TSTP Solution File: SWW263+1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWW263+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n024.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 23:21:40 EDT 2022
% Result : Timeout 300.03s 300.50s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SWW263+1 : TPTP v8.1.0. Released v5.2.0.
% 0.10/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n024.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % DateTime : Mon Jun 6 08:01:35 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.94/1.56 *** allocated 10000 integers for termspace/termends
% 0.94/1.56 *** allocated 10000 integers for clauses
% 0.94/1.56 *** allocated 10000 integers for justifications
% 0.94/1.56 *** allocated 15000 integers for termspace/termends
% 0.94/1.56 *** allocated 22500 integers for termspace/termends
% 0.94/1.56 *** allocated 33750 integers for termspace/termends
% 0.94/1.56 Bliksem 1.12
% 0.94/1.56
% 0.94/1.56
% 0.94/1.56 Automatic Strategy Selection
% 0.94/1.56
% 0.94/1.56 *** allocated 50625 integers for termspace/termends
% 0.94/1.56 *** allocated 75937 integers for termspace/termends
% 0.94/1.56 *** allocated 113905 integers for termspace/termends
% 0.94/1.56
% 0.94/1.56 Clauses:
% 0.94/1.56
% 0.94/1.56 { ! hAPP( Y, skol1( X, Y ) ) = hAPP( X, skol1( X, Y ) ), Y = X }.
% 0.94/1.56 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), v_t____ ) }.
% 0.94/1.56 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, v_t____,
% 0.94/1.56 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.94/1.56 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), v_m____ ) }.
% 0.94/1.56 { ! v_k____ = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.56 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), v_t____ ), v_k____ ) )
% 0.94/1.56 }.
% 0.94/1.56 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), v_t____ ), hAPP( hAPP
% 0.94/1.56 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, v_w____ ) ),
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, v_k____,
% 0.94/1.56 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ), v_m____ ) ),
% 0.94/1.56 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.94/1.56 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, v_t____,
% 0.94/1.56 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, v_w____ ) ),
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, v_k____,
% 0.94/1.56 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ), v_m____ ) ) ) }.
% 0.94/1.56 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.94/1.56 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, v_w____ ) ),
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, v_k____,
% 0.94/1.56 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ), v_m____ ) ) ) }.
% 0.94/1.56 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), v_t____ ),
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, v_w____ ) ), hAPP(
% 0.94/1.56 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.94/1.56 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, v_w____ ) ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Y ), Z ) ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol2( Y ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, skol2( Y ),
% 0.94/1.56 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, skol2( X ), X ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__normed__algebra( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( X, Z ), Y ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( X, U ), T ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), T ) ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( X, Y ) ), ! Y =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__normed__vector( X ), Y =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless(
% 0.94/1.56 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.94/1.56 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.94/1.56 X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.56 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 0.94/1.56 , T, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.94/1.56 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.94/1.56 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.94/1.56 c_Groups_Oone__class_Oone( X ), c_Groups_Oone__class_Oone( X ) ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.94/1.56 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.56 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.94/1.56 ) ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__ring__strict( X ), Z =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.94/1.56 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__ring__strict( X ), Y =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.94/1.56 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.94/1.56 { ! v_a____ = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.94/1.56 { ! v_w____ = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.94/1.56 { c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex,
% 0.94/1.56 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), v_w____ ), v_k____ )
% 0.94/1.56 ), v_a____ ) ) = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.94/1.56 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Y ),
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X ) ),
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) ) }.
% 0.94/1.56 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 0.94/1.56 c_Rings_Oinverse__class_Oinverse( X, c_Rings_Oinverse__class_Oinverse( X
% 0.94/1.56 , Y ) ) = Y }.
% 0.94/1.56 { ! class_RealVector_Oreal__normed__div__algebra( X ), !
% 0.94/1.56 class_Rings_Odivision__ring__inverse__zero( X ),
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( X, c_Rings_Oinverse__class_Oinverse( X,
% 0.94/1.56 Y ) ) = c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal,
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.94/1.56 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), X =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.94/1.56 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 0.94/1.56 ), X ) ) }.
% 0.94/1.56 { ! class_Rings_Odivision__ring__inverse__zero( X ), !
% 0.94/1.56 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 0.94/1.56 c_Rings_Oinverse__class_Oinverse( X, Y ), Z = Y }.
% 0.94/1.56 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Z = Y,
% 0.94/1.56 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 0.94/1.56 c_Rings_Oinverse__class_Oinverse( X, Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 0.94/1.56 ( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Z ), hAPP( hAPP
% 0.94/1.56 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.94/1.56 { ! class_Rings_Odivision__ring__inverse__zero( X ), !
% 0.94/1.56 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 0.94/1.56 c_Rings_Oinverse__class_Oinverse( X, Y ), Z = Y }.
% 0.94/1.56 { ! class_Rings_Odivision__ring( X ), ! c_Rings_Oinverse__class_Oinverse( X
% 0.94/1.56 , Z ) = c_Rings_Oinverse__class_Oinverse( X, Y ), Z =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z
% 0.94/1.56 = Y }.
% 0.94/1.56 { ! class_Rings_Odivision__ring( X ), ! c_Rings_Oinverse__class_Oinverse( X
% 0.94/1.56 , Y ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( X ) }.
% 0.94/1.56 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.56 , c_Rings_Oinverse__class_Oinverse( X, c_Rings_Oinverse__class_Oinverse(
% 0.94/1.56 X, Y ) ) = Y }.
% 0.94/1.56 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.56 , ! c_Rings_Oinverse__class_Oinverse( X, Y ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.56 { ! class_Rings_Odivision__ring__inverse__zero( X ), !
% 0.94/1.56 c_Rings_Oinverse__class_Oinverse( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.94/1.56 ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.56 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Y =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X, Y
% 0.94/1.56 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.56 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 0.94/1.56 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.56 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Oinverse( X,
% 0.94/1.56 c_Groups_Oone__class_Oone( X ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.94/1.56 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 0.94/1.56 c_Rings_Oinverse__class_Oinverse( X, hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Oinverse( X, Z
% 0.94/1.56 ) ), Y ) }.
% 0.94/1.56 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__normed__div__algebra( X ), Y =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X,
% 0.94/1.56 c_Rings_Oinverse__class_Oinverse( X, Y ) ) =
% 0.94/1.56 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal,
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), T ), Z ) = hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Y ), Z ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.94/1.56 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 X ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ), T = Y }.
% 0.94/1.56 { ! class_Rings_Olinordered__semidom( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), T )
% 0.94/1.56 , c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semidom( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.94/1.56 ), ! c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oone__class_Oone
% 0.94/1.56 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.94/1.56 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.56 , Z = c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse
% 0.94/1.56 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP(
% 0.94/1.56 hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.94/1.56 c_Rings_Oinverse__class_Oinverse( X, Z ) ),
% 0.94/1.56 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.94/1.56 { ! class_Rings_Odivision__ring( X ), ! hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = c_Groups_Oone__class_Oone
% 0.94/1.56 ( X ), c_Rings_Oinverse__class_Oinverse( X, Z ) = Y }.
% 0.94/1.56 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.56 , c_Rings_Oinverse__class_Oinverse( X, hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Y ), Z ) ) = hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Oinverse( X, Y
% 0.94/1.56 ) ), Z ) }.
% 0.94/1.56 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.94/1.56 ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.56 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.56 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.56 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 X ), Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( X ) ) }.
% 0.94/1.56 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.56 , c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.56 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.94/1.56 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.94/1.56 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.56 , Z, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.56 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.94/1.56 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.94/1.56 { ! class_Rings_Oordered__semiring( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.56 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.94/1.56 { ! class_Rings_Oordered__semiring( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.94/1.56 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.94/1.56 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.56 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.56 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 0.94/1.56 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.56 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.56 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.94/1.56 { ! class_Rings_Oordered__comm__semiring( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.94/1.56 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.94/1.56 { ! class_Rings_Oordered__semiring( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.94/1.56 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.94/1.56 { ! class_Rings_Oordered__semiring( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.94/1.56 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.94/1.56 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.56 , Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.56 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.94/1.56 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.94/1.56 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.56 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 X ), Z ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( X ) ) }.
% 0.94/1.56 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.56 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.56 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.56 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.56 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.56 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ),
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.56 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.56 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( X ) ), alpha1( X, Y, Z ), alpha9( X, Y, Z ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha1( X, Y, Z ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( X ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha9( X, Y, Z ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( X ) ) }.
% 0.94/1.56 { ! alpha9( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.56 { ! alpha9( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.94/1.56 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( X ), Y ), alpha9( X, Y, Z ) }.
% 0.94/1.56 { ! alpha1( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.94/1.56 { ! alpha1( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.56 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) ), alpha1( X, Y, Z ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), alpha2( X, Y
% 0.94/1.56 , Z ), alpha10( X, Y, Z ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha2( X, Y, Z ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha10( X, Y, Z ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.94/1.56 { ! alpha10( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.56 { ! alpha10( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.94/1.56 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) ), alpha10( X, Y, Z ) }.
% 0.94/1.56 { ! alpha2( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.94/1.56 { ! alpha2( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.56 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ), Y ), alpha2( X, Y, Z ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 0.94/1.56 X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semidom( X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.56 c_Groups_Oone__class_Oone( X ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semidom( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semidom( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.94/1.56 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semidom( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.56 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.94/1.56 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semidom( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), Y )
% 0.94/1.56 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.94/1.56 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.94/1.56 ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.94/1.56 ( X, Y ) ) ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 0.94/1.56 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.94/1.56 , Y ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.94/1.56 c_Groups_Oone__class_Oone( X ) }.
% 0.94/1.56 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.56 , Z = c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.94/1.56 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.94/1.56 c_Rings_Oinverse__class_Oinverse( X, Z ) ) = hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 0.94/1.56 Y ) ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) ),
% 0.94/1.56 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.94/1.56 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.56 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.94/1.56 c_Rings_Oinverse__class_Oinverse( X, Y ) ), Y ) =
% 0.94/1.56 c_Groups_Oone__class_Oone( X ) }.
% 0.94/1.56 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.56 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ),
% 0.94/1.56 c_Rings_Oinverse__class_Oinverse( X, Y ) ) = c_Groups_Oone__class_Oone( X
% 0.94/1.56 ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.94/1.56 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.94/1.56 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.94/1.56 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.94/1.56 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.94/1.56 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.94/1.56 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, U, T ), ! c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.94/1.56 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.94/1.56 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.56 , U ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, U, T ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.94/1.56 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, U, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.94/1.56 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.94/1.56 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.94/1.56 ! c_Orderings_Oord__class_Oless__eq( X, Z, T ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.94/1.56 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.94/1.56 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.94/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) ), Z = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.56 }.
% 0.94/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.94/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.56 }.
% 0.94/1.56 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.56 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.94/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 0.94/1.56 X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 0.94/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.94/1.56 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.94/1.56 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 0.94/1.56 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.94/1.56 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.94/1.56 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 0.94/1.56 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP
% 0.94/1.56 ( c_Power_Opower__class_Opower( X ), Y ), T ) ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.56 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ), Z ), ! c_Orderings_Oord__class_Oless(
% 0.94/1.56 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), T ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( X, Y ), c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_RealDef_Oreal ) ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless__eq(
% 0.94/1.56 tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( X, Y ),
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( X, Z ) ),
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( X, Y ) ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.94/1.56 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), hAPP(
% 0.94/1.56 hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Z ), Y ) ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( X, Z ) ), Y ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semiring__1( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, T, Y ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.94/1.56 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 X ), W ), ! c_Groups_Oplus__class_Oplus( X, U, W ) =
% 0.94/1.56 c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.56 ( X ), U ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), T )
% 0.94/1.56 ), Y ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__idom( X ), Z = Y,
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.94/1.56 X, Y, Z ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semiring__1__strict( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, T, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ), U ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), W
% 0.94/1.56 ), ! c_Groups_Oplus__class_Oplus( X, U, W ) = c_Groups_Oone__class_Oone
% 0.94/1.56 ( X ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X,
% 0.94/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), W ), T ) ), Y ) }.
% 0.94/1.56 { ! class_Rings_Ono__zero__divisors( X ), ! hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.56 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.56 { ! class_Rings_Ono__zero__divisors( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.94/1.56 X ), Z = c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.56 { ! class_Rings_Oring__no__zero__divisors( X ), ! hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.56 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.56 { ! class_Rings_Oring__no__zero__divisors( X ), ! Z =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.56 { ! class_Rings_Oring__no__zero__divisors( X ), ! Y =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.94/1.56 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.94/1.56 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.56 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.56 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.94/1.56 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.94/1.56 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.56 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.56 ( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.56 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.94/1.56 c_Groups_Oone__class_Oone( X ) }.
% 0.94/1.56 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Oone__class_Oone( X ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.56 { ! class_Rings_Osemiring( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP
% 0.94/1.56 ( c_Groups_Otimes__class_Otimes( X ), U ), T ),
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.56 ( X ), Z ), T ), Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, U, Z
% 0.94/1.56 ) ), T ), Y ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.94/1.56 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.94/1.56 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.94/1.56 { ! class_Rings_Ocomm__semiring( X ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.94/1.56 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.94/1.56 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.94/1.56 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.94/1.56 { ! class_Rings_Oring__1__no__zero__divisors( X ), Y =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( X ) }.
% 0.94/1.56 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.94/1.56 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.94/1.56 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.94/1.56 .
% 0.94/1.56 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.94/1.56 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.94/1.56 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Nat_Onat ) }.
% 0.94/1.56 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.94/1.56 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.94/1.56 , ! Z = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y )
% 0.94/1.56 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.56 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.94/1.56 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.94/1.56 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.94/1.56 = c_Groups_Oone__class_Oone( X ) }.
% 0.94/1.56 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.94/1.56 tc_Nat_Onat ) ) = Y }.
% 0.94/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP
% 0.94/1.56 ( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.94/1.56 ( c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__comm__semiring__strict( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.94/1.56 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.94/1.56 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP
% 0.94/1.56 ( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.94/1.56 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.94/1.56 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.94/1.56 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.94/1.56 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( X ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.94/1.56 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.94/1.56 ! c_Orderings_Oord__class_Oless( X, Z, T ), c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.94/1.56 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.94/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ) }
% 0.94/1.56 .
% 0.94/1.56 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.94/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.94/1.56 .
% 0.94/1.56 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.94/1.56 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.94/1.56 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( X ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.94/1.56 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.94/1.56 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( X ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.94/1.56 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.94/1.56 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.94/1.56 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.94/1.56 ! c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.94/1.56 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha3( X, Y, Z, T ),
% 0.94/1.56 alpha11( X, Y, Z, T ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha3( X, Y, Z, T ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha11( X, Y, Z, T ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.94/1.56 { ! alpha11( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.56 { ! alpha11( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( X, T, c_Groups_Ozero__class_Ozero( X ) )
% 0.94/1.56 , ! c_Orderings_Oord__class_Oless( X, Y, Z ), alpha11( X, Y, Z, T ) }.
% 0.94/1.56 { ! alpha3( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ), T ) }.
% 0.94/1.56 { ! alpha3( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T )
% 0.94/1.56 , ! c_Orderings_Oord__class_Oless( X, Z, Y ), alpha3( X, Y, Z, T ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha4( X, Y, Z, T ),
% 0.94/1.56 alpha12( X, Y, Z, T ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha4( X, Y, Z, T ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha12( X, Y, Z, T ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.94/1.56 { ! alpha12( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.56 { ! alpha12( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, T ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.94/1.56 , ! c_Orderings_Oord__class_Oless( X, Y, T ), alpha12( X, Y, Z, T ) }.
% 0.94/1.56 { ! alpha4( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.94/1.56 { ! alpha4( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.94/1.56 , ! c_Orderings_Oord__class_Oless( X, T, Y ), alpha4( X, Y, Z, T ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.94/1.56 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless(
% 0.94/1.56 X, T, c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.56 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.94/1.56 ) = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X
% 0.94/1.56 ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.56 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.94/1.56 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.94/1.56 ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.56 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.94/1.56 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero( X ) ) }
% 0.94/1.56 .
% 0.94/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, c_Groups_Oone__class_Oone( X ), Z ), c_Orderings_Oord__class_Oless(
% 0.94/1.56 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.94/1.56 , Y, c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) )
% 0.94/1.56 ) }.
% 0.94/1.56 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), ! Y =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.94/1.56 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.94/1.56 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), Y =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.94/1.56 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.56 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.94/1.56 c_Groups_Oone__class_Oone( X ), T ), c_Orderings_Oord__class_Oless( X,
% 0.94/1.56 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.94/1.56 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.94/1.56 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.94/1.56 ( tc_Nat_Onat, T, Z ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Y ), Z ), T = Z }.
% 0.94/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! T = Z, hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Y ), Z ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( X, Y ) = c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_RealDef_Oreal ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X, Y )
% 0.94/1.56 = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.94/1.56 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 0.94/1.56 tc_Nat_Onat, Z, Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.94/1.56 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( X, Z ), Y ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( X, U ), T ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, Z, U
% 0.94/1.56 ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, T ) ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( X, Z ) ),
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( X, Y ), c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_RealDef_Oreal ) ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oone__class_Oone( X ) ) =
% 0.94/1.56 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( X, Z ) ), Y ) }.
% 0.94/1.56 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol3 ) }.
% 0.94/1.56 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, skol3,
% 0.94/1.56 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.94/1.56 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, skol3,
% 0.94/1.56 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, v_w____ ) ),
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, v_k____,
% 0.94/1.56 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ), v_m____ ) ) ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__normed__div__algebra( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z,
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( X, Y ) ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( X, c_Rings_Oinverse__class_Oinverse( X,
% 0.94/1.56 Y ) ), c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, Z ) ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( X, Z ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ),
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( X, T ) ) ), Z =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.94/1.56 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.94/1.56 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone( X ) )
% 0.94/1.56 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.94/1.56 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.94/1.56 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 0.94/1.56 ), c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless__eq(
% 0.94/1.56 X, Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless(
% 0.94/1.56 X, c_Groups_Oone__class_Oone( X ), Y ) }.
% 0.94/1.56 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.56 ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X
% 0.94/1.56 , Y ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.94/1.56 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), Y ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 0.94/1.56 ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.94/1.56 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.94/1.56 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.94/1.56 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.94/1.56 c_Rings_Oinverse__class_Oinverse( X, Y ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone( X ) )
% 0.94/1.56 }.
% 0.94/1.56 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.94/1.56 ! c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone( X )
% 0.94/1.56 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X )
% 0.94/1.56 , c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.94/1.56 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.94/1.56 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, X ) ), X ) =
% 0.94/1.56 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), T ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.94/1.56 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, X ) ), T ), hAPP(
% 0.94/1.56 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.94/1.56 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, Y ) ), Z ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), T ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), T ),
% 0.94/1.56 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, X ) ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ),
% 0.94/1.56 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, Y ) ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 0.94/1.56 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.94/1.56 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, X ) }.
% 0.94/1.56 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) }.
% 0.94/1.56 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) ) }.
% 0.94/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP
% 0.94/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.94/1.56 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ) }.
% 0.94/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 0.94/1.56 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.94/1.56 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ), Y = X }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), T ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.56 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.94/1.56 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.94/1.56 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.94/1.56 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.94/1.56 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.94/1.56 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol4( X, Y ) ) }.
% 0.94/1.56 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol5( X, Y ) ) }.
% 0.94/1.56 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, T ),
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ), X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X
% 0.94/1.56 ) }.
% 0.94/1.56 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 0.94/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 0.94/1.56 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 0.94/1.56 ) }.
% 0.94/1.56 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 0.94/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 0.94/1.56 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.94/1.56 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.94/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z = X
% 0.94/1.56 , Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.56 { ! Z = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.94/1.56 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }
% 0.94/1.56 .
% 0.94/1.56 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.94/1.56 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.94/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Y = X
% 0.94/1.56 , Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.56 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.94/1.56 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.94/1.56 .
% 0.94/1.56 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.94/1.56 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.56 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.56 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ), Y = X }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Z ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, Z ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ),
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, X ) ) }.
% 0.94/1.56 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ) }.
% 0.94/1.56 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, X ) }.
% 0.94/1.56 { alpha16( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 0.94/1.56 hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.94/1.56 { alpha16( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP
% 0.94/1.56 ( X, Y ), Z ) ) }.
% 0.94/1.56 { ! alpha16( X, Y, Z ), alpha18( X, Y, Z ), Z = Y }.
% 0.94/1.56 { ! alpha16( X, Y, Z ), alpha18( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z
% 0.94/1.56 ) ) }.
% 0.94/1.56 { ! alpha18( X, Y, Z ), alpha16( X, Y, Z ) }.
% 0.94/1.56 { ! Z = Y, hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha16( X, Y, Z ) }.
% 0.94/1.56 { ! alpha18( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y )
% 0.94/1.56 }.
% 0.94/1.56 { ! alpha18( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ), hBOOL( hAPP( hAPP(
% 0.94/1.56 X, Y ), Z ) ), alpha18( X, Y, Z ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X = Y }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.94/1.56 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.94/1.56 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.94/1.56 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.94/1.56 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, c_Groups_Oplus__class_Oplus
% 0.94/1.56 ( tc_Nat_Onat, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.94/1.56 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.94/1.56 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.94/1.56 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ), Y = X }.
% 0.94/1.56 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) }.
% 0.94/1.56 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ), Z = X }.
% 0.94/1.56 { ! Z = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.94/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.94/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.94/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) =
% 0.94/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y )
% 0.94/1.56 }.
% 0.94/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP
% 0.94/1.56 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), Y ) ), X ) =
% 0.94/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), hAPP
% 0.94/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.94/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ) ), X ) =
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.94/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.94/1.56 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) = X }.
% 0.94/1.56 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), Y =
% 0.94/1.56 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.94/1.56 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X =
% 0.94/1.56 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.94/1.56 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.94/1.56 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Groups_Oone__class_Oone(
% 0.94/1.56 tc_Nat_Onat ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.94/1.56 , Y ), X ) }.
% 0.94/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.94/1.56 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 0.94/1.56 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.94/1.56 c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y = c_Groups_Oone__class_Oone(
% 0.94/1.56 tc_Nat_Onat ) }.
% 0.94/1.56 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.94/1.56 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X = c_Groups_Oone__class_Oone(
% 0.94/1.56 tc_Nat_Onat ) }.
% 0.94/1.56 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.94/1.56 c_Groups_Oone__class_Oone( tc_Nat_Onat ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.94/1.56 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.94/1.56 { ! class_Fields_Ofield__inverse__zero( X ),
% 0.94/1.56 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.56 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Nat_Onat ), X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.94/1.56 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP
% 0.94/1.56 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.94/1.56 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP
% 0.94/1.56 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Nat_Onat ), Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.94/1.56 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Nat_Onat ), Z ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Nat_Onat ), Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 0.94/1.56 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.94/1.56 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.94/1.56 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.94/1.56 Y ), X ) ) }.
% 0.94/1.56 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Nat_Onat ), X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Nat_Onat ), X ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 0.94/1.56 .
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), ! Y = X }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), Y = X,
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), Y = X }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.94/1.56 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.94/1.56 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Nat_Onat ), X ) = X }.
% 0.94/1.56 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Nat_Onat ) ) = X }.
% 0.94/1.56 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.56 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.56 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.94/1.56 tc_Nat_Onat, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.56 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = Y, X =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.56 { ! class_Fields_Ofield__inverse__zero( X ),
% 0.94/1.56 c_Rings_Oinverse__class_Oinverse( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 0.94/1.56 Z ) ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.94/1.56 { ! class_Fields_Ofield__inverse__zero( X ), !
% 0.94/1.56 c_Rings_Oinverse__class_Oinverse( X, Y ) = c_Groups_Oone__class_Oone( X )
% 0.94/1.56 , Y = c_Groups_Oone__class_Oone( X ) }.
% 0.94/1.56 { ! class_Fields_Ofield__inverse__zero( X ), ! Y =
% 0.94/1.56 c_Groups_Oone__class_Oone( X ), c_Rings_Oinverse__class_Oinverse( X, Y )
% 0.94/1.56 = c_Groups_Oone__class_Oone( X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.94/1.56 ( tc_Nat_Onat, Y, X ), Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.94/1.56 ( tc_Nat_Onat, Y, X ), X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.94/1.56 ( tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) )
% 0.94/1.56 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.94/1.56 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }
% 0.94/1.56 .
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.94/1.56 tc_Nat_Onat, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.94/1.56 .
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.94/1.56 tc_Nat_Onat, Y, T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.94/1.56 .
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, X ) =
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.94/1.56 ( tc_Nat_Onat, Y, Z ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y
% 0.94/1.56 , X ) }.
% 0.94/1.56 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) = hAPP( hAPP
% 0.94/1.56 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ), Z = Y }.
% 0.94/1.56 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y, hAPP( hAPP
% 0.94/1.56 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) = hAPP(
% 0.94/1.56 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) }.
% 0.94/1.56 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) = hAPP( hAPP
% 0.94/1.56 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ), Z = Y }.
% 0.94/1.56 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y, hAPP( hAPP
% 0.94/1.56 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) = hAPP(
% 0.94/1.56 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) }.
% 0.94/1.56 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.94/1.56 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.94/1.56 { ! Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! X =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.94/1.56 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X )
% 0.94/1.56 , X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.56 { ! c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) =
% 0.94/1.56 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.94/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.94/1.56 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) = X }.
% 0.94/1.56 { c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.94/1.56 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 0.94/1.56 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.56 ) }.
% 0.94/1.56 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.56 ), c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.56 c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Ozero__class_Ozero( X
% 0.94/1.56 ) ) }.
% 0.94/1.56 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.56 c_Rings_Oinverse__class_Oinverse( X, Y ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.56 ) }.
% 0.94/1.56 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.56 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.94/1.56 ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.94/1.56 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.56 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.94/1.56 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.56 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.94/1.56 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 0.94/1.56 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.94/1.56 , Y, c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.56 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 0.94/1.56 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.56 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.94/1.56 X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.94/1.56 X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X
% 0.94/1.56 , Y ) ) }.
% 0.94/1.56 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.94/1.56 X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X
% 0.94/1.56 , Y ) ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.94/1.56 .
% 0.94/1.56 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.94/1.56 X, Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless(
% 0.94/1.56 X, c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( X ) ) }.
% 0.94/1.56 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.94/1.56 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless( X,
% 0.94/1.56 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.94/1.56 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.94/1.56 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.94/1.56 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.94/1.56 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.94/1.56 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.94/1.56 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.94/1.56 X, c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( X ) ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.94/1.56 .
% 0.94/1.56 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.94/1.56 X, c_Rings_Oinverse__class_Oinverse( X, Z ),
% 0.94/1.56 c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.94/1.56 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.94/1.56 X, c_Rings_Oinverse__class_Oinverse( X, Z ),
% 0.94/1.56 c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.94/1.56 tc_Nat_Onat, Y, X ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.94/1.56 tc_Nat_Onat, Y, X ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 0.94/1.56 { ! class_Fields_Olinordered__field( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 0.94/1.56 , Y ), c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.94/1.56 { ! class_Fields_Olinordered__field( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 0.94/1.56 , Y ), c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.94/1.56 { ! class_Fields_Olinordered__field( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 0.94/1.56 , Z ), c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.94/1.56 { ! class_Fields_Olinordered__field( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 0.94/1.56 , Z ), c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.94/1.56 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 0.94/1.56 , Y ), c_Groups_Oone__class_Oone( X ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.56 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X )
% 0.94/1.56 , Y ) }.
% 0.94/1.56 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.56 ), c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.56 c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Oone__class_Oone( X )
% 0.94/1.56 ) }.
% 0.94/1.56 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), Y )
% 0.94/1.56 , c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse
% 0.94/1.56 ( X, Y ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.94/1.56 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.94/1.56 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.94/1.56 c_Rings_Oinverse__class_Oinverse( X, Z ) ) = hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.94/1.56 ) ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) ),
% 0.94/1.56 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.94/1.56 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 0.94/1.56 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.94/1.56 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 0.94/1.56 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, Y, c_Groups_Oone__class_Oone( X ) ) }.
% 0.94/1.56 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.94/1.56 ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 0.94/1.56 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.94/1.56 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.94/1.56 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, Y, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless(
% 0.94/1.56 X, c_Groups_Oone__class_Oone( X ), c_Rings_Oinverse__class_Oinverse( X, Y
% 0.94/1.56 ) ) }.
% 0.94/1.56 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP(
% 0.94/1.56 hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.94/1.56 c_Rings_Oinverse__class_Oinverse( X, Y ) ), Y ) =
% 0.94/1.56 c_Groups_Oone__class_Oone( X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.94/1.56 { c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex,
% 0.94/1.56 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), skol6 ), v_k____ ) )
% 0.94/1.56 , v_a____ ) ) = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.94/1.56 { c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex,
% 0.94/1.56 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), v_w____ ), v_k____ )
% 0.94/1.56 ), v_a____ ) ), c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) =
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ),
% 0.94/1.56 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) }.
% 0.94/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP(
% 0.94/1.56 hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), v_w____ ),
% 0.94/1.56 v_k____ ) ), v_a____ ) = c_Groups_Ouminus__class_Ouminus(
% 0.94/1.56 tc_Complex_Ocomplex, c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) }
% 0.94/1.56 .
% 0.94/1.56 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.94/1.56 c_RealVector_Oof__real( tc_Complex_Ocomplex, v_t____ ) ), v_w____ ) ),
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, v_w____ ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP
% 0.94/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z
% 0.94/1.56 , Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.94/1.56 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.94/1.56 ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.56 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.56 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.94/1.56 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.56 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.56 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.56 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.94/1.56 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.94/1.56 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.94/1.56 ) ) }.
% 0.94/1.56 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.94/1.56 X, Y ) }.
% 0.94/1.56 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z, Y )
% 0.94/1.56 = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus( X
% 0.94/1.56 , Y ) ) }.
% 0.94/1.56 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X, Z
% 0.94/1.56 , Y ) = c_Groups_Oplus__class_Oplus( X, Z,
% 0.94/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.94/1.56 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.94/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Oplus__class_Oplus(
% 0.94/1.56 X, Z, Y ) }.
% 0.94/1.56 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.94/1.56 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y, Y )
% 0.94/1.56 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.56 { ! class_Groups_Oab__group__add( X ), ! Z = Y,
% 0.94/1.56 c_Groups_Ominus__class_Ominus( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.94/1.56 ) }.
% 0.94/1.56 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.94/1.56 Z, Y ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.94/1.56 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.94/1.56 ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.94/1.56 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ominus__class_Ominus(
% 0.94/1.56 X, Z, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.56 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.56 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.94/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Groups_Ozero__class_Ozero( X )
% 0.94/1.56 = Y }.
% 0.94/1.56 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Ouminus__class_Ouminus( X, Y
% 0.94/1.56 ) }.
% 0.94/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.94/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ), Y = c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( X ) }.
% 0.94/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus( X
% 0.94/1.56 , Y ) }.
% 0.94/1.56 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 0.94/1.56 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.94/1.56 ) }.
% 0.94/1.56 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.94/1.56 ) }.
% 0.94/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.94/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ) = Y, Y =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.94/1.56 = Y }.
% 0.94/1.56 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.94/1.56 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.94/1.56 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.94/1.56 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.94/1.56 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.94/1.56 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, U, T ) }.
% 0.94/1.56 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.94/1.56 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.94/1.56 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.94/1.56 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.94/1.56 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.94/1.56 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.94/1.56 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.94/1.56 , Z ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ), Z ) }.
% 0.94/1.56 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.94/1.56 , Y ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.56 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.94/1.56 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ouminus__class_Ouminus
% 0.94/1.56 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.94/1.56 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.94/1.56 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 0.94/1.56 ( X, Z ) ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.94/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.94/1.56 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.94/1.56 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.94/1.56 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, U, T ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.94/1.56 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.94/1.56 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.94/1.56 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, U, T ) }.
% 0.94/1.56 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ouminus__class_Ouminus( X,
% 0.94/1.56 Y ) ), c_Orderings_Oord__class_Oless( X, Y,
% 0.94/1.56 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.94/1.56 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ouminus__class_Ouminus( X,
% 0.94/1.56 Z ) ), c_Orderings_Oord__class_Oless( X, Z,
% 0.94/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.94/1.56 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.94/1.56 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 0.94/1.56 ( X, Y ), Z ) }.
% 0.94/1.56 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.94/1.56 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 0.94/1.56 ( X, Z ), Y ) }.
% 0.94/1.56 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.94/1.56 , c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.94/1.56 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, Y, Z ), c_Orderings_Oord__class_Oless(
% 0.94/1.56 X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.94/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.94/1.56 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.94/1.56 c_Groups_Ominus__class_Ominus( X, Z, Y ), Y ) = Z }.
% 0.94/1.56 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = Z }.
% 0.94/1.56 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 0.94/1.56 , c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.94/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.94/1.56 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 0.94/1.56 , c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.94/1.56 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.94/1.56 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Z,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.94/1.56 Y ) ) = Y }.
% 0.94/1.56 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.94/1.56 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Oplus__class_Oplus( X,
% 0.94/1.56 Z, Y ) ) = Y }.
% 0.94/1.56 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.94/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 0.94/1.56 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.94/1.56 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) =
% 0.94/1.56 c_Groups_Ominus__class_Ominus( X, Y, Z ) }.
% 0.94/1.56 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 0.94/1.56 , Y ), Y = c_Groups_Ouminus__class_Ouminus( X, Z ) }.
% 0.94/1.56 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 0.94/1.56 , Z ), Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.94/1.56 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 0.94/1.56 ) = Y, c_Groups_Ouminus__class_Ouminus( X, Y ) = Z }.
% 0.94/1.56 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 0.94/1.56 ) = Z, c_Groups_Ouminus__class_Ouminus( X, Z ) = Y }.
% 0.94/1.56 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 0.94/1.56 ) = c_Groups_Ouminus__class_Ouminus( X, Y ), Z = Y }.
% 0.94/1.56 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ouminus__class_Ouminus
% 0.94/1.56 ( X, Z ) = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.94/1.56 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.94/1.56 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! U = T, Z = Y }.
% 0.94/1.56 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.94/1.56 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! Z = Y, U = T }.
% 0.94/1.56 { ! class_RealVector_Oreal__algebra__1( X ), ! c_RealVector_Oof__real( X, Z
% 0.94/1.56 ) = c_RealVector_Oof__real( X, Y ), Z = Y }.
% 0.94/1.56 { ! class_RealVector_Oreal__algebra__1( X ), ! Z = Y,
% 0.94/1.56 c_RealVector_Oof__real( X, Z ) = c_RealVector_Oof__real( X, Y ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__algebra__1( X ), !
% 0.94/1.56 class_RealVector_Oreal__normed__vector( X ), c_RealVector_Oof__real( X,
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Z, Y ) ) =
% 0.94/1.56 c_Groups_Ominus__class_Ominus( X, c_RealVector_Oof__real( X, Z ),
% 0.94/1.56 c_RealVector_Oof__real( X, Y ) ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__algebra__1( X ), c_RealVector_Oof__real( X,
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Z, Y ) ) =
% 0.94/1.56 c_Groups_Ominus__class_Ominus( X, c_RealVector_Oof__real( X, Z ),
% 0.94/1.56 c_RealVector_Oof__real( X, Y ) ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__algebra__1( X ), !
% 0.94/1.56 class_RealVector_Oreal__normed__vector( X ), c_RealVector_Oof__real( X,
% 0.94/1.56 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ) =
% 0.94/1.56 c_Groups_Ouminus__class_Ouminus( X, c_RealVector_Oof__real( X, Y ) ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__algebra__1( X ), c_RealVector_Oof__real( X,
% 0.94/1.56 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ) =
% 0.94/1.56 c_Groups_Ouminus__class_Ouminus( X, c_RealVector_Oof__real( X, Y ) ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.94/1.56 ( X, Y ) ), c_RealVector_Onorm__class_Onorm( X,
% 0.94/1.56 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 0.94/1.56 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 0.94/1.56 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 0.94/1.56 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 0.94/1.56 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.94/1.56 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.94/1.56 ), Z ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 0.94/1.56 Z = Y, Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.94/1.56 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.94/1.56 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.94/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.94/1.56 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.94/1.56 , c_Groups_Ouminus__class_Ouminus( X, Z ) ),
% 0.94/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 0.94/1.56 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.94/1.56 , c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.94/1.56 ( X, Y ) ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.94/1.56 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.94/1.56 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.94/1.56 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.94/1.56 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.94/1.56 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 0.94/1.56 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.94/1.56 ) ), Y ) }.
% 0.94/1.56 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 0.94/1.56 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.94/1.56 ( X, Y ) ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, Z,
% 0.94/1.56 Y ) ) = c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus
% 0.94/1.56 ( X, Y, Z ) ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ouminus__class_Ouminus( X, Y
% 0.94/1.56 ) ) = c_RealVector_Onorm__class_Onorm( X, Y ) }.
% 0.94/1.56 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 0.94/1.56 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ouminus__class_Ouminus( X,
% 0.94/1.56 Y ) ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.94/1.56 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.94/1.56 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 0.94/1.56 , Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.56 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 0.94/1.56 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.94/1.56 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.94/1.56 X, c_Groups_Ominus__class_Ominus( X, Z, Y ), c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( X ) ) }.
% 0.94/1.56 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.94/1.56 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.94/1.56 , Z, Y ) }.
% 0.94/1.56 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.56 ) }.
% 0.94/1.56 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.56 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.94/1.56 ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.94/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 0.94/1.56 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.56 ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.94/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.94/1.56 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.94/1.56 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.56 ) }.
% 0.94/1.56 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.56 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 0.94/1.56 ( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.94/1.56 , Y ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.94/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.56 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 0.94/1.56 ( X, Y ), Y ) }.
% 0.94/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.94/1.56 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.56 , Y ) }.
% 0.94/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.94/1.56 , Y ) }.
% 0.94/1.56 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.94/1.56 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.94/1.56 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.94/1.56 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.56 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.56 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.94/1.56 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.94/1.56 = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.94/1.56 Z ) = Y }.
% 0.94/1.56 { ! class_Groups_Oab__group__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.94/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.56 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.94/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.56 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 0.94/1.56 , Y ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.56 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.94/1.56 = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ouminus__class_Ouminus
% 0.94/1.56 ( X, Y ) }.
% 0.94/1.56 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.94/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Ozero__class_Ozero(
% 0.94/1.56 X ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.94/1.56 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.94/1.56 .
% 0.94/1.56 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.94/1.56 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.94/1.56 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__algebra__1( X ), ! c_RealVector_Oof__real( X, Y
% 0.94/1.56 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_RealDef_Oreal ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__algebra__1( X ), ! Y =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealVector_Oof__real(
% 0.94/1.56 X, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__algebra__1( X ), !
% 0.94/1.56 class_RealVector_Oreal__normed__vector( X ), c_RealVector_Oof__real( X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__algebra__1( X ), c_RealVector_Oof__real( X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.56 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.94/1.56 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus
% 0.94/1.56 ( X, Z ) }.
% 0.94/1.56 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 0.94/1.56 , Z ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.56 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.56 ( X ), Z ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.94/1.56 Z ) ), U ), T ) = Y }.
% 0.94/1.56 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.94/1.56 Z ) ), U ), T ) = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.56 ( X ), Z ), U ), Y ) }.
% 0.94/1.56 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.56 ( X ), Z ), U ), Y ), T = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.94/1.56 W ) ), U ), Y ) }.
% 0.94/1.56 { ! class_Rings_Oring( X ), ! T = c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.94/1.56 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.94/1.56 X, Z, W ) ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.56 ( X ), Z ), U ), Y ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.94/1.56 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.94/1.56 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.94/1.56 X, U, Z ) ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 0.94/1.56 Z ) ), Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 0.94/1.56 c_Groups_Ominus__class_Ominus( X, T, Y ) ) ) }.
% 0.94/1.56 { ! class_Rings_Oring( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.56 ( X ), U ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 0.94/1.56 Z ) ), Y ) ) }.
% 0.94/1.56 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = c_Groups_Oone__class_Oone
% 0.94/1.56 ( X ), Y = c_Groups_Oone__class_Oone( X ), Y =
% 0.94/1.56 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) }.
% 0.94/1.56 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.94/1.56 c_Groups_Oone__class_Oone( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.56 ( X ), Y ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.94/1.56 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.94/1.56 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ),
% 0.94/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) =
% 0.94/1.56 c_Groups_Oone__class_Oone( X ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__algebra__1( X ), c_RealVector_Oof__real( X,
% 0.94/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), Y ) )
% 0.94/1.56 = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), c_RealVector_Oof__real
% 0.94/1.56 ( X, Z ) ), c_RealVector_Oof__real( X, Y ) ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__algebra__1( X ), !
% 0.94/1.56 class_RealVector_Oreal__normed__vector( X ), c_RealVector_Oof__real( X,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ) ) =
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, c_RealVector_Oof__real( X, Z ),
% 0.94/1.56 c_RealVector_Oof__real( X, Y ) ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__algebra__1( X ), c_RealVector_Oof__real( X,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ) ) =
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, c_RealVector_Oof__real( X, Z ),
% 0.94/1.56 c_RealVector_Oof__real( X, Y ) ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__algebra__1( X ), c_RealVector_Oof__real( X,
% 0.94/1.56 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) =
% 0.94/1.56 c_Groups_Oone__class_Oone( X ) }.
% 0.94/1.56 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.56 , c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ouminus__class_Ouminus( X
% 0.94/1.56 , Y ) ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.94/1.56 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__algebra__1( X ), c_RealVector_Oof__real( X,
% 0.94/1.56 hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Z ), Y ) )
% 0.94/1.56 = hAPP( hAPP( c_Power_Opower__class_Opower( X ), c_RealVector_Oof__real(
% 0.94/1.56 X, Z ) ), Y ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__div__algebra( X ), !
% 0.94/1.56 class_Rings_Odivision__ring__inverse__zero( X ), c_RealVector_Oof__real(
% 0.94/1.56 X, c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, Y ) ) =
% 0.94/1.56 c_Rings_Oinverse__class_Oinverse( X, c_RealVector_Oof__real( X, Y ) ) }.
% 0.94/1.56 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ),
% 0.94/1.56 c_RealVector_Oof__real( tc_Complex_Ocomplex, Y ) ), X ) =
% 0.94/1.56 c_RealVector_Oof__real( tc_Complex_Ocomplex, hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.94/1.56 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.56 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.56 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.56 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ) }.
% 0.94/1.56 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.56 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.94/1.56 Z ) ), U ), T ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.56 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.94/1.56 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.56 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.56 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X, T,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.56 ( X ), c_Groups_Ominus__class_Ominus( X, Z, W ) ), U ), Y ) ) }.
% 0.94/1.56 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.56 , T, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.94/1.56 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.56 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.94/1.56 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.56 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.94/1.56 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.94/1.56 X, W, Z ) ), U ), T ), Y ) }.
% 0.94/1.56 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.56 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.94/1.56 hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.56 ( X ), Z ), U ), Y ) ) }.
% 0.94/1.56 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.56 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, hAPP
% 0.94/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus
% 0.94/1.56 ( X, Z, W ) ), U ), Y ) ) }.
% 0.94/1.56 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X, T
% 0.94/1.56 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.94/1.56 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless( X,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.56 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.94/1.56 { ! class_Rings_Oring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP
% 0.94/1.56 ( c_Groups_Otimes__class_Otimes( X ), Y ), Y ), c_Groups_Oone__class_Oone
% 0.94/1.56 ( X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) ) ),
% 0.94/1.56 c_Groups_Ominus__class_Ominus( X, Y, c_Groups_Oone__class_Oone( X ) ) ) }
% 0.94/1.56 .
% 0.94/1.56 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.56 , Z = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ominus__class_Ominus( X
% 0.94/1.56 , c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.94/1.56 c_Rings_Oinverse__class_Oinverse( X, Z ) ) = hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 0.94/1.56 Y ) ), c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ),
% 0.94/1.56 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.94/1.56 { ! class_Rings_Oring__1( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.94/1.56 ), c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.94/1.56 c_Groups_Oone__class_Oone( X ) ) ), Y ) ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, Z,
% 0.94/1.56 Y ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.94/1.56 ( X, Y ) ) ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__div__algebra( X ), Y =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealVector_Oof__real(
% 0.94/1.56 X, c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, Y ) ) =
% 0.94/1.56 c_Rings_Oinverse__class_Oinverse( X, c_RealVector_Oof__real( X, Y ) ) }.
% 0.94/1.56 { ! class_Groups_Ozero( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y, Y =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.56 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) = Y }.
% 0.94/1.56 { ! class_Groups_Oab__semigroup__mult( X ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.94/1.56 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, Z, T ) = c_Groups_Oplus__class_Oplus( X,
% 0.94/1.56 Y, T ), Z = Y }.
% 0.94/1.56 { ! class_Groups_Ocancel__ab__semigroup__add( X ), !
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.94/1.56 T, Y ), Z = Y }.
% 0.94/1.56 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.94/1.56 T, Y ), Z = Y }.
% 0.94/1.56 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.94/1.56 Y, Z ), T = Y }.
% 0.94/1.56 { ! class_Groups_Ocancel__semigroup__add( X ), ! T = Y,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.94/1.56 Y, Z ) }.
% 0.94/1.56 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.94/1.56 T, Y ), Z = Y }.
% 0.94/1.56 { ! class_Groups_Ocancel__semigroup__add( X ), ! Z = Y,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.94/1.56 T, Y ) }.
% 0.94/1.56 { ! class_Groups_Oab__semigroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.94/1.56 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.94/1.56 { ! class_Groups_Oone( X ), ! c_Groups_Oone__class_Oone( X ) = Y, Y =
% 0.94/1.56 c_Groups_Oone__class_Oone( X ) }.
% 0.94/1.56 { ! class_Groups_Oone( X ), ! Y = c_Groups_Oone__class_Oone( X ),
% 0.94/1.56 c_Groups_Oone__class_Oone( X ) = Y }.
% 0.94/1.56 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.94/1.56 , Y ) ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, U,
% 0.94/1.56 Z ) ), c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus
% 0.94/1.56 ( X, T, Y ) ) ) ) }.
% 0.94/1.56 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.94/1.56 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.94/1.56 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.94/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.94/1.56 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero( X ) =
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, Y, Y ) }.
% 0.94/1.56 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.94/1.56 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.94/1.56 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.94/1.56 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.94/1.56 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.94/1.56 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.94/1.56 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.94/1.56 U ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.94/1.56 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.94/1.56 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.94/1.56 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.94/1.56 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.94/1.56 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.94/1.56 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.94/1.56 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.94/1.56 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.94/1.56 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.94/1.56 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.94/1.56 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.94/1.56 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.94/1.56 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.94/1.56 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, Z, Y ) }.
% 0.94/1.56 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, T )
% 0.94/1.56 , c_Groups_Oplus__class_Oplus( X, Y, T ) ), c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, Z, Y ) }.
% 0.94/1.56 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, U, T ), c_Orderings_Oord__class_Oless( X,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X, Y
% 0.94/1.56 , T ) ) }.
% 0.94/1.56 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.94/1.56 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.94/1.56 , T, Y ) ) }.
% 0.94/1.56 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.94/1.56 X, c_Groups_Oplus__class_Oplus( X, Z, T ), c_Groups_Oplus__class_Oplus( X
% 0.94/1.56 , Y, T ) ) }.
% 0.94/1.56 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.94/1.56 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, Z, Y ) }.
% 0.94/1.56 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.94/1.56 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.94/1.56 , T, Y ) ) }.
% 0.94/1.56 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.94/1.56 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ), c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, T, Y ) }.
% 0.94/1.56 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, T, Y ), c_Orderings_Oord__class_Oless(
% 0.94/1.56 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.94/1.56 , Y, Z ) ) }.
% 0.94/1.56 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.94/1.56 = Y }.
% 0.94/1.56 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.94/1.56 = Y }.
% 0.94/1.56 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.94/1.56 = Y }.
% 0.94/1.56 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.94/1.56 = Y }.
% 0.94/1.56 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.94/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Z =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.94/1.56 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.94/1.56 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.94/1.56 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.94/1.56 .
% 0.94/1.56 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), T ), Z ),
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), X ) ) =
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus
% 0.94/1.56 ( tc_Nat_Onat, T, Y ) ), Z ), X ) }.
% 0.94/1.56 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.56 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.56 , c_Groups_Oplus__class_Oplus( X, Y, Z ), c_Groups_Ozero__class_Ozero( X
% 0.94/1.56 ) ) }.
% 0.94/1.56 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.56 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 0.94/1.56 Z, Y ) ) }.
% 0.94/1.56 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.56 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 0.94/1.56 Y, Z ) ) }.
% 0.94/1.56 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.56 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 0.94/1.56 .
% 0.94/1.56 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.56 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.94/1.56 .
% 0.94/1.56 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.56 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 X ), Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), ! Z =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.94/1.56 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.56 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.56 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.94/1.56 ) }.
% 0.94/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Y,
% 0.94/1.56 Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.56 ) }.
% 0.94/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.56 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X
% 0.94/1.56 , Y, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, Y, Y ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.56 ) }.
% 0.94/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.56 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.94/1.56 ), c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.94/1.56 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.94/1.56 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.94/1.56 , c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.94/1.56 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.56 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.94/1.56 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.94/1.56 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.94/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.94/1.56 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Y
% 0.94/1.56 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.94/1.56 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, Y, Y ) ), c_Orderings_Oord__class_Oless(
% 0.94/1.56 X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.94/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.94/1.56 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, U, T ), c_Orderings_Oord__class_Oless(
% 0.94/1.56 X, c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X
% 0.94/1.56 , Y, T ) ) }.
% 0.94/1.56 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, U )
% 0.94/1.56 , c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Nat_Onat ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.94/1.56 tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.94/1.56 tc_Nat_Onat ), X ), Y ), Z = Y }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Nat_Onat ), X ), ! Z = Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.56 ( tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.94/1.56 tc_Nat_Onat ), X ), Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 0.94/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP(
% 0.94/1.56 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 0.94/1.56 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.94/1.56 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.56 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.94/1.56 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.94/1.56 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.56 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.94/1.56 ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.94/1.56 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.94/1.56 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.56 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.56 ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.94/1.56 ) ) }.
% 0.94/1.56 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.56 , Z = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ominus__class_Ominus( X
% 0.94/1.56 , c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.94/1.56 c_Rings_Oinverse__class_Oinverse( X, Z ) ) =
% 0.94/1.56 c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 0.94/1.56 Y ) ), c_Groups_Ominus__class_Ominus( X, Y, Z ) ) ),
% 0.94/1.56 c_Rings_Oinverse__class_Oinverse( X, Z ) ) ) }.
% 0.94/1.56 { c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, Y, X ) =
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y,
% 0.94/1.56 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, X ) ) }.
% 0.94/1.56 { X = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), Y =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Orderings_Oord__class_Oless
% 0.94/1.56 ( tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex
% 0.94/1.56 , c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex,
% 0.94/1.56 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), X ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), skol7( X, Y ) ), Y )
% 0.94/1.56 ) ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.94/1.56 , Y ), X ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Nat_Onat ), Y ) }.
% 0.94/1.56 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 0.94/1.56 ), X ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.94/1.56 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ), X =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.94/1.56 { ! X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) }.
% 0.94/1.56 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), T ), Y ) ) = hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 0.94/1.56 tc_Nat_Onat, Z, Y ) ) }.
% 0.94/1.56 { c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ) =
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 0.94/1.56 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) }.
% 0.94/1.56 { c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ) =
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 0.94/1.56 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) }.
% 0.94/1.56 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.94/1.56 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, X ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.56 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = X }.
% 0.94/1.56 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Nat_Onat ), X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.94/1.56 ( tc_Nat_Onat, Z, X ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.94/1.56 ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.94/1.56 ( tc_Nat_Onat, Y, Z ), X ) }.
% 0.94/1.56 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.94/1.56 tc_Nat_Onat, Y, X ), X ) = Y }.
% 0.94/1.56 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.94/1.56 tc_Nat_Onat, Y, X ), Y ) = X }.
% 0.94/1.56 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.94/1.56 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.94/1.56 Z, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.94/1.56 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.94/1.56 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) =
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 0.94/1.56 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.94/1.56 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) =
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ) }.
% 0.94/1.56 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ), Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ),
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, Z ),
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = Y }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X = Z }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), ! X = Z,
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ),
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.94/1.56 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.94/1.56 ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 0.94/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) =
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.94/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.94/1.56 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal,
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ),
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ),
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ),
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.94/1.56 ( tc_Nat_Onat, Y, X ), Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ),
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.94/1.57 tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 0.94/1.57 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.57 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ) ), hAPP( hAPP
% 0.94/1.57 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) }.
% 0.94/1.57 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.57 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.57 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.94/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) = Y }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z,
% 0.94/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.94/1.57 tc_Nat_Onat, Z, X ), Y ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.94/1.57 ( tc_Nat_Onat, Z, X ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z
% 0.94/1.57 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ),
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.94/1.57 ( tc_Nat_Onat, Y, Z ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z )
% 0.94/1.57 ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.94/1.57 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.94/1.57 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.94/1.57 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.94/1.57 ) }.
% 0.94/1.57 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 0.94/1.57 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) =
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y = X }.
% 0.94/1.57 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 0.94/1.57 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) =
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.94/1.57 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) =
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X =
% 0.94/1.57 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) }.
% 0.94/1.57 { ! X = c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ),
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) =
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z,
% 0.94/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 0.94/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.94/1.57 tc_Nat_Onat, Z, Y ), X ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.94/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.94/1.57 tc_Nat_Onat, X, Z ), Y ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 0.94/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = X }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.94/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 0.94/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.94/1.57 tc_Nat_Onat, Z, X ), Y ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.94/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.94/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.94/1.57 tc_Nat_Onat, X, Y ), Y ) = X }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.94/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z, X =
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X =
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.94/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.94/1.57 tc_Nat_Onat, Z, X ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.94/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.94/1.57 tc_Nat_Onat, X, Y ), Z ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ), Y ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.94/1.57 tc_Nat_Onat, X, Z ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.94/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), Z ) }.
% 0.94/1.57 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.57 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.94/1.57 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X ) ),
% 0.94/1.57 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Y ) ),
% 0.94/1.57 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) }.
% 0.94/1.57 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.57 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.94/1.57 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.94/1.57 ( X, Y ) ), c_RealVector_Onorm__class_Onorm( X,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) ) }.
% 0.94/1.57 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.94/1.57 , alpha5( X, Y, Z ) }.
% 0.94/1.57 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.94/1.57 , alpha13( X, Y, Z ) }.
% 0.94/1.57 { ! alpha5( X, Y, Z ), ! alpha13( X, Y, Z ), hBOOL( hAPP( Z,
% 0.94/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.94/1.57 { ! alpha13( X, Y, Z ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.94/1.57 T ), hBOOL( hAPP( Z, T ) ) }.
% 0.94/1.57 { ! hBOOL( hAPP( Z, skol8( T, U, Z ) ) ), alpha13( X, Y, Z ) }.
% 0.94/1.57 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, skol8( X, Y, Z ) ),
% 0.94/1.57 alpha13( X, Y, Z ) }.
% 0.94/1.57 { ! alpha5( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 0.94/1.57 , hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.94/1.57 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), alpha5( X, Y, Z ) }.
% 0.94/1.57 { ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha5
% 0.94/1.57 ( X, Y, Z ) }.
% 0.94/1.57 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.94/1.57 , ! alpha6( X, Y, Z ) }.
% 0.94/1.57 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.94/1.57 , ! alpha14( X, Y, Z ) }.
% 0.94/1.57 { alpha6( X, Y, Z ), alpha14( X, Y, Z ), hBOOL( hAPP( Z,
% 0.94/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.94/1.57 { ! alpha14( X, Y, Z ), ! hBOOL( hAPP( Z, skol9( T, U, Z ) ) ) }.
% 0.94/1.57 { ! alpha14( X, Y, Z ), Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.94/1.57 skol9( X, Y, Z ) ) }.
% 0.94/1.57 { ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, T ), hBOOL( hAPP( Z, T
% 0.94/1.57 ) ), alpha14( X, Y, Z ) }.
% 0.94/1.57 { ! alpha6( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }
% 0.94/1.57 .
% 0.94/1.57 { ! alpha6( X, Y, Z ), ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero(
% 0.94/1.57 tc_Nat_Onat ) ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), hBOOL( hAPP( Z,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha6( X, Y, Z ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.94/1.57 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.94/1.57 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.57 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.57 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ),
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.57 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.57 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ),
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.94/1.57 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.94/1.57 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ),
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ) =
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ), T =
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.94/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! T =
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.94/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ),
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ) =
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.94/1.57 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 0.94/1.57 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) =
% 0.94/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, T,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.94/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ),
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.94/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.94/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ),
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ) =
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ),
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.94/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ) = Z }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.94/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ) = Z,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ) =
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.94/1.57 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 0.94/1.57 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) =
% 0.94/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.94/1.57 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.94/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.94/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.94/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Z ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), U ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), Y ) ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.94/1.57 , Y ) = c_Groups_Oplus__class_Oplus( X, Y, Z ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.94/1.57 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.94/1.57 ( X, Z, c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.94/1.57 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.94/1.57 ( X, c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.94/1.57 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.94/1.57 ( X, c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.94/1.57 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X
% 0.94/1.57 , U, Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.94/1.57 { c_RealVector_Oof__real( tc_Complex_Ocomplex,
% 0.94/1.57 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal,
% 0.94/1.57 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) =
% 0.94/1.57 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex,
% 0.94/1.57 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.94/1.57 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 0.94/1.57 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ),
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.94/1.57 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.94/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.94/1.57 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.94/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ),
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.94/1.57 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 0.94/1.57 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.94/1.57 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 0.94/1.57 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ),
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.94/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.94/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ),
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.94/1.57 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 0.94/1.57 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) }.
% 0.94/1.57 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.57 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.94/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 0.94/1.57 ( tc_Nat_Onat ) ) ), X ) ) }.
% 0.94/1.57 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.94/1.57 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) =
% 0.94/1.57 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.94/1.57 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.94/1.57 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) = hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 0.94/1.57 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ),
% 0.94/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 0.94/1.57 ( tc_Nat_Onat ) ) ) ) }.
% 0.94/1.57 { ! class_Power_Opower( X ), ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 0.94/1.57 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) =
% 0.94/1.57 c_Groups_Oone__class_Oone( X ) }.
% 0.94/1.57 { ! class_Power_Opower( X ), Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.94/1.57 , hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) = hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.94/1.57 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ominus__class_Ominus(
% 0.94/1.57 tc_Nat_Onat, Z, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 0.94/1.57 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless(
% 0.94/1.57 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), hAPP( hAPP
% 0.94/1.57 ( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.94/1.57 c_Power_Opower__class_Opower( X ), Z ), c_Groups_Ominus__class_Ominus(
% 0.94/1.57 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ), Z ) =
% 0.94/1.57 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.94/1.57 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.94/1.57 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.94/1.57 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.94/1.57 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.94/1.57 ( X ), ! Z = c_Groups_Oplus__class_Oplus( X, Z, Y ), Y =
% 0.94/1.57 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.57 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.94/1.57 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.94/1.57 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.94/1.57 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.94/1.57 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.94/1.57 ( X ), U = T, Z = Y, ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.94/1.57 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.57 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.94/1.57 ) }.
% 0.94/1.57 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.94/1.57 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.94/1.57 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.57 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.94/1.57 ), ! U = T }.
% 0.94/1.57 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.94/1.57 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.94/1.57 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.57 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.94/1.57 ), ! Z = Y }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.94/1.57 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.94/1.57 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Y
% 0.94/1.57 ) ), Z ) }.
% 0.94/1.57 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.94/1.57 ( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.94/1.57 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.57 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.94/1.57 ), U = Z, T = Y }.
% 0.94/1.57 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.94/1.57 ( X ), ! U = Z, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.94/1.57 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.57 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.94/1.57 ) }.
% 0.94/1.57 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.94/1.57 ( X ), ! T = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.94/1.57 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.57 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.94/1.57 ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.94/1.57 = Y }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.94/1.57 = Y }.
% 0.94/1.57 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.94/1.57 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus(
% 0.94/1.57 X, U, Z ), c_Groups_Ominus__class_Ominus( X, T, Y ) ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.94/1.57 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.94/1.57 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.94/1.57 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.94/1.57 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.94/1.57 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.94/1.57 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.94/1.57 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.94/1.57 tc_Nat_Onat ) ) = Y }.
% 0.94/1.57 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.94/1.57 ( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! W = U, T = Z, !
% 0.94/1.57 c_Groups_Oplus__class_Oplus( X, W, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) =
% 0.94/1.57 c_Groups_Oplus__class_Oplus( X, U, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.94/1.57 , Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.94/1.57 c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.94/1.57 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.94/1.57 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP
% 0.94/1.57 ( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.94/1.57 c_Groups_Oone__class_Oone( X ) ) ), Z ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.94/1.57 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = hAPP(
% 0.94/1.57 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X
% 0.94/1.57 , Z, c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ouminus__class_Ouminus( X, Y
% 0.94/1.57 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.94/1.57 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) ), Y
% 0.94/1.57 ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.94/1.57 ) = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus(
% 0.94/1.57 X, Y ) ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.94/1.57 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ozero__class_Ozero(
% 0.94/1.57 tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, Y ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y,
% 0.94/1.57 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs
% 0.94/1.57 ( tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.94/1.57 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), Y ) ), X ),
% 0.94/1.57 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.94/1.57 { c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex,
% 0.94/1.57 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP( hAPP(
% 0.94/1.57 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.94/1.57 c_RealVector_Oof__real( tc_Complex_Ocomplex, v_t____ ) ), v_w____ ) ),
% 0.94/1.57 v_k____ ) ), c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, v_a____,
% 0.94/1.57 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP(
% 0.94/1.57 hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.94/1.57 c_RealVector_Oof__real( tc_Complex_Ocomplex, v_t____ ) ), v_w____ ) ),
% 0.94/1.57 hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_s____ ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.94/1.57 c_RealVector_Oof__real( tc_Complex_Ocomplex, v_t____ ) ), v_w____ ) ) ) )
% 0.94/1.57 ) ) ) = c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, c_RealVector_Oof__real
% 0.94/1.57 ( tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.94/1.57 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.94/1.57 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), v_t____ ), v_k____ ) )
% 0.94/1.57 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.94/1.57 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP(
% 0.94/1.57 hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.94/1.57 c_RealVector_Oof__real( tc_Complex_Ocomplex, v_t____ ) ), v_w____ ) ),
% 0.94/1.57 v_k____ ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.94/1.57 tc_Complex_Ocomplex ), c_RealVector_Oof__real( tc_Complex_Ocomplex,
% 0.94/1.57 v_t____ ) ), v_w____ ) ) ), hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex
% 0.94/1.57 , v_s____ ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.94/1.57 tc_Complex_Ocomplex ), c_RealVector_Oof__real( tc_Complex_Ocomplex,
% 0.94/1.57 v_t____ ) ), v_w____ ) ) ) ) ) }.
% 0.94/1.57 { c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex,
% 0.94/1.57 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP( hAPP(
% 0.94/1.57 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.94/1.57 c_RealVector_Oof__real( tc_Complex_Ocomplex, v_t____ ) ), v_w____ ) ),
% 0.94/1.57 v_k____ ) ), c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, v_a____,
% 0.94/1.57 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP(
% 0.94/1.57 hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.94/1.57 c_RealVector_Oof__real( tc_Complex_Ocomplex, v_t____ ) ), v_w____ ) ),
% 0.94/1.57 hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_s____ ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.94/1.57 c_RealVector_Oof__real( tc_Complex_Ocomplex, v_t____ ) ), v_w____ ) ) ) )
% 0.94/1.57 ) ) = c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex,
% 0.94/1.57 c_RealVector_Oof__real( tc_Complex_Ocomplex,
% 0.94/1.57 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.94/1.57 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.94/1.57 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), v_t____ ), v_k____ ) )
% 0.94/1.57 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.94/1.57 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP(
% 0.94/1.57 hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.94/1.57 c_RealVector_Oof__real( tc_Complex_Ocomplex, v_t____ ) ), v_w____ ) ),
% 0.94/1.57 v_k____ ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.94/1.57 tc_Complex_Ocomplex ), c_RealVector_Oof__real( tc_Complex_Ocomplex,
% 0.94/1.57 v_t____ ) ), v_w____ ) ) ), hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex
% 0.94/1.57 , v_s____ ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.94/1.57 tc_Complex_Ocomplex ), c_RealVector_Oof__real( tc_Complex_Ocomplex,
% 0.94/1.57 v_t____ ) ), v_w____ ) ) ) ) }.
% 0.94/1.57 { c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex,
% 0.94/1.57 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP( hAPP(
% 0.94/1.57 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ),
% 0.94/1.57 c_RealVector_Oof__real( tc_Complex_Ocomplex, v_t____ ) ), v_k____ ) ),
% 0.94/1.57 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP(
% 0.94/1.57 hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), v_w____ ),
% 0.94/1.57 v_k____ ) ), v_a____ ) ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.94/1.57 tc_Complex_Ocomplex ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.94/1.57 tc_Complex_Ocomplex ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.94/1.57 tc_Complex_Ocomplex ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.94/1.57 tc_Complex_Ocomplex ), c_RealVector_Oof__real( tc_Complex_Ocomplex,
% 0.94/1.57 v_t____ ) ), v_w____ ) ), v_k____ ) ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.94/1.57 c_RealVector_Oof__real( tc_Complex_Ocomplex, v_t____ ) ), v_w____ ) ) ),
% 0.94/1.57 hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_s____ ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.94/1.57 c_RealVector_Oof__real( tc_Complex_Ocomplex, v_t____ ) ), v_w____ ) ) ) )
% 0.94/1.57 = c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex,
% 0.94/1.57 c_RealVector_Oof__real( tc_Complex_Ocomplex,
% 0.94/1.57 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.94/1.57 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.94/1.57 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), v_t____ ), v_k____ ) )
% 0.94/1.57 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.94/1.57 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP(
% 0.94/1.57 hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.94/1.57 c_RealVector_Oof__real( tc_Complex_Ocomplex, v_t____ ) ), v_w____ ) ),
% 0.94/1.57 v_k____ ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.94/1.57 tc_Complex_Ocomplex ), c_RealVector_Oof__real( tc_Complex_Ocomplex,
% 0.94/1.57 v_t____ ) ), v_w____ ) ) ), hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex
% 0.94/1.57 , v_s____ ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.94/1.57 tc_Complex_Ocomplex ), c_RealVector_Oof__real( tc_Complex_Ocomplex,
% 0.94/1.57 v_t____ ) ), v_w____ ) ) ) ) }.
% 0.94/1.57 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(
% 0.94/1.57 tc_Complex_Ocomplex, tc_Complex_Ocomplex, c_Polynomial_Opoly(
% 0.94/1.57 tc_Complex_Ocomplex, v_p ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.57 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ),
% 0.94/1.57 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, v_w____ ) ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.57 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.94/1.57 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_s____ ), X ) ), v_m____ ) }.
% 0.94/1.57 { c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex,
% 0.94/1.57 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP( hAPP(
% 0.94/1.57 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.94/1.57 c_RealVector_Oof__real( tc_Complex_Ocomplex, v_t____ ) ), v_w____ ) ),
% 0.94/1.57 v_k____ ) ), c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, v_a____,
% 0.94/1.57 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP(
% 0.94/1.57 hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.94/1.57 c_RealVector_Oof__real( tc_Complex_Ocomplex, v_t____ ) ), v_w____ ) ),
% 0.94/1.57 hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_s____ ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.94/1.57 c_RealVector_Oof__real( tc_Complex_Ocomplex, v_t____ ) ), v_w____ ) ) ) )
% 0.94/1.57 ) ) = c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex,
% 0.94/1.57 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP( hAPP(
% 0.94/1.57 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ),
% 0.94/1.57 c_RealVector_Oof__real( tc_Complex_Ocomplex, v_t____ ) ), v_k____ ) ),
% 0.94/1.57 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP(
% 0.94/1.57 hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), v_w____ ),
% 0.94/1.57 v_k____ ) ), v_a____ ) ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.94/1.57 tc_Complex_Ocomplex ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.94/1.57 tc_Complex_Ocomplex ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.94/1.57 tc_Complex_Ocomplex ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.94/1.57 tc_Complex_Ocomplex ), c_RealVector_Oof__real( tc_Complex_Ocomplex,
% 0.94/1.57 v_t____ ) ), v_w____ ) ), v_k____ ) ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.94/1.57 c_RealVector_Oof__real( tc_Complex_Ocomplex, v_t____ ) ), v_w____ ) ) ),
% 0.94/1.57 hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_s____ ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.94/1.57 c_RealVector_Oof__real( tc_Complex_Ocomplex, v_t____ ) ), v_w____ ) ) ) )
% 0.94/1.57 }.
% 0.94/1.57 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.57 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, c_RealVector_Oof__real
% 0.94/1.57 ( tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.94/1.57 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.94/1.57 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), v_t____ ), v_k____ ) )
% 0.94/1.57 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.94/1.57 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP(
% 0.94/1.57 hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.94/1.57 c_RealVector_Oof__real( tc_Complex_Ocomplex, v_t____ ) ), v_w____ ) ),
% 0.94/1.57 v_k____ ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.94/1.57 tc_Complex_Ocomplex ), c_RealVector_Oof__real( tc_Complex_Ocomplex,
% 0.94/1.57 v_t____ ) ), v_w____ ) ) ), hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex
% 0.94/1.57 , v_s____ ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.94/1.57 tc_Complex_Ocomplex ), c_RealVector_Oof__real( tc_Complex_Ocomplex,
% 0.94/1.57 v_t____ ) ), v_w____ ) ) ) ) ), c_Groups_Oplus__class_Oplus(
% 0.94/1.57 tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.94/1.57 c_RealVector_Oof__real( tc_Complex_Ocomplex,
% 0.94/1.57 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.94/1.57 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.94/1.57 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), v_t____ ), v_k____ ) )
% 0.94/1.57 ) ), c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP( hAPP(
% 0.94/1.57 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.94/1.57 c_RealVector_Oof__real( tc_Complex_Ocomplex, v_t____ ) ), v_w____ ) ),
% 0.94/1.57 v_k____ ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.94/1.57 tc_Complex_Ocomplex ), c_RealVector_Oof__real( tc_Complex_Ocomplex,
% 0.94/1.57 v_t____ ) ), v_w____ ) ) ), hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex
% 0.94/1.57 , v_s____ ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.94/1.57 tc_Complex_Ocomplex ), c_RealVector_Oof__real( tc_Complex_Ocomplex,
% 0.94/1.57 v_t____ ) ), v_w____ ) ) ) ) ) ) }.
% 0.94/1.57 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.57 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex,
% 0.94/1.57 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP( hAPP(
% 0.94/1.57 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.94/1.57 c_RealVector_Oof__real( tc_Complex_Ocomplex, v_t____ ) ), v_w____ ) ),
% 0.94/1.57 v_k____ ) ), c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, v_a____,
% 0.94/1.57 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP(
% 0.94/1.57 hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.94/1.57 c_RealVector_Oof__real( tc_Complex_Ocomplex, v_t____ ) ), v_w____ ) ),
% 0.94/1.57 hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_s____ ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.94/1.57 c_RealVector_Oof__real( tc_Complex_Ocomplex, v_t____ ) ), v_w____ ) ) ) )
% 0.94/1.57 ) ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.94/1.57 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 0.94/1.57 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.94/1.57 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.94/1.57 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), v_t____ ), v_k____ ) )
% 0.94/1.57 ), c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP( hAPP(
% 0.94/1.57 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.94/1.57 c_RealVector_Oof__real( tc_Complex_Ocomplex, v_t____ ) ), v_w____ ) ),
% 0.94/1.57 v_k____ ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.94/1.57 tc_Complex_Ocomplex ), c_RealVector_Oof__real( tc_Complex_Ocomplex,
% 0.94/1.57 v_t____ ) ), v_w____ ) ) ), hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex
% 0.94/1.57 , v_s____ ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.94/1.57 tc_Complex_Ocomplex ), c_RealVector_Oof__real( tc_Complex_Ocomplex,
% 0.94/1.57 v_t____ ) ), v_w____ ) ) ) ) ) ) }.
% 0.94/1.57 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.94/1.57 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.94/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ), Y ) }.
% 0.94/1.57 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.94/1.57 c_Groups_Oabs__class_Oabs( X, Y ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.94/1.57 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.57 { ! class_Groups_Oordered__ab__group__add__abs( X ), ! Y =
% 0.94/1.57 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oabs__class_Oabs( X, Y ) =
% 0.94/1.57 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.57 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.94/1.57 c_Groups_Oabs__class_Oabs( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.94/1.57 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.57 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oabs__class_Oabs( X, Y
% 0.94/1.57 ) ) }.
% 0.94/1.57 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.94/1.57 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.94/1.57 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X, hAPP
% 0.94/1.57 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 0.94/1.57 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.94/1.57 { ! class_Rings_Olinordered__idom( X ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Y ) ),
% 0.94/1.57 c_Groups_Oabs__class_Oabs( X, Y ) ) = hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.94/1.57 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.94/1.57 c_Groups_Oabs__class_Oabs( X, c_Groups_Oplus__class_Oplus( X,
% 0.94/1.57 c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ) )
% 0.94/1.57 = c_Groups_Oplus__class_Oplus( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.94/1.57 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.94/1.57 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X,
% 0.94/1.57 c_Groups_Oone__class_Oone( X ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.94/1.57 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.94/1.57 c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Z, Y ) )
% 0.94/1.57 = c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Y, Z )
% 0.94/1.57 ) }.
% 0.94/1.57 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.94/1.57 c_Groups_Oabs__class_Oabs( X, c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 0.94/1.57 c_Groups_Oabs__class_Oabs( X, Y ) }.
% 0.94/1.57 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X, hAPP
% 0.94/1.57 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.94/1.57 c_Power_Opower__class_Opower( X ), c_Groups_Oabs__class_Oabs( X, Z ) ), Y
% 0.94/1.57 ) }.
% 0.94/1.57 { ! class_Fields_Olinordered__field__inverse__zero( X ),
% 0.94/1.57 c_Groups_Oabs__class_Oabs( X, c_Rings_Oinverse__class_Oinverse( X, Y ) )
% 0.94/1.57 = c_Rings_Oinverse__class_Oinverse( X, c_Groups_Oabs__class_Oabs( X, Y )
% 0.94/1.57 ) }.
% 0.94/1.57 { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Oabs__class_Oabs
% 0.94/1.57 ( tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( X, Y ) ) =
% 0.94/1.57 c_RealVector_Onorm__class_Onorm( X, Y ) }.
% 0.94/1.57 { c_RealVector_Onorm__class_Onorm( tc_RealDef_Oreal, X ) =
% 0.94/1.57 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) }.
% 0.94/1.57 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.94/1.57 c_Groups_Oabs__class_Oabs( X, c_Groups_Oabs__class_Oabs( X, Y ) ) =
% 0.94/1.57 c_Groups_Oabs__class_Oabs( X, Y ) }.
% 0.94/1.57 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.57 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.94/1.57 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Y ),
% 0.94/1.57 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.57 }.
% 0.94/1.57 { ! class_Groups_Oordered__ab__group__add__abs( X ), ! Y =
% 0.94/1.57 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.57 c_Groups_Oabs__class_Oabs( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.57 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.57 ), c_Groups_Oabs__class_Oabs( X, Y ) = Y }.
% 0.94/1.57 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.94/1.57 c_Groups_Oabs__class_Oabs( X, Y ) = Y }.
% 0.94/1.57 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.57 c_Groups_Oabs__class_Oabs( X, Y ) ), ! Y = c_Groups_Ozero__class_Ozero( X
% 0.94/1.57 ) }.
% 0.94/1.57 { ! class_Groups_Oordered__ab__group__add__abs( X ), Y =
% 0.94/1.57 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.94/1.57 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Oabs__class_Oabs( X, Y ),
% 0.94/1.57 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.94/1.57 , c_Groups_Oabs__class_Oabs( X, Z ), Y ), ! c_Orderings_Oord__class_Oless
% 0.94/1.57 ( X, c_Groups_Oabs__class_Oabs( X, U ), T ),
% 0.94/1.57 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 0.94/1.57 c_Groups_Oabs__class_Oabs( X, U ) ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.94/1.57 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( X, Z, Y ) ), c_Groups_Oplus__class_Oplus( X
% 0.94/1.57 , c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) )
% 0.94/1.57 ) }.
% 0.94/1.57 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 0.94/1.57 c_Groups_Ominus__class_Ominus( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.94/1.57 c_Groups_Oabs__class_Oabs( X, Y ) ) ), c_Groups_Oabs__class_Oabs( X,
% 0.94/1.57 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ) }.
% 0.94/1.57 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X,
% 0.94/1.57 c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ),
% 0.94/1.57 c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Z, Y ) )
% 0.94/1.57 ) }.
% 0.94/1.57 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X,
% 0.94/1.57 c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ),
% 0.94/1.57 c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Y, Z ) )
% 0.94/1.57 ) }.
% 0.94/1.57 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.94/1.57 , Y ), c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.94/1.57 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.94/1.57 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.94/1.57 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.94/1.57 Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.57 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.94/1.57 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.94/1.57 , Z ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.57 c_Groups_Oabs__class_Oabs( X, Z ), Y ) }.
% 0.94/1.57 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.94/1.57 , Z ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.57 c_Groups_Oabs__class_Oabs( X, Z ), Y ) }.
% 0.94/1.57 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.94/1.57 Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.57 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.94/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.94/1.57 , c_Groups_Oabs__class_Oabs( X, Z ), Y ), c_Orderings_Oord__class_Oless(
% 0.94/1.57 X, Z, Y ) }.
% 0.94/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.94/1.57 , c_Groups_Oabs__class_Oabs( X, Z ), Y ), c_Orderings_Oord__class_Oless(
% 0.94/1.57 X, c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.94/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.94/1.57 , Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.94/1.57 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ),
% 0.94/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Oabs__class_Oabs( X, Z ), Y )
% 0.94/1.57 }.
% 0.94/1.57 { ! class_Fields_Olinordered__field( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.94/1.57 X ), c_Groups_Oabs__class_Oabs( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 0.94/1.57 ) ) = c_Rings_Oinverse__class_Oinverse( X, c_Groups_Oabs__class_Oabs( X
% 0.94/1.57 , Y ) ) }.
% 0.94/1.57 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X, hAPP
% 0.94/1.57 ( hAPP( c_Power_Opower__class_Opower( X ),
% 0.94/1.57 c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) ) =
% 0.94/1.57 c_Groups_Oabs__class_Oabs( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.94/1.57 ), Z ), Y ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.57 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ), X ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.57 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ), Y ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.57 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ), X ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.57 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ), Y ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.57 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ), X ) }.
% 0.94/1.57 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 0.94/1.57 c_RealVector_Onorm__class_Onorm( X, c_RealVector_Oof__real( X, Y ) ) =
% 0.94/1.57 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ) }.
% 0.94/1.57 { c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus
% 0.94/1.57 ( tc_RealDef_Oreal, Y, c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal
% 0.94/1.57 , X ) ) ) = c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 0.94/1.57 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ) ) }.
% 0.94/1.57 { ! class_Rings_Oordered__ring__abs( X ), alpha17( X, Z ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.57 ), c_Groups_Oabs__class_Oabs( X, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 0.94/1.57 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.94/1.57 { ! class_Rings_Oordered__ring__abs( X ), alpha17( X, Z ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.57 ), c_Groups_Oabs__class_Oabs( X, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 0.94/1.57 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.94/1.57 { ! alpha17( X, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.94/1.57 { ! alpha17( X, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.57 { c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.57 ), c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero
% 0.94/1.57 ( X ) ), alpha17( X, Y ) }.
% 0.94/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.94/1.57 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 0.94/1.57 Y ) = c_Groups_Oabs__class_Oabs( X, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.94/1.57 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.57 ), c_Groups_Oabs__class_Oabs( X, Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.94/1.57 X, Y ) }.
% 0.94/1.57 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.94/1.57 , c_Groups_Oabs__class_Oabs( X, Y ) ), c_Groups_Ozero__class_Ozero( X ) )
% 0.94/1.57 }.
% 0.94/1.57 { ! class_Rings_Olinordered__idom( X ), c_Orderings_Oord__class_Oless__eq(
% 0.94/1.57 X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.94/1.57 c_Power_Opower__class_Opower( X ), c_Groups_Oabs__class_Oabs( X, Z ) ), Y
% 0.94/1.57 ) ) }.
% 0.94/1.57 { ! class_Groups_Oabs__if( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Oabs__class_Oabs( X, Y ) =
% 0.94/1.57 c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.94/1.57 { ! class_Groups_Oabs__if( X ), c_Orderings_Oord__class_Oless( X, Y,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Oabs__class_Oabs( X, Y ) = Y
% 0.94/1.57 }.
% 0.94/1.57 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.94/1.57 c_Groups_Oabs__class_Oabs( X, Y ) = c_Groups_Ouminus__class_Ouminus( X, Y
% 0.94/1.57 ) }.
% 0.94/1.57 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 0.94/1.57 c_Groups_Ominus__class_Ominus( X, c_Groups_Oplus__class_Oplus( X, U, T )
% 0.94/1.57 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) ), c_Groups_Oplus__class_Oplus
% 0.94/1.57 ( X, c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, U, Z
% 0.94/1.57 ) ), c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, T,
% 0.94/1.57 Y ) ) ) ) }.
% 0.94/1.57 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 0.94/1.57 c_Groups_Ominus__class_Ominus( X, Z, Y ) ), c_Groups_Oplus__class_Oplus(
% 0.94/1.57 X, c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) )
% 0.94/1.57 ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.57 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ),
% 0.94/1.57 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Z ) ) ), Y =
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.94/1.57 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) =
% 0.94/1.57 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) }.
% 0.94/1.57 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.94/1.57 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) = X }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.94/1.57 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) =
% 0.94/1.57 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) }.
% 0.94/1.57 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.94/1.57 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) = X }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs
% 0.94/1.57 ( tc_RealDef_Oreal, X ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 0.94/1.57 , X ) }.
% 0.94/1.57 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.57 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus
% 0.94/1.57 ( tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, T, Z )
% 0.94/1.57 , c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.94/1.57 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ),
% 0.94/1.57 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) ) ),
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs
% 0.94/1.57 ( tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, T,
% 0.94/1.57 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ) ),
% 0.94/1.57 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus
% 0.94/1.57 ( tc_RealDef_Oreal, Z, c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal
% 0.94/1.57 , X ) ) ) ) ) }.
% 0.94/1.57 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.57 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 0.94/1.57 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.94/1.57 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.94/1.57 ( X, Y ) ) ), c_RealVector_Onorm__class_Onorm( X,
% 0.94/1.57 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ) }.
% 0.94/1.57 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oone__class_Oone
% 0.94/1.57 ( tc_RealDef_Oreal ), c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) )
% 0.94/1.57 ) }.
% 0.94/1.57 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol10 ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.57 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ),
% 0.94/1.57 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, v_w____ ) ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.57 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.94/1.57 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_s____ ), X ) ), skol10 ) }.
% 0.94/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.94/1.57 , c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, T, Z )
% 0.94/1.57 ), Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus
% 0.94/1.57 ( X, Z, Y ), T ) }.
% 0.94/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.94/1.57 , c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, T, Z )
% 0.94/1.57 ), Y ), c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus
% 0.94/1.57 ( X, Z, Y ) ) }.
% 0.94/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.94/1.57 , c_Groups_Ominus__class_Ominus( X, Z, Y ), T ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.94/1.57 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oabs__class_Oabs( X,
% 0.94/1.57 c_Groups_Ominus__class_Ominus( X, T, Z ) ), Y ) }.
% 0.94/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.94/1.57 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.94/1.57 ) ), c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 0.94/1.57 ) ) }.
% 0.94/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.94/1.57 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.94/1.57 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.94/1.57 ) ) }.
% 0.94/1.57 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(
% 0.94/1.57 tc_Complex_Ocomplex, tc_Complex_Ocomplex, c_Polynomial_Opoly(
% 0.94/1.57 tc_Complex_Ocomplex, v_pa____ ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.57 ( tc_Int_Oint ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint )
% 0.94/1.57 , c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) ), X ) ), ! Y =
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X =
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.57 { Y = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.94/1.57 tc_Int_Oint ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ),
% 0.94/1.57 c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) ), X ) ) }.
% 0.94/1.57 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.94/1.57 tc_Int_Oint ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ),
% 0.94/1.57 c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) ), X ) ) }.
% 0.94/1.57 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( Z, Y, X ), hAPP(
% 0.94/1.57 X, T ) = hAPP( X, U ) }.
% 0.94/1.57 { ! hAPP( X, skol11( X ) ) = hAPP( X, skol33( X ) ),
% 0.94/1.57 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( Z, Y, X ) }.
% 0.94/1.57 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ),
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) = hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.94/1.57 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 0.94/1.57 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ) }.
% 0.94/1.57 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), hAPP( hAPP(
% 0.94/1.57 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 0.94/1.57 ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.94/1.57 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.94/1.57 c_Groups_Oplus__class_Oplus( X, Y, Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.57 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.57 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.94/1.57 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.94/1.57 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.57 { ! class_RealVector_Oreal__algebra__1( X ), !
% 0.94/1.57 class_RealVector_Oreal__normed__vector( X ),
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol12( Y ) ) }.
% 0.94/1.57 { ! class_RealVector_Oreal__algebra__1( X ), !
% 0.94/1.57 class_RealVector_Oreal__normed__vector( X ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.57 c_RealVector_Onorm__class_Onorm( X, c_RealVector_Oof__real( X, Y ) ),
% 0.94/1.57 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.94/1.57 c_RealVector_Onorm__class_Onorm( tc_RealDef_Oreal, Y ) ), skol12( X ) ) )
% 0.94/1.57 }.
% 0.94/1.57 { ! c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) =
% 0.94/1.57 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ),
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.57 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, X,
% 0.94/1.57 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) ),
% 0.94/1.57 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.57 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.94/1.57 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, X,
% 0.94/1.57 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) ),
% 0.94/1.57 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.57 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, X, c_Complex_Oii ) ),
% 0.94/1.57 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.57 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.94/1.57 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, X, c_Complex_Oii ) )
% 0.94/1.57 , c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.94/1.57 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol13 ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.57 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ),
% 0.94/1.57 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, v_w____ ) ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.57 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.94/1.57 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_s____ ), X ) ), skol13 ) }.
% 0.94/1.57 { ! hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), v_c____ ) =
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.94/1.57 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.57 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.94/1.57 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), v_c____ ) ),
% 0.94/1.57 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.94/1.57 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), X ) ) ) }.
% 0.94/1.57 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex
% 0.94/1.57 , v_pa____ ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, v_k____,
% 0.94/1.57 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Groups_Oabs__class_Oabs(
% 0.94/1.57 tc_Int_Oint, X ) = c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) }.
% 0.94/1.57 { c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Groups_Oabs__class_Oabs(
% 0.94/1.57 tc_Int_Oint, X ) = X }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ominus__class_Ominus
% 0.94/1.57 ( tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.94/1.57 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ),
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.94/1.57 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 0.94/1.57 ( tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 0.94/1.57 .
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.94/1.57 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 0.94/1.57 ( tc_Int_Oint ) ) ) }.
% 0.94/1.57 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.94/1.57 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) ) =
% 0.94/1.57 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.94/1.57 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.94/1.57 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ), X ) =
% 0.94/1.57 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.94/1.57 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 0.94/1.57 c_Power_Opower__class_Opower( tc_Int_Oint ), c_Groups_Oabs__class_Oabs(
% 0.94/1.57 tc_Int_Oint, Y ) ), X ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oabs__class_Oabs(
% 0.94/1.57 tc_Int_Oint, X ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X =
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.94/1.57 { ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oabs__class_Oabs(
% 0.94/1.57 tc_Int_Oint, X ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.94/1.57 { ! c_Groups_Oabs__class_Oabs( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) =
% 0.94/1.57 c_Groups_Oone__class_Oone( tc_Int_Oint ), c_Groups_Oabs__class_Oabs(
% 0.94/1.57 tc_Int_Oint, X ) = c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.94/1.57 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y = X,
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Z ),
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.94/1.57 tc_Int_Oint, Y, T ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 0.94/1.57 .
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.94/1.57 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 0.94/1.57 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP
% 0.94/1.57 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.94/1.57 tc_Int_Oint, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 0.94/1.57 .
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.94/1.57 tc_Int_Oint ) ), X ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.57 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.94/1.57 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), X =
% 0.94/1.57 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.57 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.94/1.57 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), Y =
% 0.94/1.57 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.57 ( tc_Int_Oint ), X ), ! X = c_Groups_Oone__class_Oone( tc_Int_Oint ), ! Y
% 0.94/1.57 = c_Groups_Oone__class_Oone( tc_Int_Oint ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 0.94/1.57 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.94/1.57 tc_Int_Oint ), c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.94/1.57 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.94/1.57 ( tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.94/1.57 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.94/1.57 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.94/1.57 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.94/1.57 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ) ), X ) =
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.94/1.57 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP(
% 0.94/1.57 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.94/1.57 tc_Int_Oint ) ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X )
% 0.94/1.57 }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.94/1.57 tc_Int_Oint ) ), X ) }.
% 0.94/1.57 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) =
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.94/1.57 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y
% 0.94/1.57 = X }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.94/1.57 tc_Int_Oint ) ) ) }.
% 0.94/1.57 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.94/1.57 tc_Int_Oint ) ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.94/1.57 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X )
% 0.94/1.57 }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.94/1.57 tc_Int_Oint ) ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), ! Y = X }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), Y = X,
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.94/1.57 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) = hAPP
% 0.94/1.57 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) }.
% 0.94/1.57 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 0.94/1.57 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) = X }.
% 0.94/1.57 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero
% 0.94/1.57 ( tc_Int_Oint ) ) = X }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.57 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ),
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.94/1.57 tc_Int_Oint ), X ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.57 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.57 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) }.
% 0.94/1.57 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.94/1.57 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) = X }.
% 0.94/1.57 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.94/1.57 tc_Int_Oint ), X ) = X }.
% 0.94/1.57 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.94/1.57 tc_Int_Oint ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.94/1.57 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.94/1.57 tc_Int_Oint, c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ) =
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.94/1.57 { ! c_Groups_Ozero__class_Ozero( tc_Int_Oint ) = c_Groups_Oone__class_Oone
% 0.94/1.57 ( tc_Int_Oint ) }.
% 0.94/1.57 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.94/1.57 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ), X ) =
% 0.94/1.57 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.94/1.57 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.94/1.57 ( tc_Int_Oint, X ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.94/1.57 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.57 ( tc_Int_Oint ) ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.94/1.57 { ! c_Complex_Oii = c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) }.
% 0.94/1.57 { ! c_Complex_Oii = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.94/1.57 { c_Rings_Oinverse__class_Oinverse( tc_Complex_Ocomplex, c_Complex_Oii ) =
% 0.94/1.57 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, c_Complex_Oii ) }.
% 0.94/1.57 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.94/1.57 c_Complex_Oii ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.94/1.57 tc_Complex_Ocomplex ), c_Complex_Oii ), X ) ) =
% 0.94/1.57 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, X ) }.
% 0.94/1.57 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.94/1.57 c_Complex_Oii ), c_Complex_Oii ) = c_Groups_Ouminus__class_Ouminus(
% 0.94/1.57 tc_Complex_Ocomplex, c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) }
% 0.94/1.57 .
% 0.94/1.57 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.94/1.57 tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ),
% 0.94/1.57 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex,
% 0.94/1.57 v_pa____ ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.57 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Z,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), c_Groups_Oplus__class_Oplus
% 0.94/1.57 ( tc_Int_Oint, c_Groups_Oabs__class_Oabs( tc_Int_Oint,
% 0.94/1.57 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, Z ) ),
% 0.94/1.57 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ), X ) ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.57 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.94/1.57 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), c_Groups_Oplus__class_Oplus
% 0.94/1.57 ( tc_Int_Oint, c_Groups_Oabs__class_Oabs( tc_Int_Oint,
% 0.94/1.57 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ),
% 0.94/1.57 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ), X ) ), Y ) }.
% 0.94/1.57 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.94/1.57 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.94/1.57 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ),
% 0.94/1.57 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.94/1.57 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint,
% 0.94/1.57 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) = X }.
% 0.94/1.57 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, X ) }.
% 0.94/1.57 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) =
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ) }.
% 0.94/1.57 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ) }.
% 0.94/1.57 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus
% 0.94/1.57 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 0.94/1.57 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.94/1.57 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ),
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Z ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, Z ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ), Y = X }.
% 0.94/1.57 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.94/1.57 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.94/1.57 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) }.
% 0.94/1.57 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) =
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.94/1.57 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.94/1.57 { ! class_Groups_Ozero( X ), !
% 0.94/1.57 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.57 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.94/1.57 tc_Polynomial_Opoly( X ) ),
% 0.94/1.57 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.57 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ), X ) = hAPP(
% 0.94/1.57 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ),
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, v_c____, X ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.94/1.57 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex, X
% 0.94/1.57 ), c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(
% 0.94/1.57 tc_Complex_Ocomplex, v_pa____ ) ),
% 0.94/1.57 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( tc_Complex_Ocomplex
% 0.94/1.57 , tc_Complex_Ocomplex, c_Polynomial_Opoly( tc_Complex_Ocomplex, X ) ),
% 0.94/1.57 hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, X ), skol14( X ) ) =
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.94/1.57 { c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex,
% 0.94/1.57 skol15 ) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(
% 0.94/1.57 tc_Complex_Ocomplex, v_pa____ ) }.
% 0.94/1.57 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, skol15 ), X ) = hAPP(
% 0.94/1.57 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ),
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, v_c____, X ) ) }.
% 0.94/1.57 { c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex,
% 0.94/1.57 v_q____ ) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(
% 0.94/1.57 tc_Complex_Ocomplex, v_pa____ ) }.
% 0.94/1.57 { ! hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) =
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.94/1.57 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(
% 0.94/1.57 tc_Complex_Ocomplex, tc_Complex_Ocomplex, c_Polynomial_Opoly(
% 0.94/1.57 tc_Complex_Ocomplex, v_q____ ) ) }.
% 0.94/1.57 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(
% 0.94/1.57 tc_Complex_Ocomplex, tc_Complex_Ocomplex, c_Polynomial_Opoly(
% 0.94/1.57 tc_Complex_Ocomplex, v_q____ ) ) }.
% 0.94/1.57 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.57 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.94/1.57 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 0.94/1.57 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.94/1.57 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), X ) ) ) }.
% 0.94/1.57 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), v_c____ ) =
% 0.94/1.57 hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) }.
% 0.94/1.57 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.94/1.57 tc_Nat_Onat, c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(
% 0.94/1.57 tc_Complex_Ocomplex, v_s____ ), v_k____ ), c_Groups_Oone__class_Oone(
% 0.94/1.57 tc_Nat_Onat ) ) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(
% 0.94/1.57 tc_Complex_Ocomplex, c_Polynomial_Osmult( tc_Complex_Ocomplex,
% 0.94/1.57 c_Rings_Oinverse__class_Oinverse( tc_Complex_Ocomplex, hAPP(
% 0.94/1.57 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ), v_q____ ) ) }.
% 0.94/1.57 { ! hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), v_c____ ) =
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), hAPP(
% 0.94/1.57 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), skol16 ) =
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.57 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.94/1.57 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.94/1.57 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.57 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.94/1.57 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oone__class_Oone
% 0.94/1.57 ( tc_Int_Oint ), Y ) }.
% 0.94/1.57 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) = hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP(
% 0.94/1.57 c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 0.94/1.57 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 0.94/1.57 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 0.94/1.57 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 0.94/1.57 v_q____ ) ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ), hAPP
% 0.94/1.57 ( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ) }.
% 0.94/1.57 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ), X ) = hAPP(
% 0.94/1.57 hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP(
% 0.94/1.57 c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 0.94/1.57 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 0.94/1.57 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 0.94/1.57 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 0.94/1.57 v_q____ ) ), X ) ), hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 0.94/1.57 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ) }.
% 0.94/1.57 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 0.94/1.57 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 0.94/1.57 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 0.94/1.57 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 0.94/1.57 v_q____ ) ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) =
% 0.94/1.57 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) }.
% 0.94/1.57 { c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex,
% 0.94/1.57 v_q____ ) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(
% 0.94/1.57 tc_Complex_Ocomplex, c_Polynomial_Osmult( tc_Complex_Ocomplex,
% 0.94/1.57 c_Rings_Oinverse__class_Oinverse( tc_Complex_Ocomplex, hAPP(
% 0.94/1.57 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ), v_q____ ) ) }.
% 0.94/1.57 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(
% 0.94/1.57 tc_Complex_Ocomplex, tc_Complex_Ocomplex, c_Polynomial_Opoly(
% 0.94/1.57 tc_Complex_Ocomplex, c_Polynomial_Osmult( tc_Complex_Ocomplex,
% 0.94/1.57 c_Rings_Oinverse__class_Oinverse( tc_Complex_Ocomplex, hAPP(
% 0.94/1.57 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ), v_q____ ) ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.57 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.94/1.57 c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 0.94/1.57 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 0.94/1.57 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 0.94/1.57 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 0.94/1.57 v_q____ ) ), X ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.57 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.94/1.57 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ), X ) ),
% 0.94/1.57 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.94/1.57 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.57 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.94/1.57 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ), X ) ),
% 0.94/1.57 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.94/1.57 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ) ),
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.57 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.94/1.57 c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 0.94/1.57 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 0.94/1.57 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 0.94/1.57 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 0.94/1.57 v_q____ ) ), X ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.94/1.57 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 0.94/1.57 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 0.94/1.57 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 0.94/1.57 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 0.94/1.57 v_q____ ) ), X ) = c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, hAPP
% 0.94/1.57 ( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 0.94/1.57 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 0.94/1.57 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 0.94/1.57 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 0.94/1.57 v_q____ ) ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ), hAPP(
% 0.94/1.57 hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP( hAPP(
% 0.94/1.57 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), X ), v_k____ ) ),
% 0.94/1.57 hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_OpCons(
% 0.94/1.57 tc_Complex_Ocomplex, v_a____, v_s____ ) ), X ) ) ) }.
% 0.94/1.57 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.94/1.57 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.94/1.57 ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, T, W ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.94/1.57 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.94/1.57 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, U ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, X ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, Z ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, T ) }.
% 0.94/1.57 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.94/1.57 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.94/1.57 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.94/1.57 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.94/1.57 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, U, Y ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, U ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, U ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Y ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.94/1.57 ( tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.94/1.57 Z ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.94/1.57 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.94/1.57 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.94/1.57 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.94/1.57 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.94/1.57 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex
% 0.94/1.57 , v_pa____ ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, v_k____,
% 0.94/1.57 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), c_Orderings_Oord__class_Oless
% 0.94/1.57 ( tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex
% 0.94/1.57 , hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 0.94/1.57 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 0.94/1.57 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 0.94/1.57 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 0.94/1.57 v_q____ ) ), skol17 ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 0.94/1.57 }.
% 0.94/1.57 { ! hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 0.94/1.57 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 0.94/1.57 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 0.94/1.57 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 0.94/1.57 v_q____ ) ), skol18 ) = hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 0.94/1.57 c_Polynomial_Osmult( tc_Complex_Ocomplex,
% 0.94/1.57 c_Rings_Oinverse__class_Oinverse( tc_Complex_Ocomplex, hAPP(
% 0.94/1.57 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ), v_q____ ) ),
% 0.94/1.57 skol34 ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 0.94/1.57 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 0.94/1.57 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 0.94/1.57 c_Polynomial_OpCons( X, Z, Y ) ) = c_Groups_Ozero__class_Ozero(
% 0.94/1.57 tc_Polynomial_Opoly( X ) ), Y = c_Groups_Ozero__class_Ozero(
% 0.94/1.57 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.57 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Ozero__class_Ozero(
% 0.94/1.57 tc_Int_Oint ) ) }.
% 0.94/1.57 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 0.94/1.57 tc_Int_Oint ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.94/1.57 tc_Int_Oint, X, Y ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) }.
% 0.94/1.57 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(
% 0.94/1.57 tc_Complex_Ocomplex, tc_Complex_Ocomplex, c_Polynomial_Opoly(
% 0.94/1.57 tc_Complex_Ocomplex, c_Polynomial_OpCons( tc_Complex_Ocomplex,
% 0.94/1.57 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ), c_Polynomial_Omonom(
% 0.94/1.57 tc_Complex_Ocomplex, v_a____, c_Groups_Ominus__class_Ominus( tc_Nat_Onat
% 0.94/1.57 , v_k____, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) ) ) }.
% 0.94/1.57 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, v_k____,
% 0.94/1.57 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) =
% 0.94/1.57 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex,
% 0.94/1.57 c_Polynomial_OpCons( tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(
% 0.94/1.57 tc_Complex_Ocomplex ), c_Polynomial_Omonom( tc_Complex_Ocomplex, v_a____
% 0.94/1.57 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, v_k____,
% 0.94/1.57 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__ring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP(
% 0.94/1.57 hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.94/1.57 c_Polynomial_Omonom( X, c_Groups_Oone__class_Oone( X ), T ) ), Z ) ), Y )
% 0.94/1.57 = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.94/1.57 c_Power_Opower__class_Opower( X ), Y ), T ) ), hAPP( c_Polynomial_Opoly(
% 0.94/1.57 X, Z ), Y ) ) }.
% 0.94/1.57 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_OpCons(
% 0.94/1.57 tc_Complex_Ocomplex, c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ),
% 0.94/1.57 c_Polynomial_Omonom( tc_Complex_Ocomplex, v_a____,
% 0.94/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, v_k____,
% 0.94/1.57 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) ), skol19 ) =
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.94/1.57 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X, Y,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = c_Polynomial_OpCons( X, Y
% 0.94/1.57 , c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.94/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless(
% 0.94/1.57 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 0.94/1.57 tc_Polynomial_Opoly( X ) ) ), c_Groups_Oabs__class_Oabs(
% 0.94/1.57 tc_Polynomial_Opoly( X ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.94/1.57 tc_Polynomial_Opoly( X ), Y ) }.
% 0.94/1.57 { ! class_Rings_Olinordered__idom( X ), c_Orderings_Oord__class_Oless(
% 0.94/1.57 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 0.94/1.57 tc_Polynomial_Opoly( X ) ) ), c_Groups_Oabs__class_Oabs(
% 0.94/1.57 tc_Polynomial_Opoly( X ), Y ) = Y }.
% 0.94/1.57 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.94/1.57 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.94/1.57 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 0.94/1.57 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.57 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 0.94/1.57 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 0.94/1.57 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.94/1.57 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 0.94/1.57 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.94/1.57 tc_Polynomial_Opoly( X ) ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.94/1.57 tc_Polynomial_Opoly( X ), Y ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.57 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 0.94/1.57 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ), Z = Y }.
% 0.94/1.57 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Z = Y,
% 0.94/1.57 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ) }.
% 0.94/1.57 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 0.94/1.57 c_Polynomial_OpCons( X, Z, Y ), U = Z }.
% 0.94/1.57 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 0.94/1.57 c_Polynomial_OpCons( X, Z, Y ), T = Y }.
% 0.94/1.57 { ! class_Groups_Ozero( X ), ! U = Z, ! T = Y, c_Polynomial_OpCons( X, U, T
% 0.94/1.57 ) = c_Polynomial_OpCons( X, Z, Y ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X, T,
% 0.94/1.57 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Z, Y ) ) =
% 0.94/1.57 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ),
% 0.94/1.57 c_Polynomial_Osmult( X, T, Z ), c_Polynomial_Osmult( X, T, Y ) ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X, Z,
% 0.94/1.57 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) =
% 0.94/1.57 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ),
% 0.94/1.57 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.94/1.57 c_Polynomial_Osmult( X, T, Z ) ), Y ) = c_Polynomial_Osmult( X, T, hAPP(
% 0.94/1.57 hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y )
% 0.94/1.57 ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ),
% 0.94/1.57 c_Polynomial_Osmult( X, Z, Y ) ) = c_Polynomial_Osmult( X, Z, hAPP( hAPP
% 0.94/1.57 ( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ) ) }
% 0.94/1.57 .
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ), hAPP
% 0.94/1.57 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y
% 0.94/1.57 ) ) }.
% 0.94/1.57 { ! class_Groups_Ozero( X ), ! c_Polynomial_Omonom( X, T, Z ) =
% 0.94/1.57 c_Polynomial_Omonom( X, Y, Z ), T = Y }.
% 0.94/1.57 { ! class_Groups_Ozero( X ), ! T = Y, c_Polynomial_Omonom( X, T, Z ) =
% 0.94/1.57 c_Polynomial_Omonom( X, Y, Z ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 0.94/1.57 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Z
% 0.94/1.57 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP(
% 0.94/1.57 c_Polynomial_Opoly( X, T ), Y ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 0.94/1.57 ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 0.94/1.57 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.94/1.57 c_Groups_Oone__class_Oone( X ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 0.94/1.57 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.94/1.57 c_Groups_Ominus__class_Ominus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 0.94/1.57 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 0.94/1.57 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ) ), Y ) =
% 0.94/1.57 c_Groups_Ouminus__class_Ouminus( X, hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 0.94/1.57 ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 0.94/1.57 ( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), T ), Z
% 0.94/1.57 ) ), Y ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), hAPP(
% 0.94/1.57 c_Polynomial_Opoly( X, T ), Y ) ), Z ) }.
% 0.94/1.57 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 0.94/1.57 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, U, T ),
% 0.94/1.57 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 0.94/1.57 c_Groups_Ominus__class_Ominus( X, U, Z ), c_Groups_Ominus__class_Ominus(
% 0.94/1.57 tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 0.94/1.57 c_Polynomial_Osmult( X, Z, Y ) ) = c_Polynomial_Osmult( X, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Osmult( X,
% 0.94/1.57 c_Groups_Oone__class_Oone( X ), Y ) = Y }.
% 0.94/1.57 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.94/1.57 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 0.94/1.57 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.94/1.57 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) }.
% 0.94/1.57 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.94/1.57 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 0.94/1.57 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.94/1.57 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X,
% 0.94/1.57 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 0.94/1.57 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ),
% 0.94/1.57 c_Polynomial_Osmult( X, T, Y ), c_Polynomial_Osmult( X, Z, Y ) ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X,
% 0.94/1.57 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) =
% 0.94/1.57 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ),
% 0.94/1.57 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 0.94/1.57 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 0.94/1.57 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y =
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.57 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Y =
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.94/1.57 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, Y,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.57 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 0.94/1.57 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, T, Z ),
% 0.94/1.57 c_Polynomial_Omonom( X, Y, Z ) ) = c_Polynomial_Omonom( X,
% 0.94/1.57 c_Groups_Ominus__class_Ominus( X, T, Y ), Z ) }.
% 0.94/1.57 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.94/1.57 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, Z, Y ) ) =
% 0.94/1.57 c_Polynomial_Omonom( X, c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.94/1.57 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.94/1.57 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.94/1.57 tc_Polynomial_Opoly( X ) ), Y ) = Y }.
% 0.94/1.57 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.94/1.57 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 0.94/1.57 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Z, Y ) ) =
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ),
% 0.94/1.57 c_Polynomial_Osmult( X, T, Z ), c_Polynomial_Osmult( X, T, Y ) ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.94/1.57 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.57 { ! class_Groups_Ozero( X ), c_Polynomial_OpCons( X,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero(
% 0.94/1.57 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 0.94/1.57 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.57 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.94/1.57 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.57 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y =
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.57 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.94/1.57 c_Polynomial_OpCons( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.94/1.57 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 0.94/1.57 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.57 { ! class_Rings_Oidom( X ), ! c_Polynomial_Osmult( X, Z, Y ) =
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.94/1.57 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.94/1.57 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.57 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.57 c_Polynomial_Osmult( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.94/1.57 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.57 { ! class_Rings_Oidom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.94/1.57 tc_Polynomial_Opoly( X ) ), c_Polynomial_Osmult( X, Z, Y ) =
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oone__class_Oone(
% 0.94/1.57 tc_Polynomial_Opoly( X ) ) = c_Polynomial_OpCons( X,
% 0.94/1.57 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.94/1.57 tc_Polynomial_Opoly( X ) ) ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.94/1.57 c_Polynomial_Osmult( X, T, Z ) ), Y ) = hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( c_Polynomial_Opoly( X, Z )
% 0.94/1.57 , Y ) ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 0.94/1.57 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Z ), c_Polynomial_Osmult( X, T,
% 0.94/1.57 Y ) ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.94/1.57 c_Polynomial_Omonom( X, U, T ) ), c_Polynomial_Omonom( X, Z, Y ) ) =
% 0.94/1.57 c_Polynomial_Omonom( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U
% 0.94/1.57 ), Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, Y ) ) }.
% 0.94/1.57 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 0.94/1.57 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.57 { ! class_Groups_Ozero( X ), ! c_Polynomial_Omonom( X, Z, Y ) =
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.94/1.57 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.57 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.57 c_Polynomial_Omonom( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.94/1.57 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.94/1.57 c_Groups_Oplus__class_Oplus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 0.94/1.57 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.94/1.57 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.94/1.57 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, U, T ),
% 0.94/1.57 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( X, U, Z ), c_Groups_Oplus__class_Oplus(
% 0.94/1.57 tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Osmult( X, T, Y ) =
% 0.94/1.57 c_Polynomial_OpCons( X, Z, Y ), Y = c_Groups_Ozero__class_Ozero(
% 0.94/1.57 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.94/1.57 ( tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 0.94/1.57 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 0.94/1.57 c_Polynomial_Omonom( X, Z, Y ) ) = c_Polynomial_Omonom( X, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 0.94/1.57 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.94/1.57 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, T, Z ),
% 0.94/1.57 c_Polynomial_Omonom( X, Y, Z ) ) = c_Polynomial_Omonom( X,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.94/1.57 c_Polynomial_OpCons( X, T, Z ) ), Y ) = c_Groups_Oplus__class_Oplus( X, T
% 0.94/1.57 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), hAPP(
% 0.94/1.57 c_Polynomial_Opoly( X, Z ), Y ) ) ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 0.94/1.57 c_Polynomial_Omonom( X, T, Z ) ), Y ) = hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.94/1.57 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ),
% 0.94/1.57 c_Polynomial_OpCons( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus(
% 0.94/1.57 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, Z, T ),
% 0.94/1.57 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ) ) ) }
% 0.94/1.57 .
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.94/1.57 c_Polynomial_OpCons( X, T, Z ) ), Y ) = c_Groups_Oplus__class_Oplus(
% 0.94/1.57 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 0.94/1.57 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y ) ) ) }
% 0.94/1.57 .
% 0.94/1.57 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Oplus__class_Oplus(
% 0.94/1.57 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.94/1.57 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.94/1.57 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 0.94/1.57 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.94/1.57 tc_Polynomial_Opoly( X ) ) ) ) ), c_Polynomial_Osynthetic__div( X, Y, Z )
% 0.94/1.57 ), c_Polynomial_OpCons( X, hAPP( c_Polynomial_Opoly( X, Y ), Z ),
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) = Y }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 0.94/1.57 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus(
% 0.94/1.57 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, T,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 0.94/1.57 c_Polynomial_Opcompose( X, Z, Y ) ) ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.94/1.57 c_Polynomial_Opcompose( X, T, Z ) ), Y ) = hAPP( c_Polynomial_Opoly( X, T
% 0.94/1.57 ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 0.94/1.57 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Polynomial_OpCons( X, hAPP(
% 0.94/1.57 c_Polynomial_Opoly( X, Z ), Y ), c_Polynomial_Osynthetic__div( X, Z, Y )
% 0.94/1.57 ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__0( X ), c_Groups_Oplus__class_Oplus(
% 0.94/1.57 tc_Polynomial_Opoly( X ), Z, c_Polynomial_Osmult( X, Y,
% 0.94/1.57 c_Polynomial_Osynthetic__div( X, Z, Y ) ) ) = c_Polynomial_OpCons( X,
% 0.94/1.57 hAPP( c_Polynomial_Opoly( X, Z ), Y ), c_Polynomial_Osynthetic__div( X, Z
% 0.94/1.57 , Y ) ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 0.94/1.57 tc_Polynomial_Opoly( X ), U, c_Polynomial_Osmult( X, T, Z ) ) =
% 0.94/1.57 c_Polynomial_OpCons( X, Y, Z ), Y = hAPP( c_Polynomial_Opoly( X, U ), T )
% 0.94/1.57 }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 0.94/1.57 tc_Polynomial_Opoly( X ), U, c_Polynomial_Osmult( X, T, Z ) ) =
% 0.94/1.57 c_Polynomial_OpCons( X, Y, Z ), Z = c_Polynomial_Osynthetic__div( X, U, T
% 0.94/1.57 ) }.
% 0.94/1.57 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.94/1.57 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 0.94/1.57 tc_Polynomial_Opoly( X ) ), ! c_Polynomial_Oorder( X, Y, Z ) =
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.57 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.94/1.57 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.94/1.57 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.57 { ! class_Rings_Oidom( X ), c_Polynomial_Oorder( X, Y, Z ) =
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( c_Polynomial_Opoly( X,
% 0.94/1.57 Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.57 { ! class_Orderings_Opreorder( X ), c_Orderings_Oord__class_Oless__eq( X, Y
% 0.94/1.57 , Y ) }.
% 0.94/1.57 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.94/1.57 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.94/1.57 hAPP( Y, U ) ) }.
% 0.94/1.57 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, hAPP
% 0.94/1.57 ( Z, skol20( X, Y, Z ) ), hAPP( Y, skol20( X, Y, Z ) ) ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }.
% 0.94/1.57 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.94/1.57 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.94/1.57 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.94/1.57 ( X, Z, Y ) }.
% 0.94/1.57 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.94/1.57 ( X, Y, Z ) }.
% 0.94/1.57 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.94/1.57 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 0.94/1.57 { ! class_Orderings_Opreorder( X ), ! Z = Y,
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.94/1.57 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.94/1.57 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.94/1.57 hAPP( Y, U ) ) }.
% 0.94/1.57 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.94/1.57 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 0.94/1.57 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.94/1.57 , Y ), ! Y = Z, c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.94/1.57 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.94/1.57 ( X, Y, T ), c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.94/1.57 { ! class_Orderings_Oorder( X ), ! Z = Y, !
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 0.94/1.57 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y
% 0.94/1.57 ), ! Y = T, c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.94/1.57 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.94/1.57 , Y ), ! Z = T, c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.94/1.57 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.94/1.57 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 0.94/1.57 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.57 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.94/1.57 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.94/1.57 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 0.94/1.57 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.94/1.57 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.94/1.57 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.94/1.57 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.94/1.57 hAPP( Y, U ) ) }.
% 0.94/1.57 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.94/1.57 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.94/1.57 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.94/1.57 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.94/1.57 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.94/1.57 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.94/1.57 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.94/1.57 , ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.94/1.57 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.94/1.57 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.94/1.57 Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 0.94/1.57 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.94/1.57 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.94/1.57 , ! Z = T, c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.94/1.57 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 0.94/1.57 ! Y = T, c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.94/1.57 { ! class_Orderings_Oorder( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless(
% 0.94/1.57 X, T, Y ), c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.94/1.57 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X
% 0.94/1.57 , Y, T ), c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.94/1.57 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.94/1.57 , ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.94/1.57 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.94/1.57 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.94/1.57 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.94/1.57 , ! Y = Z }.
% 0.94/1.57 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.94/1.57 , ! Z = Y }.
% 0.94/1.57 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.94/1.57 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.94/1.57 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.94/1.57 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.94/1.57 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.94/1.57 , ! Z = Y }.
% 0.94/1.57 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 0.94/1.57 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.94/1.57 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.94/1.57 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Y = Z }.
% 0.94/1.57 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.94/1.57 ), ! Y = Z, ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.94/1.57 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.94/1.57 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.94/1.57 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.94/1.57 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Z = Y }.
% 0.94/1.57 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.94/1.57 Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.94/1.57 { ! class_Orderings_Olinorder( X ), ! Z = Y, !
% 0.94/1.57 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.94/1.57 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 0.94/1.57 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.94/1.57 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.94/1.57 Y ), ! Z = Y }.
% 0.94/1.57 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.94/1.57 Z ), ! Z = Y }.
% 0.94/1.57 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.94/1.57 Y ) }.
% 0.94/1.57 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.94/1.57 , Y ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.94/1.57 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.94/1.57 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.57 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 0.94/1.57 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.94/1.57 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.94/1.57 , ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.94/1.57 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.94/1.57 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.94/1.57 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 0.94/1.57 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.94/1.57 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.94/1.57 , Y ), Y = Z, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.94/1.57 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.94/1.57 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.94/1.57 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.94/1.57 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.94/1.57 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.57 , Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.94/1.57 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.57 , Z, Y ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.94/1.57 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.94/1.57 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.94/1.57 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.57 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.94/1.57 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.94/1.57 ( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.94/1.57 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.94/1.57 ( X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.94/1.57 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.94/1.57 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ), Z = Y }.
% 0.94/1.57 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.94/1.57 ), ! Z = Y, c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.94/1.57 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.94/1.57 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.94/1.57 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.94/1.57 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.94/1.57 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.94/1.57 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.94/1.57 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.94/1.57 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.94/1.57 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.94/1.57 ( X, Z, Y ) }.
% 0.94/1.57 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.94/1.57 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.94/1.57 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.94/1.57 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.94/1.57 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.57 , Z, Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.94/1.57 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.94/1.57 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.94/1.57 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.94/1.57 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.94/1.57 , ! Z = Y }.
% 0.94/1.57 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.94/1.57 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.94/1.57 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.94/1.57 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.94/1.57 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.94/1.57 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.94/1.57 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.94/1.57 Z ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.94/1.57 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.94/1.57 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.94/1.57 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.57 , Y, Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.94/1.57 { ! skol21 = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.94/1.57 { ! skol35 = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.57 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.94/1.57 tc_Nat_Onat, c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(
% 0.94/1.57 tc_Complex_Ocomplex, skol38 ), skol35 ), c_Groups_Oone__class_Oone(
% 0.94/1.57 tc_Nat_Onat ) ) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(
% 0.94/1.57 tc_Complex_Ocomplex, c_Polynomial_Osmult( tc_Complex_Ocomplex,
% 0.94/1.57 c_Rings_Oinverse__class_Oinverse( tc_Complex_Ocomplex, hAPP(
% 0.94/1.57 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ), v_q____ ) ) }.
% 0.94/1.57 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 0.94/1.57 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 0.94/1.57 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 0.94/1.57 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 0.94/1.57 v_q____ ) ), X ) = c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, hAPP
% 0.94/1.57 ( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 0.94/1.57 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 0.94/1.57 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 0.94/1.57 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 0.94/1.57 v_q____ ) ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ), hAPP(
% 0.94/1.57 hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP( hAPP(
% 0.94/1.57 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), X ), skol35 ) ),
% 0.94/1.57 hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_OpCons(
% 0.94/1.57 tc_Complex_Ocomplex, skol21, skol38 ) ), X ) ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.94/1.57 c_RComplete_Onatceiling( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X
% 0.94/1.57 , c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) =
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_RComplete_Onatceiling( X ),
% 0.94/1.57 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.94/1.57 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 0.94/1.57 X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }
% 0.94/1.57 .
% 0.94/1.57 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 0.94/1.57 X ), Z, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z )
% 0.94/1.57 }.
% 0.94/1.57 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.94/1.57 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z
% 0.94/1.57 ), c_Orderings_Oord__class_Oless( tc_fun( T, X ), Z, Y ) }.
% 0.94/1.57 { c_RComplete_Onatceiling( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal )
% 0.94/1.57 ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.57 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_RComplete_Onatceiling( X )
% 0.94/1.57 ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 0.94/1.57 Y ), c_RComplete_Onatceiling( X ) ) }.
% 0.94/1.57 { c_RComplete_Onatceiling( c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 0.94/1.57 = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.94/1.57 c_RComplete_Onatceiling( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.94/1.57 }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling
% 0.94/1.57 ( X ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.94/1.57 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.94/1.57 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 0.94/1.57 X ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.94/1.57 { ! class_Power_Opower( X ), c_Power_Opower__class_Opower( X ) =
% 0.94/1.57 c_Power_Opower_Opower( X, c_Groups_Oone__class_Oone( X ),
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ) ) }.
% 0.94/1.57 { ! class_RealVector_Oreal__algebra__1( X ), !
% 0.94/1.57 class_RealVector_Oreal__normed__vector( X ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol22( Y ) ) }.
% 0.94/1.57 { ! class_RealVector_Oreal__algebra__1( X ), !
% 0.94/1.57 class_RealVector_Oreal__normed__vector( X ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.57 c_RealVector_Onorm__class_Onorm( X, c_RealVector_Oof__real( X, Y ) ),
% 0.94/1.57 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.94/1.57 c_RealVector_Onorm__class_Onorm( tc_RealDef_Oreal, Y ) ), skol22( X ) ) )
% 0.94/1.57 }.
% 0.94/1.57 { hAPP( hAPP( c_Power_Opower_Opower( T, Z, Y ), X ),
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = Z }.
% 0.94/1.57 { ! class_RealVector_Oreal__normed__vector( Y ), ! class_Orderings_Oord( X
% 0.94/1.57 ), c_Orderings_Oord__class_Oless__eq( X, T, skol23( X, U, W, T ) ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( X, T, V0 ),
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.57 c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, V0 ) ),
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oone__class_Oone
% 0.94/1.57 ( tc_RealDef_Oreal ), c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, T ) )
% 0.94/1.57 ) ) }.
% 0.94/1.57 { ! class_RealVector_Oreal__normed__vector( Y ), ! class_Orderings_Oord( X
% 0.94/1.57 ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.57 c_RealVector_Onorm__class_Onorm( Y, c_Groups_Ominus__class_Ominus( Y,
% 0.94/1.57 hAPP( Z, T ), hAPP( Z, skol23( X, Y, Z, T ) ) ) ),
% 0.94/1.57 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( X, T, U ),
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.57 c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, U ) ),
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oone__class_Oone
% 0.94/1.57 ( tc_RealDef_Oreal ), c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, T ) )
% 0.94/1.57 ) ) }.
% 0.94/1.57 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol24( Z, T ) ) }.
% 0.94/1.57 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.57 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.94/1.57 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol24( X, Y ) ) ) }.
% 0.94/1.57 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol25( Y ) ) }.
% 0.94/1.57 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.57 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.94/1.57 c_RealVector_Onorm__class_Onorm( X, Y ) ),
% 0.94/1.57 c_RealVector_Onorm__class_Onorm( X, Z ) ) ), skol25( X ) ) ) }.
% 0.94/1.57 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol26( Z, T ) ) }.
% 0.94/1.57 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.57 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.94/1.57 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol26( X, Y ) ) ) }.
% 0.94/1.57 { c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex,
% 0.94/1.57 skol27 ) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(
% 0.94/1.57 tc_Complex_Ocomplex, v_pa____ ) }.
% 0.94/1.57 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, skol27 ), X ) = hAPP(
% 0.94/1.57 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ),
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, v_c____, X ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.94/1.57 c_RComplete_Onatfloor( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 0.94/1.57 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) =
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_RComplete_Onatfloor( X ),
% 0.94/1.57 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.94/1.57 { c_RComplete_Onatfloor( c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) =
% 0.94/1.57 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.94/1.57 { c_RComplete_Onatfloor( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) )
% 0.94/1.57 = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.57 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) )
% 0.94/1.57 }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatfloor( Y
% 0.94/1.57 ), c_RComplete_Onatfloor( X ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), c_RComplete_Onatfloor
% 0.94/1.57 ( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.57 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.57 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.57 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Groups_Oone__class_Oone
% 0.94/1.57 ( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_RComplete_Onatfloor( X )
% 0.94/1.57 ), c_RComplete_Onatfloor( Y ) ), c_RComplete_Onatfloor( hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.94/1.57 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ominus__class_Ominus(
% 0.94/1.57 tc_Int_Oint, X, Y ) }.
% 0.94/1.57 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.94/1.57 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint
% 0.94/1.57 ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Nat__Transfer_Otsub( X, Y )
% 0.94/1.57 ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.94/1.57 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ominus__class_Ominus(
% 0.94/1.57 tc_Int_Oint, X, Y ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.57 tc_Nat_Onat, Y ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.94/1.57 tc_RealDef_Oreal, X, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.94/1.57 c_RealDef_Oreal( tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone(
% 0.94/1.57 tc_RealDef_Oreal ) ) ), c_RComplete_Onatceiling( X ) =
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone(
% 0.94/1.57 tc_Nat_Onat ) ) }.
% 0.94/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.94/1.57 c_Polynomial_OpCons( X, Z, Y ) ), c_Polynomial_Opos__poly( X, Y ), alpha7
% 0.94/1.57 ( X, Y, Z ) }.
% 0.94/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.94/1.57 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ) }.
% 0.94/1.57 { ! class_Rings_Olinordered__idom( X ), ! alpha7( X, Y, Z ),
% 0.94/1.57 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ) }.
% 0.94/1.57 { ! alpha7( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly
% 0.94/1.57 ( X ) ) }.
% 0.94/1.57 { ! alpha7( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.94/1.57 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.94/1.57 alpha7( X, Y, Z ) }.
% 0.94/1.57 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.94/1.57 tc_Nat_Onat, X ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), c_RealDef_Oreal
% 0.94/1.57 ( tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 0.94/1.57 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.57 tc_Nat_Onat, X ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.57 tc_Nat_Onat, X ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.57 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ),
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.57 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 0.94/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.94/1.57 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 0.94/1.57 { c_RealDef_Oreal( tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.94/1.57 tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.94/1.57 tc_RealDef_Oreal ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ), c_RealDef_Oreal
% 0.94/1.57 ( tc_Nat_Onat, X ) ) }.
% 0.94/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.94/1.57 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X, hAPP( hAPP
% 0.94/1.57 ( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) }
% 0.94/1.57 .
% 0.94/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.94/1.57 { ! c_RealDef_Oreal( tc_Nat_Onat, X ) = c_Groups_Ozero__class_Ozero(
% 0.94/1.57 tc_RealDef_Oreal ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.57 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_RealDef_Oreal(
% 0.94/1.57 tc_Nat_Onat, X ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.94/1.57 { c_RealDef_Oreal( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.94/1.57 ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.94/1.57 { ! c_RealDef_Oreal( tc_Nat_Onat, Y ) = c_RealDef_Oreal( tc_Nat_Onat, X ),
% 0.94/1.57 Y = X }.
% 0.94/1.57 { ! Y = X, c_RealDef_Oreal( tc_Nat_Onat, Y ) = c_RealDef_Oreal( tc_Nat_Onat
% 0.94/1.57 , X ) }.
% 0.94/1.57 { c_RealDef_Oreal( tc_Nat_Onat, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y
% 0.94/1.57 , X ) ) = c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal
% 0.94/1.57 ( tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 0.94/1.57 { c_RealDef_Oreal( tc_Nat_Onat, c_Groups_Oone__class_Oone( tc_Nat_Onat ) )
% 0.94/1.57 = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.94/1.57 { c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, c_RealDef_Oreal( tc_Nat_Onat
% 0.94/1.57 , X ) ) = c_RealDef_Oreal( tc_Nat_Onat, X ) }.
% 0.94/1.57 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.94/1.57 c_RealDef_Oreal( tc_Nat_Onat, Y ) ), X ) = c_RealDef_Oreal( tc_Nat_Onat,
% 0.94/1.57 hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.94/1.57 { c_RealDef_Oreal( tc_Nat_Onat, hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.94/1.57 tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.94/1.57 tc_RealDef_Oreal ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ), X ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.57 tc_Nat_Onat, X ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X =
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.57 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.57 tc_Nat_Onat, X ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.94/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.94/1.57 ( tc_Polynomial_Opoly( X ), Z, Y ), Z = Y, c_Polynomial_Opos__poly( X,
% 0.94/1.57 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 0.94/1.57 { ! class_Rings_Olinordered__idom( X ), ! Z = Y,
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.94/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.94/1.57 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.94/1.57 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.94/1.57 tc_Nat_Onat, c_RComplete_Onatceiling( X ) ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.57 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.57 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 0.94/1.57 { c_RComplete_Onatceiling( c_RealDef_Oreal( tc_Nat_Onat, X ) ) = X }.
% 0.94/1.57 { c_RComplete_Onatfloor( c_RealDef_Oreal( tc_Nat_Onat, X ) ) = X }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.57 tc_Nat_Onat, c_RComplete_Onatfloor( X ) ), X ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.57 tc_Nat_Onat, Y ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 0.94/1.57 , c_RComplete_Onatfloor( X ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, c_RealDef_Oreal
% 0.94/1.57 ( tc_Nat_Onat, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.57 c_RComplete_Onatceiling( Y ), X ) }.
% 0.94/1.57 { ! X = c_RealDef_Oreal( tc_Nat_Onat, c_RComplete_Onatfloor( X ) ),
% 0.94/1.57 c_RComplete_Onatfloor( hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.94/1.57 tc_RealDef_Oreal ), X ), Y ) ) = hAPP( hAPP( c_Power_Opower__class_Opower
% 0.94/1.57 ( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ), Y ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.94/1.57 tc_Nat_Onat, X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.57 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.94/1.57 tc_Nat_Onat, X ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.57 tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.94/1.57 c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.57 tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.94/1.57 c_RealDef_Oreal( tc_Nat_Onat, X ) ), c_Orderings_Oord__class_Oless(
% 0.94/1.57 tc_Nat_Onat, Y, X ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.57 tc_Nat_Onat, Y ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.94/1.57 c_RealDef_Oreal( tc_Nat_Onat, X ), c_Groups_Oone__class_Oone(
% 0.94/1.57 tc_RealDef_Oreal ) ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.57 tc_Nat_Onat, Y ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.94/1.57 c_RealDef_Oreal( tc_Nat_Onat, X ), c_Groups_Oone__class_Oone(
% 0.94/1.57 tc_RealDef_Oreal ) ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 0.94/1.57 , X ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_RComplete_Onatfloor
% 0.94/1.57 ( X ) ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.57 c_RealDef_Oreal( tc_Nat_Onat, Y ), X ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.57 tc_Nat_Onat, Y ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 0.94/1.57 , c_RComplete_Onatfloor( X ) ) }.
% 0.94/1.57 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.94/1.57 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opos__poly( X, Y ),
% 0.94/1.57 c_Polynomial_Opos__poly( X, c_Groups_Ouminus__class_Ouminus(
% 0.94/1.57 tc_Polynomial_Opoly( X ), Y ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 0.94/1.57 X ), Y ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.94/1.57 c_RealDef_Oreal( tc_Nat_Onat, Y ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.94/1.57 tc_Nat_Onat, Y ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.57 c_RComplete_Onatceiling( X ), Y ) }.
% 0.94/1.57 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.57 tc_Nat_Onat, c_RComplete_Onatfloor( X ) ), c_Groups_Oone__class_Oone(
% 0.94/1.57 tc_RealDef_Oreal ) ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.57 tc_Nat_Onat, Y ), X ), c_RComplete_Onatfloor(
% 0.94/1.57 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.94/1.57 tc_Nat_Onat, Y ) ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.94/1.57 c_RComplete_Onatfloor( X ), Y ) }.
% 0.94/1.57 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.57 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X,
% 0.94/1.57 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), c_RealDef_Oreal(
% 0.94/1.57 tc_Nat_Onat, c_RComplete_Onatfloor( X ) ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.57 tc_Nat_Onat, Y ), X ), c_RComplete_Onatceiling(
% 0.94/1.57 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.94/1.57 tc_Nat_Onat, Y ) ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.94/1.57 c_RComplete_Onatceiling( X ), Y ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.94/1.57 tc_Nat_Onat, Y ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.94/1.57 c_RComplete_Onatfloor( X ), Y ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.94/1.57 c_RComplete_Onatfloor( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 0.94/1.57 c_RealDef_Oreal( tc_Nat_Onat, Y ) ) ) = c_Groups_Oplus__class_Oplus(
% 0.94/1.57 tc_Nat_Onat, c_RComplete_Onatfloor( X ), Y ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_RComplete_Onatfloor( Y ),
% 0.94/1.57 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ),
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, c_RealDef_Oreal(
% 0.94/1.57 tc_Nat_Onat, X ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.57 tc_Nat_Onat, Y ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal
% 0.94/1.57 , X, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.57 tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ),
% 0.94/1.57 c_RComplete_Onatfloor( X ) = Y }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.94/1.57 c_RComplete_Onatceiling( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X
% 0.94/1.57 , c_RealDef_Oreal( tc_Nat_Onat, Y ) ) ) = c_Groups_Oplus__class_Oplus(
% 0.94/1.57 tc_Nat_Onat, c_RComplete_Onatceiling( X ), Y ) }.
% 0.94/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless(
% 0.94/1.57 tc_Polynomial_Opoly( X ), Z, Y ), c_Polynomial_Opos__poly( X,
% 0.94/1.57 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 0.94/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.94/1.57 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ),
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.94/1.57 tc_Nat_Onat, Y ) ), X ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 0.94/1.57 , hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 0.94/1.57 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ), Y ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.57 tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, skol28( X ),
% 0.94/1.57 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ), X ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.94/1.57 tc_Nat_Onat, skol28( X ) ) ) }.
% 0.94/1.57 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.94/1.57 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Ouminus__class_Ouminus
% 0.94/1.57 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.94/1.57 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol29( T, U, W ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.94/1.57 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.94/1.57 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, T, Z ) ) ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.57 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.94/1.57 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, T, Z ) ), skol29( X,
% 0.94/1.57 Y, Z ) ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.57 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.94/1.57 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, hAPP(
% 0.94/1.57 c_Polynomial_Opoly( tc_Complex_Ocomplex, Y ), T ), hAPP(
% 0.94/1.57 c_Polynomial_Opoly( tc_Complex_Ocomplex, Y ), Z ) ) ), X ) }.
% 0.94/1.57 { ! class_Orderings_Oorder( X ), ! c_SEQ_Odecseq( X, Y ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, T ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, T ), hAPP( Y, Z ) ) }.
% 0.94/1.57 { ! class_Orderings_Oorder( X ), c_Orderings_Oord__class_Oless__eq(
% 0.94/1.57 tc_Nat_Onat, skol30( X, Y ), skol36( X, Y ) ), c_SEQ_Odecseq( X, Y ) }.
% 0.94/1.57 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.57 hAPP( Y, skol36( X, Y ) ), hAPP( Y, skol30( X, Y ) ) ), c_SEQ_Odecseq( X
% 0.94/1.57 , Y ) }.
% 0.94/1.57 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.94/1.57 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.94/1.57 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.94/1.57 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.94/1.57 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.94/1.57 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.94/1.57 { ! class_Groups_Ominus( X ), hAPP( c_Groups_Ominus__class_Ominus( tc_fun(
% 0.94/1.57 U, X ), T, Z ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( T, Y ),
% 0.94/1.57 hAPP( Z, Y ) ) }.
% 0.94/1.57 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 0.94/1.57 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 0.94/1.57 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 0.94/1.57 { ! class_Lattices_Oboolean__algebra( X ), c_Groups_Ouminus__class_Ouminus
% 0.94/1.57 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 0.94/1.57 { ! class_Groups_Ouminus( X ), hAPP( c_Groups_Ouminus__class_Ouminus(
% 0.94/1.57 tc_fun( T, X ), Z ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( Z, Y
% 0.94/1.57 ) ) }.
% 0.94/1.57 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.94/1.57 c_Groups_Ouminus__class_Ouminus( X, Z ) = c_Groups_Ouminus__class_Ouminus
% 0.94/1.57 ( X, Y ), Z = Y }.
% 0.94/1.57 { ! class_Lattices_Oboolean__algebra( X ), ! Z = Y,
% 0.94/1.57 c_Groups_Ouminus__class_Ouminus( X, Z ) = c_Groups_Ouminus__class_Ouminus
% 0.94/1.57 ( X, Y ) }.
% 0.94/1.57 { ! class_RealVector_Oreal__algebra__1( X ), !
% 0.94/1.57 class_RealVector_Oreal__normed__vector( X ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.57 c_RealVector_Onorm__class_Onorm( X, c_RealVector_Oof__real( X, Y ) ),
% 0.94/1.57 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.94/1.57 c_RealVector_Onorm__class_Onorm( tc_RealDef_Oreal, Y ) ), skol31( X ) ) )
% 0.94/1.57 }.
% 0.94/1.57 { ! class_Rings_Olinordered__idom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.94/1.57 tc_Polynomial_Opoly( X ) ), c_Groups_Osgn__class_Osgn(
% 0.94/1.57 tc_Polynomial_Opoly( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 0.94/1.57 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.57 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.94/1.57 tc_Polynomial_Opoly( X ) ), ! c_Orderings_Oord__class_Oless(
% 0.94/1.57 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.94/1.57 tc_Polynomial_Opoly( X ) ), Y ), c_Groups_Osgn__class_Osgn(
% 0.94/1.57 tc_Polynomial_Opoly( X ), Y ) = c_Groups_Oone__class_Oone(
% 0.94/1.57 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.57 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.94/1.57 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless(
% 0.94/1.57 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.94/1.57 tc_Polynomial_Opoly( X ) ), Y ), c_Groups_Osgn__class_Osgn(
% 0.94/1.57 tc_Polynomial_Opoly( X ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.94/1.57 tc_Polynomial_Opoly( X ), c_Groups_Oone__class_Oone( tc_Polynomial_Opoly
% 0.94/1.57 ( X ) ) ) }.
% 0.94/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.94/1.57 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) ),
% 0.94/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.94/1.57 .
% 0.94/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.94/1.57 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless( X
% 0.94/1.57 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) ) }
% 0.94/1.57 .
% 0.94/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.94/1.57 , c_Groups_Osgn__class_Osgn( X, Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.94/1.57 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.94/1.57 .
% 0.94/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.94/1.57 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.94/1.57 , c_Groups_Osgn__class_Osgn( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }
% 0.94/1.57 .
% 0.94/1.57 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 0.94/1.57 c_Groups_Osgn__class_Osgn( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.94/1.57 X ), Z ), Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.94/1.57 c_Groups_Osgn__class_Osgn( X, Z ) ), c_Groups_Osgn__class_Osgn( X, Y ) )
% 0.94/1.57 }.
% 0.94/1.57 { ! class_Rings_Olinordered__idom( X ), c_Groups_Osgn__class_Osgn( X, hAPP
% 0.94/1.57 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), c_Groups_Osgn__class_Osgn( X, Z ) ),
% 0.94/1.57 c_Groups_Osgn__class_Osgn( X, Y ) ) }.
% 0.94/1.57 { ! class_Groups_Osgn__if( X ), c_Groups_Osgn__class_Osgn( X,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.57 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.94/1.57 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.94/1.57 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.57 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.94/1.57 c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) =
% 0.94/1.57 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 0.94/1.57 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.57 }.
% 0.94/1.57 { ! class_Rings_Olinordered__idom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.94/1.57 X ), c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.57 }.
% 0.94/1.57 { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Osgn__class_Osgn
% 0.94/1.57 ( X, c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X
% 0.94/1.57 ) }.
% 0.94/1.57 { ! class_Rings_Olinordered__idom( X ), c_Groups_Osgn__class_Osgn( X,
% 0.94/1.57 c_Groups_Osgn__class_Osgn( X, Y ) ) = c_Groups_Osgn__class_Osgn( X, Y ) }
% 0.94/1.57 .
% 0.94/1.57 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 0.94/1.57 c_Groups_Osgn__class_Osgn( X, c_RealVector_Oof__real( X, Y ) ) =
% 0.94/1.57 c_RealVector_Oof__real( X, c_Groups_Osgn__class_Osgn( tc_RealDef_Oreal, Y
% 0.94/1.57 ) ) }.
% 0.94/1.57 { ! class_Rings_Olinordered__idom( X ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), c_Groups_Osgn__class_Osgn( X, Y ) ),
% 0.94/1.57 c_Groups_Oabs__class_Oabs( X, Y ) ) = Y }.
% 0.94/1.57 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X, Y ) =
% 0.94/1.57 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ),
% 0.94/1.57 c_Groups_Osgn__class_Osgn( X, Y ) ) }.
% 0.94/1.57 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 0.94/1.57 c_Groups_Osgn__class_Osgn( X, c_Groups_Oone__class_Oone( X ) ) =
% 0.94/1.57 c_Groups_Oone__class_Oone( X ) }.
% 0.94/1.57 { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Osgn__class_Osgn
% 0.94/1.57 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 0.94/1.57 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Osgn__class_Osgn( X, Y ) ) }
% 0.94/1.57 .
% 0.94/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 0.94/1.57 = c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless( X,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.94/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.94/1.57 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Groups_Osgn__class_Osgn( X, Y
% 0.94/1.57 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.94/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.94/1.57 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Groups_Osgn__class_Osgn( X, Y
% 0.94/1.57 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.94/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 0.94/1.57 = c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ),
% 0.94/1.57 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.94/1.57 .
% 0.94/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.94/1.57 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Osgn__class_Osgn( X, Y
% 0.94/1.57 ) = c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) )
% 0.94/1.57 }.
% 0.94/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.94/1.57 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Osgn__class_Osgn( X, Y
% 0.94/1.57 ) = c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) )
% 0.94/1.57 }.
% 0.94/1.57 { ! class_Groups_Osgn__if( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.57 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.57 { ! class_Groups_Osgn__if( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.94/1.57 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.94/1.57 { ! class_Groups_Osgn__if( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.94/1.57 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.94/1.57 c_Groups_Oone__class_Oone( X ) ) }.
% 0.94/1.57 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.94/1.57 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X,
% 0.94/1.57 c_Groups_Osgn__class_Osgn( X, Y ) ) = c_Groups_Ozero__class_Ozero(
% 0.94/1.57 tc_RealDef_Oreal ) }.
% 0.94/1.57 { ! class_RealVector_Oreal__normed__vector( X ), Y =
% 0.94/1.57 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X,
% 0.94/1.57 c_Groups_Osgn__class_Osgn( X, Y ) ) = c_Groups_Oone__class_Oone(
% 0.94/1.57 tc_RealDef_Oreal ) }.
% 0.94/1.57 { ! class_Rings_Oidom( X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly(
% 0.94/1.57 X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) )
% 0.94/1.57 , c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.94/1.57 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ),
% 0.94/1.57 c_Polynomial_Oorder( X, Z, Y ) ), Y ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__0( X ),
% 0.94/1.57 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X,
% 0.94/1.57 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus(
% 0.94/1.57 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, Y,
% 0.94/1.57 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) ),
% 0.94/1.57 c_Polynomial_OpCons( X, T,
% 0.94/1.57 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) ) ) }
% 0.94/1.57 .
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Y,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 0.94/1.57 , ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X, Z,
% 0.94/1.57 c_Groups_Ominus__class_Ominus( X, Y, T ) ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.94/1.57 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ), c_Rings_Odvd__class_Odvd( X
% 0.94/1.57 , Z, Y ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 0.94/1.57 , c_Rings_Odvd__class_Odvd( X, c_Groups_Ouminus__class_Ouminus( X, Z ), Y
% 0.94/1.57 ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.94/1.57 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Rings_Odvd__class_Odvd( X, Z
% 0.94/1.57 , Y ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 0.94/1.57 , c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.94/1.57 ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 0.94/1.57 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( X, U, T ) ), c_Rings_Odvd__class_Odvd( X, Z
% 0.94/1.57 , c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U,
% 0.94/1.57 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 0.94/1.57 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U, hAPP
% 0.94/1.57 ( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ),
% 0.94/1.57 c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oplus__class_Oplus( X, U, T ) )
% 0.94/1.57 }.
% 0.94/1.57 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 0.94/1.57 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( X, U, T ) ), c_Rings_Odvd__class_Odvd( X, Z
% 0.94/1.57 , c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U,
% 0.94/1.57 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 0.94/1.57 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U, hAPP
% 0.94/1.57 ( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ),
% 0.94/1.57 c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oplus__class_Oplus( X, U, T ) )
% 0.94/1.57 }.
% 0.94/1.57 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.94/1.57 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ), alpha8( X
% 0.94/1.57 , Y, T ) }.
% 0.94/1.57 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.94/1.57 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ), alpha15( X
% 0.94/1.57 , Y, Z, T ) }.
% 0.94/1.57 { ! class_Fields_Ofield( X ), ! alpha8( X, Y, T ), ! alpha15( X, Y, Z, T )
% 0.94/1.57 , c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), c_Polynomial_Osmult
% 0.94/1.57 ( X, T, Z ), Y ) }.
% 0.94/1.57 { ! alpha15( X, Y, Z, T ), T = c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.57 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.94/1.57 { ! T = c_Groups_Ozero__class_Ozero( X ), alpha15( X, Y, Z, T ) }.
% 0.94/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, Y ), alpha15( X
% 0.94/1.57 , Y, Z, T ) }.
% 0.94/1.57 { ! alpha8( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.57 { Z = c_Groups_Ozero__class_Ozero( X ), alpha8( X, Y, Z ) }.
% 0.94/1.57 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha8( X
% 0.94/1.57 , Y, Z ) }.
% 0.94/1.57 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 0.94/1.57 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ), hBOOL(
% 0.94/1.57 hAPP( Z, skol32( U, W, Z ) ) ) }.
% 0.94/1.57 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 0.94/1.57 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ),
% 0.94/1.57 c_Rings_Odvd__class_Odvd( X, Y, c_Groups_Oplus__class_Oplus( X, skol32( X
% 0.94/1.57 , Y, Z ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.94/1.57 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), !
% 0.94/1.57 c_Rings_Odvd__class_Odvd( X, Y, c_Groups_Oplus__class_Oplus( X, T,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( X ) ) ), ! hBOOL( hAPP( Z, T ) ), hBOOL(
% 0.94/1.57 hAPP( Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), skol37( X,
% 0.94/1.57 Y, Z ) ) ) ) }.
% 0.94/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Oabs__class_Oabs( X, Z )
% 0.94/1.57 = c_Groups_Oabs__class_Oabs( X, Y ), c_Rings_Odvd__class_Odvd( X, Z, Y )
% 0.94/1.57 }.
% 0.94/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.94/1.57 c_Groups_Oabs__class_Oabs( X, Z ), Y ), c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.94/1.57 ) }.
% 0.94/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.94/1.57 ), c_Rings_Odvd__class_Odvd( X, c_Groups_Oabs__class_Oabs( X, Z ), Y ) }
% 0.94/1.57 .
% 0.94/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.94/1.57 c_Groups_Oabs__class_Oabs( X, Y ) ), c_Rings_Odvd__class_Odvd( X, Z, Y )
% 0.94/1.57 }.
% 0.94/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.94/1.57 ), c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oabs__class_Oabs( X, Y ) ) }
% 0.94/1.57 .
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.94/1.57 Y ), c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 0.94/1.57 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.94/1.57 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X,
% 0.94/1.57 c_Groups_Oone__class_Oone( X ), Y ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__0( X ), !
% 0.94/1.57 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) =
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__0( X ), ! Z = c_Groups_Ozero__class_Ozero
% 0.94/1.57 ( tc_Polynomial_Opoly( X ) ),
% 0.94/1.57 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) =
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__0( X ),
% 0.94/1.57 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.94/1.57 Y ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X,
% 0.94/1.57 Z, c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.94/1.57 Y ), ! c_Rings_Odvd__class_Odvd( X, Y, T ), c_Rings_Odvd__class_Odvd( X,
% 0.94/1.58 Z, T ) }.
% 0.94/1.58 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Y, Y
% 0.94/1.58 ) }.
% 0.94/1.58 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.94/1.58 c_Groups_Ozero__class_Ozero( X ), Y ), Y = c_Groups_Ozero__class_Ozero( X
% 0.94/1.58 ) }.
% 0.94/1.58 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 0.94/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), T =
% 0.94/1.58 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 0.94/1.58 { ! class_Rings_Oidom( X ), ! T = c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.58 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.94/1.58 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) )
% 0.94/1.58 }.
% 0.94/1.58 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y ),
% 0.94/1.58 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.94/1.58 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) )
% 0.94/1.58 }.
% 0.94/1.58 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 0.94/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Z =
% 0.94/1.58 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, T, Y ) }.
% 0.94/1.58 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.58 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.94/1.58 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) )
% 0.94/1.58 }.
% 0.94/1.58 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, T, Y ),
% 0.94/1.58 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.94/1.58 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) )
% 0.94/1.58 }.
% 0.94/1.58 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Z,
% 0.94/1.58 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.94/1.58 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.94/1.58 class_Groups_Ocancel__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.58 { class_Groups_Ocancel__comm__monoid__add( tc_Complex_Ocomplex ) }.
% 0.94/1.58 { class_Groups_Ocancel__comm__monoid__add( tc_RealDef_Oreal ) }.
% 0.94/1.58 { class_Groups_Ocancel__comm__monoid__add( tc_Nat_Onat ) }.
% 0.94/1.58 { class_Groups_Ocancel__comm__monoid__add( tc_Int_Oint ) }.
% 0.94/1.58 { ! class_Lattices_Oboolean__algebra( X ), class_Lattices_Oboolean__algebra
% 0.94/1.58 ( tc_fun( Y, X ) ) }.
% 0.94/1.58 { ! class_Orderings_Opreorder( X ), class_Orderings_Opreorder( tc_fun( Y, X
% 0.94/1.58 ) ) }.
% 0.94/1.58 { ! class_Orderings_Oorder( X ), class_Orderings_Oorder( tc_fun( Y, X ) ) }
% 0.94/1.58 .
% 0.94/1.58 { ! class_Orderings_Oord( X ), class_Orderings_Oord( tc_fun( Y, X ) ) }.
% 0.94/1.58 { ! class_Groups_Ouminus( X ), class_Groups_Ouminus( tc_fun( Y, X ) ) }.
% 0.94/1.58 { ! class_Groups_Ominus( X ), class_Groups_Ominus( tc_fun( Y, X ) ) }.
% 0.94/1.58 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.94/1.58 tc_Int_Oint ) }.
% 0.94/1.58 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.94/1.58 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Int_Oint ) }.
% 0.94/1.58 { class_Rings_Olinordered__comm__semiring__strict( tc_Int_Oint ) }.
% 0.94/1.58 { class_Rings_Olinordered__semiring__1__strict( tc_Int_Oint ) }.
% 0.94/1.58 { class_Rings_Olinordered__semiring__strict( tc_Int_Oint ) }.
% 0.94/1.58 { class_Groups_Oordered__ab__semigroup__add( tc_Int_Oint ) }.
% 0.94/1.58 { class_Groups_Oordered__ab__group__add__abs( tc_Int_Oint ) }.
% 0.94/1.58 { class_Groups_Oordered__comm__monoid__add( tc_Int_Oint ) }.
% 0.94/1.58 { class_Groups_Olinordered__ab__group__add( tc_Int_Oint ) }.
% 0.94/1.58 { class_Groups_Ocancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.94/1.58 { class_Rings_Oring__1__no__zero__divisors( tc_Int_Oint ) }.
% 0.94/1.58 { class_Rings_Oordered__cancel__semiring( tc_Int_Oint ) }.
% 0.94/1.58 { class_Rings_Olinordered__ring__strict( tc_Int_Oint ) }.
% 0.94/1.58 { class_Rings_Oring__no__zero__divisors( tc_Int_Oint ) }.
% 0.94/1.58 { class_Rings_Oordered__comm__semiring( tc_Int_Oint ) }.
% 0.94/1.58 { class_Rings_Olinordered__semiring__1( tc_Int_Oint ) }.
% 0.94/1.58 { class_Groups_Oordered__ab__group__add( tc_Int_Oint ) }.
% 0.94/1.58 { class_Groups_Ocancel__semigroup__add( tc_Int_Oint ) }.
% 0.94/1.58 { class_Rings_Olinordered__semiring( tc_Int_Oint ) }.
% 0.94/1.58 { class_Rings_Olinordered__semidom( tc_Int_Oint ) }.
% 0.94/1.58 { class_Groups_Oab__semigroup__mult( tc_Int_Oint ) }.
% 0.94/1.58 { class_Groups_Ocomm__monoid__mult( tc_Int_Oint ) }.
% 0.94/1.58 { class_Groups_Oab__semigroup__add( tc_Int_Oint ) }.
% 0.94/1.58 { class_Rings_Oordered__semiring( tc_Int_Oint ) }.
% 0.94/1.58 { class_Rings_Oordered__ring__abs( tc_Int_Oint ) }.
% 0.94/1.58 { class_Rings_Ono__zero__divisors( tc_Int_Oint ) }.
% 0.94/1.58 { class_Groups_Ocomm__monoid__add( tc_Int_Oint ) }.
% 0.94/1.58 { class_Rings_Olinordered__ring( tc_Int_Oint ) }.
% 0.94/1.58 { class_Rings_Olinordered__idom( tc_Int_Oint ) }.
% 0.94/1.58 { class_Rings_Ocomm__semiring__1( tc_Int_Oint ) }.
% 0.94/1.58 { class_Rings_Ocomm__semiring__0( tc_Int_Oint ) }.
% 0.94/1.58 { class_Rings_Ocomm__semiring( tc_Int_Oint ) }.
% 0.94/1.58 { class_Groups_Oab__group__add( tc_Int_Oint ) }.
% 0.94/1.58 { class_Rings_Ozero__neq__one( tc_Int_Oint ) }.
% 0.94/1.58 { class_Rings_Oordered__ring( tc_Int_Oint ) }.
% 0.94/1.58 { class_Orderings_Opreorder( tc_Int_Oint ) }.
% 0.94/1.58 { class_Orderings_Olinorder( tc_Int_Oint ) }.
% 0.94/1.58 { class_Groups_Omonoid__mult( tc_Int_Oint ) }.
% 0.94/1.58 { class_Rings_Ocomm__ring__1( tc_Int_Oint ) }.
% 0.94/1.58 { class_Groups_Omonoid__add( tc_Int_Oint ) }.
% 0.94/1.58 { class_Rings_Osemiring__0( tc_Int_Oint ) }.
% 0.94/1.58 { class_Groups_Ogroup__add( tc_Int_Oint ) }.
% 0.94/1.58 { class_Rings_Omult__zero( tc_Int_Oint ) }.
% 0.94/1.58 { class_Rings_Ocomm__ring( tc_Int_Oint ) }.
% 0.94/1.58 { class_Orderings_Oorder( tc_Int_Oint ) }.
% 0.94/1.58 { class_Int_Oring__char__0( tc_Int_Oint ) }.
% 0.94/1.58 { class_Rings_Osemiring( tc_Int_Oint ) }.
% 0.94/1.58 { class_Orderings_Oord( tc_Int_Oint ) }.
% 0.94/1.58 { class_Groups_Ouminus( tc_Int_Oint ) }.
% 0.94/1.58 { class_Groups_Osgn__if( tc_Int_Oint ) }.
% 0.94/1.58 { class_Groups_Oabs__if( tc_Int_Oint ) }.
% 0.94/1.58 { class_Rings_Oring__1( tc_Int_Oint ) }.
% 0.94/1.58 { class_Groups_Ominus( tc_Int_Oint ) }.
% 0.94/1.58 { class_Power_Opower( tc_Int_Oint ) }.
% 0.94/1.58 { class_Groups_Ozero( tc_Int_Oint ) }.
% 0.94/1.58 { class_Rings_Oring( tc_Int_Oint ) }.
% 0.94/1.58 { class_Rings_Oidom( tc_Int_Oint ) }.
% 0.94/1.58 { class_Groups_Oone( tc_Int_Oint ) }.
% 0.94/1.58 { class_Rings_Odvd( tc_Int_Oint ) }.
% 0.94/1.58 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.94/1.58 tc_Nat_Onat ) }.
% 0.94/1.58 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.94/1.58 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Nat_Onat ) }.
% 0.94/1.58 { class_Rings_Olinordered__comm__semiring__strict( tc_Nat_Onat ) }.
% 0.94/1.58 { class_Rings_Olinordered__semiring__strict( tc_Nat_Onat ) }.
% 0.94/1.58 { class_Groups_Oordered__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.94/1.58 { class_Groups_Oordered__comm__monoid__add( tc_Nat_Onat ) }.
% 0.94/1.58 { class_Groups_Ocancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.94/1.58 { class_Rings_Oordered__cancel__semiring( tc_Nat_Onat ) }.
% 0.94/1.58 { class_Rings_Oordered__comm__semiring( tc_Nat_Onat ) }.
% 0.94/1.58 { class_Groups_Ocancel__semigroup__add( tc_Nat_Onat ) }.
% 0.94/1.58 { class_Rings_Olinordered__semiring( tc_Nat_Onat ) }.
% 0.94/1.58 { class_Rings_Olinordered__semidom( tc_Nat_Onat ) }.
% 0.94/1.58 { class_Groups_Oab__semigroup__mult( tc_Nat_Onat ) }.
% 0.94/1.58 { class_Groups_Ocomm__monoid__mult( tc_Nat_Onat ) }.
% 0.94/1.58 { class_Groups_Oab__semigroup__add( tc_Nat_Onat ) }.
% 0.94/1.58 { class_Rings_Oordered__semiring( tc_Nat_Onat ) }.
% 0.94/1.58 { class_Rings_Ono__zero__divisors( tc_Nat_Onat ) }.
% 0.94/1.58 { class_Groups_Ocomm__monoid__add( tc_Nat_Onat ) }.
% 0.94/1.58 { class_Rings_Ocomm__semiring__1( tc_Nat_Onat ) }.
% 0.94/1.58 { class_Rings_Ocomm__semiring__0( tc_Nat_Onat ) }.
% 0.94/1.58 { class_Rings_Ocomm__semiring( tc_Nat_Onat ) }.
% 0.94/1.58 { class_Rings_Ozero__neq__one( tc_Nat_Onat ) }.
% 0.94/1.58 { class_Orderings_Opreorder( tc_Nat_Onat ) }.
% 0.94/1.58 { class_Orderings_Olinorder( tc_Nat_Onat ) }.
% 0.94/1.58 { class_Groups_Omonoid__mult( tc_Nat_Onat ) }.
% 0.94/1.58 { class_Groups_Omonoid__add( tc_Nat_Onat ) }.
% 0.94/1.58 { class_Rings_Osemiring__0( tc_Nat_Onat ) }.
% 0.94/1.58 { class_Rings_Omult__zero( tc_Nat_Onat ) }.
% 0.94/1.58 { class_Orderings_Oorder( tc_Nat_Onat ) }.
% 0.94/1.58 { class_Rings_Osemiring( tc_Nat_Onat ) }.
% 0.94/1.58 { class_Orderings_Oord( tc_Nat_Onat ) }.
% 0.94/1.58 { class_Groups_Ominus( tc_Nat_Onat ) }.
% 0.94/1.58 { class_Power_Opower( tc_Nat_Onat ) }.
% 0.94/1.58 { class_Groups_Ozero( tc_Nat_Onat ) }.
% 0.94/1.58 { class_Groups_Oone( tc_Nat_Onat ) }.
% 0.94/1.58 { class_Rings_Odvd( tc_Nat_Onat ) }.
% 0.94/1.58 { class_Lattices_Oboolean__algebra( tc_HOL_Obool ) }.
% 0.94/1.58 { class_Orderings_Opreorder( tc_HOL_Obool ) }.
% 0.94/1.58 { class_Orderings_Oorder( tc_HOL_Obool ) }.
% 0.94/1.58 { class_Orderings_Oord( tc_HOL_Obool ) }.
% 0.94/1.58 { class_Groups_Ouminus( tc_HOL_Obool ) }.
% 0.94/1.58 { class_Groups_Ominus( tc_HOL_Obool ) }.
% 0.94/1.58 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.94/1.58 tc_RealDef_Oreal ) }.
% 0.94/1.58 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.94/1.58 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_RealDef_Oreal ) }
% 0.94/1.58 .
% 0.94/1.58 { class_Rings_Olinordered__comm__semiring__strict( tc_RealDef_Oreal ) }.
% 0.94/1.58 { class_Fields_Olinordered__field__inverse__zero( tc_RealDef_Oreal ) }.
% 0.94/1.58 { class_Rings_Olinordered__semiring__1__strict( tc_RealDef_Oreal ) }.
% 0.94/1.58 { class_RealVector_Oreal__normed__div__algebra( tc_RealDef_Oreal ) }.
% 0.94/1.58 { class_Rings_Olinordered__semiring__strict( tc_RealDef_Oreal ) }.
% 0.94/1.58 { class_Rings_Odivision__ring__inverse__zero( tc_RealDef_Oreal ) }.
% 0.94/1.58 { class_RealVector_Oreal__normed__algebra__1( tc_RealDef_Oreal ) }.
% 0.94/1.58 { class_Groups_Oordered__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.94/1.58 { class_Groups_Oordered__ab__group__add__abs( tc_RealDef_Oreal ) }.
% 0.94/1.58 { class_RealVector_Oreal__normed__algebra( tc_RealDef_Oreal ) }.
% 0.94/1.58 { class_Groups_Oordered__comm__monoid__add( tc_RealDef_Oreal ) }.
% 0.94/1.58 { class_Groups_Olinordered__ab__group__add( tc_RealDef_Oreal ) }.
% 0.94/1.58 { class_Groups_Ocancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.94/1.58 { class_Rings_Oring__1__no__zero__divisors( tc_RealDef_Oreal ) }.
% 0.94/1.58 { class_Rings_Oordered__cancel__semiring( tc_RealDef_Oreal ) }.
% 0.94/1.58 { class_RealVector_Oreal__normed__vector( tc_RealDef_Oreal ) }.
% 0.94/1.58 { class_Rings_Olinordered__ring__strict( tc_RealDef_Oreal ) }.
% 0.94/1.58 { class_Rings_Oring__no__zero__divisors( tc_RealDef_Oreal ) }.
% 0.94/1.58 { class_Rings_Oordered__comm__semiring( tc_RealDef_Oreal ) }.
% 0.94/1.58 { class_Rings_Olinordered__semiring__1( tc_RealDef_Oreal ) }.
% 0.94/1.58 { class_RealVector_Oreal__div__algebra( tc_RealDef_Oreal ) }.
% 0.94/1.58 { class_Groups_Oordered__ab__group__add( tc_RealDef_Oreal ) }.
% 0.94/1.58 { class_Groups_Ocancel__semigroup__add( tc_RealDef_Oreal ) }.
% 0.94/1.58 { class_Rings_Olinordered__semiring( tc_RealDef_Oreal ) }.
% 0.94/1.58 { class_RealVector_Oreal__algebra__1( tc_RealDef_Oreal ) }.
% 0.94/1.58 { class_Fields_Ofield__inverse__zero( tc_RealDef_Oreal ) }.
% 0.94/1.58 { class_Rings_Olinordered__semidom( tc_RealDef_Oreal ) }.
% 0.94/1.58 { class_Groups_Oab__semigroup__mult( tc_RealDef_Oreal ) }.
% 0.94/1.58 { class_Groups_Ocomm__monoid__mult( tc_RealDef_Oreal ) }.
% 0.94/1.58 { class_Groups_Oab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.94/1.58 { class_Fields_Olinordered__field( tc_RealDef_Oreal ) }.
% 0.94/1.58 { class_Rings_Oordered__semiring( tc_RealDef_Oreal ) }.
% 0.94/1.58 { class_Rings_Oordered__ring__abs( tc_RealDef_Oreal ) }.
% 0.94/1.58 { class_Rings_Ono__zero__divisors( tc_RealDef_Oreal ) }.
% 0.94/1.58 { class_Groups_Ocomm__monoid__add( tc_RealDef_Oreal ) }.
% 0.94/1.58 { class_Rings_Olinordered__ring( tc_RealDef_Oreal ) }.
% 0.94/1.58 { class_Rings_Olinordered__idom( tc_RealDef_Oreal ) }.
% 0.94/1.58 { class_Rings_Ocomm__semiring__1( tc_RealDef_Oreal ) }.
% 0.94/1.58 { class_Rings_Ocomm__semiring__0( tc_RealDef_Oreal ) }.
% 0.94/1.58 { class_Rings_Odivision__ring( tc_RealDef_Oreal ) }.
% 0.94/1.58 { class_Rings_Ocomm__semiring( tc_RealDef_Oreal ) }.
% 0.94/1.58 { class_Groups_Oab__group__add( tc_RealDef_Oreal ) }.
% 0.94/1.58 { class_Rings_Ozero__neq__one( tc_RealDef_Oreal ) }.
% 0.94/1.58 { class_Rings_Oordered__ring( tc_RealDef_Oreal ) }.
% 0.94/1.58 { class_Orderings_Opreorder( tc_RealDef_Oreal ) }.
% 0.94/1.58 { class_Orderings_Olinorder( tc_RealDef_Oreal ) }.
% 0.94/1.58 { class_Groups_Omonoid__mult( tc_RealDef_Oreal ) }.
% 0.94/1.58 { class_Rings_Ocomm__ring__1( tc_RealDef_Oreal ) }.
% 0.94/1.58 { class_Groups_Omonoid__add( tc_RealDef_Oreal ) }.
% 0.94/1.58 { class_Rings_Osemiring__0( tc_RealDef_Oreal ) }.
% 0.94/1.58 { class_Groups_Ogroup__add( tc_RealDef_Oreal ) }.
% 0.94/1.58 { class_Rings_Omult__zero( tc_RealDef_Oreal ) }.
% 0.94/1.58 { class_Rings_Ocomm__ring( tc_RealDef_Oreal ) }.
% 0.94/1.58 { class_Orderings_Oorder( tc_RealDef_Oreal ) }.
% 0.94/1.58 { class_Int_Oring__char__0( tc_RealDef_Oreal ) }.
% 0.94/1.58 { class_Rings_Osemiring( tc_RealDef_Oreal ) }.
% 0.94/1.58 { class_Orderings_Oord( tc_RealDef_Oreal ) }.
% 0.94/1.58 { class_Groups_Ouminus( tc_RealDef_Oreal ) }.
% 0.94/1.58 { class_Groups_Osgn__if( tc_RealDef_Oreal ) }.
% 0.94/1.58 { class_Groups_Oabs__if( tc_RealDef_Oreal ) }.
% 0.94/1.58 { class_Rings_Oring__1( tc_RealDef_Oreal ) }.
% 0.94/1.58 { class_Groups_Ominus( tc_RealDef_Oreal ) }.
% 0.94/1.58 { class_Fields_Ofield( tc_RealDef_Oreal ) }.
% 0.94/1.58 { class_Power_Opower( tc_RealDef_Oreal ) }.
% 0.94/1.58 { class_Groups_Ozero( tc_RealDef_Oreal ) }.
% 0.94/1.58 { class_Rings_Oring( tc_RealDef_Oreal ) }.
% 0.94/1.58 { class_Rings_Oidom( tc_RealDef_Oreal ) }.
% 0.94/1.58 { class_Groups_Oone( tc_RealDef_Oreal ) }.
% 0.94/1.58 { class_Rings_Odvd( tc_RealDef_Oreal ) }.
% 0.94/1.58 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.94/1.58 tc_Complex_Ocomplex ) }.
% 0.94/1.58 { class_RealVector_Oreal__normed__div__algebra( tc_Complex_Ocomplex ) }.
% 0.94/1.58 { class_Rings_Odivision__ring__inverse__zero( tc_Complex_Ocomplex ) }.
% 0.94/1.58 { class_RealVector_Oreal__normed__algebra__1( tc_Complex_Ocomplex ) }.
% 0.94/1.58 { class_RealVector_Oreal__normed__algebra( tc_Complex_Ocomplex ) }.
% 0.94/1.58 { class_Groups_Ocancel__ab__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.94/1.58 { class_Rings_Oring__1__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.94/1.58 { class_RealVector_Oreal__normed__vector( tc_Complex_Ocomplex ) }.
% 0.94/1.58 { class_Rings_Oring__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.94/1.58 { class_RealVector_Oreal__div__algebra( tc_Complex_Ocomplex ) }.
% 0.94/1.58 { class_Groups_Ocancel__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.94/1.58 { class_RealVector_Oreal__algebra__1( tc_Complex_Ocomplex ) }.
% 0.94/1.58 { class_Fields_Ofield__inverse__zero( tc_Complex_Ocomplex ) }.
% 0.94/1.58 { class_Groups_Oab__semigroup__mult( tc_Complex_Ocomplex ) }.
% 0.94/1.58 { class_Groups_Ocomm__monoid__mult( tc_Complex_Ocomplex ) }.
% 0.94/1.58 { class_Groups_Oab__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.94/1.58 { class_Rings_Ono__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.94/1.58 { class_Groups_Ocomm__monoid__add( tc_Complex_Ocomplex ) }.
% 0.94/1.58 { class_Rings_Ocomm__semiring__1( tc_Complex_Ocomplex ) }.
% 0.94/1.58 { class_Rings_Ocomm__semiring__0( tc_Complex_Ocomplex ) }.
% 0.94/1.58 { class_Rings_Odivision__ring( tc_Complex_Ocomplex ) }.
% 0.94/1.58 { class_Rings_Ocomm__semiring( tc_Complex_Ocomplex ) }.
% 0.94/1.58 { class_Groups_Oab__group__add( tc_Complex_Ocomplex ) }.
% 0.94/1.58 { class_Rings_Ozero__neq__one( tc_Complex_Ocomplex ) }.
% 0.94/1.58 { class_Groups_Omonoid__mult( tc_Complex_Ocomplex ) }.
% 0.94/1.58 { class_Rings_Ocomm__ring__1( tc_Complex_Ocomplex ) }.
% 0.94/1.58 { class_Groups_Omonoid__add( tc_Complex_Ocomplex ) }.
% 0.94/1.58 { class_Rings_Osemiring__0( tc_Complex_Ocomplex ) }.
% 0.94/1.58 { class_Groups_Ogroup__add( tc_Complex_Ocomplex ) }.
% 0.94/1.58 { class_Rings_Omult__zero( tc_Complex_Ocomplex ) }.
% 0.94/1.58 { class_Rings_Ocomm__ring( tc_Complex_Ocomplex ) }.
% 0.94/1.58 { class_Int_Oring__char__0( tc_Complex_Ocomplex ) }.
% 0.94/1.58 { class_Rings_Osemiring( tc_Complex_Ocomplex ) }.
% 0.94/1.58 { class_Groups_Ouminus( tc_Complex_Ocomplex ) }.
% 0.94/1.58 { class_Rings_Oring__1( tc_Complex_Ocomplex ) }.
% 0.94/1.58 { class_Groups_Ominus( tc_Complex_Ocomplex ) }.
% 0.94/1.58 { class_Fields_Ofield( tc_Complex_Ocomplex ) }.
% 0.94/1.58 { class_Power_Opower( tc_Complex_Ocomplex ) }.
% 0.94/1.58 { class_Groups_Ozero( tc_Complex_Ocomplex ) }.
% 0.94/1.58 { class_Rings_Oring( tc_Complex_Ocomplex ) }.
% 0.94/1.58 { class_Rings_Oidom( tc_Complex_Ocomplex ) }.
% 0.94/1.58 { class_Groups_Oone( tc_Complex_Ocomplex ) }.
% 0.94/1.58 { class_Rings_Odvd( tc_Complex_Ocomplex ) }.
% 0.94/1.58 { ! class_Rings_Oidom( X ),
% 0.94/1.58 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.94/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.58 { ! class_Rings_Olinordered__idom( X ),
% 0.94/1.58 class_Groups_Oordered__cancel__ab__semigroup__add( tc_Polynomial_Opoly( X
% 0.94/1.58 ) ) }.
% 0.94/1.58 { ! class_Rings_Olinordered__idom( X ),
% 0.94/1.58 class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Polynomial_Opoly(
% 0.94/1.58 X ) ) }.
% 0.94/1.58 { ! class_Rings_Olinordered__idom( X ),
% 0.94/1.58 class_Rings_Olinordered__comm__semiring__strict( tc_Polynomial_Opoly( X )
% 0.94/1.58 ) }.
% 0.94/1.58 { ! class_Rings_Olinordered__idom( X ),
% 0.94/1.58 class_Rings_Olinordered__semiring__1__strict( tc_Polynomial_Opoly( X ) )
% 0.94/1.58 }.
% 0.94/1.58 { ! class_Rings_Olinordered__idom( X ),
% 0.94/1.58 class_Rings_Olinordered__semiring__strict( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.58 { ! class_Rings_Olinordered__idom( X ),
% 0.94/1.58 class_Groups_Oordered__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.58 { ! class_Rings_Olinordered__idom( X ),
% 0.94/1.58 class_Groups_Oordered__ab__group__add__abs( tc_Polynomial_Opoly( X ) ) }
% 0.94/1.58 .
% 0.94/1.58 { ! class_Rings_Olinordered__idom( X ),
% 0.94/1.58 class_Groups_Oordered__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.58 { ! class_Rings_Olinordered__idom( X ),
% 0.94/1.58 class_Groups_Olinordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.58 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.94/1.58 class_Groups_Ocancel__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.58 { ! class_Rings_Oidom( X ), class_Rings_Oring__1__no__zero__divisors(
% 0.94/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.58 { ! class_Rings_Olinordered__idom( X ),
% 0.94/1.58 class_Rings_Oordered__cancel__semiring( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.58 { ! class_Rings_Olinordered__idom( X ),
% 0.94/1.58 class_Rings_Olinordered__ring__strict( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.58 { ! class_Rings_Oidom( X ), class_Rings_Oring__no__zero__divisors(
% 0.94/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.58 { ! class_Rings_Olinordered__idom( X ),
% 0.94/1.58 class_Rings_Oordered__comm__semiring( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.58 { ! class_Rings_Olinordered__idom( X ),
% 0.94/1.58 class_Rings_Olinordered__semiring__1( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.58 { ! class_Rings_Olinordered__idom( X ),
% 0.94/1.58 class_Groups_Oordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.58 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.94/1.58 class_Groups_Ocancel__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.58 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semiring(
% 0.94/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.58 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semidom(
% 0.94/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.58 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Oab__semigroup__mult
% 0.94/1.58 ( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.58 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Ocomm__monoid__mult(
% 0.94/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.58 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Oab__semigroup__add
% 0.94/1.58 ( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.58 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__semiring(
% 0.94/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.58 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__ring__abs(
% 0.94/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.58 { ! class_Rings_Oidom( X ), class_Rings_Ono__zero__divisors(
% 0.94/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.58 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Ocomm__monoid__add(
% 0.94/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.58 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__ring(
% 0.94/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.58 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__idom(
% 0.94/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.58 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ocomm__semiring__1(
% 0.94/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.58 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring__0(
% 0.94/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.58 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring(
% 0.94/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.58 { ! class_Groups_Oab__group__add( X ), class_Groups_Oab__group__add(
% 0.94/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.58 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ozero__neq__one(
% 0.94/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.58 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__ring(
% 0.94/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.58 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Opreorder(
% 0.94/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.58 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Olinorder(
% 0.94/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.58 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Omonoid__mult(
% 0.94/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.58 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Ocomm__ring__1(
% 0.94/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.58 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Omonoid__add(
% 0.94/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.58 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring__0(
% 0.94/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.58 { ! class_Groups_Oab__group__add( X ), class_Groups_Ogroup__add(
% 0.94/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.58 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Omult__zero(
% 0.94/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.58 { ! class_Rings_Ocomm__ring( X ), class_Rings_Ocomm__ring(
% 0.94/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.58 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oorder(
% 0.94/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.58 { ! class_Rings_Olinordered__idom( X ), class_Int_Oring__char__0(
% 0.94/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.58 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring(
% 0.94/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.58 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oord(
% 0.94/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.58 { ! class_Groups_Oab__group__add( X ), class_Groups_Ouminus(
% 0.94/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.58 { ! class_Rings_Olinordered__idom( X ), class_Groups_Osgn__if(
% 0.94/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.58 { ! class_Rings_Olinordered__idom( X ), class_Groups_Oabs__if(
% 0.94/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.58 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Oring__1(
% 0.94/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.58 { ! class_Groups_Oab__group__add( X ), class_Groups_Ominus(
% 0.94/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.58 { ! class_Rings_Ocomm__semiring__1( X ), class_Power_Opower(
% 0.94/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.58 { ! class_Groups_Ozero( X ), class_Groups_Ozero( tc_Polynomial_Opoly( X ) )
% 0.94/1.58 }.
% 0.94/1.58 { ! class_Rings_Ocomm__ring( X ), class_Rings_Oring( tc_Polynomial_Opoly( X
% 0.94/1.58 ) ) }.
% 0.94/1.58 { ! class_Rings_Oidom( X ), class_Rings_Oidom( tc_Polynomial_Opoly( X ) ) }
% 0.94/1.58 .
% 0.94/1.58 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Oone(
% 0.94/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.58 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Odvd(
% 0.94/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.58 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.94/1.58 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.94/1.58 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), v_t____ ), v_k____ ) )
% 0.94/1.58 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), v_t____
% 0.94/1.58 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP(
% 0.94/1.58 hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.94/1.58 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, v_w____ ) ),
% 0.94/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, v_k____,
% 0.94/1.58 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ), v_m____ ) ) ), hAPP( hAPP
% 0.94/1.58 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.94/1.58 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), v_t____ ), v_k____ ) )
% 0.94/1.58 , c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) }.
% 0.94/1.58
% 0.94/1.58 *** allocated 15000 integers for clauses
% 0.94/1.58 *** allocated 22500 integers for clauses
% 0.94/1.58 *** allocated 33750 integers for clauses
% 0.94/1.58 *** allocated 50625 integers for clauses
% 0.94/1.58 *** allocated 75937 integers for clauses
% 0.94/1.58 *** allocated 113905 integers for clauses
% 0.94/1.58 percentage equality = 0.260452, percentage horn = 0.928198
% 0.94/1.58 This is a problem with some equality
% 0.94/1.58
% 0.94/1.58
% 0.94/1.58
% 0.94/1.58 Options Used:
% 0.94/1.58
% 0.94/1.58 useres = 1
% 0.94/1.58 useparamod = 1
% 0.94/1.58 useeqrefl = 1
% 0.94/1.58 useeqfact = 1
% 0.94/1.58 usefactor = 1
% 0.94/1.58 usesimpsplitting = 0
% 0.94/1.58 usesimpdemod = 5
% 0.94/1.58 usesimpres = 3
% 0.94/1.58
% 0.94/1.58 resimpinuse = 1000
% 0.94/1.58 resimpclauses = 20000
% 0.94/1.58 substype = eqrewr
% 0.94/1.58 backwardsubs = 1
% 0.94/1.58 selectoldest = 5
% 0.94/1.58
% 0.94/1.58 litorderings [0] = split
% 0.94/1.58 litorderings [1] = extend the termordering, first sorting on arguments
% 0.94/1.58
% 0.94/1.58 termordering = kbo
% 0.94/1.58
% 0.94/1.58 litapriori = 0
% 0.94/1.58 termapriori = 1
% 0.94/1.58 litaposteriori = 0
% 0.94/1.58 termaposteriori = 0
% 0.94/1.58 demodaposteriori = 0
% 0.94/1.58 ordereqreflfact = 0
% 0.94/1.58
% 0.94/1.58 litselect = negord
% 0.94/1.58
% 0.94/1.58 maxweight = 15
% 0.94/1.58 maxdepth = 30000
% 0.94/1.58 maxlength = 115
% 0.94/1.58 maxnrvars = 195
% 0.94/1.58 excuselevel = 1
% 0.94/1.58 increasemaxweight = 1
% 0.94/1.58
% 0.94/1.58 maxselected = 10000000
% 0.94/1.58 maxnrclauses = 10000000
% 0.94/1.58
% 0.94/1.58 showgenerated = 0
% 0.94/1.58 showkept = 0
% 0.94/1.58 showselected = 0
% 0.94/1.58 showdeleted = 0
% 0.94/1.58 showresimp = 1
% 0.94/1.58 showstatus = 2000
% 0.94/1.58
% 0.94/1.58 prologoutput = 0
% 0.94/1.58 nrgoals = 5000000
% 0.94/1.58 totalproof = 1
% 0.94/1.58
% 0.94/1.58 Symbols occurring in the translation:
% 0.94/1.58
% 0.94/1.58 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.94/1.58 . [1, 2] (w:1, o:223, a:1, s:1, b:0),
% 0.94/1.58 ! [4, 1] (w:0, o:126, a:1, s:1, b:0),
% 0.94/1.58 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.94/1.58 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.94/1.58 hAPP [38, 2] (w:1, o:247, a:1, s:1, b:0),
% 0.94/1.58 tc_RealDef_Oreal [39, 0] (w:1, o:27, a:1, s:1, b:0),
% 0.94/1.58 c_Groups_Ozero__class_Ozero [40, 1] (w:1, o:131, a:1, s:1, b:0),
% 0.94/1.58 v_t____ [41, 0] (w:1, o:29, a:1, s:1, b:0),
% 0.94/1.58 c_Orderings_Oord__class_Oless [42, 3] (w:1, o:270, a:1, s:1, b:0),
% 0.94/1.58 c_Groups_Oone__class_Oone [43, 1] (w:1, o:132, a:1, s:1, b:0),
% 0.94/1.58 v_m____ [44, 0] (w:1, o:30, a:1, s:1, b:0),
% 0.94/1.58 v_k____ [45, 0] (w:1, o:31, a:1, s:1, b:0),
% 0.94/1.58 tc_Nat_Onat [46, 0] (w:1, o:32, a:1, s:1, b:0),
% 0.94/1.58 c_Power_Opower__class_Opower [47, 1] (w:1, o:133, a:1, s:1, b:0),
% 0.94/1.58 c_Groups_Otimes__class_Otimes [48, 1] (w:1, o:134, a:1, s:1, b:0),
% 0.94/1.58 tc_Complex_Ocomplex [49, 0] (w:1, o:33, a:1, s:1, b:0),
% 0.94/1.58 v_w____ [50, 0] (w:1, o:34, a:1, s:1, b:0),
% 0.94/1.58 c_RealVector_Onorm__class_Onorm [51, 2] (w:1, o:248, a:1, s:1, b:0),
% 0.94/1.58
% 0.94/1.58 c_Groups_Oplus__class_Oplus [52, 3] (w:1, o:273, a:1, s:1, b:0),
% 0.94/1.58 c_Rings_Oinverse__class_Oinverse [53, 2] (w:1, o:249, a:1, s:1, b:0)
% 0.94/1.58 ,
% 0.94/1.58 c_Orderings_Oord__class_Oless__eq [54, 3] (w:1, o:274, a:1, s:1, b:0)
% 0.94/1.58 ,
% 0.94/1.58 class_Rings_Olinordered__semidom [58, 1] (w:1, o:137, a:1, s:1, b:0)
% 0.94/1.58 ,
% 0.94/1.58 class_RealVector_Oreal__normed__algebra [65, 1] (w:1, o:138, a:1, s:1
% 0.94/1.58 , b:0),
% 0.94/1.58 class_RealVector_Oreal__normed__vector [67, 1] (w:1, o:139, a:1, s:1
% 0.94/1.58 , b:0),
% 0.94/1.58 class_Rings_Olinordered__ring [69, 1] (w:1, o:135, a:1, s:1, b:0),
% 0.94/1.58 class_Rings_Olinordered__ring__strict [71, 1] (w:1, o:136, a:1, s:1
% 0.94/1.58 , b:0),
% 0.94/1.58 v_a____ [72, 0] (w:1, o:78, a:1, s:1, b:0),
% 0.94/1.58 class_Rings_Odivision__ring__inverse__zero [75, 1] (w:1, o:145, a:1
% 0.94/1.58 , s:1, b:0),
% 0.94/1.58 class_RealVector_Oreal__normed__div__algebra [76, 1] (w:1, o:146, a:1
% 0.94/1.58 , s:1, b:0),
% 0.94/1.58 class_Rings_Odivision__ring [83, 1] (w:1, o:147, a:1, s:1, b:0),
% 0.94/1.58 class_Groups_Omonoid__mult [84, 1] (w:1, o:153, a:1, s:1, b:0),
% 0.94/1.58 class_Rings_Oordered__cancel__semiring [85, 1] (w:1, o:157, a:1, s:1
% 0.94/1.58 , b:0),
% 0.94/1.58 class_Rings_Oordered__ring [86, 1] (w:1, o:158, a:1, s:1, b:0),
% 0.94/1.58 class_Rings_Oordered__semiring [89, 1] (w:1, o:160, a:1, s:1, b:0),
% 0.94/1.58 class_Rings_Oordered__comm__semiring [90, 1] (w:1, o:161, a:1, s:1
% 0.94/1.58 , b:0),
% 0.94/1.58 class_Power_Opower [91, 1] (w:1, o:166, a:1, s:1, b:0),
% 0.94/1.58 class_Rings_Olinordered__semiring__strict [92, 1] (w:1, o:167, a:1
% 0.94/1.58 , s:1, b:0),
% 0.94/1.58 class_Rings_Olinordered__semiring [93, 1] (w:1, o:168, a:1, s:1, b:0)
% 0.94/1.58 ,
% 0.94/1.58 class_Rings_Olinordered__idom [95, 1] (w:1, o:169, a:1, s:1, b:0),
% 0.94/1.58 class_RealVector_Oreal__normed__algebra__1 [96, 1] (w:1, o:170, a:1
% 0.94/1.58 , s:1, b:0),
% 0.94/1.58 class_Rings_Olinordered__semiring__1 [99, 1] (w:1, o:171, a:1, s:1
% 0.94/1.58 , b:0),
% 0.94/1.58 class_Rings_Olinordered__semiring__1__strict [100, 1] (w:1, o:172, a:
% 0.94/1.58 1, s:1, b:0),
% 0.94/1.58 class_Rings_Ono__zero__divisors [101, 1] (w:1, o:156, a:1, s:1, b:0)
% 0.94/1.58 ,
% 0.94/1.58 class_Rings_Oring__no__zero__divisors [102, 1] (w:1, o:173, a:1, s:1
% 0.94/1.58 , b:0),
% 0.94/1.58 class_Rings_Omult__zero [103, 1] (w:1, o:155, a:1, s:1, b:0),
% 0.94/1.58 class_Rings_Ozero__neq__one [104, 1] (w:1, o:174, a:1, s:1, b:0),
% 0.94/1.58 class_Rings_Osemiring [106, 1] (w:1, o:178, a:1, s:1, b:0),
% 0.94/1.58 class_Rings_Ocomm__semiring [109, 1] (w:1, o:142, a:1, s:1, b:0),
% 0.94/1.58 class_Rings_Oring__1__no__zero__divisors [112, 1] (w:1, o:175, a:1
% 0.94/1.58 , s:1, b:0),
% 0.94/1.58 class_Groups_Ocomm__monoid__mult [113, 1] (w:1, o:179, a:1, s:1, b:0)
% 0.94/1.58 ,
% 0.94/1.58 class_Rings_Olinordered__comm__semiring__strict [114, 1] (w:1, o:154
% 0.94/1.58 , a:1, s:1, b:0),
% 0.94/1.58 class_Rings_Osemiring__0 [115, 1] (w:1, o:180, a:1, s:1, b:0),
% 0.94/1.58 class_Fields_Olinordered__field [118, 1] (w:1, o:148, a:1, s:1, b:0)
% 0.94/1.58 ,
% 0.94/1.58 class_Fields_Olinordered__field__inverse__zero [119, 1] (w:1, o:149
% 0.94/1.58 , a:1, s:1, b:0),
% 0.94/1.58 hBOOL [130, 1] (w:1, o:181, a:1, s:1, b:0),
% 0.94/1.58 class_Fields_Ofield__inverse__zero [135, 1] (w:1, o:150, a:1, s:1, b:
% 0.94/1.58 0),
% 0.94/1.58 class_Fields_Ofield [136, 1] (w:1, o:151, a:1, s:1, b:0),
% 0.94/1.58 c_Groups_Ominus__class_Ominus [138, 3] (w:1, o:275, a:1, s:1, b:0),
% 0.94/1.58 c_Groups_Ouminus__class_Ouminus [139, 2] (w:1, o:251, a:1, s:1, b:0)
% 0.94/1.58 ,
% 0.94/1.58 c_RealVector_Oof__real [140, 2] (w:1, o:252, a:1, s:1, b:0),
% 0.94/1.58 class_Groups_Oordered__comm__monoid__add [141, 1] (w:1, o:182, a:1
% 0.94/1.58 , s:1, b:0),
% 0.94/1.58 class_Groups_Ogroup__add [142, 1] (w:1, o:183, a:1, s:1, b:0),
% 0.94/1.58 class_Groups_Oab__group__add [143, 1] (w:1, o:184, a:1, s:1, b:0),
% 0.94/1.58 class_Groups_Olinordered__ab__group__add [144, 1] (w:1, o:152, a:1
% 0.94/1.58 , s:1, b:0),
% 0.94/1.58 class_Groups_Oordered__ab__group__add [146, 1] (w:1, o:185, a:1, s:1
% 0.94/1.58 , b:0),
% 0.94/1.58 class_RealVector_Oreal__algebra__1 [147, 1] (w:1, o:186, a:1, s:1, b:
% 0.94/1.58 0),
% 0.94/1.58 class_Rings_Oidom [148, 1] (w:1, o:187, a:1, s:1, b:0),
% 0.94/1.58 class_Rings_Oring [149, 1] (w:1, o:176, a:1, s:1, b:0),
% 0.94/1.58 class_RealVector_Oreal__div__algebra [151, 1] (w:1, o:188, a:1, s:1
% 0.94/1.58 , b:0),
% 0.94/1.58 class_Rings_Oring__1 [152, 1] (w:1, o:177, a:1, s:1, b:0),
% 0.94/1.58 class_Groups_Ozero [153, 1] (w:1, o:189, a:1, s:1, b:0),
% 0.94/1.58 class_Groups_Oab__semigroup__mult [154, 1] (w:1, o:190, a:1, s:1, b:0
% 0.94/1.58 ),
% 0.94/1.58 class_Groups_Ocancel__semigroup__add [155, 1] (w:1, o:191, a:1, s:1
% 0.94/1.58 , b:0),
% 0.94/1.58 class_Groups_Ocancel__ab__semigroup__add [156, 1] (w:1, o:192, a:1
% 0.94/1.58 , s:1, b:0),
% 0.94/1.58 class_Groups_Oab__semigroup__add [157, 1] (w:1, o:193, a:1, s:1, b:0)
% 0.94/1.58 ,
% 0.94/1.58 class_Groups_Oone [158, 1] (w:1, o:194, a:1, s:1, b:0),
% 0.94/1.58 class_Groups_Ocomm__monoid__add [159, 1] (w:1, o:195, a:1, s:1, b:0)
% 0.94/1.58 ,
% 0.94/1.58 class_Groups_Omonoid__add [160, 1] (w:1, o:196, a:1, s:1, b:0),
% 0.94/1.58 class_Groups_Oordered__ab__semigroup__add__imp__le [161, 1] (w:1, o:
% 0.94/1.58 197, a:1, s:1, b:0),
% 0.94/1.58 class_Groups_Oordered__ab__semigroup__add [162, 1] (w:1, o:198, a:1
% 0.94/1.58 , s:1, b:0),
% 0.94/1.58 class_Groups_Oordered__cancel__ab__semigroup__add [163, 1] (w:1, o:
% 0.94/1.58 199, a:1, s:1, b:0),
% 0.94/1.58 class_Rings_Ocomm__semiring__1 [167, 1] (w:1, o:144, a:1, s:1, b:0),
% 0.94/1.58
% 0.94/1.58 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct [
% 0.94/1.58 176, 1] (w:1, o:201, a:1, s:1, b:0),
% 0.94/1.58 class_Rings_Ocomm__ring__1 [178, 1] (w:1, o:140, a:1, s:1, b:0),
% 0.94/1.58 c_Groups_Oabs__class_Oabs [179, 2] (w:1, o:253, a:1, s:1, b:0),
% 0.94/1.58 v_s____ [180, 0] (w:1, o:28, a:1, s:1, b:0),
% 0.94/1.58 c_Polynomial_Opoly [181, 2] (w:1, o:254, a:1, s:1, b:0),
% 0.94/1.58 v_p [182, 0] (w:1, o:107, a:1, s:1, b:0),
% 3.46/3.85 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant [183, 3] (w:1
% 3.46/3.85 , o:271, a:1, s:1, b:0),
% 3.46/3.85 class_Groups_Oordered__ab__group__add__abs [184, 1] (w:1, o:202, a:1
% 3.46/3.85 , s:1, b:0),
% 3.46/3.85 class_Rings_Oordered__ring__abs [186, 1] (w:1, o:159, a:1, s:1, b:0)
% 3.46/3.85 ,
% 3.46/3.85 class_Groups_Oabs__if [187, 1] (w:1, o:203, a:1, s:1, b:0),
% 3.46/3.85 v_pa____ [189, 0] (w:1, o:108, a:1, s:1, b:0),
% 3.46/3.85 tc_Int_Oint [190, 0] (w:1, o:110, a:1, s:1, b:0),
% 3.46/3.85 c_Complex_Oii [194, 0] (w:1, o:113, a:1, s:1, b:0),
% 3.46/3.85 v_c____ [195, 0] (w:1, o:114, a:1, s:1, b:0),
% 3.46/3.85 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize [196, 2] (w:1, o:
% 3.46/3.85 250, a:1, s:1, b:0),
% 3.46/3.85 tc_Polynomial_Opoly [200, 1] (w:1, o:213, a:1, s:1, b:0),
% 3.46/3.85 v_q____ [201, 0] (w:1, o:116, a:1, s:1, b:0),
% 3.46/3.85 c_Polynomial_Osmult [203, 3] (w:1, o:276, a:1, s:1, b:0),
% 3.46/3.85 c_Polynomial_OpCons [204, 3] (w:1, o:278, a:1, s:1, b:0),
% 3.46/3.85 class_Rings_Ocomm__semiring__0 [207, 1] (w:1, o:143, a:1, s:1, b:0),
% 3.46/3.85
% 3.46/3.85 c_Polynomial_Omonom [208, 3] (w:1, o:279, a:1, s:1, b:0),
% 3.46/3.85 class_Int_Oring__char__0 [210, 1] (w:1, o:214, a:1, s:1, b:0),
% 3.46/3.85 class_Rings_Ocomm__ring [211, 1] (w:1, o:141, a:1, s:1, b:0),
% 3.46/3.85 c_Polynomial_Osynthetic__div [212, 3] (w:1, o:280, a:1, s:1, b:0),
% 3.46/3.85 c_Polynomial_Opcompose [213, 3] (w:1, o:281, a:1, s:1, b:0),
% 3.46/3.85 c_Polynomial_Oorder [214, 3] (w:1, o:277, a:1, s:1, b:0),
% 3.46/3.85 class_Orderings_Opreorder [215, 1] (w:1, o:164, a:1, s:1, b:0),
% 3.46/3.85 class_Orderings_Oord [216, 1] (w:1, o:162, a:1, s:1, b:0),
% 3.46/3.85 tc_fun [217, 2] (w:1, o:263, a:1, s:1, b:0),
% 3.46/3.85 class_Orderings_Olinorder [218, 1] (w:1, o:165, a:1, s:1, b:0),
% 3.46/3.85 class_Orderings_Oorder [219, 1] (w:1, o:163, a:1, s:1, b:0),
% 3.46/3.85 c_RComplete_Onatceiling [221, 1] (w:1, o:215, a:1, s:1, b:0),
% 3.46/3.85 c_Power_Opower_Opower [222, 3] (w:1, o:282, a:1, s:1, b:0),
% 3.46/3.85 c_RComplete_Onatfloor [228, 1] (w:1, o:216, a:1, s:1, b:0),
% 3.46/3.85 c_Nat__Transfer_Otsub [229, 2] (w:1, o:264, a:1, s:1, b:0),
% 3.46/3.85 c_RealDef_Oreal [230, 2] (w:1, o:265, a:1, s:1, b:0),
% 3.46/3.85 c_Polynomial_Opos__poly [231, 2] (w:1, o:266, a:1, s:1, b:0),
% 3.46/3.85 c_SEQ_Odecseq [232, 2] (w:1, o:267, a:1, s:1, b:0),
% 3.46/3.85 class_Lattices_Oboolean__algebra [233, 1] (w:1, o:218, a:1, s:1, b:0)
% 3.46/3.85 ,
% 3.46/3.85 class_Groups_Ominus [236, 1] (w:1, o:219, a:1, s:1, b:0),
% 3.46/3.85 class_Lattices_Oab__semigroup__idem__mult [237, 1] (w:1, o:217, a:1
% 3.46/3.85 , s:1, b:0),
% 3.46/3.85 class_Groups_Ouminus [238, 1] (w:1, o:220, a:1, s:1, b:0),
% 3.46/3.85 c_Groups_Osgn__class_Osgn [239, 2] (w:1, o:268, a:1, s:1, b:0),
% 3.46/3.85 class_Groups_Osgn__if [240, 1] (w:1, o:221, a:1, s:1, b:0),
% 3.46/3.85 c_Rings_Odvd__class_Odvd [241, 3] (w:1, o:283, a:1, s:1, b:0),
% 3.46/3.85 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly [243, 3] (w:
% 3.46/3.85 1, o:272, a:1, s:1, b:0),
% 3.46/3.85 class_Rings_Odvd [246, 1] (w:1, o:200, a:1, s:1, b:0),
% 3.46/3.85 class_Groups_Ocancel__comm__monoid__add [249, 1] (w:1, o:222, a:1, s:
% 3.46/3.85 1, b:0),
% 3.46/3.85 tc_HOL_Obool [251, 0] (w:1, o:109, a:1, s:1, b:0),
% 3.46/3.85 alpha1 [252, 3] (w:1, o:284, a:1, s:1, b:1),
% 3.46/3.85 alpha2 [253, 3] (w:1, o:290, a:1, s:1, b:1),
% 3.46/3.85 alpha3 [254, 4] (w:1, o:302, a:1, s:1, b:1),
% 3.46/3.85 alpha4 [255, 4] (w:1, o:303, a:1, s:1, b:1),
% 3.46/3.85 alpha5 [256, 3] (w:1, o:291, a:1, s:1, b:1),
% 3.46/3.85 alpha6 [257, 3] (w:1, o:292, a:1, s:1, b:1),
% 3.46/3.85 alpha7 [258, 3] (w:1, o:293, a:1, s:1, b:1),
% 3.46/3.85 alpha8 [259, 3] (w:1, o:294, a:1, s:1, b:1),
% 3.46/3.85 alpha9 [260, 3] (w:1, o:295, a:1, s:1, b:1),
% 3.46/3.85 alpha10 [261, 3] (w:1, o:285, a:1, s:1, b:1),
% 3.46/3.85 alpha11 [262, 4] (w:1, o:304, a:1, s:1, b:1),
% 3.46/3.85 alpha12 [263, 4] (w:1, o:305, a:1, s:1, b:1),
% 3.46/3.85 alpha13 [264, 3] (w:1, o:286, a:1, s:1, b:1),
% 3.46/3.85 alpha14 [265, 3] (w:1, o:287, a:1, s:1, b:1),
% 3.46/3.85 alpha15 [266, 4] (w:1, o:306, a:1, s:1, b:1),
% 3.46/3.85 alpha16 [267, 3] (w:1, o:288, a:1, s:1, b:1),
% 3.46/3.85 alpha17 [268, 2] (w:1, o:269, a:1, s:1, b:1),
% 3.46/3.85 alpha18 [269, 3] (w:1, o:289, a:1, s:1, b:1),
% 3.46/3.85 skol1 [270, 2] (w:1, o:255, a:1, s:1, b:1),
% 3.46/3.85 skol2 [271, 1] (w:1, o:207, a:1, s:1, b:1),
% 3.46/3.85 skol3 [272, 0] (w:1, o:15, a:1, s:1, b:1),
% 13.26/13.69 skol4 [273, 2] (w:1, o:258, a:1, s:1, b:1),
% 13.26/13.69 skol5 [274, 2] (w:1, o:259, a:1, s:1, b:1),
% 13.26/13.69 skol6 [275, 0] (w:1, o:16, a:1, s:1, b:1),
% 13.26/13.69 skol7 [276, 2] (w:1, o:260, a:1, s:1, b:1),
% 13.26/13.69 skol8 [277, 3] (w:1, o:296, a:1, s:1, b:1),
% 13.26/13.69 skol9 [278, 3] (w:1, o:297, a:1, s:1, b:1),
% 13.26/13.69 skol10 [279, 0] (w:1, o:17, a:1, s:1, b:1),
% 13.26/13.69 skol11 [280, 1] (w:1, o:204, a:1, s:1, b:1),
% 13.26/13.69 skol12 [281, 1] (w:1, o:205, a:1, s:1, b:1),
% 13.26/13.69 skol13 [282, 0] (w:1, o:18, a:1, s:1, b:1),
% 13.26/13.69 skol14 [283, 1] (w:1, o:206, a:1, s:1, b:1),
% 13.26/13.69 skol15 [284, 0] (w:1, o:19, a:1, s:1, b:1),
% 13.26/13.69 skol16 [285, 0] (w:1, o:20, a:1, s:1, b:1),
% 13.26/13.69 skol17 [286, 0] (w:1, o:21, a:1, s:1, b:1),
% 13.26/13.69 skol18 [287, 0] (w:1, o:22, a:1, s:1, b:1),
% 13.26/13.69 skol19 [288, 0] (w:1, o:23, a:1, s:1, b:1),
% 13.26/13.69 skol20 [289, 3] (w:1, o:298, a:1, s:1, b:1),
% 13.26/13.69 skol21 [290, 0] (w:1, o:13, a:1, s:1, b:1),
% 13.26/13.69 skol22 [291, 1] (w:1, o:208, a:1, s:1, b:1),
% 13.26/13.69 skol23 [292, 4] (w:1, o:307, a:1, s:1, b:1),
% 13.26/13.69 skol24 [293, 2] (w:1, o:261, a:1, s:1, b:1),
% 13.26/13.69 skol25 [294, 1] (w:1, o:209, a:1, s:1, b:1),
% 13.26/13.69 skol26 [295, 2] (w:1, o:262, a:1, s:1, b:1),
% 13.26/13.69 skol27 [296, 0] (w:1, o:14, a:1, s:1, b:1),
% 13.26/13.69 skol28 [297, 1] (w:1, o:210, a:1, s:1, b:1),
% 13.26/13.69 skol29 [298, 3] (w:1, o:299, a:1, s:1, b:1),
% 13.26/13.69 skol30 [299, 2] (w:1, o:256, a:1, s:1, b:1),
% 13.26/13.69 skol31 [300, 1] (w:1, o:211, a:1, s:1, b:1),
% 13.26/13.69 skol32 [301, 3] (w:1, o:300, a:1, s:1, b:1),
% 13.26/13.69 skol33 [302, 1] (w:1, o:212, a:1, s:1, b:1),
% 13.26/13.69 skol34 [303, 0] (w:1, o:24, a:1, s:1, b:1),
% 13.26/13.69 skol35 [304, 0] (w:1, o:25, a:1, s:1, b:1),
% 13.26/13.69 skol36 [305, 2] (w:1, o:257, a:1, s:1, b:1),
% 13.26/13.69 skol37 [306, 3] (w:1, o:301, a:1, s:1, b:1),
% 13.26/13.69 skol38 [307, 0] (w:1, o:26, a:1, s:1, b:1).
% 13.26/13.69
% 13.26/13.69
% 13.26/13.69 Starting Search:
% 13.26/13.69
% 13.26/13.69 *** allocated 170857 integers for clauses
% 13.26/13.69 Resimplifying inuse:
% 13.26/13.69 Done
% 13.26/13.69
% 13.26/13.69
% 13.26/13.69 Intermediate Status:
% 13.26/13.69 Generated: 2982
% 13.26/13.69 Kept: 2001
% 13.26/13.69 Inuse: 64
% 13.26/13.69 Deleted: 2
% 13.26/13.69 Deletedinuse: 0
% 13.26/13.69
% 13.26/13.69 *** allocated 256285 integers for clauses
% 13.26/13.69 *** allocated 170857 integers for termspace/termends
% 13.26/13.69 Resimplifying inuse:
% 13.26/13.69 Done
% 13.26/13.69
% 13.26/13.69 *** allocated 384427 integers for clauses
% 13.26/13.69
% 13.26/13.69 Intermediate Status:
% 13.26/13.69 Generated: 6834
% 13.26/13.69 Kept: 4002
% 13.26/13.69 Inuse: 170
% 13.26/13.69 Deleted: 8
% 13.26/13.69 Deletedinuse: 2
% 13.26/13.69
% 13.26/13.69 Resimplifying inuse:
% 13.26/13.69 Done
% 13.26/13.69
% 13.26/13.69 *** allocated 256285 integers for termspace/termends
% 13.26/13.69 Resimplifying inuse:
% 13.26/13.69 Done
% 13.26/13.69
% 13.26/13.69
% 13.26/13.69 Intermediate Status:
% 13.26/13.69 Generated: 18179
% 13.26/13.69 Kept: 6079
% 13.26/13.69 Inuse: 200
% 13.26/13.69 Deleted: 8
% 13.26/13.69 Deletedinuse: 2
% 13.26/13.69
% 13.26/13.69 Resimplifying inuse:
% 13.26/13.69 Done
% 13.26/13.69
% 13.26/13.69 *** allocated 576640 integers for clauses
% 13.26/13.69 *** allocated 384427 integers for termspace/termends
% 13.26/13.69 Resimplifying inuse:
% 13.26/13.69 Done
% 13.26/13.69
% 13.26/13.69
% 13.26/13.69 Intermediate Status:
% 13.26/13.69 Generated: 26357
% 13.26/13.69 Kept: 8140
% 13.26/13.69 Inuse: 250
% 13.26/13.69 Deleted: 8
% 13.26/13.69 Deletedinuse: 2
% 13.26/13.69
% 13.26/13.69 Resimplifying inuse:
% 13.26/13.69 Done
% 13.26/13.69
% 13.26/13.69 *** allocated 864960 integers for clauses
% 13.26/13.69
% 13.26/13.69 Intermediate Status:
% 13.26/13.69 Generated: 35698
% 13.26/13.69 Kept: 10628
% 13.26/13.69 Inuse: 270
% 13.26/13.69 Deleted: 8
% 13.26/13.69 Deletedinuse: 2
% 13.26/13.69
% 13.26/13.69 Resimplifying inuse:
% 13.26/13.69 Done
% 13.26/13.69
% 13.26/13.69 *** allocated 576640 integers for termspace/termends
% 13.26/13.69 Resimplifying inuse:
% 13.26/13.69 Done
% 13.26/13.69
% 13.26/13.69
% 13.26/13.69 Intermediate Status:
% 13.26/13.69 Generated: 44705
% 13.26/13.69 Kept: 12725
% 13.26/13.69 Inuse: 315
% 13.26/13.69 Deleted: 8
% 13.26/13.69 Deletedinuse: 2
% 13.26/13.69
% 13.26/13.69 Resimplifying inuse:
% 13.26/13.69 Done
% 13.26/13.69
% 13.26/13.69 Resimplifying inuse:
% 13.26/13.69 Done
% 13.26/13.69
% 13.26/13.69
% 13.26/13.69 Intermediate Status:
% 13.26/13.69 Generated: 51225
% 13.26/13.69 Kept: 14754
% 13.26/13.69 Inuse: 385
% 13.26/13.69 Deleted: 8
% 13.26/13.69 Deletedinuse: 2
% 13.26/13.69
% 13.26/13.69 Resimplifying inuse:
% 13.26/13.69 Done
% 13.26/13.69
% 13.26/13.69 Resimplifying inuse:
% 13.26/13.69 Done
% 13.26/13.69
% 13.26/13.69
% 13.26/13.69 Intermediate Status:
% 13.26/13.69 Generated: 57118
% 13.26/13.69 Kept: 16762
% 13.26/13.69 Inuse: 454
% 13.26/13.69 Deleted: 8
% 13.26/13.69 Deletedinuse: 2
% 13.26/13.69
% 13.26/13.69 Resimplifying inuse:
% 13.26/13.69 Done
% 13.26/13.69
% 13.26/13.69 *** allocated 1297440 integers for clauses
% 13.26/13.69 *** allocated 864960 integers for termspace/termends
% 13.26/13.69
% 13.26/13.69 Intermediate Status:
% 13.26/13.69 Generated: 68202
% 13.26/13.69 Kept: 18937
% 13.26/13.69 Inuse: 470
% 13.26/13.69 Deleted: 8
% 13.26/13.69 Deletedinuse: 2
% 13.26/13.69
% 13.26/13.69 Resimplifying inuse:
% 13.26/13.69 Done
% 13.26/13.69
% 13.26/13.69 Resimplifying inuse:
% 13.26/13.69 Done
% 13.26/13.69
% 13.26/13.69 Resimplifying clauses:
% 13.26/13.69 Done
% 13.26/13.69
% 13.26/13.69
% 13.26/13.69 Intermediate Status:
% 13.26/13.69 Generated: 75111
% 13.26/13.69 Kept: 21106
% 13.26/13.69 Inuse: 485
% 13.26/13.69 Deleted: 229
% 13.26/13.69 Deletedinuse: 2
% 13.26/13.69
% 13.26/13.69 Resimplifying inuse:
% 13.26/13.69 Done
% 13.26/13.69
% 13.26/13.69 Resimplifying inuse:
% 13.26/13.69 Done
% 13.26/13.69
% 13.26/13.69
% 13.26/13.69 Intermediate Status:
% 13.26/13.69 Generated: 82037
% 13.26/13.69 Kept: 23116
% 13.26/13.69 Inuse: 522
% 13.26/13.69 Deleted: 229
% 82.95/83.38 Deletedinuse: 2
% 82.95/83.38
% 82.95/83.38 Resimplifying inuse:
% 82.95/83.38 Done
% 82.95/83.38
% 82.95/83.38 Resimplifying inuse:
% 82.95/83.38 Done
% 82.95/83.38
% 82.95/83.38 *** allocated 1297440 integers for termspace/termends
% 82.95/83.38
% 82.95/83.38 Intermediate Status:
% 82.95/83.38 Generated: 92126
% 82.95/83.38 Kept: 25914
% 82.95/83.38 Inuse: 555
% 82.95/83.38 Deleted: 229
% 82.95/83.38 Deletedinuse: 2
% 82.95/83.38
% 82.95/83.38 Resimplifying inuse:
% 82.95/83.38 Done
% 82.95/83.38
% 82.95/83.38 *** allocated 1946160 integers for clauses
% 82.95/83.38 Resimplifying inuse:
% 82.95/83.38 Done
% 82.95/83.38
% 82.95/83.38
% 82.95/83.38 Intermediate Status:
% 82.95/83.38 Generated: 99329
% 82.95/83.38 Kept: 27937
% 82.95/83.38 Inuse: 575
% 82.95/83.38 Deleted: 229
% 82.95/83.38 Deletedinuse: 2
% 82.95/83.38
% 82.95/83.38 Resimplifying inuse:
% 82.95/83.38 Done
% 82.95/83.38
% 82.95/83.38
% 82.95/83.38 Intermediate Status:
% 82.95/83.38 Generated: 104822
% 82.95/83.38 Kept: 30225
% 82.95/83.38 Inuse: 590
% 82.95/83.38 Deleted: 229
% 82.95/83.38 Deletedinuse: 2
% 82.95/83.38
% 82.95/83.38 Resimplifying inuse:
% 82.95/83.38 Done
% 82.95/83.38
% 82.95/83.38 Resimplifying inuse:
% 82.95/83.38 Done
% 82.95/83.38
% 82.95/83.38
% 82.95/83.38 Intermediate Status:
% 82.95/83.38 Generated: 116564
% 82.95/83.38 Kept: 33086
% 82.95/83.38 Inuse: 615
% 82.95/83.38 Deleted: 229
% 82.95/83.38 Deletedinuse: 2
% 82.95/83.38
% 82.95/83.38 Resimplifying inuse:
% 82.95/83.38 Done
% 82.95/83.38
% 82.95/83.38
% 82.95/83.38 Intermediate Status:
% 82.95/83.38 Generated: 129244
% 82.95/83.38 Kept: 35701
% 82.95/83.38 Inuse: 625
% 82.95/83.38 Deleted: 229
% 82.95/83.38 Deletedinuse: 2
% 82.95/83.38
% 82.95/83.38 Resimplifying inuse:
% 82.95/83.38 Done
% 82.95/83.38
% 82.95/83.38 *** allocated 1946160 integers for termspace/termends
% 82.95/83.38
% 82.95/83.38 Intermediate Status:
% 82.95/83.38 Generated: 140243
% 82.95/83.38 Kept: 37759
% 82.95/83.38 Inuse: 630
% 82.95/83.38 Deleted: 229
% 82.95/83.38 Deletedinuse: 2
% 82.95/83.38
% 82.95/83.38 Resimplifying inuse:
% 82.95/83.38 Done
% 82.95/83.38
% 82.95/83.38 Resimplifying inuse:
% 82.95/83.38 Done
% 82.95/83.38
% 82.95/83.38
% 82.95/83.38 Intermediate Status:
% 82.95/83.38 Generated: 148289
% 82.95/83.38 Kept: 39792
% 82.95/83.38 Inuse: 673
% 82.95/83.38 Deleted: 229
% 82.95/83.38 Deletedinuse: 2
% 82.95/83.38
% 82.95/83.38 Resimplifying inuse:
% 82.95/83.38 Done
% 82.95/83.38
% 82.95/83.38 *** allocated 2919240 integers for clauses
% 82.95/83.38
% 82.95/83.38 Intermediate Status:
% 82.95/83.38 Generated: 154794
% 82.95/83.38 Kept: 41995
% 82.95/83.38 Inuse: 690
% 82.95/83.38 Deleted: 229
% 82.95/83.38 Deletedinuse: 2
% 82.95/83.38
% 82.95/83.38 Resimplifying inuse:
% 82.95/83.38 Done
% 82.95/83.38
% 82.95/83.38 Resimplifying clauses:
% 82.95/83.38 Done
% 82.95/83.38
% 82.95/83.38 Resimplifying inuse:
% 82.95/83.38 Done
% 82.95/83.38
% 82.95/83.38
% 82.95/83.38 Intermediate Status:
% 82.95/83.38 Generated: 166833
% 82.95/83.38 Kept: 44656
% 82.95/83.38 Inuse: 700
% 82.95/83.38 Deleted: 569
% 82.95/83.38 Deletedinuse: 2
% 82.95/83.38
% 82.95/83.38 Resimplifying inuse:
% 82.95/83.38 Done
% 82.95/83.38
% 82.95/83.38 Resimplifying inuse:
% 82.95/83.38 Done
% 82.95/83.38
% 82.95/83.38
% 82.95/83.38 Intermediate Status:
% 82.95/83.38 Generated: 173669
% 82.95/83.38 Kept: 46662
% 82.95/83.38 Inuse: 732
% 82.95/83.38 Deleted: 569
% 82.95/83.38 Deletedinuse: 2
% 82.95/83.38
% 82.95/83.38 Resimplifying inuse:
% 82.95/83.38 Done
% 82.95/83.38
% 82.95/83.38 Resimplifying inuse:
% 82.95/83.38 Done
% 82.95/83.38
% 82.95/83.38
% 82.95/83.38 Intermediate Status:
% 82.95/83.38 Generated: 180687
% 82.95/83.38 Kept: 48686
% 82.95/83.38 Inuse: 760
% 82.95/83.38 Deleted: 569
% 82.95/83.38 Deletedinuse: 2
% 82.95/83.38
% 82.95/83.38 Resimplifying inuse:
% 82.95/83.38 Done
% 82.95/83.38
% 82.95/83.38 Resimplifying inuse:
% 82.95/83.38 Done
% 82.95/83.38
% 82.95/83.38
% 82.95/83.38 Intermediate Status:
% 82.95/83.38 Generated: 187679
% 82.95/83.38 Kept: 50738
% 82.95/83.38 Inuse: 790
% 82.95/83.38 Deleted: 569
% 82.95/83.38 Deletedinuse: 2
% 82.95/83.38
% 82.95/83.38 Resimplifying inuse:
% 82.95/83.38 Done
% 82.95/83.38
% 82.95/83.38 Resimplifying inuse:
% 82.95/83.38 Done
% 82.95/83.38
% 82.95/83.38
% 82.95/83.38 Intermediate Status:
% 82.95/83.38 Generated: 194812
% 82.95/83.38 Kept: 52894
% 82.95/83.38 Inuse: 840
% 82.95/83.38 Deleted: 569
% 82.95/83.38 Deletedinuse: 2
% 82.95/83.38
% 82.95/83.38 Resimplifying inuse:
% 82.95/83.38 Done
% 82.95/83.38
% 82.95/83.38 Resimplifying inuse:
% 82.95/83.38 Done
% 82.95/83.38
% 82.95/83.38
% 82.95/83.38 Intermediate Status:
% 82.95/83.38 Generated: 202502
% 82.95/83.38 Kept: 54909
% 82.95/83.38 Inuse: 887
% 82.95/83.38 Deleted: 569
% 82.95/83.38 Deletedinuse: 2
% 82.95/83.38
% 82.95/83.38 Resimplifying inuse:
% 82.95/83.38 Done
% 82.95/83.38
% 82.95/83.38 *** allocated 2919240 integers for termspace/termends
% 82.95/83.38 Resimplifying inuse:
% 82.95/83.38 Done
% 82.95/83.38
% 82.95/83.38
% 82.95/83.38 Intermediate Status:
% 82.95/83.38 Generated: 215166
% 82.95/83.38 Kept: 58340
% 82.95/83.38 Inuse: 900
% 82.95/83.38 Deleted: 569
% 82.95/83.38 Deletedinuse: 2
% 82.95/83.38
% 82.95/83.38 Resimplifying inuse:
% 82.95/83.38 Done
% 82.95/83.38
% 82.95/83.38 Resimplifying inuse:
% 82.95/83.38 Done
% 82.95/83.38
% 82.95/83.38
% 82.95/83.38 Intermediate Status:
% 82.95/83.38 Generated: 229299
% 82.95/83.38 Kept: 61573
% 82.95/83.38 Inuse: 935
% 82.95/83.38 Deleted: 569
% 82.95/83.38 Deletedinuse: 2
% 82.95/83.38
% 82.95/83.38 Resimplifying inuse:
% 82.95/83.38 Done
% 82.95/83.38
% 82.95/83.38 Resimplifying clauses:
% 82.95/83.38 Done
% 82.95/83.38
% 82.95/83.38
% 82.95/83.38 Intermediate Status:
% 82.95/83.38 Generated: 241938
% 82.95/83.38 Kept: 63792
% 82.95/83.38 Inuse: 950
% 82.95/83.38 Deleted: 890
% 82.95/83.38 Deletedinuse: 3
% 82.95/83.38
% 82.95/83.38 Resimplifying inuse:
% 82.95/83.38 Done
% 82.95/83.38
% 82.95/83.38 *** allocated 4378860 integers for clauses
% 82.95/83.38
% 82.95/83.38 Intermediate Status:
% 82.95/83.38 Generated: 249921
% 82.95/83.38 Kept: 67103
% 82.95/83.38 Inuse: 965
% 82.95/83.38 Deleted: 890
% 82.95/83.38 Deletedinuse: 3
% 82.95/83.38
% 82.95/83.38 Resimplifying inuse:
% 82.95/83.38 Done
% 82.95/83.38
% 82.95/83.38 Resimplifying inuse:
% 82.95/83.38 Done
% 82.95/83.38
% 82.95/83.38
% 82.95/83.38 Intermediate Status:
% 82.95/83.38 Generated: 258308
% 82.95/83.38 Kept: 69106
% 82.95/83.38 Inuse: 998
% 82.95/83.38 Deleted: 891
% 82.95/83.38 Deletedinuse: 4
% 82.95/83.38
% 82.95/83.38 Resimplifying inuse:
% 82.95/83.38 Done
% 82.95/83.38
% 82.95/83.38 Resimplifying inuse:
% 82.95/83.38 Done
% 82.95/83.38
% 82.95/83.38
% 82.95/83.38 Intermediate Status:
% 82.95/83.38 Generated: 270770
% 82.95/83.38 Kept: 72552
% 82.95/83.38 Inuse: 1015
% 82.95/83.38 Deleted: 891
% 82.95/83.38 Deletedinuse: 4
% 82.95/83.38
% 82.95/83.38 Resimplifying inuse:
% 82.95/83.38 Done
% 82.95/83.38
% 82.95/83.38 Resimplifying inuse:
% 82.95/83.38 Done
% 82.95/83.38
% 82.95/83.38
% 82.95/83.38 Intermediate Status:
% 82.95/83.38 Generated: 278832
% 82.95/83.38 Kept: 74768
% 82.95/83.38 Inuse: 1050
% 82.95/83.38 Deleted: 891
% 82.95/83.38 Deletedinuse: 4
% 82.95/83.38
% 82.95/83.38 Resimplifying inuse:
% 82.95/83.38 Done
% 82.95/83.38
% 82.95/83.38 Resimplifying inuse:
% 82.95/83.38 Done
% 82.95/83.38
% 82.95/83.38
% 82.95/83.38 Intermediate Status:
% 82.95/83.38 Generated: 288370
% 82.95/83.38 Kept: 77320
% 82.95/83.38 Inuse: 1060
% 82.95/83.38 Deleted: 891
% 82.95/83.38 Deletedinuse: 4
% 82.95/83.38
% 82.95/83.38 Resimplifying inuse:
% 82.95/83.38 Done
% 82.95/83.38
% 82.95/83.38 Resimplifying inuse:
% 82.95/83.38 Done
% 82.95/83.38
% 82.95/83.38
% 82.95/83.38 Intermediate Status:
% 82.95/83.38 Generated: 296449
% 82.95/83.38 Kept: 79364
% 82.95/83.38 Inuse: 1087
% 82.95/83.38 Deleted: 891
% 207.36/207.80 Deletedinuse: 4
% 207.36/207.80
% 207.36/207.80 Resimplifying inuse:
% 207.36/207.80 Done
% 207.36/207.80
% 207.36/207.80
% 207.36/207.80 Intermediate Status:
% 207.36/207.80 Generated: 311487
% 207.36/207.80 Kept: 83366
% 207.36/207.80 Inuse: 1120
% 207.36/207.80 Deleted: 891
% 207.36/207.80 Deletedinuse: 4
% 207.36/207.80
% 207.36/207.80 Resimplifying inuse:
% 207.36/207.80 Done
% 207.36/207.80
% 207.36/207.80 Resimplifying clauses:
% 207.36/207.80 Done
% 207.36/207.80
% 207.36/207.80 *** allocated 4378860 integers for termspace/termends
% 207.36/207.80
% 207.36/207.80 Intermediate Status:
% 207.36/207.80 Generated: 318967
% 207.36/207.80 Kept: 86799
% 207.36/207.80 Inuse: 1130
% 207.36/207.80 Deleted: 1428
% 207.36/207.80 Deletedinuse: 4
% 207.36/207.80
% 207.36/207.80 Resimplifying inuse:
% 207.36/207.80 Done
% 207.36/207.80
% 207.36/207.80
% 207.36/207.80 Intermediate Status:
% 207.36/207.80 Generated: 327594
% 207.36/207.80 Kept: 88843
% 207.36/207.80 Inuse: 1133
% 207.36/207.80 Deleted: 1428
% 207.36/207.80 Deletedinuse: 4
% 207.36/207.80
% 207.36/207.80 Resimplifying inuse:
% 207.36/207.80 Done
% 207.36/207.80
% 207.36/207.80
% 207.36/207.80 Intermediate Status:
% 207.36/207.80 Generated: 337735
% 207.36/207.80 Kept: 94567
% 207.36/207.80 Inuse: 1140
% 207.36/207.80 Deleted: 1428
% 207.36/207.80 Deletedinuse: 4
% 207.36/207.80
% 207.36/207.80 Resimplifying inuse:
% 207.36/207.80 Done
% 207.36/207.80
% 207.36/207.80 Resimplifying inuse:
% 207.36/207.80 Done
% 207.36/207.80
% 207.36/207.80 *** allocated 6568290 integers for clauses
% 207.36/207.80
% 207.36/207.80 Intermediate Status:
% 207.36/207.80 Generated: 346167
% 207.36/207.80 Kept: 96718
% 207.36/207.80 Inuse: 1195
% 207.36/207.80 Deleted: 1429
% 207.36/207.80 Deletedinuse: 5
% 207.36/207.80
% 207.36/207.80 Resimplifying inuse:
% 207.36/207.80 Done
% 207.36/207.80
% 207.36/207.80 Resimplifying inuse:
% 207.36/207.80 Done
% 207.36/207.80
% 207.36/207.80
% 207.36/207.80 Intermediate Status:
% 207.36/207.80 Generated: 354608
% 207.36/207.80 Kept: 99043
% 207.36/207.80 Inuse: 1230
% 207.36/207.80 Deleted: 1429
% 207.36/207.80 Deletedinuse: 5
% 207.36/207.80
% 207.36/207.80 Resimplifying inuse:
% 207.36/207.80 Done
% 207.36/207.80
% 207.36/207.80
% 207.36/207.80 Intermediate Status:
% 207.36/207.80 Generated: 380331
% 207.36/207.80 Kept: 102044
% 207.36/207.80 Inuse: 1235
% 207.36/207.80 Deleted: 1429
% 207.36/207.80 Deletedinuse: 5
% 207.36/207.80
% 207.36/207.80 Resimplifying inuse:
% 207.36/207.80 Done
% 207.36/207.80
% 207.36/207.80
% 207.36/207.80 Intermediate Status:
% 207.36/207.80 Generated: 408839
% 207.36/207.80 Kept: 105438
% 207.36/207.80 Inuse: 1245
% 207.36/207.80 Deleted: 1429
% 207.36/207.80 Deletedinuse: 5
% 207.36/207.80
% 207.36/207.80 Resimplifying inuse:
% 207.36/207.80 Done
% 207.36/207.80
% 207.36/207.80 Resimplifying clauses:
% 207.36/207.80 Done
% 207.36/207.80
% 207.36/207.80
% 207.36/207.80 Intermediate Status:
% 207.36/207.80 Generated: 430989
% 207.36/207.80 Kept: 108848
% 207.36/207.80 Inuse: 1255
% 207.36/207.80 Deleted: 1937
% 207.36/207.80 Deletedinuse: 5
% 207.36/207.80
% 207.36/207.80 Resimplifying inuse:
% 207.36/207.80 Done
% 207.36/207.80
% 207.36/207.80 Resimplifying inuse:
% 207.36/207.80 Done
% 207.36/207.80
% 207.36/207.80
% 207.36/207.80 Intermediate Status:
% 207.36/207.80 Generated: 449619
% 207.36/207.80 Kept: 113113
% 207.36/207.80 Inuse: 1280
% 207.36/207.80 Deleted: 1939
% 207.36/207.80 Deletedinuse: 7
% 207.36/207.80
% 207.36/207.80 Resimplifying inuse:
% 207.36/207.80 Done
% 207.36/207.80
% 207.36/207.80 Resimplifying inuse:
% 207.36/207.80 Done
% 207.36/207.80
% 207.36/207.80
% 207.36/207.80 Intermediate Status:
% 207.36/207.80 Generated: 463777
% 207.36/207.80 Kept: 120204
% 207.36/207.80 Inuse: 1305
% 207.36/207.80 Deleted: 1939
% 207.36/207.80 Deletedinuse: 7
% 207.36/207.80
% 207.36/207.80 Resimplifying inuse:
% 207.36/207.80 Done
% 207.36/207.80
% 207.36/207.80 Resimplifying inuse:
% 207.36/207.80 Done
% 207.36/207.80
% 207.36/207.80
% 207.36/207.80 Intermediate Status:
% 207.36/207.80 Generated: 480136
% 207.36/207.80 Kept: 124438
% 207.36/207.80 Inuse: 1335
% 207.36/207.80 Deleted: 1939
% 207.36/207.80 Deletedinuse: 7
% 207.36/207.80
% 207.36/207.80 Resimplifying inuse:
% 207.36/207.80 Done
% 207.36/207.80
% 207.36/207.80
% 207.36/207.80 Intermediate Status:
% 207.36/207.80 Generated: 495200
% 207.36/207.80 Kept: 128230
% 207.36/207.80 Inuse: 1350
% 207.36/207.80 Deleted: 1939
% 207.36/207.80 Deletedinuse: 7
% 207.36/207.80
% 207.36/207.80 Resimplifying inuse:
% 207.36/207.80 Done
% 207.36/207.80
% 207.36/207.80 Resimplifying clauses:
% 207.36/207.80 Done
% 207.36/207.80
% 207.36/207.80
% 207.36/207.80 Intermediate Status:
% 207.36/207.80 Generated: 510377
% 207.36/207.80 Kept: 131946
% 207.36/207.80 Inuse: 1360
% 207.36/207.80 Deleted: 2522
% 207.36/207.80 Deletedinuse: 7
% 207.36/207.80
% 207.36/207.80 Resimplifying inuse:
% 207.36/207.80 Done
% 207.36/207.80
% 207.36/207.80 Resimplifying inuse:
% 207.36/207.80 Done
% 207.36/207.80
% 207.36/207.80
% 207.36/207.80 Intermediate Status:
% 207.36/207.80 Generated: 519146
% 207.36/207.80 Kept: 133949
% 207.36/207.80 Inuse: 1385
% 207.36/207.80 Deleted: 2522
% 207.36/207.80 Deletedinuse: 7
% 207.36/207.80
% 207.36/207.80 Resimplifying inuse:
% 207.36/207.80 Done
% 207.36/207.80
% 207.36/207.80
% 207.36/207.80 Intermediate Status:
% 207.36/207.80 Generated: 528985
% 207.36/207.80 Kept: 138311
% 207.36/207.80 Inuse: 1400
% 207.36/207.80 Deleted: 2522
% 207.36/207.80 Deletedinuse: 7
% 207.36/207.80
% 207.36/207.80 Resimplifying inuse:
% 207.36/207.80 Done
% 207.36/207.80
% 207.36/207.80
% 207.36/207.80 Intermediate Status:
% 207.36/207.80 Generated: 535640
% 207.36/207.80 Kept: 141907
% 207.36/207.80 Inuse: 1405
% 207.36/207.80 Deleted: 2522
% 207.36/207.80 Deletedinuse: 7
% 207.36/207.80
% 207.36/207.80 Resimplifying inuse:
% 207.36/207.80 Done
% 207.36/207.80
% 207.36/207.80 *** allocated 6568290 integers for termspace/termends
% 207.36/207.80
% 207.36/207.80 Intermediate Status:
% 207.36/207.80 Generated: 545717
% 207.36/207.80 Kept: 146117
% 207.36/207.80 Inuse: 1424
% 207.36/207.80 Deleted: 2523
% 207.36/207.80 Deletedinuse: 7
% 207.36/207.80
% 207.36/207.80 Resimplifying inuse:
% 207.36/207.80 Done
% 207.36/207.80
% 207.36/207.80 Resimplifying inuse:
% 207.36/207.80 Done
% 207.36/207.80
% 207.36/207.80
% 207.36/207.80 Intermediate Status:
% 207.36/207.80 Generated: 554893
% 207.36/207.80 Kept: 148117
% 207.36/207.80 Inuse: 1447
% 207.36/207.80 Deleted: 2523
% 207.36/207.80 Deletedinuse: 7
% 207.36/207.80
% 207.36/207.80 Resimplifying inuse:
% 207.36/207.80 Done
% 207.36/207.80
% 207.36/207.80 Resimplifying clauses:
% 207.36/207.80 Done
% 207.36/207.80
% 207.36/207.80 *** allocated 9852435 integers for clauses
% 207.36/207.80
% 207.36/207.80 Intermediate Status:
% 207.36/207.80 Generated: 571566
% 207.36/207.80 Kept: 155969
% 207.36/207.80 Inuse: 1464
% 207.36/207.80 Deleted: 3036
% 207.36/207.80 Deletedinuse: 7
% 207.36/207.80
% 207.36/207.80 Resimplifying inuse:
% 207.36/207.80 Done
% 207.36/207.80
% 207.36/207.80 Resimplifying inuse:
% 207.36/207.80 Done
% 207.36/207.80
% 207.36/207.80
% 207.36/207.80 Intermediate Status:
% 207.36/207.80 Generated: 581966
% 207.36/207.80 Kept: 160733
% 207.36/207.80 Inuse: 1484
% 207.36/207.80 Deleted: 3036
% 207.36/207.80 Deletedinuse: 7
% 207.36/207.80
% 207.36/207.80 Resimplifying inuse:
% 207.36/207.80 Done
% 207.36/207.80
% 207.36/207.80
% 207.36/207.80 Intermediate Status:
% 207.36/207.80 Generated: 589386
% 207.36/207.80 Kept: 164586
% 207.36/207.80 Inuse: 1489
% 207.36/207.80 Deleted: 3036
% 207.36/207.80 Deletedinuse: 7
% 207.36/207.80
% 207.36/207.80 Resimplifying inuse:
% 207.36/207.80 Done
% 207.36/207.80
% 207.36/207.80
% 207.36/207.80 Intermediate Status:
% 207.36/207.80 Generated: 596947
% 207.36/207.80 Kept: 168500
% 207.36/207.80 Inuse: 1498
% 207.36/207.80 Deleted: 3037
% 207.36/207.80 Deletedinuse: 7
% 207.36/207.80
% 207.36/207.80 Resimplifying inuse:
% 207.36/207.80 Done
% 207.36/207.80
% 207.36/207.80 Resimplifying clauses:
% 207.36/207.80 Done
% 207.36/207.80
% 207.36/207.80
% 207.36/207.80 Intermediate Status:
% 207.36/207.80 Generated: 604879
% 207.36/207.80 Kept: 172826
% 207.36/207.80 Inuse: 1508
% 207.36/207.80 Deleted: 3248
% 207.36/207.80 Deletedinuse: 9
% 207.36/207.80
% 207.36/207.80 ResimplifyCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------