TSTP Solution File: SWW205+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWW205+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Wed Jul 20 23:21:13 EDT 2022
% Result : Timeout 300.04s 300.50s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWW205+1 : TPTP v8.1.0. Released v5.2.0.
% 0.06/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % DateTime : Mon Jun 6 02:33:01 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.97/1.62 *** allocated 10000 integers for termspace/termends
% 0.97/1.62 *** allocated 10000 integers for clauses
% 0.97/1.62 *** allocated 10000 integers for justifications
% 0.97/1.62 *** allocated 15000 integers for termspace/termends
% 0.97/1.62 *** allocated 22500 integers for termspace/termends
% 0.97/1.62 *** allocated 33750 integers for termspace/termends
% 0.97/1.62 Bliksem 1.12
% 0.97/1.62
% 0.97/1.62
% 0.97/1.62 Automatic Strategy Selection
% 0.97/1.62
% 0.97/1.62 *** allocated 50625 integers for termspace/termends
% 0.97/1.62 *** allocated 75937 integers for termspace/termends
% 0.97/1.62 *** allocated 113905 integers for termspace/termends
% 0.97/1.62
% 0.97/1.62 Clauses:
% 0.97/1.62
% 0.97/1.62 { ! hAPP( Y, skol1( X, Y ) ) = hAPP( X, skol1( X, Y ) ), Y = X }.
% 0.97/1.62 { c_SEQ_Osubseq( v_ga____ ) }.
% 0.97/1.62 { c_SEQ_Osubseq( v_f____ ) }.
% 0.97/1.62 { c_SEQ_Omonoseq( tc_RealDef_Oreal, c_COMBB( tc_Complex_Ocomplex,
% 0.97/1.62 tc_RealDef_Oreal, tc_Nat_Onat, c_Complex_ORe, c_COMBB( tc_Nat_Onat,
% 0.97/1.62 tc_Complex_Ocomplex, tc_Nat_Onat, v_s, v_f____ ) ) ) }.
% 0.97/1.62 { c_SEQ_Omonoseq( tc_RealDef_Oreal, c_COMBB( tc_Complex_Ocomplex,
% 0.97/1.62 tc_RealDef_Oreal, tc_Nat_Onat, c_Complex_OIm, c_COMBB( tc_Nat_Onat,
% 0.97/1.62 tc_Complex_Ocomplex, tc_Nat_Onat, v_s, c_COMBB( tc_Nat_Onat, tc_Nat_Onat
% 0.97/1.62 , tc_Nat_Onat, v_f____, v_ga____ ) ) ) ) }.
% 0.97/1.62 { c_SEQ_Osubseq( skol2 ) }.
% 0.97/1.62 { c_SEQ_Omonoseq( tc_RealDef_Oreal, c_COMBB( tc_Complex_Ocomplex,
% 0.97/1.62 tc_RealDef_Oreal, tc_Nat_Onat, c_Complex_OIm, c_COMBB( tc_Nat_Onat,
% 0.97/1.62 tc_Complex_Ocomplex, tc_Nat_Onat, v_s, c_COMBB( tc_Nat_Onat, tc_Nat_Onat
% 0.97/1.62 , tc_Nat_Onat, v_f____, skol2 ) ) ) ) }.
% 0.97/1.62 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.62 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP( v_s, X ) ),
% 0.97/1.62 v_r ) }.
% 0.97/1.62 { c_SEQ_Osubseq( skol3 ) }.
% 0.97/1.62 { c_SEQ_Omonoseq( tc_RealDef_Oreal, c_COMBB( tc_Nat_Onat, tc_RealDef_Oreal
% 0.97/1.62 , tc_Nat_Onat, c_Fun_Ocomp( tc_Complex_Ocomplex, tc_RealDef_Oreal,
% 0.97/1.62 tc_Nat_Onat, c_Complex_ORe, v_s ), skol3 ) ) }.
% 0.97/1.62 { c_Lim_OisUCont( tc_Complex_Ocomplex, tc_RealDef_Oreal, c_Complex_ORe ) }
% 0.97/1.62 .
% 0.97/1.62 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.97/1.62 c_SEQ_OBseq( X, c_COMBB( tc_Nat_Onat, X, tc_Nat_Onat, Y, c_COMBC(
% 0.97/1.62 tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.62 tc_Nat_Onat ), Z ) ) ) }.
% 0.97/1.62 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, c_COMBB
% 0.97/1.62 ( tc_Nat_Onat, X, tc_Nat_Onat, Y, c_COMBC( tc_Nat_Onat, tc_Nat_Onat,
% 0.97/1.62 tc_Nat_Onat, c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ) ) ),
% 0.97/1.62 c_SEQ_OBseq( X, Y ) }.
% 0.97/1.62 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, c_COMBB
% 0.97/1.62 ( X, X, tc_Nat_Onat, c_Groups_Ouminus__class_Ouminus( X ), Y ) ),
% 0.97/1.62 c_SEQ_OBseq( X, Y ) }.
% 0.97/1.62 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.97/1.62 c_SEQ_OBseq( X, c_COMBB( X, X, tc_Nat_Onat,
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) }.
% 0.97/1.62 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OCauchy( X, Y ),
% 0.97/1.62 c_SEQ_OBseq( X, Y ) }.
% 0.97/1.62 { c_SEQ_Osubseq( skol4 ) }.
% 0.97/1.62 { c_SEQ_Omonoseq( tc_RealDef_Oreal, c_COMBB( tc_Nat_Onat, tc_RealDef_Oreal
% 0.97/1.62 , tc_Nat_Onat, c_Fun_Ocomp( tc_Nat_Onat, tc_RealDef_Oreal, tc_Nat_Onat,
% 0.97/1.62 c_Fun_Ocomp( tc_Complex_Ocomplex, tc_RealDef_Oreal, tc_Nat_Onat,
% 0.97/1.62 c_Complex_OIm, v_s ), v_f____ ), skol4 ) ) }.
% 0.97/1.62 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.62 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, hAPP( c_Complex_ORe, hAPP(
% 0.97/1.62 v_s, X ) ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal )
% 0.97/1.62 , v_r ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) }.
% 0.97/1.62 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.62 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP( v_s,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), v_r ) }.
% 0.97/1.62 { c_Lim_OisUCont( tc_Complex_Ocomplex, tc_RealDef_Oreal, c_Complex_OIm ) }
% 0.97/1.62 .
% 0.97/1.62 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( c_Complex_ORe
% 0.97/1.62 , X ), c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), ! c_SEQ_Omonoseq( X, Y ), alpha1( X, Y ),
% 0.97/1.62 alpha12( X, Y ) }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), ! alpha1( X, Y ), c_SEQ_Omonoseq( X, Y ) }
% 0.97/1.62 .
% 0.97/1.62 { ! class_Orderings_Oorder( X ), ! alpha12( X, Y ), c_SEQ_Omonoseq( X, Y )
% 0.97/1.62 }.
% 0.97/1.62 { ! alpha12( X, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, T
% 0.97/1.62 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, T ), hAPP( Y, Z ) ) }
% 0.97/1.62 .
% 0.97/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, skol5( X, Y ), skol59( X
% 0.97/1.62 , Y ) ), alpha12( X, Y ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, skol59( X, Y ) ), hAPP(
% 0.97/1.62 Y, skol5( X, Y ) ) ), alpha12( X, Y ) }.
% 0.97/1.62 { ! alpha1( X, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, T
% 0.97/1.62 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, Z ), hAPP( Y, T ) ) }
% 0.97/1.62 .
% 0.97/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, skol6( X, Y ), skol60( X
% 0.97/1.62 , Y ) ), alpha1( X, Y ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, skol6( X, Y ) ), hAPP( Y
% 0.97/1.62 , skol60( X, Y ) ) ), alpha1( X, Y ) }.
% 0.97/1.62 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.62 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, hAPP( c_Complex_OIm, X ) ),
% 0.97/1.62 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) }.
% 0.97/1.62 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.62 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, hAPP( c_Complex_ORe, X ) ),
% 0.97/1.62 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) }.
% 0.97/1.62 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal ),
% 0.97/1.62 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ),
% 0.97/1.62 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) }.
% 0.97/1.62 { hAPP( c_Complex_OIm, hAPP( c_Groups_Ouminus__class_Ouminus(
% 0.97/1.62 tc_Complex_Ocomplex ), X ) ) = hAPP( c_Groups_Ouminus__class_Ouminus(
% 0.97/1.62 tc_RealDef_Oreal ), hAPP( c_Complex_OIm, X ) ) }.
% 0.97/1.62 { hAPP( c_Complex_ORe, hAPP( c_Groups_Ouminus__class_Ouminus(
% 0.97/1.62 tc_Complex_Ocomplex ), X ) ) = hAPP( c_Groups_Ouminus__class_Ouminus(
% 0.97/1.62 tc_RealDef_Oreal ), hAPP( c_Complex_ORe, X ) ) }.
% 0.97/1.62 { ! c_SEQ_OCauchy( tc_Complex_Ocomplex, X ), c_SEQ_OCauchy(
% 0.97/1.62 tc_RealDef_Oreal, c_COMBB( tc_Complex_Ocomplex, tc_RealDef_Oreal,
% 0.97/1.62 tc_Nat_Onat, c_Complex_OIm, X ) ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__group__add( X ), ! c_SEQ_Omonoseq( X, Y ),
% 0.97/1.62 c_SEQ_Omonoseq( X, c_COMBB( X, X, tc_Nat_Onat,
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) }.
% 0.97/1.62 { ! class_RealVector_Ometric__space( X ), ! c_SEQ_OCauchy( X, Y ), !
% 0.97/1.62 c_SEQ_Osubseq( Z ), c_SEQ_OCauchy( X, c_Fun_Ocomp( tc_Nat_Onat, X,
% 0.97/1.62 tc_Nat_Onat, Y, Z ) ) }.
% 0.97/1.62 { ! c_SEQ_OCauchy( tc_Complex_Ocomplex, X ), c_SEQ_OCauchy(
% 0.97/1.62 tc_RealDef_Oreal, c_COMBB( tc_Complex_Ocomplex, tc_RealDef_Oreal,
% 0.97/1.62 tc_Nat_Onat, c_Complex_ORe, X ) ) }.
% 0.97/1.62 { ! hAPP( c_Complex_ORe, Y ) = hAPP( c_Complex_ORe, X ), ! hAPP(
% 0.97/1.62 c_Complex_OIm, Y ) = hAPP( c_Complex_OIm, X ), Y = X }.
% 0.97/1.62 { ! Y = X, hAPP( c_Complex_ORe, Y ) = hAPP( c_Complex_ORe, X ) }.
% 0.97/1.62 { ! Y = X, hAPP( c_Complex_OIm, Y ) = hAPP( c_Complex_OIm, X ) }.
% 0.97/1.62 { ! hAPP( c_Complex_ORe, Y ) = hAPP( c_Complex_ORe, X ), ! hAPP(
% 0.97/1.62 c_Complex_OIm, Y ) = hAPP( c_Complex_OIm, X ), Y = X }.
% 0.97/1.62 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.62 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ),
% 0.97/1.62 c_RealVector_Onorm__class_Onorm( X, Z ) ),
% 0.97/1.62 c_RealVector_Onorm__class_Onorm( X, Y ) ) ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X ), c_Groups_Oabs__class_Oabs( X, Y ) )
% 0.97/1.62 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.62 ), c_Groups_Oabs__class_Oabs( X, Y ) = hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X ), Y ) }.
% 0.97/1.62 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), v_r ) }.
% 0.97/1.62 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.62 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), T ), Z ) ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal ), Y ) ), hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal ), X ) ) ) ), hAPP(
% 0.97/1.62 hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ),
% 0.97/1.62 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), T ), hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal ), Y ) ) ) ),
% 0.97/1.62 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), Z ), hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal ), X ) ) ) ) ) }.
% 0.97/1.62 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 0.97/1.62 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oone__class_Oone( X ) ) =
% 0.97/1.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X ), Y ), c_Groups_Oabs__class_Oabs( X,
% 0.97/1.62 Y ) ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.97/1.62 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.97/1.62 Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X ), Z ), Y ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X ), Z ), Y ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.97/1.62 Y ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X ), Z ), Y ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.97/1.62 Y ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.97/1.62 Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X ), Z ), Y ) }.
% 0.97/1.62 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.62 c_RealVector_Onorm__class_Onorm( X, Y ), c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_RealDef_Oreal ) ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless__eq(
% 0.97/1.62 tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( X, Y ),
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, hAPP
% 0.97/1.62 ( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 0.97/1.62 c_Groups_Oabs__class_Oabs( X, Y ) ) ) }.
% 0.97/1.62 { hAPP( c_Complex_OIm, c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.62 { hAPP( c_Complex_ORe, c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) )
% 0.97/1.62 = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.62 { hAPP( c_Complex_OIm, c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) )
% 0.97/1.62 = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.62 { c_RealVector_Onorm__class_Onorm( tc_RealDef_Oreal, X ) =
% 0.97/1.62 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) }.
% 0.97/1.62 { ! c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) =
% 0.97/1.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.97/1.62 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), Y ), hAPP
% 0.97/1.62 ( c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal ), X ) ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y = X }.
% 0.97/1.62 { ! Y = X, hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), Y )
% 0.97/1.62 , hAPP( c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal ), X ) ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.62 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), Y ), X ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X = hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal ), Y ) }.
% 0.97/1.62 { ! X = hAPP( c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal ), Y ),
% 0.97/1.62 hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), Y ), X ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.62 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.97/1.62 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), Y ), X ),
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal ), Y ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal ), Y ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), Y ), X ),
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), Y ), X ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal ), Y ), X ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal ), Y ), X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.97/1.62 { ! c_SEQ_Osubseq( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.97/1.62 hAPP( X, Y ) ) }.
% 0.97/1.62 { hAPP( c_Complex_ORe, hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 0.97/1.62 tc_Complex_Ocomplex ), Y ), X ) ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), hAPP( c_Complex_ORe, Y )
% 0.97/1.62 ), hAPP( c_Complex_ORe, X ) ) }.
% 0.97/1.62 { hAPP( c_Complex_OIm, hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 0.97/1.62 tc_Complex_Ocomplex ), Y ), X ) ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), hAPP( c_Complex_OIm, Y )
% 0.97/1.62 ), hAPP( c_Complex_OIm, X ) ) }.
% 0.97/1.62 { hAPP( c_Complex_ORe, c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) =
% 0.97/1.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.97/1.62 { ! class_Groups_Ozero( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y, Y =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) = Y }.
% 0.97/1.62 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.62 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Y ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ),
% 0.97/1.62 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex ), Y ), X ) ) ),
% 0.97/1.62 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) ) }.
% 0.97/1.62 { ! class_Groups_Ocancel__semigroup__add( X ), ! hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), Z ), T ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), Y ), T ), Z = Y }.
% 0.97/1.62 { ! class_Groups_Ocancel__ab__semigroup__add( X ), ! hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), T ), Z ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), T ), Y ), Z = Y }.
% 0.97/1.62 { ! class_Groups_Ocancel__semigroup__add( X ), ! hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), T ), Z ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), T ), Y ), Z = Y }.
% 0.97/1.62 { ! class_Groups_Ocancel__semigroup__add( X ), ! hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), T ), Z ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), Y ), Z ), T = Y }.
% 0.97/1.62 { ! class_Groups_Ocancel__semigroup__add( X ), ! T = Y, hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), T ), Z ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) }.
% 0.97/1.62 { ! class_Groups_Ocancel__semigroup__add( X ), ! hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), T ), Z ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), T ), Y ), Z = Y }.
% 0.97/1.62 { ! class_Groups_Ocancel__semigroup__add( X ), ! Z = Y, hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), T ), Z ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), T ), Y ) }.
% 0.97/1.62 { ! class_Groups_Oab__semigroup__add( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.97/1.62 ( X ), T ), Z ) ), Y ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), T
% 0.97/1.62 ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) }.
% 0.97/1.62 { ! class_Groups_Oone( X ), ! c_Groups_Oone__class_Oone( X ) = Y, Y =
% 0.97/1.62 c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.62 { ! class_Groups_Oone( X ), ! Y = c_Groups_Oone__class_Oone( X ),
% 0.97/1.62 c_Groups_Oone__class_Oone( X ) = Y }.
% 0.97/1.62 { ! class_Groups_Ogroup__add( X ), ! hAPP( c_Groups_Ouminus__class_Ouminus
% 0.97/1.62 ( X ), Z ) = hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ), Z = Y }.
% 0.97/1.62 { ! class_Groups_Ogroup__add( X ), ! Z = Y, hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X ), Z ) = hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X ), Y ) }.
% 0.97/1.62 { ! class_Groups_Ogroup__add( X ), ! hAPP( c_Groups_Ouminus__class_Ouminus
% 0.97/1.62 ( X ), Z ) = Y, hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ) = Z }.
% 0.97/1.62 { ! class_Groups_Ogroup__add( X ), ! hAPP( c_Groups_Ouminus__class_Ouminus
% 0.97/1.62 ( X ), Y ) = Z, hAPP( c_Groups_Ouminus__class_Ouminus( X ), Z ) = Y }.
% 0.97/1.62 { ! class_Groups_Ogroup__add( X ), ! Z = hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X ), Y ), Y = hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X ), Z ) }.
% 0.97/1.62 { ! class_Groups_Ogroup__add( X ), ! Y = hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X ), Z ), Z = hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X ), Y ) }.
% 0.97/1.62 { ! class_Groups_Ogroup__add( X ), hAPP( c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.62 ), hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ) ) = Y }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ), Y = X }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Z ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, Z ) }.
% 0.97/1.62 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ) }.
% 0.97/1.62 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, X ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.97/1.62 c_Groups_Oabs__class_Oabs( X, c_Groups_Oabs__class_Oabs( X, Y ) ) =
% 0.97/1.62 c_Groups_Oabs__class_Oabs( X, Y ) }.
% 0.97/1.62 { ! class_Groups_Ocomm__monoid__add( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), Y ), c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.62 = Y }.
% 0.97/1.62 { ! class_Groups_Omonoid__add( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.97/1.62 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.97/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), Y ), Y ), Y =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero( X ) = hAPP
% 0.97/1.62 ( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Y ) }.
% 0.97/1.62 { ! class_Groups_Ocomm__monoid__add( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), c_Groups_Ozero__class_Ozero( X ) ), Y )
% 0.97/1.62 = Y }.
% 0.97/1.62 { ! class_Groups_Omonoid__add( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.97/1.62 ( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) = Y }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), Z ), T ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), Y ), T ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), Z ), U ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), Y ), T ) ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), Z ), T ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), Y ), T ) ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) }.
% 0.97/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), ! hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X ), Y ) = Y, Y =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), hAPP( c_Groups_Ouminus__class_Ouminus(
% 0.97/1.62 X ), Y ) = Y }.
% 0.97/1.62 { ! class_Groups_Ogroup__add( X ), ! hAPP( c_Groups_Ouminus__class_Ouminus
% 0.97/1.62 ( X ), Y ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.62 hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y = hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X ), Y ), Y =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), Y = hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X ), Y ) }.
% 0.97/1.62 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.97/1.62 hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ),
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) = Y }.
% 0.97/1.62 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) = hAPP( c_Groups_Ouminus__class_Ouminus
% 0.97/1.62 ( X ), Y ) }.
% 0.97/1.62 { ! class_Groups_Ogroup__add( X ), hAPP( c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.62 ), c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.62 }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X ), Y ), hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X ), Z ) ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X ), Z ), hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X ), Y ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X ), Z ), hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X ), Z ), Y ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X ), Y ), Z ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X ), Y ), Z ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X ), Z ), Y ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X ), Y ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X ), Z ) ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X ), Z ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) }.
% 0.97/1.62 { ! class_Groups_Ogroup__add( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.97/1.62 ( X ), hAPP( c_Groups_Ouminus__class_Ouminus( X ), Z ) ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) = Y }.
% 0.97/1.62 { ! class_Groups_Ogroup__add( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.97/1.62 ( X ), Z ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X ), Z ) ), Y ) ) = Y }.
% 0.97/1.62 { ! class_Groups_Ogroup__add( X ), hAPP( c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.62 ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) = hAPP( hAPP
% 0.97/1.62 ( c_Groups_Oplus__class_Oplus( X ), hAPP( c_Groups_Ouminus__class_Ouminus
% 0.97/1.62 ( X ), Y ) ), hAPP( c_Groups_Ouminus__class_Ouminus( X ), Z ) ) }.
% 0.97/1.62 { ! class_Groups_Oab__group__add( X ), hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), hAPP( c_Groups_Ouminus__class_Ouminus(
% 0.97/1.62 X ), Z ) ), hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ) ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.97/1.62 c_Groups_Oabs__class_Oabs( X, Y ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__group__add__abs( X ), ! Y =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oabs__class_Oabs( X, Y ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.97/1.62 c_Groups_Oabs__class_Oabs( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.97/1.62 c_RealVector_Onorm__class_Onorm( X, Y ) = c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_RealDef_Oreal ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X, Y )
% 0.97/1.62 = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.62 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.97/1.62 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.97/1.62 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oabs__class_Oabs( X, Y
% 0.97/1.62 ) ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.97/1.62 c_Groups_Oabs__class_Oabs( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus( X
% 0.97/1.62 ), c_Groups_Oabs__class_Oabs( X, Z ) ), c_Groups_Oabs__class_Oabs( X, Y
% 0.97/1.62 ) ) ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ),
% 0.97/1.62 c_Groups_Oabs__class_Oabs( X, Z ) ), c_Groups_Oabs__class_Oabs( X, Y ) )
% 0.97/1.62 }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.97/1.62 c_Groups_Oabs__class_Oabs( X, hAPP( c_Groups_Ouminus__class_Ouminus( X )
% 0.97/1.62 , Y ) ) = c_Groups_Oabs__class_Oabs( X, Y ) }.
% 0.97/1.62 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.97/1.62 c_RealVector_Onorm__class_Onorm( X, hAPP( c_Groups_Ouminus__class_Ouminus
% 0.97/1.62 ( X ), Y ) ) = c_RealVector_Onorm__class_Onorm( X, Y ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), Z ), Y ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), Z ), X ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.62 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ), X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal ), X ), Y ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.62 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ), X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal ), X ), Y ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.62 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ), X ) }.
% 0.97/1.62 { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Oabs__class_Oabs
% 0.97/1.62 ( tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( X, Y ) ) =
% 0.97/1.62 c_RealVector_Onorm__class_Onorm( X, Y ) }.
% 0.97/1.62 { c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), Y ), hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal ), X ) ) ) =
% 0.97/1.62 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), X ), hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal ), Y ) ) ) }.
% 0.97/1.62 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.62 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Z ),
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.62 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) }.
% 0.97/1.62 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) }.
% 0.97/1.62 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.62 X ), Z ), ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Z ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 0.97/1.62 .
% 0.97/1.62 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.62 X ), Z ), ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Z ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.97/1.62 .
% 0.97/1.62 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.62 X ), Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), ! Z =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.97/1.62 ( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.62 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.97/1.62 ( X ), Y ), Z ) ) }.
% 0.97/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), Y ), Y ), c_Groups_Ozero__class_Ozero(
% 0.97/1.62 X ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.62 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), Y ), Y ), c_Groups_Ozero__class_Ozero(
% 0.97/1.62 X ) ) }.
% 0.97/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.62 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Y ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.62 ) }.
% 0.97/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.62 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.97/1.62 ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Y ) ) }.
% 0.97/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X ), Y ), Y ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.62 ) }.
% 0.97/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.62 ), c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X ), Y ), Y ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X ), Y ), c_Groups_Ozero__class_Ozero( X
% 0.97/1.62 ) ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.62 X ), Y ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.62 ), c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X ), Y ), c_Groups_Ozero__class_Ozero( X
% 0.97/1.62 ) ) }.
% 0.97/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X ), Y ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.62 ) }.
% 0.97/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.62 ), c_Orderings_Oord__class_Oless__eq( X, Y, hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.62 hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.62 ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.62 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.97/1.62 ), hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ) ) }.
% 0.97/1.62 { ! class_Groups_Ogroup__add( X ), ! hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) = c_Groups_Ozero__class_Ozero
% 0.97/1.62 ( X ), hAPP( c_Groups_Ouminus__class_Ouminus( X ), Z ) = Y }.
% 0.97/1.62 { ! class_Groups_Ogroup__add( X ), ! hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) = c_Groups_Ozero__class_Ozero
% 0.97/1.62 ( X ), Y = hAPP( c_Groups_Ouminus__class_Ouminus( X ), Z ) }.
% 0.97/1.62 { ! class_Groups_Ogroup__add( X ), ! Y = hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X ), Z ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) = c_Groups_Ozero__class_Ozero
% 0.97/1.62 ( X ) }.
% 0.97/1.62 { ! class_Groups_Oab__group__add( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), hAPP( c_Groups_Ouminus__class_Ouminus(
% 0.97/1.62 X ), Y ) ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_Groups_Ogroup__add( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.97/1.62 ( X ), hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ) ), Y ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_Groups_Ogroup__add( X ), ! Z = hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X ), Y ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) = c_Groups_Ozero__class_Ozero
% 0.97/1.62 ( X ) }.
% 0.97/1.62 { ! class_Groups_Ogroup__add( X ), ! hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) = c_Groups_Ozero__class_Ozero
% 0.97/1.62 ( X ), Z = hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ) }.
% 0.97/1.62 { ! class_Groups_Ogroup__add( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.97/1.62 ( X ), Y ), hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ) ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.62 ), c_Groups_Oabs__class_Oabs( X, Y ) = Y }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Y ),
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.62 }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__group__add__abs( X ), ! Y =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.62 c_Groups_Oabs__class_Oabs( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.62 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.97/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.97/1.62 { ! class_RealVector_Ometric__space( Y ), ! class_RealVector_Ometric__space
% 0.97/1.62 ( X ), ! c_Lim_OisUCont( X, Y, Z ), ! c_SEQ_OCauchy( X, T ),
% 0.97/1.62 c_SEQ_OCauchy( Y, c_COMBB( X, Y, tc_Nat_Onat, Z, T ) ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__semidom( X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.62 c_Groups_Oone__class_Oone( X ) ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__semidom( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.62 { ! class_Orderings_Opreorder( X ), c_Orderings_Oord__class_Oless__eq( X, Y
% 0.97/1.62 , Y ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ), X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ), X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), Z ), X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ), X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), T ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) }.
% 0.97/1.62 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.97/1.62 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.97/1.62 hAPP( Y, U ) ) }.
% 0.97/1.62 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, hAPP
% 0.97/1.62 ( Z, skol7( X, Y, Z ) ), hAPP( Y, skol7( X, Y, Z ) ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }.
% 0.97/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.62 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.97/1.62 ( X, Z, Y ) }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.97/1.62 ( X, Y, Z ) }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.62 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 0.97/1.62 { ! class_Orderings_Opreorder( X ), ! Z = Y,
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.62 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.97/1.62 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.97/1.62 hAPP( Y, U ) ) }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.62 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.62 , Y ), ! Y = Z, c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.97/1.62 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.97/1.62 ( X, Y, T ), c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), ! Z = Y, !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 0.97/1.62 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y
% 0.97/1.62 ), ! Y = T, c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.62 , Y ), ! Z = T, c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.62 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 0.97/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.62 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.62 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.62 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.97/1.62 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.97/1.62 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.97/1.62 hAPP( Y, U ) ) }.
% 0.97/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.62 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.97/1.62 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) = hAPP(
% 0.97/1.62 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Y ) }.
% 0.97/1.62 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) }.
% 0.97/1.62 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP( hAPP
% 0.97/1.62 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.62 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) = hAPP
% 0.97/1.62 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ), Y = X }.
% 0.97/1.62 { ! Y = X, hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y )
% 0.97/1.62 = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) }.
% 0.97/1.62 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) = hAPP
% 0.97/1.62 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Y ), Z = X }.
% 0.97/1.62 { ! Z = X, hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y )
% 0.97/1.62 = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Y ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ), Y = X }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ) }.
% 0.97/1.62 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ) }.
% 0.97/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, X ) }.
% 0.97/1.62 { ! hAPP( W, hAPP( U, T ) ) = hAPP( Z, hAPP( Y, X ) ), hAPP( c_Fun_Ocomp(
% 0.97/1.62 V4, V3, V2, W, U ), T ) = hAPP( c_Fun_Ocomp( V1, V3, V0, Z, Y ), X ) }.
% 0.97/1.62 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Oone__class_Oone( X ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.97/1.62 c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.62 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ),
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) = X }.
% 0.97/1.62 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ),
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = X }.
% 0.97/1.62 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.62 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.62 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.62 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) = Y, X
% 0.97/1.62 = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.62 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X,
% 0.97/1.62 c_Groups_Oone__class_Oone( X ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Y ) ) }.
% 0.97/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X = hAPP( hAPP
% 0.97/1.62 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), skol8( X, Y ) ) }.
% 0.97/1.62 { ! X = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), Z ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X = hAPP( hAPP
% 0.97/1.62 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), skol9( X, Y ) ) }.
% 0.97/1.62 { ! X = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), Z ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), ! c_SEQ_Odecseq( X, Y ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, T ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, T ), hAPP( Y, Z ) ) }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), c_Orderings_Oord__class_Oless__eq(
% 0.97/1.62 tc_Nat_Onat, skol10( X, Y ), skol61( X, Y ) ), c_SEQ_Odecseq( X, Y ) }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.62 hAPP( Y, skol61( X, Y ) ), hAPP( Y, skol10( X, Y ) ) ), c_SEQ_Odecseq( X
% 0.97/1.62 , Y ) }.
% 0.97/1.62 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X ), Z ), hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X ), Y ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.97/1.62 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X ), Z ), hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) }.
% 0.97/1.62 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X ), Y ), hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X ), Z ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), c_Groups_Ozero__class_Ozero( X ) ), Y )
% 0.97/1.62 = Y }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), Y ), c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.62 = Y }.
% 0.97/1.62 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.62 ( X ), ! Z = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), Y ), Y =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.62 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z = hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) }.
% 0.97/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), ! hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), Y ), Y ) = c_Groups_Ozero__class_Ozero
% 0.97/1.62 ( X ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.97/1.62 ( X ), Y ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), ! c_SEQ_Oincseq( X, Y ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, T ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, Z ), hAPP( Y, T ) ) }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), c_Orderings_Oord__class_Oless__eq(
% 0.97/1.62 tc_Nat_Onat, skol11( X, Y ), skol62( X, Y ) ), c_SEQ_Oincseq( X, Y ) }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.62 hAPP( Y, skol11( X, Y ) ), hAPP( Y, skol62( X, Y ) ) ), c_SEQ_Oincseq( X
% 0.97/1.62 , Y ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__group__add( X ), ! c_SEQ_Odecseq( X, Y ),
% 0.97/1.62 c_SEQ_Oincseq( X, c_COMBB( X, X, tc_Nat_Onat,
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__group__add( X ), ! c_SEQ_Oincseq( X, c_COMBB
% 0.97/1.62 ( X, X, tc_Nat_Onat, c_Groups_Ouminus__class_Ouminus( X ), Y ) ),
% 0.97/1.62 c_SEQ_Odecseq( X, Y ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.97/1.62 ( X ), U ), T ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), Y )
% 0.97/1.62 ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), U ), Z ) ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.97/1.62 ( X ), T ), Z ) ), Y ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ),
% 0.97/1.62 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), T ), Y ) ), Z ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.97/1.62 ( X ), T ), Z ) ), Y ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), T
% 0.97/1.62 ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), T ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.97/1.62 ( X ), T ), Z ) ), Y ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), T ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), Z ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) }.
% 0.97/1.62 { ! class_Lattices_Oboolean__algebra( X ), ! hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X ), Z ) = hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X ), Y ), Z = Y }.
% 0.97/1.62 { ! class_Lattices_Oboolean__algebra( X ), ! Z = Y, hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X ), Z ) = hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X ), Y ) }.
% 0.97/1.62 { ! class_Groups_Ouminus( X ), hAPP( hAPP( c_Groups_Ouminus__class_Ouminus
% 0.97/1.62 ( tc_fun( T, X ) ), Z ), Y ) = hAPP( c_Groups_Ouminus__class_Ouminus( X )
% 0.97/1.62 , hAPP( Z, Y ) ) }.
% 0.97/1.62 { ! class_Lattices_Oboolean__algebra( X ), hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X ), hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) = Y }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), ! c_SEQ_Oincseq( X, Y ), c_SEQ_Omonoseq( X
% 0.97/1.62 , Y ) }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), ! c_SEQ_Odecseq( X, Y ), c_SEQ_Omonoseq( X
% 0.97/1.62 , Y ) }.
% 0.97/1.62 { ! class_Groups_Ouminus( X ), hAPP( hAPP( c_Groups_Ouminus__class_Ouminus
% 0.97/1.62 ( tc_fun( T, X ) ), Z ), Y ) = hAPP( c_Groups_Ouminus__class_Ouminus( X )
% 0.97/1.62 , hAPP( Z, Y ) ) }.
% 0.97/1.62 { c_Complex_Oexpi( c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) =
% 0.97/1.62 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) }.
% 0.97/1.62 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, skol12( U, W, V0, T )
% 0.97/1.62 ), c_SEQ_OBseq( X, Y ) }.
% 0.97/1.62 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.62 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol12( X, Y, Z, T ) ) ), Z
% 0.97/1.62 ), c_SEQ_OBseq( X, Y ) }.
% 0.97/1.62 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X,
% 0.97/1.62 c_Groups_Osgn__class_Osgn( X, Y ) ) = c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_RealDef_Oreal ) }.
% 0.97/1.62 { ! class_RealVector_Oreal__normed__vector( X ), Y =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X,
% 0.97/1.62 c_Groups_Osgn__class_Osgn( X, Y ) ) = c_Groups_Oone__class_Oone(
% 0.97/1.62 tc_RealDef_Oreal ) }.
% 0.97/1.62 { ! class_Groups_Ozero( X ), !
% 0.97/1.62 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.62 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Polynomial_Opoly( X ) ),
% 0.97/1.62 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.97/1.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), c_SEQ_OBseq(
% 0.97/1.62 tc_RealDef_Oreal, hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal )
% 0.97/1.62 , X ) ) }.
% 0.97/1.62 { hAPP( c_Fun_Ocomp( W, U, T, c_COMBK( U, W, Z ), Y ), X ) = Z }.
% 0.97/1.62 { hAPP( c_Fun_Ocomp( W, U, T, Z, Y ), X ) = hAPP( Z, hAPP( Y, X ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.97/1.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), c_SEQ_Omonoseq(
% 0.97/1.62 tc_RealDef_Oreal, hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal )
% 0.97/1.62 , X ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.97/1.62 tc_Nat_Onat ) ) = Y }.
% 0.97/1.62 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 0.97/1.62 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.97/1.62 c_RealVector_Onorm__class_Onorm( X, Z ) ), Y ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__idom( X ), c_Groups_Osgn__class_Osgn( X,
% 0.97/1.62 c_Groups_Osgn__class_Osgn( X, Y ) ) = c_Groups_Osgn__class_Osgn( X, Y ) }
% 0.97/1.62 .
% 0.97/1.62 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.62 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.97/1.62 c_RealVector_Onorm__class_Onorm( X, Z ) ), Y ) ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 0.97/1.62 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.62 }.
% 0.97/1.62 { ! class_Rings_Olinordered__idom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.62 X ), c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.62 }.
% 0.97/1.62 { ! class_Groups_Osgn__if( X ), c_Groups_Osgn__class_Osgn( X,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Osgn__class_Osgn
% 0.97/1.62 ( X, c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X
% 0.97/1.62 ) }.
% 0.97/1.62 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.97/1.62 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 0.97/1.62 c_Groups_Osgn__class_Osgn( X, c_Groups_Oone__class_Oone( X ) ) =
% 0.97/1.62 c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.62 { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Osgn__class_Osgn
% 0.97/1.62 ( X, hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ) ) = hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X ), c_Groups_Osgn__class_Osgn( X, Y ) )
% 0.97/1.62 }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.62 { c_Fun_Ocomp( V0, W, U, T, c_Fun_Ocomp( Z, V0, U, Y, X ) ) = c_Fun_Ocomp(
% 0.97/1.62 Z, W, U, c_Fun_Ocomp( V0, W, Z, T, Y ), X ) }.
% 0.97/1.62 { hAPP( c_Fun_Ocomp( W, U, T, Z, Y ), X ) = hAPP( Z, hAPP( Y, X ) ) }.
% 0.97/1.62 { ! c_Fun_Ocomp( W, U, T, Z, Y ) = X, hAPP( Z, hAPP( Y, V0 ) ) = hAPP( X,
% 0.97/1.62 V0 ) }.
% 0.97/1.62 { ! c_Fun_Ocomp( V1, V0, W, T, Z ) = c_Fun_Ocomp( U, V0, W, Y, X ), hAPP( T
% 0.97/1.62 , hAPP( Z, V2 ) ) = hAPP( Y, hAPP( X, V2 ) ) }.
% 0.97/1.62 { ! c_Fun_Ocomp( V1, V0, W, T, Z ) = c_Fun_Ocomp( U, V0, W, Y, X ), hAPP( T
% 0.97/1.62 , hAPP( Z, V2 ) ) = hAPP( Y, hAPP( X, V2 ) ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__semidom( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.97/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oone__class_Oone
% 0.97/1.62 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__semidom( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), T )
% 0.97/1.62 , c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__idom( X ), c_Orderings_Oord__class_Oless__eq(
% 0.97/1.62 X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), c_Groups_Oabs__class_Oabs( X, Z ) ), Y
% 0.97/1.62 ) ) }.
% 0.97/1.62 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), ! Y =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.97/1.62 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.62 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), Y =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.97/1.62 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X, hAPP
% 0.97/1.62 ( hAPP( c_Power_Opower__class_Opower( X ), hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X ), Z ) ), Y ) ) =
% 0.97/1.62 c_Groups_Oabs__class_Oabs( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.97/1.62 ), Z ), Y ) ) }.
% 0.97/1.62 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.97/1.62 , Y ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.97/1.62 c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.62 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.97/1.62 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.97/1.62 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.97/1.62 .
% 0.97/1.62 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.97/1.62 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.97/1.62 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Nat_Onat ) }.
% 0.97/1.62 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.97/1.62 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.97/1.62 , ! Z = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 0.97/1.62 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y )
% 0.97/1.62 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.97/1.62 tc_Nat_Onat ) ) = Y }.
% 0.97/1.62 { ! class_Rings_Oring__1__no__zero__divisors( X ), Y =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 0.97/1.62 ( X ) }.
% 0.97/1.62 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.97/1.62 = c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X, hAPP
% 0.97/1.62 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), c_Groups_Oabs__class_Oabs( X, Z ) ), Y
% 0.97/1.62 ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__semidom( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.97/1.62 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__semidom( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.62 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.97/1.62 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__semidom( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), Y )
% 0.97/1.62 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.97/1.62 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.62 c_RComplete_Onatceiling( hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 0.97/1.62 tc_RealDef_Oreal ), X ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 0.97/1.62 ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ),
% 0.97/1.62 c_RComplete_Onatceiling( X ) ), c_Groups_Oone__class_Oone( tc_Nat_Onat )
% 0.97/1.62 ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.62 c_RComplete_Onatfloor( hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 0.97/1.62 tc_RealDef_Oreal ), X ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 0.97/1.62 ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ),
% 0.97/1.62 c_RComplete_Onatfloor( X ) ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) )
% 0.97/1.62 }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.97/1.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), c_SEQ_Oconvergent(
% 0.97/1.62 tc_RealDef_Oreal, hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal )
% 0.97/1.62 , X ) ) }.
% 0.97/1.62 { hAPP( c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex ), X ) =
% 0.97/1.62 c_Complex_Ocomplex_OComplex( hAPP( c_Groups_Ouminus__class_Ouminus(
% 0.97/1.62 tc_RealDef_Oreal ), hAPP( c_Complex_ORe, X ) ), hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal ), hAPP( c_Complex_OIm
% 0.97/1.62 , X ) ) ) }.
% 0.97/1.62 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex ), Y ), X )
% 0.97/1.62 = c_Complex_Ocomplex_OComplex( hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 0.97/1.62 tc_RealDef_Oreal ), hAPP( c_Complex_ORe, Y ) ), hAPP( c_Complex_ORe, X )
% 0.97/1.62 ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), hAPP(
% 0.97/1.62 c_Complex_OIm, Y ) ), hAPP( c_Complex_OIm, X ) ) ) }.
% 0.97/1.62 { hAPP( c_RealVector_Oof__real( tc_Complex_Ocomplex ), hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal ),
% 0.97/1.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) = hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex ),
% 0.97/1.62 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) }.
% 0.97/1.62 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol13( Z, T ) ) }.
% 0.97/1.62 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.62 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, Z ) ), skol13( X, Y ) ) }.
% 0.97/1.62 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.62 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol63( X, Y, Z ) ) ), Z ),
% 0.97/1.62 c_SEQ_OBseq( X, Y ) }.
% 0.97/1.62 { ! class_RealVector_Ometric__space( X ), c_SEQ_Oconvergent( X, c_COMBK( X
% 0.97/1.62 , tc_Nat_Onat, Y ) ) }.
% 0.97/1.62 { ! class_RealVector_Oreal__algebra__1( X ), ! hAPP( c_RealVector_Oof__real
% 0.97/1.62 ( X ), Z ) = hAPP( c_RealVector_Oof__real( X ), Y ), Z = Y }.
% 0.97/1.62 { ! class_RealVector_Oreal__algebra__1( X ), ! Z = Y, hAPP(
% 0.97/1.62 c_RealVector_Oof__real( X ), Z ) = hAPP( c_RealVector_Oof__real( X ), Y )
% 0.97/1.62 }.
% 0.97/1.62 { ! class_RealVector_Oreal__algebra__1( X ), !
% 0.97/1.62 class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_Oconvergent(
% 0.97/1.62 tc_RealDef_Oreal, Y ), c_SEQ_Oconvergent( X, c_COMBB( tc_RealDef_Oreal, X
% 0.97/1.62 , tc_Nat_Onat, c_RealVector_Oof__real( X ), Y ) ) }.
% 0.97/1.62 { ! c_Complex_Ocomplex_OComplex( T, Z ) = c_Complex_Ocomplex_OComplex( Y, X
% 0.97/1.62 ), T = Y }.
% 0.97/1.62 { ! c_Complex_Ocomplex_OComplex( T, Z ) = c_Complex_Ocomplex_OComplex( Y, X
% 0.97/1.62 ), Z = X }.
% 0.97/1.62 { ! T = Y, ! Z = X, c_Complex_Ocomplex_OComplex( T, Z ) =
% 0.97/1.62 c_Complex_Ocomplex_OComplex( Y, X ) }.
% 0.97/1.62 { ! class_RealVector_Oreal__algebra__1( X ), !
% 0.97/1.62 class_RealVector_Oreal__normed__vector( X ), c_Lim_OisUCont(
% 0.97/1.62 tc_RealDef_Oreal, X, c_RealVector_Oof__real( X ) ) }.
% 0.97/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.97/1.62 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.62 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.62 , ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.97/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.62 Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.62 , ! Z = T, c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.97/1.62 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 0.97/1.62 ! Y = T, c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless(
% 0.97/1.62 X, T, Y ), c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.97/1.62 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X
% 0.97/1.62 , Y, T ), c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.62 , ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.62 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.62 , ! Y = Z }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.62 , ! Z = Y }.
% 0.97/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.62 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.62 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.62 , ! Z = Y }.
% 0.97/1.62 { ! class_Rings_Olinordered__idom( X ), Z = Y,
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.97/1.62 X, Y, Z ) }.
% 0.97/1.62 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 0.97/1.62 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.97/1.62 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Y = Z }.
% 0.97/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.97/1.62 ), ! Y = Z, ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.97/1.62 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.97/1.62 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Z = Y }.
% 0.97/1.62 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.97/1.62 Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.62 { ! class_Orderings_Olinorder( X ), ! Z = Y, !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.62 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 0.97/1.62 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.62 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.62 Y ), ! Z = Y }.
% 0.97/1.62 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.97/1.62 Z ), ! Z = Y }.
% 0.97/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.97/1.62 Y ) }.
% 0.97/1.62 { ! c_Complex_Ocomplex_OComplex( Z, Y ) = hAPP( c_RealVector_Oof__real(
% 0.97/1.62 tc_Complex_Ocomplex ), X ), Z = X }.
% 0.97/1.62 { ! c_Complex_Ocomplex_OComplex( Z, Y ) = hAPP( c_RealVector_Oof__real(
% 0.97/1.62 tc_Complex_Ocomplex ), X ), Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_RealDef_Oreal ) }.
% 0.97/1.62 { ! Z = X, ! Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.97/1.62 c_Complex_Ocomplex_OComplex( Z, Y ) = hAPP( c_RealVector_Oof__real(
% 0.97/1.62 tc_Complex_Ocomplex ), X ) }.
% 0.97/1.62 { hAPP( c_RealVector_Oof__real( tc_Complex_Ocomplex ), X ) =
% 0.97/1.62 c_Complex_Ocomplex_OComplex( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_RealDef_Oreal ) ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.62 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.62 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.97/1.62 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.62 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.62 ( tc_Nat_Onat, T, Z ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.62 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.62 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.97/1.62 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.62 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.97/1.62 c_Groups_Oone__class_Oone( X ), T ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.62 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.97/1.62 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex ),
% 0.97/1.62 c_Complex_Ocomplex_OComplex( Z, Y ) ), hAPP( c_RealVector_Oof__real(
% 0.97/1.62 tc_Complex_Ocomplex ), X ) ) = c_Complex_Ocomplex_OComplex( hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), Z ), X ), Y ) }.
% 0.97/1.62 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex ), hAPP(
% 0.97/1.62 c_RealVector_Oof__real( tc_Complex_Ocomplex ), Z ) ),
% 0.97/1.62 c_Complex_Ocomplex_OComplex( Y, X ) ) = c_Complex_Ocomplex_OComplex( hAPP
% 0.97/1.62 ( hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), Z ), Y ), X ) }
% 0.97/1.62 .
% 0.97/1.62 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), hAPP(
% 0.97/1.62 c_RealVector_Oof__real( tc_Complex_Ocomplex ), Y ) ), X ) = hAPP(
% 0.97/1.62 c_RealVector_Oof__real( tc_Complex_Ocomplex ), hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.97/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.97/1.62 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.97/1.62 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.62 , Y, Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.62 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.62 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.97/1.62 Z ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.62 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.62 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.62 , ! Z = Y }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.62 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.62 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.62 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.97/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.62 , Z, Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.62 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.62 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.97/1.62 ( X, Z, Y ) }.
% 0.97/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.97/1.62 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.97/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.62 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.97/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ), Z = Y }.
% 0.97/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.97/1.62 ), ! Z = Y, c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.97/1.62 ( X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.97/1.62 ( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.62 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.62 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.62 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.62 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.62 , Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.97/1.62 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.62 , Z, Y ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.62 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.62 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.62 , Y ), Y = Z, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.62 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.62 , ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.97/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.62 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.62 , Y ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.97/1.62 ( X ), T ), Z ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Z ) )
% 0.97/1.62 , c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, T, Y ), c_Orderings_Oord__class_Oless(
% 0.97/1.62 X, hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.97/1.62 ( X ), T ), Z ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), T ), Y ) )
% 0.97/1.62 , c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.97/1.62 X, hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ) }.
% 0.97/1.62 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.97/1.62 X, hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), T ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), Y ), T ) ) }.
% 0.97/1.62 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.97/1.62 X, hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ) }.
% 0.97/1.62 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.62 ( X, U, T ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), Z ), U ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), Y ), T ) ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.97/1.62 ( X ), Z ), T ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), T ) )
% 0.97/1.62 , c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.97/1.62 ( X ), T ), Z ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), T ), Y ) )
% 0.97/1.62 , c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.62 { hAPP( c_Complex_ORe, hAPP( c_RealVector_Oof__real( tc_Complex_Ocomplex )
% 0.97/1.62 , X ) ) = X }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, Z, hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X ), Y ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, Y, hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X ), Z ) ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, Y, hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X ), Z ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, Z, hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, hAPP( c_Groups_Ouminus__class_Ouminus(
% 0.97/1.62 X ), Z ), Y ), c_Orderings_Oord__class_Oless( X, hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X ), Y ), Z ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, hAPP( c_Groups_Ouminus__class_Ouminus(
% 0.97/1.62 X ), Y ), Z ), c_Orderings_Oord__class_Oless( X, hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X ), Z ), Y ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, hAPP( c_Groups_Ouminus__class_Ouminus(
% 0.97/1.62 X ), Z ), hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, Y, Z ), c_Orderings_Oord__class_Oless(
% 0.97/1.62 X, hAPP( c_Groups_Ouminus__class_Ouminus( X ), Z ), hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), ! Y = X }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), Y = X,
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), Y = X }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.97/1.62 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.97/1.62 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 0.97/1.62 c_Groups_Osgn__class_Osgn( X, hAPP( c_RealVector_Oof__real( X ), Y ) ) =
% 0.97/1.62 hAPP( c_RealVector_Oof__real( X ), c_Groups_Osgn__class_Osgn(
% 0.97/1.62 tc_RealDef_Oreal, Y ) ) }.
% 0.97/1.62 { hAPP( c_Complex_ORe, c_Complex_Ocomplex_OComplex( Y, X ) ) = Y }.
% 0.97/1.62 { hAPP( c_Complex_OIm, c_Complex_Ocomplex_OComplex( Y, X ) ) = X }.
% 0.97/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.62 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.62 , T, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.62 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.62 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.62 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), hAPP(
% 0.97/1.62 hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.97/1.62 { c_RComplete_Onatfloor( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) )
% 0.97/1.62 = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.62 { ! class_SEQ_Ocomplete__space( X ), ! c_SEQ_OCauchy( X, Y ),
% 0.97/1.62 c_SEQ_Oconvergent( X, Y ) }.
% 0.97/1.62 { ! class_SEQ_Ocomplete__space( X ), ! c_SEQ_Oconvergent( X, Y ),
% 0.97/1.62 c_SEQ_OCauchy( X, Y ) }.
% 0.97/1.62 { ! class_SEQ_Ocomplete__space( X ), ! c_SEQ_OCauchy( X, Y ),
% 0.97/1.62 c_SEQ_Oconvergent( X, Y ) }.
% 0.97/1.62 { ! class_RealVector_Ometric__space( X ), ! c_SEQ_Oconvergent( X, Y ),
% 0.97/1.62 c_SEQ_OCauchy( X, Y ) }.
% 0.97/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) )
% 0.97/1.62 }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatfloor( Y
% 0.97/1.62 ), c_RComplete_Onatfloor( X ) ) }.
% 0.97/1.62 { c_RComplete_Onatfloor( c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) =
% 0.97/1.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.97/1.62 { c_RComplete_Onatceiling( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal )
% 0.97/1.62 ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_RComplete_Onatceiling( X )
% 0.97/1.62 ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 0.97/1.62 Y ), c_RComplete_Onatceiling( X ) ) }.
% 0.97/1.62 { ! c_SEQ_OCauchy( tc_RealDef_Oreal, X ), c_SEQ_Oconvergent(
% 0.97/1.62 tc_RealDef_Oreal, X ) }.
% 0.97/1.62 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_Oconvergent( X, Y
% 0.97/1.62 ), ! c_SEQ_Oconvergent( X, Z ), c_SEQ_Oconvergent( X, c_COMBS(
% 0.97/1.62 tc_Nat_Onat, X, X, c_COMBB( X, tc_fun( X, X ), tc_Nat_Onat,
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) }.
% 0.97/1.62 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_Oconvergent( X, Y
% 0.97/1.62 ), c_SEQ_Oconvergent( X, c_COMBB( X, X, tc_Nat_Onat,
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) }.
% 0.97/1.62 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_Oconvergent( X,
% 0.97/1.62 c_COMBB( X, X, tc_Nat_Onat, c_Groups_Ouminus__class_Ouminus( X ), Y ) ),
% 0.97/1.62 c_SEQ_Oconvergent( X, Y ) }.
% 0.97/1.62 { c_RComplete_Onatceiling( c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 0.97/1.62 = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.62 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), Z ), ! c_Orderings_Oord__class_Oless(
% 0.97/1.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), T ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.97/1.62 { ! class_RealVector_Oreal__algebra__1( X ), hAPP( c_RealVector_Oof__real(
% 0.97/1.62 X ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_RealVector_Oreal__algebra__1( X ), !
% 0.97/1.62 class_RealVector_Oreal__normed__vector( X ), hAPP( c_RealVector_Oof__real
% 0.97/1.62 ( X ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_RealVector_Oreal__algebra__1( X ), ! hAPP( c_RealVector_Oof__real
% 0.97/1.62 ( X ), Y ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.62 { ! class_RealVector_Oreal__algebra__1( X ), ! Y =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP(
% 0.97/1.62 c_RealVector_Oof__real( X ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { hAPP( c_Complex_OIm, hAPP( c_RealVector_Oof__real( tc_Complex_Ocomplex )
% 0.97/1.62 , X ) ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.62 { ! class_RealVector_Oreal__algebra__1( X ), hAPP( c_RealVector_Oof__real(
% 0.97/1.62 X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), Z ), Y
% 0.97/1.62 ) ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP(
% 0.97/1.62 c_RealVector_Oof__real( X ), Z ) ), hAPP( c_RealVector_Oof__real( X ), Y
% 0.97/1.62 ) ) }.
% 0.97/1.62 { ! class_RealVector_Oreal__algebra__1( X ), !
% 0.97/1.62 class_RealVector_Oreal__normed__vector( X ), hAPP( c_RealVector_Oof__real
% 0.97/1.62 ( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), Z ),
% 0.97/1.62 Y ) ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP(
% 0.97/1.62 c_RealVector_Oof__real( X ), Z ) ), hAPP( c_RealVector_Oof__real( X ), Y
% 0.97/1.62 ) ) }.
% 0.97/1.62 { ! class_RealVector_Oreal__algebra__1( X ), hAPP( c_RealVector_Oof__real(
% 0.97/1.62 X ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) =
% 0.97/1.62 c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.62 { ! class_RealVector_Oreal__algebra__1( X ), hAPP( c_RealVector_Oof__real(
% 0.97/1.62 X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Z ), Y
% 0.97/1.62 ) ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), hAPP(
% 0.97/1.62 c_RealVector_Oof__real( X ), Z ) ), Y ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.62 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless(
% 0.97/1.62 X, T, hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) }.
% 0.97/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.97/1.62 ( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Y ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.97/1.62 .
% 0.97/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.97/1.62 ( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Y ) ) }.
% 0.97/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.97/1.62 ( X ), Y ), Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.97/1.62 .
% 0.97/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.97/1.62 ( X ), Y ), Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.62 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.62 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.97/1.62 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.62 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) }.
% 0.97/1.62 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.62 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.62 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), Y ), Z ), c_Groups_Ozero__class_Ozero(
% 0.97/1.62 X ) ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.62 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Y ),
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Y,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.62 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.97/1.62 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Y ),
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.62 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.97/1.62 ( X ), Z ), U ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), T ) )
% 0.97/1.62 }.
% 0.97/1.62 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, U, T ), c_Orderings_Oord__class_Oless(
% 0.97/1.62 X, hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), U ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), Y ), T ) ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.62 ( X, c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero( X ) ) }
% 0.97/1.62 .
% 0.97/1.62 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.97/1.62 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.62 , Y, hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.97/1.62 .
% 0.97/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.62 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.97/1.62 , Y, hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ) ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.97/1.62 ( c_Groups_Ouminus__class_Ouminus( X ), Y ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.97/1.62 .
% 0.97/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.97/1.62 ( c_Groups_Ouminus__class_Ouminus( X ), Y ) ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, hAPP( c_Groups_Ouminus__class_Ouminus(
% 0.97/1.62 X ), Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.97/1.62 .
% 0.97/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, hAPP( c_Groups_Ouminus__class_Ouminus(
% 0.97/1.62 X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, hAPP( c_Groups_Ouminus__class_Ouminus(
% 0.97/1.62 X ), Y ), Y ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.97/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, hAPP( c_Groups_Ouminus__class_Ouminus(
% 0.97/1.62 X ), Y ), Y ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.62 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless
% 0.97/1.62 ( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.97/1.62 { ! class_RealVector_Oreal__algebra__1( X ), hAPP( c_RealVector_Oof__real(
% 0.97/1.62 X ), hAPP( c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal ), Y ) ) =
% 0.97/1.62 hAPP( c_Groups_Ouminus__class_Ouminus( X ), hAPP( c_RealVector_Oof__real
% 0.97/1.62 ( X ), Y ) ) }.
% 0.97/1.62 { ! class_RealVector_Oreal__algebra__1( X ), !
% 0.97/1.62 class_RealVector_Oreal__normed__vector( X ), hAPP( c_RealVector_Oof__real
% 0.97/1.62 ( X ), hAPP( c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal ), Y ) ) =
% 0.97/1.62 hAPP( c_Groups_Ouminus__class_Ouminus( X ), hAPP( c_RealVector_Oof__real
% 0.97/1.62 ( X ), Y ) ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.97/1.62 , Y, hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ),
% 0.97/1.62 c_Groups_Oone__class_Oone( X ) ) ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.62 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), Y ), Z ), T = Z }.
% 0.97/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.62 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! T = Z, hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), Y ), Z ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Oabs__class_Oabs( X, Y ),
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.62 c_Groups_Oabs__class_Oabs( X, Y ) ), ! Y = c_Groups_Ozero__class_Ozero( X
% 0.97/1.62 ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__group__add__abs( X ), Y =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.62 c_Groups_Oabs__class_Oabs( X, Y ) = Y }.
% 0.97/1.62 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 0.97/1.62 c_RealVector_Onorm__class_Onorm( X, hAPP( c_RealVector_Oof__real( X ), Y
% 0.97/1.62 ) ) = c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.62 , c_Groups_Oabs__class_Oabs( X, Z ), Y ), c_Orderings_Oord__class_Oless(
% 0.97/1.62 X, Z, Y ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.62 , c_Groups_Oabs__class_Oabs( X, Z ), Y ), c_Orderings_Oord__class_Oless(
% 0.97/1.62 X, hAPP( c_Groups_Ouminus__class_Ouminus( X ), Z ), Y ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.62 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X ), Z ), Y ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Oabs__class_Oabs( X, Z ), Y )
% 0.97/1.62 }.
% 0.97/1.62 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.62 c_RealVector_Onorm__class_Onorm( X, Y ), c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_RealDef_Oreal ) ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.62 , c_Groups_Osgn__class_Osgn( X, Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.97/1.62 .
% 0.97/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.62 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.97/1.62 , c_Groups_Osgn__class_Osgn( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }
% 0.97/1.62 .
% 0.97/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.62 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.97/1.62 .
% 0.97/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.62 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless( X
% 0.97/1.62 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) ) }
% 0.97/1.62 .
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.62 c_Groups_Osgn__class_Osgn( tc_RealDef_Oreal, X ) =
% 0.97/1.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.97/1.62 { c_Complex_Ocomplex_OComplex( hAPP( c_Complex_ORe, X ), hAPP(
% 0.97/1.62 c_Complex_OIm, X ) ) = X }.
% 0.97/1.62 { ! c_Complex_Ocomplex_OComplex( Y, X ) = c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Complex_Ocomplex ), Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal
% 0.97/1.62 ) }.
% 0.97/1.62 { ! c_Complex_Ocomplex_OComplex( Y, X ) = c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Complex_Ocomplex ), X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal
% 0.97/1.62 ) }.
% 0.97/1.62 { ! Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! X =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.97/1.62 c_Complex_Ocomplex_OComplex( Y, X ) = c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Complex_Ocomplex ) }.
% 0.97/1.62 { c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) =
% 0.97/1.62 c_Complex_Ocomplex_OComplex( c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_RealDef_Oreal ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), c_RComplete_Onatfloor
% 0.97/1.62 ( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.62 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex ),
% 0.97/1.62 c_Complex_Ocomplex_OComplex( T, Z ) ), c_Complex_Ocomplex_OComplex( Y, X
% 0.97/1.62 ) ) = c_Complex_Ocomplex_OComplex( hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), T ), Y ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), Z ), X ) ) }.
% 0.97/1.62 { hAPP( c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex ),
% 0.97/1.62 c_Complex_Ocomplex_OComplex( Y, X ) ) = c_Complex_Ocomplex_OComplex( hAPP
% 0.97/1.62 ( c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal ), Y ), hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal ), X ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.97/1.62 c_RComplete_Onatceiling( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.97/1.62 }.
% 0.97/1.62 { ! class_RealVector_Oreal__algebra__1( X ), !
% 0.97/1.62 class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OCauchy(
% 0.97/1.62 tc_RealDef_Oreal, Y ), c_SEQ_OCauchy( X, c_COMBB( tc_RealDef_Oreal, X,
% 0.97/1.62 tc_Nat_Onat, c_RealVector_Oof__real( X ), Y ) ) }.
% 0.97/1.62 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.62 ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.62 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.62 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) }.
% 0.97/1.62 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.62 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.62 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.62 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) }.
% 0.97/1.62 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.62 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) }.
% 0.97/1.62 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.62 ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) }.
% 0.97/1.62 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.62 ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.97/1.62 ) ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), Y ), Z ), c_Groups_Ozero__class_Ozero(
% 0.97/1.62 X ) ) }.
% 0.97/1.62 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.62 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.97/1.62 ) ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), Y ), Z ), c_Groups_Ozero__class_Ozero(
% 0.97/1.62 X ) ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.62 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP
% 0.97/1.62 ( c_Power_Opower__class_Opower( X ), Y ), T ) ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.62 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.97/1.62 , c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), c_Groups_Oone__class_Oone( X ) ),
% 0.97/1.62 c_Groups_Oone__class_Oone( X ) ) ) }.
% 0.97/1.62 { ! c_SEQ_OBseq( tc_RealDef_Oreal, X ), ! c_SEQ_Omonoseq( tc_RealDef_Oreal
% 0.97/1.62 , X ), c_SEQ_Oconvergent( tc_RealDef_Oreal, X ) }.
% 0.97/1.62 { ! class_Groups_Oabs__if( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Oabs__class_Oabs( X, Y ) =
% 0.97/1.62 hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ) }.
% 0.97/1.62 { ! class_Groups_Oabs__if( X ), c_Orderings_Oord__class_Oless( X, Y,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Oabs__class_Oabs( X, Y ) = Y
% 0.97/1.62 }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.62 c_Groups_Oabs__class_Oabs( X, Y ) = hAPP( c_Groups_Ouminus__class_Ouminus
% 0.97/1.62 ( X ), Y ) }.
% 0.97/1.62 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.97/1.62 c_RealVector_Onorm__class_Onorm( X, Y ) ), ! Y =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_RealVector_Oreal__normed__vector( X ), Y =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless(
% 0.97/1.62 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.97/1.62 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 0.97/1.62 = c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.62 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Groups_Osgn__class_Osgn( X, Y
% 0.97/1.62 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.62 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Groups_Osgn__class_Osgn( X, Y
% 0.97/1.62 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.62 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.62 c_RealVector_Onorm__class_Onorm( X, Z ), Y ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.62 c_RealVector_Onorm__class_Onorm( X, U ), T ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.62 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), Z ), U ) ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), Y ), T ) ) }.
% 0.97/1.62 { ! X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.97/1.62 c_Groups_Osgn__class_Osgn( tc_RealDef_Oreal, X ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.62 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.62 c_Groups_Osgn__class_Osgn( tc_RealDef_Oreal, X ) =
% 0.97/1.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.97/1.62 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.62 c_Groups_Osgn__class_Osgn( tc_RealDef_Oreal, X ) = hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal ),
% 0.97/1.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.97/1.62 { ! X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.97/1.62 c_Groups_Osgn__class_Osgn( tc_RealDef_Oreal, X ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.62 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.62 c_Groups_Osgn__class_Osgn( tc_RealDef_Oreal, X ) =
% 0.97/1.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.97/1.62 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.62 c_Groups_Osgn__class_Osgn( tc_RealDef_Oreal, X ) = hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal ),
% 0.97/1.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), Y ), X ),
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal ), Y ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal ), Y ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), Y ), X ),
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), Y ), X ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal ), Y ), X ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal ), Y ), X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.97/1.62 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) = hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal ), X ) }.
% 0.97/1.62 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.97/1.62 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) = X }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.97/1.62 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) = hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal ), X ) }.
% 0.97/1.62 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.97/1.62 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) = X }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Groups_Oone__class_Oone
% 0.97/1.62 ( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ),
% 0.97/1.62 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) ),
% 0.97/1.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) }.
% 0.97/1.62 { ! c_Complex_Ocomplex_OComplex( Y, X ) = c_Groups_Oone__class_Oone(
% 0.97/1.62 tc_Complex_Ocomplex ), Y = c_Groups_Oone__class_Oone( tc_RealDef_Oreal )
% 0.97/1.62 }.
% 0.97/1.62 { ! c_Complex_Ocomplex_OComplex( Y, X ) = c_Groups_Oone__class_Oone(
% 0.97/1.62 tc_Complex_Ocomplex ), X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal
% 0.97/1.62 ) }.
% 0.97/1.62 { ! Y = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), ! X =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.97/1.62 c_Complex_Ocomplex_OComplex( Y, X ) = c_Groups_Oone__class_Oone(
% 0.97/1.62 tc_Complex_Ocomplex ) }.
% 0.97/1.62 { c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) =
% 0.97/1.62 c_Complex_Ocomplex_OComplex( c_Groups_Oone__class_Oone( tc_RealDef_Oreal
% 0.97/1.62 ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.97/1.62 { ! class_SEQ_Ocomplete__space( X ), ! c_SEQ_Oconvergent( X, Y ), !
% 0.97/1.62 c_SEQ_Osubseq( Z ), c_SEQ_Oconvergent( X, c_Fun_Ocomp( tc_Nat_Onat, X,
% 0.97/1.62 tc_Nat_Onat, Y, Z ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling
% 0.97/1.62 ( X ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.97/1.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.97/1.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 0.97/1.62 X ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.62 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.62 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.62 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 0.97/1.62 = hAPP( c_Groups_Ouminus__class_Ouminus( X ), c_Groups_Oone__class_Oone
% 0.97/1.62 ( X ) ), c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero
% 0.97/1.62 ( X ) ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.62 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Osgn__class_Osgn( X, Y
% 0.97/1.62 ) = hAPP( c_Groups_Ouminus__class_Ouminus( X ),
% 0.97/1.62 c_Groups_Oone__class_Oone( X ) ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.62 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Osgn__class_Osgn( X, Y
% 0.97/1.62 ) = hAPP( c_Groups_Ouminus__class_Ouminus( X ),
% 0.97/1.62 c_Groups_Oone__class_Oone( X ) ) }.
% 0.97/1.62 { ! class_Groups_Osgn__if( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.62 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_Groups_Osgn__if( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.62 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.62 { ! class_Groups_Osgn__if( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.62 c_Groups_Osgn__class_Osgn( X, Y ) = hAPP( c_Groups_Ouminus__class_Ouminus
% 0.97/1.62 ( X ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.97/1.62 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ),
% 0.97/1.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.97/1.62 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) ) ) }.
% 0.97/1.62 { c_Complex_Ocomplex_Ocomplex__size( c_Complex_Ocomplex_OComplex( Y, X ) )
% 0.97/1.62 = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.62 { c_Nat_Osize__class_Osize( tc_Complex_Ocomplex,
% 0.97/1.62 c_Complex_Ocomplex_OComplex( Y, X ) ) = c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Nat_Onat ) }.
% 0.97/1.62 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol14( Z, T ) ) }.
% 0.97/1.62 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.62 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), hAPP( Y, Z ) ), hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X ), skol64( X, Y ) ) ) ), skol14( X, Y
% 0.97/1.62 ) ) }.
% 0.97/1.62 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.62 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), hAPP( Y, skol70( X, Y, Z, T ) ) ), hAPP
% 0.97/1.62 ( c_Groups_Ouminus__class_Ouminus( X ), T ) ) ), Z ), c_SEQ_OBseq( X, Y )
% 0.97/1.62 }.
% 0.97/1.62 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol15( Z, T ) ) }.
% 0.97/1.62 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.62 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), hAPP( Y, Z ) ), hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X ), hAPP( Y, skol65( X, Y ) ) ) ) ),
% 0.97/1.62 skol15( X, Y ) ) }.
% 0.97/1.62 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.62 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), hAPP( Y, skol71( X, Y, Z, T ) ) ), hAPP
% 0.97/1.62 ( c_Groups_Ouminus__class_Ouminus( X ), hAPP( Y, T ) ) ) ), Z ),
% 0.97/1.62 c_SEQ_OBseq( X, Y ) }.
% 0.97/1.62 { c_Complex_Ocomplex_Ocomplex__case( T, Z, c_Complex_Ocomplex_OComplex( Y,
% 0.97/1.62 X ) ) = hAPP( hAPP( Z, Y ), X ) }.
% 0.97/1.62 { c_Complex_Ocomplex_Ocomplex__rec( T, Z, c_Complex_Ocomplex_OComplex( Y, X
% 0.97/1.62 ) ) = hAPP( hAPP( Z, Y ), X ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.62 tc_Nat_Onat, Y ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.97/1.62 tc_RealDef_Oreal, X, hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 0.97/1.62 tc_RealDef_Oreal ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ),
% 0.97/1.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ),
% 0.97/1.62 c_RComplete_Onatceiling( X ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 0.97/1.62 tc_Nat_Onat ), Y ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.62 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.97/1.62 tc_Nat_Onat, X ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.62 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.62 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 0.97/1.62 { alpha22( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 0.97/1.62 hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.97/1.62 { alpha22( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP
% 0.97/1.62 ( X, Y ), Z ) ) }.
% 0.97/1.62 { ! alpha22( X, Y, Z ), alpha26( X, Y, Z ), Z = Y }.
% 0.97/1.62 { ! alpha22( X, Y, Z ), alpha26( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z
% 0.97/1.62 ) ) }.
% 0.97/1.62 { ! alpha26( X, Y, Z ), alpha22( X, Y, Z ) }.
% 0.97/1.62 { ! Z = Y, hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha22( X, Y, Z ) }.
% 0.97/1.62 { ! alpha26( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y )
% 0.97/1.62 }.
% 0.97/1.62 { ! alpha26( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ), hBOOL( hAPP( hAPP(
% 0.97/1.62 X, Y ), Z ) ), alpha26( X, Y, Z ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X = Y }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.97/1.62 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.97/1.62 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.97/1.62 { ! c_RealDef_Oreal( tc_Nat_Onat, Y ) = c_RealDef_Oreal( tc_Nat_Onat, X ),
% 0.97/1.62 Y = X }.
% 0.97/1.62 { ! Y = X, c_RealDef_Oreal( tc_Nat_Onat, Y ) = c_RealDef_Oreal( tc_Nat_Onat
% 0.97/1.62 , X ) }.
% 0.97/1.62 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 0.97/1.62 X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }
% 0.97/1.62 .
% 0.97/1.62 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 0.97/1.62 X ), Z, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z )
% 0.97/1.62 }.
% 0.97/1.62 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.97/1.62 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z
% 0.97/1.62 ), c_Orderings_Oord__class_Oless( tc_fun( T, X ), Z, Y ) }.
% 0.97/1.62 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.97/1.62 c_RealDef_Oreal( tc_Nat_Onat, Y ) ), X ) = c_RealDef_Oreal( tc_Nat_Onat,
% 0.97/1.62 hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.62 { c_RealDef_Oreal( tc_Nat_Onat, hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.97/1.62 tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.97/1.62 tc_RealDef_Oreal ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ), X ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.62 ( tc_Int_Oint ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint )
% 0.97/1.62 , c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) ), X ) ), ! Y =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.62 { Y = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Int_Oint ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ),
% 0.97/1.62 c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) ), X ) ) }.
% 0.97/1.62 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Int_Oint ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ),
% 0.97/1.62 c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) ), X ) ) }.
% 0.97/1.62 { c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, c_RealDef_Oreal( tc_Nat_Onat
% 0.97/1.62 , X ) ) = c_RealDef_Oreal( tc_Nat_Onat, X ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.62 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 0.97/1.62 ( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Z ), hAPP( hAPP
% 0.97/1.62 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.62 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.97/1.62 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), X =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.62 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.62 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 0.97/1.62 ), X ) ) }.
% 0.97/1.62 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Nat_Onat ), X ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.62 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Nat_Onat ), X ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.62 ( tc_Nat_Onat ), X ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 0.97/1.62 .
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), Z ), X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), T ), X ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), Z ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), T ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ), X ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ), Y ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.62 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.62 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.62 { c_RComplete_Onatfloor( c_RealDef_Oreal( tc_Nat_Onat, X ) ) = X }.
% 0.97/1.62 { c_RComplete_Onatceiling( c_RealDef_Oreal( tc_Nat_Onat, X ) ) = X }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.97/1.62 tc_Nat_Onat, X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.62 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.97/1.62 tc_Nat_Onat, X ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.97/1.62 tc_Nat_Onat, Y ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.97/1.62 c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.97/1.62 tc_Nat_Onat, Y ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.97/1.62 c_RealDef_Oreal( tc_Nat_Onat, X ) ), c_Orderings_Oord__class_Oless(
% 0.97/1.62 tc_Nat_Onat, Y, X ) }.
% 0.97/1.62 { ! c_SEQ_Osubseq( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z
% 0.97/1.62 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( X, Y ), hAPP( X, Z
% 0.97/1.62 ) ) }.
% 0.97/1.62 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol16( X ), skol66( X ) ),
% 0.97/1.62 c_SEQ_Osubseq( X ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( X, skol16( X ) ),
% 0.97/1.62 hAPP( X, skol66( X ) ) ), c_SEQ_Osubseq( X ) }.
% 0.97/1.62 { c_RealDef_Oreal( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.97/1.62 ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.62 { ! c_RealDef_Oreal( tc_Nat_Onat, X ) = c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_RealDef_Oreal ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.62 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_RealDef_Oreal(
% 0.97/1.62 tc_Nat_Onat, X ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.97/1.62 tc_Nat_Onat, Y ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.62 c_RComplete_Onatfloor( X ), Y ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.62 tc_Nat_Onat, X ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.62 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.62 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 0.97/1.62 { c_RealDef_Oreal( tc_Nat_Onat, hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 0.97/1.62 tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 0.97/1.62 tc_RealDef_Oreal ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ), c_RealDef_Oreal
% 0.97/1.62 ( tc_Nat_Onat, X ) ) }.
% 0.97/1.62 { c_RealDef_Oreal( tc_Nat_Onat, c_Groups_Oone__class_Oone( tc_Nat_Onat ) )
% 0.97/1.62 = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.62 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ),
% 0.97/1.62 Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Nat_Onat ), X ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.62 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.62 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.62 { ! X = c_RealDef_Oreal( tc_Nat_Onat, c_RComplete_Onatfloor( X ) ),
% 0.97/1.62 c_RComplete_Onatfloor( hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.97/1.62 tc_RealDef_Oreal ), X ), Y ) ) = hAPP( hAPP( c_Power_Opower__class_Opower
% 0.97/1.62 ( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ), Y ) }.
% 0.97/1.62 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.97/1.62 tc_Nat_Onat, c_RComplete_Onatceiling( X ) ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.62 tc_Nat_Onat, X ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.62 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.62 tc_Nat_Onat, X ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.62 tc_Nat_Onat, c_RComplete_Onatfloor( X ) ), X ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.62 tc_Nat_Onat, Y ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 0.97/1.62 , c_RComplete_Onatfloor( X ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, c_RealDef_Oreal
% 0.97/1.62 ( tc_Nat_Onat, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.62 c_RComplete_Onatceiling( Y ), X ) }.
% 0.97/1.62 { ! c_SEQ_Oconvergent( tc_Complex_Ocomplex, X ), c_SEQ_Oconvergent(
% 0.97/1.62 tc_RealDef_Oreal, c_COMBB( tc_Complex_Ocomplex, tc_RealDef_Oreal,
% 0.97/1.62 tc_Nat_Onat, c_Complex_ORe, X ) ) }.
% 0.97/1.62 { ! c_SEQ_Oconvergent( tc_Complex_Ocomplex, X ), c_SEQ_Oconvergent(
% 0.97/1.62 tc_RealDef_Oreal, c_COMBB( tc_Complex_Ocomplex, tc_RealDef_Oreal,
% 0.97/1.62 tc_Nat_Onat, c_Complex_OIm, X ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.62 tc_Nat_Onat, Y ), hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 0.97/1.62 tc_RealDef_Oreal ), c_RealDef_Oreal( tc_Nat_Onat, X ) ),
% 0.97/1.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.62 tc_Nat_Onat, Y ), hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 0.97/1.62 tc_RealDef_Oreal ), c_RealDef_Oreal( tc_Nat_Onat, X ) ),
% 0.97/1.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_RComplete_Onatfloor
% 0.97/1.62 ( X ) ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.62 c_RealDef_Oreal( tc_Nat_Onat, Y ), X ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.62 tc_Nat_Onat, Y ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 0.97/1.62 , c_RComplete_Onatfloor( X ) ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), T ), Z ) = hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), Y ), Z ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.97/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.62 X ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ), T = Y }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 0.97/1.62 X ), Y ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.97/1.62 c_RealDef_Oreal( tc_Nat_Onat, Y ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.97/1.62 tc_Nat_Onat, Y ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.62 c_RComplete_Onatceiling( X ), Y ) }.
% 0.97/1.62 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.97/1.62 tc_Nat_Onat, c_RComplete_Onatfloor( X ) ) ), c_Groups_Oone__class_Oone(
% 0.97/1.62 tc_RealDef_Oreal ) ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.62 c_RComplete_Onatfloor( hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 0.97/1.62 tc_RealDef_Oreal ), X ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ) ) = hAPP(
% 0.97/1.62 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), c_RComplete_Onatfloor(
% 0.97/1.62 X ) ), Y ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), c_RComplete_Onatfloor( Y ) )
% 0.97/1.62 , c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, c_RealDef_Oreal(
% 0.97/1.62 tc_Nat_Onat, X ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.62 tc_Nat_Onat, Y ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal
% 0.97/1.62 , X, hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ),
% 0.97/1.62 c_RealDef_Oreal( tc_Nat_Onat, Y ) ), c_Groups_Oone__class_Oone(
% 0.97/1.62 tc_RealDef_Oreal ) ) ), c_RComplete_Onatfloor( X ) = Y }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.62 c_RComplete_Onatceiling( hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 0.97/1.62 tc_RealDef_Oreal ), X ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ) ) = hAPP(
% 0.97/1.62 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), c_RComplete_Onatceiling
% 0.97/1.62 ( X ) ), Y ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.62 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.97/1.62 , Y ), X ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Nat_Onat ), Y ) }.
% 0.97/1.62 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 0.97/1.62 ), X ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.62 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.62 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.62 c_RealVector_Onorm__class_Onorm( X, hAPP( Z, skol17( X, Y, Z ) ) ), Y ),
% 0.97/1.62 c_SEQ_OBseq( X, Z ) }.
% 0.97/1.62 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol18( Z, T ) ) }.
% 0.97/1.62 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.62 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, Z ) ), skol18( X, Y ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.97/1.62 tc_Nat_Onat, Y ) ), X ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal )
% 0.97/1.62 ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ), hAPP(
% 0.97/1.62 hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), X ),
% 0.97/1.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ), Y ) ) }.
% 0.97/1.62 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.97/1.62 hAPP( X, Y ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol19( Z, Y
% 0.97/1.62 ), Y ) }.
% 0.97/1.62 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.97/1.62 hAPP( X, Y ) ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.97/1.62 skol19( X, Y ) ), ! hBOOL( hAPP( X, Z ) ) }.
% 0.97/1.62 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.97/1.62 hAPP( X, Y ) ), hBOOL( hAPP( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 0.97/1.62 tc_Nat_Onat ), skol19( X, Y ) ), c_Groups_Oone__class_Oone( tc_Nat_Onat )
% 0.97/1.62 ) ) ) }.
% 0.97/1.62 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Int_Oint ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.97/1.62 { ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.97/1.62 c_Groups_Osgn__class_Osgn( tc_Int_Oint, X ) = c_Groups_Ozero__class_Ozero
% 0.97/1.62 ( tc_Int_Oint ) }.
% 0.97/1.62 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Int_Oint ), X ), c_Groups_Osgn__class_Osgn( tc_Int_Oint, X ) =
% 0.97/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.97/1.62 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Int_Oint ), X ), c_Groups_Osgn__class_Osgn( tc_Int_Oint, X ) = hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), c_Groups_Oone__class_Oone
% 0.97/1.62 ( tc_Int_Oint ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Int_Oint ), X ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.62 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oabs__class_Oabs(
% 0.97/1.62 tc_Int_Oint, X ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.97/1.62 { ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oabs__class_Oabs(
% 0.97/1.62 tc_Int_Oint, X ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 0.97/1.62 tc_Int_Oint ) ), X ) ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) )
% 0.97/1.62 , c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 0.97/1.62 tc_Int_Oint ) ), X ) ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) )
% 0.97/1.62 }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Int_Oint ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ),
% 0.97/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ),
% 0.97/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ),
% 0.97/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ),
% 0.97/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ),
% 0.97/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y = X }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ),
% 0.97/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ) }.
% 0.97/1.62 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ),
% 0.97/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ),
% 0.97/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ),
% 0.97/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), Z ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ), Z ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Z ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), T ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ), Z ) ) }.
% 0.97/1.62 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y = X,
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), ! Y = X }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), Y = X,
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.97/1.62 { ! class_RealVector_Oreal__algebra__1( X ), hAPP( c_RealVector_Oof__real(
% 0.97/1.62 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ),
% 0.97/1.62 Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP(
% 0.97/1.62 c_RealVector_Oof__real( X ), Z ) ), hAPP( c_RealVector_Oof__real( X ), Y
% 0.97/1.62 ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Groups_Oabs__class_Oabs(
% 0.97/1.62 tc_Int_Oint, X ) = hAPP( c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ),
% 0.97/1.62 X ) }.
% 0.97/1.62 { c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Groups_Oabs__class_Oabs(
% 0.97/1.62 tc_Int_Oint, X ) = X }.
% 0.97/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( tc_Int_Oint ), c_Groups_Oabs__class_Oabs(
% 0.97/1.62 tc_Int_Oint, Y ) ), X ) ) }.
% 0.97/1.62 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.62 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.97/1.62 c_RealVector_Onorm__class_Onorm( X, Z ) ),
% 0.97/1.62 c_RealVector_Onorm__class_Onorm( X, Y ) ) ) }.
% 0.97/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.62 c_RealVector_Onorm__class_Onorm( X, Z ), Y ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.62 c_RealVector_Onorm__class_Onorm( X, U ), T ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.62 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), T ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.97/1.62 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.97/1.62 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.97/1.62 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.97/1.62 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.97/1.62 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.97/1.62 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_Rings_Ono__zero__divisors( X ), ! hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.62 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_Rings_Ono__zero__divisors( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.62 X ), Z = c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_Rings_Oring__no__zero__divisors( X ), ! hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.62 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_Rings_Oring__no__zero__divisors( X ), ! Z =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_Rings_Oring__no__zero__divisors( X ), ! Y =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.62 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.62 ( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.62 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.62 ( X ), U = T, Z = Y, ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP
% 0.97/1.62 ( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), U ), Y ) ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 0.97/1.62 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.62 ( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), U ), Y ) ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), ! U = T }.
% 0.97/1.62 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.62 ( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), U ), Y ) ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), ! Z = Y }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ), Z ) }.
% 0.97/1.62 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.62 ( X ), ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), U ), Y ) ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ), U = Z, T = Y }.
% 0.97/1.62 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.62 ( X ), ! U = Z, hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP
% 0.97/1.62 ( c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), U ), Y ) ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.97/1.62 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.62 ( X ), ! T = Y, hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP
% 0.97/1.62 ( c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), U ), Y ) ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.97/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.62 { ! class_Rings_Osemiring( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X
% 0.97/1.62 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP(
% 0.97/1.62 hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ), Y ) ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), U ), Z ) ), T ) ), Y ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.97/1.62 = Y }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.97/1.62 = Y }.
% 0.97/1.62 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.97/1.62 = Y }.
% 0.97/1.62 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.97/1.62 = Y }.
% 0.97/1.62 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.97/1.62 = Y }.
% 0.97/1.62 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.97/1.62 = Y }.
% 0.97/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( c_Groups_Ouminus__class_Ouminus
% 0.97/1.62 ( X ), Z ) ), Y ) = hAPP( c_Groups_Ouminus__class_Ouminus( X ), hAPP(
% 0.97/1.62 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( c_Groups_Ouminus__class_Ouminus
% 0.97/1.62 ( X ), Z ) ), Y ) = hAPP( c_Groups_Ouminus__class_Ouminus( X ), hAPP(
% 0.97/1.62 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) = hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) = hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.62 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.97/1.62 ), Z ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 0.97/1.62 Z = Y, Z = hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ) }.
% 0.97/1.62 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.97/1.62 { ! class_Rings_Oidom( X ), ! Z = hAPP( c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.62 ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP
% 0.97/1.62 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.97/1.62 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.97/1.62 , hAPP( c_Groups_Ouminus__class_Ouminus( X ), Z ) ), hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 0.97/1.62 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.97/1.62 , hAPP( c_Groups_Ouminus__class_Ouminus( X ), Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) }.
% 0.97/1.62 { ! class_Rings_Oring( X ), hAPP( c_Groups_Ouminus__class_Ouminus( X ),
% 0.97/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( c_Groups_Ouminus__class_Ouminus
% 0.97/1.62 ( X ), Z ) ), Y ) }.
% 0.97/1.62 { ! class_Rings_Oring( X ), hAPP( c_Groups_Ouminus__class_Ouminus( X ),
% 0.97/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP(
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) }.
% 0.97/1.62 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.97/1.62 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.97/1.62 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) = hAPP( hAPP
% 0.97/1.62 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ), Z = Y }.
% 0.97/1.62 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y, hAPP( hAPP
% 0.97/1.62 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) = hAPP(
% 0.97/1.62 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) }.
% 0.97/1.62 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) = hAPP( hAPP
% 0.97/1.62 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ), Z = Y }.
% 0.97/1.62 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y, hAPP( hAPP
% 0.97/1.62 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) = hAPP(
% 0.97/1.62 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__idom( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Y ) ),
% 0.97/1.62 c_Groups_Oabs__class_Oabs( X, Y ) ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X, hAPP
% 0.97/1.62 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 0.97/1.62 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.97/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.97/1.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) = X }.
% 0.97/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP
% 0.97/1.62 ( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), Z ), Y ) ), X ) = hAPP
% 0.97/1.62 ( hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) ), hAPP( hAPP
% 0.97/1.62 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.97/1.62 { ! c_Groups_Ozero__class_Ozero( tc_Int_Oint ) = c_Groups_Oone__class_Oone
% 0.97/1.62 ( tc_Int_Oint ) }.
% 0.97/1.62 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 0.97/1.62 tc_Int_Oint ) ), X ) ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint )
% 0.97/1.62 }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), Y ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), U ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Z ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) }.
% 0.97/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.63 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 0.97/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 0.97/1.63 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 0.97/1.63 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 0.97/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP
% 0.97/1.63 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), Y ) ), X ) =
% 0.97/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), hAPP
% 0.97/1.63 ( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.97/1.63 { ! class_Groups_Oab__semigroup__mult( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) =
% 0.97/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y )
% 0.97/1.63 }.
% 0.97/1.63 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 0.97/1.63 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.97/1.63 c_RealVector_Onorm__class_Onorm( X, Z ) ),
% 0.97/1.63 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 0.97/1.63 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP(
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), X ) ), X ) =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.97/1.63 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ),
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) = X }.
% 0.97/1.63 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ),
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) = X }.
% 0.97/1.63 { hAPP( c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ),
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.97/1.63 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 0.97/1.63 c_Groups_Osgn__class_Osgn( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.63 X ), Z ), Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.97/1.63 c_Groups_Osgn__class_Osgn( X, Z ) ), c_Groups_Osgn__class_Osgn( X, Y ) )
% 0.97/1.63 }.
% 0.97/1.63 { ! class_Rings_Olinordered__idom( X ), c_Groups_Osgn__class_Osgn( X, hAPP
% 0.97/1.63 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Osgn__class_Osgn( X, Z ) ),
% 0.97/1.63 c_Groups_Osgn__class_Osgn( X, Y ) ) }.
% 0.97/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), ! c_SEQ_Oconvergent( X, Y
% 0.97/1.63 ), ! c_SEQ_Oconvergent( X, Z ), c_SEQ_Oconvergent( X, c_COMBS(
% 0.97/1.63 tc_Nat_Onat, X, X, c_COMBB( X, tc_fun( X, X ), tc_Nat_Onat,
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), ! c_SEQ_Oconvergent( X, Y
% 0.97/1.63 ), c_SEQ_Oconvergent( X, c_COMBC( tc_Nat_Onat, X, X, c_COMBB( X, tc_fun
% 0.97/1.63 ( X, X ), tc_Nat_Onat, c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), ! c_SEQ_Oconvergent( X, Y
% 0.97/1.63 ), c_SEQ_Oconvergent( X, c_COMBB( X, X, tc_Nat_Onat, hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), ! c_SEQ_OCauchy( X, Y ),
% 0.97/1.63 c_SEQ_OCauchy( X, c_COMBB( X, X, tc_Nat_Onat, hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), ! c_SEQ_OCauchy( X, Y ),
% 0.97/1.63 c_SEQ_OCauchy( X, c_COMBC( tc_Nat_Onat, X, X, c_COMBB( X, tc_fun( X, X )
% 0.97/1.63 , tc_Nat_Onat, c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), c_Lim_OisUCont( X, X,
% 0.97/1.63 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ) ) }.
% 0.97/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), c_Lim_OisUCont( X, X,
% 0.97/1.63 c_COMBC( X, X, X, c_Groups_Otimes__class_Otimes( X ), Y ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 0.97/1.63 X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), alpha2( X, Y
% 0.97/1.63 , Z ), alpha13( X, Y, Z ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha2( X, Y, Z ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha13( X, Y, Z ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.63 { ! alpha13( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.63 { ! alpha13( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.97/1.63 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( X ) ), alpha13( X, Y, Z ) }.
% 0.97/1.63 { ! alpha2( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.97/1.63 { ! alpha2( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.63 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( X ), Y ), alpha2( X, Y, Z ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( X ) ), alpha3( X, Y, Z ), alpha14( X, Y, Z ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha3( X, Y, Z ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( X ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha14( X, Y, Z ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( X ) ) }.
% 0.97/1.63 { ! alpha14( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.63 { ! alpha14( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.97/1.63 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( X ), Y ), alpha14( X, Y, Z ) }.
% 0.97/1.63 { ! alpha3( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.97/1.63 { ! alpha3( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.63 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( X ) ), alpha3( X, Y, Z ) }.
% 0.97/1.63 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.63 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.63 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.63 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.63 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.63 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ),
% 0.97/1.63 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.63 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.63 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.63 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.97/1.63 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.63 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.63 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.63 X ), Z ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( X ) ) }.
% 0.97/1.63 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.63 , Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.63 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.97/1.63 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.63 { ! class_Rings_Oordered__semiring( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.97/1.63 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.97/1.63 { ! class_Rings_Oordered__semiring( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.97/1.63 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.63 { ! class_Rings_Oordered__comm__semiring( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.97/1.63 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.63 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.63 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.63 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.97/1.63 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.63 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.63 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 0.97/1.63 { ! class_Rings_Oordered__semiring( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.97/1.63 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.63 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.97/1.63 { ! class_Rings_Oordered__semiring( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.63 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.63 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.97/1.63 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.63 , c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.63 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.97/1.63 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.63 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.63 , Z, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.63 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.97/1.63 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.63 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.97/1.63 ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.63 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.97/1.63 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.63 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.63 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.63 X ), Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( X ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.63 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 0.97/1.63 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha4( X, Y, Z, T ),
% 0.97/1.63 alpha15( X, Y, Z, T ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha4( X, Y, Z, T ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha15( X, Y, Z, T ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.63 { ! alpha15( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.63 { ! alpha15( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, T ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.63 , ! c_Orderings_Oord__class_Oless( X, Y, T ), alpha15( X, Y, Z, T ) }.
% 0.97/1.63 { ! alpha4( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.97/1.63 { ! alpha4( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.97/1.63 , ! c_Orderings_Oord__class_Oless( X, T, Y ), alpha4( X, Y, Z, T ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha5( X, Y, Z, T ),
% 0.97/1.63 alpha16( X, Y, Z, T ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha5( X, Y, Z, T ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha16( X, Y, Z, T ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.63 { ! alpha16( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.63 { ! alpha16( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( X, T, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.63 , ! c_Orderings_Oord__class_Oless( X, Y, Z ), alpha16( X, Y, Z, T ) }.
% 0.97/1.63 { ! alpha5( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( X ), T ) }.
% 0.97/1.63 { ! alpha5( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T )
% 0.97/1.63 , ! c_Orderings_Oord__class_Oless( X, Z, Y ), alpha5( X, Y, Z, T ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.63 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.63 ! c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless
% 0.97/1.63 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.97/1.63 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.63 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.97/1.63 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.63 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.63 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( X ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.63 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.63 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( X ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.97/1.63 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.97/1.63 .
% 0.97/1.63 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.97/1.63 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ) }
% 0.97/1.63 .
% 0.97/1.63 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.63 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.63 ! c_Orderings_Oord__class_Oless( X, Z, T ), c_Orderings_Oord__class_Oless
% 0.97/1.63 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.97/1.63 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.63 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.97/1.63 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( X ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.63 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.63 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.63 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.97/1.63 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP
% 0.97/1.63 ( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.63 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.97/1.63 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.97/1.63 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__comm__semiring__strict( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.63 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.97/1.63 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.97/1.63 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.63 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.97/1.63 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.97/1.63 ( c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.63 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.97/1.63 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP
% 0.97/1.63 ( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 0.97/1.63 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.63 ( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! W = U, T = Z, ! hAPP( hAPP
% 0.97/1.63 ( c_Groups_Oplus__class_Oplus( X ), W ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) = hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( X ), U ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.63 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.63 ( X, c_Groups_Oone__class_Oone( X ), Z ), c_Orderings_Oord__class_Oless(
% 0.97/1.63 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( X ), Y ), Y ) = hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( X ), c_Groups_Oone__class_Oone( X ) ),
% 0.97/1.63 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.97/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( X ), Z ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( X ), Y ), c_Groups_Oone__class_Oone( X ) ) )
% 0.97/1.63 , Z ) }.
% 0.97/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) = hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( X ), Z ), c_Groups_Oone__class_Oone( X ) ) )
% 0.97/1.63 , Y ) }.
% 0.97/1.63 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = c_Groups_Oone__class_Oone
% 0.97/1.63 ( X ), Y = c_Groups_Oone__class_Oone( X ), Y = hAPP(
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( X ), c_Groups_Oone__class_Oone( X ) ) }
% 0.97/1.63 .
% 0.97/1.63 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.97/1.63 c_Groups_Oone__class_Oone( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.63 ( X ), Y ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.63 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y = hAPP(
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( X ), c_Groups_Oone__class_Oone( X ) ),
% 0.97/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) =
% 0.97/1.63 c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.63 { ! class_Rings_Ocomm__ring__1( X ), hAPP( c_Groups_Ouminus__class_Ouminus
% 0.97/1.63 ( X ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP(
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( X ), c_Groups_Oone__class_Oone( X ) ) )
% 0.97/1.63 , Y ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.63 , c_Groups_Oabs__class_Oabs( X, Z ), Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.63 ( X, c_Groups_Oabs__class_Oabs( X, U ), T ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 0.97/1.63 c_Groups_Oabs__class_Oabs( X, U ) ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.97/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), T ), Y ) ) = hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ) }.
% 0.97/1.63 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.97/1.63 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), hAPP( hAPP
% 0.97/1.63 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ) ), hAPP(
% 0.97/1.63 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.63 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), hAPP( hAPP
% 0.97/1.63 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ) ), hAPP(
% 0.97/1.63 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.63 { ! Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! X =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ) ), hAPP( hAPP
% 0.97/1.63 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.63 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP(
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ) ), hAPP( hAPP
% 0.97/1.63 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__idom( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Osgn__class_Osgn( X, Y ) ),
% 0.97/1.63 c_Groups_Oabs__class_Oabs( X, Y ) ) = Y }.
% 0.97/1.63 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X, Y ) =
% 0.97/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ),
% 0.97/1.63 c_Groups_Osgn__class_Osgn( X, Y ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.63 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.63 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.63 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.63 ! c_Orderings_Oord__class_Oless__eq( X, Z, T ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.63 ( X, U, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.97/1.63 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.63 ( X, U, T ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.97/1.63 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.97/1.63 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.63 , U ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, U, T ), ! c_Orderings_Oord__class_Oless
% 0.97/1.63 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.97/1.63 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.63 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.97/1.63 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.97/1.63 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.97/1.63 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.63 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.97/1.63 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.97/1.63 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.97/1.63 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.97/1.63 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.97/1.63 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 0.97/1.63 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.97/1.63 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.97/1.63 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 0.97/1.63 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.97/1.63 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 0.97/1.63 Y ) = c_Groups_Oabs__class_Oabs( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.63 { ! class_Rings_Oordered__ring__abs( X ), alpha23( X, Z ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.63 ), c_Groups_Oabs__class_Oabs( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 0.97/1.63 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.97/1.63 { ! class_Rings_Oordered__ring__abs( X ), alpha23( X, Z ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.63 ), c_Groups_Oabs__class_Oabs( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 0.97/1.63 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.97/1.63 { ! alpha23( X, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.97/1.63 { ! alpha23( X, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.63 { c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.63 ), c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( X ) ), alpha23( X, Y ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.63 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.97/1.63 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.63 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.97/1.63 X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.97/1.63 { ! class_Rings_Oring__1( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.97/1.63 ), hAPP( c_Groups_Ouminus__class_Ouminus( X ), Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), hAPP( c_Groups_Ouminus__class_Ouminus
% 0.97/1.63 ( X ), c_Groups_Oone__class_Oone( X ) ) ), Y ) ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ),
% 0.97/1.63 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Z ) ) ), Y =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__semiring__1( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, T, Y ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.97/1.63 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.63 X ), W ), ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), U ), W ) =
% 0.97/1.63 c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.63 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), W ), T ) ), Y ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.63 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ) ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.97/1.63 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.63 c_RealVector_Onorm__class_Onorm( X, Z ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ),
% 0.97/1.63 c_RealVector_Onorm__class_Onorm( X, T ) ) ), Z =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__semiring__1__strict( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.63 ( X, T, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( X ), U ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), W
% 0.97/1.63 ), ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), U ), W ) =
% 0.97/1.63 c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless( X, hAPP(
% 0.97/1.63 hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), W ), T ) ), Y ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.63 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.97/1.63 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.97/1.63 ( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ), ! Z =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.63 }.
% 0.97/1.63 { ! class_Rings_Olinordered__ring__strict( X ), Z =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.97/1.63 ( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP(
% 0.97/1.63 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__ring__strict( X ), Y =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.97/1.63 ( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP(
% 0.97/1.63 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 0.97/1.63 X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.97/1.63 c_Groups_Ozero__class_Ozero( X ) ), Z = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.63 }.
% 0.97/1.63 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.97/1.63 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.63 }.
% 0.97/1.63 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.63 , c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.97/1.63 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.63 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 0.97/1.63 ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.63 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.97/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z = X
% 0.97/1.63 , Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.63 { ! Z = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.97/1.63 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }
% 0.97/1.63 .
% 0.97/1.63 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.97/1.63 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.97/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Y = X
% 0.97/1.63 , Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.63 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.97/1.63 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.97/1.63 .
% 0.97/1.63 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.97/1.63 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.63 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.63 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.63 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) }.
% 0.97/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) }.
% 0.97/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP( hAPP
% 0.97/1.63 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP
% 0.97/1.63 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.97/1.63 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) }.
% 0.97/1.63 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), T ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.97/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) = X }.
% 0.97/1.63 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), Y =
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.97/1.63 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X =
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.97/1.63 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Groups_Oone__class_Oone(
% 0.97/1.63 tc_Nat_Onat ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.97/1.63 , Y ), X ) }.
% 0.97/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 0.97/1.63 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y = c_Groups_Oone__class_Oone(
% 0.97/1.63 tc_Nat_Onat ) }.
% 0.97/1.63 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X = c_Groups_Oone__class_Oone(
% 0.97/1.63 tc_Nat_Onat ) }.
% 0.97/1.63 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.97/1.63 { ! c_Groups_Oabs__class_Oabs( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) =
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_Int_Oint ), c_Groups_Oabs__class_Oabs(
% 0.97/1.63 tc_Int_Oint, X ) = c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.97/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) = X }.
% 0.97/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) = X }.
% 0.97/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP
% 0.97/1.63 ( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), X ) ) = hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.97/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 0.97/1.63 ( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.97/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP(
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), Y ) ), X ) = hAPP(
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.97/1.63 { hAPP( c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), X ) ) = hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP(
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), Y ) ), hAPP(
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), X ) ) }.
% 0.97/1.63 { hAPP( c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), hAPP(
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), X ) ) = X }.
% 0.97/1.63 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, X ) }.
% 0.97/1.63 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Z ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, Z ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ), Y = X }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), X ) ) }.
% 0.97/1.63 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 0.97/1.63 ( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), X ) ) }.
% 0.97/1.63 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), X ) ) = hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), X ) ) }.
% 0.97/1.63 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), X ) = hAPP(
% 0.97/1.63 hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ), Y ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.97/1.63 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.97/1.63 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.63 Y ), X ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_Nat_Onat ), Z ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( tc_Nat_Onat ), Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 0.97/1.63 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_Nat_Onat ), Y ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.97/1.63 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.97/1.63 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP
% 0.97/1.63 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.97/1.63 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP
% 0.97/1.63 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 0.97/1.63 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP
% 0.97/1.63 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.63 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), X =
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.63 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), Y =
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( tc_Int_Oint ), X ), ! X = c_Groups_Oone__class_Oone( tc_Int_Oint ), ! Y
% 0.97/1.63 = c_Groups_Oone__class_Oone( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.97/1.63 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X )
% 0.97/1.63 , X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.63 { c_RealDef_Oreal( tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.63 tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.63 tc_RealDef_Oreal ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ), c_RealDef_Oreal
% 0.97/1.63 ( tc_Nat_Onat, X ) ) }.
% 0.97/1.63 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), hAPP( hAPP
% 0.97/1.63 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ) }.
% 0.97/1.63 { c_Complex_Oexpi( hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 0.97/1.63 tc_Complex_Ocomplex ), Y ), X ) ) = hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), c_Complex_Oexpi( Y
% 0.97/1.63 ) ), c_Complex_Oexpi( X ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 0.97/1.63 ) }.
% 0.97/1.63 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 0.97/1.63 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 0.97/1.63 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X
% 0.97/1.63 ) }.
% 0.97/1.63 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 0.97/1.63 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 0.97/1.63 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.97/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.97/1.63 c_Complex_Ocomplex_OComplex( Z, Y ) ), hAPP( c_RealVector_Oof__real(
% 0.97/1.63 tc_Complex_Ocomplex ), X ) ) = c_Complex_Ocomplex_OComplex( hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.97/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP(
% 0.97/1.63 c_RealVector_Oof__real( tc_Complex_Ocomplex ), Z ) ),
% 0.97/1.63 c_Complex_Ocomplex_OComplex( Y, X ) ) = c_Complex_Ocomplex_OComplex( hAPP
% 0.97/1.63 ( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), Y ), hAPP
% 0.97/1.63 ( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) ) }.
% 0.97/1.63 { hAPP( c_Complex_OIm, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.63 tc_Complex_Ocomplex ), Y ), X ) ) = hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( c_Complex_ORe, Y
% 0.97/1.63 ) ), hAPP( c_Complex_OIm, X ) ) ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( c_Complex_OIm, Y
% 0.97/1.63 ) ), hAPP( c_Complex_ORe, X ) ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_RComplete_Onatfloor( X )
% 0.97/1.63 ), c_RComplete_Onatfloor( Y ) ), c_RComplete_Onatfloor( hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__ring__strict( X ), ! hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.97/1.63 .
% 0.97/1.63 { ! class_Rings_Olinordered__ring__strict( X ), ! hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 0.97/1.63 .
% 0.97/1.63 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.63 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( tc_Int_Oint ), X ), ! X = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 0.97/1.63 tc_Int_Oint ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.63 tc_Int_Oint ), X ), Y ) ), ! c_Orderings_Oord__class_Oless__eq(
% 0.97/1.63 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( tc_Int_Oint ), X ), ! X = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 0.97/1.63 tc_Int_Oint ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.63 tc_Int_Oint ), X ), Y ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.63 Z, X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_Int_Oint ), Y ) }.
% 0.97/1.63 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ) ), T ) = hAPP(
% 0.97/1.63 hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ),
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, T, W ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.97/1.63 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, U ) }.
% 0.97/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP(
% 0.97/1.63 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.97/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) = hAPP
% 0.97/1.63 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) }.
% 0.97/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 0.97/1.63 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP
% 0.97/1.63 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ),
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ) ), Z ), hAPP( hAPP
% 0.97/1.63 ( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ) ), X ) ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, U ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, U ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Y ) }.
% 0.97/1.63 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ) ), T ) = hAPP(
% 0.97/1.63 hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.97/1.63 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, U, Y ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ) ), Z ), hAPP( hAPP
% 0.97/1.63 ( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ) ), X ) ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, Z ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, T ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP
% 0.97/1.63 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z
% 0.97/1.63 , Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.97/1.63 { X = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), Y =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Orderings_Oord__class_Oless
% 0.97/1.63 ( tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex
% 0.97/1.63 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex ),
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), X ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), skol20( X, Y ) ), Y
% 0.97/1.63 ) ) ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.97/1.63 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.97/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Z =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.97/1.63 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.97/1.63 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.97/1.63 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.97/1.63 .
% 0.97/1.63 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), T ), Z ) ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ) ), X ) ) = hAPP(
% 0.97/1.63 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), T ), Y ) ), Z ) ), X ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 0.97/1.63 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP(
% 0.97/1.63 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 0.97/1.63 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( tc_Nat_Onat ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.63 tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.63 tc_Nat_Onat ), X ), Y ), Z = Y }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( tc_Nat_Onat ), X ), ! Z = Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.63 ( tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.63 tc_Nat_Onat ), X ), Y ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) }.
% 0.97/1.63 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_Int_Oint ) ) }.
% 0.97/1.63 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 0.97/1.63 tc_Int_Oint ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ), Y ) ) }.
% 0.97/1.63 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ), X =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.63 { ! X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) }.
% 0.97/1.63 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol21 ) }.
% 0.97/1.63 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.63 c_RealVector_Onorm__class_Onorm( tc_RealDef_Oreal, hAPP( c_Complex_OIm, X
% 0.97/1.63 ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.97/1.63 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ), skol21 ) ) }
% 0.97/1.63 .
% 0.97/1.63 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol22 ) }.
% 0.97/1.63 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.63 c_RealVector_Onorm__class_Onorm( tc_RealDef_Oreal, hAPP( c_Complex_ORe, X
% 0.97/1.63 ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.97/1.63 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ), skol22 ) ) }
% 0.97/1.63 .
% 0.97/1.63 { ! class_RealVector_Oreal__algebra__1( X ), !
% 0.97/1.63 class_RealVector_Oreal__normed__vector( X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol23( Y ) ) }.
% 0.97/1.63 { ! class_RealVector_Oreal__algebra__1( X ), !
% 0.97/1.63 class_RealVector_Oreal__normed__vector( X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.63 c_RealVector_Onorm__class_Onorm( X, hAPP( c_RealVector_Oof__real( X ), Y
% 0.97/1.63 ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.97/1.63 c_RealVector_Onorm__class_Onorm( tc_RealDef_Oreal, Y ) ), skol23( X ) ) )
% 0.97/1.63 }.
% 0.97/1.63 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol24 ) }.
% 0.97/1.63 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.63 c_RealVector_Onorm__class_Onorm( tc_RealDef_Oreal, hAPP( c_Complex_OIm, X
% 0.97/1.63 ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.97/1.63 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ), skol24 ) ) }
% 0.97/1.63 .
% 0.97/1.63 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol25 ) }.
% 0.97/1.63 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.63 c_RealVector_Onorm__class_Onorm( tc_RealDef_Oreal, hAPP( c_Complex_ORe, X
% 0.97/1.63 ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.97/1.63 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ), skol25 ) ) }
% 0.97/1.63 .
% 0.97/1.63 { ! class_RealVector_Oreal__algebra__1( X ), !
% 0.97/1.63 class_RealVector_Oreal__normed__vector( X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol26( Y ) ) }.
% 0.97/1.63 { ! class_RealVector_Oreal__algebra__1( X ), !
% 0.97/1.63 class_RealVector_Oreal__normed__vector( X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.63 c_RealVector_Onorm__class_Onorm( X, hAPP( c_RealVector_Oof__real( X ), Y
% 0.97/1.63 ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.97/1.63 c_RealVector_Onorm__class_Onorm( tc_RealDef_Oreal, Y ) ), skol26( X ) ) )
% 0.97/1.63 }.
% 0.97/1.63 { ! class_Power_Opower( X ), c_Power_Opower__class_Opower( X ) =
% 0.97/1.63 c_Power_Opower_Opower( X, c_Groups_Oone__class_Oone( X ),
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ) ) }.
% 0.97/1.63 { hAPP( hAPP( c_Power_Opower_Opower( T, Z, Y ), X ),
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = Z }.
% 0.97/1.63 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol27( Z, T ) ) }.
% 0.97/1.63 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.63 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.97/1.63 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol27( X, Y ) ) ) }.
% 0.97/1.63 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol28( Z, T ) ) }.
% 0.97/1.63 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.63 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.97/1.63 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol28( X, Y ) ) ) }.
% 0.97/1.63 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol29( Y ) ) }.
% 0.97/1.63 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.63 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.97/1.63 c_RealVector_Onorm__class_Onorm( X, Y ) ),
% 0.97/1.63 c_RealVector_Onorm__class_Onorm( X, Z ) ) ), skol29( X ) ) ) }.
% 0.97/1.63 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.63 c_RealVector_Onorm__class_Onorm( tc_RealDef_Oreal, hAPP( c_Complex_OIm, X
% 0.97/1.63 ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.97/1.63 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ), skol30 ) ) }
% 0.97/1.63 .
% 0.97/1.63 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.63 c_RealVector_Onorm__class_Onorm( tc_RealDef_Oreal, hAPP( c_Complex_ORe, X
% 0.97/1.63 ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.97/1.63 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ), skol31 ) ) }
% 0.97/1.63 .
% 0.97/1.63 { ! class_RealVector_Oreal__algebra__1( X ), !
% 0.97/1.63 class_RealVector_Oreal__normed__vector( X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.63 c_RealVector_Onorm__class_Onorm( X, hAPP( c_RealVector_Oof__real( X ), Y
% 0.97/1.63 ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.97/1.63 c_RealVector_Onorm__class_Onorm( tc_RealDef_Oreal, Y ) ), skol32( X ) ) )
% 0.97/1.63 }.
% 0.97/1.63 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ),
% 0.97/1.63 c_Complex_Orcis( Z, Y ) ), X ) = c_Complex_Orcis( hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.97/1.63 tc_Nat_Onat, X ) ), Y ) ) }.
% 0.97/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), Y ), X
% 0.97/1.63 ) = c_Complex_Ocomplex_OComplex( c_Groups_Ominus__class_Ominus(
% 0.97/1.63 tc_RealDef_Oreal, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.63 tc_RealDef_Oreal ), hAPP( c_Complex_ORe, Y ) ), hAPP( c_Complex_ORe, X )
% 0.97/1.63 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP(
% 0.97/1.63 c_Complex_OIm, Y ) ), hAPP( c_Complex_OIm, X ) ) ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( c_Complex_ORe, Y
% 0.97/1.63 ) ), hAPP( c_Complex_OIm, X ) ) ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( c_Complex_OIm, Y
% 0.97/1.63 ) ), hAPP( c_Complex_ORe, X ) ) ) ) }.
% 0.97/1.63 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.97/1.63 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.97/1.63 ( X, Y ) ) ), c_RealVector_Onorm__class_Onorm( X,
% 0.97/1.63 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ) }.
% 0.97/1.63 { ! class_Groups_Oab__group__add( X ), hAPP(
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( X ), c_Groups_Ominus__class_Ominus( X, Z
% 0.97/1.63 , Y ) ) = c_Groups_Ominus__class_Ominus( X, Y, Z ) }.
% 0.97/1.63 { ! class_Groups_Ogroup__add( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.97/1.63 ( X ), c_Groups_Ominus__class_Ominus( X, Z, Y ) ), Y ) = Z }.
% 0.97/1.63 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, hAPP(
% 0.97/1.63 hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), Y ), Y ) = Z }.
% 0.97/1.63 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.63 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.97/1.63 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.63 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.63 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.97/1.63 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, U, T ) }.
% 0.97/1.63 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.97/1.63 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.97/1.63 ( X, Y ) ), c_RealVector_Onorm__class_Onorm( X,
% 0.97/1.63 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ) }.
% 0.97/1.63 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 0.97/1.63 , Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.63 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 0.97/1.63 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.63 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.97/1.63 X, c_Groups_Ominus__class_Ominus( X, Z, Y ), c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( X ) ) }.
% 0.97/1.63 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.97/1.63 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.97/1.63 , Z, Y ) }.
% 0.97/1.63 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( X ), Y ) = hAPP(
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( X ), Y ) }.
% 0.97/1.63 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.97/1.63 ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), hAPP(
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) }.
% 0.97/1.63 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.97/1.63 hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ) ) = hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) }.
% 0.97/1.63 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X, Z
% 0.97/1.63 , Y ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), hAPP(
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) }.
% 0.97/1.63 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z, Y )
% 0.97/1.63 = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), hAPP(
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) }.
% 0.97/1.63 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X,
% 0.97/1.63 c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ),
% 0.97/1.63 c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Y, Z ) )
% 0.97/1.63 ) }.
% 0.97/1.63 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X,
% 0.97/1.63 c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ),
% 0.97/1.63 c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Z, Y ) )
% 0.97/1.63 ) }.
% 0.97/1.63 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 0.97/1.63 c_Groups_Ominus__class_Ominus( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.97/1.63 c_Groups_Oabs__class_Oabs( X, Y ) ) ), c_Groups_Oabs__class_Oabs( X,
% 0.97/1.63 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ),
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ),
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.97/1.63 { ! class_RealVector_Oreal__algebra__1( X ), !
% 0.97/1.63 class_RealVector_Oreal__normed__vector( X ), hAPP( c_RealVector_Oof__real
% 0.97/1.63 ( X ), c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Z, Y ) ) =
% 0.97/1.63 c_Groups_Ominus__class_Ominus( X, hAPP( c_RealVector_Oof__real( X ), Z )
% 0.97/1.63 , hAPP( c_RealVector_Oof__real( X ), Y ) ) }.
% 0.97/1.63 { ! class_RealVector_Oreal__algebra__1( X ), hAPP( c_RealVector_Oof__real(
% 0.97/1.63 X ), c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Z, Y ) ) =
% 0.97/1.63 c_Groups_Ominus__class_Ominus( X, hAPP( c_RealVector_Oof__real( X ), Z )
% 0.97/1.63 , hAPP( c_RealVector_Oof__real( X ), Y ) ) }.
% 0.97/1.63 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.97/1.63 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, Z,
% 0.97/1.63 Y ) ) = c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus
% 0.97/1.63 ( X, Y, Z ) ) }.
% 0.97/1.63 { ! class_Groups_Ominus( X ), hAPP( c_Groups_Ominus__class_Ominus( tc_fun(
% 0.97/1.63 U, X ), T, Z ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( T, Y ),
% 0.97/1.63 hAPP( Z, Y ) ) }.
% 0.97/1.63 { ! class_Groups_Ominus( X ), hAPP( c_Groups_Ominus__class_Ominus( tc_fun(
% 0.97/1.63 U, X ), T, Z ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( T, Y ),
% 0.97/1.63 hAPP( Z, Y ) ) }.
% 0.97/1.63 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.97/1.63 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! U = T, Z = Y }.
% 0.97/1.63 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.97/1.63 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! Z = Y, U = T }.
% 0.97/1.63 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.97/1.63 c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Z, Y ) )
% 0.97/1.63 = c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Y, Z )
% 0.97/1.63 ) }.
% 0.97/1.63 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.63 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.97/1.63 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, U, T ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.63 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.63 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.97/1.63 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, U, T ) }.
% 0.97/1.63 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.97/1.63 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y, Y )
% 0.97/1.63 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.63 { ! class_Groups_Oab__group__add( X ), ! Z = Y,
% 0.97/1.63 c_Groups_Ominus__class_Ominus( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.97/1.63 ) }.
% 0.97/1.63 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.97/1.63 Z, Y ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.97/1.63 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.97/1.63 ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.97/1.63 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ominus__class_Ominus(
% 0.97/1.63 X, Z, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.63 { c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ) = hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), Y ), hAPP(
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal ), X ) ) }.
% 0.97/1.63 { c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ) = hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), Y ), hAPP(
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal ), X ) ) }.
% 0.97/1.63 { ! class_Rings_Oring( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), U ), c_Groups_Ominus__class_Ominus( X
% 0.97/1.63 , T, Y ) ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.97/1.63 c_Groups_Ominus__class_Ominus( X, U, Z ) ), Y ) ) }.
% 0.97/1.63 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.97/1.63 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.97/1.63 ( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.97/1.63 c_Groups_Ominus__class_Ominus( X, U, Z ) ), c_Groups_Ominus__class_Ominus
% 0.97/1.63 ( X, T, Y ) ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.97/1.63 c_Groups_Ominus__class_Ominus( X, U, Z ) ), Y ) ) ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ominus__class_Ominus( X
% 0.97/1.63 , T, Y ) ) ) }.
% 0.97/1.63 { ! class_Rings_Oring( X ), ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( X )
% 0.97/1.63 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) = hAPP
% 0.97/1.63 ( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.97/1.63 Z ) ), U ) ), T ) = Y }.
% 0.97/1.63 { ! class_Rings_Oring( X ), ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( X )
% 0.97/1.63 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.97/1.63 c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ) ), T ) = Y, hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) = hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) }.
% 0.97/1.63 { ! class_Rings_Oring( X ), ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( X )
% 0.97/1.63 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) = hAPP
% 0.97/1.63 ( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ), T = hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.97/1.63 W ) ), U ) ), Y ) }.
% 0.97/1.63 { ! class_Rings_Oring( X ), ! T = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 0.97/1.63 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.97/1.63 c_Groups_Ominus__class_Ominus( X, Z, W ) ), U ) ), Y ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) = hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) }.
% 0.97/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 0.97/1.63 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 0.97/1.63 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 0.97/1.63 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 0.97/1.63 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.63 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.63 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.97/1.63 Z ) ), U ) ), T ), Y ) }.
% 0.97/1.63 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.63 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.97/1.63 Z ) ), U ) ), T ), Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP
% 0.97/1.63 ( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) ) }.
% 0.97/1.63 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.63 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.97/1.63 W ) ), U ) ), Y ) ) }.
% 0.97/1.63 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.63 , T, hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.97/1.63 W ) ), U ) ), Y ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) ) }.
% 0.97/1.63 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.97/1.63 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.97/1.63 W ) ), U ) ), Y ) ) }.
% 0.97/1.63 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X, T
% 0.97/1.63 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.97/1.63 W ) ), U ) ), Y ) ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) ) }.
% 0.97/1.63 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.97/1.63 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.97/1.63 ( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.97/1.63 c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ) ), T ), Y ) }.
% 0.97/1.63 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.97/1.63 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.97/1.63 Z ) ), U ) ), T ), Y ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) ) }.
% 0.97/1.63 { ! class_Rings_Oring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP
% 0.97/1.63 ( c_Groups_Otimes__class_Otimes( X ), Y ), Y ), c_Groups_Oone__class_Oone
% 0.97/1.63 ( X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( X ), Y ), c_Groups_Oone__class_Oone( X ) ) )
% 0.97/1.63 , c_Groups_Ominus__class_Ominus( X, Y, c_Groups_Oone__class_Oone( X ) ) )
% 0.97/1.63 }.
% 0.97/1.63 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 0.97/1.63 c_Groups_Ominus__class_Ominus( X, Z, Y ) ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 0.97/1.63 c_Groups_Oabs__class_Oabs( X, Y ) ) ) }.
% 0.97/1.63 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 0.97/1.63 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.97/1.63 ( X ), U ), T ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), Y ) )
% 0.97/1.63 ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ),
% 0.97/1.63 c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, U, Z ) )
% 0.97/1.63 ), c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, T, Y
% 0.97/1.63 ) ) ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.63 , c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, T, Z )
% 0.97/1.63 ), Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus
% 0.97/1.63 ( X, Z, Y ), T ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.63 , c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, T, Z )
% 0.97/1.63 ), Y ), c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.63 , c_Groups_Ominus__class_Ominus( X, Z, Y ), T ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Oabs__class_Oabs( X,
% 0.97/1.63 c_Groups_Ominus__class_Ominus( X, T, Z ) ), Y ) }.
% 0.97/1.63 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.97/1.63 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.97/1.63 ( X, Y ) ), c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) ) }.
% 0.97/1.63 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.63 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, Z,
% 0.97/1.63 Y ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ),
% 0.97/1.63 c_RealVector_Onorm__class_Onorm( X, Z ) ),
% 0.97/1.63 c_RealVector_Onorm__class_Onorm( X, Y ) ) ) }.
% 0.97/1.63 { c_Complex_Orcis( X, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) =
% 0.97/1.63 hAPP( c_RealVector_Oof__real( tc_Complex_Ocomplex ), X ) }.
% 0.97/1.63 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.97/1.63 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex ), Y ), X ) ),
% 0.97/1.63 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Y ) ),
% 0.97/1.63 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) }.
% 0.97/1.63 { c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, c_Complex_Orcis( Y
% 0.97/1.63 , X ) ) = c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ) }.
% 0.97/1.63 { c_Complex_Orcis( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ) =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.97/1.63 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.63 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X,
% 0.97/1.63 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), U ), T ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ),
% 0.97/1.63 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, U,
% 0.97/1.63 Z ) ) ), c_RealVector_Onorm__class_Onorm( X,
% 0.97/1.63 c_Groups_Ominus__class_Ominus( X, T, Y ) ) ) ) }.
% 0.97/1.63 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X,
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), c_RealDef_Oreal(
% 0.97/1.63 tc_Nat_Onat, c_RComplete_Onatfloor( X ) ) ) }.
% 0.97/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.97/1.63 c_Complex_Ocomplex_OComplex( T, Z ) ), c_Complex_Ocomplex_OComplex( Y, X
% 0.97/1.63 ) ) = c_Complex_Ocomplex_OComplex( c_Groups_Ominus__class_Ominus(
% 0.97/1.63 tc_RealDef_Oreal, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.63 tc_RealDef_Oreal ), T ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.63 tc_RealDef_Oreal ), Z ), X ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 0.97/1.63 tc_RealDef_Oreal ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.63 tc_RealDef_Oreal ), T ), X ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.63 ( tc_RealDef_Oreal ), Z ), Y ) ) ) }.
% 0.97/1.63 { hAPP( c_Complex_ORe, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.63 tc_Complex_Ocomplex ), Y ), X ) ) = c_Groups_Ominus__class_Ominus(
% 0.97/1.63 tc_RealDef_Oreal, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.63 tc_RealDef_Oreal ), hAPP( c_Complex_ORe, Y ) ), hAPP( c_Complex_ORe, X )
% 0.97/1.63 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP(
% 0.97/1.63 c_Complex_OIm, Y ) ), hAPP( c_Complex_OIm, X ) ) ) }.
% 0.97/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.97/1.63 c_Complex_Orcis( T, Z ) ), c_Complex_Orcis( Y, X ) ) = c_Complex_Orcis(
% 0.97/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), T ), Y ),
% 0.97/1.63 hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), Z ), X ) ) }
% 0.97/1.63 .
% 0.97/1.63 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OCauchy( X, Y ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, skol33( X, Y, Z ), T ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, skol33( X, Y, Z ), U ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X,
% 0.97/1.63 hAPP( Y, T ), hAPP( Y, U ) ) ), Z ) }.
% 0.97/1.63 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OCauchy( X, Y ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), alpha6( X, Y, Z ) }
% 0.97/1.63 .
% 0.97/1.63 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol34( Z, T ) ),
% 0.97/1.63 c_SEQ_OCauchy( X, Y ) }.
% 0.97/1.63 { ! class_RealVector_Oreal__normed__vector( X ), ! alpha6( X, Y, skol34( X
% 0.97/1.63 , Y ) ), c_SEQ_OCauchy( X, Y ) }.
% 0.97/1.63 { ! alpha6( X, Y, Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.63 skol35( X, Y, Z ), T ), alpha17( X, Y, Z, skol35( X, Y, Z ), T ) }.
% 0.97/1.63 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, skol67( U, W, V0, T )
% 0.97/1.63 ), alpha6( X, Y, Z ) }.
% 0.97/1.63 { ! alpha17( X, Y, Z, T, skol67( X, Y, Z, T ) ), alpha6( X, Y, Z ) }.
% 0.97/1.63 { ! alpha17( X, Y, Z, T, U ), ! c_Orderings_Oord__class_Oless__eq(
% 0.97/1.63 tc_Nat_Onat, T, W ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X,
% 0.97/1.63 hAPP( Y, U ), hAPP( Y, W ) ) ), Z ) }.
% 0.97/1.63 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, skol36( W, V0, V1, T,
% 0.97/1.63 V2 ) ), alpha17( X, Y, Z, T, U ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X,
% 0.97/1.63 hAPP( Y, U ), hAPP( Y, skol36( X, Y, Z, T, U ) ) ) ), Z ), alpha17( X, Y
% 0.97/1.63 , Z, T, U ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ),
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.63 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.97/1.63 ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X = Z }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), ! X = Z,
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = Y }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, Z ),
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ),
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 0.97/1.63 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ), Y ) }.
% 0.97/1.63 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ), X ) = Y }.
% 0.97/1.63 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ), Y ) = X }.
% 0.97/1.63 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.63 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.97/1.63 Z, hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.63 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) =
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 0.97/1.63 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Y ) ) =
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ominus__class_Ominus
% 0.97/1.63 ( tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ),
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.97/1.63 { hAPP( c_Complex_OIm, c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex,
% 0.97/1.63 Y, X ) ) = c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, hAPP(
% 0.97/1.63 c_Complex_OIm, Y ), hAPP( c_Complex_OIm, X ) ) }.
% 0.97/1.63 { hAPP( c_Complex_ORe, c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex,
% 0.97/1.63 Y, X ) ) = c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, hAPP(
% 0.97/1.63 c_Complex_ORe, Y ), hAPP( c_Complex_ORe, X ) ) }.
% 0.97/1.63 { c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex,
% 0.97/1.63 c_Complex_Ocomplex_OComplex( T, Z ), c_Complex_Ocomplex_OComplex( Y, X )
% 0.97/1.63 ) = c_Complex_Ocomplex_OComplex( c_Groups_Ominus__class_Ominus(
% 0.97/1.63 tc_RealDef_Oreal, T, Y ), c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal
% 0.97/1.63 , Z, X ) ) }.
% 0.97/1.63 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_Nat_Onat ), X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.63 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = X }.
% 0.97/1.63 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, X ) =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.63 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.63 ( tc_Nat_Onat, Y, Z ), X ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.63 ( tc_Nat_Onat, Z, X ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.97/1.63 ) }.
% 0.97/1.63 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) = hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), hAPP(
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), X ) ) }.
% 0.97/1.63 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), hAPP(
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), X ) ) =
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z,
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ), X ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Y ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Y ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ), Y ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ),
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = X }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ),
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ), Y ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ), X ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ), X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), c_Groups_Ominus__class_Ominus
% 0.97/1.63 ( tc_Nat_Onat, X, Y ) ), Y ) = X }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z, X = hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X = hAPP(
% 0.97/1.63 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ),
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ), Y ) = hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ),
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), c_Groups_Ominus__class_Ominus
% 0.97/1.63 ( tc_Nat_Onat, X, Y ) ), Z ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat
% 0.97/1.63 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ), Y ) }
% 0.97/1.63 .
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ), Y ) = hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), c_Groups_Ominus__class_Ominus
% 0.97/1.63 ( tc_Nat_Onat, X, Y ) ), Z ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.63 ( tc_Nat_Onat, Y, Z ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z )
% 0.97/1.63 ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.63 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.97/1.63 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.63 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.97/1.63 ) }.
% 0.97/1.63 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ),
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) = Y }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z,
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ), Y ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ), Y ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z,
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 0.97/1.63 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.63 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.63 ( tc_Nat_Onat, Y, X ), Y ) }.
% 0.97/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) =
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.97/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) ) =
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.97/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ), X ) =
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.97/1.63 { c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, Y, X ) = hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex ), Y ), hAPP(
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex ), X ) ) }.
% 0.97/1.63 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.97/1.63 , alpha7( X, Y, Z ) }.
% 0.97/1.63 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.97/1.63 , alpha18( X, Y, Z ) }.
% 0.97/1.63 { ! alpha7( X, Y, Z ), ! alpha18( X, Y, Z ), hBOOL( hAPP( Z,
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.97/1.63 { ! alpha18( X, Y, Z ), ! Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 0.97/1.63 tc_Nat_Onat ), X ), T ), hBOOL( hAPP( Z, T ) ) }.
% 0.97/1.63 { ! hBOOL( hAPP( Z, skol37( T, U, Z ) ) ), alpha18( X, Y, Z ) }.
% 0.97/1.63 { Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), skol37(
% 0.97/1.63 X, Y, Z ) ), alpha18( X, Y, Z ) }.
% 0.97/1.63 { ! alpha7( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 0.97/1.63 , hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.97/1.63 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), alpha7( X, Y, Z ) }.
% 0.97/1.63 { ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha7
% 0.97/1.63 ( X, Y, Z ) }.
% 0.97/1.63 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.97/1.63 , ! alpha8( X, Y, Z ) }.
% 0.97/1.63 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.97/1.63 , ! alpha19( X, Y, Z ) }.
% 0.97/1.63 { alpha8( X, Y, Z ), alpha19( X, Y, Z ), hBOOL( hAPP( Z,
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.97/1.63 { ! alpha19( X, Y, Z ), ! hBOOL( hAPP( Z, skol38( T, U, Z ) ) ) }.
% 0.97/1.63 { ! alpha19( X, Y, Z ), Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 0.97/1.63 tc_Nat_Onat ), X ), skol38( X, Y, Z ) ) }.
% 0.97/1.63 { ! Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), T ),
% 0.97/1.63 hBOOL( hAPP( Z, T ) ), alpha19( X, Y, Z ) }.
% 0.97/1.63 { ! alpha8( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }
% 0.97/1.63 .
% 0.97/1.63 { ! alpha8( X, Y, Z ), ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_Nat_Onat ) ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), hBOOL( hAPP( Z,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha8( X, Y, Z ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 0.97/1.63 ( tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 0.97/1.63 .
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 0.97/1.63 ( tc_Int_Oint ) ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), T ) = hAPP(
% 0.97/1.63 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), Z ), T = hAPP(
% 0.97/1.63 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ) ), Z ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! T = hAPP(
% 0.97/1.63 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ) ), Z ), hAPP(
% 0.97/1.63 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), T ) = hAPP(
% 0.97/1.63 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), Z ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), T ), hAPP( hAPP
% 0.97/1.63 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), Z ) ) =
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, T, hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ) ), Z ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), T ), hAPP( hAPP
% 0.97/1.63 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), Z ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ) ), Z ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ) ), Z ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), T ), hAPP( hAPP
% 0.97/1.63 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), Z ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), T ) = hAPP(
% 0.97/1.63 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), Z ), hAPP( hAPP
% 0.97/1.63 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ) ), T ) = Z }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ) ), T ) = Z,
% 0.97/1.63 hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), T ) = hAPP(
% 0.97/1.63 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), Z ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), T ), hAPP( hAPP
% 0.97/1.63 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), Z ) ) =
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ) ), T ), Z ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), T ), hAPP( hAPP
% 0.97/1.63 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), Z ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ) ), T ), Z ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ) ), T ), Z ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), T ), hAPP( hAPP
% 0.97/1.63 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), Z ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), c_RealDef_Oreal
% 0.97/1.63 ( tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.63 tc_Nat_Onat, X ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), T ), hAPP( hAPP
% 0.97/1.63 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), Z ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ) ), Z ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ) ), Z ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), T ), hAPP( hAPP
% 0.97/1.63 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), Z ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), T ), hAPP( hAPP
% 0.97/1.63 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), Z ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ) ), T ), Z ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ) ), T ), Z ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), T ), hAPP( hAPP
% 0.97/1.63 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), Z ) ) }.
% 0.97/1.63 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.63 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 0.97/1.63 ( tc_Nat_Onat ) ) ), X ) ) }.
% 0.97/1.63 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) =
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.97/1.63 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) = hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ),
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 0.97/1.63 ( tc_Nat_Onat ) ) ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.63 tc_Nat_Onat, Y ), X ), c_RComplete_Onatfloor(
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.97/1.63 tc_Nat_Onat, Y ) ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.97/1.63 c_RComplete_Onatfloor( X ), Y ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.63 tc_Nat_Onat, Y ), X ), c_RComplete_Onatceiling(
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.97/1.63 tc_Nat_Onat, Y ) ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.97/1.63 c_RComplete_Onatceiling( X ), Y ) }.
% 0.97/1.63 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless(
% 0.97/1.63 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), hAPP( hAPP
% 0.97/1.63 ( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), Z ), c_Groups_Ominus__class_Ominus(
% 0.97/1.63 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ), Z ) =
% 0.97/1.63 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) }.
% 0.97/1.63 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.63 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, Y, X ) ), hAPP( hAPP
% 0.97/1.63 ( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ),
% 0.97/1.63 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, hAPP( c_Complex_ORe, Y )
% 0.97/1.63 , hAPP( c_Complex_ORe, X ) ) ) ), c_Groups_Oabs__class_Oabs(
% 0.97/1.63 tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, hAPP(
% 0.97/1.63 c_Complex_OIm, Y ), hAPP( c_Complex_OIm, X ) ) ) ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), c_Groups_Oabs__class_Oabs(
% 0.97/1.63 tc_Int_Oint, c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ) ),
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ), X ) ), Y ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, hAPP
% 0.97/1.63 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), c_Groups_Oabs__class_Oabs(
% 0.97/1.63 tc_Int_Oint, c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, Z ) ) ),
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ), X ) ) ) }.
% 0.97/1.63 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.63 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ), Y ) }.
% 0.97/1.63 { ! class_Power_Opower( X ), ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 0.97/1.63 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) =
% 0.97/1.63 c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.63 { ! class_Power_Opower( X ), Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.97/1.63 , hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) = hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ominus__class_Ominus(
% 0.97/1.63 tc_Nat_Onat, Z, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 0.97/1.63 { ! c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) =
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex ), X ),
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) ),
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, X,
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) ),
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex ), X ), c_Complex_Oii )
% 0.97/1.63 ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, X, c_Complex_Oii ) )
% 0.97/1.63 , c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.97/1.63 { hAPP( c_Complex_ORe, c_Complex_Oii ) = c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_RealDef_Oreal ) }.
% 0.97/1.63 { hAPP( c_Complex_OIm, c_Complex_Oii ) = c_Groups_Oone__class_Oone(
% 0.97/1.63 tc_RealDef_Oreal ) }.
% 0.97/1.63 { ! c_Complex_Oii = c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) }.
% 0.97/1.63 { ! c_Complex_Oii = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.97/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.97/1.63 c_Complex_Oii ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.63 tc_Complex_Ocomplex ), c_Complex_Oii ), X ) ) = hAPP(
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex ), X ) }.
% 0.97/1.63 { ! c_Complex_Ocomplex_OComplex( Y, X ) = c_Complex_Oii, Y =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.63 { ! c_Complex_Ocomplex_OComplex( Y, X ) = c_Complex_Oii, X =
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.97/1.63 { ! Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! X =
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ),
% 0.97/1.63 c_Complex_Ocomplex_OComplex( Y, X ) = c_Complex_Oii }.
% 0.97/1.63 { c_Complex_Oii = c_Complex_Ocomplex_OComplex( c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( tc_RealDef_Oreal ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.97/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.97/1.63 c_Complex_Oii ), c_Complex_Ocomplex_OComplex( Y, X ) ) =
% 0.97/1.63 c_Complex_Ocomplex_OComplex( hAPP( c_Groups_Ouminus__class_Ouminus(
% 0.97/1.63 tc_RealDef_Oreal ), X ), Y ) }.
% 0.97/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.97/1.63 c_Complex_Ocomplex_OComplex( Y, X ) ), c_Complex_Oii ) =
% 0.97/1.63 c_Complex_Ocomplex_OComplex( hAPP( c_Groups_Ouminus__class_Ouminus(
% 0.97/1.63 tc_RealDef_Oreal ), X ), Y ) }.
% 0.97/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.97/1.63 c_Complex_Oii ), c_Complex_Oii ) = hAPP( c_Groups_Ouminus__class_Ouminus
% 0.97/1.63 ( tc_Complex_Ocomplex ), c_Groups_Oone__class_Oone( tc_Complex_Ocomplex )
% 0.97/1.63 ) }.
% 0.97/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP(
% 0.97/1.63 c_RealVector_Oof__real( tc_Complex_Ocomplex ), X ) ), c_Complex_Oii ) =
% 0.97/1.63 c_Complex_Ocomplex_OComplex( c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_RealDef_Oreal ), X ) }.
% 0.97/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.97/1.63 c_Complex_Oii ), hAPP( c_RealVector_Oof__real( tc_Complex_Ocomplex ), X )
% 0.97/1.63 ) = c_Complex_Ocomplex_OComplex( c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_RealDef_Oreal ), X ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.63 tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, skol39( X ),
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ), X ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.97/1.63 tc_Nat_Onat, skol39( X ) ) ) }.
% 0.97/1.63 { ! class_RealVector_Oreal__normed__vector( Y ), ! class_Orderings_Oord( X
% 0.97/1.63 ), c_Orderings_Oord__class_Oless__eq( X, T, skol40( X, U, W, T ) ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, T, V0 ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, V0 ) ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ),
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.97/1.63 c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, T ) ) ) ) }.
% 0.97/1.63 { ! class_RealVector_Oreal__normed__vector( Y ), ! class_Orderings_Oord( X
% 0.97/1.63 ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_RealVector_Onorm__class_Onorm( Y, c_Groups_Ominus__class_Ominus( Y,
% 0.97/1.63 hAPP( Z, T ), hAPP( Z, skol40( X, Y, Z, T ) ) ) ),
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, T, U ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, U ) ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ),
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.97/1.63 c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, T ) ) ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.97/1.63 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ominus__class_Ominus(
% 0.97/1.63 tc_Int_Oint, X, Y ) }.
% 0.97/1.63 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.97/1.63 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint
% 0.97/1.63 ) }.
% 0.97/1.63 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.97/1.63 hAPP( c_Groups_Ouminus__class_Ouminus( X ), Z ), hAPP(
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) = hAPP(
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( X ), c_Groups_Ominus__class_Ominus( X, Z
% 0.97/1.63 , Y ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Nat__Transfer_Otsub( X, Y )
% 0.97/1.63 ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.97/1.63 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ominus__class_Ominus(
% 0.97/1.63 tc_Int_Oint, X, Y ) }.
% 0.97/1.63 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.97/1.63 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), U ), T ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( X ), c_Groups_Ominus__class_Ominus( X, U, Z
% 0.97/1.63 ) ), c_Groups_Ominus__class_Ominus( X, T, Y ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( tc_Int_Oint ), X ), hBOOL( hAPP( Y, skol41( Z, Y ) ) ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! hBOOL( hAPP( Y, U ) )
% 0.97/1.63 , hBOOL( hAPP( Y, c_Groups_Ominus__class_Ominus( tc_Int_Oint, U, hAPP(
% 0.97/1.63 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), T ), X ) ) ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( Y, c_Groups_Ominus__class_Ominus(
% 0.97/1.63 tc_Int_Oint, skol41( X, Y ), X ) ) ), ! c_Orderings_Oord__class_Oless__eq
% 0.97/1.63 ( tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), ! hBOOL(
% 0.97/1.63 hAPP( Y, T ) ), hBOOL( hAPP( Y, c_Groups_Ominus__class_Ominus(
% 0.97/1.63 tc_Int_Oint, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 0.97/1.63 , Z ), X ) ) ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, Z ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol42( T, U, W ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, Z ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, T ) ), skol42( X, Y,
% 0.97/1.63 Z ) ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, T ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, Z ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, T ) ), skol42( X, Y,
% 0.97/1.63 Z ) ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, T, Z ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( tc_Int_Oint ), X ), hBOOL( hAPP( Y, skol43( Z, Y ) ) ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! hBOOL( hAPP( Y, U ) )
% 0.97/1.63 , hBOOL( hAPP( Y, hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint )
% 0.97/1.63 , U ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), T ), X )
% 0.97/1.63 ) ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( Y, hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), skol43( X, Y ) ), X ) ) ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), ! hBOOL( hAPP( Y, T ) )
% 0.97/1.63 , hBOOL( hAPP( Y, hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint )
% 0.97/1.63 , T ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X )
% 0.97/1.63 ) ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol44( Z, T ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), skol44( X, Y ) ), X ) =
% 0.97/1.63 Y }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), ! hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Z ), X ) = Y, Z =
% 0.97/1.63 skol44( X, Y ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol45( Z, T ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), skol45( X, Y ) ), X ) =
% 0.97/1.63 Y }.
% 0.97/1.63 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol46( Y ) ) }.
% 0.97/1.63 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.63 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.97/1.63 c_RealVector_Onorm__class_Onorm( X, Y ) ),
% 0.97/1.63 c_RealVector_Onorm__class_Onorm( X, Z ) ) ), skol46( X ) ) ) }.
% 0.97/1.63 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol47( Z, T ) ) }.
% 0.97/1.63 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.63 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.97/1.63 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol47( X, Y ) ) ) }.
% 0.97/1.63 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol48( Z, T ) ) }.
% 0.97/1.63 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.63 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.97/1.63 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol48( X, Y ) ) ) }.
% 0.97/1.63 { ! c_SEQ_OBseq( tc_RealDef_Oreal, X ), c_Orderings_Oord__class_Oless__eq(
% 0.97/1.63 tc_Nat_Onat, skol49( X ), skol68( X ) ), c_SEQ_Oconvergent(
% 0.97/1.63 tc_RealDef_Oreal, X ) }.
% 0.97/1.63 { ! c_SEQ_OBseq( tc_RealDef_Oreal, X ), ! c_Orderings_Oord__class_Oless__eq
% 0.97/1.63 ( tc_RealDef_Oreal, hAPP( X, skol49( X ) ), hAPP( X, skol68( X ) ) ),
% 0.97/1.63 c_SEQ_Oconvergent( tc_RealDef_Oreal, X ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.63 c_Transcendental_Oln( hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.97/1.63 tc_RealDef_Oreal ), X ), Y ) ) = hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.97/1.63 tc_Nat_Onat, Y ) ), c_Transcendental_Oln( X ) ) }.
% 0.97/1.63 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_Oconvergent( X, Y
% 0.97/1.63 ), c_SEQ_Olim( X, c_COMBB( X, X, tc_Nat_Onat,
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) = hAPP(
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( X ), c_SEQ_Olim( X, Y ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 0.97/1.63 ), c_Transcendental_Oln( Y ) ), c_Orderings_Oord__class_Oless(
% 0.97/1.63 tc_RealDef_Oreal, X, Y ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, Y ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 0.97/1.63 ), c_Transcendental_Oln( Y ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.97/1.63 c_Transcendental_Oln( X ) = c_Transcendental_Oln( Y ), X = Y }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), ! X = Y,
% 0.97/1.63 c_Transcendental_Oln( X ) = c_Transcendental_Oln( Y ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 0.97/1.63 ), X ) }.
% 0.97/1.63 { c_Transcendental_Oln( c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_Transcendental_Oln
% 0.97/1.63 ( X ), c_Transcendental_Oln( Y ) ), c_Orderings_Oord__class_Oless__eq(
% 0.97/1.63 tc_RealDef_Oreal, X, Y ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_Transcendental_Oln
% 0.97/1.63 ( X ), c_Transcendental_Oln( Y ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 0.97/1.63 ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 0.97/1.63 ) ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 0.97/1.63 ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 0.97/1.63 ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 0.97/1.63 ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.63 c_Transcendental_Oln( X ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal
% 0.97/1.63 ), X = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), ! X =
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_Transcendental_Oln( X )
% 0.97/1.63 = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 0.97/1.63 ) ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 0.97/1.63 ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 0.97/1.63 ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 0.97/1.63 ) ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 0.97/1.63 ) ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 0.97/1.63 ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.97/1.63 c_Transcendental_Oln( hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.63 tc_RealDef_Oreal ), X ), Y ) ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.97/1.63 ( tc_RealDef_Oreal ), c_Transcendental_Oln( X ) ), c_Transcendental_Oln(
% 0.97/1.63 Y ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_Transcendental_Oln
% 0.97/1.63 ( hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ),
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) ), X ) }.
% 0.97/1.63 { alpha24( X, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP(
% 0.97/1.63 X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Z ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z, hAPP( X, Y ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, skol50( T, Y, U ), Y ) }
% 0.97/1.63 .
% 0.97/1.63 { alpha24( X, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP(
% 0.97/1.63 X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Z ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z, hAPP( X, Y ) ), hAPP(
% 0.97/1.63 X, skol50( X, Y, Z ) ) = Z }.
% 0.97/1.63 { ! alpha24( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol51( Z
% 0.97/1.63 , Y ), Y ) }.
% 0.97/1.63 { ! alpha24( X, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.63 c_Groups_Oabs__class_Oabs( tc_Int_Oint, c_Groups_Ominus__class_Ominus(
% 0.97/1.63 tc_Int_Oint, hAPP( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 0.97/1.63 tc_Nat_Onat ), skol51( X, Y ) ), c_Groups_Oone__class_Oone( tc_Nat_Onat )
% 0.97/1.63 ) ), hAPP( X, skol51( X, Y ) ) ) ), c_Groups_Oone__class_Oone(
% 0.97/1.63 tc_Int_Oint ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oabs__class_Oabs
% 0.97/1.63 ( tc_Int_Oint, c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( X, hAPP
% 0.97/1.63 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ),
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ), hAPP( X, Z ) ) ),
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), alpha24( X, Y ) }.
% 0.97/1.63 { alpha25( X, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP(
% 0.97/1.63 X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Z ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z, hAPP( X, Y ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, skol52( T, Y, U ), Y ) }
% 0.97/1.63 .
% 0.97/1.63 { alpha25( X, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP(
% 0.97/1.63 X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Z ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z, hAPP( X, Y ) ), hAPP(
% 0.97/1.63 X, skol52( X, Y, Z ) ) = Z }.
% 0.97/1.63 { ! alpha25( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol53( Z
% 0.97/1.63 , Y ), Y ) }.
% 0.97/1.63 { ! alpha25( X, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.63 c_Groups_Oabs__class_Oabs( tc_Int_Oint, c_Groups_Ominus__class_Ominus(
% 0.97/1.63 tc_Int_Oint, hAPP( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 0.97/1.63 tc_Nat_Onat ), skol53( X, Y ) ), c_Groups_Oone__class_Oone( tc_Nat_Onat )
% 0.97/1.63 ) ), hAPP( X, skol53( X, Y ) ) ) ), c_Groups_Oone__class_Oone(
% 0.97/1.63 tc_Int_Oint ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oabs__class_Oabs
% 0.97/1.63 ( tc_Int_Oint, c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( X, hAPP
% 0.97/1.63 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ),
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ), hAPP( X, Z ) ) ),
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), alpha25( X, Y ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, Z ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol54( T, U, W ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, Z ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, T ) ), skol54( X, Y,
% 0.97/1.63 Z ) ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, T ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, Z ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, T ) ), skol54( X, Y,
% 0.97/1.63 Z ) ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, T, Z ) }.
% 0.97/1.63 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.63 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol55( X, Y, Z ) ) ), Z ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, T ) ), c_RealDef_Oreal(
% 0.97/1.63 tc_Nat_Onat, c_Nat_OSuc( skol69( X, Y ) ) ) ) }.
% 0.97/1.63 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol72( X, Y, Z ) ) ),
% 0.97/1.63 c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Z ) ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol73( T, U ) ) }.
% 0.97/1.63 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol72( X, Y, Z ) ) ),
% 0.97/1.63 c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Z ) ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.63 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, T ) ), skol73( X, Y ) ) }.
% 0.97/1.63 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( X ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.97/1.63 X ) ) }.
% 0.97/1.63 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_Nat_Onat ), c_Nat_OSuc( X ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.97/1.63 tc_Nat_Onat, X, c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) )
% 0.97/1.63 ) ) = X }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.63 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.97/1.63 tc_Nat_Onat, c_Nat_OSuc( X ) ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), Z ) =
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), Z ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, c_Nat_OSuc(
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) ) =
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ), c_Nat_OSuc( X ) ) }
% 0.97/1.63 .
% 0.97/1.63 { c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_Nat_Onat ) ) ) = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) =
% 0.97/1.63 c_Nat_OSuc( c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.97/1.63 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 0.97/1.63 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.63 ( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) }.
% 0.97/1.63 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.63 ( tc_Nat_Onat, c_Nat_OSuc( Z ), Y ), c_Nat_OSuc( X ) ) =
% 0.97/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.63 ( tc_Nat_Onat, Z, Y ), X ) }.
% 0.97/1.63 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.97/1.63 X ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 0.97/1.63 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.63 ( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__semidom( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ) ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.63 ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ) = hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.97/1.63 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.63 X ), Y ), Z = Y }.
% 0.97/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.63 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.97/1.63 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ) ) }.
% 0.97/1.63 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.97/1.63 , Z ), c_Nat_OSuc( c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.97/1.63 ) ) ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc(
% 0.97/1.63 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), Z = Y, Z =
% 0.97/1.63 hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ) }.
% 0.97/1.63 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.97/1.63 { ! class_Rings_Oidom( X ), ! Z = hAPP( c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.63 ), Y ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc(
% 0.97/1.63 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP
% 0.97/1.63 ( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.97/1.63 { ! c_SEQ_Osubseq( X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( X
% 0.97/1.63 , Y ), hAPP( X, c_Nat_OSuc( Y ) ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( X, skol56( X ) ),
% 0.97/1.63 hAPP( X, c_Nat_OSuc( skol56( X ) ) ) ), c_SEQ_Osubseq( X ) }.
% 0.97/1.63 { hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), c_Nat_OSuc( X ) ) =
% 0.97/1.63 hAPP( hAPP( Z, Y ), hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), X
% 0.97/1.63 ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.97/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.97/1.63 ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.97/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.97/1.63 ), X ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.97/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.97/1.63 ), X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.97/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.97/1.63 ), X ) ) }.
% 0.97/1.63 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z
% 0.97/1.63 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.63 c_Nat_OSuc( Z ) ), X ), Y = X }.
% 0.97/1.63 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.63 c_Nat_OSuc( Z ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.63 tc_Nat_Onat ), c_Nat_OSuc( Z ) ), X ) }.
% 0.97/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Y )
% 0.97/1.63 ), X ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ),
% 0.97/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), c_Nat_OSuc
% 0.97/1.63 ( X ) ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ),
% 0.97/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.63 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.63 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y = c_Nat_OSuc
% 0.97/1.63 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.63 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.63 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X = c_Nat_OSuc
% 0.97/1.63 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.63 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.97/1.63 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 0.97/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 0.97/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.97/1.63 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.97/1.63 , Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.97/1.63 , Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.97/1.63 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( c_Nat_OSuc(
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), X =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X = c_Nat_OSuc(
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha9( X, Y ) }.
% 0.97/1.63 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.97/1.63 { ! alpha9( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.97/1.63 c_Nat_OSuc( X ) ) }.
% 0.97/1.63 { ! alpha9( X, Y ), Y = c_Nat_OSuc( skol57( Z, Y ) ) }.
% 0.97/1.63 { ! alpha9( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol57( X,
% 0.97/1.63 Y ), X ) }.
% 0.97/1.63 { ! Y = c_Nat_OSuc( Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.97/1.63 ), alpha9( X, Y ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.63 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( skol58( X ) ) }.
% 0.97/1.63 { ! X = c_Nat_OSuc( Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.97/1.63 { ! c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ), alpha10( X, Y ),
% 0.97/1.63 alpha20( X, Y ) }.
% 0.97/1.63 { ! alpha10( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.97/1.63 ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) }.
% 0.97/1.63 { ! alpha20( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.97/1.63 ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) }.
% 0.97/1.63 { ! alpha20( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.63 { ! alpha20( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_Nat_Onat ) ) }.
% 0.97/1.63 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha20( X, Y ) }.
% 0.97/1.63 { ! alpha10( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_Nat_Onat ) ) }.
% 0.97/1.63 { ! alpha10( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.63 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha10( X, Y ) }.
% 0.97/1.63 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.63 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha11( X, Y )
% 0.97/1.63 , alpha21( X, Y ) }.
% 0.97/1.63 { ! alpha11( X, Y ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat )
% 0.97/1.63 , Y ), X ) = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.63 { ! alpha21( X, Y ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat )
% 0.97/1.63 , Y ), X ) = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.63 { ! alpha21( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.63 { ! alpha21( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_Nat_Onat ) ) }.
% 0.97/1.63 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha21( X, Y ) }.
% 0.97/1.63 { ! alpha11( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_Nat_Onat ) ) }.
% 0.97/1.63 { ! alpha11( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.63 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha11( X, Y ) }.
% 0.97/1.63 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) ) }.
% 0.97/1.63 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( hAPP( hAPP(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Y ) ) ) }.
% 0.97/1.63 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.97/1.63 class_Groups_Ocancel__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.63 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring__0(
% 0.97/1.63 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.63 { ! class_Rings_Ocomm__ring( X ), class_Rings_Ocomm__ring(
% 0.97/1.63 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.63 { class_Groups_Ocancel__comm__monoid__add( tc_Complex_Ocomplex ) }.
% 0.97/1.63 { class_Rings_Ocomm__semiring__0( tc_Complex_Ocomplex ) }.
% 0.97/1.63 { class_Rings_Ocomm__ring( tc_Complex_Ocomplex ) }.
% 0.97/1.63 { class_Groups_Ocancel__comm__monoid__add( tc_RealDef_Oreal ) }.
% 0.97/1.63 { class_Rings_Ocomm__semiring__0( tc_RealDef_Oreal ) }.
% 0.97/1.63 { class_Rings_Ocomm__ring( tc_RealDef_Oreal ) }.
% 0.97/1.63 { class_Groups_Ocancel__comm__monoid__add( tc_Nat_Onat ) }.
% 0.97/1.63 { class_Rings_Ocomm__semiring__0( tc_Nat_Onat ) }.
% 0.97/1.63 { class_Groups_Ocancel__comm__monoid__add( tc_Int_Oint ) }.
% 0.97/1.63 { class_Rings_Ocomm__semiring__0( tc_Int_Oint ) }.
% 0.97/1.63 { class_Rings_Ocomm__ring( tc_Int_Oint ) }.
% 0.97/1.63 { ! class_Lattices_Oboolean__algebra( X ), class_Lattices_Oboolean__algebra
% 0.97/1.63 ( tc_fun( Y, X ) ) }.
% 0.97/1.63 { ! class_Orderings_Opreorder( X ), class_Orderings_Opreorder( tc_fun( Y, X
% 0.97/1.63 ) ) }.
% 0.97/1.63 { ! class_Orderings_Oorder( X ), class_Orderings_Oorder( tc_fun( Y, X ) ) }
% 0.97/1.63 .
% 0.97/1.63 { ! class_Orderings_Oord( X ), class_Orderings_Oord( tc_fun( Y, X ) ) }.
% 0.97/1.63 { ! class_Groups_Ouminus( X ), class_Groups_Ouminus( tc_fun( Y, X ) ) }.
% 0.97/1.63 { ! class_Groups_Ominus( X ), class_Groups_Ominus( tc_fun( Y, X ) ) }.
% 0.97/1.63 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.97/1.63 tc_Int_Oint ) }.
% 0.97/1.63 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.97/1.63 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Int_Oint ) }.
% 0.97/1.63 { class_Rings_Olinordered__comm__semiring__strict( tc_Int_Oint ) }.
% 0.97/1.63 { class_Rings_Olinordered__semiring__1__strict( tc_Int_Oint ) }.
% 0.97/1.63 { class_Rings_Olinordered__semiring__strict( tc_Int_Oint ) }.
% 0.97/1.63 { class_Groups_Oordered__ab__semigroup__add( tc_Int_Oint ) }.
% 0.97/1.63 { class_Groups_Oordered__ab__group__add__abs( tc_Int_Oint ) }.
% 0.97/1.63 { class_Groups_Oordered__comm__monoid__add( tc_Int_Oint ) }.
% 0.97/1.63 { class_Groups_Olinordered__ab__group__add( tc_Int_Oint ) }.
% 0.97/1.63 { class_Groups_Ocancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.97/1.63 { class_Rings_Oring__1__no__zero__divisors( tc_Int_Oint ) }.
% 0.97/1.63 { class_Rings_Oordered__cancel__semiring( tc_Int_Oint ) }.
% 0.97/1.63 { class_Rings_Olinordered__ring__strict( tc_Int_Oint ) }.
% 0.97/1.63 { class_Rings_Oring__no__zero__divisors( tc_Int_Oint ) }.
% 0.97/1.63 { class_Rings_Oordered__comm__semiring( tc_Int_Oint ) }.
% 0.97/1.63 { class_Rings_Olinordered__semiring__1( tc_Int_Oint ) }.
% 0.97/1.63 { class_Groups_Oordered__ab__group__add( tc_Int_Oint ) }.
% 0.97/1.63 { class_Groups_Ocancel__semigroup__add( tc_Int_Oint ) }.
% 0.97/1.63 { class_Rings_Olinordered__semiring( tc_Int_Oint ) }.
% 0.97/1.63 { class_Rings_Olinordered__semidom( tc_Int_Oint ) }.
% 0.97/1.63 { class_Groups_Oab__semigroup__mult( tc_Int_Oint ) }.
% 0.97/1.63 { class_Groups_Ocomm__monoid__mult( tc_Int_Oint ) }.
% 0.97/1.63 { class_Groups_Oab__semigroup__add( tc_Int_Oint ) }.
% 0.97/1.63 { class_Rings_Oordered__semiring( tc_Int_Oint ) }.
% 0.97/1.63 { class_Rings_Oordered__ring__abs( tc_Int_Oint ) }.
% 0.97/1.63 { class_Rings_Ono__zero__divisors( tc_Int_Oint ) }.
% 0.97/1.63 { class_Groups_Ocomm__monoid__add( tc_Int_Oint ) }.
% 0.97/1.63 { class_Rings_Olinordered__ring( tc_Int_Oint ) }.
% 0.97/1.63 { class_Rings_Olinordered__idom( tc_Int_Oint ) }.
% 0.97/1.63 { class_Rings_Ocomm__semiring__1( tc_Int_Oint ) }.
% 0.97/1.63 { class_Rings_Ocomm__semiring( tc_Int_Oint ) }.
% 0.97/1.63 { class_Groups_Oab__group__add( tc_Int_Oint ) }.
% 0.97/1.63 { class_Rings_Ozero__neq__one( tc_Int_Oint ) }.
% 0.97/1.63 { class_Rings_Oordered__ring( tc_Int_Oint ) }.
% 0.97/1.63 { class_Orderings_Opreorder( tc_Int_Oint ) }.
% 0.97/1.63 { class_Orderings_Olinorder( tc_Int_Oint ) }.
% 0.97/1.63 { class_Groups_Omonoid__mult( tc_Int_Oint ) }.
% 0.97/1.63 { class_Rings_Ocomm__ring__1( tc_Int_Oint ) }.
% 0.97/1.63 { class_Groups_Omonoid__add( tc_Int_Oint ) }.
% 0.97/1.63 { class_Rings_Osemiring__0( tc_Int_Oint ) }.
% 0.97/1.63 { class_Groups_Ogroup__add( tc_Int_Oint ) }.
% 0.97/1.63 { class_Rings_Omult__zero( tc_Int_Oint ) }.
% 0.97/1.63 { class_Orderings_Oorder( tc_Int_Oint ) }.
% 0.97/1.63 { class_Rings_Osemiring( tc_Int_Oint ) }.
% 0.97/1.63 { class_Orderings_Oord( tc_Int_Oint ) }.
% 0.97/1.63 { class_Groups_Ouminus( tc_Int_Oint ) }.
% 0.97/1.63 { class_Groups_Osgn__if( tc_Int_Oint ) }.
% 0.97/1.63 { class_Groups_Oabs__if( tc_Int_Oint ) }.
% 0.97/1.63 { class_Rings_Oring__1( tc_Int_Oint ) }.
% 0.97/1.63 { class_Groups_Ominus( tc_Int_Oint ) }.
% 0.97/1.63 { class_Power_Opower( tc_Int_Oint ) }.
% 0.97/1.63 { class_Groups_Ozero( tc_Int_Oint ) }.
% 0.97/1.63 { class_Rings_Oring( tc_Int_Oint ) }.
% 0.97/1.63 { class_Rings_Oidom( tc_Int_Oint ) }.
% 0.97/1.63 { class_Groups_Oone( tc_Int_Oint ) }.
% 0.97/1.63 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.97/1.63 tc_Nat_Onat ) }.
% 0.97/1.63 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.97/1.63 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Nat_Onat ) }.
% 0.97/1.63 { class_Rings_Olinordered__comm__semiring__strict( tc_Nat_Onat ) }.
% 0.97/1.63 { class_Rings_Olinordered__semiring__strict( tc_Nat_Onat ) }.
% 0.97/1.63 { class_Groups_Oordered__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.97/1.63 { class_Groups_Oordered__comm__monoid__add( tc_Nat_Onat ) }.
% 0.97/1.63 { class_Groups_Ocancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.97/1.63 { class_Rings_Oordered__cancel__semiring( tc_Nat_Onat ) }.
% 0.97/1.63 { class_Rings_Oordered__comm__semiring( tc_Nat_Onat ) }.
% 0.97/1.63 { class_Groups_Ocancel__semigroup__add( tc_Nat_Onat ) }.
% 0.97/1.63 { class_Rings_Olinordered__semiring( tc_Nat_Onat ) }.
% 0.97/1.63 { class_Rings_Olinordered__semidom( tc_Nat_Onat ) }.
% 0.97/1.63 { class_Groups_Oab__semigroup__mult( tc_Nat_Onat ) }.
% 0.97/1.63 { class_Groups_Ocomm__monoid__mult( tc_Nat_Onat ) }.
% 0.97/1.63 { class_Groups_Oab__semigroup__add( tc_Nat_Onat ) }.
% 0.97/1.63 { class_Rings_Oordered__semiring( tc_Nat_Onat ) }.
% 0.97/1.63 { class_Rings_Ono__zero__divisors( tc_Nat_Onat ) }.
% 0.97/1.63 { class_Groups_Ocomm__monoid__add( tc_Nat_Onat ) }.
% 0.97/1.63 { class_Rings_Ocomm__semiring__1( tc_Nat_Onat ) }.
% 0.97/1.63 { class_Rings_Ocomm__semiring( tc_Nat_Onat ) }.
% 0.97/1.63 { class_Rings_Ozero__neq__one( tc_Nat_Onat ) }.
% 0.97/1.63 { class_Orderings_Opreorder( tc_Nat_Onat ) }.
% 0.97/1.63 { class_Orderings_Olinorder( tc_Nat_Onat ) }.
% 0.97/1.63 { class_Groups_Omonoid__mult( tc_Nat_Onat ) }.
% 0.97/1.63 { class_Groups_Omonoid__add( tc_Nat_Onat ) }.
% 0.97/1.63 { class_Rings_Osemiring__0( tc_Nat_Onat ) }.
% 0.97/1.63 { class_Rings_Omult__zero( tc_Nat_Onat ) }.
% 0.97/1.63 { class_Orderings_Oorder( tc_Nat_Onat ) }.
% 0.97/1.63 { class_Rings_Osemiring( tc_Nat_Onat ) }.
% 0.97/1.63 { class_Orderings_Oord( tc_Nat_Onat ) }.
% 0.97/1.63 { class_Groups_Ominus( tc_Nat_Onat ) }.
% 0.97/1.63 { class_Power_Opower( tc_Nat_Onat ) }.
% 0.97/1.63 { class_Groups_Ozero( tc_Nat_Onat ) }.
% 0.97/1.63 { class_Groups_Oone( tc_Nat_Onat ) }.
% 0.97/1.63 { class_Lattices_Oboolean__algebra( tc_HOL_Obool ) }.
% 0.97/1.63 { class_Orderings_Opreorder( tc_HOL_Obool ) }.
% 0.97/1.63 { class_Orderings_Oorder( tc_HOL_Obool ) }.
% 0.97/1.63 { class_Orderings_Oord( tc_HOL_Obool ) }.
% 0.97/1.63 { class_Groups_Ouminus( tc_HOL_Obool ) }.
% 0.97/1.63 { class_Groups_Ominus( tc_HOL_Obool ) }.
% 0.97/1.63 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.97/1.63 tc_RealDef_Oreal ) }.
% 0.97/1.63 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_RealDef_Oreal ) }
% 0.97/1.64 .
% 0.97/1.64 { class_Rings_Olinordered__comm__semiring__strict( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Rings_Olinordered__semiring__1__strict( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_RealVector_Oreal__normed__div__algebra( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Rings_Olinordered__semiring__strict( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_RealVector_Oreal__normed__algebra__1( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Groups_Oordered__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Groups_Oordered__ab__group__add__abs( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_RealVector_Oreal__normed__algebra( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Groups_Oordered__comm__monoid__add( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Groups_Olinordered__ab__group__add( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Groups_Ocancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Rings_Oring__1__no__zero__divisors( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Rings_Oordered__cancel__semiring( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_RealVector_Oreal__normed__vector( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Rings_Olinordered__ring__strict( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Rings_Oring__no__zero__divisors( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Rings_Oordered__comm__semiring( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Rings_Olinordered__semiring__1( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Groups_Oordered__ab__group__add( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Groups_Ocancel__semigroup__add( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Rings_Olinordered__semiring( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_RealVector_Oreal__algebra__1( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Rings_Olinordered__semidom( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Groups_Oab__semigroup__mult( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_RealVector_Ometric__space( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Groups_Ocomm__monoid__mult( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Groups_Oab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Rings_Oordered__semiring( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Rings_Oordered__ring__abs( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Rings_Ono__zero__divisors( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Groups_Ocomm__monoid__add( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Rings_Olinordered__ring( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Rings_Olinordered__idom( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Rings_Ocomm__semiring__1( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Rings_Ocomm__semiring( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Groups_Oab__group__add( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_SEQ_Ocomplete__space( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Rings_Ozero__neq__one( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Rings_Oordered__ring( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Orderings_Opreorder( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Orderings_Olinorder( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Groups_Omonoid__mult( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Rings_Ocomm__ring__1( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Groups_Omonoid__add( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Rings_Osemiring__0( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Groups_Ogroup__add( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Rings_Omult__zero( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Orderings_Oorder( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Rings_Osemiring( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Orderings_Oord( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Groups_Ouminus( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Groups_Osgn__if( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Groups_Oabs__if( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Rings_Oring__1( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Groups_Ominus( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Power_Opower( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Groups_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Rings_Oring( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Rings_Oidom( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Groups_Oone( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.97/1.64 tc_Complex_Ocomplex ) }.
% 0.97/1.64 { class_RealVector_Oreal__normed__div__algebra( tc_Complex_Ocomplex ) }.
% 0.97/1.64 { class_RealVector_Oreal__normed__algebra__1( tc_Complex_Ocomplex ) }.
% 0.97/1.64 { class_RealVector_Oreal__normed__algebra( tc_Complex_Ocomplex ) }.
% 0.97/1.64 { class_Groups_Ocancel__ab__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.97/1.64 { class_Rings_Oring__1__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.97/1.64 { class_RealVector_Oreal__normed__vector( tc_Complex_Ocomplex ) }.
% 0.97/1.64 { class_Rings_Oring__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.97/1.64 { class_Groups_Ocancel__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.97/1.64 { class_RealVector_Oreal__algebra__1( tc_Complex_Ocomplex ) }.
% 0.97/1.64 { class_Groups_Oab__semigroup__mult( tc_Complex_Ocomplex ) }.
% 0.97/1.64 { class_RealVector_Ometric__space( tc_Complex_Ocomplex ) }.
% 0.97/1.64 { class_Groups_Ocomm__monoid__mult( tc_Complex_Ocomplex ) }.
% 0.97/1.64 { class_Groups_Oab__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.97/1.64 { class_Rings_Ono__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.97/1.64 { class_Groups_Ocomm__monoid__add( tc_Complex_Ocomplex ) }.
% 0.97/1.64 { class_Rings_Ocomm__semiring__1( tc_Complex_Ocomplex ) }.
% 0.97/1.64 { class_Rings_Ocomm__semiring( tc_Complex_Ocomplex ) }.
% 0.97/1.64 { class_Groups_Oab__group__add( tc_Complex_Ocomplex ) }.
% 0.97/1.64 { class_SEQ_Ocomplete__space( tc_Complex_Ocomplex ) }.
% 0.97/1.64 { class_Rings_Ozero__neq__one( tc_Complex_Ocomplex ) }.
% 0.97/1.64 { class_Groups_Omonoid__mult( tc_Complex_Ocomplex ) }.
% 0.97/1.64 { class_Rings_Ocomm__ring__1( tc_Complex_Ocomplex ) }.
% 0.97/1.64 { class_Groups_Omonoid__add( tc_Complex_Ocomplex ) }.
% 0.97/1.64 { class_Rings_Osemiring__0( tc_Complex_Ocomplex ) }.
% 0.97/1.64 { class_Groups_Ogroup__add( tc_Complex_Ocomplex ) }.
% 0.97/1.64 { class_Rings_Omult__zero( tc_Complex_Ocomplex ) }.
% 0.97/1.64 { class_Rings_Osemiring( tc_Complex_Ocomplex ) }.
% 0.97/1.64 { class_Groups_Ouminus( tc_Complex_Ocomplex ) }.
% 0.97/1.64 { class_Rings_Oring__1( tc_Complex_Ocomplex ) }.
% 0.97/1.64 { class_Groups_Ominus( tc_Complex_Ocomplex ) }.
% 0.97/1.64 { class_Power_Opower( tc_Complex_Ocomplex ) }.
% 0.97/1.64 { class_Groups_Ozero( tc_Complex_Ocomplex ) }.
% 0.97/1.64 { class_Rings_Oring( tc_Complex_Ocomplex ) }.
% 0.97/1.64 { class_Rings_Oidom( tc_Complex_Ocomplex ) }.
% 0.97/1.64 { class_Groups_Oone( tc_Complex_Ocomplex ) }.
% 0.97/1.64 { ! class_Rings_Oidom( X ),
% 0.97/1.64 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__idom( X ),
% 0.97/1.64 class_Groups_Oordered__cancel__ab__semigroup__add( tc_Polynomial_Opoly( X
% 0.97/1.64 ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__idom( X ),
% 0.97/1.64 class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Polynomial_Opoly(
% 0.97/1.64 X ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__idom( X ),
% 0.97/1.64 class_Rings_Olinordered__comm__semiring__strict( tc_Polynomial_Opoly( X )
% 0.97/1.64 ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__idom( X ),
% 0.97/1.64 class_Rings_Olinordered__semiring__1__strict( tc_Polynomial_Opoly( X ) )
% 0.97/1.64 }.
% 0.97/1.64 { ! class_Rings_Olinordered__idom( X ),
% 0.97/1.64 class_Rings_Olinordered__semiring__strict( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__idom( X ),
% 0.97/1.64 class_Groups_Oordered__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__idom( X ),
% 0.97/1.64 class_Groups_Oordered__ab__group__add__abs( tc_Polynomial_Opoly( X ) ) }
% 0.97/1.64 .
% 0.97/1.64 { ! class_Rings_Olinordered__idom( X ),
% 0.97/1.64 class_Groups_Oordered__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__idom( X ),
% 0.97/1.64 class_Groups_Olinordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.97/1.64 class_Groups_Ocancel__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Rings_Oidom( X ), class_Rings_Oring__1__no__zero__divisors(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__idom( X ),
% 0.97/1.64 class_Rings_Oordered__cancel__semiring( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__idom( X ),
% 0.97/1.64 class_Rings_Olinordered__ring__strict( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Rings_Oidom( X ), class_Rings_Oring__no__zero__divisors(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__idom( X ),
% 0.97/1.64 class_Rings_Oordered__comm__semiring( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__idom( X ),
% 0.97/1.64 class_Rings_Olinordered__semiring__1( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__idom( X ),
% 0.97/1.64 class_Groups_Oordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.97/1.64 class_Groups_Ocancel__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semiring(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semidom(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Oab__semigroup__mult
% 0.97/1.64 ( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Ocomm__monoid__mult(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Oab__semigroup__add
% 0.97/1.64 ( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__semiring(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__ring__abs(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Rings_Oidom( X ), class_Rings_Ono__zero__divisors(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Ocomm__monoid__add(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__ring(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__idom(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ocomm__semiring__1(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Groups_Oab__group__add( X ), class_Groups_Oab__group__add(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ozero__neq__one(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__ring(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Opreorder(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Olinorder(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Omonoid__mult(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Ocomm__ring__1(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Omonoid__add(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring__0(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Groups_Oab__group__add( X ), class_Groups_Ogroup__add(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Omult__zero(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oorder(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oord(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Groups_Oab__group__add( X ), class_Groups_Ouminus(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__idom( X ), class_Groups_Osgn__if(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__idom( X ), class_Groups_Oabs__if(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Oring__1(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Groups_Oab__group__add( X ), class_Groups_Ominus(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__1( X ), class_Power_Opower(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Groups_Ozero( X ), class_Groups_Ozero( tc_Polynomial_Opoly( X ) )
% 0.97/1.64 }.
% 0.97/1.64 { ! class_Rings_Ocomm__ring( X ), class_Rings_Oring( tc_Polynomial_Opoly( X
% 0.97/1.64 ) ) }.
% 0.97/1.64 { ! class_Rings_Oidom( X ), class_Rings_Oidom( tc_Polynomial_Opoly( X ) ) }
% 0.97/1.64 .
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Oone(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { hAPP( c_COMBK( T, Z, Y ), X ) = Y }.
% 0.97/1.64 { hAPP( c_COMBB( W, U, T, Z, Y ), X ) = hAPP( Z, hAPP( Y, X ) ) }.
% 0.97/1.64 { hAPP( c_COMBC( W, U, T, Z, Y ), X ) = hAPP( hAPP( Z, X ), Y ) }.
% 0.97/1.64 { hAPP( c_COMBS( W, U, T, Z, Y ), X ) = hAPP( hAPP( Z, X ), hAPP( Y, X ) )
% 0.97/1.64 }.
% 0.97/1.64 { ! c_SEQ_OBseq( tc_RealDef_Oreal, c_COMBB( tc_Complex_Ocomplex,
% 0.97/1.64 tc_RealDef_Oreal, tc_Nat_Onat, c_Complex_ORe, c_COMBB( tc_Nat_Onat,
% 0.97/1.64 tc_Complex_Ocomplex, tc_Nat_Onat, v_s, v_f____ ) ) ) }.
% 0.97/1.64
% 0.97/1.64 *** allocated 15000 integers for clauses
% 0.97/1.64 *** allocated 22500 integers for clauses
% 0.97/1.64 *** allocated 33750 integers for clauses
% 0.97/1.64 *** allocated 50625 integers for clauses
% 0.97/1.64 *** allocated 75937 integers for clauses
% 0.97/1.64 percentage equality = 0.248171, percentage horn = 0.932563
% 0.97/1.64 This is a problem with some equality
% 0.97/1.64
% 0.97/1.64
% 0.97/1.64
% 0.97/1.64 Options Used:
% 0.97/1.64
% 0.97/1.64 useres = 1
% 0.97/1.64 useparamod = 1
% 0.97/1.64 useeqrefl = 1
% 0.97/1.64 useeqfact = 1
% 0.97/1.64 usefactor = 1
% 0.97/1.64 usesimpsplitting = 0
% 0.97/1.64 usesimpdemod = 5
% 0.97/1.64 usesimpres = 3
% 0.97/1.64
% 0.97/1.64 resimpinuse = 1000
% 0.97/1.64 resimpclauses = 20000
% 0.97/1.64 substype = eqrewr
% 0.97/1.64 backwardsubs = 1
% 0.97/1.64 selectoldest = 5
% 0.97/1.64
% 0.97/1.64 litorderings [0] = split
% 0.97/1.64 litorderings [1] = extend the termordering, first sorting on arguments
% 0.97/1.64
% 0.97/1.64 termordering = kbo
% 0.97/1.64
% 0.97/1.64 litapriori = 0
% 0.97/1.64 termapriori = 1
% 0.97/1.64 litaposteriori = 0
% 0.97/1.64 termaposteriori = 0
% 0.97/1.64 demodaposteriori = 0
% 0.97/1.64 ordereqreflfact = 0
% 0.97/1.64
% 0.97/1.64 litselect = negord
% 0.97/1.64
% 0.97/1.64 maxweight = 15
% 0.97/1.64 maxdepth = 30000
% 0.97/1.64 maxlength = 115
% 0.97/1.64 maxnrvars = 195
% 0.97/1.64 excuselevel = 1
% 0.97/1.64 increasemaxweight = 1
% 0.97/1.64
% 0.97/1.64 maxselected = 10000000
% 0.97/1.64 maxnrclauses = 10000000
% 0.97/1.64
% 0.97/1.64 showgenerated = 0
% 0.97/1.64 showkept = 0
% 0.97/1.64 showselected = 0
% 0.97/1.64 showdeleted = 0
% 0.97/1.64 showresimp = 1
% 0.97/1.64 showstatus = 2000
% 0.97/1.64
% 0.97/1.64 prologoutput = 0
% 0.97/1.64 nrgoals = 5000000
% 0.97/1.64 totalproof = 1
% 0.97/1.64
% 0.97/1.64 Symbols occurring in the translation:
% 0.97/1.64
% 0.97/1.64 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.97/1.64 . [1, 2] (w:1, o:241, a:1, s:1, b:0),
% 0.97/1.64 ! [4, 1] (w:0, o:140, a:1, s:1, b:0),
% 0.97/1.64 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.97/1.64 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.97/1.64 hAPP [38, 2] (w:1, o:265, a:1, s:1, b:0),
% 0.97/1.64 v_ga____ [39, 0] (w:1, o:14, a:1, s:1, b:0),
% 0.97/1.64 c_SEQ_Osubseq [40, 1] (w:1, o:148, a:1, s:1, b:0),
% 0.97/1.64 v_f____ [41, 0] (w:1, o:13, a:1, s:1, b:0),
% 0.97/1.64 tc_RealDef_Oreal [42, 0] (w:1, o:24, a:1, s:1, b:0),
% 0.97/1.64 tc_Complex_Ocomplex [43, 0] (w:1, o:25, a:1, s:1, b:0),
% 0.97/1.64 tc_Nat_Onat [44, 0] (w:1, o:26, a:1, s:1, b:0),
% 0.97/1.64 c_Complex_ORe [45, 0] (w:1, o:27, a:1, s:1, b:0),
% 0.97/1.64 v_s [46, 0] (w:1, o:29, a:1, s:1, b:0),
% 0.97/1.64 c_COMBB [47, 5] (w:1, o:367, a:1, s:1, b:0),
% 0.97/1.64 c_SEQ_Omonoseq [48, 2] (w:1, o:269, a:1, s:1, b:0),
% 0.97/1.64 c_Complex_OIm [49, 0] (w:1, o:30, a:1, s:1, b:0),
% 0.97/1.64 c_RealVector_Onorm__class_Onorm [52, 2] (w:1, o:266, a:1, s:1, b:0),
% 0.97/1.64
% 0.97/1.64 v_r [53, 0] (w:1, o:28, a:1, s:1, b:0),
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq [54, 3] (w:1, o:326, a:1, s:1, b:0)
% 0.97/1.64 ,
% 0.97/1.64 c_Fun_Ocomp [56, 5] (w:1, o:368, a:1, s:1, b:0),
% 0.97/1.64 c_Lim_OisUCont [57, 3] (w:1, o:327, a:1, s:1, b:0),
% 0.97/1.64 class_RealVector_Oreal__normed__vector [61, 1] (w:1, o:149, a:1, s:1
% 0.97/1.64 , b:0),
% 0.97/1.64 c_SEQ_OBseq [62, 2] (w:1, o:270, a:1, s:1, b:0),
% 0.97/1.64 c_Groups_Oplus__class_Oplus [63, 1] (w:1, o:151, a:1, s:1, b:0),
% 0.97/1.64 c_COMBC [64, 5] (w:1, o:369, a:1, s:1, b:0),
% 0.97/1.64 c_Groups_Ouminus__class_Ouminus [65, 1] (w:1, o:153, a:1, s:1, b:0),
% 0.97/1.64
% 0.97/1.64 c_SEQ_OCauchy [66, 2] (w:1, o:271, a:1, s:1, b:0),
% 0.97/1.64 c_Groups_Oabs__class_Oabs [67, 2] (w:1, o:273, a:1, s:1, b:0),
% 0.97/1.64 c_Groups_Oone__class_Oone [68, 1] (w:1, o:150, a:1, s:1, b:0),
% 0.97/1.64 c_Groups_Ozero__class_Ozero [69, 1] (w:1, o:154, a:1, s:1, b:0),
% 0.97/1.64 class_Orderings_Oorder [71, 1] (w:1, o:155, a:1, s:1, b:0),
% 0.97/1.64 class_Groups_Oordered__ab__group__add [74, 1] (w:1, o:156, a:1, s:1
% 0.97/1.64 , b:0),
% 0.97/1.64 class_RealVector_Ometric__space [75, 1] (w:1, o:157, a:1, s:1, b:0),
% 0.97/1.64
% 0.97/1.64 class_Groups_Oordered__ab__group__add__abs [80, 1] (w:1, o:158, a:1
% 0.97/1.64 , s:1, b:0),
% 0.97/1.64 class_RealVector_Oreal__normed__algebra__1 [83, 1] (w:1, o:159, a:1
% 0.97/1.64 , s:1, b:0),
% 0.97/1.64 class_Groups_Ozero [88, 1] (w:1, o:160, a:1, s:1, b:0),
% 0.97/1.64 class_Groups_Ocancel__semigroup__add [92, 1] (w:1, o:161, a:1, s:1
% 0.97/1.64 , b:0),
% 0.97/1.64 class_Groups_Ocancel__ab__semigroup__add [93, 1] (w:1, o:162, a:1, s:
% 0.97/1.64 1, b:0),
% 0.97/1.64 class_Groups_Oab__semigroup__add [95, 1] (w:1, o:163, a:1, s:1, b:0)
% 0.97/1.64 ,
% 0.97/1.64 class_Groups_Oone [96, 1] (w:1, o:164, a:1, s:1, b:0),
% 0.97/1.64 class_Groups_Ogroup__add [97, 1] (w:1, o:165, a:1, s:1, b:0),
% 0.97/1.64 class_Groups_Ocomm__monoid__add [101, 1] (w:1, o:166, a:1, s:1, b:0)
% 0.97/1.64 ,
% 0.97/1.64 class_Groups_Omonoid__add [102, 1] (w:1, o:168, a:1, s:1, b:0),
% 0.97/1.64 class_Groups_Olinordered__ab__group__add [103, 1] (w:1, o:167, a:1
% 0.97/1.64 , s:1, b:0),
% 0.97/1.64 class_Groups_Oordered__ab__semigroup__add__imp__le [104, 1] (w:1, o:
% 0.97/1.64 169, a:1, s:1, b:0),
% 0.97/1.64 class_Groups_Oordered__ab__semigroup__add [106, 1] (w:1, o:170, a:1
% 0.97/1.64 , s:1, b:0),
% 0.97/1.64 class_Groups_Oab__group__add [107, 1] (w:1, o:171, a:1, s:1, b:0),
% 0.97/1.64 class_Groups_Oordered__comm__monoid__add [109, 1] (w:1, o:172, a:1
% 0.97/1.64 , s:1, b:0),
% 0.97/1.64 class_Rings_Olinordered__semidom [112, 1] (w:1, o:175, a:1, s:1, b:0)
% 0.97/1.64 ,
% 0.97/1.64 class_Orderings_Opreorder [113, 1] (w:1, o:177, a:1, s:1, b:0),
% 0.97/1.64 class_Orderings_Oord [114, 1] (w:1, o:176, a:1, s:1, b:0),
% 0.97/1.64 tc_fun [115, 2] (w:1, o:307, a:1, s:1, b:0),
% 0.97/1.64 class_Orderings_Olinorder [116, 1] (w:1, o:178, a:1, s:1, b:0),
% 0.97/1.64 class_Rings_Ozero__neq__one [124, 1] (w:1, o:179, a:1, s:1, b:0),
% 0.97/1.64 class_Rings_Olinordered__idom [125, 1] (w:1, o:180, a:1, s:1, b:0),
% 0.97/1.64 c_SEQ_Odecseq [128, 2] (w:1, o:309, a:1, s:1, b:0),
% 0.97/1.64 class_Lattices_Oboolean__algebra [129, 1] (w:1, o:182, a:1, s:1, b:0)
% 0.97/1.64 ,
% 0.97/1.64 class_Rings_Ocomm__semiring__1 [130, 1] (w:1, o:186, a:1, s:1, b:0),
% 0.97/1.64
% 0.97/1.64 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct [
% 0.97/1.64 131, 1] (w:1, o:210, a:1, s:1, b:0),
% 0.97/1.64 c_SEQ_Oincseq [132, 2] (w:1, o:310, a:1, s:1, b:0),
% 0.97/1.64 class_Groups_Ouminus [134, 1] (w:1, o:211, a:1, s:1, b:0),
% 0.97/1.64 c_Complex_Oexpi [135, 1] (w:1, o:212, a:1, s:1, b:0),
% 0.97/1.64 c_Groups_Osgn__class_Osgn [138, 2] (w:1, o:311, a:1, s:1, b:0),
% 0.97/1.64 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize [140, 2] (w:1, o:
% 0.97/1.64 272, a:1, s:1, b:0),
% 0.97/1.64 tc_Polynomial_Opoly [141, 1] (w:1, o:225, a:1, s:1, b:0),
% 0.97/1.64 c_Power_Opower__class_Opower [142, 1] (w:1, o:226, a:1, s:1, b:0),
% 0.97/1.64 c_COMBK [143, 3] (w:1, o:328, a:1, s:1, b:0),
% 0.97/1.64 class_RealVector_Oreal__normed__div__algebra [144, 1] (w:1, o:187, a:
% 0.97/1.64 1, s:1, b:0),
% 0.97/1.64 class_Groups_Osgn__if [145, 1] (w:1, o:227, a:1, s:1, b:0),
% 0.97/1.64 class_Power_Opower [151, 1] (w:1, o:228, a:1, s:1, b:0),
% 0.97/1.64 class_Rings_Osemiring__0 [152, 1] (w:1, o:192, a:1, s:1, b:0),
% 0.97/1.64 class_Rings_Omult__zero [153, 1] (w:1, o:198, a:1, s:1, b:0),
% 0.97/1.64 class_Rings_Ono__zero__divisors [154, 1] (w:1, o:199, a:1, s:1, b:0)
% 0.97/1.64 ,
% 0.97/1.64 class_Groups_Omonoid__mult [155, 1] (w:1, o:229, a:1, s:1, b:0),
% 0.97/1.64 class_Rings_Oring__1__no__zero__divisors [156, 1] (w:1, o:188, a:1
% 0.97/1.64 , s:1, b:0),
% 0.97/1.64 c_RComplete_Onatceiling [157, 1] (w:1, o:145, a:1, s:1, b:0),
% 0.97/1.64 c_RComplete_Onatfloor [158, 1] (w:1, o:146, a:1, s:1, b:0),
% 0.97/1.64 c_SEQ_Oconvergent [159, 2] (w:1, o:308, a:1, s:1, b:0),
% 0.97/1.64 c_Complex_Ocomplex_OComplex [160, 2] (w:1, o:312, a:1, s:1, b:0),
% 0.97/1.64 c_RealVector_Oof__real [161, 1] (w:1, o:147, a:1, s:1, b:0),
% 0.97/1.64 c_Orderings_Oord__class_Oless [163, 3] (w:1, o:329, a:1, s:1, b:0),
% 0.97/1.64 class_RealVector_Oreal__algebra__1 [164, 1] (w:1, o:200, a:1, s:1, b:
% 0.97/1.64 0),
% 0.97/1.64 class_Groups_Oordered__cancel__ab__semigroup__add [170, 1] (w:1, o:
% 0.97/1.64 230, a:1, s:1, b:0),
% 0.97/1.64 class_SEQ_Ocomplete__space [171, 1] (w:1, o:231, a:1, s:1, b:0),
% 0.97/1.64 c_COMBS [173, 5] (w:1, o:370, a:1, s:1, b:0),
% 0.97/1.64 class_Groups_Oabs__if [174, 1] (w:1, o:232, a:1, s:1, b:0),
% 0.97/1.64 c_Complex_Ocomplex_Ocomplex__size [178, 1] (w:1, o:233, a:1, s:1, b:0
% 0.97/1.64 ),
% 0.97/1.64 c_Nat_Osize__class_Osize [179, 2] (w:1, o:313, a:1, s:1, b:0),
% 0.97/1.64 c_Complex_Ocomplex_Ocomplex__case [182, 3] (w:1, o:330, a:1, s:1, b:0
% 0.97/1.64 ),
% 0.97/1.64 c_Complex_Ocomplex_Ocomplex__rec [183, 3] (w:1, o:331, a:1, s:1, b:0)
% 0.97/1.64 ,
% 0.97/1.64 c_RealDef_Oreal [184, 2] (w:1, o:267, a:1, s:1, b:0),
% 0.97/1.64 hBOOL [186, 1] (w:1, o:234, a:1, s:1, b:0),
% 0.97/1.64 tc_Int_Oint [188, 0] (w:1, o:120, a:1, s:1, b:0),
% 0.97/1.64 c_Groups_Otimes__class_Otimes [189, 1] (w:1, o:152, a:1, s:1, b:0),
% 0.97/1.64 class_RealVector_Oreal__normed__algebra [195, 1] (w:1, o:201, a:1, s:
% 0.97/1.64 1, b:0),
% 0.97/1.64 class_Rings_Oring__no__zero__divisors [196, 1] (w:1, o:189, a:1, s:1
% 0.97/1.64 , b:0),
% 0.97/1.64 class_Rings_Osemiring [202, 1] (w:1, o:202, a:1, s:1, b:0),
% 0.97/1.64 class_Rings_Ocomm__semiring [203, 1] (w:1, o:203, a:1, s:1, b:0),
% 0.97/1.64 class_Groups_Ocomm__monoid__mult [204, 1] (w:1, o:235, a:1, s:1, b:0)
% 0.97/1.64 ,
% 0.97/1.64 class_Rings_Oidom [205, 1] (w:1, o:204, a:1, s:1, b:0),
% 0.97/1.64 class_Rings_Oring [206, 1] (w:1, o:190, a:1, s:1, b:0),
% 0.97/1.64 class_Lattices_Oab__semigroup__idem__mult [214, 1] (w:1, o:181, a:1
% 1.56/1.96 , s:1, b:0),
% 1.56/1.96 class_Groups_Oab__semigroup__mult [216, 1] (w:1, o:236, a:1, s:1, b:0
% 1.56/1.96 ),
% 1.56/1.96 class_Rings_Olinordered__ring [217, 1] (w:1, o:173, a:1, s:1, b:0),
% 1.56/1.96 class_Rings_Olinordered__ring__strict [218, 1] (w:1, o:174, a:1, s:1
% 1.56/1.96 , b:0),
% 1.56/1.96 class_Rings_Oordered__cancel__semiring [219, 1] (w:1, o:205, a:1, s:1
% 1.56/1.96 , b:0),
% 1.56/1.96 class_Rings_Oordered__ring [220, 1] (w:1, o:206, a:1, s:1, b:0),
% 1.56/1.96 class_Rings_Oordered__semiring [221, 1] (w:1, o:208, a:1, s:1, b:0),
% 1.56/1.96
% 1.56/1.96 class_Rings_Oordered__comm__semiring [222, 1] (w:1, o:209, a:1, s:1
% 1.56/1.96 , b:0),
% 1.56/1.96 class_Rings_Olinordered__semiring__strict [223, 1] (w:1, o:193, a:1
% 1.56/1.96 , s:1, b:0),
% 1.56/1.96 class_Rings_Olinordered__comm__semiring__strict [224, 1] (w:1, o:194
% 1.56/1.96 , a:1, s:1, b:0),
% 1.56/1.96 class_Rings_Ocomm__ring__1 [225, 1] (w:1, o:183, a:1, s:1, b:0),
% 1.56/1.96 class_Rings_Olinordered__semiring [228, 1] (w:1, o:195, a:1, s:1, b:0
% 1.56/1.96 ),
% 1.56/1.96 class_Rings_Oordered__ring__abs [229, 1] (w:1, o:207, a:1, s:1, b:0)
% 1.56/1.96 ,
% 1.56/1.96 class_Rings_Oring__1 [230, 1] (w:1, o:191, a:1, s:1, b:0),
% 1.56/1.96 class_Rings_Olinordered__semiring__1 [232, 1] (w:1, o:196, a:1, s:1
% 1.56/1.96 , b:0),
% 1.56/1.96 class_Rings_Olinordered__semiring__1__strict [233, 1] (w:1, o:197, a:
% 1.56/1.96 1, s:1, b:0),
% 1.56/1.96 c_Power_Opower_Opower [237, 3] (w:1, o:332, a:1, s:1, b:0),
% 1.56/1.96 c_Complex_Orcis [242, 2] (w:1, o:314, a:1, s:1, b:0),
% 1.56/1.96 c_Groups_Ominus__class_Ominus [243, 3] (w:1, o:333, a:1, s:1, b:0),
% 1.56/1.96 class_Groups_Ominus [245, 1] (w:1, o:237, a:1, s:1, b:0),
% 1.56/1.96 c_Complex_Oii [255, 0] (w:1, o:132, a:1, s:1, b:0),
% 1.56/1.96 c_Nat__Transfer_Otsub [257, 2] (w:1, o:315, a:1, s:1, b:0),
% 1.56/1.96 c_Transcendental_Oln [260, 1] (w:1, o:238, a:1, s:1, b:0),
% 1.56/1.96 c_SEQ_Olim [261, 2] (w:1, o:268, a:1, s:1, b:0),
% 1.56/1.96 c_Nat_OSuc [262, 1] (w:1, o:239, a:1, s:1, b:0),
% 1.56/1.96 class_Groups_Ocancel__comm__monoid__add [265, 1] (w:1, o:240, a:1, s:
% 1.56/1.96 1, b:0),
% 1.56/1.96 class_Rings_Ocomm__semiring__0 [266, 1] (w:1, o:185, a:1, s:1, b:0),
% 1.56/1.96
% 1.56/1.96 class_Rings_Ocomm__ring [267, 1] (w:1, o:184, a:1, s:1, b:0),
% 1.56/1.96 tc_HOL_Obool [269, 0] (w:1, o:119, a:1, s:1, b:0),
% 1.56/1.96 alpha1 [274, 2] (w:1, o:316, a:1, s:1, b:1),
% 1.56/1.96 alpha2 [275, 3] (w:1, o:338, a:1, s:1, b:1),
% 1.56/1.96 alpha3 [276, 3] (w:1, o:341, a:1, s:1, b:1),
% 1.56/1.96 alpha4 [277, 4] (w:1, o:358, a:1, s:1, b:1),
% 1.56/1.96 alpha5 [278, 4] (w:1, o:359, a:1, s:1, b:1),
% 1.56/1.96 alpha6 [279, 3] (w:1, o:342, a:1, s:1, b:1),
% 1.56/1.96 alpha7 [280, 3] (w:1, o:343, a:1, s:1, b:1),
% 1.56/1.96 alpha8 [281, 3] (w:1, o:344, a:1, s:1, b:1),
% 1.56/1.96 alpha9 [282, 2] (w:1, o:317, a:1, s:1, b:1),
% 1.56/1.96 alpha10 [283, 2] (w:1, o:318, a:1, s:1, b:1),
% 1.56/1.96 alpha11 [284, 2] (w:1, o:319, a:1, s:1, b:1),
% 1.56/1.96 alpha12 [285, 2] (w:1, o:320, a:1, s:1, b:1),
% 1.56/1.96 alpha13 [286, 3] (w:1, o:334, a:1, s:1, b:1),
% 1.56/1.96 alpha14 [287, 3] (w:1, o:335, a:1, s:1, b:1),
% 1.56/1.96 alpha15 [288, 4] (w:1, o:360, a:1, s:1, b:1),
% 1.56/1.96 alpha16 [289, 4] (w:1, o:361, a:1, s:1, b:1),
% 1.56/1.96 alpha17 [290, 5] (w:1, o:371, a:1, s:1, b:1),
% 1.56/1.96 alpha18 [291, 3] (w:1, o:336, a:1, s:1, b:1),
% 1.56/1.96 alpha19 [292, 3] (w:1, o:337, a:1, s:1, b:1),
% 1.56/1.96 alpha20 [293, 2] (w:1, o:321, a:1, s:1, b:1),
% 1.56/1.96 alpha21 [294, 2] (w:1, o:322, a:1, s:1, b:1),
% 1.56/1.96 alpha22 [295, 3] (w:1, o:339, a:1, s:1, b:1),
% 1.56/1.96 alpha23 [296, 2] (w:1, o:323, a:1, s:1, b:1),
% 1.56/1.96 alpha24 [297, 2] (w:1, o:324, a:1, s:1, b:1),
% 1.56/1.96 alpha25 [298, 2] (w:1, o:325, a:1, s:1, b:1),
% 1.56/1.96 alpha26 [299, 3] (w:1, o:340, a:1, s:1, b:1),
% 1.56/1.96 skol1 [300, 2] (w:1, o:274, a:1, s:1, b:1),
% 1.56/1.96 skol2 [301, 0] (w:1, o:15, a:1, s:1, b:1),
% 1.56/1.96 skol3 [302, 0] (w:1, o:20, a:1, s:1, b:1),
% 1.56/1.96 skol4 [303, 0] (w:1, o:23, a:1, s:1, b:1),
% 1.56/1.96 skol5 [304, 2] (w:1, o:281, a:1, s:1, b:1),
% 1.56/1.96 skol6 [305, 2] (w:1, o:286, a:1, s:1, b:1),
% 1.56/1.96 skol7 [306, 3] (w:1, o:346, a:1, s:1, b:1),
% 1.56/1.96 skol8 [307, 2] (w:1, o:288, a:1, s:1, b:1),
% 1.56/1.96 skol9 [308, 2] (w:1, o:289, a:1, s:1, b:1),
% 1.56/1.96 skol10 [309, 2] (w:1, o:290, a:1, s:1, b:1),
% 1.56/1.96 skol11 [310, 2] (w:1, o:291, a:1, s:1, b:1),
% 1.56/1.96 skol12 [311, 4] (w:1, o:362, a:1, s:1, b:1),
% 6.64/7.02 skol13 [312, 2] (w:1, o:292, a:1, s:1, b:1),
% 6.64/7.02 skol14 [313, 2] (w:1, o:293, a:1, s:1, b:1),
% 6.64/7.02 skol15 [314, 2] (w:1, o:294, a:1, s:1, b:1),
% 6.64/7.02 skol16 [315, 1] (w:1, o:213, a:1, s:1, b:1),
% 6.64/7.02 skol17 [316, 3] (w:1, o:347, a:1, s:1, b:1),
% 6.64/7.02 skol18 [317, 2] (w:1, o:295, a:1, s:1, b:1),
% 6.64/7.02 skol19 [318, 2] (w:1, o:296, a:1, s:1, b:1),
% 6.64/7.02 skol20 [319, 2] (w:1, o:297, a:1, s:1, b:1),
% 6.64/7.02 skol21 [320, 0] (w:1, o:16, a:1, s:1, b:1),
% 6.64/7.02 skol22 [321, 0] (w:1, o:17, a:1, s:1, b:1),
% 6.64/7.02 skol23 [322, 1] (w:1, o:214, a:1, s:1, b:1),
% 6.64/7.02 skol24 [323, 0] (w:1, o:18, a:1, s:1, b:1),
% 6.64/7.02 skol25 [324, 0] (w:1, o:19, a:1, s:1, b:1),
% 6.64/7.02 skol26 [325, 1] (w:1, o:215, a:1, s:1, b:1),
% 6.64/7.02 skol27 [326, 2] (w:1, o:298, a:1, s:1, b:1),
% 6.64/7.02 skol28 [327, 2] (w:1, o:299, a:1, s:1, b:1),
% 6.64/7.02 skol29 [328, 1] (w:1, o:216, a:1, s:1, b:1),
% 6.64/7.02 skol30 [329, 0] (w:1, o:21, a:1, s:1, b:1),
% 6.64/7.02 skol31 [330, 0] (w:1, o:22, a:1, s:1, b:1),
% 6.64/7.02 skol32 [331, 1] (w:1, o:217, a:1, s:1, b:1),
% 6.64/7.02 skol33 [332, 3] (w:1, o:348, a:1, s:1, b:1),
% 6.64/7.02 skol34 [333, 2] (w:1, o:300, a:1, s:1, b:1),
% 6.64/7.02 skol35 [334, 3] (w:1, o:349, a:1, s:1, b:1),
% 6.64/7.02 skol36 [335, 5] (w:1, o:372, a:1, s:1, b:1),
% 6.64/7.02 skol37 [336, 3] (w:1, o:350, a:1, s:1, b:1),
% 6.64/7.02 skol38 [337, 3] (w:1, o:351, a:1, s:1, b:1),
% 6.64/7.02 skol39 [338, 1] (w:1, o:218, a:1, s:1, b:1),
% 6.64/7.02 skol40 [339, 4] (w:1, o:363, a:1, s:1, b:1),
% 6.64/7.02 skol41 [340, 2] (w:1, o:275, a:1, s:1, b:1),
% 6.64/7.02 skol42 [341, 3] (w:1, o:352, a:1, s:1, b:1),
% 6.64/7.02 skol43 [342, 2] (w:1, o:276, a:1, s:1, b:1),
% 6.64/7.02 skol44 [343, 2] (w:1, o:277, a:1, s:1, b:1),
% 6.64/7.02 skol45 [344, 2] (w:1, o:278, a:1, s:1, b:1),
% 6.64/7.02 skol46 [345, 1] (w:1, o:219, a:1, s:1, b:1),
% 6.64/7.02 skol47 [346, 2] (w:1, o:279, a:1, s:1, b:1),
% 6.64/7.02 skol48 [347, 2] (w:1, o:280, a:1, s:1, b:1),
% 6.64/7.02 skol49 [348, 1] (w:1, o:220, a:1, s:1, b:1),
% 6.64/7.02 skol50 [349, 3] (w:1, o:353, a:1, s:1, b:1),
% 6.64/7.02 skol51 [350, 2] (w:1, o:282, a:1, s:1, b:1),
% 6.64/7.02 skol52 [351, 3] (w:1, o:354, a:1, s:1, b:1),
% 6.64/7.02 skol53 [352, 2] (w:1, o:283, a:1, s:1, b:1),
% 6.64/7.02 skol54 [353, 3] (w:1, o:355, a:1, s:1, b:1),
% 6.64/7.02 skol55 [354, 3] (w:1, o:356, a:1, s:1, b:1),
% 6.64/7.02 skol56 [355, 1] (w:1, o:221, a:1, s:1, b:1),
% 6.64/7.02 skol57 [356, 2] (w:1, o:284, a:1, s:1, b:1),
% 6.64/7.02 skol58 [357, 1] (w:1, o:222, a:1, s:1, b:1),
% 6.64/7.02 skol59 [358, 2] (w:1, o:285, a:1, s:1, b:1),
% 6.64/7.02 skol60 [359, 2] (w:1, o:301, a:1, s:1, b:1),
% 6.64/7.02 skol61 [360, 2] (w:1, o:302, a:1, s:1, b:1),
% 6.64/7.02 skol62 [361, 2] (w:1, o:303, a:1, s:1, b:1),
% 6.64/7.02 skol63 [362, 3] (w:1, o:345, a:1, s:1, b:1),
% 6.64/7.02 skol64 [363, 2] (w:1, o:304, a:1, s:1, b:1),
% 6.64/7.02 skol65 [364, 2] (w:1, o:305, a:1, s:1, b:1),
% 6.64/7.02 skol66 [365, 1] (w:1, o:223, a:1, s:1, b:1),
% 6.64/7.02 skol67 [366, 4] (w:1, o:364, a:1, s:1, b:1),
% 6.64/7.02 skol68 [367, 1] (w:1, o:224, a:1, s:1, b:1),
% 6.64/7.02 skol69 [368, 2] (w:1, o:306, a:1, s:1, b:1),
% 6.64/7.02 skol70 [369, 4] (w:1, o:365, a:1, s:1, b:1),
% 6.64/7.02 skol71 [370, 4] (w:1, o:366, a:1, s:1, b:1),
% 6.64/7.02 skol72 [371, 3] (w:1, o:357, a:1, s:1, b:1),
% 6.64/7.02 skol73 [372, 2] (w:1, o:287, a:1, s:1, b:1).
% 6.64/7.02
% 6.64/7.02
% 6.64/7.02 Starting Search:
% 6.64/7.02
% 6.64/7.02 *** allocated 113905 integers for clauses
% 6.64/7.02 *** allocated 170857 integers for clauses
% 6.64/7.02 Resimplifying inuse:
% 6.64/7.02 Done
% 6.64/7.02
% 6.64/7.02
% 6.64/7.02 Intermediate Status:
% 6.64/7.02 Generated: 2900
% 6.64/7.02 Kept: 2010
% 6.64/7.02 Inuse: 66
% 6.64/7.02 Deleted: 0
% 6.64/7.02 Deletedinuse: 0
% 6.64/7.02
% 6.64/7.02 *** allocated 256285 integers for clauses
% 6.64/7.02 Resimplifying inuse:
% 6.64/7.02 Done
% 6.64/7.02
% 6.64/7.02 *** allocated 170857 integers for termspace/termends
% 6.64/7.02 *** allocated 384427 integers for clauses
% 6.64/7.02 Resimplifying inuse:
% 6.64/7.02 Done
% 6.64/7.02
% 6.64/7.02
% 6.64/7.02 Intermediate Status:
% 6.64/7.02 Generated: 8268
% 6.64/7.02 Kept: 4424
% 6.64/7.02 Inuse: 304
% 6.64/7.02 Deleted: 7
% 6.64/7.02 Deletedinuse: 0
% 6.64/7.02
% 6.64/7.02 Resimplifying inuse:
% 6.64/7.02 Done
% 6.64/7.02
% 6.64/7.02 *** allocated 256285 integers for termspace/termends
% 6.64/7.02 *** allocated 576640 integers for clauses
% 6.64/7.02 Resimplifying inuse:
% 6.64/7.02 Done
% 6.64/7.02
% 6.64/7.02
% 6.64/7.02 Intermediate Status:
% 6.64/7.02 Generated: 13122
% 6.64/7.02 Kept: 6454
% 6.64/7.02 Inuse: 369
% 6.64/7.02 Deleted: 7
% 6.64/7.02 Deletedinuse: 0
% 6.64/7.02
% 6.64/7.02 Resimplifying inuse:
% 6.64/7.02 Done
% 6.64/7.02
% 6.64/7.02
% 6.64/7.02 Intermediate Status:
% 6.64/7.02 Generated: 20143
% 6.64/7.02 Kept: 8705
% 6.64/7.02 Inuse: 399
% 34.51/34.87 Deleted: 7
% 34.51/34.87 Deletedinuse: 0
% 34.51/34.87
% 34.51/34.87 Resimplifying inuse:
% 34.51/34.87 Done
% 34.51/34.87
% 34.51/34.87 *** allocated 384427 integers for termspace/termends
% 34.51/34.87 *** allocated 864960 integers for clauses
% 34.51/34.87 Resimplifying inuse:
% 34.51/34.87 Done
% 34.51/34.87
% 34.51/34.87
% 34.51/34.87 Intermediate Status:
% 34.51/34.87 Generated: 26016
% 34.51/34.87 Kept: 10708
% 34.51/34.87 Inuse: 422
% 34.51/34.87 Deleted: 7
% 34.51/34.87 Deletedinuse: 0
% 34.51/34.87
% 34.51/34.87 Resimplifying inuse:
% 34.51/34.87 Done
% 34.51/34.87
% 34.51/34.87 Resimplifying inuse:
% 34.51/34.87 Done
% 34.51/34.87
% 34.51/34.87
% 34.51/34.87 Intermediate Status:
% 34.51/34.87 Generated: 32179
% 34.51/34.87 Kept: 13002
% 34.51/34.87 Inuse: 454
% 34.51/34.87 Deleted: 7
% 34.51/34.87 Deletedinuse: 0
% 34.51/34.87
% 34.51/34.87 Resimplifying inuse:
% 34.51/34.87 Done
% 34.51/34.87
% 34.51/34.87 Resimplifying inuse:
% 34.51/34.87 Done
% 34.51/34.87
% 34.51/34.87 *** allocated 1297440 integers for clauses
% 34.51/34.87 *** allocated 576640 integers for termspace/termends
% 34.51/34.87
% 34.51/34.87 Intermediate Status:
% 34.51/34.87 Generated: 39068
% 34.51/34.87 Kept: 15983
% 34.51/34.87 Inuse: 509
% 34.51/34.87 Deleted: 7
% 34.51/34.87 Deletedinuse: 0
% 34.51/34.87
% 34.51/34.87 Resimplifying inuse:
% 34.51/34.87 Done
% 34.51/34.87
% 34.51/34.87 Resimplifying inuse:
% 34.51/34.87 Done
% 34.51/34.87
% 34.51/34.87
% 34.51/34.87 Intermediate Status:
% 34.51/34.87 Generated: 42953
% 34.51/34.87 Kept: 18028
% 34.51/34.87 Inuse: 539
% 34.51/34.87 Deleted: 7
% 34.51/34.87 Deletedinuse: 0
% 34.51/34.87
% 34.51/34.87 Resimplifying inuse:
% 34.51/34.87 Done
% 34.51/34.87
% 34.51/34.87
% 34.51/34.87 Intermediate Status:
% 34.51/34.87 Generated: 47272
% 34.51/34.87 Kept: 20372
% 34.51/34.87 Inuse: 572
% 34.51/34.87 Deleted: 9
% 34.51/34.87 Deletedinuse: 0
% 34.51/34.87
% 34.51/34.87 Resimplifying inuse:
% 34.51/34.87 Done
% 34.51/34.87
% 34.51/34.87 Resimplifying clauses:
% 34.51/34.87 Done
% 34.51/34.87
% 34.51/34.87 Resimplifying inuse:
% 34.51/34.87 Done
% 34.51/34.87
% 34.51/34.87
% 34.51/34.87 Intermediate Status:
% 34.51/34.87 Generated: 50948
% 34.51/34.87 Kept: 22373
% 34.51/34.87 Inuse: 604
% 34.51/34.87 Deleted: 280
% 34.51/34.87 Deletedinuse: 2
% 34.51/34.87
% 34.51/34.87 Resimplifying inuse:
% 34.51/34.87 Done
% 34.51/34.87
% 34.51/34.87 Resimplifying inuse:
% 34.51/34.87 Done
% 34.51/34.87
% 34.51/34.87 *** allocated 1946160 integers for clauses
% 34.51/34.87 *** allocated 864960 integers for termspace/termends
% 34.51/34.87
% 34.51/34.87 Intermediate Status:
% 34.51/34.87 Generated: 59553
% 34.51/34.87 Kept: 25070
% 34.51/34.87 Inuse: 662
% 34.51/34.87 Deleted: 280
% 34.51/34.87 Deletedinuse: 2
% 34.51/34.87
% 34.51/34.87 Resimplifying inuse:
% 34.51/34.87 Done
% 34.51/34.87
% 34.51/34.87 Resimplifying inuse:
% 34.51/34.87 Done
% 34.51/34.87
% 34.51/34.87
% 34.51/34.87 Intermediate Status:
% 34.51/34.87 Generated: 66520
% 34.51/34.87 Kept: 27143
% 34.51/34.87 Inuse: 692
% 34.51/34.87 Deleted: 280
% 34.51/34.87 Deletedinuse: 2
% 34.51/34.87
% 34.51/34.87 Resimplifying inuse:
% 34.51/34.87 Done
% 34.51/34.87
% 34.51/34.87 Resimplifying inuse:
% 34.51/34.87 Done
% 34.51/34.87
% 34.51/34.87
% 34.51/34.87 Intermediate Status:
% 34.51/34.87 Generated: 73433
% 34.51/34.87 Kept: 29824
% 34.51/34.87 Inuse: 737
% 34.51/34.87 Deleted: 280
% 34.51/34.87 Deletedinuse: 2
% 34.51/34.87
% 34.51/34.87 Resimplifying inuse:
% 34.51/34.87 Done
% 34.51/34.87
% 34.51/34.87 Resimplifying inuse:
% 34.51/34.87 Done
% 34.51/34.87
% 34.51/34.87
% 34.51/34.87 Intermediate Status:
% 34.51/34.87 Generated: 79152
% 34.51/34.87 Kept: 31847
% 34.51/34.87 Inuse: 765
% 34.51/34.87 Deleted: 280
% 34.51/34.87 Deletedinuse: 2
% 34.51/34.87
% 34.51/34.87 Resimplifying inuse:
% 34.51/34.87 Done
% 34.51/34.87
% 34.51/34.87 Resimplifying inuse:
% 34.51/34.87 Done
% 34.51/34.87
% 34.51/34.87
% 34.51/34.87 Intermediate Status:
% 34.51/34.87 Generated: 82591
% 34.51/34.87 Kept: 33853
% 34.51/34.87 Inuse: 776
% 34.51/34.87 Deleted: 280
% 34.51/34.87 Deletedinuse: 2
% 34.51/34.87
% 34.51/34.87 Resimplifying inuse:
% 34.51/34.87 Done
% 34.51/34.87
% 34.51/34.87 Resimplifying inuse:
% 34.51/34.87 Done
% 34.51/34.87
% 34.51/34.87
% 34.51/34.87 Intermediate Status:
% 34.51/34.87 Generated: 90097
% 34.51/34.87 Kept: 36059
% 34.51/34.87 Inuse: 827
% 34.51/34.87 Deleted: 280
% 34.51/34.87 Deletedinuse: 2
% 34.51/34.87
% 34.51/34.87 *** allocated 1297440 integers for termspace/termends
% 34.51/34.87 Resimplifying inuse:
% 34.51/34.87 Done
% 34.51/34.87
% 34.51/34.87
% 34.51/34.87 Intermediate Status:
% 34.51/34.87 Generated: 99065
% 34.51/34.87 Kept: 38456
% 34.51/34.87 Inuse: 847
% 34.51/34.87 Deleted: 280
% 34.51/34.87 Deletedinuse: 2
% 34.51/34.87
% 34.51/34.87 Resimplifying inuse:
% 34.51/34.87 Done
% 34.51/34.87
% 34.51/34.87 Resimplifying inuse:
% 34.51/34.87 Done
% 34.51/34.87
% 34.51/34.87 *** allocated 2919240 integers for clauses
% 34.51/34.87
% 34.51/34.87 Intermediate Status:
% 34.51/34.87 Generated: 106772
% 34.51/34.87 Kept: 40528
% 34.51/34.87 Inuse: 892
% 34.51/34.87 Deleted: 280
% 34.51/34.87 Deletedinuse: 2
% 34.51/34.87
% 34.51/34.87 Resimplifying clauses:
% 34.51/34.87 Done
% 34.51/34.87
% 34.51/34.87 Resimplifying inuse:
% 34.51/34.87 Done
% 34.51/34.87
% 34.51/34.87 Resimplifying inuse:
% 34.51/34.87 Done
% 34.51/34.87
% 34.51/34.87
% 34.51/34.87 Intermediate Status:
% 34.51/34.87 Generated: 121734
% 34.51/34.87 Kept: 43006
% 34.51/34.87 Inuse: 907
% 34.51/34.87 Deleted: 617
% 34.51/34.87 Deletedinuse: 2
% 34.51/34.87
% 34.51/34.87 Resimplifying inuse:
% 34.51/34.87 Done
% 34.51/34.87
% 34.51/34.87
% 34.51/34.87 Intermediate Status:
% 34.51/34.87 Generated: 131240
% 34.51/34.87 Kept: 45539
% 34.51/34.87 Inuse: 917
% 34.51/34.87 Deleted: 617
% 34.51/34.87 Deletedinuse: 2
% 34.51/34.87
% 34.51/34.87 Resimplifying inuse:
% 34.51/34.87 Done
% 34.51/34.87
% 34.51/34.87 Resimplifying inuse:
% 34.51/34.87 Done
% 34.51/34.87
% 34.51/34.87
% 34.51/34.87 Intermediate Status:
% 34.51/34.87 Generated: 140112
% 34.51/34.87 Kept: 49278
% 34.51/34.87 Inuse: 952
% 34.51/34.87 Deleted: 617
% 34.51/34.87 Deletedinuse: 2
% 34.51/34.87
% 34.51/34.87 Resimplifying inuse:
% 34.51/34.87 Done
% 34.51/34.87
% 34.51/34.87
% 34.51/34.87 Intermediate Status:
% 34.51/34.87 Generated: 143927
% 34.51/34.87 Kept: 51879
% 34.51/34.87 Inuse: 957
% 34.51/34.87 Deleted: 617
% 34.51/34.87 Deletedinuse: 2
% 34.51/34.87
% 34.51/34.87 Resimplifying inuse:
% 34.51/34.87 Done
% 34.51/34.87
% 34.51/34.87
% 34.51/34.87 Intermediate Status:
% 34.51/34.87 Generated: 152491
% 34.51/34.87 Kept: 54427
% 34.51/34.87 Inuse: 960
% 34.51/34.87 Deleted: 624
% 34.51/34.87 Deletedinuse: 2
% 34.51/34.87
% 34.51/34.87 Resimplifying inuse:
% 34.51/34.87 Done
% 34.51/34.87
% 34.51/34.87
% 34.51/34.87 Intermediate Status:
% 34.51/34.87 Generated: 155694
% 34.51/34.87 Kept: 56816
% 34.51/34.87 Inuse: 961
% 34.51/34.87 Deleted: 629
% 34.51/34.87 Deletedinuse: 3
% 34.51/34.87
% 34.51/34.87 Resimplifying inuse:
% 34.51/34.87 Done
% 34.51/34.87
% 34.51/34.87 *** allocated 1946160 integers for termspace/termends
% 34.51/34.87 Resimplifying inuse:
% 34.51/34.87 Done
% 34.51/34.87
% 34.51/34.87
% 34.51/34.87 Intermediate Status:
% 34.51/34.87 Generated: 163123
% 34.51/34.87 Kept: 59055
% 34.51/34.87 Inuse: 988
% 34.51/34.87 Deleted: 652
% 34.51/34.87 Deletedinuse: 3
% 34.51/34.87
% 34.51/34.87 Resimplifying inuse:
% 34.51/34.87 Done
% 34.51/34.87
% 34.51/34.87 Resimplifying inuse:
% 34.51/34.87 Done
% 34.51/34.87
% 34.51/34.87
% 34.51/34.87 Intermediate Status:
% 34.51/34.87 Generated: 174102
% 34.51/34.87 Kept: 62200
% 34.51/34.87 Inuse: 1006
% 34.51/34.87 Deleted: 660
% 34.51/34.87 Deletedinuse: 5
% 34.51/34.87
% 34.51/34.87 Resimplifying inuse:
% 86.53/86.96 Done
% 86.53/86.96
% 86.53/86.96 Resimplifying clauses:
% 86.53/86.96 Done
% 86.53/86.96
% 86.53/86.96 *** allocated 4378860 integers for clauses
% 86.53/86.96
% 86.53/86.96 Intermediate Status:
% 86.53/86.96 Generated: 179076
% 86.53/86.96 Kept: 64713
% 86.53/86.96 Inuse: 1017
% 86.53/86.96 Deleted: 2623
% 86.53/86.96 Deletedinuse: 5
% 86.53/86.96
% 86.53/86.96 Resimplifying inuse:
% 86.53/86.96 Done
% 86.53/86.96
% 86.53/86.96 Resimplifying inuse:
% 86.53/86.96 Done
% 86.53/86.96
% 86.53/86.96
% 86.53/86.96 Intermediate Status:
% 86.53/86.96 Generated: 187519
% 86.53/86.96 Kept: 66842
% 86.53/86.96 Inuse: 1067
% 86.53/86.96 Deleted: 2623
% 86.53/86.96 Deletedinuse: 5
% 86.53/86.96
% 86.53/86.96 Resimplifying inuse:
% 86.53/86.96 Done
% 86.53/86.96
% 86.53/86.96
% 86.53/86.96 Intermediate Status:
% 86.53/86.96 Generated: 196177
% 86.53/86.96 Kept: 68862
% 86.53/86.96 Inuse: 1072
% 86.53/86.96 Deleted: 2623
% 86.53/86.96 Deletedinuse: 5
% 86.53/86.96
% 86.53/86.96 Resimplifying inuse:
% 86.53/86.96 Done
% 86.53/86.96
% 86.53/86.96 Resimplifying inuse:
% 86.53/86.96 Done
% 86.53/86.96
% 86.53/86.96
% 86.53/86.96 Intermediate Status:
% 86.53/86.96 Generated: 204960
% 86.53/86.96 Kept: 72191
% 86.53/86.96 Inuse: 1117
% 86.53/86.96 Deleted: 2623
% 86.53/86.96 Deletedinuse: 5
% 86.53/86.96
% 86.53/86.96 Resimplifying inuse:
% 86.53/86.96 Done
% 86.53/86.96
% 86.53/86.96
% 86.53/86.96 Intermediate Status:
% 86.53/86.96 Generated: 208852
% 86.53/86.96 Kept: 75068
% 86.53/86.96 Inuse: 1122
% 86.53/86.96 Deleted: 2623
% 86.53/86.96 Deletedinuse: 5
% 86.53/86.96
% 86.53/86.96 Resimplifying inuse:
% 86.53/86.96 Done
% 86.53/86.96
% 86.53/86.96 Resimplifying inuse:
% 86.53/86.96 Done
% 86.53/86.96
% 86.53/86.96
% 86.53/86.96 Intermediate Status:
% 86.53/86.96 Generated: 215358
% 86.53/86.96 Kept: 77081
% 86.53/86.96 Inuse: 1163
% 86.53/86.96 Deleted: 2623
% 86.53/86.96 Deletedinuse: 5
% 86.53/86.96
% 86.53/86.96
% 86.53/86.96 Intermediate Status:
% 86.53/86.96 Generated: 219360
% 86.53/86.96 Kept: 80070
% 86.53/86.96 Inuse: 1167
% 86.53/86.96 Deleted: 2623
% 86.53/86.96 Deletedinuse: 5
% 86.53/86.96
% 86.53/86.96 Resimplifying inuse:
% 86.53/86.96 Done
% 86.53/86.96
% 86.53/86.96
% 86.53/86.96 Intermediate Status:
% 86.53/86.96 Generated: 225166
% 86.53/86.96 Kept: 83471
% 86.53/86.96 Inuse: 1187
% 86.53/86.96 Deleted: 2623
% 86.53/86.96 Deletedinuse: 5
% 86.53/86.96
% 86.53/86.96 Resimplifying inuse:
% 86.53/86.96 Done
% 86.53/86.96
% 86.53/86.96 Resimplifying clauses:
% 86.53/86.96 Done
% 86.53/86.96
% 86.53/86.96 Resimplifying inuse:
% 86.53/86.96 Done
% 86.53/86.96
% 86.53/86.96
% 86.53/86.96 Intermediate Status:
% 86.53/86.96 Generated: 233096
% 86.53/86.96 Kept: 85820
% 86.53/86.96 Inuse: 1226
% 86.53/86.96 Deleted: 2715
% 86.53/86.96 Deletedinuse: 5
% 86.53/86.96
% 86.53/86.96 Resimplifying inuse:
% 86.53/86.96 Done
% 86.53/86.96
% 86.53/86.96 *** allocated 2919240 integers for termspace/termends
% 86.53/86.96
% 86.53/86.96 Intermediate Status:
% 86.53/86.96 Generated: 240116
% 86.53/86.96 Kept: 87962
% 86.53/86.96 Inuse: 1241
% 86.53/86.96 Deleted: 2715
% 86.53/86.96 Deletedinuse: 5
% 86.53/86.96
% 86.53/86.96 Resimplifying inuse:
% 86.53/86.96 Done
% 86.53/86.96
% 86.53/86.96 Resimplifying inuse:
% 86.53/86.96 Done
% 86.53/86.96
% 86.53/86.96
% 86.53/86.96 Intermediate Status:
% 86.53/86.96 Generated: 252640
% 86.53/86.96 Kept: 91200
% 86.53/86.96 Inuse: 1256
% 86.53/86.96 Deleted: 2715
% 86.53/86.96 Deletedinuse: 5
% 86.53/86.96
% 86.53/86.96 Resimplifying inuse:
% 86.53/86.96 Done
% 86.53/86.96
% 86.53/86.96
% 86.53/86.96 Intermediate Status:
% 86.53/86.96 Generated: 257833
% 86.53/86.96 Kept: 93272
% 86.53/86.96 Inuse: 1266
% 86.53/86.96 Deleted: 2715
% 86.53/86.96 Deletedinuse: 5
% 86.53/86.96
% 86.53/86.96 Resimplifying inuse:
% 86.53/86.96 Done
% 86.53/86.96
% 86.53/86.96 Resimplifying inuse:
% 86.53/86.96 Done
% 86.53/86.96
% 86.53/86.96
% 86.53/86.96 Intermediate Status:
% 86.53/86.96 Generated: 263941
% 86.53/86.96 Kept: 95366
% 86.53/86.96 Inuse: 1296
% 86.53/86.96 Deleted: 2715
% 86.53/86.96 Deletedinuse: 5
% 86.53/86.96
% 86.53/86.96 Resimplifying inuse:
% 86.53/86.96 Done
% 86.53/86.96
% 86.53/86.96 *** allocated 6568290 integers for clauses
% 86.53/86.96 Resimplifying inuse:
% 86.53/86.96 Done
% 86.53/86.96
% 86.53/86.96
% 86.53/86.96 Intermediate Status:
% 86.53/86.96 Generated: 281363
% 86.53/86.96 Kept: 99545
% 86.53/86.96 Inuse: 1336
% 86.53/86.96 Deleted: 2715
% 86.53/86.96 Deletedinuse: 5
% 86.53/86.96
% 86.53/86.96 Resimplifying inuse:
% 86.53/86.96 Done
% 86.53/86.96
% 86.53/86.96
% 86.53/86.96 Intermediate Status:
% 86.53/86.96 Generated: 295812
% 86.53/86.96 Kept: 103486
% 86.53/86.96 Inuse: 1351
% 86.53/86.96 Deleted: 2716
% 86.53/86.96 Deletedinuse: 6
% 86.53/86.96
% 86.53/86.96 Resimplifying inuse:
% 86.53/86.96 Done
% 86.53/86.96
% 86.53/86.96 Resimplifying clauses:
% 86.53/86.96 Done
% 86.53/86.96
% 86.53/86.96
% 86.53/86.96 Intermediate Status:
% 86.53/86.96 Generated: 308160
% 86.53/86.96 Kept: 106793
% 86.53/86.96 Inuse: 1356
% 86.53/86.96 Deleted: 3007
% 86.53/86.96 Deletedinuse: 6
% 86.53/86.96
% 86.53/86.96 Resimplifying inuse:
% 86.53/86.96 Done
% 86.53/86.96
% 86.53/86.96 Resimplifying inuse:
% 86.53/86.96 Done
% 86.53/86.96
% 86.53/86.96
% 86.53/86.96 Intermediate Status:
% 86.53/86.96 Generated: 322029
% 86.53/86.96 Kept: 110328
% 86.53/86.96 Inuse: 1371
% 86.53/86.96 Deleted: 3007
% 86.53/86.96 Deletedinuse: 6
% 86.53/86.96
% 86.53/86.96 Resimplifying inuse:
% 86.53/86.96 Done
% 86.53/86.96
% 86.53/86.96 Resimplifying inuse:
% 86.53/86.96 Done
% 86.53/86.96
% 86.53/86.96
% 86.53/86.96 Intermediate Status:
% 86.53/86.96 Generated: 328588
% 86.53/86.96 Kept: 112383
% 86.53/86.96 Inuse: 1409
% 86.53/86.96 Deleted: 3007
% 86.53/86.96 Deletedinuse: 6
% 86.53/86.96
% 86.53/86.96 Resimplifying inuse:
% 86.53/86.96 Done
% 86.53/86.96
% 86.53/86.96
% 86.53/86.96 Intermediate Status:
% 86.53/86.96 Generated: 340740
% 86.53/86.96 Kept: 115290
% 86.53/86.96 Inuse: 1421
% 86.53/86.96 Deleted: 3007
% 86.53/86.96 Deletedinuse: 6
% 86.53/86.96
% 86.53/86.96 Resimplifying inuse:
% 86.53/86.96 Done
% 86.53/86.96
% 86.53/86.96
% 86.53/86.96 Intermediate Status:
% 86.53/86.96 Generated: 352305
% 86.53/86.96 Kept: 122629
% 86.53/86.96 Inuse: 1436
% 86.53/86.96 Deleted: 3007
% 86.53/86.96 Deletedinuse: 6
% 86.53/86.96
% 86.53/86.96 Resimplifying inuse:
% 86.53/86.96 Done
% 86.53/86.96
% 86.53/86.96
% 86.53/86.96 Intermediate Status:
% 86.53/86.96 Generated: 357727
% 86.53/86.96 Kept: 126237
% 86.53/86.96 Inuse: 1441
% 86.53/86.96 Deleted: 3007
% 86.53/86.96 Deletedinuse: 6
% 86.53/86.96
% 86.53/86.96 Resimplifying inuse:
% 86.53/86.96 Done
% 86.53/86.96
% 86.53/86.96 Resimplifying clauses:
% 86.53/86.96 Done
% 86.53/86.96
% 86.53/86.96 Resimplifying inuse:
% 86.53/86.96 Done
% 86.53/86.96
% 86.53/86.96
% 86.53/86.96 Intermediate Status:
% 86.53/86.96 Generated: 366676
% 86.53/86.96 Kept: 128394
% 86.53/86.96 Inuse: 1466
% 86.53/86.96 Deleted: 3095
% 86.53/86.96 Deletedinuse: 6
% 86.53/86.96
% 86.53/86.96 Resimplifying inuse:
% 86.53/86.96 Done
% 86.53/86.96
% 86.53/86.96 Resimplifying inuse:
% 86.53/86.96 Done
% 86.53/86.96
% 86.53/86.96
% 86.53/86.96 Intermediate Status:
% 86.53/86.96 Generated: 373783
% 86.53/86.96 Kept: 130441
% 86.53/86.96 Inuse: 1493
% 86.53/86.96 Deleted: 3095
% 86.53/86.96 Deletedinuse: 6
% 86.53/86.96
% 86.53/86.96 *** allocated 4378860 integers for termspace/termends
% 86.53/86.96
% 86.53/86.96 Intermediate Status:
% 86.53/86.96 Generated: 383856
% 86.53/86.96 Kept: 135522
% 86.53/86.96 Inuse: 1496
% 86.53/86.96 Deleted: 3095
% 86.53/86.96 Deletedinuse: 6
% 86.53/86.96
% 86.53/86.96 Resimplifying inuse:
% 86.53/86.96 Done
% 86.53/86.96
% 86.53/86.96
% 86.53/86.96 Intermediate Status:
% 86.53/86.96 Generated: 397991
% 192.49/192.99 Kept: 141293
% 192.49/192.99 Inuse: 1516
% 192.49/192.99 Deleted: 3097
% 192.49/192.99 Deletedinuse: 8
% 192.49/192.99
% 192.49/192.99 Resimplifying inuse:
% 192.49/192.99 Done
% 192.49/192.99
% 192.49/192.99 Resimplifying inuse:
% 192.49/192.99 Done
% 192.49/192.99
% 192.49/192.99
% 192.49/192.99 Intermediate Status:
% 192.49/192.99 Generated: 406682
% 192.49/192.99 Kept: 143321
% 192.49/192.99 Inuse: 1551
% 192.49/192.99 Deleted: 3097
% 192.49/192.99 Deletedinuse: 8
% 192.49/192.99
% 192.49/192.99 Resimplifying inuse:
% 192.49/192.99 Done
% 192.49/192.99
% 192.49/192.99 Resimplifying inuse:
% 192.49/192.99 Done
% 192.49/192.99
% 192.49/192.99
% 192.49/192.99 Intermediate Status:
% 192.49/192.99 Generated: 414981
% 192.49/192.99 Kept: 145548
% 192.49/192.99 Inuse: 1576
% 192.49/192.99 Deleted: 3097
% 192.49/192.99 Deletedinuse: 8
% 192.49/192.99
% 192.49/192.99 Resimplifying inuse:
% 192.49/192.99 Done
% 192.49/192.99
% 192.49/192.99 Resimplifying clauses:
% 192.49/192.99 Done
% 192.49/192.99
% 192.49/192.99 Resimplifying inuse:
% 192.49/192.99 Done
% 192.49/192.99
% 192.49/192.99
% 192.49/192.99 Intermediate Status:
% 192.49/192.99 Generated: 423418
% 192.49/192.99 Kept: 147568
% 192.49/192.99 Inuse: 1609
% 192.49/192.99 Deleted: 3271
% 192.49/192.99 Deletedinuse: 8
% 192.49/192.99
% 192.49/192.99 Resimplifying inuse:
% 192.49/192.99 Done
% 192.49/192.99
% 192.49/192.99 *** allocated 9852435 integers for clauses
% 192.49/192.99
% 192.49/192.99 Intermediate Status:
% 192.49/192.99 Generated: 435597
% 192.49/192.99 Kept: 154689
% 192.49/192.99 Inuse: 1616
% 192.49/192.99 Deleted: 3271
% 192.49/192.99 Deletedinuse: 8
% 192.49/192.99
% 192.49/192.99 Resimplifying inuse:
% 192.49/192.99 Done
% 192.49/192.99
% 192.49/192.99 Resimplifying inuse:
% 192.49/192.99 Done
% 192.49/192.99
% 192.49/192.99
% 192.49/192.99 Intermediate Status:
% 192.49/192.99 Generated: 444113
% 192.49/192.99 Kept: 156692
% 192.49/192.99 Inuse: 1643
% 192.49/192.99 Deleted: 3271
% 192.49/192.99 Deletedinuse: 8
% 192.49/192.99
% 192.49/192.99 Resimplifying inuse:
% 192.49/192.99 Done
% 192.49/192.99
% 192.49/192.99 Resimplifying inuse:
% 192.49/192.99 Done
% 192.49/192.99
% 192.49/192.99
% 192.49/192.99 Intermediate Status:
% 192.49/192.99 Generated: 453215
% 192.49/192.99 Kept: 158710
% 192.49/192.99 Inuse: 1682
% 192.49/192.99 Deleted: 3271
% 192.49/192.99 Deletedinuse: 8
% 192.49/192.99
% 192.49/192.99 Resimplifying inuse:
% 192.49/192.99 Done
% 192.49/192.99
% 192.49/192.99 Resimplifying inuse:
% 192.49/192.99 Done
% 192.49/192.99
% 192.49/192.99
% 192.49/192.99 Intermediate Status:
% 192.49/192.99 Generated: 462609
% 192.49/192.99 Kept: 161129
% 192.49/192.99 Inuse: 1711
% 192.49/192.99 Deleted: 3271
% 192.49/192.99 Deletedinuse: 8
% 192.49/192.99
% 192.49/192.99 Resimplifying inuse:
% 192.49/192.99 Done
% 192.49/192.99
% 192.49/192.99
% 192.49/192.99 Intermediate Status:
% 192.49/192.99 Generated: 470245
% 192.49/192.99 Kept: 165069
% 192.49/192.99 Inuse: 1721
% 192.49/192.99 Deleted: 3271
% 192.49/192.99 Deletedinuse: 8
% 192.49/192.99
% 192.49/192.99 Resimplifying inuse:
% 192.49/192.99 Done
% 192.49/192.99
% 192.49/192.99 Resimplifying inuse:
% 192.49/192.99 Done
% 192.49/192.99
% 192.49/192.99 Resimplifying clauses:
% 192.49/192.99 Done
% 192.49/192.99
% 192.49/192.99
% 192.49/192.99 Intermediate Status:
% 192.49/192.99 Generated: 478357
% 192.49/192.99 Kept: 167448
% 192.49/192.99 Inuse: 1746
% 192.49/192.99 Deleted: 3336
% 192.49/192.99 Deletedinuse: 8
% 192.49/192.99
% 192.49/192.99 Resimplifying inuse:
% 192.49/192.99 Done
% 192.49/192.99
% 192.49/192.99 Resimplifying inuse:
% 192.49/192.99 Done
% 192.49/192.99
% 192.49/192.99
% 192.49/192.99 Intermediate Status:
% 192.49/192.99 Generated: 486409
% 192.49/192.99 Kept: 169692
% 192.49/192.99 Inuse: 1771
% 192.49/192.99 Deleted: 3336
% 192.49/192.99 Deletedinuse: 8
% 192.49/192.99
% 192.49/192.99 Resimplifying inuse:
% 192.49/192.99 Done
% 192.49/192.99
% 192.49/192.99 Resimplifying inuse:
% 192.49/192.99 Done
% 192.49/192.99
% 192.49/192.99
% 192.49/192.99 Intermediate Status:
% 192.49/192.99 Generated: 495519
% 192.49/192.99 Kept: 172128
% 192.49/192.99 Inuse: 1796
% 192.49/192.99 Deleted: 3336
% 192.49/192.99 Deletedinuse: 8
% 192.49/192.99
% 192.49/192.99 Resimplifying inuse:
% 192.49/192.99 Done
% 192.49/192.99
% 192.49/192.99 Resimplifying inuse:
% 192.49/192.99 Done
% 192.49/192.99
% 192.49/192.99
% 192.49/192.99 Intermediate Status:
% 192.49/192.99 Generated: 502594
% 192.49/192.99 Kept: 174204
% 192.49/192.99 Inuse: 1821
% 192.49/192.99 Deleted: 3336
% 192.49/192.99 Deletedinuse: 8
% 192.49/192.99
% 192.49/192.99 Resimplifying inuse:
% 192.49/192.99 Done
% 192.49/192.99
% 192.49/192.99 Resimplifying inuse:
% 192.49/192.99 Done
% 192.49/192.99
% 192.49/192.99
% 192.49/192.99 Intermediate Status:
% 192.49/192.99 Generated: 510261
% 192.49/192.99 Kept: 176233
% 192.49/192.99 Inuse: 1849
% 192.49/192.99 Deleted: 3336
% 192.49/192.99 Deletedinuse: 8
% 192.49/192.99
% 192.49/192.99 Resimplifying inuse:
% 192.49/192.99 Done
% 192.49/192.99
% 192.49/192.99 Resimplifying inuse:
% 192.49/192.99 Done
% 192.49/192.99
% 192.49/192.99
% 192.49/192.99 Intermediate Status:
% 192.49/192.99 Generated: 516657
% 192.49/192.99 Kept: 178264
% 192.49/192.99 Inuse: 1870
% 192.49/192.99 Deleted: 3337
% 192.49/192.99 Deletedinuse: 9
% 192.49/192.99
% 192.49/192.99 Resimplifying inuse:
% 192.49/192.99 Done
% 192.49/192.99
% 192.49/192.99
% 192.49/192.99 Intermediate Status:
% 192.49/192.99 Generated: 532181
% 192.49/192.99 Kept: 180588
% 192.49/192.99 Inuse: 1876
% 192.49/192.99 Deleted: 3337
% 192.49/192.99 Deletedinuse: 9
% 192.49/192.99
% 192.49/192.99
% 192.49/192.99 Intermediate Status:
% 192.49/192.99 Generated: 540274
% 192.49/192.99 Kept: 184735
% 192.49/192.99 Inuse: 1886
% 192.49/192.99 Deleted: 3337
% 192.49/192.99 Deletedinuse: 9
% 192.49/192.99
% 192.49/192.99 Resimplifying inuse:
% 192.49/192.99 Done
% 192.49/192.99
% 192.49/192.99 Resimplifying inuse:
% 192.49/192.99 Done
% 192.49/192.99
% 192.49/192.99 Resimplifying clauses:
% 192.49/192.99 Done
% 192.49/192.99
% 192.49/192.99
% 192.49/192.99 Intermediate Status:
% 192.49/192.99 Generated: 548562
% 192.49/192.99 Kept: 186739
% 192.49/192.99 Inuse: 1916
% 192.49/192.99 Deleted: 3493
% 192.49/192.99 Deletedinuse: 9
% 192.49/192.99
% 192.49/192.99 Resimplifying inuse:
% 192.49/192.99 Done
% 192.49/192.99
% 192.49/192.99 Resimplifying inuse:
% 192.49/192.99 Done
% 192.49/192.99
% 192.49/192.99
% 192.49/192.99 Intermediate Status:
% 192.49/192.99 Generated: 556595
% 192.49/192.99 Kept: 188743
% 192.49/192.99 Inuse: 1944
% 192.49/192.99 Deleted: 3493
% 192.49/192.99 Deletedinuse: 9
% 192.49/192.99
% 192.49/192.99
% 192.49/192.99 Intermediate Status:
% 192.49/192.99 Generated: 563673
% 192.49/192.99 Kept: 193368
% 192.49/192.99 Inuse: 1946
% 192.49/192.99 Deleted: 3493
% 192.49/192.99 Deletedinuse: 9
% 192.49/192.99
% 192.49/192.99 Resimplifying inuse:
% 192.49/192.99 Done
% 192.49/192.99
% 192.49/192.99 *** allocated 6568290 integers for termspace/termends
% 192.49/192.99
% 192.49/192.99 Intermediate Status:
% 192.49/192.99 Generated: 570423
% 192.49/192.99 Kept: 197970
% 192.49/192.99 Inuse: 1951
% 192.49/192.99 Deleted: 3495
% 192.49/192.99 Deletedinuse: 11
% 192.49/192.99
% 192.49/192.99 Resimplifying inuse:
% 192.49/192.99 Done
% 192.49/192.99
% 192.49/192.99 Resimplifying inuse:
% 192.49/192.99 Done
% 192.49/192.99
% 192.49/192.99
% 192.49/192.99 Intermediate Status:
% 192.49/192.99 Generated: 578442
% 192.49/192.99 Kept: 200104
% 192.49/192.99 Inuse: 1976
% 192.49/192.99 Deleted: 3495
% 192.49/192.99 Deletedinuse: 11
% 192.49/192.99
% 192.49/192.99 Resimplifying inuse:
% 192.49/192.99 Done
% 192.49/192.99
% 192.49/192.99 Resimplifying inuse:
% 192.49/192.99 Done
% 192.49/192.99
% 192.49/192.99
% 192.49/192.99 Intermediate Status:
% 192.49/192.99 Generated: 584792
% 192.49/192.99 Kept: 202293
% 192.49/192.99 Inuse: 1996
% 192.49/192.99 Deleted: 3496
% 192.49/192.99 Deletedinuse: 12
% 192.49/192.99
% 192.49/192.99 Resimplifying inuse:
% 192.49/192.99 Done
% 192.49/192.99
% 192.49/192.99 Resimplifying inuse:
% 192.49/192.99 Done
% 192.49/192.99
% 192.49/192.99
% 192.49/192.99 Intermediate Status:
% 192.49/192.99 Generated: 591758
% 192.49/192.99 Kept: 204639
% 192.49/192.99 Inuse: 2016
% 192.49/192.99 Deleted: 3496
% 192.49/192.99 Deletedinuse: 12
% 192.49/192.99
% 192.49/192.99 Resimplifying inuse:
% 192.49/192.99 Done
% 192.49/192.99
% 192.49/192.99 Resimplifying inuse:
% 192.49/192.99 Done
% 192.49/192.99
% 192.49/192.99 ResCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------