0.99/1.51 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.51 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Oab__semigroup__add
% 0.99/1.51 ( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.51 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__semiring(
% 0.99/1.51 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.51 { ! class_Rings_Oidom( X ), class_Rings_Ono__zero__divisors(
% 0.99/1.51 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.51 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Ocomm__monoid__add(
% 0.99/1.51 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.51 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__ring(
% 0.99/1.51 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.51 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__idom(
% 0.99/1.51 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.51 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ocomm__semiring__1(
% 0.99/1.51 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.51 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring__0(
% 0.99/1.51 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.51 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring(
% 0.99/1.51 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.51 { ! class_Groups_Oab__group__add( X ), class_Groups_Oab__group__add(
% 0.99/1.51 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.51 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ozero__neq__one(
% 0.99/1.51 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.51 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__ring(
% 0.99/1.51 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.51 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Opreorder(
% 0.99/1.51 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.51 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Olinorder(
% 0.99/1.51 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.51 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Omonoid__mult(
% 0.99/1.51 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.51 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Ocomm__ring__1(
% 0.99/1.51 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.51 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Omonoid__add(
% 0.99/1.51 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.51 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring__0(
% 0.99/1.51 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.51 { ! class_Groups_Oab__group__add( X ), class_Groups_Ogroup__add(
% 0.99/1.51 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.51 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Omult__zero(
% 0.99/1.51 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.51 { ! class_Rings_Ocomm__ring( X ), class_Rings_Ocomm__ring(
% 0.99/1.51 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.51 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oorder(
% 0.99/1.51 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.51 { ! class_Rings_Olinordered__idom( X ), class_Int_Oring__char__0(
% 0.99/1.51 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.51 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring(
% 0.99/1.51 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.51 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oord(
% 0.99/1.51 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.51 { ! class_Groups_Oab__group__add( X ), class_Groups_Ouminus(
% 0.99/1.51 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.51 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Oring__1(
% 0.99/1.51 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.51 { ! class_Rings_Ocomm__semiring__1( X ), class_Power_Opower(
% 0.99/1.51 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.51 { ! class_Groups_Ozero( X ), class_Groups_Ozero( tc_Polynomial_Opoly( X ) )
% 0.99/1.51 }.
% 0.99/1.51 { ! class_Rings_Ocomm__ring( X ), class_Rings_Oring( tc_Polynomial_Opoly( X
% 0.99/1.51 ) ) }.
% 0.99/1.51 { ! class_Rings_Oidom( X ), class_Rings_Oidom( tc_Polynomial_Opoly( X ) ) }
% 0.99/1.51 .
% 0.99/1.51 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Oone(
% 0.99/1.51 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.51 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Odvd(
% 0.99/1.51 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.51 { ! hBOOL( c_fequal( Y, X ) ), Y = X }.
% 0.99/1.51 { ! Y = X, hBOOL( c_fequal( Y, X ) ) }.
% 0.99/1.51 { ! c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.99/1.51 c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 0.99/1.51 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 0.99/1.51 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 0.99/1.51 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 0.99/1.51 v_q____ ) ), v_w____ ) ) = c_RealVector_Onorm__class_Onorm(
% 0.99/1.51 tc_Complex_Ocomplex, c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex,
% 0.99/1.51 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ), hAPP( hAPP(
% 0.99/1.51 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), v_a____ ), hAPP(
% 0.99/1.51 hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), v_w____ ),
% 0.99/1.51 v_k____ ) ) ) ) }.
% 0.99/1.51
% 0.99/1.51 *** allocated 15000 integers for clauses
% 0.99/1.51 *** allocated 22500 integers for clauses
% 0.99/1.51 *** allocated 33750 integers for clauses
% 0.99/1.51 *** allocated 50625 integers for clauses
% 0.99/1.51 *** allocated 75937 integers for clauses
% 0.99/1.51 percentage equality = 0.252626, percentage horn = 0.923025
% 0.99/1.51 This is a problem with some equality
% 0.99/1.51
% 0.99/1.51
% 0.99/1.51
% 0.99/1.51 Options Used:
% 0.99/1.51
% 0.99/1.51 useres = 1
% 0.99/1.51 useparamod = 1
% 0.99/1.51 useeqrefl = 1
% 0.99/1.51 useeqfact = 1
% 0.99/1.51 usefactor = 1
% 0.99/1.51 usesimpsplitting = 0
% 0.99/1.51 usesimpdemod = 5
% 0.99/1.51 usesimpres = 3
% 0.99/1.51
% 0.99/1.51 resimpinuse = 1000
% 0.99/1.51 resimpclauses = 20000
% 0.99/1.51 substype = eqrewr
% 0.99/1.51 backwardsubs = 1
% 0.99/1.51 selectoldest = 5
% 0.99/1.51
% 0.99/1.51 litorderings [0] = split
% 0.99/1.51 litorderings [1] = extend the termordering, first sorting on arguments
% 0.99/1.51
% 0.99/1.51 termordering = kbo
% 0.99/1.51
% 0.99/1.51 litapriori = 0
% 0.99/1.51 termapriori = 1
% 0.99/1.51 litaposteriori = 0
% 0.99/1.51 termaposteriori = 0
% 0.99/1.51 demodaposteriori = 0
% 0.99/1.51 ordereqreflfact = 0
% 0.99/1.51
% 0.99/1.51 litselect = negord
% 0.99/1.51
% 0.99/1.51 maxweight = 15
% 0.99/1.51 maxdepth = 30000
% 0.99/1.51 maxlength = 115
% 0.99/1.51 maxnrvars = 195
% 0.99/1.51 excuselevel = 1
% 0.99/1.51 increasemaxweight = 1
% 0.99/1.51
% 0.99/1.51 maxselected = 10000000
% 0.99/1.51 maxnrclauses = 10000000
% 0.99/1.51
% 0.99/1.51 showgenerated = 0
% 0.99/1.51 showkept = 0
% 0.99/1.51 showselected = 0
% 0.99/1.51 showdeleted = 0
% 0.99/1.51 showresimp = 1
% 0.99/1.51 showstatus = 2000
% 0.99/1.51
% 0.99/1.51 prologoutput = 0
% 0.99/1.51 nrgoals = 5000000
% 0.99/1.51 totalproof = 1
% 0.99/1.51
% 0.99/1.51 Symbols occurring in the translation:
% 0.99/1.51
% 0.99/1.51 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.99/1.51 . [1, 2] (w:1, o:215, a:1, s:1, b:0),
% 0.99/1.51 ! [4, 1] (w:0, o:121, a:1, s:1, b:0),
% 0.99/1.51 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.99/1.51 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.99/1.51 hAPP [38, 2] (w:1, o:239, a:1, s:1, b:0),
% 0.99/1.51 v_s____ [39, 0] (w:1, o:15, a:1, s:1, b:0),
% 0.99/1.51 tc_Complex_Ocomplex [40, 0] (w:1, o:24, a:1, s:1, b:0),
% 0.99/1.51 tc_Polynomial_Opoly [41, 1] (w:1, o:135, a:1, s:1, b:0),
% 0.99/1.51 c_Groups_Ozero__class_Ozero [42, 1] (w:1, o:136, a:1, s:1, b:0),
% 0.99/1.51 v_a____ [43, 0] (w:1, o:25, a:1, s:1, b:0),
% 0.99/1.51 v_p [44, 0] (w:1, o:26, a:1, s:1, b:0),
% 0.99/1.51 c_Polynomial_Opoly [45, 2] (w:1, o:240, a:1, s:1, b:0),
% 0.99/1.51 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant [46, 3] (w:1, o:
% 0.99/1.51 296, a:1, s:1, b:0),
% 0.99/1.51 v_q____ [47, 0] (w:1, o:28, a:1, s:1, b:0),
% 0.99/1.51 c_Rings_Oinverse__class_Oinverse [48, 2] (w:1, o:241, a:1, s:1, b:0)
% 0.99/1.51 ,
% 0.99/1.51 c_Polynomial_Osmult [49, 3] (w:1, o:299, a:1, s:1, b:0),
% 0.99/1.51 c_Groups_Oone__class_Oone [50, 1] (w:1, o:137, a:1, s:1, b:0),
% 0.99/1.51 v_k____ [51, 0] (w:1, o:29, a:1, s:1, b:0),
% 0.99/1.51 tc_Nat_Onat [52, 0] (w:1, o:30, a:1, s:1, b:0),
% 0.99/1.51 c_Groups_Otimes__class_Otimes [54, 1] (w:1, o:138, a:1, s:1, b:0),
% 0.99/1.51 v_w____ [55, 0] (w:1, o:33, a:1, s:1, b:0),
% 0.99/1.51 c_Power_Opower__class_Opower [56, 1] (w:1, o:139, a:1, s:1, b:0),
% 0.99/1.51 c_Polynomial_OpCons [57, 3] (w:1, o:301, a:1, s:1, b:0),
% 0.99/1.51 c_Groups_Oplus__class_Oplus [58, 3] (w:1, o:303, a:1, s:1, b:0),
% 0.99/1.51 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize [59, 2] (w:1, o:242
% 0.99/1.51 , a:1, s:1, b:0),
% 0.99/1.51 class_Rings_Odivision__ring [63, 1] (w:1, o:145, a:1, s:1, b:0),
% 0.99/1.51 class_Fields_Ofield [64, 1] (w:1, o:146, a:1, s:1, b:0),
% 0.99/1.51 class_Rings_Ocomm__semiring__0 [68, 1] (w:1, o:142, a:1, s:1, b:0),
% 0.99/1.51 class_RealVector_Oreal__normed__div__algebra [69, 1] (w:1, o:147, a:1
% 0.99/1.51 , s:1, b:0),
% 0.99/1.51 c_RealVector_Onorm__class_Onorm [70, 2] (w:1, o:243, a:1, s:1, b:0),
% 0.99/1.51
% 0.99/1.51 tc_RealDef_Oreal [71, 0] (w:1, o:51, a:1, s:1, b:0),
% 0.99/1.51 v_pa____ [73, 0] (w:1, o:27, a:1, s:1, b:0),
% 0.99/1.51 class_Rings_Ocomm__semiring__1 [74, 1] (w:1, o:143, a:1, s:1, b:0),
% 0.99/1.51 class_Groups_Ocomm__monoid__add [76, 1] (w:1, o:151, a:1, s:1, b:0),
% 0.99/1.51
% 0.99/1.51 class_Groups_Ozero [78, 1] (w:1, o:152, a:1, s:1, b:0),
% 0.99/1.51 class_Groups_Omonoid__mult [84, 1] (w:1, o:154, a:1, s:1, b:0),
% 0.99/1.51 class_Int_Oring__char__0 [85, 1] (w:1, o:155, a:1, s:1, b:0),
% 0.99/1.51 class_Rings_Oidom [86, 1] (w:1, o:156, a:1, s:1, b:0),
% 0.99/1.51 class_Power_Opower [88, 1] (w:1, o:161, a:1, s:1, b:0),
% 0.99/1.51 class_Rings_Odivision__ring__inverse__zero [89, 1] (w:1, o:162, a:1
% 0.99/1.51 , s:1, b:0),
% 0.99/1.51 class_Rings_Ono__zero__divisors [90, 1] (w:1, o:173, a:1, s:1, b:0),
% 0.99/1.51
% 0.99/1.51 class_Rings_Oring__no__zero__divisors [91, 1] (w:1, o:174, a:1, s:1
% 0.99/1.51 , b:0),
% 0.99/1.51 class_RealVector_Oreal__normed__algebra [92, 1] (w:1, o:175, a:1, s:1
% 0.99/1.51 , b:0),
% 0.99/1.51 class_Rings_Omult__zero [93, 1] (w:1, o:172, a:1, s:1, b:0),
% 0.99/1.51 class_Rings_Ozero__neq__one [95, 1] (w:1, o:176, a:1, s:1, b:0),
% 0.99/1.51 class_Rings_Osemiring [97, 1] (w:1, o:180, a:1, s:1, b:0),
% 0.99/1.51 class_Rings_Ocomm__semiring [100, 1] (w:1, o:144, a:1, s:1, b:0),
% 0.99/1.51 class_Rings_Oring__1__no__zero__divisors [103, 1] (w:1, o:177, a:1
% 0.99/1.51 , s:1, b:0),
% 0.99/1.51 class_Groups_Ocomm__monoid__mult [105, 1] (w:1, o:181, a:1, s:1, b:0)
% 0.99/1.51 ,
% 0.99/1.51 class_RealVector_Oreal__normed__vector [107, 1] (w:1, o:182, a:1, s:1
% 0.99/1.51 , b:0),
% 0.99/1.51 class_Fields_Ofield__inverse__zero [108, 1] (w:1, o:148, a:1, s:1, b:
% 0.99/1.51 0),
% 0.99/1.51 class_RealVector_Oreal__normed__algebra__1 [109, 1] (w:1, o:183, a:1
% 0.99/1.51 , s:1, b:0),
% 0.99/1.51 class_Rings_Osemiring__0 [110, 1] (w:1, o:184, a:1, s:1, b:0),
% 0.99/1.51 c_Orderings_Oord__class_Oless [112, 3] (w:1, o:297, a:1, s:1, b:0),
% 0.99/1.51 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct [
% 0.99/1.51 115, 1] (w:1, o:190, a:1, s:1, b:0),
% 0.99/1.51 class_Rings_Olinordered__ring__strict [117, 1] (w:1, o:163, a:1, s:1
% 0.99/1.51 , b:0),
% 0.99/1.51 c_Polynomial_Oorder [118, 3] (w:1, o:300, a:1, s:1, b:0),
% 0.99/1.51 c_Power_Opower_Opower [119, 3] (w:1, o:304, a:1, s:1, b:0),
% 0.99/1.51 v_c____ [123, 0] (w:1, o:84, a:1, s:1, b:0),
% 0.99/1.51 c_Orderings_Oord__class_Oless__eq [125, 3] (w:1, o:298, a:1, s:1, b:0
% 0.99/1.51 ),
% 0.99/1.51 class_Rings_Olinordered__idom [126, 1] (w:1, o:164, a:1, s:1, b:0),
% 0.99/1.51 class_Rings_Olinordered__semidom [127, 1] (w:1, o:166, a:1, s:1, b:0)
% 0.99/1.51 ,
% 0.99/1.51 class_Rings_Olinordered__ring [129, 1] (w:1, o:165, a:1, s:1, b:0),
% 0.99/1.51 class_Rings_Olinordered__semiring__strict [131, 1] (w:1, o:167, a:1
% 0.99/1.51 , s:1, b:0),
% 0.99/1.51 class_Rings_Olinordered__comm__semiring__strict [132, 1] (w:1, o:168
% 0.99/1.51 , a:1, s:1, b:0),
% 0.99/1.51 class_Fields_Olinordered__field__inverse__zero [134, 1] (w:1, o:149
% 0.99/1.51 , a:1, s:1, b:0),
% 0.99/1.51 class_Fields_Olinordered__field [135, 1] (w:1, o:150, a:1, s:1, b:0)
% 0.99/1.51 ,
% 0.99/1.51 hBOOL [149, 1] (w:1, o:191, a:1, s:1, b:0),
% 0.99/1.51 class_Rings_Oordered__cancel__semiring [157, 1] (w:1, o:185, a:1, s:1
% 0.99/1.51 , b:0),
% 0.99/1.51 class_Rings_Oordered__ring [158, 1] (w:1, o:186, a:1, s:1, b:0),
% 0.99/1.51 class_Rings_Oordered__semiring [159, 1] (w:1, o:187, a:1, s:1, b:0),
% 0.99/1.51
% 0.99/1.51 class_Rings_Oordered__comm__semiring [160, 1] (w:1, o:188, a:1, s:1
% 0.99/1.51 , b:0),
% 0.99/1.51 class_Rings_Olinordered__semiring [161, 1] (w:1, o:169, a:1, s:1, b:0
% 0.99/1.51 ),
% 0.99/1.51 class_Rings_Olinordered__semiring__1 [166, 1] (w:1, o:170, a:1, s:1
% 0.99/1.51 , b:0),
% 0.99/1.51 class_Rings_Olinordered__semiring__1__strict [167, 1] (w:1, o:171, a:
% 0.99/1.51 1, s:1, b:0),
% 0.99/1.51 class_Groups_Oordered__comm__monoid__add [168, 1] (w:1, o:192, a:1
% 0.99/1.51 , s:1, b:0),
% 0.99/1.51 class_Groups_Oab__semigroup__mult [171, 1] (w:1, o:193, a:1, s:1, b:0
% 0.99/1.51 ),
% 0.99/1.51 class_Groups_Oab__semigroup__add [172, 1] (w:1, o:194, a:1, s:1, b:0)
% 0.99/1.51 ,
% 0.99/1.51 class_Groups_Ocancel__semigroup__add [173, 1] (w:1, o:195, a:1, s:1
% 0.99/1.51 , b:0),
% 0.99/1.51 class_Groups_Ocancel__ab__semigroup__add [174, 1] (w:1, o:196, a:1
% 0.99/1.51 , s:1, b:0),
% 0.99/1.51 class_Groups_Oone [175, 1] (w:1, o:197, a:1, s:1, b:0),
% 0.99/1.51 class_Groups_Omonoid__add [176, 1] (w:1, o:198, a:1, s:1, b:0),
% 0.99/1.51 class_Groups_Olinordered__ab__group__add [177, 1] (w:1, o:153, a:1
% 0.99/1.51 , s:1, b:0),
% 0.99/1.51 class_Groups_Oordered__ab__semigroup__add__imp__le [178, 1] (w:1, o:
% 0.99/1.51 199, a:1, s:1, b:0),
% 0.99/1.51 class_Groups_Oordered__ab__semigroup__add [179, 1] (w:1, o:200, a:1
% 0.99/1.51 , s:1, b:0),
% 0.99/1.51 class_Groups_Oordered__cancel__ab__semigroup__add [180, 1] (w:1, o:
% 0.99/1.51 201, a:1, s:1, b:0),
% 0.99/1.51 c_Polynomial_Opcompose [181, 3] (w:1, o:305, a:1, s:1, b:0),
% 0.99/1.51 class_Orderings_Opreorder [183, 1] (w:1, o:159, a:1, s:1, b:0),
% 0.99/1.51 c_Polynomial_Osynthetic__div [184, 3] (w:1, o:306, a:1, s:1, b:0),
% 0.99/1.51 class_Orderings_Olinorder [185, 1] (w:1, o:160, a:1, s:1, b:0),
% 0.99/1.51 class_Orderings_Oord [186, 1] (w:1, o:157, a:1, s:1, b:0),
% 0.99/1.51 tc_fun [187, 2] (w:1, o:280, a:1, s:1, b:0),
% 0.99/1.51 class_Orderings_Oorder [188, 1] (w:1, o:158, a:1, s:1, b:0),
% 0.99/1.51 tc_Int_Oint [189, 0] (w:1, o:110, a:1, s:1, b:0),
% 0.99/1.51 class_Rings_Ocomm__ring__1 [190, 1] (w:1, o:140, a:1, s:1, b:0),
% 0.99/1.51 c_Groups_Ouminus__class_Ouminus [191, 2] (w:1, o:281, a:1, s:1, b:0)
% 0.99/1.51 ,
% 0.99/1.51 class_Groups_Oordered__ab__group__add [193, 1] (w:1, o:202, a:1, s:1
% 0.99/1.51 , b:0),
% 0.99/1.51 class_Groups_Oab__group__add [194, 1] (w:1, o:203, a:1, s:1, b:0),
% 0.99/1.51 class_Groups_Ogroup__add [195, 1] (w:1, o:204, a:1, s:1, b:0),
% 0.99/1.51 class_Rings_Oring [196, 1] (w:1, o:178, a:1, s:1, b:0),
% 0.99/1.51 class_Rings_Ocomm__ring [197, 1] (w:1, o:141, a:1, s:1, b:0),
% 0.99/1.51 class_Rings_Oring__1 [198, 1] (w:1, o:179, a:1, s:1, b:0),
% 0.99/1.51 c_Polynomial_Opos__poly [204, 2] (w:1, o:282, a:1, s:1, b:0),
% 0.99/1.51 c_SEQ_Odecseq [206, 2] (w:1, o:284, a:1, s:1, b:0),
% 0.99/1.51 class_Lattices_Oboolean__algebra [208, 1] (w:1, o:206, a:1, s:1, b:0)
% 0.99/1.51 ,
% 0.99/1.51 class_Lattices_Oab__semigroup__idem__mult [209, 1] (w:1, o:205, a:1
% 0.99/1.51 , s:1, b:0),
% 0.99/1.51 class_Groups_Ouminus [211, 1] (w:1, o:207, a:1, s:1, b:0),
% 0.99/1.51 c_Polynomial_Omonom [212, 3] (w:1, o:307, a:1, s:1, b:0),
% 0.99/1.51 c_Rings_Odvd__class_Odvd [213, 3] (w:1, o:308, a:1, s:1, b:0),
% 0.99/1.51 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly [215, 3] (w:
% 0.99/1.51 1, o:302, a:1, s:1, b:0),
% 0.99/1.51 class_Rings_Odvd [216, 1] (w:1, o:189, a:1, s:1, b:0),
% 0.99/1.51 c_Nat_OSuc [218, 1] (w:1, o:208, a:1, s:1, b:0),
% 0.99/1.51 c_Polynomial_Opoly__rec [225, 5] (w:1, o:340, a:1, s:1, b:0),
% 0.99/1.51 c_fequal [226, 2] (w:1, o:285, a:1, s:1, b:0),
% 0.99/1.51 c_If [227, 4] (w:1, o:331, a:1, s:1, b:0),
% 0.99/1.51 c_RealDef_Oreal [229, 2] (w:1, o:283, a:1, s:1, b:0),
% 0.99/1.51 c_SEQ_OBseq [230, 2] (w:1, o:286, a:1, s:1, b:0),
% 4.05/4.40 c_RComplete_Onatceiling [232, 1] (w:1, o:209, a:1, s:1, b:0),
% 4.05/4.40 c_RComplete_Onatfloor [233, 1] (w:1, o:210, a:1, s:1, b:0),
% 4.05/4.40 c_Complex_Orcis [234, 2] (w:1, o:287, a:1, s:1, b:0),
% 4.05/4.40 c_Transcendental_Oln [238, 1] (w:1, o:211, a:1, s:1, b:0),
% 4.05/4.40 c_SEQ_Oincseq [239, 2] (w:1, o:288, a:1, s:1, b:0),
% 4.05/4.40 c_Complex_Ocis [240, 1] (w:1, o:212, a:1, s:1, b:0),
% 4.05/4.40 c_Complex_Oexpi [241, 1] (w:1, o:213, a:1, s:1, b:0),
% 4.05/4.40 c_Groups_Ominus__class_Ominus [243, 3] (w:1, o:309, a:1, s:1, b:0),
% 4.05/4.40 class_Groups_Ocancel__comm__monoid__add [249, 1] (w:1, o:214, a:1, s:
% 4.05/4.40 1, b:0),
% 4.05/4.40 tc_HOL_Obool [251, 0] (w:1, o:109, a:1, s:1, b:0),
% 4.05/4.40 alpha1 [252, 4] (w:1, o:332, a:1, s:1, b:1),
% 4.05/4.40 alpha2 [253, 4] (w:1, o:336, a:1, s:1, b:1),
% 4.05/4.40 alpha3 [254, 3] (w:1, o:311, a:1, s:1, b:1),
% 4.05/4.40 alpha4 [255, 3] (w:1, o:312, a:1, s:1, b:1),
% 4.05/4.40 alpha5 [256, 3] (w:1, o:313, a:1, s:1, b:1),
% 4.05/4.40 alpha6 [257, 3] (w:1, o:314, a:1, s:1, b:1),
% 4.05/4.40 alpha7 [258, 2] (w:1, o:289, a:1, s:1, b:1),
% 4.05/4.40 alpha8 [259, 2] (w:1, o:290, a:1, s:1, b:1),
% 4.05/4.40 alpha9 [260, 2] (w:1, o:291, a:1, s:1, b:1),
% 4.05/4.40 alpha10 [261, 2] (w:1, o:292, a:1, s:1, b:1),
% 4.05/4.40 alpha11 [262, 2] (w:1, o:293, a:1, s:1, b:1),
% 4.05/4.40 alpha12 [263, 4] (w:1, o:333, a:1, s:1, b:1),
% 4.05/4.40 alpha13 [264, 4] (w:1, o:334, a:1, s:1, b:1),
% 4.05/4.40 alpha14 [265, 3] (w:1, o:315, a:1, s:1, b:1),
% 4.05/4.40 alpha15 [266, 3] (w:1, o:316, a:1, s:1, b:1),
% 4.05/4.40 alpha16 [267, 4] (w:1, o:335, a:1, s:1, b:1),
% 4.05/4.40 alpha17 [268, 2] (w:1, o:294, a:1, s:1, b:1),
% 4.05/4.40 alpha18 [269, 2] (w:1, o:295, a:1, s:1, b:1),
% 4.05/4.40 alpha19 [270, 3] (w:1, o:317, a:1, s:1, b:1),
% 4.05/4.40 alpha20 [271, 3] (w:1, o:310, a:1, s:1, b:1),
% 4.05/4.40 skol1 [272, 2] (w:1, o:244, a:1, s:1, b:1),
% 4.05/4.40 skol2 [273, 0] (w:1, o:17, a:1, s:1, b:1),
% 4.05/4.40 skol3 [274, 1] (w:1, o:127, a:1, s:1, b:1),
% 4.05/4.40 skol4 [275, 0] (w:1, o:18, a:1, s:1, b:1),
% 4.05/4.40 skol5 [276, 0] (w:1, o:19, a:1, s:1, b:1),
% 4.05/4.40 skol6 [277, 0] (w:1, o:22, a:1, s:1, b:1),
% 4.05/4.40 skol7 [278, 2] (w:1, o:250, a:1, s:1, b:1),
% 4.05/4.40 skol8 [279, 1] (w:1, o:128, a:1, s:1, b:1),
% 4.05/4.40 skol9 [280, 2] (w:1, o:251, a:1, s:1, b:1),
% 4.05/4.40 skol10 [281, 2] (w:1, o:252, a:1, s:1, b:1),
% 4.05/4.40 skol11 [282, 3] (w:1, o:318, a:1, s:1, b:1),
% 4.05/4.40 skol12 [283, 3] (w:1, o:319, a:1, s:1, b:1),
% 4.05/4.40 skol13 [284, 0] (w:1, o:16, a:1, s:1, b:1),
% 4.05/4.40 skol14 [285, 2] (w:1, o:253, a:1, s:1, b:1),
% 4.05/4.40 skol15 [286, 2] (w:1, o:254, a:1, s:1, b:1),
% 4.05/4.40 skol16 [287, 1] (w:1, o:129, a:1, s:1, b:1),
% 4.05/4.40 skol17 [288, 2] (w:1, o:255, a:1, s:1, b:1),
% 4.05/4.40 skol18 [289, 3] (w:1, o:320, a:1, s:1, b:1),
% 4.05/4.40 skol19 [290, 1] (w:1, o:130, a:1, s:1, b:1),
% 4.05/4.40 skol20 [291, 2] (w:1, o:256, a:1, s:1, b:1),
% 4.05/4.40 skol21 [292, 2] (w:1, o:257, a:1, s:1, b:1),
% 4.05/4.40 skol22 [293, 2] (w:1, o:258, a:1, s:1, b:1),
% 4.05/4.40 skol23 [294, 2] (w:1, o:259, a:1, s:1, b:1),
% 4.05/4.40 skol24 [295, 2] (w:1, o:260, a:1, s:1, b:1),
% 4.05/4.40 skol25 [296, 2] (w:1, o:261, a:1, s:1, b:1),
% 4.05/4.40 skol26 [297, 2] (w:1, o:262, a:1, s:1, b:1),
% 4.05/4.40 skol27 [298, 2] (w:1, o:263, a:1, s:1, b:1),
% 4.05/4.40 skol28 [299, 2] (w:1, o:264, a:1, s:1, b:1),
% 4.05/4.40 skol29 [300, 1] (w:1, o:126, a:1, s:1, b:1),
% 4.05/4.40 skol30 [301, 3] (w:1, o:321, a:1, s:1, b:1),
% 4.05/4.40 skol31 [302, 2] (w:1, o:265, a:1, s:1, b:1),
% 4.05/4.40 skol32 [303, 2] (w:1, o:266, a:1, s:1, b:1),
% 4.05/4.40 skol33 [304, 2] (w:1, o:267, a:1, s:1, b:1),
% 4.05/4.40 skol34 [305, 3] (w:1, o:322, a:1, s:1, b:1),
% 4.05/4.40 skol35 [306, 3] (w:1, o:323, a:1, s:1, b:1),
% 4.05/4.40 skol36 [307, 2] (w:1, o:268, a:1, s:1, b:1),
% 4.05/4.40 skol37 [308, 2] (w:1, o:269, a:1, s:1, b:1),
% 4.05/4.40 skol38 [309, 2] (w:1, o:270, a:1, s:1, b:1),
% 4.05/4.40 skol39 [310, 2] (w:1, o:271, a:1, s:1, b:1),
% 4.05/4.40 skol40 [311, 3] (w:1, o:324, a:1, s:1, b:1),
% 4.05/4.40 skol41 [312, 1] (w:1, o:131, a:1, s:1, b:1),
% 4.05/4.40 skol42 [313, 1] (w:1, o:132, a:1, s:1, b:1),
% 4.05/4.40 skol43 [314, 2] (w:1, o:272, a:1, s:1, b:1),
% 4.05/4.40 skol44 [315, 4] (w:1, o:337, a:1, s:1, b:1),
% 4.05/4.40 skol45 [316, 2] (w:1, o:273, a:1, s:1, b:1),
% 4.05/4.40 skol46 [317, 2] (w:1, o:274, a:1, s:1, b:1),
% 17.06/17.41 skol47 [318, 1] (w:1, o:133, a:1, s:1, b:1),
% 17.06/17.41 skol48 [319, 2] (w:1, o:275, a:1, s:1, b:1),
% 17.06/17.41 skol49 [320, 2] (w:1, o:276, a:1, s:1, b:1),
% 17.06/17.41 skol50 [321, 0] (w:1, o:20, a:1, s:1, b:1),
% 17.06/17.41 skol51 [322, 1] (w:1, o:134, a:1, s:1, b:1),
% 17.06/17.41 skol52 [323, 0] (w:1, o:21, a:1, s:1, b:1),
% 17.06/17.41 skol53 [324, 2] (w:1, o:277, a:1, s:1, b:1),
% 17.06/17.41 skol54 [325, 3] (w:1, o:325, a:1, s:1, b:1),
% 17.06/17.41 skol55 [326, 3] (w:1, o:326, a:1, s:1, b:1),
% 17.06/17.41 skol56 [327, 3] (w:1, o:327, a:1, s:1, b:1),
% 17.06/17.41 skol57 [328, 3] (w:1, o:328, a:1, s:1, b:1),
% 17.06/17.41 skol58 [329, 2] (w:1, o:278, a:1, s:1, b:1),
% 17.06/17.41 skol59 [330, 2] (w:1, o:279, a:1, s:1, b:1),
% 17.06/17.41 skol60 [331, 2] (w:1, o:245, a:1, s:1, b:1),
% 17.06/17.41 skol61 [332, 2] (w:1, o:246, a:1, s:1, b:1),
% 17.06/17.41 skol62 [333, 2] (w:1, o:247, a:1, s:1, b:1),
% 17.06/17.41 skol63 [334, 0] (w:1, o:23, a:1, s:1, b:1),
% 17.06/17.41 skol64 [335, 3] (w:1, o:329, a:1, s:1, b:1),
% 17.06/17.41 skol65 [336, 3] (w:1, o:330, a:1, s:1, b:1),
% 17.06/17.41 skol66 [337, 4] (w:1, o:338, a:1, s:1, b:1),
% 17.06/17.41 skol67 [338, 4] (w:1, o:339, a:1, s:1, b:1),
% 17.06/17.41 skol68 [339, 2] (w:1, o:248, a:1, s:1, b:1),
% 17.06/17.41 skol69 [340, 2] (w:1, o:249, a:1, s:1, b:1).
% 17.06/17.41
% 17.06/17.41
% 17.06/17.41 Starting Search:
% 17.06/17.41
% 17.06/17.41 *** allocated 113905 integers for clauses
% 17.06/17.41 *** allocated 170857 integers for clauses
% 17.06/17.41 Resimplifying inuse:
% 17.06/17.41 Done
% 17.06/17.41
% 17.06/17.41
% 17.06/17.41 Intermediate Status:
% 17.06/17.41 Generated: 3127
% 17.06/17.41 Kept: 2091
% 17.06/17.41 Inuse: 73
% 17.06/17.41 Deleted: 8
% 17.06/17.41 Deletedinuse: 0
% 17.06/17.41
% 17.06/17.41 *** allocated 256285 integers for clauses
% 17.06/17.41 *** allocated 170857 integers for termspace/termends
% 17.06/17.41 Resimplifying inuse:
% 17.06/17.41 Done
% 17.06/17.41
% 17.06/17.41 *** allocated 384427 integers for clauses
% 17.06/17.41 Resimplifying inuse:
% 17.06/17.41 Done
% 17.06/17.41
% 17.06/17.41
% 17.06/17.41 Intermediate Status:
% 17.06/17.41 Generated: 12064
% 17.06/17.41 Kept: 4093
% 17.06/17.41 Inuse: 145
% 17.06/17.41 Deleted: 11
% 17.06/17.41 Deletedinuse: 0
% 17.06/17.41
% 17.06/17.41 *** allocated 256285 integers for termspace/termends
% 17.06/17.41 Resimplifying inuse:
% 17.06/17.41 Done
% 17.06/17.41
% 17.06/17.41 *** allocated 576640 integers for clauses
% 17.06/17.41
% 17.06/17.41 Intermediate Status:
% 17.06/17.41 Generated: 18089
% 17.06/17.41 Kept: 6208
% 17.06/17.41 Inuse: 185
% 17.06/17.41 Deleted: 11
% 17.06/17.41 Deletedinuse: 0
% 17.06/17.41
% 17.06/17.41 Resimplifying inuse:
% 17.06/17.41 Done
% 17.06/17.41
% 17.06/17.41 Resimplifying inuse:
% 17.06/17.41 Done
% 17.06/17.41
% 17.06/17.41 *** allocated 384427 integers for termspace/termends
% 17.06/17.41
% 17.06/17.41 Intermediate Status:
% 17.06/17.41 Generated: 22645
% 17.06/17.41 Kept: 8237
% 17.06/17.41 Inuse: 229
% 17.06/17.41 Deleted: 12
% 17.06/17.41 Deletedinuse: 0
% 17.06/17.41
% 17.06/17.41 Resimplifying inuse:
% 17.06/17.41 Done
% 17.06/17.41
% 17.06/17.41 Resimplifying inuse:
% 17.06/17.41 Done
% 17.06/17.41
% 17.06/17.41 *** allocated 864960 integers for clauses
% 17.06/17.41
% 17.06/17.41 Intermediate Status:
% 17.06/17.41 Generated: 27773
% 17.06/17.41 Kept: 10262
% 17.06/17.41 Inuse: 287
% 17.06/17.41 Deleted: 14
% 17.06/17.41 Deletedinuse: 0
% 17.06/17.41
% 17.06/17.41 Resimplifying inuse:
% 17.06/17.41 Done
% 17.06/17.41
% 17.06/17.41 *** allocated 576640 integers for termspace/termends
% 17.06/17.41
% 17.06/17.41 Intermediate Status:
% 17.06/17.41 Generated: 37740
% 17.06/17.41 Kept: 12333
% 17.06/17.41 Inuse: 312
% 17.06/17.41 Deleted: 14
% 17.06/17.41 Deletedinuse: 0
% 17.06/17.41
% 17.06/17.41 Resimplifying inuse:
% 17.06/17.41 Done
% 17.06/17.41
% 17.06/17.41 Resimplifying inuse:
% 17.06/17.41 Done
% 17.06/17.41
% 17.06/17.41
% 17.06/17.41 Intermediate Status:
% 17.06/17.41 Generated: 47834
% 17.06/17.41 Kept: 14338
% 17.06/17.41 Inuse: 343
% 17.06/17.41 Deleted: 14
% 17.06/17.41 Deletedinuse: 0
% 17.06/17.41
% 17.06/17.41 Resimplifying inuse:
% 17.06/17.41 Done
% 17.06/17.41
% 17.06/17.41 Resimplifying inuse:
% 17.06/17.41 Done
% 17.06/17.41
% 17.06/17.41 *** allocated 1297440 integers for clauses
% 17.06/17.41
% 17.06/17.41 Intermediate Status:
% 17.06/17.41 Generated: 53803
% 17.06/17.41 Kept: 16340
% 17.06/17.41 Inuse: 379
% 17.06/17.41 Deleted: 14
% 17.06/17.41 Deletedinuse: 0
% 17.06/17.41
% 17.06/17.41 Resimplifying inuse:
% 17.06/17.41 Done
% 17.06/17.41
% 17.06/17.41 Resimplifying inuse:
% 17.06/17.41 Done
% 17.06/17.41
% 17.06/17.41 *** allocated 864960 integers for termspace/termends
% 17.06/17.41
% 17.06/17.41 Intermediate Status:
% 17.06/17.41 Generated: 61996
% 17.06/17.41 Kept: 18351
% 17.06/17.41 Inuse: 401
% 17.06/17.41 Deleted: 16
% 17.06/17.41 Deletedinuse: 0
% 17.06/17.41
% 17.06/17.41 Resimplifying inuse:
% 17.06/17.41 Done
% 17.06/17.41
% 17.06/17.41
% 17.06/17.41 Intermediate Status:
% 17.06/17.41 Generated: 86988
% 17.06/17.41 Kept: 20968
% 17.06/17.41 Inuse: 425
% 17.06/17.41 Deleted: 16
% 17.06/17.41 Deletedinuse: 0
% 17.06/17.41
% 17.06/17.41 Resimplifying inuse:
% 17.06/17.41 Done
% 17.06/17.41
% 17.06/17.41 Resimplifying clauses:
% 17.06/17.41 Done
% 17.06/17.41
% 17.06/17.41 Resimplifying inuse:
% 17.06/17.41 Done
% 17.06/17.41
% 17.06/17.41
% 17.06/17.41 Intermediate Status:
% 17.06/17.41 Generated: 92665
% 17.06/17.41 Kept: 22984
% 17.06/17.41 Inuse: 435
% 17.06/17.41 Deleted: 210
% 17.06/17.41 Deletedinuse: 0
% 17.06/17.41
% 17.06/17.41 Resimplifying inuse:
% 17.06/17.41 Done
% 17.06/17.41
% 17.06/17.41 Resimplifying inuse:
% 17.06/17.41 Done
% 17.06/17.41
% 17.06/17.41
% 17.06/17.41 Intermediate Status:
% 17.06/17.41 Generated: 98718
% 17.06/17.41 Kept: 24985
% 17.06/17.41 Inuse: 463
% 17.06/17.41 Deleted: 210
% 17.06/17.41 Deletedinuse: 0
% 17.06/17.41
% 17.06/17.41 Resimplifying inuse:
% 17.06/17.41 Done
% 17.06/17.41
% 17.06/17.41 *** allocated 1946160 integers for clauses
% 17.06/17.41 Resimplifying inuse:
% 17.06/17.41 Done
% 17.06/17.41
% 17.06/17.41
% 17.06/17.41 Intermediate Status:
% 17.06/17.41 Generated: 105290
% 17.06/17.41 Kept: 27308
% 17.06/17.41 Inuse: 490
% 17.06/17.41 Deleted: 210
% 17.06/17.41 Deletedinuse: 0
% 17.06/17.41
% 17.06/17.41 Resimplifying inuse:
% 17.06/17.41 Done
% 17.06/17.41
% 17.06/17.41
% 17.06/17.41 Intermediate Status:
% 17.06/17.41 Generated: 120371
% 17.06/17.41 Kept: 29855
% 17.06/17.41 Inuse: 515
% 17.06/17.41 Deleted: 210
% 17.06/17.41 Deletedinuse: 0
% 60.92/61.36
% 60.92/61.36 Resimplifying inuse:
% 60.92/61.36 Done
% 60.92/61.36
% 60.92/61.36 *** allocated 1297440 integers for termspace/termends
% 60.92/61.36 Resimplifying inuse:
% 60.92/61.36 Done
% 60.92/61.36
% 60.92/61.36
% 60.92/61.36 Intermediate Status:
% 60.92/61.36 Generated: 127584
% 60.92/61.36 Kept: 31866
% 60.92/61.36 Inuse: 551
% 60.92/61.36 Deleted: 210
% 60.92/61.36 Deletedinuse: 0
% 60.92/61.36
% 60.92/61.36 Resimplifying inuse:
% 60.92/61.36 Done
% 60.92/61.36
% 60.92/61.36 Resimplifying inuse:
% 60.92/61.36 Done
% 60.92/61.36
% 60.92/61.36
% 60.92/61.36 Intermediate Status:
% 60.92/61.36 Generated: 148499
% 60.92/61.36 Kept: 34981
% 60.92/61.36 Inuse: 570
% 60.92/61.36 Deleted: 210
% 60.92/61.36 Deletedinuse: 0
% 60.92/61.36
% 60.92/61.36 Resimplifying inuse:
% 60.92/61.36 Done
% 60.92/61.36
% 60.92/61.36 Resimplifying inuse:
% 60.92/61.36 Done
% 60.92/61.36
% 60.92/61.36
% 60.92/61.36 Intermediate Status:
% 60.92/61.36 Generated: 156487
% 60.92/61.36 Kept: 37261
% 60.92/61.36 Inuse: 590
% 60.92/61.36 Deleted: 210
% 60.92/61.36 Deletedinuse: 0
% 60.92/61.36
% 60.92/61.36 Resimplifying inuse:
% 60.92/61.36 Done
% 60.92/61.36
% 60.92/61.36 *** allocated 2919240 integers for clauses
% 60.92/61.36
% 60.92/61.36 Intermediate Status:
% 60.92/61.36 Generated: 179858
% 60.92/61.36 Kept: 39447
% 60.92/61.36 Inuse: 600
% 60.92/61.36 Deleted: 210
% 60.92/61.36 Deletedinuse: 0
% 60.92/61.36
% 60.92/61.36 Resimplifying inuse:
% 60.92/61.36 Done
% 60.92/61.36
% 60.92/61.36 Resimplifying inuse:
% 60.92/61.36 Done
% 60.92/61.36
% 60.92/61.36
% 60.92/61.36 Intermediate Status:
% 60.92/61.36 Generated: 189412
% 60.92/61.36 Kept: 41877
% 60.92/61.36 Inuse: 610
% 60.92/61.36 Deleted: 210
% 60.92/61.36 Deletedinuse: 0
% 60.92/61.36
% 60.92/61.36 Resimplifying inuse:
% 60.92/61.36 Done
% 60.92/61.36
% 60.92/61.36 Resimplifying clauses:
% 60.92/61.36 Done
% 60.92/61.36
% 60.92/61.36 *** allocated 1946160 integers for termspace/termends
% 60.92/61.36 Resimplifying inuse:
% 60.92/61.36 Done
% 60.92/61.36
% 60.92/61.36
% 60.92/61.36 Intermediate Status:
% 60.92/61.36 Generated: 197982
% 60.92/61.36 Kept: 43878
% 60.92/61.36 Inuse: 625
% 60.92/61.36 Deleted: 309
% 60.92/61.36 Deletedinuse: 0
% 60.92/61.36
% 60.92/61.36 Resimplifying inuse:
% 60.92/61.36 Done
% 60.92/61.36
% 60.92/61.36 Resimplifying inuse:
% 60.92/61.36 Done
% 60.92/61.36
% 60.92/61.36
% 60.92/61.36 Intermediate Status:
% 60.92/61.36 Generated: 209295
% 60.92/61.36 Kept: 47104
% 60.92/61.36 Inuse: 655
% 60.92/61.36 Deleted: 309
% 60.92/61.36 Deletedinuse: 0
% 60.92/61.36
% 60.92/61.36 Resimplifying inuse:
% 60.92/61.36 Done
% 60.92/61.36
% 60.92/61.36 Resimplifying inuse:
% 60.92/61.36 Done
% 60.92/61.36
% 60.92/61.36
% 60.92/61.36 Intermediate Status:
% 60.92/61.36 Generated: 216294
% 60.92/61.36 Kept: 49296
% 60.92/61.36 Inuse: 680
% 60.92/61.36 Deleted: 309
% 60.92/61.36 Deletedinuse: 0
% 60.92/61.36
% 60.92/61.36 Resimplifying inuse:
% 60.92/61.36 Done
% 60.92/61.36
% 60.92/61.36 Resimplifying inuse:
% 60.92/61.36 Done
% 60.92/61.36
% 60.92/61.36
% 60.92/61.36 Intermediate Status:
% 60.92/61.36 Generated: 223323
% 60.92/61.36 Kept: 51313
% 60.92/61.36 Inuse: 693
% 60.92/61.36 Deleted: 309
% 60.92/61.36 Deletedinuse: 0
% 60.92/61.36
% 60.92/61.36 Resimplifying inuse:
% 60.92/61.36 Done
% 60.92/61.36
% 60.92/61.36
% 60.92/61.36 Intermediate Status:
% 60.92/61.36 Generated: 230367
% 60.92/61.36 Kept: 53414
% 60.92/61.36 Inuse: 705
% 60.92/61.36 Deleted: 309
% 60.92/61.36 Deletedinuse: 0
% 60.92/61.36
% 60.92/61.36 Resimplifying inuse:
% 60.92/61.36 Done
% 60.92/61.36
% 60.92/61.36 Resimplifying inuse:
% 60.92/61.36 Done
% 60.92/61.36
% 60.92/61.36
% 60.92/61.36 Intermediate Status:
% 60.92/61.36 Generated: 236315
% 60.92/61.36 Kept: 55443
% 60.92/61.36 Inuse: 746
% 60.92/61.36 Deleted: 309
% 60.92/61.36 Deletedinuse: 0
% 60.92/61.36
% 60.92/61.36 Resimplifying inuse:
% 60.92/61.36 Done
% 60.92/61.36
% 60.92/61.36 Resimplifying inuse:
% 60.92/61.36 Done
% 60.92/61.36
% 60.92/61.36
% 60.92/61.36 Intermediate Status:
% 60.92/61.36 Generated: 244980
% 60.92/61.36 Kept: 57548
% 60.92/61.36 Inuse: 790
% 60.92/61.36 Deleted: 309
% 60.92/61.36 Deletedinuse: 0
% 60.92/61.36
% 60.92/61.36 Resimplifying inuse:
% 60.92/61.36 Done
% 60.92/61.36
% 60.92/61.36 Resimplifying inuse:
% 60.92/61.36 Done
% 60.92/61.36
% 60.92/61.36
% 60.92/61.36 Intermediate Status:
% 60.92/61.36 Generated: 254381
% 60.92/61.36 Kept: 59639
% 60.92/61.36 Inuse: 815
% 60.92/61.36 Deleted: 309
% 60.92/61.36 Deletedinuse: 0
% 60.92/61.36
% 60.92/61.36 Resimplifying inuse:
% 60.92/61.36 Done
% 60.92/61.36
% 60.92/61.36 Resimplifying inuse:
% 60.92/61.36 Done
% 60.92/61.36
% 60.92/61.36 *** allocated 4378860 integers for clauses
% 60.92/61.36
% 60.92/61.36 Intermediate Status:
% 60.92/61.36 Generated: 263708
% 60.92/61.36 Kept: 61792
% 60.92/61.36 Inuse: 840
% 60.92/61.36 Deleted: 309
% 60.92/61.36 Deletedinuse: 0
% 60.92/61.36
% 60.92/61.36 Resimplifying clauses:
% 60.92/61.36 Done
% 60.92/61.36
% 60.92/61.36 *** allocated 2919240 integers for termspace/termends
% 60.92/61.36 Resimplifying inuse:
% 60.92/61.36 Done
% 60.92/61.36
% 60.92/61.36
% 60.92/61.36 Intermediate Status:
% 60.92/61.36 Generated: 272598
% 60.92/61.36 Kept: 63799
% 60.92/61.36 Inuse: 862
% 60.92/61.36 Deleted: 355
% 60.92/61.36 Deletedinuse: 0
% 60.92/61.36
% 60.92/61.36 Resimplifying inuse:
% 60.92/61.36 Done
% 60.92/61.36
% 60.92/61.36 Resimplifying inuse:
% 60.92/61.36 Done
% 60.92/61.36
% 60.92/61.36
% 60.92/61.36 Intermediate Status:
% 60.92/61.36 Generated: 289569
% 60.92/61.36 Kept: 66907
% 60.92/61.36 Inuse: 895
% 60.92/61.36 Deleted: 355
% 60.92/61.36 Deletedinuse: 0
% 60.92/61.36
% 60.92/61.36 Resimplifying inuse:
% 60.92/61.36 Done
% 60.92/61.36
% 60.92/61.36 Resimplifying inuse:
% 60.92/61.36 Done
% 60.92/61.36
% 60.92/61.36
% 60.92/61.36 Intermediate Status:
% 60.92/61.36 Generated: 299531
% 60.92/61.36 Kept: 68912
% 60.92/61.36 Inuse: 927
% 60.92/61.36 Deleted: 355
% 60.92/61.36 Deletedinuse: 0
% 60.92/61.36
% 60.92/61.36 Resimplifying inuse:
% 60.92/61.36 Done
% 60.92/61.36
% 60.92/61.36 Resimplifying inuse:
% 60.92/61.36 Done
% 60.92/61.36
% 60.92/61.36
% 60.92/61.36 Intermediate Status:
% 60.92/61.36 Generated: 308544
% 60.92/61.36 Kept: 70934
% 60.92/61.36 Inuse: 943
% 60.92/61.36 Deleted: 355
% 60.92/61.36 Deletedinuse: 0
% 60.92/61.36
% 60.92/61.36 Resimplifying inuse:
% 60.92/61.36 Done
% 60.92/61.36
% 60.92/61.36 Resimplifying inuse:
% 60.92/61.36 Done
% 60.92/61.36
% 60.92/61.36
% 60.92/61.36 Intermediate Status:
% 60.92/61.36 Generated: 316838
% 60.92/61.36 Kept: 72938
% 60.92/61.36 Inuse: 955
% 60.92/61.36 Deleted: 355
% 60.92/61.36 Deletedinuse: 0
% 60.92/61.36
% 60.92/61.36
% 60.92/61.36 Intermediate Status:
% 60.92/61.36 Generated: 324582
% 60.92/61.36 Kept: 76209
% 60.92/61.36 Inuse: 965
% 60.92/61.36 Deleted: 355
% 60.92/61.36 Deletedinuse: 0
% 60.92/61.36
% 60.92/61.36 Resimplifying inuse:
% 60.92/61.36 Done
% 60.92/61.36
% 60.92/61.36 Resimplifying inuse:
% 60.92/61.36 Done
% 60.92/61.36
% 60.92/61.36
% 60.92/61.36 Intermediate Status:
% 60.92/61.36 Generated: 331583
% 60.92/61.36 Kept: 78314
% 60.92/61.36 Inuse: 985
% 60.92/61.36 Deleted: 355
% 60.92/61.36 Deletedinuse: 0
% 60.92/61.36
% 60.92/61.36 Resimplifying inuse:
% 60.92/61.36 Done
% 60.92/61.36
% 60.92/61.36
% 60.92/61.36 Intermediate Status:
% 60.92/61.36 Generated: 338002
% 60.92/61.36 Kept: 81563
% 60.92/61.36 Inuse: 1008
% 60.92/61.36 Deleted: 355
% 60.92/61.36 Deletedinuse: 0
% 60.92/61.36
% 60.92/61.36 Resimplifying inuse:
% 60.92/61.36 Done
% 60.92/61.36
% 60.92/61.36 Resimplifying clauses:
% 60.92/61.36 Done
% 60.92/61.36
% 60.92/61.36 Resimplifying inuse:
% 60.92/61.36 Done
% 60.92/61.36
% 60.92/61.36
% 60.92/61.36 Intermediate Status:
% 60.92/61.36 Generated: 351014
% 60.92/61.36 Kept: 83579
% 60.92/61.36 Inuse: 1048
% 60.92/61.36 Deleted: 425
% 60.92/61.36 Deletedinuse: 0
% 153.48/153.91
% 153.48/153.91 Resimplifying inuse:
% 153.48/153.91 Done
% 153.48/153.91
% 153.48/153.91 Resimplifying inuse:
% 153.48/153.91 Done
% 153.48/153.91
% 153.48/153.91
% 153.48/153.91 Intermediate Status:
% 153.48/153.91 Generated: 360860
% 153.48/153.91 Kept: 85789
% 153.48/153.91 Inuse: 1080
% 153.48/153.91 Deleted: 425
% 153.48/153.91 Deletedinuse: 0
% 153.48/153.91
% 153.48/153.91 Resimplifying inuse:
% 153.48/153.91 Done
% 153.48/153.91
% 153.48/153.91
% 153.48/153.91 Intermediate Status:
% 153.48/153.91 Generated: 369277
% 153.48/153.91 Kept: 89437
% 153.48/153.91 Inuse: 1100
% 153.48/153.91 Deleted: 425
% 153.48/153.91 Deletedinuse: 0
% 153.48/153.91
% 153.48/153.91 Resimplifying inuse:
% 153.48/153.91 Done
% 153.48/153.91
% 153.48/153.91 *** allocated 4378860 integers for termspace/termends
% 153.48/153.91
% 153.48/153.91 Intermediate Status:
% 153.48/153.91 Generated: 411508
% 153.48/153.91 Kept: 93596
% 153.48/153.91 Inuse: 1115
% 153.48/153.91 Deleted: 425
% 153.48/153.91 Deletedinuse: 0
% 153.48/153.91
% 153.48/153.91 Resimplifying inuse:
% 153.48/153.91 Done
% 153.48/153.91
% 153.48/153.91 *** allocated 6568290 integers for clauses
% 153.48/153.91 Resimplifying inuse:
% 153.48/153.91 Done
% 153.48/153.91
% 153.48/153.91
% 153.48/153.91 Intermediate Status:
% 153.48/153.91 Generated: 422894
% 153.48/153.91 Kept: 95710
% 153.48/153.91 Inuse: 1140
% 153.48/153.91 Deleted: 425
% 153.48/153.91 Deletedinuse: 0
% 153.48/153.91
% 153.48/153.91 Resimplifying inuse:
% 153.48/153.91 Done
% 153.48/153.91
% 153.48/153.91 Resimplifying inuse:
% 153.48/153.91 Done
% 153.48/153.91
% 153.48/153.91
% 153.48/153.91 Intermediate Status:
% 153.48/153.91 Generated: 434448
% 153.48/153.91 Kept: 98372
% 153.48/153.91 Inuse: 1150
% 153.48/153.91 Deleted: 425
% 153.48/153.91 Deletedinuse: 0
% 153.48/153.91
% 153.48/153.91 Resimplifying inuse:
% 153.48/153.91 Done
% 153.48/153.91
% 153.48/153.91
% 153.48/153.91 Intermediate Status:
% 153.48/153.91 Generated: 470089
% 153.48/153.91 Kept: 102746
% 153.48/153.91 Inuse: 1160
% 153.48/153.91 Deleted: 425
% 153.48/153.91 Deletedinuse: 0
% 153.48/153.91
% 153.48/153.91 Resimplifying inuse:
% 153.48/153.91 Done
% 153.48/153.91
% 153.48/153.91 Resimplifying clauses:
% 153.48/153.91 Done
% 153.48/153.91
% 153.48/153.91
% 153.48/153.91 Intermediate Status:
% 153.48/153.91 Generated: 491869
% 153.48/153.91 Kept: 105505
% 153.48/153.91 Inuse: 1165
% 153.48/153.91 Deleted: 638
% 153.48/153.91 Deletedinuse: 0
% 153.48/153.91
% 153.48/153.91 Resimplifying inuse:
% 153.48/153.91 Done
% 153.48/153.91
% 153.48/153.91
% 153.48/153.91 Intermediate Status:
% 153.48/153.91 Generated: 499016
% 153.48/153.91 Kept: 107609
% 153.48/153.91 Inuse: 1170
% 153.48/153.91 Deleted: 638
% 153.48/153.91 Deletedinuse: 0
% 153.48/153.91
% 153.48/153.91 Resimplifying inuse:
% 153.48/153.91 Done
% 153.48/153.91
% 153.48/153.91
% 153.48/153.91 Intermediate Status:
% 153.48/153.91 Generated: 511395
% 153.48/153.91 Kept: 113908
% 153.48/153.91 Inuse: 1185
% 153.48/153.91 Deleted: 638
% 153.48/153.91 Deletedinuse: 0
% 153.48/153.91
% 153.48/153.91 Resimplifying inuse:
% 153.48/153.91 Done
% 153.48/153.91
% 153.48/153.91 Resimplifying inuse:
% 153.48/153.91 Done
% 153.48/153.91
% 153.48/153.91
% 153.48/153.91 Intermediate Status:
% 153.48/153.91 Generated: 530034
% 153.48/153.91 Kept: 118639
% 153.48/153.91 Inuse: 1220
% 153.48/153.91 Deleted: 638
% 153.48/153.91 Deletedinuse: 0
% 153.48/153.91
% 153.48/153.91 Resimplifying inuse:
% 153.48/153.91 Done
% 153.48/153.91
% 153.48/153.91
% 153.48/153.91 Intermediate Status:
% 153.48/153.91 Generated: 544277
% 153.48/153.91 Kept: 121991
% 153.48/153.91 Inuse: 1235
% 153.48/153.91 Deleted: 639
% 153.48/153.91 Deletedinuse: 1
% 153.48/153.91
% 153.48/153.91 Resimplifying inuse:
% 153.48/153.91 Done
% 153.48/153.91
% 153.48/153.91
% 153.48/153.91 Intermediate Status:
% 153.48/153.91 Generated: 550875
% 153.48/153.91 Kept: 125339
% 153.48/153.91 Inuse: 1240
% 153.48/153.91 Deleted: 639
% 153.48/153.91 Deletedinuse: 1
% 153.48/153.91
% 153.48/153.91 Resimplifying inuse:
% 153.48/153.91 Done
% 153.48/153.91
% 153.48/153.91 Resimplifying clauses:
% 153.48/153.91 Done
% 153.48/153.91
% 153.48/153.91
% 153.48/153.91 Intermediate Status:
% 153.48/153.91 Generated: 565706
% 153.48/153.91 Kept: 132230
% 153.48/153.91 Inuse: 1260
% 153.48/153.91 Deleted: 828
% 153.48/153.91 Deletedinuse: 1
% 153.48/153.91
% 153.48/153.91 Resimplifying inuse:
% 153.48/153.91 Done
% 153.48/153.91
% 153.48/153.91
% 153.48/153.91 Intermediate Status:
% 153.48/153.91 Generated: 577894
% 153.48/153.91 Kept: 135076
% 153.48/153.91 Inuse: 1273
% 153.48/153.91 Deleted: 828
% 153.48/153.91 Deletedinuse: 1
% 153.48/153.91
% 153.48/153.91 Resimplifying inuse:
% 153.48/153.91 Done
% 153.48/153.91
% 153.48/153.91 Resimplifying inuse:
% 153.48/153.91 Done
% 153.48/153.91
% 153.48/153.91
% 153.48/153.91 Intermediate Status:
% 153.48/153.91 Generated: 585732
% 153.48/153.91 Kept: 137132
% 153.48/153.91 Inuse: 1300
% 153.48/153.91 Deleted: 1034
% 153.48/153.91 Deletedinuse: 207
% 153.48/153.91
% 153.48/153.91 Resimplifying inuse:
% 153.48/153.91 Done
% 153.48/153.91
% 153.48/153.91 Resimplifying inuse:
% 153.48/153.91 Done
% 153.48/153.91
% 153.48/153.91
% 153.48/153.91 Intermediate Status:
% 153.48/153.91 Generated: 598370
% 153.48/153.91 Kept: 140095
% 153.48/153.91 Inuse: 1325
% 153.48/153.91 Deleted: 1034
% 153.48/153.91 Deletedinuse: 207
% 153.48/153.91
% 153.48/153.91 Resimplifying inuse:
% 153.48/153.91 Done
% 153.48/153.91
% 153.48/153.91 Resimplifying inuse:
% 153.48/153.91 Done
% 153.48/153.91
% 153.48/153.91
% 153.48/153.91 Intermediate Status:
% 153.48/153.91 Generated: 609016
% 153.48/153.91 Kept: 142602
% 153.48/153.91 Inuse: 1361
% 153.48/153.91 Deleted: 1040
% 153.48/153.91 Deletedinuse: 209
% 153.48/153.91
% 153.48/153.91 Resimplifying inuse:
% 153.48/153.91 Done
% 153.48/153.91
% 153.48/153.91 *** allocated 6568290 integers for termspace/termends
% 153.48/153.91 Resimplifying inuse:
% 153.48/153.91 Done
% 153.48/153.91
% 153.48/153.91 *** allocated 9852435 integers for clauses
% 153.48/153.91
% 153.48/153.91 Intermediate Status:
% 153.48/153.91 Generated: 625534
% 153.48/153.91 Kept: 144905
% 153.48/153.91 Inuse: 1371
% 153.48/153.91 Deleted: 1041
% 153.48/153.91 Deletedinuse: 210
% 153.48/153.91
% 153.48/153.91 Resimplifying inuse:
% 153.48/153.91 Done
% 153.48/153.91
% 153.48/153.91 Resimplifying clauses:
% 153.48/153.91 Done
% 153.48/153.91
% 153.48/153.91 Resimplifying inuse:
% 153.48/153.91 Done
% 153.48/153.91
% 153.48/153.91
% 153.48/153.91 Intermediate Status:
% 153.48/153.91 Generated: 634335
% 153.48/153.91 Kept: 147221
% 153.48/153.91 Inuse: 1396
% 153.48/153.91 Deleted: 7829
% 153.48/153.91 Deletedinuse: 210
% 153.48/153.91
% 153.48/153.91 Resimplifying inuse:
% 153.48/153.91 Done
% 153.48/153.91
% 153.48/153.91 Resimplifying inuse:
% 153.48/153.91 Done
% 153.48/153.91
% 153.48/153.91
% 153.48/153.91 Intermediate Status:
% 153.48/153.91 Generated: 649033
% 153.48/153.91 Kept: 149701
% 153.48/153.91 Inuse: 1416
% 153.48/153.91 Deleted: 7829
% 153.48/153.91 Deletedinuse: 210
% 153.48/153.91
% 153.48/153.91 Resimplifying inuse:
% 153.48/153.91 Done
% 153.48/153.91
% 153.48/153.91 Resimplifying inuse:
% 153.48/153.91 Done
% 153.48/153.91
% 153.48/153.91
% 153.48/153.91 Intermediate Status:
% 153.48/153.91 Generated: 657338
% 153.48/153.91 Kept: 151835
% 153.48/153.91 Inuse: 1436
% 153.48/153.91 Deleted: 7829
% 153.48/153.91 Deletedinuse: 210
% 153.48/153.91
% 153.48/153.91 Resimplifying inuse:
% 153.48/153.91 Done
% 153.48/153.91
% 153.48/153.91
% 153.48/153.91 Intermediate Status:
% 153.48/153.91 Generated: 663433
% 153.48/153.91 Kept: 153850
% 153.48/153.91 Inuse: 1466
% 153.48/153.91 Deleted: 7829
% 153.48/153.91 Deletedinuse: 210
% 153.48/153.91
% 153.48/153.91 Resimplifying inuse:
% 153.48/153.91 Done
% 153.48/153.91
% 153.48/153.91 Resimplifying inuse:
% 153.48/153.91 Done
% 153.48/153.91
% 153.48/153.91
% 153.48/153.91 Intermediate Status:
% 153.48/153.91 Generated: 669520
% 153.48/153.91 Kept: 155880
% 153.48/153.91 Inuse: 1496
% 153.48/153.91 Deleted: 7829
% 153.48/153.91 Deletedinuse: 210
% 153.48/153.91
% 153.48/153.91 Resimplifying inuse:
% 153.48/153.91 Done
% 153.48/153.91
% 153.48/153.91 Resimplifying inuse:
% 153.48/153.91 Done
% 153.48/153.91
% 153.48/153.91
% 153.48/153.91 Intermediate Status:
% 153.48/153.91 Generated: 675944
% 153.48/153.91 Kept: 157962
% 153.48/153.91 Inuse: Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------