TSTP Solution File: ANA022-2 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : ANA022-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n005.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 : Thu Jul 14 18:38:22 EDT 2022
% Result : Unsatisfiable 1.42s 1.77s
% Output : Refutation 1.42s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ANA022-2 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : bliksem %s
% 0.12/0.33 % Computer : n005.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % DateTime : Fri Jul 8 06:05:07 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.42/1.77 *** allocated 10000 integers for termspace/termends
% 1.42/1.77 *** allocated 10000 integers for clauses
% 1.42/1.77 *** allocated 10000 integers for justifications
% 1.42/1.77 Bliksem 1.12
% 1.42/1.77
% 1.42/1.77
% 1.42/1.77 Automatic Strategy Selection
% 1.42/1.77
% 1.42/1.77 Clauses:
% 1.42/1.77 [
% 1.42/1.77 [ 'c_lessequals'( 'v_k'( X ), 'v_f'( X ), 't_b' ) ],
% 1.42/1.77 [ ~( 'c_lessequals'( 'c_Orderings_Omax'( 'c_minus'( 'v_k'( 'v_x' ),
% 1.42/1.77 'v_g'( 'v_x' ), 't_b' ), 'c_0', 't_b' ), 'c_HOL_Oabs'( 'c_minus'( 'v_f'(
% 1.42/1.77 'v_x' ), 'v_g'( 'v_x' ), 't_b' ), 't_b' ), 't_b' ) ) ],
% 1.42/1.77 [ 'class_Ring__and__Field_Oordered__idom'( 't_b' ) ],
% 1.42/1.77 [ ~( 'class_OrderedGroup_Olordered__ab__group__abs'( X ) ),
% 1.42/1.77 'c_lessequals'( 'c_0', 'c_HOL_Oabs'( Y, X ), X ) ],
% 1.42/1.77 [ ~( 'class_OrderedGroup_Olordered__ab__group__abs'( X ) ), =(
% 1.42/1.77 'c_HOL_Oabs'( 'c_uminus'( Y, X ), X ), 'c_HOL_Oabs'( Y, X ) ) ],
% 1.42/1.77 [ ~( 'class_OrderedGroup_Olordered__ab__group__abs'( X ) ), ~(
% 1.42/1.77 'c_lessequals'( Y, 'c_0', X ) ), =( 'c_HOL_Oabs'( Y, X ), 'c_uminus'( Y,
% 1.42/1.77 X ) ) ],
% 1.42/1.77 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.42/1.77 , ~( 'c_lessequals'( 'c_plus'( Y, Z, X ), 'c_plus'( T, Z, X ), X ) ),
% 1.42/1.77 'c_lessequals'( Y, T, X ) ],
% 1.42/1.77 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( 'c_plus'( 'c_0'
% 1.42/1.77 , Y, X ), Y ) ],
% 1.42/1.77 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( 'c_plus'( Y,
% 1.42/1.77 'c_minus'( Z, T, X ), X ), 'c_minus'( 'c_plus'( Y, Z, X ), T, X ) ) ]
% 1.42/1.77 ,
% 1.42/1.77 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( 'c_plus'( 'c_minus'(
% 1.42/1.77 Y, Z, X ), T, X ), 'c_minus'( 'c_plus'( Y, T, X ), Z, X ) ) ],
% 1.42/1.77 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~(
% 1.42/1.77 'c_lessequals'( Y, 'c_plus'( Z, T, X ), X ) ), 'c_lessequals'( 'c_minus'(
% 1.42/1.77 Y, T, X ), Z, X ) ],
% 1.42/1.77 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~(
% 1.42/1.77 'c_lessequals'( Y, Z, X ) ), 'c_lessequals'( 'c_minus'( Y, Z, X ), 'c_0'
% 1.42/1.77 , X ) ],
% 1.42/1.77 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( 'c_minus'( Y,
% 1.42/1.77 'c_uminus'( Z, X ), X ), 'c_plus'( Y, Z, X ) ) ],
% 1.42/1.77 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( 'c_minus'( Y, Y, X
% 1.42/1.77 ), 'c_0' ) ],
% 1.42/1.77 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( 'c_uminus'(
% 1.42/1.77 'c_minus'( Y, Z, X ), X ), 'c_minus'( Z, Y, X ) ) ],
% 1.42/1.77 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_less'( Y, Z, X ),
% 1.42/1.77 'c_lessequals'( Z, Y, X ) ],
% 1.42/1.77 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 1.42/1.77 , ~( 'c_lessequals'( T, Z, X ) ), 'c_lessequals'( 'c_Orderings_Omax'( T,
% 1.42/1.77 Y, X ), Z, X ) ],
% 1.42/1.77 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) ),
% 1.42/1.77 ~( 'c_lessequals'( T, Y, X ) ), 'c_lessequals'( T, Z, X ) ],
% 1.42/1.77 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_less'( Y, Z, X ) ),
% 1.42/1.77 'c_lessequals'( Y, Z, X ) ],
% 1.42/1.77 [ ~( 'class_LOrder_Ojoin__semilorder'( X ) ), 'class_Orderings_Oorder'(
% 1.42/1.77 X ) ],
% 1.42/1.77 [ ~( 'class_OrderedGroup_Olordered__ab__group__abs'( X ) ),
% 1.42/1.77 'class_OrderedGroup_Opordered__ab__group__add'( X ) ],
% 1.42/1.77 [ ~( 'class_OrderedGroup_Olordered__ab__group__abs'( X ) ),
% 1.42/1.77 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ],
% 1.42/1.77 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.42/1.77 'class_OrderedGroup_Ocomm__monoid__add'( X ) ],
% 1.42/1.77 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.42/1.77 'class_Orderings_Olinorder'( X ) ],
% 1.42/1.77 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.42/1.77 'class_LOrder_Ojoin__semilorder'( X ) ],
% 1.42/1.77 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.42/1.77 'class_OrderedGroup_Oab__group__add'( X ) ],
% 1.42/1.77 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.42/1.77 'class_OrderedGroup_Olordered__ab__group__abs'( X ) ]
% 1.42/1.77 ] .
% 1.42/1.77
% 1.42/1.77
% 1.42/1.77 percentage equality = 0.131148, percentage horn = 0.962963
% 1.42/1.77 This is a problem with some equality
% 1.42/1.77
% 1.42/1.77
% 1.42/1.77
% 1.42/1.77 Options Used:
% 1.42/1.77
% 1.42/1.77 useres = 1
% 1.42/1.77 useparamod = 1
% 1.42/1.77 useeqrefl = 1
% 1.42/1.77 useeqfact = 1
% 1.42/1.77 usefactor = 1
% 1.42/1.77 usesimpsplitting = 0
% 1.42/1.77 usesimpdemod = 5
% 1.42/1.77 usesimpres = 3
% 1.42/1.77
% 1.42/1.77 resimpinuse = 1000
% 1.42/1.77 resimpclauses = 20000
% 1.42/1.77 substype = eqrewr
% 1.42/1.77 backwardsubs = 1
% 1.42/1.77 selectoldest = 5
% 1.42/1.77
% 1.42/1.77 litorderings [0] = split
% 1.42/1.77 litorderings [1] = extend the termordering, first sorting on arguments
% 1.42/1.77
% 1.42/1.77 termordering = kbo
% 1.42/1.77
% 1.42/1.77 litapriori = 0
% 1.42/1.77 termapriori = 1
% 1.42/1.77 litaposteriori = 0
% 1.42/1.77 termaposteriori = 0
% 1.42/1.77 demodaposteriori = 0
% 1.42/1.77 ordereqreflfact = 0
% 1.42/1.77
% 1.42/1.77 litselect = negord
% 1.42/1.77
% 1.42/1.77 maxweight = 15
% 1.42/1.77 maxdepth = 30000
% 1.42/1.77 maxlength = 115
% 1.42/1.77 maxnrvars = 195
% 1.42/1.77 excuselevel = 1
% 1.42/1.77 increasemaxweight = 1
% 1.42/1.77
% 1.42/1.77 maxselected = 10000000
% 1.42/1.77 maxnrclauses = 10000000
% 1.42/1.77
% 1.42/1.77 showgenerated = 0
% 1.42/1.77 showkept = 0
% 1.42/1.77 showselected = 0
% 1.42/1.77 showdeleted = 0
% 1.42/1.77 showresimp = 1
% 1.42/1.77 showstatus = 2000
% 1.42/1.77
% 1.42/1.77 prologoutput = 1
% 1.42/1.77 nrgoals = 5000000
% 1.42/1.77 totalproof = 1
% 1.42/1.77
% 1.42/1.77 Symbols occurring in the translation:
% 1.42/1.77
% 1.42/1.77 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.42/1.77 . [1, 2] (w:1, o:39, a:1, s:1, b:0),
% 1.42/1.77 ! [4, 1] (w:0, o:22, a:1, s:1, b:0),
% 1.42/1.77 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.42/1.77 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.42/1.77 'v_k' [40, 1] (w:1, o:27, a:1, s:1, b:0),
% 1.42/1.77 'v_f' [41, 1] (w:1, o:28, a:1, s:1, b:0),
% 1.42/1.77 't_b' [42, 0] (w:1, o:10, a:1, s:1, b:0),
% 1.42/1.77 'c_lessequals' [43, 3] (w:1, o:66, a:1, s:1, b:0),
% 1.42/1.77 'v_x' [44, 0] (w:1, o:11, a:1, s:1, b:0),
% 1.42/1.77 'v_g' [45, 1] (w:1, o:29, a:1, s:1, b:0),
% 1.42/1.77 'c_minus' [46, 3] (w:1, o:68, a:1, s:1, b:0),
% 1.42/1.77 'c_0' [47, 0] (w:1, o:12, a:1, s:1, b:0),
% 1.42/1.77 'c_Orderings_Omax' [48, 3] (w:1, o:69, a:1, s:1, b:0),
% 1.42/1.77 'c_HOL_Oabs' [49, 2] (w:1, o:64, a:1, s:1, b:0),
% 1.42/1.77 'class_Ring__and__Field_Oordered__idom' [50, 1] (w:1, o:30, a:1, s:1
% 1.42/1.77 , b:0),
% 1.42/1.77 'class_OrderedGroup_Olordered__ab__group__abs' [52, 1] (w:1, o:31, a:
% 1.42/1.77 1, s:1, b:0),
% 1.42/1.77 'c_uminus' [54, 2] (w:1, o:65, a:1, s:1, b:0),
% 1.42/1.77 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le' [55, 1]
% 1.42/1.77 (w:1, o:32, a:1, s:1, b:0),
% 1.42/1.77 'c_plus' [57, 3] (w:1, o:70, a:1, s:1, b:0),
% 1.42/1.77 'class_OrderedGroup_Ocomm__monoid__add' [59, 1] (w:1, o:33, a:1, s:1
% 1.42/1.77 , b:0),
% 1.42/1.77 'class_OrderedGroup_Oab__group__add' [61, 1] (w:1, o:34, a:1, s:1, b:
% 1.42/1.77 0),
% 1.42/1.77 'class_OrderedGroup_Opordered__ab__group__add' [62, 1] (w:1, o:35, a:
% 1.42/1.77 1, s:1, b:0),
% 1.42/1.77 'class_Orderings_Olinorder' [63, 1] (w:1, o:36, a:1, s:1, b:0),
% 1.42/1.77 'c_less' [65, 3] (w:1, o:67, a:1, s:1, b:0),
% 1.42/1.77 'class_Orderings_Oorder' [68, 1] (w:1, o:37, a:1, s:1, b:0),
% 1.42/1.77 'class_LOrder_Ojoin__semilorder' [70, 1] (w:1, o:38, a:1, s:1, b:0)
% 1.42/1.77 .
% 1.42/1.77
% 1.42/1.77
% 1.42/1.77 Starting Search:
% 1.42/1.77
% 1.42/1.77 Resimplifying inuse:
% 1.42/1.77 Done
% 1.42/1.77
% 1.42/1.77
% 1.42/1.77 Intermediate Status:
% 1.42/1.77 Generated: 11634
% 1.42/1.77 Kept: 2032
% 1.42/1.77 Inuse: 257
% 1.42/1.77 Deleted: 17
% 1.42/1.77 Deletedinuse: 5
% 1.42/1.77
% 1.42/1.77 Resimplifying inuse:
% 1.42/1.77 Done
% 1.42/1.77
% 1.42/1.77 Resimplifying inuse:
% 1.42/1.77 Done
% 1.42/1.77
% 1.42/1.77
% 1.42/1.77 Intermediate Status:
% 1.42/1.77 Generated: 35818
% 1.42/1.77 Kept: 4033
% 1.42/1.77 Inuse: 417
% 1.42/1.77 Deleted: 59
% 1.42/1.77 Deletedinuse: 19
% 1.42/1.77
% 1.42/1.77 Resimplifying inuse:
% 1.42/1.77 Done
% 1.42/1.77
% 1.42/1.77
% 1.42/1.77 Bliksems!, er is een bewijs:
% 1.42/1.77 % SZS status Unsatisfiable
% 1.42/1.77 % SZS output start Refutation
% 1.42/1.77
% 1.42/1.77 clause( 0, [ 'c_lessequals'( 'v_k'( X ), 'v_f'( X ), 't_b' ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 1, [ ~( 'c_lessequals'( 'c_Orderings_Omax'( 'c_minus'( 'v_k'( 'v_x'
% 1.42/1.77 ), 'v_g'( 'v_x' ), 't_b' ), 'c_0', 't_b' ), 'c_HOL_Oabs'( 'c_minus'(
% 1.42/1.77 'v_f'( 'v_x' ), 'v_g'( 'v_x' ), 't_b' ), 't_b' ), 't_b' ) ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 2, [ 'class_Ring__and__Field_Oordered__idom'( 't_b' ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 3, [ ~( 'class_OrderedGroup_Olordered__ab__group__abs'( X ) ),
% 1.42/1.77 'c_lessequals'( 'c_0', 'c_HOL_Oabs'( Y, X ), X ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 4, [ ~( 'class_OrderedGroup_Olordered__ab__group__abs'( X ) ), =(
% 1.42/1.77 'c_HOL_Oabs'( 'c_uminus'( Y, X ), X ), 'c_HOL_Oabs'( Y, X ) ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 5, [ ~( 'class_OrderedGroup_Olordered__ab__group__abs'( X ) ), ~(
% 1.42/1.77 'c_lessequals'( Y, 'c_0', X ) ), =( 'c_uminus'( Y, X ), 'c_HOL_Oabs'( Y,
% 1.42/1.77 X ) ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 6, [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'(
% 1.42/1.77 X ) ), ~( 'c_lessequals'( 'c_plus'( Y, Z, X ), 'c_plus'( T, Z, X ), X ) )
% 1.42/1.77 , 'c_lessequals'( Y, T, X ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 7, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( 'c_plus'(
% 1.42/1.77 'c_0', Y, X ), Y ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 8, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( 'c_plus'( Y
% 1.42/1.77 , 'c_minus'( Z, T, X ), X ), 'c_minus'( 'c_plus'( Y, Z, X ), T, X ) ) ]
% 1.42/1.77 )
% 1.42/1.77 .
% 1.42/1.77 clause( 9, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( 'c_plus'(
% 1.42/1.77 'c_minus'( Y, Z, X ), T, X ), 'c_minus'( 'c_plus'( Y, T, X ), Z, X ) ) ]
% 1.42/1.77 )
% 1.42/1.77 .
% 1.42/1.77 clause( 10, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~(
% 1.42/1.77 'c_lessequals'( Y, 'c_plus'( Z, T, X ), X ) ), 'c_lessequals'( 'c_minus'(
% 1.42/1.77 Y, T, X ), Z, X ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 11, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~(
% 1.42/1.77 'c_lessequals'( Y, Z, X ) ), 'c_lessequals'( 'c_minus'( Y, Z, X ), 'c_0'
% 1.42/1.77 , X ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 12, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( 'c_minus'(
% 1.42/1.77 Y, 'c_uminus'( Z, X ), X ), 'c_plus'( Y, Z, X ) ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 13, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( 'c_minus'(
% 1.42/1.77 Y, Y, X ), 'c_0' ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 14, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( 'c_uminus'(
% 1.42/1.77 'c_minus'( Y, Z, X ), X ), 'c_minus'( Z, Y, X ) ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 15, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_less'( Y, Z, X ),
% 1.42/1.77 'c_lessequals'( Z, Y, X ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 16, [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y,
% 1.42/1.77 Z, X ) ), ~( 'c_lessequals'( T, Z, X ) ), 'c_lessequals'(
% 1.42/1.77 'c_Orderings_Omax'( T, Y, X ), Z, X ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 17, [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_lessequals'( Y, Z,
% 1.42/1.77 X ) ), ~( 'c_lessequals'( T, Y, X ) ), 'c_lessequals'( T, Z, X ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 18, [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_less'( Y, Z, X ) )
% 1.42/1.77 , 'c_lessequals'( Y, Z, X ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 19, [ ~( 'class_LOrder_Ojoin__semilorder'( X ) ),
% 1.42/1.77 'class_Orderings_Oorder'( X ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 20, [ ~( 'class_OrderedGroup_Olordered__ab__group__abs'( X ) ),
% 1.42/1.77 'class_OrderedGroup_Opordered__ab__group__add'( X ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 21, [ ~( 'class_OrderedGroup_Olordered__ab__group__abs'( X ) ),
% 1.42/1.77 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 22, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.42/1.77 'class_OrderedGroup_Ocomm__monoid__add'( X ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 23, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.42/1.77 'class_Orderings_Olinorder'( X ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 24, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.42/1.77 'class_LOrder_Ojoin__semilorder'( X ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 25, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.42/1.77 'class_OrderedGroup_Oab__group__add'( X ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 26, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.42/1.77 'class_OrderedGroup_Olordered__ab__group__abs'( X ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 28, [ 'class_OrderedGroup_Olordered__ab__group__abs'( 't_b' ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 29, [ 'class_OrderedGroup_Oab__group__add'( 't_b' ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 30, [ 'class_LOrder_Ojoin__semilorder'( 't_b' ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 31, [ 'class_Orderings_Olinorder'( 't_b' ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 32, [ 'class_OrderedGroup_Ocomm__monoid__add'( 't_b' ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 34, [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'(
% 1.42/1.77 X ), ~( 'class_Ring__and__Field_Oordered__idom'( X ) ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 35, [ 'c_lessequals'( 'c_0', 'c_HOL_Oabs'( X, 't_b' ), 't_b' ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 36, [ 'c_lessequals'( 'c_0', 'c_HOL_Oabs'( X, Y ), Y ), ~(
% 1.42/1.77 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 37, [ 'class_OrderedGroup_Opordered__ab__group__add'( 't_b' ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 39, [ =( 'c_HOL_Oabs'( 'c_uminus'( X, 't_b' ), 't_b' ),
% 1.42/1.77 'c_HOL_Oabs'( X, 't_b' ) ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 40, [ =( 'c_HOL_Oabs'( 'c_uminus'( X, Y ), Y ), 'c_HOL_Oabs'( X, Y
% 1.42/1.77 ) ), ~( 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 41, [ 'class_Orderings_Oorder'( 't_b' ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 42, [ 'class_Orderings_Oorder'( X ), ~(
% 1.42/1.77 'class_Ring__and__Field_Oordered__idom'( X ) ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 44, [ ~( 'c_lessequals'( X, 'c_0', Y ) ), =( 'c_uminus'( X, Y ),
% 1.42/1.77 'c_HOL_Oabs'( X, Y ) ), ~( 'class_Ring__and__Field_Oordered__idom'( Y ) )
% 1.42/1.77 ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 46, [ =( 'c_minus'( X, X, 't_b' ), 'c_0' ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 47, [ =( 'c_minus'( X, X, Y ), 'c_0' ), ~(
% 1.42/1.77 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 52, [ =( 'c_plus'( 'c_0', X, 't_b' ), X ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 53, [ =( 'c_plus'( 'c_0', X, Y ), X ), ~(
% 1.42/1.77 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 59, [ ~( 'c_lessequals'( 'c_plus'( Z, X, Y ), X, Y ) ),
% 1.42/1.77 'c_lessequals'( Z, 'c_0', Y ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 1.42/1.77 Y ) ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 60, [ =( 'c_plus'( X, 'c_minus'( Y, Z, 't_b' ), 't_b' ), 'c_minus'(
% 1.42/1.77 'c_plus'( X, Y, 't_b' ), Z, 't_b' ) ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 63, [ =( 'c_minus'( 'c_plus'( Z, X, Y ), X, Y ), 'c_plus'( Z, 'c_0'
% 1.42/1.77 , Y ) ), ~( 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 68, [ ~( 'c_less'( X, Y, Z ) ), 'c_lessequals'( X, Y, Z ), ~(
% 1.42/1.77 'class_Ring__and__Field_Oordered__idom'( Z ) ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 69, [ ~( 'c_less'( X, Y, 't_b' ) ), 'c_lessequals'( X, Y, 't_b' ) ]
% 1.42/1.77 )
% 1.42/1.77 .
% 1.42/1.77 clause( 72, [ ~( 'c_less'( X, 'c_0', 't_b' ) ), =( 'c_uminus'( X, 't_b' ),
% 1.42/1.77 'c_HOL_Oabs'( X, 't_b' ) ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 81, [ =( 'c_minus'( 'c_plus'( X, Y, 't_b' ), X, 't_b' ), Y ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 82, [ ~( 'class_OrderedGroup_Oab__group__add'( Y ) ), =( 'c_minus'(
% 1.42/1.77 'c_plus'( X, Z, Y ), X, Y ), 'c_plus'( 'c_0', Z, Y ) ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 83, [ =( 'c_minus'( 'c_plus'( 'c_plus'( X, Y, 't_b' ), Z, 't_b' ),
% 1.42/1.77 X, 't_b' ), 'c_plus'( Y, Z, 't_b' ) ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 87, [ =( 'c_minus'( X, 'c_0', 't_b' ), X ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 89, [ 'c_lessequals'( Y, Z, X ), 'c_lessequals'( Z, Y, X ), ~(
% 1.42/1.77 'class_Ring__and__Field_Oordered__idom'( X ) ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 90, [ 'c_lessequals'( X, Y, 't_b' ), 'c_lessequals'( Y, X, 't_b' )
% 1.42/1.77 ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 94, [ 'c_less'( X, Y, 't_b' ), 'c_lessequals'( Y, X, 't_b' ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 95, [ 'c_less'( X, Y, Z ), 'c_lessequals'( Y, X, Z ), ~(
% 1.42/1.77 'class_Ring__and__Field_Oordered__idom'( Z ) ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 97, [ 'c_lessequals'( X, X, 't_b' ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 111, [ ~( 'c_lessequals'( 'c_plus'( X, Y, 't_b' ), 'c_plus'( Z, X,
% 1.42/1.77 't_b' ), 't_b' ) ), 'c_lessequals'( Y, Z, 't_b' ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 126, [ 'c_lessequals'( 'c_minus'( X, Y, 't_b' ), 'c_0', 't_b' ),
% 1.42/1.77 'c_lessequals'( Y, X, 't_b' ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 135, [ ~( 'c_lessequals'( Y, Z, X ) ), ~(
% 1.42/1.77 'class_OrderedGroup_Olordered__ab__group__abs'( X ) ), =( 'c_uminus'(
% 1.42/1.77 'c_minus'( Y, Z, X ), X ), 'c_HOL_Oabs'( 'c_minus'( Y, Z, X ), X ) ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 137, [ ~( 'c_lessequals'( X, Y, Z ) ), 'c_lessequals'( 'c_minus'( X
% 1.42/1.77 , Y, Z ), 'c_0', Z ), ~( 'class_OrderedGroup_Olordered__ab__group__abs'(
% 1.42/1.77 Z ) ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 139, [ 'c_lessequals'( 'c_minus'( 'v_k'( X ), 'v_f'( X ), 't_b' ),
% 1.42/1.77 'c_0', 't_b' ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 153, [ =( 'c_minus'( X, 'c_uminus'( Y, Z ), Z ), 'c_plus'( X, Y, Z
% 1.42/1.77 ) ), ~( 'class_Ring__and__Field_Oordered__idom'( Z ) ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 162, [ ~( 'class_OrderedGroup_Oab__group__add'( Y ) ), =( 'c_plus'(
% 1.42/1.77 'c_uminus'( X, Y ), X, Y ), 'c_0' ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 175, [ =( 'c_uminus'( 'c_minus'( X, Y, Z ), Z ), 'c_minus'( Y, X, Z
% 1.42/1.77 ) ), ~( 'class_Ring__and__Field_Oordered__idom'( Z ) ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 177, [ ~( 'class_OrderedGroup_Oab__group__add'( Z ) ), =( 'c_minus'(
% 1.42/1.77 'c_uminus'( Y, Z ), X, Z ), 'c_uminus'( 'c_plus'( X, Y, Z ), Z ) ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 178, [ =( 'c_minus'( 'c_0', X, 't_b' ), 'c_uminus'( X, 't_b' ) ) ]
% 1.42/1.77 )
% 1.42/1.77 .
% 1.42/1.77 clause( 183, [ ~( 'class_OrderedGroup_Oab__group__add'( Y ) ), =(
% 1.42/1.77 'c_uminus'( 'c_0', Y ), 'c_0' ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 186, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( 'c_plus'(
% 1.42/1.77 Y, 'c_0', X ), 'c_minus'( Y, 'c_0', X ) ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 188, [ =( 'c_uminus'( 'c_uminus'( X, 't_b' ), 't_b' ), X ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 190, [ ~( 'c_lessequals'( 'c_0', X, 't_b' ) ), 'c_lessequals'(
% 1.42/1.77 'c_uminus'( X, 't_b' ), 'c_0', 't_b' ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 191, [ =( 'c_plus'( 'c_uminus'( X, 't_b' ), Y, 't_b' ), 'c_minus'(
% 1.42/1.77 Y, X, 't_b' ) ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 192, [ =( 'c_plus'( Y, 'c_uminus'( X, 't_b' ), 't_b' ), 'c_minus'(
% 1.42/1.77 Y, X, 't_b' ) ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 201, [ ~( 'c_lessequals'( X, Y, 't_b' ) ), 'c_lessequals'(
% 1.42/1.77 'c_Orderings_Omax'( X, Z, 't_b' ), Y, 't_b' ), 'c_less'( Y, Z, 't_b' ) ]
% 1.42/1.77 )
% 1.42/1.77 .
% 1.42/1.77 clause( 215, [ ~( 'c_lessequals'( X, Y, 't_b' ) ), 'c_lessequals'(
% 1.42/1.77 'c_Orderings_Omax'( X, Y, 't_b' ), Y, 't_b' ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 236, [ ~( 'c_lessequals'( 'c_uminus'( X, 't_b' ), 'c_0', 't_b' ) )
% 1.42/1.77 , =( 'c_HOL_Oabs'( X, 't_b' ), X ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 277, [ ~( 'c_lessequals'( X, 'c_0', 't_b' ) ), 'c_lessequals'( X,
% 1.42/1.77 'c_HOL_Oabs'( Y, 't_b' ), 't_b' ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 285, [ ~( 'c_lessequals'( 'v_f'( X ), Y, 't_b' ) ), 'c_lessequals'(
% 1.42/1.77 'v_k'( X ), Y, 't_b' ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 304, [ ~( 'c_lessequals'( 'c_Orderings_Omax'( 'c_minus'( 'v_k'(
% 1.42/1.77 'v_x' ), 'v_g'( 'v_x' ), 't_b' ), 'c_0', 't_b' ), 'c_0', 't_b' ) ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 441, [ ~( 'c_lessequals'( 'c_0', X, 't_b' ) ), =( 'c_HOL_Oabs'( X,
% 1.42/1.77 't_b' ), X ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 465, [ =( 'c_HOL_Oabs'( X, 't_b' ), X ), 'c_lessequals'( X, 'c_0',
% 1.42/1.77 't_b' ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 478, [ =( 'c_HOL_Oabs'( X, 't_b' ), X ), =( 'c_uminus'( X, 't_b' )
% 1.42/1.77 , 'c_HOL_Oabs'( X, 't_b' ) ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 895, [ ~( 'c_lessequals'( 'c_0', X, Y ) ), 'c_lessequals'(
% 1.42/1.77 'c_uminus'( X, Y ), 'c_0', Y ), ~(
% 1.42/1.77 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 1042, [ ~( 'class_Ring__and__Field_Oordered__idom'( Y ) ), =(
% 1.42/1.77 'c_minus'( 'c_0', X, Y ), 'c_uminus'( X, Y ) ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 1046, [ =( 'c_uminus'( 'c_uminus'( X, Y ), Y ), 'c_minus'( X, 'c_0'
% 1.42/1.77 , Y ) ), ~( 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 1047, [ ~( 'class_Ring__and__Field_Oordered__idom'( Y ) ), =(
% 1.42/1.77 'c_minus'( X, 'c_0', Y ), X ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 1336, [ 'c_lessequals'( X, Y, 't_b' ), =( 'c_HOL_Oabs'( 'c_minus'(
% 1.42/1.77 Y, X, 't_b' ), 't_b' ), 'c_minus'( X, Y, 't_b' ) ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 1344, [ =( 'c_HOL_Oabs'( X, 't_b' ), X ), ~( 'c_less'( 'c_HOL_Oabs'(
% 1.42/1.77 X, 't_b' ), 'c_0', 't_b' ) ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 1393, [ 'c_lessequals'( 'c_0', X, 't_b' ), ~( 'c_less'(
% 1.42/1.77 'c_HOL_Oabs'( X, 't_b' ), 'c_0', 't_b' ) ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 1515, [ =( 'c_HOL_Oabs'( X, 't_b' ), X ), ~( 'c_lessequals'(
% 1.42/1.77 'c_HOL_Oabs'( X, 't_b' ), 'c_0', 't_b' ) ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 1539, [ 'c_lessequals'( 'c_0', X, 't_b' ), ~( 'c_lessequals'(
% 1.42/1.77 'c_HOL_Oabs'( X, 't_b' ), 'c_0', 't_b' ) ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 2641, [ 'c_lessequals'( X, Y, 't_b' ), ~( 'c_lessequals'( 'c_0',
% 1.42/1.77 'c_minus'( Y, X, 't_b' ), 't_b' ) ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 2780, [ 'c_lessequals'( X, Y, 't_b' ), ~( 'c_lessequals'( 'c_minus'(
% 1.42/1.77 X, Y, 't_b' ), 'c_0', 't_b' ) ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 2781, [ 'c_lessequals'( X, Y, 't_b' ), ~( 'c_less'( 'c_minus'( X, Y
% 1.42/1.77 , 't_b' ), 'c_0', 't_b' ) ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 2908, [ 'c_lessequals'( 'c_plus'( X, Y, 't_b' ), X, 't_b' ), ~(
% 1.42/1.77 'c_lessequals'( Y, 'c_0', 't_b' ) ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 3395, [ 'c_lessequals'( 'c_minus'( 'c_plus'( X, 'v_k'( Y ), 't_b' )
% 1.42/1.77 , 'v_f'( Y ), 't_b' ), X, 't_b' ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 4069, [ ~( 'c_lessequals'( 'c_0', X, Y ) ), ~(
% 1.42/1.77 'class_Ring__and__Field_Oordered__idom'( Y ) ), =( 'c_HOL_Oabs'( X, Y ),
% 1.42/1.77 X ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 4073, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.42/1.77 'c_HOL_Oabs'( Y, X ), Y ), 'c_less'( Y, 'c_0', X ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 4406, [ 'c_lessequals'( 'c_plus'( Y, 'v_k'( X ), 't_b' ), 'c_plus'(
% 1.42/1.77 'v_f'( X ), Y, 't_b' ), 't_b' ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 4432, [ 'c_lessequals'( 'c_minus'( 'v_k'( X ), Y, 't_b' ),
% 1.42/1.77 'c_minus'( 'v_f'( X ), Y, 't_b' ), 't_b' ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 4493, [ ~( 'c_lessequals'( 'c_minus'( 'v_k'( 'v_x' ), 'v_g'( 'v_x'
% 1.42/1.77 ), 't_b' ), 'c_0', 't_b' ) ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 4587, [ ~( 'c_lessequals'( 'v_k'( 'v_x' ), 'v_g'( 'v_x' ), 't_b' )
% 1.42/1.77 ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 4650, [ ~( 'c_lessequals'( 'v_f'( 'v_x' ), 'v_g'( 'v_x' ), 't_b' )
% 1.42/1.77 ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 4655, [ ~( 'c_less'( 'c_minus'( 'v_f'( 'v_x' ), 'v_g'( 'v_x' ),
% 1.42/1.77 't_b' ), 'c_0', 't_b' ) ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 4696, [ =( 'c_HOL_Oabs'( 'c_minus'( 'v_f'( 'v_x' ), 'v_g'( 'v_x' )
% 1.42/1.77 , 't_b' ), 't_b' ), 'c_minus'( 'v_f'( 'v_x' ), 'v_g'( 'v_x' ), 't_b' ) )
% 1.42/1.77 ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 4778, [ 'c_less'( 'c_minus'( 'v_f'( 'v_x' ), 'v_g'( 'v_x' ), 't_b'
% 1.42/1.77 ), 'c_0', 't_b' ) ] )
% 1.42/1.77 .
% 1.42/1.77 clause( 4780, [] )
% 1.42/1.77 .
% 1.42/1.77
% 1.42/1.77
% 1.42/1.77 % SZS output end Refutation
% 1.42/1.77 found a proof!
% 1.42/1.77
% 1.42/1.77 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 1.42/1.77
% 1.42/1.77 initialclauses(
% 1.42/1.77 [ clause( 4782, [ 'c_lessequals'( 'v_k'( X ), 'v_f'( X ), 't_b' ) ] )
% 1.42/1.77 , clause( 4783, [ ~( 'c_lessequals'( 'c_Orderings_Omax'( 'c_minus'( 'v_k'(
% 1.42/1.77 'v_x' ), 'v_g'( 'v_x' ), 't_b' ), 'c_0', 't_b' ), 'c_HOL_Oabs'( 'c_minus'(
% 1.42/1.77 'v_f'( 'v_x' ), 'v_g'( 'v_x' ), 't_b' ), 't_b' ), 't_b' ) ) ] )
% 1.42/1.77 , clause( 4784, [ 'class_Ring__and__Field_Oordered__idom'( 't_b' ) ] )
% 1.42/1.77 , clause( 4785, [ ~( 'class_OrderedGroup_Olordered__ab__group__abs'( X ) )
% 1.42/1.77 , 'c_lessequals'( 'c_0', 'c_HOL_Oabs'( Y, X ), X ) ] )
% 1.42/1.77 , clause( 4786, [ ~( 'class_OrderedGroup_Olordered__ab__group__abs'( X ) )
% 1.42/1.77 , =( 'c_HOL_Oabs'( 'c_uminus'( Y, X ), X ), 'c_HOL_Oabs'( Y, X ) ) ] )
% 1.42/1.77 , clause( 4787, [ ~( 'class_OrderedGroup_Olordered__ab__group__abs'( X ) )
% 1.42/1.77 , ~( 'c_lessequals'( Y, 'c_0', X ) ), =( 'c_HOL_Oabs'( Y, X ), 'c_uminus'(
% 1.42/1.77 Y, X ) ) ] )
% 1.42/1.77 , clause( 4788, [ ~(
% 1.42/1.77 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), ~(
% 1.42/1.77 'c_lessequals'( 'c_plus'( Y, Z, X ), 'c_plus'( T, Z, X ), X ) ),
% 1.42/1.77 'c_lessequals'( Y, T, X ) ] )
% 1.42/1.77 , clause( 4789, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.42/1.77 'c_plus'( 'c_0', Y, X ), Y ) ] )
% 1.42/1.77 , clause( 4790, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.42/1.77 'c_plus'( Y, 'c_minus'( Z, T, X ), X ), 'c_minus'( 'c_plus'( Y, Z, X ), T
% 1.42/1.77 , X ) ) ] )
% 1.42/1.77 , clause( 4791, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.42/1.77 'c_plus'( 'c_minus'( Y, Z, X ), T, X ), 'c_minus'( 'c_plus'( Y, T, X ), Z
% 1.42/1.77 , X ) ) ] )
% 1.42/1.77 , clause( 4792, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.42/1.77 , ~( 'c_lessequals'( Y, 'c_plus'( Z, T, X ), X ) ), 'c_lessequals'(
% 1.42/1.77 'c_minus'( Y, T, X ), Z, X ) ] )
% 1.42/1.77 , clause( 4793, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.42/1.77 , ~( 'c_lessequals'( Y, Z, X ) ), 'c_lessequals'( 'c_minus'( Y, Z, X ),
% 1.42/1.77 'c_0', X ) ] )
% 1.42/1.77 , clause( 4794, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.42/1.77 'c_minus'( Y, 'c_uminus'( Z, X ), X ), 'c_plus'( Y, Z, X ) ) ] )
% 1.42/1.77 , clause( 4795, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.42/1.77 'c_minus'( Y, Y, X ), 'c_0' ) ] )
% 1.42/1.77 , clause( 4796, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.42/1.77 'c_uminus'( 'c_minus'( Y, Z, X ), X ), 'c_minus'( Z, Y, X ) ) ] )
% 1.42/1.77 , clause( 4797, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_less'( Y, Z, X
% 1.42/1.77 ), 'c_lessequals'( Z, Y, X ) ] )
% 1.42/1.77 , clause( 4798, [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'(
% 1.42/1.77 Y, Z, X ) ), ~( 'c_lessequals'( T, Z, X ) ), 'c_lessequals'(
% 1.42/1.77 'c_Orderings_Omax'( T, Y, X ), Z, X ) ] )
% 1.42/1.77 , clause( 4799, [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_lessequals'( Y
% 1.42/1.77 , Z, X ) ), ~( 'c_lessequals'( T, Y, X ) ), 'c_lessequals'( T, Z, X ) ]
% 1.42/1.77 )
% 1.42/1.77 , clause( 4800, [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_less'( Y, Z, X
% 1.42/1.77 ) ), 'c_lessequals'( Y, Z, X ) ] )
% 1.42/1.77 , clause( 4801, [ ~( 'class_LOrder_Ojoin__semilorder'( X ) ),
% 1.42/1.77 'class_Orderings_Oorder'( X ) ] )
% 1.42/1.77 , clause( 4802, [ ~( 'class_OrderedGroup_Olordered__ab__group__abs'( X ) )
% 1.42/1.77 , 'class_OrderedGroup_Opordered__ab__group__add'( X ) ] )
% 1.42/1.77 , clause( 4803, [ ~( 'class_OrderedGroup_Olordered__ab__group__abs'( X ) )
% 1.42/1.77 , 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ] )
% 1.42/1.77 , clause( 4804, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.42/1.77 'class_OrderedGroup_Ocomm__monoid__add'( X ) ] )
% 1.42/1.77 , clause( 4805, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.42/1.77 'class_Orderings_Olinorder'( X ) ] )
% 1.42/1.77 , clause( 4806, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.42/1.77 'class_LOrder_Ojoin__semilorder'( X ) ] )
% 1.42/1.77 , clause( 4807, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.42/1.77 'class_OrderedGroup_Oab__group__add'( X ) ] )
% 1.42/1.77 , clause( 4808, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.42/1.77 'class_OrderedGroup_Olordered__ab__group__abs'( X ) ] )
% 1.42/1.77 ] ).
% 1.42/1.77
% 1.42/1.77
% 1.42/1.77
% 1.42/1.77 subsumption(
% 1.42/1.77 clause( 0, [ 'c_lessequals'( 'v_k'( X ), 'v_f'( X ), 't_b' ) ] )
% 1.42/1.77 , clause( 4782, [ 'c_lessequals'( 'v_k'( X ), 'v_f'( X ), 't_b' ) ] )
% 1.42/1.77 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.42/1.77
% 1.42/1.77
% 1.42/1.77 subsumption(
% 1.42/1.77 clause( 1, [ ~( 'c_lessequals'( 'c_Orderings_Omax'( 'c_minus'( 'v_k'( 'v_x'
% 1.42/1.77 ), 'v_g'( 'v_x' ), 't_b' ), 'c_0', 't_b' ), 'c_HOL_Oabs'( 'c_minus'(
% 1.42/1.77 'v_f'( 'v_x' ), 'v_g'( 'v_x' ), 't_b' ), 't_b' ), 't_b' ) ) ] )
% 1.42/1.77 , clause( 4783, [ ~( 'c_lessequals'( 'c_Orderings_Omax'( 'c_minus'( 'v_k'(
% 1.42/1.77 'v_x' ), 'v_g'( 'v_x' ), 't_b' ), 'c_0', 't_b' ), 'c_HOL_Oabs'( 'c_minus'(
% 1.42/1.77 'v_f'( 'v_x' ), 'v_g'( 'v_x' ), 't_b' ), 't_b' ), 't_b' ) ) ] )
% 1.42/1.77 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.42/1.77
% 1.42/1.77
% 1.42/1.77 subsumption(
% 1.42/1.77 clause( 2, [ 'class_Ring__and__Field_Oordered__idom'( 't_b' ) ] )
% 1.42/1.77 , clause( 4784, [ 'class_Ring__and__Field_Oordered__idom'( 't_b' ) ] )
% 1.42/1.77 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.42/1.77
% 1.42/1.77
% 1.42/1.77 subsumption(
% 1.42/1.77 clause( 3, [ ~( 'class_OrderedGroup_Olordered__ab__group__abs'( X ) ),
% 1.42/1.77 'c_lessequals'( 'c_0', 'c_HOL_Oabs'( Y, X ), X ) ] )
% 1.42/1.77 , clause( 4785, [ ~( 'class_OrderedGroup_Olordered__ab__group__abs'( X ) )
% 1.42/1.77 , 'c_lessequals'( 'c_0', 'c_HOL_Oabs'( Y, X ), X ) ] )
% 1.42/1.77 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.42/1.77 ), ==>( 1, 1 )] ) ).
% 1.42/1.77
% 1.42/1.77
% 1.42/1.77 subsumption(
% 1.42/1.77 clause( 4, [ ~( 'class_OrderedGroup_Olordered__ab__group__abs'( X ) ), =(
% 1.42/1.77 'c_HOL_Oabs'( 'c_uminus'( Y, X ), X ), 'c_HOL_Oabs'( Y, X ) ) ] )
% 1.42/1.77 , clause( 4786, [ ~( 'class_OrderedGroup_Olordered__ab__group__abs'( X ) )
% 1.42/1.77 , =( 'c_HOL_Oabs'( 'c_uminus'( Y, X ), X ), 'c_HOL_Oabs'( Y, X ) ) ] )
% 1.42/1.77 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.42/1.77 ), ==>( 1, 1 )] ) ).
% 1.42/1.77
% 1.42/1.77
% 1.42/1.77 eqswap(
% 1.42/1.77 clause( 4811, [ =( 'c_uminus'( X, Y ), 'c_HOL_Oabs'( X, Y ) ), ~(
% 1.42/1.77 'class_OrderedGroup_Olordered__ab__group__abs'( Y ) ), ~( 'c_lessequals'(
% 1.42/1.77 X, 'c_0', Y ) ) ] )
% 1.42/1.77 , clause( 4787, [ ~( 'class_OrderedGroup_Olordered__ab__group__abs'( X ) )
% 1.42/1.77 , ~( 'c_lessequals'( Y, 'c_0', X ) ), =( 'c_HOL_Oabs'( Y, X ), 'c_uminus'(
% 1.42/1.77 Y, X ) ) ] )
% 1.42/1.77 , 2, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 1.42/1.77
% 1.42/1.77
% 1.42/1.77 subsumption(
% 1.42/1.77 clause( 5, [ ~( 'class_OrderedGroup_Olordered__ab__group__abs'( X ) ), ~(
% 1.42/1.77 'c_lessequals'( Y, 'c_0', X ) ), =( 'c_uminus'( Y, X ), 'c_HOL_Oabs'( Y,
% 1.42/1.77 X ) ) ] )
% 1.42/1.77 , clause( 4811, [ =( 'c_uminus'( X, Y ), 'c_HOL_Oabs'( X, Y ) ), ~(
% 1.42/1.77 'class_OrderedGroup_Olordered__ab__group__abs'( Y ) ), ~( 'c_lessequals'(
% 1.42/1.77 X, 'c_0', Y ) ) ] )
% 1.42/1.77 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 2
% 1.42/1.77 ), ==>( 1, 0 ), ==>( 2, 1 )] ) ).
% 1.42/1.77
% 1.42/1.77
% 1.42/1.77 subsumption(
% 1.42/1.77 clause( 6, [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'(
% 1.42/1.77 X ) ), ~( 'c_lessequals'( 'c_plus'( Y, Z, X ), 'c_plus'( T, Z, X ), X ) )
% 1.42/1.77 , 'c_lessequals'( Y, T, X ) ] )
% 1.42/1.77 , clause( 4788, [ ~(
% 1.42/1.77 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), ~(
% 1.42/1.77 'c_lessequals'( 'c_plus'( Y, Z, X ), 'c_plus'( T, Z, X ), X ) ),
% 1.42/1.77 'c_lessequals'( Y, T, X ) ] )
% 1.42/1.77 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 1.42/1.77 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 1.42/1.77
% 1.42/1.77
% 1.42/1.77 subsumption(
% 1.42/1.77 clause( 7, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( 'c_plus'(
% 1.42/1.77 'c_0', Y, X ), Y ) ] )
% 1.42/1.77 , clause( 4789, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.42/1.77 'c_plus'( 'c_0', Y, X ), Y ) ] )
% 1.42/1.77 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.42/1.77 ), ==>( 1, 1 )] ) ).
% 1.42/1.77
% 1.42/1.77
% 1.42/1.77 subsumption(
% 1.42/1.77 clause( 8, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( 'c_plus'( Y
% 1.42/1.77 , 'c_minus'( Z, T, X ), X ), 'c_minus'( 'c_plus'( Y, Z, X ), T, X ) ) ]
% 1.42/1.77 )
% 1.42/1.77 , clause( 4790, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.42/1.77 'c_plus'( Y, 'c_minus'( Z, T, X ), X ), 'c_minus'( 'c_plus'( Y, Z, X ), T
% 1.42/1.77 , X ) ) ] )
% 1.42/1.77 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 1.42/1.77 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 )] ) ).
% 1.42/1.77
% 1.42/1.77
% 1.42/1.77 subsumption(
% 1.42/1.77 clause( 9, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( 'c_plus'(
% 1.42/1.77 'c_minus'( Y, Z, X ), T, X ), 'c_minus'( 'c_plus'( Y, T, X ), Z, X ) ) ]
% 1.42/1.77 )
% 1.42/1.77 , clause( 4791, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.42/1.77 'c_plus'( 'c_minus'( Y, Z, X ), T, X ), 'c_minus'( 'c_plus'( Y, T, X ), Z
% 1.42/1.77 , X ) ) ] )
% 1.42/1.77 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 1.42/1.77 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 )] ) ).
% 1.42/1.77
% 1.42/1.77
% 1.42/1.77 subsumption(
% 1.42/1.77 clause( 10, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~(
% 1.42/1.77 'c_lessequals'( Y, 'c_plus'( Z, T, X ), X ) ), 'c_lessequals'( 'c_minus'(
% 1.42/1.77 Y, T, X ), Z, X ) ] )
% 1.42/1.77 , clause( 4792, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.42/1.77 , ~( 'c_lessequals'( Y, 'c_plus'( Z, T, X ), X ) ), 'c_lessequals'(
% 1.42/1.77 'c_minus'( Y, T, X ), Z, X ) ] )
% 1.42/1.77 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 1.42/1.77 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 1.42/1.77
% 1.42/1.77
% 1.42/1.77 subsumption(
% 1.42/1.77 clause( 11, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~(
% 1.42/1.77 'c_lessequals'( Y, Z, X ) ), 'c_lessequals'( 'c_minus'( Y, Z, X ), 'c_0'
% 1.42/1.77 , X ) ] )
% 1.42/1.77 , clause( 4793, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.42/1.77 , ~( 'c_lessequals'( Y, Z, X ) ), 'c_lessequals'( 'c_minus'( Y, Z, X ),
% 1.42/1.77 'c_0', X ) ] )
% 1.42/1.77 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 1.42/1.77 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 1.42/1.77
% 1.42/1.77
% 1.42/1.77 subsumption(
% 1.42/1.77 clause( 12, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( 'c_minus'(
% 1.42/1.77 Y, 'c_uminus'( Z, X ), X ), 'c_plus'( Y, Z, X ) ) ] )
% 1.42/1.77 , clause( 4794, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.42/1.77 'c_minus'( Y, 'c_uminus'( Z, X ), X ), 'c_plus'( Y, Z, X ) ) ] )
% 1.42/1.77 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 1.42/1.77 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 )] ) ).
% 1.42/1.77
% 1.42/1.77
% 1.42/1.77 subsumption(
% 1.42/1.77 clause( 13, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( 'c_minus'(
% 1.42/1.77 Y, Y, X ), 'c_0' ) ] )
% 1.42/1.77 , clause( 4795, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.42/1.77 'c_minus'( Y, Y, X ), 'c_0' ) ] )
% 1.42/1.77 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.42/1.77 ), ==>( 1, 1 )] ) ).
% 1.42/1.77
% 1.42/1.77
% 1.42/1.77 subsumption(
% 1.42/1.77 clause( 14, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( 'c_uminus'(
% 1.42/1.77 'c_minus'( Y, Z, X ), X ), 'c_minus'( Z, Y, X ) ) ] )
% 1.42/1.77 , clause( 4796, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.42/1.77 'c_uminus'( 'c_minus'( Y, Z, X ), X ), 'c_minus'( Z, Y, X ) ) ] )
% 1.42/1.77 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 1.42/1.77 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 )] ) ).
% 1.42/1.77
% 1.42/1.77
% 1.42/1.77 subsumption(
% 1.42/1.77 clause( 15, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_less'( Y, Z, X ),
% 1.42/1.77 'c_lessequals'( Z, Y, X ) ] )
% 1.42/1.77 , clause( 4797, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_less'( Y, Z, X
% 1.42/1.77 ), 'c_lessequals'( Z, Y, X ) ] )
% 1.42/1.77 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 1.42/1.77 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 1.42/1.77
% 1.42/1.77
% 1.42/1.77 subsumption(
% 1.42/1.77 clause( 16, [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y,
% 1.42/1.77 Z, X ) ), ~( 'c_lessequals'( T, Z, X ) ), 'c_lessequals'(
% 1.42/1.77 'c_Orderings_Omax'( T, Y, X ), Z, X ) ] )
% 1.42/1.77 , clause( 4798, [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'(
% 1.42/1.77 Y, Z, X ) ), ~( 'c_lessequals'( T, Z, X ) ), 'c_lessequals'(
% 1.42/1.77 'c_Orderings_Omax'( T, Y, X ), Z, X ) ] )
% 1.42/1.77 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 1.42/1.77 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 ), ==>( 3, 3 )] )
% 1.42/1.77 ).
% 1.42/1.77
% 1.42/1.77
% 1.42/1.77 subsumption(
% 1.42/1.77 clause( 17, [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_lessequals'( Y, Z,
% 1.42/1.77 X ) ), ~( 'c_lessequals'( T, Y, X ) ), 'c_lessequals'( T, Z, X ) ] )
% 1.42/1.77 , clause( 4799, [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_lessequals'( Y
% 1.42/1.77 , Z, X ) ), ~( 'c_lessequals'( T, Y, X ) ), 'c_lessequals'( T, Z, X ) ]
% 1.42/1.77 )
% 1.42/1.77 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 1.42/1.77 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 ), ==>( 3, 3 )] )
% 1.42/1.77 ).
% 1.42/1.77
% 1.42/1.77
% 1.42/1.77 subsumption(
% 1.42/1.77 clause( 18, [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_less'( Y, Z, X ) )
% 1.42/1.77 , 'c_lessequals'( Y, Z, X ) ] )
% 1.42/1.77 , clause( 4800, [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_less'( Y, Z, X
% 1.42/1.77 ) ), 'c_lessequals'( Y, Z, X ) ] )
% 1.42/1.77 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 1.42/1.77 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 1.42/1.77
% 1.42/1.77
% 1.42/1.77 subsumption(
% 1.42/1.77 clause( 19, [ ~( 'class_LOrder_Ojoin__semilorder'( X ) ),
% 1.42/1.77 'class_Orderings_Oorder'( X ) ] )
% 1.42/1.77 , clause( 4801, [ ~( 'class_LOrder_Ojoin__semilorder'( X ) ),
% 1.42/1.77 'class_Orderings_Oorder'( X ) ] )
% 1.42/1.77 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 1.42/1.77 1 )] ) ).
% 1.42/1.77
% 1.42/1.77
% 1.42/1.77 subsumption(
% 1.42/1.77 clause( 20, [ ~( 'class_OrderedGroup_Olordered__ab__group__abs'( X ) ),
% 1.42/1.77 'class_OrderedGroup_Opordered__ab__group__add'( X ) ] )
% 1.42/1.77 , clause( 4802, [ ~( 'class_OrderedGroup_Olordered__ab__group__abs'( X ) )
% 1.42/1.77 , 'class_OrderedGroup_Opordered__ab__group__add'( X ) ] )
% 1.42/1.77 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 1.42/1.77 1 )] ) ).
% 1.42/1.77
% 1.42/1.77
% 1.42/1.77 subsumption(
% 1.42/1.77 clause( 21, [ ~( 'class_OrderedGroup_Olordered__ab__group__abs'( X ) ),
% 1.42/1.77 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ] )
% 1.42/1.77 , clause( 4803, [ ~( 'class_OrderedGroup_Olordered__ab__group__abs'( X ) )
% 1.42/1.77 , 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ] )
% 1.42/1.77 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 1.42/1.77 1 )] ) ).
% 1.42/1.77
% 1.42/1.77
% 1.42/1.77 subsumption(
% 1.42/1.77 clause( 22, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.42/1.77 'class_OrderedGroup_Ocomm__monoid__add'( X ) ] )
% 1.42/1.77 , clause( 4804, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.42/1.77 'class_OrderedGroup_Ocomm__monoid__add'( X ) ] )
% 1.42/1.77 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 1.42/1.77 1 )] ) ).
% 1.42/1.77
% 1.42/1.77
% 1.42/1.77 subsumption(
% 1.42/1.77 clause( 23, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.42/1.77 'class_Orderings_Olinorder'( X ) ] )
% 1.42/1.77 , clause( 4805, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.42/1.77 'class_Orderings_Olinorder'( X ) ] )
% 1.42/1.77 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 1.42/1.77 1 )] ) ).
% 1.42/1.77
% 1.42/1.77
% 1.42/1.77 subsumption(
% 1.42/1.77 clause( 24, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.42/1.77 'class_LOrder_Ojoin__semilorder'( X ) ] )
% 1.42/1.77 , clause( 4806, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.42/1.77 'class_LOrder_Ojoin__semilorder'( X ) ] )
% 1.42/1.77 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 1.42/1.77 1 )] ) ).
% 1.42/1.77
% 1.42/1.77
% 1.42/1.77 subsumption(
% 1.42/1.77 clause( 25, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.42/1.77 'class_OrderedGroup_Oab__group__add'( X ) ] )
% 1.42/1.77 , clause( 4807, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.42/1.77 'class_OrderedGroup_Oab__group__add'( X ) ] )
% 1.42/1.77 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 1.42/1.77 1 )] ) ).
% 1.42/1.77
% 1.42/1.77
% 1.42/1.77 subsumption(
% 1.42/1.77 clause( 26, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.42/1.77 'class_OrderedGroup_Olordered__ab__group__abs'( X ) ] )
% 1.42/1.77 , clause( 4808, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.42/1.77 'class_OrderedGroup_Olordered__ab__group__abs'( X ) ] )
% 1.42/1.77 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 1.42/1.77 1 )] ) ).
% 1.42/1.77
% 1.42/1.77
% 1.42/1.77 resolution(
% 1.42/1.77 clause( 4974, [ 'class_OrderedGroup_Olordered__ab__group__abs'( 't_b' ) ]
% 1.42/1.77 )
% 1.42/1.77 , clause( 26, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.42/1.77 'class_OrderedGroup_Olordered__ab__group__abs'( X ) ] )
% 1.42/1.77 , 0, clause( 2, [ 'class_Ring__and__Field_Oordered__idom'( 't_b' ) ] )
% 1.42/1.77 , 0, substitution( 0, [ :=( X, 't_b' )] ), substitution( 1, [] )).
% 1.42/1.77
% 1.42/1.77
% 1.42/1.77 subsumption(
% 1.42/1.77 clause( 28, [ 'class_OrderedGroup_Olordered__ab__group__abs'( 't_b' ) ] )
% 1.42/1.77 , clause( 4974, [ 'class_OrderedGroup_Olordered__ab__group__abs'( 't_b' ) ]
% 1.42/1.77 )
% 1.42/1.77 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.42/1.77
% 1.42/1.77
% 1.42/1.77 resolution(
% 1.42/1.77 clause( 4975, [ 'class_OrderedGroup_Oab__group__add'( 't_b' ) ] )
% 1.42/1.77 , clause( 25, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.42/1.77 'class_OrderedGroup_Oab__group__add'( X ) ] )
% 1.42/1.77 , 0, clause( 2, [ 'class_Ring__and__Field_Oordered__idom'( 't_b' ) ] )
% 1.42/1.77 , 0, substitution( 0, [ :=( X, 't_b' )] ), substitution( 1, [] )).
% 1.42/1.77
% 1.42/1.77
% 1.42/1.77 subsumption(
% 1.42/1.77 clause( 29, [ 'class_OrderedGroup_Oab__group__add'( 't_b' ) ] )
% 1.42/1.77 , clause( 4975, [ 'class_OrderedGroup_Oab__group__add'( 't_b' ) ] )
% 1.42/1.77 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.42/1.77
% 1.42/1.77
% 1.42/1.77 resolution(
% 1.42/1.77 clause( 4976, [ 'class_LOrder_Ojoin__semilorder'( 't_b' ) ] )
% 1.42/1.77 , clause( 24, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.42/1.77 'class_LOrder_Ojoin__semilorder'( X ) ] )
% 1.42/1.77 , 0, clause( 2, [ 'class_Ring__and__Field_Oordered__idom'( 't_b' ) ] )
% 1.42/1.77 , 0, substitution( 0, [ :=( X, 't_b' )] ), substitution( 1, [] )).
% 1.42/1.77
% 1.42/1.77
% 1.42/1.77 subsumption(
% 1.42/1.77 clause( 30, [ 'class_LOrder_Ojoin__semilorder'( 't_b' ) ] )
% 1.42/1.77 , clause( 4976, [ 'class_LOrder_Ojoin__semilorder'( 't_b' ) ] )
% 1.42/1.77 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.42/1.77
% 1.42/1.77
% 1.42/1.77 resolution(
% 1.42/1.77 clause( 4977, [ 'class_Orderings_Olinorder'( 't_b' ) ] )
% 1.42/1.77 , clause( 23, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.42/1.77 'class_Orderings_Olinorder'( X ) ] )
% 1.42/1.77 , 0, clause( 2, [ 'class_Ring__and__Field_Oordered__idom'( 't_b' ) ] )
% 1.42/1.77 , 0, substitution( 0, [ :=( X, 't_b' )] ), substitution( 1, [] )).
% 1.42/1.77
% 1.42/1.77
% 1.42/1.77 subsumption(
% 1.42/1.77 clause( 31, [ 'class_Orderings_Olinorder'( 't_b' ) ] )
% 1.42/1.77 , clause( 4977, [ 'class_Orderings_Olinorder'( 't_b' ) ] )
% 1.42/1.77 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.42/1.77
% 1.42/1.77
% 1.42/1.77 resolution(
% 1.42/1.77 clause( 4978, [ 'class_OrderedGroup_Ocomm__monoid__add'( 't_b' ) ] )
% 1.42/1.77 , clause( 22, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.42/1.77 'class_OrderedGroup_Ocomm__monoid__add'( X ) ] )
% 1.42/1.77 , 0, clause( 2, [ 'class_Ring__and__Field_Oordered__idom'( 't_b' ) ] )
% 1.42/1.77 , 0, substitution( 0, [ :=( X, 't_b' )] ), substitution( 1, [] )).
% 1.42/1.77
% 1.42/1.77
% 1.42/1.77 subsumption(
% 1.42/1.77 clause( 32, [ 'class_OrderedGroup_Ocomm__monoid__add'( 't_b' ) ] )
% 1.42/1.77 , clause( 4978, [ 'class_OrderedGroup_Ocomm__monoid__add'( 't_b' ) ] )
% 1.42/1.77 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.42/1.77
% 1.42/1.77
% 1.42/1.77 resolution(
% 1.42/1.77 clause( 4979, [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'(
% 1.42/1.77 X ), ~( 'class_Ring__and__Field_Oordered__idom'( X ) ) ] )
% 1.42/1.77 , clause( 21, [ ~( 'class_OrderedGroup_Olordered__ab__group__abs'( X ) ),
% 1.42/1.77 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ] )
% 1.42/1.77 , 0, clause( 26, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.42/1.77 'class_OrderedGroup_Olordered__ab__group__abs'( X ) ] )
% 1.42/1.77 , 1, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 1.42/1.77 ).
% 1.42/1.77
% 1.42/1.77
% 1.42/1.77 subsumption(
% 1.42/1.77 clause( 34, [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'(
% 1.42/1.77 X ), ~( 'class_Ring__and__Field_Oordered__idom'( X ) ) ] )
% 1.42/1.77 , clause( 4979, [
% 1.42/1.77 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ), ~(
% 1.42/1.77 'class_Ring__and__Field_Oordered__idom'( X ) ) ] )
% 1.42/1.77 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 1.42/1.77 1 )] ) ).
% 1.42/1.77
% 1.42/1.77
% 1.42/1.77 resolution(
% 1.42/1.77 clause( 4980, [ 'c_lessequals'( 'c_0', 'c_HOL_Oabs'( X, 't_b' ), 't_b' ) ]
% 1.42/1.77 )
% 1.42/1.77 , clause( 3, [ ~( 'class_OrderedGroup_Olordered__ab__group__abs'( X ) ),
% 1.42/1.77 'c_lessequals'( 'c_0', 'c_HOL_Oabs'( Y, X ), X ) ] )
% 1.42/1.77 , 0, clause( 28, [ 'class_OrderedGroup_Olordered__ab__group__abs'( 't_b' )
% 1.42/1.77 ] )
% 1.42/1.77 , 0, substitution( 0, [ :=( X, 't_b' ), :=( Y, X )] ), substitution( 1, [] )
% 1.42/1.77 ).
% 1.42/1.77
% 1.42/1.77
% 1.42/1.77 subsumption(
% 1.42/1.77 clause( 35, [ 'c_lessequals'( 'c_0', 'c_HOL_Oabs'( X, 't_b' ), 't_b' ) ] )
% 1.42/1.77 , clause( 4980, [ 'c_lessequals'( 'c_0', 'c_HOL_Oabs'( X, 't_b' ), 't_b' )
% 1.42/1.77 ] )
% 1.42/1.77 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.42/1.77
% 1.42/1.77
% 1.42/1.77 resolution(
% 1.42/1.77 clause( 4981, [ 'c_lessequals'( 'c_0', 'c_HOL_Oabs'( Y, X ), X ), ~(
% 1.42/1.77 'class_Ring__and__Field_Oordered__idom'( X ) ) ] )
% 1.42/1.77 , clause( 3, [ ~( 'class_OrderedGroup_Olordered__ab__group__abs'( X ) ),
% 1.42/1.77 'c_lessequals'( 'c_0', 'c_HOL_Oabs'( Y, X ), X ) ] )
% 1.42/1.77 , 0, clause( 26, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.42/1.77 'class_OrderedGroup_Olordered__ab__group__abs'( X ) ] )
% 1.42/1.77 , 1, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [ :=( X
% 1.42/1.77 , X )] )).
% 1.42/1.77
% 1.42/1.77
% 1.42/1.77 subsumption(
% 1.42/1.77 clause( 36, [ 'c_lessequals'( 'c_0', 'c_HOL_Oabs'( X, Y ), Y ), ~(
% 1.42/1.77 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.42/1.77 , clause( 4981, [ 'c_lessequals'( 'c_0', 'c_HOL_Oabs'( Y, X ), X ), ~(
% 1.42/1.77 'class_Ring__and__Field_Oordered__idom'( X ) ) ] )
% 1.42/1.77 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 1.42/1.77 ), ==>( 1, 1 )] ) ).
% 1.42/1.77
% 1.42/1.77
% 1.42/1.77 resolution(
% 1.42/1.77 clause( 4982, [ 'class_OrderedGroup_Opordered__ab__group__add'( 't_b' ) ]
% 1.42/1.77 )
% 1.42/1.77 , clause( 20, [ ~( 'class_OrderedGroup_Olordered__ab__group__abs'( X ) ),
% 1.42/1.77 'class_OrderedGroup_Opordered__ab__group__add'( X ) ] )
% 1.42/1.77 , 0, clause( 28, [ 'class_OrderedGroup_Olordered__ab__group__abs'( 't_b' )
% 1.42/1.77 ] )
% 1.42/1.77 , 0, substitution( 0, [ :=( X, 't_b' )] ), substitution( 1, [] )).
% 1.42/1.77
% 1.42/1.77
% 1.42/1.77 subsumption(
% 1.42/1.77 clause( 37, [ 'class_OrderedGroup_Opordered__ab__group__add'( 't_b' ) ] )
% 1.42/1.77 , clause( 4982, [ 'class_OrderedGroup_Opordered__ab__group__add'( 't_b' ) ]
% 1.42/1.77 )
% 1.42/1.77 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.42/1.77
% 1.42/1.77
% 1.42/1.77 eqswap(
% 1.42/1.77 clause( 4983, [ =( 'c_HOL_Oabs'( X, Y ), 'c_HOL_Oabs'( 'c_uminus'( X, Y ),
% 1.42/1.77 Y ) ), ~( 'class_OrderedGroup_Olordered__ab__group__abs'( Y ) ) ] )
% 1.42/1.77 , clause( 4, [ ~( 'class_OrderedGroup_Olordered__ab__group__abs'( X ) ),
% 1.42/1.77 =( 'c_HOL_Oabs'( 'c_uminus'( Y, X ), X ), 'c_HOL_Oabs'( Y, X ) ) ] )
% 1.42/1.77 , 1, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 1.42/1.77
% 1.42/1.77
% 1.42/1.77 resolution(
% 1.42/1.77 clause( 4984, [ =( 'c_HOL_Oabs'( X, 't_b' ), 'c_HOL_Oabs'( 'c_uminus'( X,
% 1.42/1.77 't_b' ), 't_b' ) ) ] )
% 1.42/1.77 , clause( 4983, [ =( 'c_HOL_Oabs'( X, Y ), 'c_HOL_Oabs'( 'c_uminus'( X, Y )
% 1.42/1.77 , Y ) ), ~( 'class_OrderedGroup_Olordered__ab__group__abs'( Y ) ) ] )
% 1.42/1.77 , 1, clause( 28, [ 'class_OrderedGroup_Olordered__ab__group__abs'( 't_b' )
% 1.42/1.77 ] )
% 1.42/1.77 , 0, substitution( 0, [ :=( X, X ), :=( Y, 't_b' )] ), substitution( 1, [] )
% 1.42/1.77 ).
% 1.42/1.77
% 1.42/1.77
% 1.42/1.77 eqswap(
% 1.42/1.77 clause( 4985, [ =( 'c_HOL_Oabs'( 'c_uminus'( X, 't_b' ), 't_b' ),
% 1.42/1.77 'c_HOL_Oabs'( X, 't_b' ) ) ] )
% 1.42/1.77 , clause( 4984, [ =( 'c_HOL_Oabs'( X, 't_b' ), 'c_HOL_Oabs'( 'c_uminus'( X
% 1.42/1.77 , 't_b' ), 't_b' ) ) ] )
% 1.42/1.77 , 0, substitution( 0, [ :=( X, X )] )).
% 1.42/1.77
% 1.42/1.77
% 1.42/1.77 subsumption(
% 1.42/1.77 clause( 39, [ =( 'c_HOL_Oabs'( 'c_uminus'( X, 't_b' ), 't_b' ),
% 1.42/1.77 'c_HOL_Oabs'( X, 't_b' ) ) ] )
% 1.42/1.77 , clause( 4985, [ =( 'c_HOL_Oabs'( 'c_uminus'( X, 't_b' ), 't_b' ),
% 1.42/1.77 'c_HOL_Oabs'( X, 't_b' ) ) ] )
% 1.42/1.77 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.42/1.77
% 1.42/1.77
% 1.42/1.77 eqswap(
% 1.42/1.77 clause( 4986, [ =( 'c_HOL_Oabs'( X, Y ), 'c_HOL_Oabs'( 'c_uminus'( X, Y ),
% 1.42/1.77 Y ) ), ~( 'class_OrderedGroup_Olordered__ab__group__abs'( Y ) ) ] )
% 1.42/1.77 , clause( 4, [ ~( 'class_OrderedGroup_Olordered__ab__group__abs'( X ) ),
% 1.42/1.77 =( 'c_HOL_Oabs'( 'c_uminus'( Y, X ), X ), 'c_HOL_Oabs'( Y, X ) ) ] )
% 1.42/1.77 , 1, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 1.42/1.77
% 1.42/1.77
% 1.42/1.77 resolution(
% 1.42/1.77 clause( 4987, [ =( 'c_HOL_Oabs'( X, Y ), 'c_HOL_Oabs'( 'c_uminus'( X, Y ),
% 1.42/1.77 Y ) ), ~( 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.42/1.77 , clause( 4986, [ =( 'c_HOL_Oabs'( X, Y ), 'c_HOL_Oabs'( 'c_uminus'( X, Y )
% 1.42/1.77 , Y ) ), ~( 'class_OrderedGroup_Olordered__ab__group__abs'( Y ) ) ] )
% 1.42/1.77 , 1, clause( 26, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.42/1.77 'class_OrderedGroup_Olordered__ab__group__abs'( X ) ] )
% 1.42/1.77 , 1, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [ :=( X
% 1.42/1.77 , Y )] )).
% 1.42/1.77
% 1.42/1.77
% 1.42/1.77 eqswap(
% 1.42/1.77 clause( 4988, [ =( 'c_HOL_Oabs'( 'c_uminus'( X, Y ), Y ), 'c_HOL_Oabs'( X,
% 1.42/1.77 Y ) ), ~( 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.42/1.77 , clause( 4987, [ =( 'c_HOL_Oabs'( X, Y ), 'c_HOL_Oabs'( 'c_uminus'( X, Y )
% 1.42/1.77 , Y ) ), ~( 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.42/1.77 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 1.42/1.77
% 1.42/1.77
% 1.42/1.77 subsumption(
% 1.42/1.77 clause( 40, [ =( 'c_HOL_Oabs'( 'c_uminus'( X, Y ), Y ), 'c_HOL_Oabs'( X, Y
% 1.42/1.77 ) ), ~( 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.42/1.77 , clause( 4988, [ =( 'c_HOL_Oabs'( 'c_uminus'( X, Y ), Y ), 'c_HOL_Oabs'( X
% 1.42/1.77 , Y ) ), ~( 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.42/1.77 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.42/1.77 ), ==>( 1, 1 )] ) ).
% 1.42/1.77
% 1.42/1.77
% 1.42/1.77 resolution(
% 1.42/1.77 clause( 4989, [ 'class_Orderings_Oorder'( 't_b' ) ] )
% 1.42/1.77 , clause( 19, [ ~( 'class_LOrder_Ojoin__semilorder'( X ) ),
% 1.42/1.77 'class_Orderings_Oorder'( X ) ] )
% 1.42/1.77 , 0, clause( 30, [ 'class_LOrder_Ojoin__semilorder'( 't_b' ) ] )
% 1.42/1.77 , 0, substitution( 0, [ :=( X, 't_b' )] ), substitution( 1, [] )).
% 1.42/1.77
% 1.42/1.77
% 1.42/1.77 subsumption(
% 1.42/1.77 clause( 41, [ 'class_Orderings_Oorder'( 't_b' ) ] )
% 1.42/1.77 , clause( 4989, [ 'class_Orderings_Oorder'( 't_b' ) ] )
% 1.42/1.77 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.42/1.77
% 1.42/1.77
% 1.42/1.77 resolution(
% 1.42/1.77 clause( 4990, [ 'class_Orderings_Oorder'( X ), ~(
% 1.42/1.77 'class_Ring__and__Field_Oordered__idom'( X ) ) ] )
% 1.42/1.77 , clause( 19, [ ~( 'class_LOrder_Ojoin__semilorder'( X ) ),
% 1.42/1.77 'class_Orderings_Oorder'( X ) ] )
% 1.42/1.77 , 0, clause( 24, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.42/1.77 'class_LOrder_Ojoin__semilorder'( X ) ] )
% 1.42/1.77 , 1, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 1.42/1.77 ).
% 1.42/1.77
% 1.42/1.77
% 1.42/1.77 subsumption(
% 1.42/1.77 clause( 42, [ 'class_Orderings_Oorder'( X ), ~(
% 1.42/1.77 'class_Ring__and__Field_Oordered__idom'( X ) ) ] )
% 1.42/1.77 , clause( 4990, [ 'class_Orderings_Oorder'( X ), ~(
% 1.42/1.77 'class_Ring__and__Field_Oordered__idom'( X ) ) ] )
% 1.42/1.77 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 1.42/1.77 1 )] ) ).
% 1.42/1.77
% 1.42/1.77
% 1.42/1.77 eqswap(
% 1.42/1.77 clause( 4991, [ =( 'c_HOL_Oabs'( X, Y ), 'c_uminus'( X, Y ) ), ~(
% 1.42/1.77 'class_OrderedGroup_Olordered__ab__group__abs'( Y ) ), ~( 'c_lessequals'(
% 1.42/1.77 X, 'c_0', Y ) ) ] )
% 1.42/1.77 , clause( 5, [ ~( 'class_OrderedGroup_Olordered__ab__group__abs'( X ) ),
% 1.42/1.77 ~( 'c_lessequals'( Y, 'c_0', X ) ), =( 'c_uminus'( Y, X ), 'c_HOL_Oabs'(
% 1.42/1.77 Y, X ) ) ] )
% 1.42/1.77 , 2, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 1.42/1.77
% 1.42/1.77
% 1.42/1.77 resolution(
% 1.42/1.77 clause( 4992, [ =( 'c_HOL_Oabs'( X, Y ), 'c_uminus'( X, Y ) ), ~(
% 1.42/1.77 'c_lessequals'( X, 'c_0', Y ) ), ~(
% 1.42/1.77 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.42/1.77 , clause( 4991, [ =( 'c_HOL_Oabs'( X, Y ), 'c_uminus'( X, Y ) ), ~(
% 1.42/1.77 'class_OrderedGroup_Olordered__ab__group__abs'( Y ) ), ~( 'c_lessequals'(
% 1.42/1.77 X, 'c_0', Y ) ) ] )
% 1.42/1.77 , 1, clause( 26, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.42/1.77 'class_OrderedGroup_Olordered__ab__group__abs'( X ) ] )
% 1.42/1.77 , 1, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [ :=( X
% 1.42/1.77 , Y )] )).
% 1.42/1.77
% 1.42/1.77
% 1.42/1.77 eqswap(
% 1.42/1.77 clause( 4993, [ =( 'c_uminus'( X, Y ), 'c_HOL_Oabs'( X, Y ) ), ~(
% 1.42/1.77 'c_lessequals'( X, 'c_0', Y ) ), ~(
% 1.42/1.77 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.42/1.77 , clause( 4992, [ =( 'c_HOL_Oabs'( X, Y ), 'c_uminus'( X, Y ) ), ~(
% 1.42/1.77 'c_lessequals'( X, 'c_0', Y ) ), ~(
% 1.42/1.77 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.42/1.77 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 1.42/1.77
% 1.42/1.77
% 1.42/1.77 subsumption(
% 1.42/1.77 clause( 44, [ ~( 'c_lessequals'( X, 'c_0', Y ) ), =( 'c_uminus'( X, Y ),
% 1.42/1.77 'c_HOL_Oabs'( X, Y ) ), ~( 'class_Ring__and__Field_Oordered__idom'( Y ) )
% 1.42/1.77 ] )
% 1.42/1.77 , clause( 4993, [ =( 'c_uminus'( X, Y ), 'c_HOL_Oabs'( X, Y ) ), ~(
% 1.42/1.77 'c_lessequals'( X, 'c_0', Y ) ), ~(
% 1.42/1.77 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.42/1.77 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 1
% 1.42/1.77 ), ==>( 1, 0 ), ==>( 2, 2 )] ) ).
% 1.42/1.77
% 1.42/1.77
% 1.42/1.77 eqswap(
% 1.42/1.77 clause( 4994, [ =( 'c_0', 'c_minus'( X, X, Y ) ), ~(
% 1.42/1.77 'class_OrderedGroup_Oab__group__add'( Y ) ) ] )
% 1.42/1.77 , clause( 13, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.42/1.77 'c_minus'( Y, Y, X ), 'c_0' ) ] )
% 1.42/1.77 , 1, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 1.42/1.77
% 1.42/1.77
% 1.42/1.77 resolution(
% 1.42/1.77 clause( 4995, [ =( 'c_0', 'c_minus'( X, X, 't_b' ) ) ] )
% 1.42/1.77 , clause( 4994, [ =( 'c_0', 'c_minus'( X, X, Y ) ), ~(
% 1.42/1.77 'class_OrderedGroup_Oab__group__add'( Y ) ) ] )
% 1.42/1.77 , 1, clause( 29, [ 'class_OrderedGroup_Oab__group__add'( 't_b' ) ] )
% 1.42/1.77 , 0, substitution( 0, [ :=( X, X ), :=( Y, 't_b' )] ), substitution( 1, [] )
% 1.42/1.77 ).
% 1.42/1.77
% 1.42/1.77
% 1.42/1.77 eqswap(
% 1.42/1.77 clause( 4996, [ =( 'c_minus'( X, X, 't_b' ), 'c_0' ) ] )
% 1.42/1.77 , clause( 4995, [ =( 'c_0', 'c_minus'( X, X, 't_b' ) ) ] )
% 1.42/1.77 , 0, substitution( 0, [ :=( X, X )] )).
% 1.42/1.77
% 1.42/1.77
% 1.42/1.77 subsumption(
% 1.42/1.77 clause( 46, [ =( 'c_minus'( X, X, 't_b' ), 'c_0' ) ] )
% 1.42/1.77 , clause( 4996, [ =( 'c_minus'( X, X, 't_b' ), 'c_0' ) ] )
% 1.42/1.77 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.42/1.77
% 1.42/1.77
% 1.42/1.77 eqswap(
% 1.42/1.77 clause( 4997, [ =( 'c_0', 'c_minus'( X, X, Y ) ), ~(
% 1.42/1.77 'class_OrderedGroup_Oab__group__add'( Y ) ) ] )
% 1.42/1.77 , clause( 13, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.42/1.77 'c_minus'( Y, Y, X ), 'c_0' ) ] )
% 1.42/1.77 , 1, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 1.42/1.77
% 1.42/1.77
% 1.42/1.77 resolution(
% 1.42/1.78 clause( 4998, [ =( 'c_0', 'c_minus'( X, X, Y ) ), ~(
% 1.42/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.42/1.78 , clause( 4997, [ =( 'c_0', 'c_minus'( X, X, Y ) ), ~(
% 1.42/1.78 'class_OrderedGroup_Oab__group__add'( Y ) ) ] )
% 1.42/1.78 , 1, clause( 25, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.42/1.78 'class_OrderedGroup_Oab__group__add'( X ) ] )
% 1.42/1.78 , 1, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [ :=( X
% 1.42/1.78 , Y )] )).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 eqswap(
% 1.42/1.78 clause( 4999, [ =( 'c_minus'( X, X, Y ), 'c_0' ), ~(
% 1.42/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.42/1.78 , clause( 4998, [ =( 'c_0', 'c_minus'( X, X, Y ) ), ~(
% 1.42/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.42/1.78 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 subsumption(
% 1.42/1.78 clause( 47, [ =( 'c_minus'( X, X, Y ), 'c_0' ), ~(
% 1.42/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.42/1.78 , clause( 4999, [ =( 'c_minus'( X, X, Y ), 'c_0' ), ~(
% 1.42/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.42/1.78 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.42/1.78 ), ==>( 1, 1 )] ) ).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 eqswap(
% 1.42/1.78 clause( 5000, [ =( X, 'c_plus'( 'c_0', X, Y ) ), ~(
% 1.42/1.78 'class_OrderedGroup_Ocomm__monoid__add'( Y ) ) ] )
% 1.42/1.78 , clause( 7, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.42/1.78 'c_plus'( 'c_0', Y, X ), Y ) ] )
% 1.42/1.78 , 1, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 resolution(
% 1.42/1.78 clause( 5001, [ =( X, 'c_plus'( 'c_0', X, 't_b' ) ) ] )
% 1.42/1.78 , clause( 5000, [ =( X, 'c_plus'( 'c_0', X, Y ) ), ~(
% 1.42/1.78 'class_OrderedGroup_Ocomm__monoid__add'( Y ) ) ] )
% 1.42/1.78 , 1, clause( 32, [ 'class_OrderedGroup_Ocomm__monoid__add'( 't_b' ) ] )
% 1.42/1.78 , 0, substitution( 0, [ :=( X, X ), :=( Y, 't_b' )] ), substitution( 1, [] )
% 1.42/1.78 ).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 eqswap(
% 1.42/1.78 clause( 5002, [ =( 'c_plus'( 'c_0', X, 't_b' ), X ) ] )
% 1.42/1.78 , clause( 5001, [ =( X, 'c_plus'( 'c_0', X, 't_b' ) ) ] )
% 1.42/1.78 , 0, substitution( 0, [ :=( X, X )] )).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 subsumption(
% 1.42/1.78 clause( 52, [ =( 'c_plus'( 'c_0', X, 't_b' ), X ) ] )
% 1.42/1.78 , clause( 5002, [ =( 'c_plus'( 'c_0', X, 't_b' ), X ) ] )
% 1.42/1.78 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 eqswap(
% 1.42/1.78 clause( 5003, [ =( X, 'c_plus'( 'c_0', X, Y ) ), ~(
% 1.42/1.78 'class_OrderedGroup_Ocomm__monoid__add'( Y ) ) ] )
% 1.42/1.78 , clause( 7, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.42/1.78 'c_plus'( 'c_0', Y, X ), Y ) ] )
% 1.42/1.78 , 1, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 resolution(
% 1.42/1.78 clause( 5004, [ =( X, 'c_plus'( 'c_0', X, Y ) ), ~(
% 1.42/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.42/1.78 , clause( 5003, [ =( X, 'c_plus'( 'c_0', X, Y ) ), ~(
% 1.42/1.78 'class_OrderedGroup_Ocomm__monoid__add'( Y ) ) ] )
% 1.42/1.78 , 1, clause( 22, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.42/1.78 'class_OrderedGroup_Ocomm__monoid__add'( X ) ] )
% 1.42/1.78 , 1, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [ :=( X
% 1.42/1.78 , Y )] )).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 eqswap(
% 1.42/1.78 clause( 5005, [ =( 'c_plus'( 'c_0', X, Y ), X ), ~(
% 1.42/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.42/1.78 , clause( 5004, [ =( X, 'c_plus'( 'c_0', X, Y ) ), ~(
% 1.42/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.42/1.78 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 subsumption(
% 1.42/1.78 clause( 53, [ =( 'c_plus'( 'c_0', X, Y ), X ), ~(
% 1.42/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.42/1.78 , clause( 5005, [ =( 'c_plus'( 'c_0', X, Y ), X ), ~(
% 1.42/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.42/1.78 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.42/1.78 ), ==>( 1, 1 )] ) ).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 paramod(
% 1.42/1.78 clause( 5008, [ ~( 'c_lessequals'( 'c_plus'( X, Y, Z ), Y, Z ) ), ~(
% 1.42/1.78 'class_Ring__and__Field_Oordered__idom'( Z ) ), ~(
% 1.42/1.78 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( Z ) ),
% 1.42/1.78 'c_lessequals'( X, 'c_0', Z ) ] )
% 1.42/1.78 , clause( 53, [ =( 'c_plus'( 'c_0', X, Y ), X ), ~(
% 1.42/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.42/1.78 , 0, clause( 6, [ ~(
% 1.42/1.78 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), ~(
% 1.42/1.78 'c_lessequals'( 'c_plus'( Y, Z, X ), 'c_plus'( T, Z, X ), X ) ),
% 1.42/1.78 'c_lessequals'( Y, T, X ) ] )
% 1.42/1.78 , 1, 6, substitution( 0, [ :=( X, Y ), :=( Y, Z )] ), substitution( 1, [
% 1.42/1.78 :=( X, Z ), :=( Y, X ), :=( Z, Y ), :=( T, 'c_0' )] )).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 resolution(
% 1.42/1.78 clause( 5009, [ ~( 'c_lessequals'( 'c_plus'( X, Y, Z ), Y, Z ) ), ~(
% 1.42/1.78 'class_Ring__and__Field_Oordered__idom'( Z ) ), 'c_lessequals'( X, 'c_0'
% 1.42/1.78 , Z ), ~( 'class_Ring__and__Field_Oordered__idom'( Z ) ) ] )
% 1.42/1.78 , clause( 5008, [ ~( 'c_lessequals'( 'c_plus'( X, Y, Z ), Y, Z ) ), ~(
% 1.42/1.78 'class_Ring__and__Field_Oordered__idom'( Z ) ), ~(
% 1.42/1.78 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( Z ) ),
% 1.42/1.78 'c_lessequals'( X, 'c_0', Z ) ] )
% 1.42/1.78 , 2, clause( 34, [
% 1.42/1.78 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ), ~(
% 1.42/1.78 'class_Ring__and__Field_Oordered__idom'( X ) ) ] )
% 1.42/1.78 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 1.42/1.78 substitution( 1, [ :=( X, Z )] )).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 factor(
% 1.42/1.78 clause( 5010, [ ~( 'c_lessequals'( 'c_plus'( X, Y, Z ), Y, Z ) ), ~(
% 1.42/1.78 'class_Ring__and__Field_Oordered__idom'( Z ) ), 'c_lessequals'( X, 'c_0'
% 1.42/1.78 , Z ) ] )
% 1.42/1.78 , clause( 5009, [ ~( 'c_lessequals'( 'c_plus'( X, Y, Z ), Y, Z ) ), ~(
% 1.42/1.78 'class_Ring__and__Field_Oordered__idom'( Z ) ), 'c_lessequals'( X, 'c_0'
% 1.42/1.78 , Z ), ~( 'class_Ring__and__Field_Oordered__idom'( Z ) ) ] )
% 1.42/1.78 , 1, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 subsumption(
% 1.42/1.78 clause( 59, [ ~( 'c_lessequals'( 'c_plus'( Z, X, Y ), X, Y ) ),
% 1.42/1.78 'c_lessequals'( Z, 'c_0', Y ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 1.42/1.78 Y ) ) ] )
% 1.42/1.78 , clause( 5010, [ ~( 'c_lessequals'( 'c_plus'( X, Y, Z ), Y, Z ) ), ~(
% 1.42/1.78 'class_Ring__and__Field_Oordered__idom'( Z ) ), 'c_lessequals'( X, 'c_0'
% 1.42/1.78 , Z ) ] )
% 1.42/1.78 , substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] ),
% 1.42/1.78 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 2 ), ==>( 2, 1 )] ) ).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 eqswap(
% 1.42/1.78 clause( 5011, [ =( 'c_minus'( 'c_plus'( X, Y, T ), Z, T ), 'c_plus'( X,
% 1.42/1.78 'c_minus'( Y, Z, T ), T ) ), ~( 'class_OrderedGroup_Oab__group__add'( T )
% 1.42/1.78 ) ] )
% 1.42/1.78 , clause( 8, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( 'c_plus'(
% 1.42/1.78 Y, 'c_minus'( Z, T, X ), X ), 'c_minus'( 'c_plus'( Y, Z, X ), T, X ) ) ]
% 1.42/1.78 )
% 1.42/1.78 , 1, substitution( 0, [ :=( X, T ), :=( Y, X ), :=( Z, Y ), :=( T, Z )] )
% 1.42/1.78 ).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 resolution(
% 1.42/1.78 clause( 5012, [ =( 'c_minus'( 'c_plus'( X, Y, 't_b' ), Z, 't_b' ), 'c_plus'(
% 1.42/1.78 X, 'c_minus'( Y, Z, 't_b' ), 't_b' ) ) ] )
% 1.42/1.78 , clause( 5011, [ =( 'c_minus'( 'c_plus'( X, Y, T ), Z, T ), 'c_plus'( X,
% 1.42/1.78 'c_minus'( Y, Z, T ), T ) ), ~( 'class_OrderedGroup_Oab__group__add'( T )
% 1.42/1.78 ) ] )
% 1.42/1.78 , 1, clause( 29, [ 'class_OrderedGroup_Oab__group__add'( 't_b' ) ] )
% 1.42/1.78 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, 't_b' )] )
% 1.42/1.78 , substitution( 1, [] )).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 eqswap(
% 1.42/1.78 clause( 5013, [ =( 'c_plus'( X, 'c_minus'( Y, Z, 't_b' ), 't_b' ),
% 1.42/1.78 'c_minus'( 'c_plus'( X, Y, 't_b' ), Z, 't_b' ) ) ] )
% 1.42/1.78 , clause( 5012, [ =( 'c_minus'( 'c_plus'( X, Y, 't_b' ), Z, 't_b' ),
% 1.42/1.78 'c_plus'( X, 'c_minus'( Y, Z, 't_b' ), 't_b' ) ) ] )
% 1.42/1.78 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 subsumption(
% 1.42/1.78 clause( 60, [ =( 'c_plus'( X, 'c_minus'( Y, Z, 't_b' ), 't_b' ), 'c_minus'(
% 1.42/1.78 'c_plus'( X, Y, 't_b' ), Z, 't_b' ) ) ] )
% 1.42/1.78 , clause( 5013, [ =( 'c_plus'( X, 'c_minus'( Y, Z, 't_b' ), 't_b' ),
% 1.42/1.78 'c_minus'( 'c_plus'( X, Y, 't_b' ), Z, 't_b' ) ) ] )
% 1.42/1.78 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 1.42/1.78 permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 eqswap(
% 1.42/1.78 clause( 5015, [ =( 'c_minus'( 'c_plus'( X, Y, T ), Z, T ), 'c_plus'( X,
% 1.42/1.78 'c_minus'( Y, Z, T ), T ) ), ~( 'class_OrderedGroup_Oab__group__add'( T )
% 1.42/1.78 ) ] )
% 1.42/1.78 , clause( 8, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( 'c_plus'(
% 1.42/1.78 Y, 'c_minus'( Z, T, X ), X ), 'c_minus'( 'c_plus'( Y, Z, X ), T, X ) ) ]
% 1.42/1.78 )
% 1.42/1.78 , 1, substitution( 0, [ :=( X, T ), :=( Y, X ), :=( Z, Y ), :=( T, Z )] )
% 1.42/1.78 ).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 paramod(
% 1.42/1.78 clause( 5017, [ =( 'c_minus'( 'c_plus'( X, Y, Z ), Y, Z ), 'c_plus'( X,
% 1.42/1.78 'c_0', Z ) ), ~( 'class_Ring__and__Field_Oordered__idom'( Z ) ), ~(
% 1.42/1.78 'class_OrderedGroup_Oab__group__add'( Z ) ) ] )
% 1.42/1.78 , clause( 47, [ =( 'c_minus'( X, X, Y ), 'c_0' ), ~(
% 1.42/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.42/1.78 , 0, clause( 5015, [ =( 'c_minus'( 'c_plus'( X, Y, T ), Z, T ), 'c_plus'( X
% 1.42/1.78 , 'c_minus'( Y, Z, T ), T ) ), ~( 'class_OrderedGroup_Oab__group__add'( T
% 1.42/1.78 ) ) ] )
% 1.42/1.78 , 0, 10, substitution( 0, [ :=( X, Y ), :=( Y, Z )] ), substitution( 1, [
% 1.42/1.78 :=( X, X ), :=( Y, Y ), :=( Z, Y ), :=( T, Z )] )).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 resolution(
% 1.42/1.78 clause( 5018, [ =( 'c_minus'( 'c_plus'( X, Y, Z ), Y, Z ), 'c_plus'( X,
% 1.42/1.78 'c_0', Z ) ), ~( 'class_Ring__and__Field_Oordered__idom'( Z ) ), ~(
% 1.42/1.78 'class_Ring__and__Field_Oordered__idom'( Z ) ) ] )
% 1.42/1.78 , clause( 5017, [ =( 'c_minus'( 'c_plus'( X, Y, Z ), Y, Z ), 'c_plus'( X,
% 1.42/1.78 'c_0', Z ) ), ~( 'class_Ring__and__Field_Oordered__idom'( Z ) ), ~(
% 1.42/1.78 'class_OrderedGroup_Oab__group__add'( Z ) ) ] )
% 1.42/1.78 , 2, clause( 25, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.42/1.78 'class_OrderedGroup_Oab__group__add'( X ) ] )
% 1.42/1.78 , 1, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 1.42/1.78 substitution( 1, [ :=( X, Z )] )).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 factor(
% 1.42/1.78 clause( 5021, [ =( 'c_minus'( 'c_plus'( X, Y, Z ), Y, Z ), 'c_plus'( X,
% 1.42/1.78 'c_0', Z ) ), ~( 'class_Ring__and__Field_Oordered__idom'( Z ) ) ] )
% 1.42/1.78 , clause( 5018, [ =( 'c_minus'( 'c_plus'( X, Y, Z ), Y, Z ), 'c_plus'( X,
% 1.42/1.78 'c_0', Z ) ), ~( 'class_Ring__and__Field_Oordered__idom'( Z ) ), ~(
% 1.42/1.78 'class_Ring__and__Field_Oordered__idom'( Z ) ) ] )
% 1.42/1.78 , 1, 2, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 subsumption(
% 1.42/1.78 clause( 63, [ =( 'c_minus'( 'c_plus'( Z, X, Y ), X, Y ), 'c_plus'( Z, 'c_0'
% 1.42/1.78 , Y ) ), ~( 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.42/1.78 , clause( 5021, [ =( 'c_minus'( 'c_plus'( X, Y, Z ), Y, Z ), 'c_plus'( X,
% 1.42/1.78 'c_0', Z ) ), ~( 'class_Ring__and__Field_Oordered__idom'( Z ) ) ] )
% 1.42/1.78 , substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] ),
% 1.42/1.78 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 )] ) ).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 resolution(
% 1.42/1.78 clause( 5022, [ ~( 'c_less'( Y, Z, X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.42/1.78 'class_Ring__and__Field_Oordered__idom'( X ) ) ] )
% 1.42/1.78 , clause( 18, [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_less'( Y, Z, X )
% 1.42/1.78 ), 'c_lessequals'( Y, Z, X ) ] )
% 1.42/1.78 , 0, clause( 42, [ 'class_Orderings_Oorder'( X ), ~(
% 1.42/1.78 'class_Ring__and__Field_Oordered__idom'( X ) ) ] )
% 1.42/1.78 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 1.42/1.78 substitution( 1, [ :=( X, X )] )).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 subsumption(
% 1.42/1.78 clause( 68, [ ~( 'c_less'( X, Y, Z ) ), 'c_lessequals'( X, Y, Z ), ~(
% 1.42/1.78 'class_Ring__and__Field_Oordered__idom'( Z ) ) ] )
% 1.42/1.78 , clause( 5022, [ ~( 'c_less'( Y, Z, X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.42/1.78 'class_Ring__and__Field_Oordered__idom'( X ) ) ] )
% 1.42/1.78 , substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] ),
% 1.42/1.78 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 resolution(
% 1.42/1.78 clause( 5023, [ ~( 'c_less'( X, Y, 't_b' ) ), 'c_lessequals'( X, Y, 't_b' )
% 1.42/1.78 ] )
% 1.42/1.78 , clause( 18, [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_less'( Y, Z, X )
% 1.42/1.78 ), 'c_lessequals'( Y, Z, X ) ] )
% 1.42/1.78 , 0, clause( 41, [ 'class_Orderings_Oorder'( 't_b' ) ] )
% 1.42/1.78 , 0, substitution( 0, [ :=( X, 't_b' ), :=( Y, X ), :=( Z, Y )] ),
% 1.42/1.78 substitution( 1, [] )).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 subsumption(
% 1.42/1.78 clause( 69, [ ~( 'c_less'( X, Y, 't_b' ) ), 'c_lessequals'( X, Y, 't_b' ) ]
% 1.42/1.78 )
% 1.42/1.78 , clause( 5023, [ ~( 'c_less'( X, Y, 't_b' ) ), 'c_lessequals'( X, Y, 't_b'
% 1.42/1.78 ) ] )
% 1.42/1.78 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.42/1.78 ), ==>( 1, 1 )] ) ).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 eqswap(
% 1.42/1.78 clause( 5024, [ =( 'c_HOL_Oabs'( X, Y ), 'c_uminus'( X, Y ) ), ~(
% 1.42/1.78 'class_OrderedGroup_Olordered__ab__group__abs'( Y ) ), ~( 'c_lessequals'(
% 1.42/1.78 X, 'c_0', Y ) ) ] )
% 1.42/1.78 , clause( 5, [ ~( 'class_OrderedGroup_Olordered__ab__group__abs'( X ) ),
% 1.42/1.78 ~( 'c_lessequals'( Y, 'c_0', X ) ), =( 'c_uminus'( Y, X ), 'c_HOL_Oabs'(
% 1.42/1.78 Y, X ) ) ] )
% 1.42/1.78 , 2, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 resolution(
% 1.42/1.78 clause( 5025, [ =( 'c_HOL_Oabs'( X, 't_b' ), 'c_uminus'( X, 't_b' ) ), ~(
% 1.42/1.78 'class_OrderedGroup_Olordered__ab__group__abs'( 't_b' ) ), ~( 'c_less'( X
% 1.42/1.78 , 'c_0', 't_b' ) ) ] )
% 1.42/1.78 , clause( 5024, [ =( 'c_HOL_Oabs'( X, Y ), 'c_uminus'( X, Y ) ), ~(
% 1.42/1.78 'class_OrderedGroup_Olordered__ab__group__abs'( Y ) ), ~( 'c_lessequals'(
% 1.42/1.78 X, 'c_0', Y ) ) ] )
% 1.42/1.78 , 2, clause( 69, [ ~( 'c_less'( X, Y, 't_b' ) ), 'c_lessequals'( X, Y,
% 1.42/1.78 't_b' ) ] )
% 1.42/1.78 , 1, substitution( 0, [ :=( X, X ), :=( Y, 't_b' )] ), substitution( 1, [
% 1.42/1.78 :=( X, X ), :=( Y, 'c_0' )] )).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 resolution(
% 1.42/1.78 clause( 5026, [ =( 'c_HOL_Oabs'( X, 't_b' ), 'c_uminus'( X, 't_b' ) ), ~(
% 1.42/1.78 'c_less'( X, 'c_0', 't_b' ) ) ] )
% 1.42/1.78 , clause( 5025, [ =( 'c_HOL_Oabs'( X, 't_b' ), 'c_uminus'( X, 't_b' ) ),
% 1.42/1.78 ~( 'class_OrderedGroup_Olordered__ab__group__abs'( 't_b' ) ), ~( 'c_less'(
% 1.42/1.78 X, 'c_0', 't_b' ) ) ] )
% 1.42/1.78 , 1, clause( 28, [ 'class_OrderedGroup_Olordered__ab__group__abs'( 't_b' )
% 1.42/1.78 ] )
% 1.42/1.78 , 0, substitution( 0, [ :=( X, X )] ), substitution( 1, [] )).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 eqswap(
% 1.42/1.78 clause( 5027, [ =( 'c_uminus'( X, 't_b' ), 'c_HOL_Oabs'( X, 't_b' ) ), ~(
% 1.42/1.78 'c_less'( X, 'c_0', 't_b' ) ) ] )
% 1.42/1.78 , clause( 5026, [ =( 'c_HOL_Oabs'( X, 't_b' ), 'c_uminus'( X, 't_b' ) ),
% 1.42/1.78 ~( 'c_less'( X, 'c_0', 't_b' ) ) ] )
% 1.42/1.78 , 0, substitution( 0, [ :=( X, X )] )).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 subsumption(
% 1.42/1.78 clause( 72, [ ~( 'c_less'( X, 'c_0', 't_b' ) ), =( 'c_uminus'( X, 't_b' ),
% 1.42/1.78 'c_HOL_Oabs'( X, 't_b' ) ) ] )
% 1.42/1.78 , clause( 5027, [ =( 'c_uminus'( X, 't_b' ), 'c_HOL_Oabs'( X, 't_b' ) ),
% 1.42/1.78 ~( 'c_less'( X, 'c_0', 't_b' ) ) ] )
% 1.42/1.78 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 1 ), ==>( 1,
% 1.42/1.78 0 )] ) ).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 eqswap(
% 1.42/1.78 clause( 5029, [ =( 'c_minus'( 'c_plus'( X, T, Z ), Y, Z ), 'c_plus'(
% 1.42/1.78 'c_minus'( X, Y, Z ), T, Z ) ), ~( 'class_OrderedGroup_Oab__group__add'(
% 1.42/1.78 Z ) ) ] )
% 1.42/1.78 , clause( 9, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( 'c_plus'(
% 1.42/1.78 'c_minus'( Y, Z, X ), T, X ), 'c_minus'( 'c_plus'( Y, T, X ), Z, X ) ) ]
% 1.42/1.78 )
% 1.42/1.78 , 1, substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y ), :=( T, T )] )
% 1.42/1.78 ).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 paramod(
% 1.42/1.78 clause( 5032, [ =( 'c_minus'( 'c_plus'( X, Y, 't_b' ), X, 't_b' ), 'c_plus'(
% 1.42/1.78 'c_0', Y, 't_b' ) ), ~( 'class_OrderedGroup_Oab__group__add'( 't_b' ) ) ]
% 1.42/1.78 )
% 1.42/1.78 , clause( 46, [ =( 'c_minus'( X, X, 't_b' ), 'c_0' ) ] )
% 1.42/1.78 , 0, clause( 5029, [ =( 'c_minus'( 'c_plus'( X, T, Z ), Y, Z ), 'c_plus'(
% 1.42/1.78 'c_minus'( X, Y, Z ), T, Z ) ), ~( 'class_OrderedGroup_Oab__group__add'(
% 1.42/1.78 Z ) ) ] )
% 1.42/1.78 , 0, 9, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ),
% 1.42/1.78 :=( Y, X ), :=( Z, 't_b' ), :=( T, Y )] )).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 paramod(
% 1.42/1.78 clause( 5033, [ =( 'c_minus'( 'c_plus'( X, Y, 't_b' ), X, 't_b' ), Y ), ~(
% 1.42/1.78 'class_OrderedGroup_Oab__group__add'( 't_b' ) ) ] )
% 1.42/1.78 , clause( 52, [ =( 'c_plus'( 'c_0', X, 't_b' ), X ) ] )
% 1.42/1.78 , 0, clause( 5032, [ =( 'c_minus'( 'c_plus'( X, Y, 't_b' ), X, 't_b' ),
% 1.42/1.78 'c_plus'( 'c_0', Y, 't_b' ) ), ~( 'class_OrderedGroup_Oab__group__add'(
% 1.42/1.78 't_b' ) ) ] )
% 1.42/1.78 , 0, 8, substitution( 0, [ :=( X, Y )] ), substitution( 1, [ :=( X, X ),
% 1.42/1.78 :=( Y, Y )] )).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 resolution(
% 1.42/1.78 clause( 5034, [ =( 'c_minus'( 'c_plus'( X, Y, 't_b' ), X, 't_b' ), Y ) ] )
% 1.42/1.78 , clause( 5033, [ =( 'c_minus'( 'c_plus'( X, Y, 't_b' ), X, 't_b' ), Y ),
% 1.42/1.78 ~( 'class_OrderedGroup_Oab__group__add'( 't_b' ) ) ] )
% 1.42/1.78 , 1, clause( 29, [ 'class_OrderedGroup_Oab__group__add'( 't_b' ) ] )
% 1.42/1.78 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [] )
% 1.42/1.78 ).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 subsumption(
% 1.42/1.78 clause( 81, [ =( 'c_minus'( 'c_plus'( X, Y, 't_b' ), X, 't_b' ), Y ) ] )
% 1.42/1.78 , clause( 5034, [ =( 'c_minus'( 'c_plus'( X, Y, 't_b' ), X, 't_b' ), Y ) ]
% 1.42/1.78 )
% 1.42/1.78 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.42/1.78 )] ) ).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 eqswap(
% 1.42/1.78 clause( 5037, [ =( 'c_minus'( 'c_plus'( X, T, Z ), Y, Z ), 'c_plus'(
% 1.42/1.78 'c_minus'( X, Y, Z ), T, Z ) ), ~( 'class_OrderedGroup_Oab__group__add'(
% 1.42/1.78 Z ) ) ] )
% 1.42/1.78 , clause( 9, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( 'c_plus'(
% 1.42/1.78 'c_minus'( Y, Z, X ), T, X ), 'c_minus'( 'c_plus'( Y, T, X ), Z, X ) ) ]
% 1.42/1.78 )
% 1.42/1.78 , 1, substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y ), :=( T, T )] )
% 1.42/1.78 ).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 paramod(
% 1.42/1.78 clause( 5039, [ =( 'c_minus'( 'c_plus'( X, Y, Z ), X, Z ), 'c_plus'( 'c_0'
% 1.42/1.78 , Y, Z ) ), ~( 'class_OrderedGroup_Oab__group__add'( Z ) ), ~(
% 1.42/1.78 'class_OrderedGroup_Oab__group__add'( Z ) ) ] )
% 1.42/1.78 , clause( 13, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.42/1.78 'c_minus'( Y, Y, X ), 'c_0' ) ] )
% 1.42/1.78 , 1, clause( 5037, [ =( 'c_minus'( 'c_plus'( X, T, Z ), Y, Z ), 'c_plus'(
% 1.42/1.78 'c_minus'( X, Y, Z ), T, Z ) ), ~( 'class_OrderedGroup_Oab__group__add'(
% 1.42/1.78 Z ) ) ] )
% 1.42/1.78 , 0, 9, substitution( 0, [ :=( X, Z ), :=( Y, X )] ), substitution( 1, [
% 1.42/1.78 :=( X, X ), :=( Y, X ), :=( Z, Z ), :=( T, Y )] )).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 factor(
% 1.42/1.78 clause( 5041, [ =( 'c_minus'( 'c_plus'( X, Y, Z ), X, Z ), 'c_plus'( 'c_0'
% 1.42/1.78 , Y, Z ) ), ~( 'class_OrderedGroup_Oab__group__add'( Z ) ) ] )
% 1.42/1.78 , clause( 5039, [ =( 'c_minus'( 'c_plus'( X, Y, Z ), X, Z ), 'c_plus'(
% 1.42/1.78 'c_0', Y, Z ) ), ~( 'class_OrderedGroup_Oab__group__add'( Z ) ), ~(
% 1.42/1.78 'class_OrderedGroup_Oab__group__add'( Z ) ) ] )
% 1.42/1.78 , 1, 2, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 subsumption(
% 1.42/1.78 clause( 82, [ ~( 'class_OrderedGroup_Oab__group__add'( Y ) ), =( 'c_minus'(
% 1.42/1.78 'c_plus'( X, Z, Y ), X, Y ), 'c_plus'( 'c_0', Z, Y ) ) ] )
% 1.42/1.78 , clause( 5041, [ =( 'c_minus'( 'c_plus'( X, Y, Z ), X, Z ), 'c_plus'(
% 1.42/1.78 'c_0', Y, Z ) ), ~( 'class_OrderedGroup_Oab__group__add'( Z ) ) ] )
% 1.42/1.78 , substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, Y )] ),
% 1.42/1.78 permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 eqswap(
% 1.42/1.78 clause( 5047, [ =( 'c_minus'( 'c_plus'( X, T, Z ), Y, Z ), 'c_plus'(
% 1.42/1.78 'c_minus'( X, Y, Z ), T, Z ) ), ~( 'class_OrderedGroup_Oab__group__add'(
% 1.42/1.78 Z ) ) ] )
% 1.42/1.78 , clause( 9, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( 'c_plus'(
% 1.42/1.78 'c_minus'( Y, Z, X ), T, X ), 'c_minus'( 'c_plus'( Y, T, X ), Z, X ) ) ]
% 1.42/1.78 )
% 1.42/1.78 , 1, substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y ), :=( T, T )] )
% 1.42/1.78 ).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 paramod(
% 1.42/1.78 clause( 5052, [ =( 'c_minus'( 'c_plus'( 'c_plus'( X, Y, 't_b' ), Z, 't_b' )
% 1.42/1.78 , X, 't_b' ), 'c_plus'( Y, Z, 't_b' ) ), ~(
% 1.42/1.78 'class_OrderedGroup_Oab__group__add'( 't_b' ) ) ] )
% 1.42/1.78 , clause( 81, [ =( 'c_minus'( 'c_plus'( X, Y, 't_b' ), X, 't_b' ), Y ) ] )
% 1.42/1.78 , 0, clause( 5047, [ =( 'c_minus'( 'c_plus'( X, T, Z ), Y, Z ), 'c_plus'(
% 1.42/1.78 'c_minus'( X, Y, Z ), T, Z ) ), ~( 'class_OrderedGroup_Oab__group__add'(
% 1.42/1.78 Z ) ) ] )
% 1.42/1.78 , 0, 12, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 1.42/1.78 :=( X, 'c_plus'( X, Y, 't_b' ) ), :=( Y, X ), :=( Z, 't_b' ), :=( T, Z )] )
% 1.42/1.78 ).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 resolution(
% 1.42/1.78 clause( 5053, [ =( 'c_minus'( 'c_plus'( 'c_plus'( X, Y, 't_b' ), Z, 't_b' )
% 1.42/1.78 , X, 't_b' ), 'c_plus'( Y, Z, 't_b' ) ) ] )
% 1.42/1.78 , clause( 5052, [ =( 'c_minus'( 'c_plus'( 'c_plus'( X, Y, 't_b' ), Z, 't_b'
% 1.42/1.78 ), X, 't_b' ), 'c_plus'( Y, Z, 't_b' ) ), ~(
% 1.42/1.78 'class_OrderedGroup_Oab__group__add'( 't_b' ) ) ] )
% 1.42/1.78 , 1, clause( 29, [ 'class_OrderedGroup_Oab__group__add'( 't_b' ) ] )
% 1.42/1.78 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 1.42/1.78 substitution( 1, [] )).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 subsumption(
% 1.42/1.78 clause( 83, [ =( 'c_minus'( 'c_plus'( 'c_plus'( X, Y, 't_b' ), Z, 't_b' ),
% 1.42/1.78 X, 't_b' ), 'c_plus'( Y, Z, 't_b' ) ) ] )
% 1.42/1.78 , clause( 5053, [ =( 'c_minus'( 'c_plus'( 'c_plus'( X, Y, 't_b' ), Z, 't_b'
% 1.42/1.78 ), X, 't_b' ), 'c_plus'( Y, Z, 't_b' ) ) ] )
% 1.42/1.78 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 1.42/1.78 permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 eqswap(
% 1.42/1.78 clause( 5056, [ =( Y, 'c_minus'( 'c_plus'( X, Y, 't_b' ), X, 't_b' ) ) ] )
% 1.42/1.78 , clause( 81, [ =( 'c_minus'( 'c_plus'( X, Y, 't_b' ), X, 't_b' ), Y ) ] )
% 1.42/1.78 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 paramod(
% 1.42/1.78 clause( 5057, [ =( X, 'c_minus'( X, 'c_0', 't_b' ) ), ~(
% 1.42/1.78 'class_Ring__and__Field_Oordered__idom'( 't_b' ) ) ] )
% 1.42/1.78 , clause( 53, [ =( 'c_plus'( 'c_0', X, Y ), X ), ~(
% 1.42/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.42/1.78 , 0, clause( 5056, [ =( Y, 'c_minus'( 'c_plus'( X, Y, 't_b' ), X, 't_b' ) )
% 1.42/1.78 ] )
% 1.42/1.78 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, 't_b' )] ), substitution( 1
% 1.42/1.78 , [ :=( X, 'c_0' ), :=( Y, X )] )).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 resolution(
% 1.42/1.78 clause( 5058, [ =( X, 'c_minus'( X, 'c_0', 't_b' ) ) ] )
% 1.42/1.78 , clause( 5057, [ =( X, 'c_minus'( X, 'c_0', 't_b' ) ), ~(
% 1.42/1.78 'class_Ring__and__Field_Oordered__idom'( 't_b' ) ) ] )
% 1.42/1.78 , 1, clause( 2, [ 'class_Ring__and__Field_Oordered__idom'( 't_b' ) ] )
% 1.42/1.78 , 0, substitution( 0, [ :=( X, X )] ), substitution( 1, [] )).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 eqswap(
% 1.42/1.78 clause( 5059, [ =( 'c_minus'( X, 'c_0', 't_b' ), X ) ] )
% 1.42/1.78 , clause( 5058, [ =( X, 'c_minus'( X, 'c_0', 't_b' ) ) ] )
% 1.42/1.78 , 0, substitution( 0, [ :=( X, X )] )).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 subsumption(
% 1.42/1.78 clause( 87, [ =( 'c_minus'( X, 'c_0', 't_b' ), X ) ] )
% 1.42/1.78 , clause( 5059, [ =( 'c_minus'( X, 'c_0', 't_b' ), X ) ] )
% 1.42/1.78 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 resolution(
% 1.42/1.78 clause( 5060, [ 'c_lessequals'( X, Y, Z ), ~(
% 1.42/1.78 'class_Ring__and__Field_Oordered__idom'( Z ) ), ~(
% 1.42/1.78 'class_Orderings_Olinorder'( Z ) ), 'c_lessequals'( Y, X, Z ) ] )
% 1.42/1.78 , clause( 68, [ ~( 'c_less'( X, Y, Z ) ), 'c_lessequals'( X, Y, Z ), ~(
% 1.42/1.78 'class_Ring__and__Field_Oordered__idom'( Z ) ) ] )
% 1.42/1.78 , 0, clause( 15, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_less'( Y, Z, X
% 1.42/1.78 ), 'c_lessequals'( Z, Y, X ) ] )
% 1.42/1.78 , 1, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 1.42/1.78 substitution( 1, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] )).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 resolution(
% 1.42/1.78 clause( 5064, [ 'c_lessequals'( X, Y, Z ), ~(
% 1.42/1.78 'class_Ring__and__Field_Oordered__idom'( Z ) ), 'c_lessequals'( Y, X, Z )
% 1.42/1.78 , ~( 'class_Ring__and__Field_Oordered__idom'( Z ) ) ] )
% 1.42/1.78 , clause( 5060, [ 'c_lessequals'( X, Y, Z ), ~(
% 1.42/1.78 'class_Ring__and__Field_Oordered__idom'( Z ) ), ~(
% 1.42/1.78 'class_Orderings_Olinorder'( Z ) ), 'c_lessequals'( Y, X, Z ) ] )
% 1.42/1.78 , 2, clause( 23, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.42/1.78 'class_Orderings_Olinorder'( X ) ] )
% 1.42/1.78 , 1, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 1.42/1.78 substitution( 1, [ :=( X, Z )] )).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 factor(
% 1.42/1.78 clause( 5066, [ 'c_lessequals'( X, Y, Z ), ~(
% 1.42/1.78 'class_Ring__and__Field_Oordered__idom'( Z ) ), 'c_lessequals'( Y, X, Z )
% 1.42/1.78 ] )
% 1.42/1.78 , clause( 5064, [ 'c_lessequals'( X, Y, Z ), ~(
% 1.42/1.78 'class_Ring__and__Field_Oordered__idom'( Z ) ), 'c_lessequals'( Y, X, Z )
% 1.42/1.78 , ~( 'class_Ring__and__Field_Oordered__idom'( Z ) ) ] )
% 1.42/1.78 , 1, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 subsumption(
% 1.42/1.78 clause( 89, [ 'c_lessequals'( Y, Z, X ), 'c_lessequals'( Z, Y, X ), ~(
% 1.42/1.78 'class_Ring__and__Field_Oordered__idom'( X ) ) ] )
% 1.42/1.78 , clause( 5066, [ 'c_lessequals'( X, Y, Z ), ~(
% 1.42/1.78 'class_Ring__and__Field_Oordered__idom'( Z ) ), 'c_lessequals'( Y, X, Z )
% 1.42/1.78 ] )
% 1.42/1.78 , substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, X )] ),
% 1.42/1.78 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 2 ), ==>( 2, 1 )] ) ).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 resolution(
% 1.42/1.78 clause( 5068, [ 'c_lessequals'( X, Y, 't_b' ), ~(
% 1.42/1.78 'class_Orderings_Olinorder'( 't_b' ) ), 'c_lessequals'( Y, X, 't_b' ) ]
% 1.42/1.78 )
% 1.42/1.78 , clause( 69, [ ~( 'c_less'( X, Y, 't_b' ) ), 'c_lessequals'( X, Y, 't_b' )
% 1.42/1.78 ] )
% 1.42/1.78 , 0, clause( 15, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_less'( Y, Z, X
% 1.42/1.78 ), 'c_lessequals'( Z, Y, X ) ] )
% 1.42/1.78 , 1, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [ :=( X
% 1.42/1.78 , 't_b' ), :=( Y, X ), :=( Z, Y )] )).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 resolution(
% 1.42/1.78 clause( 5071, [ 'c_lessequals'( X, Y, 't_b' ), 'c_lessequals'( Y, X, 't_b'
% 1.42/1.78 ) ] )
% 1.42/1.78 , clause( 5068, [ 'c_lessequals'( X, Y, 't_b' ), ~(
% 1.42/1.78 'class_Orderings_Olinorder'( 't_b' ) ), 'c_lessequals'( Y, X, 't_b' ) ]
% 1.42/1.78 )
% 1.42/1.78 , 1, clause( 31, [ 'class_Orderings_Olinorder'( 't_b' ) ] )
% 1.42/1.78 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [] )
% 1.42/1.78 ).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 subsumption(
% 1.42/1.78 clause( 90, [ 'c_lessequals'( X, Y, 't_b' ), 'c_lessequals'( Y, X, 't_b' )
% 1.42/1.78 ] )
% 1.42/1.78 , clause( 5071, [ 'c_lessequals'( X, Y, 't_b' ), 'c_lessequals'( Y, X,
% 1.42/1.78 't_b' ) ] )
% 1.42/1.78 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.42/1.78 ), ==>( 1, 1 )] ) ).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 resolution(
% 1.42/1.78 clause( 5073, [ 'c_less'( X, Y, 't_b' ), 'c_lessequals'( Y, X, 't_b' ) ] )
% 1.42/1.78 , clause( 15, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_less'( Y, Z, X )
% 1.42/1.78 , 'c_lessequals'( Z, Y, X ) ] )
% 1.42/1.78 , 0, clause( 31, [ 'class_Orderings_Olinorder'( 't_b' ) ] )
% 1.42/1.78 , 0, substitution( 0, [ :=( X, 't_b' ), :=( Y, X ), :=( Z, Y )] ),
% 1.42/1.78 substitution( 1, [] )).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 subsumption(
% 1.42/1.78 clause( 94, [ 'c_less'( X, Y, 't_b' ), 'c_lessequals'( Y, X, 't_b' ) ] )
% 1.42/1.78 , clause( 5073, [ 'c_less'( X, Y, 't_b' ), 'c_lessequals'( Y, X, 't_b' ) ]
% 1.42/1.78 )
% 1.42/1.78 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.42/1.78 ), ==>( 1, 1 )] ) ).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 resolution(
% 1.42/1.78 clause( 5074, [ 'c_less'( Y, Z, X ), 'c_lessequals'( Z, Y, X ), ~(
% 1.42/1.78 'class_Ring__and__Field_Oordered__idom'( X ) ) ] )
% 1.42/1.78 , clause( 15, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_less'( Y, Z, X )
% 1.42/1.78 , 'c_lessequals'( Z, Y, X ) ] )
% 1.42/1.78 , 0, clause( 23, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.42/1.78 'class_Orderings_Olinorder'( X ) ] )
% 1.42/1.78 , 1, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 1.42/1.78 substitution( 1, [ :=( X, X )] )).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 subsumption(
% 1.42/1.78 clause( 95, [ 'c_less'( X, Y, Z ), 'c_lessequals'( Y, X, Z ), ~(
% 1.42/1.78 'class_Ring__and__Field_Oordered__idom'( Z ) ) ] )
% 1.42/1.78 , clause( 5074, [ 'c_less'( Y, Z, X ), 'c_lessequals'( Z, Y, X ), ~(
% 1.42/1.78 'class_Ring__and__Field_Oordered__idom'( X ) ) ] )
% 1.42/1.78 , substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] ),
% 1.42/1.78 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 factor(
% 1.42/1.78 clause( 5075, [ 'c_lessequals'( X, X, 't_b' ) ] )
% 1.42/1.78 , clause( 90, [ 'c_lessequals'( X, Y, 't_b' ), 'c_lessequals'( Y, X, 't_b'
% 1.42/1.78 ) ] )
% 1.42/1.78 , 0, 1, substitution( 0, [ :=( X, X ), :=( Y, X )] )).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 subsumption(
% 1.42/1.78 clause( 97, [ 'c_lessequals'( X, X, 't_b' ) ] )
% 1.42/1.78 , clause( 5075, [ 'c_lessequals'( X, X, 't_b' ) ] )
% 1.42/1.78 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 paramod(
% 1.42/1.78 clause( 5077, [ 'c_lessequals'( Y, Z, 't_b' ), ~(
% 1.42/1.78 'class_OrderedGroup_Opordered__ab__group__add'( 't_b' ) ), ~(
% 1.42/1.78 'c_lessequals'( 'c_plus'( X, Y, 't_b' ), 'c_plus'( Z, X, 't_b' ), 't_b' )
% 1.42/1.78 ) ] )
% 1.42/1.78 , clause( 81, [ =( 'c_minus'( 'c_plus'( X, Y, 't_b' ), X, 't_b' ), Y ) ] )
% 1.42/1.78 , 0, clause( 10, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.42/1.78 , ~( 'c_lessequals'( Y, 'c_plus'( Z, T, X ), X ) ), 'c_lessequals'(
% 1.42/1.78 'c_minus'( Y, T, X ), Z, X ) ] )
% 1.42/1.78 , 2, 1, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 1.42/1.78 :=( X, 't_b' ), :=( Y, 'c_plus'( X, Y, 't_b' ) ), :=( Z, Z ), :=( T, X )] )
% 1.42/1.78 ).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 resolution(
% 1.42/1.78 clause( 5078, [ 'c_lessequals'( X, Y, 't_b' ), ~( 'c_lessequals'( 'c_plus'(
% 1.42/1.78 Z, X, 't_b' ), 'c_plus'( Y, Z, 't_b' ), 't_b' ) ) ] )
% 1.42/1.78 , clause( 5077, [ 'c_lessequals'( Y, Z, 't_b' ), ~(
% 1.42/1.78 'class_OrderedGroup_Opordered__ab__group__add'( 't_b' ) ), ~(
% 1.42/1.78 'c_lessequals'( 'c_plus'( X, Y, 't_b' ), 'c_plus'( Z, X, 't_b' ), 't_b' )
% 1.42/1.78 ) ] )
% 1.42/1.78 , 1, clause( 37, [ 'class_OrderedGroup_Opordered__ab__group__add'( 't_b' )
% 1.42/1.78 ] )
% 1.42/1.78 , 0, substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] ),
% 1.42/1.78 substitution( 1, [] )).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 subsumption(
% 1.42/1.78 clause( 111, [ ~( 'c_lessequals'( 'c_plus'( X, Y, 't_b' ), 'c_plus'( Z, X,
% 1.42/1.78 't_b' ), 't_b' ) ), 'c_lessequals'( Y, Z, 't_b' ) ] )
% 1.42/1.78 , clause( 5078, [ 'c_lessequals'( X, Y, 't_b' ), ~( 'c_lessequals'(
% 1.42/1.78 'c_plus'( Z, X, 't_b' ), 'c_plus'( Y, Z, 't_b' ), 't_b' ) ) ] )
% 1.42/1.78 , substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, X )] ),
% 1.42/1.78 permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 resolution(
% 1.42/1.78 clause( 5079, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( 't_b' )
% 1.42/1.78 ), 'c_lessequals'( 'c_minus'( X, Y, 't_b' ), 'c_0', 't_b' ),
% 1.42/1.78 'c_lessequals'( Y, X, 't_b' ) ] )
% 1.42/1.78 , clause( 11, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.42/1.78 ~( 'c_lessequals'( Y, Z, X ) ), 'c_lessequals'( 'c_minus'( Y, Z, X ),
% 1.42/1.78 'c_0', X ) ] )
% 1.42/1.78 , 1, clause( 90, [ 'c_lessequals'( X, Y, 't_b' ), 'c_lessequals'( Y, X,
% 1.42/1.78 't_b' ) ] )
% 1.42/1.78 , 0, substitution( 0, [ :=( X, 't_b' ), :=( Y, X ), :=( Z, Y )] ),
% 1.42/1.78 substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 resolution(
% 1.42/1.78 clause( 5080, [ 'c_lessequals'( 'c_minus'( X, Y, 't_b' ), 'c_0', 't_b' ),
% 1.42/1.78 'c_lessequals'( Y, X, 't_b' ) ] )
% 1.42/1.78 , clause( 5079, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( 't_b'
% 1.42/1.78 ) ), 'c_lessequals'( 'c_minus'( X, Y, 't_b' ), 'c_0', 't_b' ),
% 1.42/1.78 'c_lessequals'( Y, X, 't_b' ) ] )
% 1.42/1.78 , 0, clause( 37, [ 'class_OrderedGroup_Opordered__ab__group__add'( 't_b' )
% 1.42/1.78 ] )
% 1.42/1.78 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [] )
% 1.42/1.78 ).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 subsumption(
% 1.42/1.78 clause( 126, [ 'c_lessequals'( 'c_minus'( X, Y, 't_b' ), 'c_0', 't_b' ),
% 1.42/1.78 'c_lessequals'( Y, X, 't_b' ) ] )
% 1.42/1.78 , clause( 5080, [ 'c_lessequals'( 'c_minus'( X, Y, 't_b' ), 'c_0', 't_b' )
% 1.42/1.78 , 'c_lessequals'( Y, X, 't_b' ) ] )
% 1.42/1.78 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.42/1.78 ), ==>( 1, 1 )] ) ).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 eqswap(
% 1.42/1.78 clause( 5081, [ =( 'c_HOL_Oabs'( X, Y ), 'c_uminus'( X, Y ) ), ~(
% 1.42/1.78 'class_OrderedGroup_Olordered__ab__group__abs'( Y ) ), ~( 'c_lessequals'(
% 1.42/1.78 X, 'c_0', Y ) ) ] )
% 1.42/1.78 , clause( 5, [ ~( 'class_OrderedGroup_Olordered__ab__group__abs'( X ) ),
% 1.42/1.78 ~( 'c_lessequals'( Y, 'c_0', X ) ), =( 'c_uminus'( Y, X ), 'c_HOL_Oabs'(
% 1.42/1.78 Y, X ) ) ] )
% 1.42/1.78 , 2, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 resolution(
% 1.42/1.78 clause( 5082, [ =( 'c_HOL_Oabs'( 'c_minus'( X, Y, Z ), Z ), 'c_uminus'(
% 1.42/1.78 'c_minus'( X, Y, Z ), Z ) ), ~(
% 1.42/1.78 'class_OrderedGroup_Olordered__ab__group__abs'( Z ) ), ~(
% 1.42/1.78 'class_OrderedGroup_Opordered__ab__group__add'( Z ) ), ~( 'c_lessequals'(
% 1.42/1.78 X, Y, Z ) ) ] )
% 1.42/1.78 , clause( 5081, [ =( 'c_HOL_Oabs'( X, Y ), 'c_uminus'( X, Y ) ), ~(
% 1.42/1.78 'class_OrderedGroup_Olordered__ab__group__abs'( Y ) ), ~( 'c_lessequals'(
% 1.42/1.78 X, 'c_0', Y ) ) ] )
% 1.42/1.78 , 2, clause( 11, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.42/1.78 , ~( 'c_lessequals'( Y, Z, X ) ), 'c_lessequals'( 'c_minus'( Y, Z, X ),
% 1.42/1.78 'c_0', X ) ] )
% 1.42/1.78 , 2, substitution( 0, [ :=( X, 'c_minus'( X, Y, Z ) ), :=( Y, Z )] ),
% 1.42/1.78 substitution( 1, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] )).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 resolution(
% 1.42/1.78 clause( 5083, [ =( 'c_HOL_Oabs'( 'c_minus'( X, Y, Z ), Z ), 'c_uminus'(
% 1.42/1.78 'c_minus'( X, Y, Z ), Z ) ), ~(
% 1.42/1.78 'class_OrderedGroup_Olordered__ab__group__abs'( Z ) ), ~( 'c_lessequals'(
% 1.42/1.78 X, Y, Z ) ), ~( 'class_OrderedGroup_Olordered__ab__group__abs'( Z ) ) ]
% 1.42/1.78 )
% 1.42/1.78 , clause( 5082, [ =( 'c_HOL_Oabs'( 'c_minus'( X, Y, Z ), Z ), 'c_uminus'(
% 1.42/1.78 'c_minus'( X, Y, Z ), Z ) ), ~(
% 1.42/1.78 'class_OrderedGroup_Olordered__ab__group__abs'( Z ) ), ~(
% 1.42/1.78 'class_OrderedGroup_Opordered__ab__group__add'( Z ) ), ~( 'c_lessequals'(
% 1.42/1.78 X, Y, Z ) ) ] )
% 1.42/1.78 , 2, clause( 20, [ ~( 'class_OrderedGroup_Olordered__ab__group__abs'( X ) )
% 1.42/1.78 , 'class_OrderedGroup_Opordered__ab__group__add'( X ) ] )
% 1.42/1.78 , 1, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 1.42/1.78 substitution( 1, [ :=( X, Z )] )).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 eqswap(
% 1.42/1.78 clause( 5084, [ =( 'c_uminus'( 'c_minus'( X, Y, Z ), Z ), 'c_HOL_Oabs'(
% 1.42/1.78 'c_minus'( X, Y, Z ), Z ) ), ~(
% 1.42/1.78 'class_OrderedGroup_Olordered__ab__group__abs'( Z ) ), ~( 'c_lessequals'(
% 1.42/1.78 X, Y, Z ) ), ~( 'class_OrderedGroup_Olordered__ab__group__abs'( Z ) ) ]
% 1.42/1.78 )
% 1.42/1.78 , clause( 5083, [ =( 'c_HOL_Oabs'( 'c_minus'( X, Y, Z ), Z ), 'c_uminus'(
% 1.42/1.78 'c_minus'( X, Y, Z ), Z ) ), ~(
% 1.42/1.78 'class_OrderedGroup_Olordered__ab__group__abs'( Z ) ), ~( 'c_lessequals'(
% 1.42/1.78 X, Y, Z ) ), ~( 'class_OrderedGroup_Olordered__ab__group__abs'( Z ) ) ]
% 1.42/1.78 )
% 1.42/1.78 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 factor(
% 1.42/1.78 clause( 5085, [ =( 'c_uminus'( 'c_minus'( X, Y, Z ), Z ), 'c_HOL_Oabs'(
% 1.42/1.78 'c_minus'( X, Y, Z ), Z ) ), ~(
% 1.42/1.78 'class_OrderedGroup_Olordered__ab__group__abs'( Z ) ), ~( 'c_lessequals'(
% 1.42/1.78 X, Y, Z ) ) ] )
% 1.42/1.78 , clause( 5084, [ =( 'c_uminus'( 'c_minus'( X, Y, Z ), Z ), 'c_HOL_Oabs'(
% 1.42/1.78 'c_minus'( X, Y, Z ), Z ) ), ~(
% 1.42/1.78 'class_OrderedGroup_Olordered__ab__group__abs'( Z ) ), ~( 'c_lessequals'(
% 1.42/1.78 X, Y, Z ) ), ~( 'class_OrderedGroup_Olordered__ab__group__abs'( Z ) ) ]
% 1.42/1.78 )
% 1.42/1.78 , 1, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 subsumption(
% 1.42/1.78 clause( 135, [ ~( 'c_lessequals'( Y, Z, X ) ), ~(
% 1.42/1.78 'class_OrderedGroup_Olordered__ab__group__abs'( X ) ), =( 'c_uminus'(
% 1.42/1.78 'c_minus'( Y, Z, X ), X ), 'c_HOL_Oabs'( 'c_minus'( Y, Z, X ), X ) ) ] )
% 1.42/1.78 , clause( 5085, [ =( 'c_uminus'( 'c_minus'( X, Y, Z ), Z ), 'c_HOL_Oabs'(
% 1.42/1.78 'c_minus'( X, Y, Z ), Z ) ), ~(
% 1.42/1.78 'class_OrderedGroup_Olordered__ab__group__abs'( Z ) ), ~( 'c_lessequals'(
% 1.42/1.78 X, Y, Z ) ) ] )
% 1.42/1.78 , substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, X )] ),
% 1.42/1.78 permutation( 0, [ ==>( 0, 2 ), ==>( 1, 1 ), ==>( 2, 0 )] ) ).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 resolution(
% 1.42/1.78 clause( 5087, [ ~( 'c_lessequals'( Y, Z, X ) ), 'c_lessequals'( 'c_minus'(
% 1.42/1.78 Y, Z, X ), 'c_0', X ), ~( 'class_OrderedGroup_Olordered__ab__group__abs'(
% 1.42/1.78 X ) ) ] )
% 1.42/1.78 , clause( 11, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.42/1.78 ~( 'c_lessequals'( Y, Z, X ) ), 'c_lessequals'( 'c_minus'( Y, Z, X ),
% 1.42/1.78 'c_0', X ) ] )
% 1.42/1.78 , 0, clause( 20, [ ~( 'class_OrderedGroup_Olordered__ab__group__abs'( X ) )
% 1.42/1.78 , 'class_OrderedGroup_Opordered__ab__group__add'( X ) ] )
% 1.42/1.78 , 1, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 1.42/1.78 substitution( 1, [ :=( X, X )] )).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 subsumption(
% 1.42/1.78 clause( 137, [ ~( 'c_lessequals'( X, Y, Z ) ), 'c_lessequals'( 'c_minus'( X
% 1.42/1.78 , Y, Z ), 'c_0', Z ), ~( 'class_OrderedGroup_Olordered__ab__group__abs'(
% 1.42/1.78 Z ) ) ] )
% 1.42/1.78 , clause( 5087, [ ~( 'c_lessequals'( Y, Z, X ) ), 'c_lessequals'( 'c_minus'(
% 1.42/1.78 Y, Z, X ), 'c_0', X ), ~( 'class_OrderedGroup_Olordered__ab__group__abs'(
% 1.42/1.78 X ) ) ] )
% 1.42/1.78 , substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] ),
% 1.42/1.78 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 resolution(
% 1.42/1.78 clause( 5088, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( 't_b' )
% 1.42/1.78 ), 'c_lessequals'( 'c_minus'( 'v_k'( X ), 'v_f'( X ), 't_b' ), 'c_0',
% 1.42/1.78 't_b' ) ] )
% 1.42/1.78 , clause( 11, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.42/1.78 ~( 'c_lessequals'( Y, Z, X ) ), 'c_lessequals'( 'c_minus'( Y, Z, X ),
% 1.42/1.78 'c_0', X ) ] )
% 1.42/1.78 , 1, clause( 0, [ 'c_lessequals'( 'v_k'( X ), 'v_f'( X ), 't_b' ) ] )
% 1.42/1.78 , 0, substitution( 0, [ :=( X, 't_b' ), :=( Y, 'v_k'( X ) ), :=( Z, 'v_f'(
% 1.42/1.78 X ) )] ), substitution( 1, [ :=( X, X )] )).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 resolution(
% 1.42/1.78 clause( 5089, [ 'c_lessequals'( 'c_minus'( 'v_k'( X ), 'v_f'( X ), 't_b' )
% 1.42/1.78 , 'c_0', 't_b' ) ] )
% 1.42/1.78 , clause( 5088, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( 't_b'
% 1.42/1.78 ) ), 'c_lessequals'( 'c_minus'( 'v_k'( X ), 'v_f'( X ), 't_b' ), 'c_0',
% 1.42/1.78 't_b' ) ] )
% 1.42/1.78 , 0, clause( 37, [ 'class_OrderedGroup_Opordered__ab__group__add'( 't_b' )
% 1.42/1.78 ] )
% 1.42/1.78 , 0, substitution( 0, [ :=( X, X )] ), substitution( 1, [] )).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 subsumption(
% 1.42/1.78 clause( 139, [ 'c_lessequals'( 'c_minus'( 'v_k'( X ), 'v_f'( X ), 't_b' ),
% 1.42/1.78 'c_0', 't_b' ) ] )
% 1.42/1.78 , clause( 5089, [ 'c_lessequals'( 'c_minus'( 'v_k'( X ), 'v_f'( X ), 't_b'
% 1.42/1.78 ), 'c_0', 't_b' ) ] )
% 1.42/1.78 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 eqswap(
% 1.42/1.78 clause( 5090, [ =( 'c_plus'( X, Y, Z ), 'c_minus'( X, 'c_uminus'( Y, Z ), Z
% 1.42/1.78 ) ), ~( 'class_OrderedGroup_Oab__group__add'( Z ) ) ] )
% 1.42/1.78 , clause( 12, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.42/1.78 'c_minus'( Y, 'c_uminus'( Z, X ), X ), 'c_plus'( Y, Z, X ) ) ] )
% 1.42/1.78 , 1, substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] )).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 resolution(
% 1.42/1.78 clause( 5091, [ =( 'c_plus'( X, Y, Z ), 'c_minus'( X, 'c_uminus'( Y, Z ), Z
% 1.42/1.78 ) ), ~( 'class_Ring__and__Field_Oordered__idom'( Z ) ) ] )
% 1.42/1.78 , clause( 5090, [ =( 'c_plus'( X, Y, Z ), 'c_minus'( X, 'c_uminus'( Y, Z )
% 1.42/1.78 , Z ) ), ~( 'class_OrderedGroup_Oab__group__add'( Z ) ) ] )
% 1.42/1.78 , 1, clause( 25, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.42/1.78 'class_OrderedGroup_Oab__group__add'( X ) ] )
% 1.42/1.78 , 1, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 1.42/1.78 substitution( 1, [ :=( X, Z )] )).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 eqswap(
% 1.42/1.78 clause( 5092, [ =( 'c_minus'( X, 'c_uminus'( Y, Z ), Z ), 'c_plus'( X, Y, Z
% 1.42/1.78 ) ), ~( 'class_Ring__and__Field_Oordered__idom'( Z ) ) ] )
% 1.42/1.78 , clause( 5091, [ =( 'c_plus'( X, Y, Z ), 'c_minus'( X, 'c_uminus'( Y, Z )
% 1.42/1.78 , Z ) ), ~( 'class_Ring__and__Field_Oordered__idom'( Z ) ) ] )
% 1.42/1.78 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 subsumption(
% 1.42/1.78 clause( 153, [ =( 'c_minus'( X, 'c_uminus'( Y, Z ), Z ), 'c_plus'( X, Y, Z
% 1.42/1.78 ) ), ~( 'class_Ring__and__Field_Oordered__idom'( Z ) ) ] )
% 1.42/1.78 , clause( 5092, [ =( 'c_minus'( X, 'c_uminus'( Y, Z ), Z ), 'c_plus'( X, Y
% 1.42/1.78 , Z ) ), ~( 'class_Ring__and__Field_Oordered__idom'( Z ) ) ] )
% 1.42/1.78 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 1.42/1.78 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 )] ) ).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 eqswap(
% 1.42/1.78 clause( 5093, [ =( 'c_plus'( X, Y, Z ), 'c_minus'( X, 'c_uminus'( Y, Z ), Z
% 1.42/1.78 ) ), ~( 'class_OrderedGroup_Oab__group__add'( Z ) ) ] )
% 1.42/1.78 , clause( 12, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.42/1.78 'c_minus'( Y, 'c_uminus'( Z, X ), X ), 'c_plus'( Y, Z, X ) ) ] )
% 1.42/1.78 , 1, substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] )).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 paramod(
% 1.42/1.78 clause( 5095, [ =( 'c_plus'( 'c_uminus'( X, Y ), X, Y ), 'c_0' ), ~(
% 1.42/1.78 'class_OrderedGroup_Oab__group__add'( Y ) ), ~(
% 1.42/1.78 'class_OrderedGroup_Oab__group__add'( Y ) ) ] )
% 1.42/1.78 , clause( 13, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.42/1.78 'c_minus'( Y, Y, X ), 'c_0' ) ] )
% 1.42/1.78 , 1, clause( 5093, [ =( 'c_plus'( X, Y, Z ), 'c_minus'( X, 'c_uminus'( Y, Z
% 1.42/1.78 ), Z ) ), ~( 'class_OrderedGroup_Oab__group__add'( Z ) ) ] )
% 1.42/1.78 , 0, 7, substitution( 0, [ :=( X, Y ), :=( Y, 'c_uminus'( X, Y ) )] ),
% 1.42/1.78 substitution( 1, [ :=( X, 'c_uminus'( X, Y ) ), :=( Y, X ), :=( Z, Y )] )
% 1.42/1.78 ).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 factor(
% 1.42/1.78 clause( 5096, [ =( 'c_plus'( 'c_uminus'( X, Y ), X, Y ), 'c_0' ), ~(
% 1.42/1.78 'class_OrderedGroup_Oab__group__add'( Y ) ) ] )
% 1.42/1.78 , clause( 5095, [ =( 'c_plus'( 'c_uminus'( X, Y ), X, Y ), 'c_0' ), ~(
% 1.42/1.78 'class_OrderedGroup_Oab__group__add'( Y ) ), ~(
% 1.42/1.78 'class_OrderedGroup_Oab__group__add'( Y ) ) ] )
% 1.42/1.78 , 1, 2, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 subsumption(
% 1.42/1.78 clause( 162, [ ~( 'class_OrderedGroup_Oab__group__add'( Y ) ), =( 'c_plus'(
% 1.42/1.78 'c_uminus'( X, Y ), X, Y ), 'c_0' ) ] )
% 1.42/1.78 , clause( 5096, [ =( 'c_plus'( 'c_uminus'( X, Y ), X, Y ), 'c_0' ), ~(
% 1.42/1.78 'class_OrderedGroup_Oab__group__add'( Y ) ) ] )
% 1.42/1.78 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 1
% 1.42/1.78 ), ==>( 1, 0 )] ) ).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 eqswap(
% 1.42/1.78 clause( 5099, [ =( 'c_minus'( Y, X, Z ), 'c_uminus'( 'c_minus'( X, Y, Z ),
% 1.42/1.78 Z ) ), ~( 'class_OrderedGroup_Oab__group__add'( Z ) ) ] )
% 1.42/1.78 , clause( 14, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.42/1.78 'c_uminus'( 'c_minus'( Y, Z, X ), X ), 'c_minus'( Z, Y, X ) ) ] )
% 1.42/1.78 , 1, substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] )).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 resolution(
% 1.42/1.78 clause( 5100, [ =( 'c_minus'( X, Y, Z ), 'c_uminus'( 'c_minus'( Y, X, Z ),
% 1.42/1.78 Z ) ), ~( 'class_Ring__and__Field_Oordered__idom'( Z ) ) ] )
% 1.42/1.78 , clause( 5099, [ =( 'c_minus'( Y, X, Z ), 'c_uminus'( 'c_minus'( X, Y, Z )
% 1.42/1.78 , Z ) ), ~( 'class_OrderedGroup_Oab__group__add'( Z ) ) ] )
% 1.42/1.78 , 1, clause( 25, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.42/1.78 'class_OrderedGroup_Oab__group__add'( X ) ] )
% 1.42/1.78 , 1, substitution( 0, [ :=( X, Y ), :=( Y, X ), :=( Z, Z )] ),
% 1.42/1.78 substitution( 1, [ :=( X, Z )] )).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 eqswap(
% 1.42/1.78 clause( 5101, [ =( 'c_uminus'( 'c_minus'( Y, X, Z ), Z ), 'c_minus'( X, Y,
% 1.42/1.78 Z ) ), ~( 'class_Ring__and__Field_Oordered__idom'( Z ) ) ] )
% 1.42/1.78 , clause( 5100, [ =( 'c_minus'( X, Y, Z ), 'c_uminus'( 'c_minus'( Y, X, Z )
% 1.42/1.78 , Z ) ), ~( 'class_Ring__and__Field_Oordered__idom'( Z ) ) ] )
% 1.42/1.78 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 subsumption(
% 1.42/1.78 clause( 175, [ =( 'c_uminus'( 'c_minus'( X, Y, Z ), Z ), 'c_minus'( Y, X, Z
% 1.42/1.78 ) ), ~( 'class_Ring__and__Field_Oordered__idom'( Z ) ) ] )
% 1.42/1.78 , clause( 5101, [ =( 'c_uminus'( 'c_minus'( Y, X, Z ), Z ), 'c_minus'( X, Y
% 1.42/1.78 , Z ) ), ~( 'class_Ring__and__Field_Oordered__idom'( Z ) ) ] )
% 1.42/1.78 , substitution( 0, [ :=( X, Y ), :=( Y, X ), :=( Z, Z )] ),
% 1.42/1.78 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 )] ) ).
% 1.42/1.78
% 1.42/1.78
% 1.42/1.78 eqswap(
% 1.42/1.78 clause( 5103, [ =( 'c_minus'( Y, X, Z ), 'c_uminus'( 'c_minus'( X, Y, Z ),
% 1.42/1.78 Z ) ), ~( 'class_OrderedGroup_Oab__group__add'( Z ) ) ] )
% 1.42/1.78 , clause( 14, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.42/1.78 'c_uminus'( 'c_minus'( Y, Z, X ), X ), 'c_minus'( Z, Y, X ) ) ] )
% 1.42/1.78 , 1, substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 paramod(
% 1.43/1.78 clause( 5109, [ =( 'c_minus'( 'c_uminus'( X, Y ), Z, Y ), 'c_uminus'(
% 1.43/1.78 'c_plus'( Z, X, Y ), Y ) ), ~( 'class_OrderedGroup_Oab__group__add'( Y )
% 1.43/1.78 ), ~( 'class_OrderedGroup_Oab__group__add'( Y ) ) ] )
% 1.43/1.78 , clause( 12, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.43/1.78 'c_minus'( Y, 'c_uminus'( Z, X ), X ), 'c_plus'( Y, Z, X ) ) ] )
% 1.43/1.78 , 1, clause( 5103, [ =( 'c_minus'( Y, X, Z ), 'c_uminus'( 'c_minus'( X, Y,
% 1.43/1.78 Z ), Z ) ), ~( 'class_OrderedGroup_Oab__group__add'( Z ) ) ] )
% 1.43/1.78 , 0, 8, substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, X )] ),
% 1.43/1.78 substitution( 1, [ :=( X, Z ), :=( Y, 'c_uminus'( X, Y ) ), :=( Z, Y )] )
% 1.43/1.78 ).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 factor(
% 1.43/1.78 clause( 5111, [ =( 'c_minus'( 'c_uminus'( X, Y ), Z, Y ), 'c_uminus'(
% 1.43/1.78 'c_plus'( Z, X, Y ), Y ) ), ~( 'class_OrderedGroup_Oab__group__add'( Y )
% 1.43/1.78 ) ] )
% 1.43/1.78 , clause( 5109, [ =( 'c_minus'( 'c_uminus'( X, Y ), Z, Y ), 'c_uminus'(
% 1.43/1.78 'c_plus'( Z, X, Y ), Y ) ), ~( 'class_OrderedGroup_Oab__group__add'( Y )
% 1.43/1.78 ), ~( 'class_OrderedGroup_Oab__group__add'( Y ) ) ] )
% 1.43/1.78 , 1, 2, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 subsumption(
% 1.43/1.78 clause( 177, [ ~( 'class_OrderedGroup_Oab__group__add'( Z ) ), =( 'c_minus'(
% 1.43/1.78 'c_uminus'( Y, Z ), X, Z ), 'c_uminus'( 'c_plus'( X, Y, Z ), Z ) ) ] )
% 1.43/1.78 , clause( 5111, [ =( 'c_minus'( 'c_uminus'( X, Y ), Z, Y ), 'c_uminus'(
% 1.43/1.78 'c_plus'( Z, X, Y ), Y ) ), ~( 'class_OrderedGroup_Oab__group__add'( Y )
% 1.43/1.78 ) ] )
% 1.43/1.78 , substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, X )] ),
% 1.43/1.78 permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 eqswap(
% 1.43/1.78 clause( 5117, [ =( 'c_minus'( Y, X, Z ), 'c_uminus'( 'c_minus'( X, Y, Z ),
% 1.43/1.78 Z ) ), ~( 'class_OrderedGroup_Oab__group__add'( Z ) ) ] )
% 1.43/1.78 , clause( 14, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.43/1.78 'c_uminus'( 'c_minus'( Y, Z, X ), X ), 'c_minus'( Z, Y, X ) ) ] )
% 1.43/1.78 , 1, substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 paramod(
% 1.43/1.78 clause( 5119, [ =( 'c_minus'( 'c_0', X, 't_b' ), 'c_uminus'( X, 't_b' ) ),
% 1.43/1.78 ~( 'class_OrderedGroup_Oab__group__add'( 't_b' ) ) ] )
% 1.43/1.78 , clause( 87, [ =( 'c_minus'( X, 'c_0', 't_b' ), X ) ] )
% 1.43/1.78 , 0, clause( 5117, [ =( 'c_minus'( Y, X, Z ), 'c_uminus'( 'c_minus'( X, Y,
% 1.43/1.78 Z ), Z ) ), ~( 'class_OrderedGroup_Oab__group__add'( Z ) ) ] )
% 1.43/1.78 , 0, 6, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ),
% 1.43/1.78 :=( Y, 'c_0' ), :=( Z, 't_b' )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 resolution(
% 1.43/1.78 clause( 5120, [ =( 'c_minus'( 'c_0', X, 't_b' ), 'c_uminus'( X, 't_b' ) ) ]
% 1.43/1.78 )
% 1.43/1.78 , clause( 5119, [ =( 'c_minus'( 'c_0', X, 't_b' ), 'c_uminus'( X, 't_b' ) )
% 1.43/1.78 , ~( 'class_OrderedGroup_Oab__group__add'( 't_b' ) ) ] )
% 1.43/1.78 , 1, clause( 29, [ 'class_OrderedGroup_Oab__group__add'( 't_b' ) ] )
% 1.43/1.78 , 0, substitution( 0, [ :=( X, X )] ), substitution( 1, [] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 subsumption(
% 1.43/1.78 clause( 178, [ =( 'c_minus'( 'c_0', X, 't_b' ), 'c_uminus'( X, 't_b' ) ) ]
% 1.43/1.78 )
% 1.43/1.78 , clause( 5120, [ =( 'c_minus'( 'c_0', X, 't_b' ), 'c_uminus'( X, 't_b' ) )
% 1.43/1.78 ] )
% 1.43/1.78 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 eqswap(
% 1.43/1.78 clause( 5123, [ =( 'c_minus'( Y, X, Z ), 'c_uminus'( 'c_minus'( X, Y, Z ),
% 1.43/1.78 Z ) ), ~( 'class_OrderedGroup_Oab__group__add'( Z ) ) ] )
% 1.43/1.78 , clause( 14, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.43/1.78 'c_uminus'( 'c_minus'( Y, Z, X ), X ), 'c_minus'( Z, Y, X ) ) ] )
% 1.43/1.78 , 1, substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 paramod(
% 1.43/1.78 clause( 5125, [ =( 'c_minus'( X, X, Y ), 'c_uminus'( 'c_0', Y ) ), ~(
% 1.43/1.78 'class_OrderedGroup_Oab__group__add'( Y ) ), ~(
% 1.43/1.78 'class_OrderedGroup_Oab__group__add'( Y ) ) ] )
% 1.43/1.78 , clause( 13, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.43/1.78 'c_minus'( Y, Y, X ), 'c_0' ) ] )
% 1.43/1.78 , 1, clause( 5123, [ =( 'c_minus'( Y, X, Z ), 'c_uminus'( 'c_minus'( X, Y,
% 1.43/1.78 Z ), Z ) ), ~( 'class_OrderedGroup_Oab__group__add'( Z ) ) ] )
% 1.43/1.78 , 0, 6, substitution( 0, [ :=( X, Y ), :=( Y, X )] ), substitution( 1, [
% 1.43/1.78 :=( X, X ), :=( Y, X ), :=( Z, Y )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 paramod(
% 1.43/1.78 clause( 5126, [ =( 'c_0', 'c_uminus'( 'c_0', Y ) ), ~(
% 1.43/1.78 'class_OrderedGroup_Oab__group__add'( Y ) ), ~(
% 1.43/1.78 'class_OrderedGroup_Oab__group__add'( Y ) ), ~(
% 1.43/1.78 'class_OrderedGroup_Oab__group__add'( Y ) ) ] )
% 1.43/1.78 , clause( 13, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.43/1.78 'c_minus'( Y, Y, X ), 'c_0' ) ] )
% 1.43/1.78 , 1, clause( 5125, [ =( 'c_minus'( X, X, Y ), 'c_uminus'( 'c_0', Y ) ), ~(
% 1.43/1.78 'class_OrderedGroup_Oab__group__add'( Y ) ), ~(
% 1.43/1.78 'class_OrderedGroup_Oab__group__add'( Y ) ) ] )
% 1.43/1.78 , 0, 1, substitution( 0, [ :=( X, Y ), :=( Y, X )] ), substitution( 1, [
% 1.43/1.78 :=( X, X ), :=( Y, Y )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 factor(
% 1.43/1.78 clause( 5128, [ =( 'c_0', 'c_uminus'( 'c_0', X ) ), ~(
% 1.43/1.78 'class_OrderedGroup_Oab__group__add'( X ) ), ~(
% 1.43/1.78 'class_OrderedGroup_Oab__group__add'( X ) ) ] )
% 1.43/1.78 , clause( 5126, [ =( 'c_0', 'c_uminus'( 'c_0', Y ) ), ~(
% 1.43/1.78 'class_OrderedGroup_Oab__group__add'( Y ) ), ~(
% 1.43/1.78 'class_OrderedGroup_Oab__group__add'( Y ) ), ~(
% 1.43/1.78 'class_OrderedGroup_Oab__group__add'( Y ) ) ] )
% 1.43/1.78 , 1, 2, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 factor(
% 1.43/1.78 clause( 5129, [ =( 'c_0', 'c_uminus'( 'c_0', X ) ), ~(
% 1.43/1.78 'class_OrderedGroup_Oab__group__add'( X ) ) ] )
% 1.43/1.78 , clause( 5128, [ =( 'c_0', 'c_uminus'( 'c_0', X ) ), ~(
% 1.43/1.78 'class_OrderedGroup_Oab__group__add'( X ) ), ~(
% 1.43/1.78 'class_OrderedGroup_Oab__group__add'( X ) ) ] )
% 1.43/1.78 , 1, 2, substitution( 0, [ :=( X, X )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 eqswap(
% 1.43/1.78 clause( 5133, [ =( 'c_uminus'( 'c_0', X ), 'c_0' ), ~(
% 1.43/1.78 'class_OrderedGroup_Oab__group__add'( X ) ) ] )
% 1.43/1.78 , clause( 5129, [ =( 'c_0', 'c_uminus'( 'c_0', X ) ), ~(
% 1.43/1.78 'class_OrderedGroup_Oab__group__add'( X ) ) ] )
% 1.43/1.78 , 0, substitution( 0, [ :=( X, X )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 subsumption(
% 1.43/1.78 clause( 183, [ ~( 'class_OrderedGroup_Oab__group__add'( Y ) ), =(
% 1.43/1.78 'c_uminus'( 'c_0', Y ), 'c_0' ) ] )
% 1.43/1.78 , clause( 5133, [ =( 'c_uminus'( 'c_0', X ), 'c_0' ), ~(
% 1.43/1.78 'class_OrderedGroup_Oab__group__add'( X ) ) ] )
% 1.43/1.78 , substitution( 0, [ :=( X, Y )] ), permutation( 0, [ ==>( 0, 1 ), ==>( 1,
% 1.43/1.78 0 )] ) ).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 eqswap(
% 1.43/1.78 clause( 5139, [ =( 'c_plus'( X, Y, Z ), 'c_minus'( X, 'c_uminus'( Y, Z ), Z
% 1.43/1.78 ) ), ~( 'class_OrderedGroup_Oab__group__add'( Z ) ) ] )
% 1.43/1.78 , clause( 12, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.43/1.78 'c_minus'( Y, 'c_uminus'( Z, X ), X ), 'c_plus'( Y, Z, X ) ) ] )
% 1.43/1.78 , 1, substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 paramod(
% 1.43/1.78 clause( 5140, [ =( 'c_plus'( X, 'c_0', Y ), 'c_minus'( X, 'c_0', Y ) ), ~(
% 1.43/1.78 'class_OrderedGroup_Oab__group__add'( Y ) ), ~(
% 1.43/1.78 'class_OrderedGroup_Oab__group__add'( Y ) ) ] )
% 1.43/1.78 , clause( 183, [ ~( 'class_OrderedGroup_Oab__group__add'( Y ) ), =(
% 1.43/1.78 'c_uminus'( 'c_0', Y ), 'c_0' ) ] )
% 1.43/1.78 , 1, clause( 5139, [ =( 'c_plus'( X, Y, Z ), 'c_minus'( X, 'c_uminus'( Y, Z
% 1.43/1.78 ), Z ) ), ~( 'class_OrderedGroup_Oab__group__add'( Z ) ) ] )
% 1.43/1.78 , 0, 7, substitution( 0, [ :=( X, Z ), :=( Y, Y )] ), substitution( 1, [
% 1.43/1.78 :=( X, X ), :=( Y, 'c_0' ), :=( Z, Y )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 factor(
% 1.43/1.78 clause( 5141, [ =( 'c_plus'( X, 'c_0', Y ), 'c_minus'( X, 'c_0', Y ) ), ~(
% 1.43/1.78 'class_OrderedGroup_Oab__group__add'( Y ) ) ] )
% 1.43/1.78 , clause( 5140, [ =( 'c_plus'( X, 'c_0', Y ), 'c_minus'( X, 'c_0', Y ) ),
% 1.43/1.78 ~( 'class_OrderedGroup_Oab__group__add'( Y ) ), ~(
% 1.43/1.78 'class_OrderedGroup_Oab__group__add'( Y ) ) ] )
% 1.43/1.78 , 1, 2, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 subsumption(
% 1.43/1.78 clause( 186, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( 'c_plus'(
% 1.43/1.78 Y, 'c_0', X ), 'c_minus'( Y, 'c_0', X ) ) ] )
% 1.43/1.78 , clause( 5141, [ =( 'c_plus'( X, 'c_0', Y ), 'c_minus'( X, 'c_0', Y ) ),
% 1.43/1.78 ~( 'class_OrderedGroup_Oab__group__add'( Y ) ) ] )
% 1.43/1.78 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 1
% 1.43/1.78 ), ==>( 1, 0 )] ) ).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 eqswap(
% 1.43/1.78 clause( 5145, [ =( 'c_minus'( Y, X, Z ), 'c_uminus'( 'c_minus'( X, Y, Z ),
% 1.43/1.78 Z ) ), ~( 'class_OrderedGroup_Oab__group__add'( Z ) ) ] )
% 1.43/1.78 , clause( 14, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.43/1.78 'c_uminus'( 'c_minus'( Y, Z, X ), X ), 'c_minus'( Z, Y, X ) ) ] )
% 1.43/1.78 , 1, substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 paramod(
% 1.43/1.78 clause( 5149, [ =( 'c_minus'( X, 'c_0', 't_b' ), 'c_uminus'( 'c_uminus'( X
% 1.43/1.78 , 't_b' ), 't_b' ) ), ~( 'class_OrderedGroup_Oab__group__add'( 't_b' ) )
% 1.43/1.78 ] )
% 1.43/1.78 , clause( 178, [ =( 'c_minus'( 'c_0', X, 't_b' ), 'c_uminus'( X, 't_b' ) )
% 1.43/1.78 ] )
% 1.43/1.78 , 0, clause( 5145, [ =( 'c_minus'( Y, X, Z ), 'c_uminus'( 'c_minus'( X, Y,
% 1.43/1.78 Z ), Z ) ), ~( 'class_OrderedGroup_Oab__group__add'( Z ) ) ] )
% 1.43/1.78 , 0, 6, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, 'c_0' )
% 1.43/1.78 , :=( Y, X ), :=( Z, 't_b' )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 paramod(
% 1.43/1.78 clause( 5150, [ =( X, 'c_uminus'( 'c_uminus'( X, 't_b' ), 't_b' ) ), ~(
% 1.43/1.78 'class_OrderedGroup_Oab__group__add'( 't_b' ) ) ] )
% 1.43/1.78 , clause( 87, [ =( 'c_minus'( X, 'c_0', 't_b' ), X ) ] )
% 1.43/1.78 , 0, clause( 5149, [ =( 'c_minus'( X, 'c_0', 't_b' ), 'c_uminus'(
% 1.43/1.78 'c_uminus'( X, 't_b' ), 't_b' ) ), ~(
% 1.43/1.78 'class_OrderedGroup_Oab__group__add'( 't_b' ) ) ] )
% 1.43/1.78 , 0, 1, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 1.43/1.78 ).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 resolution(
% 1.43/1.78 clause( 5151, [ =( X, 'c_uminus'( 'c_uminus'( X, 't_b' ), 't_b' ) ) ] )
% 1.43/1.78 , clause( 5150, [ =( X, 'c_uminus'( 'c_uminus'( X, 't_b' ), 't_b' ) ), ~(
% 1.43/1.78 'class_OrderedGroup_Oab__group__add'( 't_b' ) ) ] )
% 1.43/1.78 , 1, clause( 29, [ 'class_OrderedGroup_Oab__group__add'( 't_b' ) ] )
% 1.43/1.78 , 0, substitution( 0, [ :=( X, X )] ), substitution( 1, [] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 eqswap(
% 1.43/1.78 clause( 5152, [ =( 'c_uminus'( 'c_uminus'( X, 't_b' ), 't_b' ), X ) ] )
% 1.43/1.78 , clause( 5151, [ =( X, 'c_uminus'( 'c_uminus'( X, 't_b' ), 't_b' ) ) ] )
% 1.43/1.78 , 0, substitution( 0, [ :=( X, X )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 subsumption(
% 1.43/1.78 clause( 188, [ =( 'c_uminus'( 'c_uminus'( X, 't_b' ), 't_b' ), X ) ] )
% 1.43/1.78 , clause( 5152, [ =( 'c_uminus'( 'c_uminus'( X, 't_b' ), 't_b' ), X ) ] )
% 1.43/1.78 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 paramod(
% 1.43/1.78 clause( 5154, [ 'c_lessequals'( 'c_uminus'( X, 't_b' ), 'c_0', 't_b' ), ~(
% 1.43/1.78 'class_OrderedGroup_Opordered__ab__group__add'( 't_b' ) ), ~(
% 1.43/1.78 'c_lessequals'( 'c_0', X, 't_b' ) ) ] )
% 1.43/1.78 , clause( 178, [ =( 'c_minus'( 'c_0', X, 't_b' ), 'c_uminus'( X, 't_b' ) )
% 1.43/1.78 ] )
% 1.43/1.78 , 0, clause( 11, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.43/1.78 , ~( 'c_lessequals'( Y, Z, X ) ), 'c_lessequals'( 'c_minus'( Y, Z, X ),
% 1.43/1.78 'c_0', X ) ] )
% 1.43/1.78 , 2, 1, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, 't_b' )
% 1.43/1.78 , :=( Y, 'c_0' ), :=( Z, X )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 resolution(
% 1.43/1.78 clause( 5155, [ 'c_lessequals'( 'c_uminus'( X, 't_b' ), 'c_0', 't_b' ), ~(
% 1.43/1.78 'c_lessequals'( 'c_0', X, 't_b' ) ) ] )
% 1.43/1.78 , clause( 5154, [ 'c_lessequals'( 'c_uminus'( X, 't_b' ), 'c_0', 't_b' ),
% 1.43/1.78 ~( 'class_OrderedGroup_Opordered__ab__group__add'( 't_b' ) ), ~(
% 1.43/1.78 'c_lessequals'( 'c_0', X, 't_b' ) ) ] )
% 1.43/1.78 , 1, clause( 37, [ 'class_OrderedGroup_Opordered__ab__group__add'( 't_b' )
% 1.43/1.78 ] )
% 1.43/1.78 , 0, substitution( 0, [ :=( X, X )] ), substitution( 1, [] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 subsumption(
% 1.43/1.78 clause( 190, [ ~( 'c_lessequals'( 'c_0', X, 't_b' ) ), 'c_lessequals'(
% 1.43/1.78 'c_uminus'( X, 't_b' ), 'c_0', 't_b' ) ] )
% 1.43/1.78 , clause( 5155, [ 'c_lessequals'( 'c_uminus'( X, 't_b' ), 'c_0', 't_b' ),
% 1.43/1.78 ~( 'c_lessequals'( 'c_0', X, 't_b' ) ) ] )
% 1.43/1.78 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 1 ), ==>( 1,
% 1.43/1.78 0 )] ) ).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 eqswap(
% 1.43/1.78 clause( 5157, [ =( 'c_minus'( 'c_plus'( X, T, Z ), Y, Z ), 'c_plus'(
% 1.43/1.78 'c_minus'( X, Y, Z ), T, Z ) ), ~( 'class_OrderedGroup_Oab__group__add'(
% 1.43/1.78 Z ) ) ] )
% 1.43/1.78 , clause( 9, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( 'c_plus'(
% 1.43/1.78 'c_minus'( Y, Z, X ), T, X ), 'c_minus'( 'c_plus'( Y, T, X ), Z, X ) ) ]
% 1.43/1.78 )
% 1.43/1.78 , 1, substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y ), :=( T, T )] )
% 1.43/1.78 ).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 paramod(
% 1.43/1.78 clause( 5159, [ =( 'c_minus'( 'c_plus'( 'c_0', X, 't_b' ), Y, 't_b' ),
% 1.43/1.78 'c_plus'( 'c_uminus'( Y, 't_b' ), X, 't_b' ) ), ~(
% 1.43/1.78 'class_OrderedGroup_Oab__group__add'( 't_b' ) ) ] )
% 1.43/1.78 , clause( 178, [ =( 'c_minus'( 'c_0', X, 't_b' ), 'c_uminus'( X, 't_b' ) )
% 1.43/1.78 ] )
% 1.43/1.78 , 0, clause( 5157, [ =( 'c_minus'( 'c_plus'( X, T, Z ), Y, Z ), 'c_plus'(
% 1.43/1.78 'c_minus'( X, Y, Z ), T, Z ) ), ~( 'class_OrderedGroup_Oab__group__add'(
% 1.43/1.78 Z ) ) ] )
% 1.43/1.78 , 0, 9, substitution( 0, [ :=( X, Y )] ), substitution( 1, [ :=( X, 'c_0' )
% 1.43/1.78 , :=( Y, Y ), :=( Z, 't_b' ), :=( T, X )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 paramod(
% 1.43/1.78 clause( 5160, [ =( 'c_minus'( X, Y, 't_b' ), 'c_plus'( 'c_uminus'( Y, 't_b'
% 1.43/1.78 ), X, 't_b' ) ), ~( 'class_OrderedGroup_Oab__group__add'( 't_b' ) ) ] )
% 1.43/1.78 , clause( 52, [ =( 'c_plus'( 'c_0', X, 't_b' ), X ) ] )
% 1.43/1.78 , 0, clause( 5159, [ =( 'c_minus'( 'c_plus'( 'c_0', X, 't_b' ), Y, 't_b' )
% 1.43/1.78 , 'c_plus'( 'c_uminus'( Y, 't_b' ), X, 't_b' ) ), ~(
% 1.43/1.78 'class_OrderedGroup_Oab__group__add'( 't_b' ) ) ] )
% 1.43/1.78 , 0, 2, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ),
% 1.43/1.78 :=( Y, Y )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 resolution(
% 1.43/1.78 clause( 5161, [ =( 'c_minus'( X, Y, 't_b' ), 'c_plus'( 'c_uminus'( Y, 't_b'
% 1.43/1.78 ), X, 't_b' ) ) ] )
% 1.43/1.78 , clause( 5160, [ =( 'c_minus'( X, Y, 't_b' ), 'c_plus'( 'c_uminus'( Y,
% 1.43/1.78 't_b' ), X, 't_b' ) ), ~( 'class_OrderedGroup_Oab__group__add'( 't_b' ) )
% 1.43/1.78 ] )
% 1.43/1.78 , 1, clause( 29, [ 'class_OrderedGroup_Oab__group__add'( 't_b' ) ] )
% 1.43/1.78 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [] )
% 1.43/1.78 ).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 eqswap(
% 1.43/1.78 clause( 5162, [ =( 'c_plus'( 'c_uminus'( Y, 't_b' ), X, 't_b' ), 'c_minus'(
% 1.43/1.78 X, Y, 't_b' ) ) ] )
% 1.43/1.78 , clause( 5161, [ =( 'c_minus'( X, Y, 't_b' ), 'c_plus'( 'c_uminus'( Y,
% 1.43/1.78 't_b' ), X, 't_b' ) ) ] )
% 1.43/1.78 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 subsumption(
% 1.43/1.78 clause( 191, [ =( 'c_plus'( 'c_uminus'( X, 't_b' ), Y, 't_b' ), 'c_minus'(
% 1.43/1.78 Y, X, 't_b' ) ) ] )
% 1.43/1.78 , clause( 5162, [ =( 'c_plus'( 'c_uminus'( Y, 't_b' ), X, 't_b' ),
% 1.43/1.78 'c_minus'( X, Y, 't_b' ) ) ] )
% 1.43/1.78 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 1.43/1.78 )] ) ).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 eqswap(
% 1.43/1.78 clause( 5164, [ =( 'c_minus'( 'c_plus'( X, Y, T ), Z, T ), 'c_plus'( X,
% 1.43/1.78 'c_minus'( Y, Z, T ), T ) ), ~( 'class_OrderedGroup_Oab__group__add'( T )
% 1.43/1.78 ) ] )
% 1.43/1.78 , clause( 8, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( 'c_plus'(
% 1.43/1.78 Y, 'c_minus'( Z, T, X ), X ), 'c_minus'( 'c_plus'( Y, Z, X ), T, X ) ) ]
% 1.43/1.78 )
% 1.43/1.78 , 1, substitution( 0, [ :=( X, T ), :=( Y, X ), :=( Z, Y ), :=( T, Z )] )
% 1.43/1.78 ).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 paramod(
% 1.43/1.78 clause( 5167, [ =( 'c_minus'( 'c_plus'( X, 'c_0', 't_b' ), Y, 't_b' ),
% 1.43/1.78 'c_plus'( X, 'c_uminus'( Y, 't_b' ), 't_b' ) ), ~(
% 1.43/1.78 'class_OrderedGroup_Oab__group__add'( 't_b' ) ) ] )
% 1.43/1.78 , clause( 178, [ =( 'c_minus'( 'c_0', X, 't_b' ), 'c_uminus'( X, 't_b' ) )
% 1.43/1.78 ] )
% 1.43/1.78 , 0, clause( 5164, [ =( 'c_minus'( 'c_plus'( X, Y, T ), Z, T ), 'c_plus'( X
% 1.43/1.78 , 'c_minus'( Y, Z, T ), T ) ), ~( 'class_OrderedGroup_Oab__group__add'( T
% 1.43/1.78 ) ) ] )
% 1.43/1.78 , 0, 10, substitution( 0, [ :=( X, Y )] ), substitution( 1, [ :=( X, X ),
% 1.43/1.78 :=( Y, 'c_0' ), :=( Z, Y ), :=( T, 't_b' )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 paramod(
% 1.43/1.78 clause( 5168, [ =( 'c_minus'( 'c_minus'( X, 'c_0', 't_b' ), Y, 't_b' ),
% 1.43/1.78 'c_plus'( X, 'c_uminus'( Y, 't_b' ), 't_b' ) ), ~(
% 1.43/1.78 'class_OrderedGroup_Oab__group__add'( 't_b' ) ), ~(
% 1.43/1.78 'class_OrderedGroup_Oab__group__add'( 't_b' ) ) ] )
% 1.43/1.78 , clause( 186, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.43/1.78 'c_plus'( Y, 'c_0', X ), 'c_minus'( Y, 'c_0', X ) ) ] )
% 1.43/1.78 , 1, clause( 5167, [ =( 'c_minus'( 'c_plus'( X, 'c_0', 't_b' ), Y, 't_b' )
% 1.43/1.78 , 'c_plus'( X, 'c_uminus'( Y, 't_b' ), 't_b' ) ), ~(
% 1.43/1.78 'class_OrderedGroup_Oab__group__add'( 't_b' ) ) ] )
% 1.43/1.78 , 0, 2, substitution( 0, [ :=( X, 't_b' ), :=( Y, X )] ), substitution( 1
% 1.43/1.78 , [ :=( X, X ), :=( Y, Y )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 factor(
% 1.43/1.78 clause( 5169, [ =( 'c_minus'( 'c_minus'( X, 'c_0', 't_b' ), Y, 't_b' ),
% 1.43/1.78 'c_plus'( X, 'c_uminus'( Y, 't_b' ), 't_b' ) ), ~(
% 1.43/1.78 'class_OrderedGroup_Oab__group__add'( 't_b' ) ) ] )
% 1.43/1.78 , clause( 5168, [ =( 'c_minus'( 'c_minus'( X, 'c_0', 't_b' ), Y, 't_b' ),
% 1.43/1.78 'c_plus'( X, 'c_uminus'( Y, 't_b' ), 't_b' ) ), ~(
% 1.43/1.78 'class_OrderedGroup_Oab__group__add'( 't_b' ) ), ~(
% 1.43/1.78 'class_OrderedGroup_Oab__group__add'( 't_b' ) ) ] )
% 1.43/1.78 , 1, 2, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 paramod(
% 1.43/1.78 clause( 5170, [ =( 'c_minus'( X, Y, 't_b' ), 'c_plus'( X, 'c_uminus'( Y,
% 1.43/1.78 't_b' ), 't_b' ) ), ~( 'class_OrderedGroup_Oab__group__add'( 't_b' ) ) ]
% 1.43/1.78 )
% 1.43/1.78 , clause( 87, [ =( 'c_minus'( X, 'c_0', 't_b' ), X ) ] )
% 1.43/1.78 , 0, clause( 5169, [ =( 'c_minus'( 'c_minus'( X, 'c_0', 't_b' ), Y, 't_b' )
% 1.43/1.78 , 'c_plus'( X, 'c_uminus'( Y, 't_b' ), 't_b' ) ), ~(
% 1.43/1.78 'class_OrderedGroup_Oab__group__add'( 't_b' ) ) ] )
% 1.43/1.78 , 0, 2, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ),
% 1.43/1.78 :=( Y, Y )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 resolution(
% 1.43/1.78 clause( 5171, [ =( 'c_minus'( X, Y, 't_b' ), 'c_plus'( X, 'c_uminus'( Y,
% 1.43/1.78 't_b' ), 't_b' ) ) ] )
% 1.43/1.78 , clause( 5170, [ =( 'c_minus'( X, Y, 't_b' ), 'c_plus'( X, 'c_uminus'( Y,
% 1.43/1.78 't_b' ), 't_b' ) ), ~( 'class_OrderedGroup_Oab__group__add'( 't_b' ) ) ]
% 1.43/1.78 )
% 1.43/1.78 , 1, clause( 29, [ 'class_OrderedGroup_Oab__group__add'( 't_b' ) ] )
% 1.43/1.78 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [] )
% 1.43/1.78 ).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 eqswap(
% 1.43/1.78 clause( 5172, [ =( 'c_plus'( X, 'c_uminus'( Y, 't_b' ), 't_b' ), 'c_minus'(
% 1.43/1.78 X, Y, 't_b' ) ) ] )
% 1.43/1.78 , clause( 5171, [ =( 'c_minus'( X, Y, 't_b' ), 'c_plus'( X, 'c_uminus'( Y,
% 1.43/1.78 't_b' ), 't_b' ) ) ] )
% 1.43/1.78 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 subsumption(
% 1.43/1.78 clause( 192, [ =( 'c_plus'( Y, 'c_uminus'( X, 't_b' ), 't_b' ), 'c_minus'(
% 1.43/1.78 Y, X, 't_b' ) ) ] )
% 1.43/1.78 , clause( 5172, [ =( 'c_plus'( X, 'c_uminus'( Y, 't_b' ), 't_b' ),
% 1.43/1.78 'c_minus'( X, Y, 't_b' ) ) ] )
% 1.43/1.78 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 1.43/1.78 )] ) ).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 resolution(
% 1.43/1.78 clause( 5173, [ ~( 'class_Orderings_Olinorder'( 't_b' ) ), ~(
% 1.43/1.78 'c_lessequals'( Z, Y, 't_b' ) ), 'c_lessequals'( 'c_Orderings_Omax'( Z, X
% 1.43/1.78 , 't_b' ), Y, 't_b' ), 'c_less'( Y, X, 't_b' ) ] )
% 1.43/1.78 , clause( 16, [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y
% 1.43/1.78 , Z, X ) ), ~( 'c_lessequals'( T, Z, X ) ), 'c_lessequals'(
% 1.43/1.78 'c_Orderings_Omax'( T, Y, X ), Z, X ) ] )
% 1.43/1.78 , 1, clause( 94, [ 'c_less'( X, Y, 't_b' ), 'c_lessequals'( Y, X, 't_b' ) ]
% 1.43/1.78 )
% 1.43/1.78 , 1, substitution( 0, [ :=( X, 't_b' ), :=( Y, X ), :=( Z, Y ), :=( T, Z )] )
% 1.43/1.78 , substitution( 1, [ :=( X, Y ), :=( Y, X )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 resolution(
% 1.43/1.78 clause( 5175, [ ~( 'c_lessequals'( X, Y, 't_b' ) ), 'c_lessequals'(
% 1.43/1.78 'c_Orderings_Omax'( X, Z, 't_b' ), Y, 't_b' ), 'c_less'( Y, Z, 't_b' ) ]
% 1.43/1.78 )
% 1.43/1.78 , clause( 5173, [ ~( 'class_Orderings_Olinorder'( 't_b' ) ), ~(
% 1.43/1.78 'c_lessequals'( Z, Y, 't_b' ) ), 'c_lessequals'( 'c_Orderings_Omax'( Z, X
% 1.43/1.78 , 't_b' ), Y, 't_b' ), 'c_less'( Y, X, 't_b' ) ] )
% 1.43/1.78 , 0, clause( 31, [ 'class_Orderings_Olinorder'( 't_b' ) ] )
% 1.43/1.78 , 0, substitution( 0, [ :=( X, Z ), :=( Y, Y ), :=( Z, X )] ),
% 1.43/1.78 substitution( 1, [] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 subsumption(
% 1.43/1.78 clause( 201, [ ~( 'c_lessequals'( X, Y, 't_b' ) ), 'c_lessequals'(
% 1.43/1.78 'c_Orderings_Omax'( X, Z, 't_b' ), Y, 't_b' ), 'c_less'( Y, Z, 't_b' ) ]
% 1.43/1.78 )
% 1.43/1.78 , clause( 5175, [ ~( 'c_lessequals'( X, Y, 't_b' ) ), 'c_lessequals'(
% 1.43/1.78 'c_Orderings_Omax'( X, Z, 't_b' ), Y, 't_b' ), 'c_less'( Y, Z, 't_b' ) ]
% 1.43/1.78 )
% 1.43/1.78 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 1.43/1.78 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 resolution(
% 1.43/1.78 clause( 5176, [ ~( 'class_Orderings_Olinorder'( 't_b' ) ), ~(
% 1.43/1.78 'c_lessequals'( Y, X, 't_b' ) ), 'c_lessequals'( 'c_Orderings_Omax'( Y, X
% 1.43/1.78 , 't_b' ), X, 't_b' ) ] )
% 1.43/1.78 , clause( 16, [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y
% 1.43/1.78 , Z, X ) ), ~( 'c_lessequals'( T, Z, X ) ), 'c_lessequals'(
% 1.43/1.78 'c_Orderings_Omax'( T, Y, X ), Z, X ) ] )
% 1.43/1.78 , 1, clause( 97, [ 'c_lessequals'( X, X, 't_b' ) ] )
% 1.43/1.78 , 0, substitution( 0, [ :=( X, 't_b' ), :=( Y, X ), :=( Z, X ), :=( T, Y )] )
% 1.43/1.78 , substitution( 1, [ :=( X, X )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 resolution(
% 1.43/1.78 clause( 5178, [ ~( 'c_lessequals'( X, Y, 't_b' ) ), 'c_lessequals'(
% 1.43/1.78 'c_Orderings_Omax'( X, Y, 't_b' ), Y, 't_b' ) ] )
% 1.43/1.78 , clause( 5176, [ ~( 'class_Orderings_Olinorder'( 't_b' ) ), ~(
% 1.43/1.78 'c_lessequals'( Y, X, 't_b' ) ), 'c_lessequals'( 'c_Orderings_Omax'( Y, X
% 1.43/1.78 , 't_b' ), X, 't_b' ) ] )
% 1.43/1.78 , 0, clause( 31, [ 'class_Orderings_Olinorder'( 't_b' ) ] )
% 1.43/1.78 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] ), substitution( 1, [] )
% 1.43/1.78 ).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 subsumption(
% 1.43/1.78 clause( 215, [ ~( 'c_lessequals'( X, Y, 't_b' ) ), 'c_lessequals'(
% 1.43/1.78 'c_Orderings_Omax'( X, Y, 't_b' ), Y, 't_b' ) ] )
% 1.43/1.78 , clause( 5178, [ ~( 'c_lessequals'( X, Y, 't_b' ) ), 'c_lessequals'(
% 1.43/1.78 'c_Orderings_Omax'( X, Y, 't_b' ), Y, 't_b' ) ] )
% 1.43/1.78 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.43/1.78 ), ==>( 1, 1 )] ) ).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 eqswap(
% 1.43/1.78 clause( 5179, [ =( X, 'c_uminus'( 'c_uminus'( X, 't_b' ), 't_b' ) ) ] )
% 1.43/1.78 , clause( 188, [ =( 'c_uminus'( 'c_uminus'( X, 't_b' ), 't_b' ), X ) ] )
% 1.43/1.78 , 0, substitution( 0, [ :=( X, X )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 paramod(
% 1.43/1.78 clause( 5182, [ =( X, 'c_HOL_Oabs'( 'c_uminus'( X, 't_b' ), 't_b' ) ), ~(
% 1.43/1.78 'class_OrderedGroup_Olordered__ab__group__abs'( 't_b' ) ), ~(
% 1.43/1.78 'c_lessequals'( 'c_uminus'( X, 't_b' ), 'c_0', 't_b' ) ) ] )
% 1.43/1.78 , clause( 5, [ ~( 'class_OrderedGroup_Olordered__ab__group__abs'( X ) ),
% 1.43/1.78 ~( 'c_lessequals'( Y, 'c_0', X ) ), =( 'c_uminus'( Y, X ), 'c_HOL_Oabs'(
% 1.43/1.78 Y, X ) ) ] )
% 1.43/1.78 , 2, clause( 5179, [ =( X, 'c_uminus'( 'c_uminus'( X, 't_b' ), 't_b' ) ) ]
% 1.43/1.78 )
% 1.43/1.78 , 0, 2, substitution( 0, [ :=( X, 't_b' ), :=( Y, 'c_uminus'( X, 't_b' ) )] )
% 1.43/1.78 , substitution( 1, [ :=( X, X )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 paramod(
% 1.43/1.78 clause( 5193, [ =( X, 'c_HOL_Oabs'( X, 't_b' ) ), ~(
% 1.43/1.78 'class_OrderedGroup_Olordered__ab__group__abs'( 't_b' ) ), ~(
% 1.43/1.78 'class_OrderedGroup_Olordered__ab__group__abs'( 't_b' ) ), ~(
% 1.43/1.78 'c_lessequals'( 'c_uminus'( X, 't_b' ), 'c_0', 't_b' ) ) ] )
% 1.43/1.78 , clause( 4, [ ~( 'class_OrderedGroup_Olordered__ab__group__abs'( X ) ),
% 1.43/1.78 =( 'c_HOL_Oabs'( 'c_uminus'( Y, X ), X ), 'c_HOL_Oabs'( Y, X ) ) ] )
% 1.43/1.78 , 1, clause( 5182, [ =( X, 'c_HOL_Oabs'( 'c_uminus'( X, 't_b' ), 't_b' ) )
% 1.43/1.78 , ~( 'class_OrderedGroup_Olordered__ab__group__abs'( 't_b' ) ), ~(
% 1.43/1.78 'c_lessequals'( 'c_uminus'( X, 't_b' ), 'c_0', 't_b' ) ) ] )
% 1.43/1.78 , 0, 2, substitution( 0, [ :=( X, 't_b' ), :=( Y, X )] ), substitution( 1
% 1.43/1.78 , [ :=( X, X )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 factor(
% 1.43/1.78 clause( 5194, [ =( X, 'c_HOL_Oabs'( X, 't_b' ) ), ~(
% 1.43/1.78 'class_OrderedGroup_Olordered__ab__group__abs'( 't_b' ) ), ~(
% 1.43/1.78 'c_lessequals'( 'c_uminus'( X, 't_b' ), 'c_0', 't_b' ) ) ] )
% 1.43/1.78 , clause( 5193, [ =( X, 'c_HOL_Oabs'( X, 't_b' ) ), ~(
% 1.43/1.78 'class_OrderedGroup_Olordered__ab__group__abs'( 't_b' ) ), ~(
% 1.43/1.78 'class_OrderedGroup_Olordered__ab__group__abs'( 't_b' ) ), ~(
% 1.43/1.78 'c_lessequals'( 'c_uminus'( X, 't_b' ), 'c_0', 't_b' ) ) ] )
% 1.43/1.78 , 1, 2, substitution( 0, [ :=( X, X )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 resolution(
% 1.43/1.78 clause( 5195, [ =( X, 'c_HOL_Oabs'( X, 't_b' ) ), ~( 'c_lessequals'(
% 1.43/1.78 'c_uminus'( X, 't_b' ), 'c_0', 't_b' ) ) ] )
% 1.43/1.78 , clause( 5194, [ =( X, 'c_HOL_Oabs'( X, 't_b' ) ), ~(
% 1.43/1.78 'class_OrderedGroup_Olordered__ab__group__abs'( 't_b' ) ), ~(
% 1.43/1.78 'c_lessequals'( 'c_uminus'( X, 't_b' ), 'c_0', 't_b' ) ) ] )
% 1.43/1.78 , 1, clause( 28, [ 'class_OrderedGroup_Olordered__ab__group__abs'( 't_b' )
% 1.43/1.78 ] )
% 1.43/1.78 , 0, substitution( 0, [ :=( X, X )] ), substitution( 1, [] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 eqswap(
% 1.43/1.78 clause( 5196, [ =( 'c_HOL_Oabs'( X, 't_b' ), X ), ~( 'c_lessequals'(
% 1.43/1.78 'c_uminus'( X, 't_b' ), 'c_0', 't_b' ) ) ] )
% 1.43/1.78 , clause( 5195, [ =( X, 'c_HOL_Oabs'( X, 't_b' ) ), ~( 'c_lessequals'(
% 1.43/1.78 'c_uminus'( X, 't_b' ), 'c_0', 't_b' ) ) ] )
% 1.43/1.78 , 0, substitution( 0, [ :=( X, X )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 subsumption(
% 1.43/1.78 clause( 236, [ ~( 'c_lessequals'( 'c_uminus'( X, 't_b' ), 'c_0', 't_b' ) )
% 1.43/1.78 , =( 'c_HOL_Oabs'( X, 't_b' ), X ) ] )
% 1.43/1.78 , clause( 5196, [ =( 'c_HOL_Oabs'( X, 't_b' ), X ), ~( 'c_lessequals'(
% 1.43/1.78 'c_uminus'( X, 't_b' ), 'c_0', 't_b' ) ) ] )
% 1.43/1.78 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 1 ), ==>( 1,
% 1.43/1.78 0 )] ) ).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 resolution(
% 1.43/1.78 clause( 5197, [ ~( 'class_Orderings_Oorder'( 't_b' ) ), ~( 'c_lessequals'(
% 1.43/1.78 Y, 'c_0', 't_b' ) ), 'c_lessequals'( Y, 'c_HOL_Oabs'( X, 't_b' ), 't_b' )
% 1.43/1.78 ] )
% 1.43/1.78 , clause( 17, [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_lessequals'( Y, Z
% 1.43/1.78 , X ) ), ~( 'c_lessequals'( T, Y, X ) ), 'c_lessequals'( T, Z, X ) ] )
% 1.43/1.78 , 1, clause( 35, [ 'c_lessequals'( 'c_0', 'c_HOL_Oabs'( X, 't_b' ), 't_b' )
% 1.43/1.78 ] )
% 1.43/1.78 , 0, substitution( 0, [ :=( X, 't_b' ), :=( Y, 'c_0' ), :=( Z, 'c_HOL_Oabs'(
% 1.43/1.78 X, 't_b' ) ), :=( T, Y )] ), substitution( 1, [ :=( X, X )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 resolution(
% 1.43/1.78 clause( 5199, [ ~( 'c_lessequals'( X, 'c_0', 't_b' ) ), 'c_lessequals'( X,
% 1.43/1.78 'c_HOL_Oabs'( Y, 't_b' ), 't_b' ) ] )
% 1.43/1.78 , clause( 5197, [ ~( 'class_Orderings_Oorder'( 't_b' ) ), ~( 'c_lessequals'(
% 1.43/1.78 Y, 'c_0', 't_b' ) ), 'c_lessequals'( Y, 'c_HOL_Oabs'( X, 't_b' ), 't_b' )
% 1.43/1.78 ] )
% 1.43/1.78 , 0, clause( 41, [ 'class_Orderings_Oorder'( 't_b' ) ] )
% 1.43/1.78 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] ), substitution( 1, [] )
% 1.43/1.78 ).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 subsumption(
% 1.43/1.78 clause( 277, [ ~( 'c_lessequals'( X, 'c_0', 't_b' ) ), 'c_lessequals'( X,
% 1.43/1.78 'c_HOL_Oabs'( Y, 't_b' ), 't_b' ) ] )
% 1.43/1.78 , clause( 5199, [ ~( 'c_lessequals'( X, 'c_0', 't_b' ) ), 'c_lessequals'( X
% 1.43/1.78 , 'c_HOL_Oabs'( Y, 't_b' ), 't_b' ) ] )
% 1.43/1.78 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.43/1.78 ), ==>( 1, 1 )] ) ).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 resolution(
% 1.43/1.78 clause( 5201, [ ~( 'class_Orderings_Oorder'( 't_b' ) ), ~( 'c_lessequals'(
% 1.43/1.78 'v_f'( X ), Y, 't_b' ) ), 'c_lessequals'( 'v_k'( X ), Y, 't_b' ) ] )
% 1.43/1.78 , clause( 17, [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_lessequals'( Y, Z
% 1.43/1.78 , X ) ), ~( 'c_lessequals'( T, Y, X ) ), 'c_lessequals'( T, Z, X ) ] )
% 1.43/1.78 , 2, clause( 0, [ 'c_lessequals'( 'v_k'( X ), 'v_f'( X ), 't_b' ) ] )
% 1.43/1.78 , 0, substitution( 0, [ :=( X, 't_b' ), :=( Y, 'v_f'( X ) ), :=( Z, Y ),
% 1.43/1.78 :=( T, 'v_k'( X ) )] ), substitution( 1, [ :=( X, X )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 resolution(
% 1.43/1.78 clause( 5203, [ ~( 'c_lessequals'( 'v_f'( X ), Y, 't_b' ) ), 'c_lessequals'(
% 1.43/1.78 'v_k'( X ), Y, 't_b' ) ] )
% 1.43/1.78 , clause( 5201, [ ~( 'class_Orderings_Oorder'( 't_b' ) ), ~( 'c_lessequals'(
% 1.43/1.78 'v_f'( X ), Y, 't_b' ) ), 'c_lessequals'( 'v_k'( X ), Y, 't_b' ) ] )
% 1.43/1.78 , 0, clause( 41, [ 'class_Orderings_Oorder'( 't_b' ) ] )
% 1.43/1.78 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [] )
% 1.43/1.78 ).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 subsumption(
% 1.43/1.78 clause( 285, [ ~( 'c_lessequals'( 'v_f'( X ), Y, 't_b' ) ), 'c_lessequals'(
% 1.43/1.78 'v_k'( X ), Y, 't_b' ) ] )
% 1.43/1.78 , clause( 5203, [ ~( 'c_lessequals'( 'v_f'( X ), Y, 't_b' ) ),
% 1.43/1.78 'c_lessequals'( 'v_k'( X ), Y, 't_b' ) ] )
% 1.43/1.78 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.43/1.78 ), ==>( 1, 1 )] ) ).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 resolution(
% 1.43/1.78 clause( 5204, [ ~( 'c_lessequals'( 'c_Orderings_Omax'( 'c_minus'( 'v_k'(
% 1.43/1.78 'v_x' ), 'v_g'( 'v_x' ), 't_b' ), 'c_0', 't_b' ), 'c_0', 't_b' ) ) ] )
% 1.43/1.78 , clause( 1, [ ~( 'c_lessequals'( 'c_Orderings_Omax'( 'c_minus'( 'v_k'(
% 1.43/1.78 'v_x' ), 'v_g'( 'v_x' ), 't_b' ), 'c_0', 't_b' ), 'c_HOL_Oabs'( 'c_minus'(
% 1.43/1.78 'v_f'( 'v_x' ), 'v_g'( 'v_x' ), 't_b' ), 't_b' ), 't_b' ) ) ] )
% 1.43/1.78 , 0, clause( 277, [ ~( 'c_lessequals'( X, 'c_0', 't_b' ) ), 'c_lessequals'(
% 1.43/1.78 X, 'c_HOL_Oabs'( Y, 't_b' ), 't_b' ) ] )
% 1.43/1.78 , 1, substitution( 0, [] ), substitution( 1, [ :=( X, 'c_Orderings_Omax'(
% 1.43/1.78 'c_minus'( 'v_k'( 'v_x' ), 'v_g'( 'v_x' ), 't_b' ), 'c_0', 't_b' ) ),
% 1.43/1.78 :=( Y, 'c_minus'( 'v_f'( 'v_x' ), 'v_g'( 'v_x' ), 't_b' ) )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 subsumption(
% 1.43/1.78 clause( 304, [ ~( 'c_lessequals'( 'c_Orderings_Omax'( 'c_minus'( 'v_k'(
% 1.43/1.78 'v_x' ), 'v_g'( 'v_x' ), 't_b' ), 'c_0', 't_b' ), 'c_0', 't_b' ) ) ] )
% 1.43/1.78 , clause( 5204, [ ~( 'c_lessequals'( 'c_Orderings_Omax'( 'c_minus'( 'v_k'(
% 1.43/1.78 'v_x' ), 'v_g'( 'v_x' ), 't_b' ), 'c_0', 't_b' ), 'c_0', 't_b' ) ) ] )
% 1.43/1.78 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 eqswap(
% 1.43/1.78 clause( 5205, [ =( 'c_HOL_Oabs'( X, Y ), 'c_uminus'( X, Y ) ), ~(
% 1.43/1.78 'c_lessequals'( X, 'c_0', Y ) ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.43/1.78 , clause( 44, [ ~( 'c_lessequals'( X, 'c_0', Y ) ), =( 'c_uminus'( X, Y ),
% 1.43/1.78 'c_HOL_Oabs'( X, Y ) ), ~( 'class_Ring__and__Field_Oordered__idom'( Y ) )
% 1.43/1.78 ] )
% 1.43/1.78 , 1, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 resolution(
% 1.43/1.78 clause( 5208, [ =( 'c_HOL_Oabs'( 'c_uminus'( X, 't_b' ), 't_b' ),
% 1.43/1.78 'c_uminus'( 'c_uminus'( X, 't_b' ), 't_b' ) ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( 't_b' ) ), ~( 'c_lessequals'(
% 1.43/1.78 'c_0', X, 't_b' ) ) ] )
% 1.43/1.78 , clause( 5205, [ =( 'c_HOL_Oabs'( X, Y ), 'c_uminus'( X, Y ) ), ~(
% 1.43/1.78 'c_lessequals'( X, 'c_0', Y ) ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.43/1.78 , 1, clause( 190, [ ~( 'c_lessequals'( 'c_0', X, 't_b' ) ), 'c_lessequals'(
% 1.43/1.78 'c_uminus'( X, 't_b' ), 'c_0', 't_b' ) ] )
% 1.43/1.78 , 1, substitution( 0, [ :=( X, 'c_uminus'( X, 't_b' ) ), :=( Y, 't_b' )] )
% 1.43/1.78 , substitution( 1, [ :=( X, X )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 paramod(
% 1.43/1.78 clause( 5209, [ =( 'c_HOL_Oabs'( 'c_uminus'( X, 't_b' ), 't_b' ), X ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( 't_b' ) ), ~( 'c_lessequals'(
% 1.43/1.78 'c_0', X, 't_b' ) ) ] )
% 1.43/1.78 , clause( 188, [ =( 'c_uminus'( 'c_uminus'( X, 't_b' ), 't_b' ), X ) ] )
% 1.43/1.78 , 0, clause( 5208, [ =( 'c_HOL_Oabs'( 'c_uminus'( X, 't_b' ), 't_b' ),
% 1.43/1.78 'c_uminus'( 'c_uminus'( X, 't_b' ), 't_b' ) ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( 't_b' ) ), ~( 'c_lessequals'(
% 1.43/1.78 'c_0', X, 't_b' ) ) ] )
% 1.43/1.78 , 0, 6, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 1.43/1.78 ).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 paramod(
% 1.43/1.78 clause( 5210, [ =( 'c_HOL_Oabs'( X, 't_b' ), X ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( 't_b' ) ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( 't_b' ) ), ~( 'c_lessequals'(
% 1.43/1.78 'c_0', X, 't_b' ) ) ] )
% 1.43/1.78 , clause( 40, [ =( 'c_HOL_Oabs'( 'c_uminus'( X, Y ), Y ), 'c_HOL_Oabs'( X,
% 1.43/1.78 Y ) ), ~( 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.43/1.78 , 0, clause( 5209, [ =( 'c_HOL_Oabs'( 'c_uminus'( X, 't_b' ), 't_b' ), X )
% 1.43/1.78 , ~( 'class_Ring__and__Field_Oordered__idom'( 't_b' ) ), ~(
% 1.43/1.78 'c_lessequals'( 'c_0', X, 't_b' ) ) ] )
% 1.43/1.78 , 0, 1, substitution( 0, [ :=( X, X ), :=( Y, 't_b' )] ), substitution( 1
% 1.43/1.78 , [ :=( X, X )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 factor(
% 1.43/1.78 clause( 5211, [ =( 'c_HOL_Oabs'( X, 't_b' ), X ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( 't_b' ) ), ~( 'c_lessequals'(
% 1.43/1.78 'c_0', X, 't_b' ) ) ] )
% 1.43/1.78 , clause( 5210, [ =( 'c_HOL_Oabs'( X, 't_b' ), X ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( 't_b' ) ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( 't_b' ) ), ~( 'c_lessequals'(
% 1.43/1.78 'c_0', X, 't_b' ) ) ] )
% 1.43/1.78 , 1, 2, substitution( 0, [ :=( X, X )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 resolution(
% 1.43/1.78 clause( 5212, [ =( 'c_HOL_Oabs'( X, 't_b' ), X ), ~( 'c_lessequals'( 'c_0'
% 1.43/1.78 , X, 't_b' ) ) ] )
% 1.43/1.78 , clause( 5211, [ =( 'c_HOL_Oabs'( X, 't_b' ), X ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( 't_b' ) ), ~( 'c_lessequals'(
% 1.43/1.78 'c_0', X, 't_b' ) ) ] )
% 1.43/1.78 , 1, clause( 2, [ 'class_Ring__and__Field_Oordered__idom'( 't_b' ) ] )
% 1.43/1.78 , 0, substitution( 0, [ :=( X, X )] ), substitution( 1, [] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 subsumption(
% 1.43/1.78 clause( 441, [ ~( 'c_lessequals'( 'c_0', X, 't_b' ) ), =( 'c_HOL_Oabs'( X,
% 1.43/1.78 't_b' ), X ) ] )
% 1.43/1.78 , clause( 5212, [ =( 'c_HOL_Oabs'( X, 't_b' ), X ), ~( 'c_lessequals'(
% 1.43/1.78 'c_0', X, 't_b' ) ) ] )
% 1.43/1.78 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 1 ), ==>( 1,
% 1.43/1.78 0 )] ) ).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 eqswap(
% 1.43/1.78 clause( 5214, [ =( X, 'c_HOL_Oabs'( X, 't_b' ) ), ~( 'c_lessequals'( 'c_0'
% 1.43/1.78 , X, 't_b' ) ) ] )
% 1.43/1.78 , clause( 441, [ ~( 'c_lessequals'( 'c_0', X, 't_b' ) ), =( 'c_HOL_Oabs'( X
% 1.43/1.78 , 't_b' ), X ) ] )
% 1.43/1.78 , 1, substitution( 0, [ :=( X, X )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 resolution(
% 1.43/1.78 clause( 5215, [ =( X, 'c_HOL_Oabs'( X, 't_b' ) ), 'c_lessequals'( X, 'c_0'
% 1.43/1.78 , 't_b' ), ~( 'class_Ring__and__Field_Oordered__idom'( 't_b' ) ) ] )
% 1.43/1.78 , clause( 5214, [ =( X, 'c_HOL_Oabs'( X, 't_b' ) ), ~( 'c_lessequals'(
% 1.43/1.78 'c_0', X, 't_b' ) ) ] )
% 1.43/1.78 , 1, clause( 89, [ 'c_lessequals'( Y, Z, X ), 'c_lessequals'( Z, Y, X ),
% 1.43/1.78 ~( 'class_Ring__and__Field_Oordered__idom'( X ) ) ] )
% 1.43/1.78 , 0, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, 't_b' ),
% 1.43/1.78 :=( Y, 'c_0' ), :=( Z, X )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 resolution(
% 1.43/1.78 clause( 5216, [ =( X, 'c_HOL_Oabs'( X, 't_b' ) ), 'c_lessequals'( X, 'c_0'
% 1.43/1.78 , 't_b' ) ] )
% 1.43/1.78 , clause( 5215, [ =( X, 'c_HOL_Oabs'( X, 't_b' ) ), 'c_lessequals'( X,
% 1.43/1.78 'c_0', 't_b' ), ~( 'class_Ring__and__Field_Oordered__idom'( 't_b' ) ) ]
% 1.43/1.78 )
% 1.43/1.78 , 2, clause( 2, [ 'class_Ring__and__Field_Oordered__idom'( 't_b' ) ] )
% 1.43/1.78 , 0, substitution( 0, [ :=( X, X )] ), substitution( 1, [] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 eqswap(
% 1.43/1.78 clause( 5217, [ =( 'c_HOL_Oabs'( X, 't_b' ), X ), 'c_lessequals'( X, 'c_0'
% 1.43/1.78 , 't_b' ) ] )
% 1.43/1.78 , clause( 5216, [ =( X, 'c_HOL_Oabs'( X, 't_b' ) ), 'c_lessequals'( X,
% 1.43/1.78 'c_0', 't_b' ) ] )
% 1.43/1.78 , 0, substitution( 0, [ :=( X, X )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 subsumption(
% 1.43/1.78 clause( 465, [ =( 'c_HOL_Oabs'( X, 't_b' ), X ), 'c_lessequals'( X, 'c_0',
% 1.43/1.78 't_b' ) ] )
% 1.43/1.78 , clause( 5217, [ =( 'c_HOL_Oabs'( X, 't_b' ), X ), 'c_lessequals'( X,
% 1.43/1.78 'c_0', 't_b' ) ] )
% 1.43/1.78 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 1.43/1.78 1 )] ) ).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 eqswap(
% 1.43/1.78 clause( 5218, [ =( X, 'c_HOL_Oabs'( X, 't_b' ) ), 'c_lessequals'( X, 'c_0'
% 1.43/1.78 , 't_b' ) ] )
% 1.43/1.78 , clause( 465, [ =( 'c_HOL_Oabs'( X, 't_b' ), X ), 'c_lessequals'( X, 'c_0'
% 1.43/1.78 , 't_b' ) ] )
% 1.43/1.78 , 0, substitution( 0, [ :=( X, X )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 eqswap(
% 1.43/1.78 clause( 5219, [ =( 'c_HOL_Oabs'( X, Y ), 'c_uminus'( X, Y ) ), ~(
% 1.43/1.78 'c_lessequals'( X, 'c_0', Y ) ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.43/1.78 , clause( 44, [ ~( 'c_lessequals'( X, 'c_0', Y ) ), =( 'c_uminus'( X, Y ),
% 1.43/1.78 'c_HOL_Oabs'( X, Y ) ), ~( 'class_Ring__and__Field_Oordered__idom'( Y ) )
% 1.43/1.78 ] )
% 1.43/1.78 , 1, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 resolution(
% 1.43/1.78 clause( 5220, [ =( 'c_HOL_Oabs'( X, 't_b' ), 'c_uminus'( X, 't_b' ) ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( 't_b' ) ), =( X, 'c_HOL_Oabs'( X
% 1.43/1.78 , 't_b' ) ) ] )
% 1.43/1.78 , clause( 5219, [ =( 'c_HOL_Oabs'( X, Y ), 'c_uminus'( X, Y ) ), ~(
% 1.43/1.78 'c_lessequals'( X, 'c_0', Y ) ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.43/1.78 , 1, clause( 5218, [ =( X, 'c_HOL_Oabs'( X, 't_b' ) ), 'c_lessequals'( X,
% 1.43/1.78 'c_0', 't_b' ) ] )
% 1.43/1.78 , 1, substitution( 0, [ :=( X, X ), :=( Y, 't_b' )] ), substitution( 1, [
% 1.43/1.78 :=( X, X )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 resolution(
% 1.43/1.78 clause( 5221, [ =( 'c_HOL_Oabs'( X, 't_b' ), 'c_uminus'( X, 't_b' ) ), =( X
% 1.43/1.78 , 'c_HOL_Oabs'( X, 't_b' ) ) ] )
% 1.43/1.78 , clause( 5220, [ =( 'c_HOL_Oabs'( X, 't_b' ), 'c_uminus'( X, 't_b' ) ),
% 1.43/1.78 ~( 'class_Ring__and__Field_Oordered__idom'( 't_b' ) ), =( X, 'c_HOL_Oabs'(
% 1.43/1.78 X, 't_b' ) ) ] )
% 1.43/1.78 , 1, clause( 2, [ 'class_Ring__and__Field_Oordered__idom'( 't_b' ) ] )
% 1.43/1.78 , 0, substitution( 0, [ :=( X, X )] ), substitution( 1, [] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 eqswap(
% 1.43/1.78 clause( 5223, [ =( 'c_HOL_Oabs'( X, 't_b' ), X ), =( 'c_HOL_Oabs'( X, 't_b'
% 1.43/1.78 ), 'c_uminus'( X, 't_b' ) ) ] )
% 1.43/1.78 , clause( 5221, [ =( 'c_HOL_Oabs'( X, 't_b' ), 'c_uminus'( X, 't_b' ) ),
% 1.43/1.78 =( X, 'c_HOL_Oabs'( X, 't_b' ) ) ] )
% 1.43/1.78 , 1, substitution( 0, [ :=( X, X )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 eqswap(
% 1.43/1.78 clause( 5224, [ =( 'c_uminus'( X, 't_b' ), 'c_HOL_Oabs'( X, 't_b' ) ), =(
% 1.43/1.78 'c_HOL_Oabs'( X, 't_b' ), X ) ] )
% 1.43/1.78 , clause( 5223, [ =( 'c_HOL_Oabs'( X, 't_b' ), X ), =( 'c_HOL_Oabs'( X,
% 1.43/1.78 't_b' ), 'c_uminus'( X, 't_b' ) ) ] )
% 1.43/1.78 , 1, substitution( 0, [ :=( X, X )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 subsumption(
% 1.43/1.78 clause( 478, [ =( 'c_HOL_Oabs'( X, 't_b' ), X ), =( 'c_uminus'( X, 't_b' )
% 1.43/1.78 , 'c_HOL_Oabs'( X, 't_b' ) ) ] )
% 1.43/1.78 , clause( 5224, [ =( 'c_uminus'( X, 't_b' ), 'c_HOL_Oabs'( X, 't_b' ) ),
% 1.43/1.78 =( 'c_HOL_Oabs'( X, 't_b' ), X ) ] )
% 1.43/1.78 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 1 ), ==>( 1,
% 1.43/1.78 0 )] ) ).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 paramod(
% 1.43/1.78 clause( 5226, [ ~( 'c_lessequals'( 'c_0', X, Y ) ), ~(
% 1.43/1.78 'class_OrderedGroup_Oab__group__add'( Y ) ), 'c_lessequals'( 'c_uminus'(
% 1.43/1.78 X, Y ), 'c_0', Y ), ~( 'class_Ring__and__Field_Oordered__idom'( Y ) ) ]
% 1.43/1.78 )
% 1.43/1.78 , clause( 162, [ ~( 'class_OrderedGroup_Oab__group__add'( Y ) ), =(
% 1.43/1.78 'c_plus'( 'c_uminus'( X, Y ), X, Y ), 'c_0' ) ] )
% 1.43/1.78 , 1, clause( 59, [ ~( 'c_lessequals'( 'c_plus'( Z, X, Y ), X, Y ) ),
% 1.43/1.78 'c_lessequals'( Z, 'c_0', Y ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 1.43/1.78 Y ) ) ] )
% 1.43/1.78 , 0, 2, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 1.43/1.78 :=( X, X ), :=( Y, Y ), :=( Z, 'c_uminus'( X, Y ) )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 resolution(
% 1.43/1.78 clause( 5227, [ ~( 'c_lessequals'( 'c_0', X, Y ) ), 'c_lessequals'(
% 1.43/1.78 'c_uminus'( X, Y ), 'c_0', Y ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.43/1.78 , clause( 5226, [ ~( 'c_lessequals'( 'c_0', X, Y ) ), ~(
% 1.43/1.78 'class_OrderedGroup_Oab__group__add'( Y ) ), 'c_lessequals'( 'c_uminus'(
% 1.43/1.78 X, Y ), 'c_0', Y ), ~( 'class_Ring__and__Field_Oordered__idom'( Y ) ) ]
% 1.43/1.78 )
% 1.43/1.78 , 1, clause( 25, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.43/1.78 'class_OrderedGroup_Oab__group__add'( X ) ] )
% 1.43/1.78 , 1, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [ :=( X
% 1.43/1.78 , Y )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 factor(
% 1.43/1.78 clause( 5228, [ ~( 'c_lessequals'( 'c_0', X, Y ) ), 'c_lessequals'(
% 1.43/1.78 'c_uminus'( X, Y ), 'c_0', Y ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.43/1.78 , clause( 5227, [ ~( 'c_lessequals'( 'c_0', X, Y ) ), 'c_lessequals'(
% 1.43/1.78 'c_uminus'( X, Y ), 'c_0', Y ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.43/1.78 , 2, 3, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 subsumption(
% 1.43/1.78 clause( 895, [ ~( 'c_lessequals'( 'c_0', X, Y ) ), 'c_lessequals'(
% 1.43/1.78 'c_uminus'( X, Y ), 'c_0', Y ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.43/1.78 , clause( 5228, [ ~( 'c_lessequals'( 'c_0', X, Y ) ), 'c_lessequals'(
% 1.43/1.78 'c_uminus'( X, Y ), 'c_0', Y ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.43/1.78 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.43/1.78 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 eqswap(
% 1.43/1.78 clause( 5230, [ =( 'c_plus'( X, 'c_0', Z ), 'c_minus'( 'c_plus'( X, Y, Z )
% 1.43/1.78 , Y, Z ) ), ~( 'class_Ring__and__Field_Oordered__idom'( Z ) ) ] )
% 1.43/1.78 , clause( 63, [ =( 'c_minus'( 'c_plus'( Z, X, Y ), X, Y ), 'c_plus'( Z,
% 1.43/1.78 'c_0', Y ) ), ~( 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.43/1.78 , 0, substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, X )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 paramod(
% 1.43/1.78 clause( 5235, [ =( 'c_plus'( 'c_uminus'( X, Y ), 'c_0', Y ), 'c_minus'(
% 1.43/1.78 'c_0', X, Y ) ), ~( 'class_OrderedGroup_Oab__group__add'( Y ) ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.43/1.78 , clause( 162, [ ~( 'class_OrderedGroup_Oab__group__add'( Y ) ), =(
% 1.43/1.78 'c_plus'( 'c_uminus'( X, Y ), X, Y ), 'c_0' ) ] )
% 1.43/1.78 , 1, clause( 5230, [ =( 'c_plus'( X, 'c_0', Z ), 'c_minus'( 'c_plus'( X, Y
% 1.43/1.78 , Z ), Y, Z ) ), ~( 'class_Ring__and__Field_Oordered__idom'( Z ) ) ] )
% 1.43/1.78 , 0, 8, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 1.43/1.78 :=( X, 'c_uminus'( X, Y ) ), :=( Y, X ), :=( Z, Y )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 paramod(
% 1.43/1.78 clause( 5236, [ =( 'c_minus'( 'c_uminus'( X, Y ), 'c_0', Y ), 'c_minus'(
% 1.43/1.78 'c_0', X, Y ) ), ~( 'class_OrderedGroup_Oab__group__add'( Y ) ), ~(
% 1.43/1.78 'class_OrderedGroup_Oab__group__add'( Y ) ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.43/1.78 , clause( 186, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.43/1.78 'c_plus'( Y, 'c_0', X ), 'c_minus'( Y, 'c_0', X ) ) ] )
% 1.43/1.78 , 1, clause( 5235, [ =( 'c_plus'( 'c_uminus'( X, Y ), 'c_0', Y ), 'c_minus'(
% 1.43/1.78 'c_0', X, Y ) ), ~( 'class_OrderedGroup_Oab__group__add'( Y ) ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.43/1.78 , 0, 1, substitution( 0, [ :=( X, Y ), :=( Y, 'c_uminus'( X, Y ) )] ),
% 1.43/1.78 substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 factor(
% 1.43/1.78 clause( 5237, [ =( 'c_minus'( 'c_uminus'( X, Y ), 'c_0', Y ), 'c_minus'(
% 1.43/1.78 'c_0', X, Y ) ), ~( 'class_OrderedGroup_Oab__group__add'( Y ) ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.43/1.78 , clause( 5236, [ =( 'c_minus'( 'c_uminus'( X, Y ), 'c_0', Y ), 'c_minus'(
% 1.43/1.78 'c_0', X, Y ) ), ~( 'class_OrderedGroup_Oab__group__add'( Y ) ), ~(
% 1.43/1.78 'class_OrderedGroup_Oab__group__add'( Y ) ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.43/1.78 , 1, 2, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 paramod(
% 1.43/1.78 clause( 5238, [ =( 'c_uminus'( 'c_plus'( 'c_0', X, Y ), Y ), 'c_minus'(
% 1.43/1.78 'c_0', X, Y ) ), ~( 'class_OrderedGroup_Oab__group__add'( Y ) ), ~(
% 1.43/1.78 'class_OrderedGroup_Oab__group__add'( Y ) ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.43/1.78 , clause( 177, [ ~( 'class_OrderedGroup_Oab__group__add'( Z ) ), =(
% 1.43/1.78 'c_minus'( 'c_uminus'( Y, Z ), X, Z ), 'c_uminus'( 'c_plus'( X, Y, Z ), Z
% 1.43/1.78 ) ) ] )
% 1.43/1.78 , 1, clause( 5237, [ =( 'c_minus'( 'c_uminus'( X, Y ), 'c_0', Y ),
% 1.43/1.78 'c_minus'( 'c_0', X, Y ) ), ~( 'class_OrderedGroup_Oab__group__add'( Y )
% 1.43/1.78 ), ~( 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.43/1.78 , 0, 1, substitution( 0, [ :=( X, 'c_0' ), :=( Y, X ), :=( Z, Y )] ),
% 1.43/1.78 substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 factor(
% 1.43/1.78 clause( 5239, [ =( 'c_uminus'( 'c_plus'( 'c_0', X, Y ), Y ), 'c_minus'(
% 1.43/1.78 'c_0', X, Y ) ), ~( 'class_OrderedGroup_Oab__group__add'( Y ) ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.43/1.78 , clause( 5238, [ =( 'c_uminus'( 'c_plus'( 'c_0', X, Y ), Y ), 'c_minus'(
% 1.43/1.78 'c_0', X, Y ) ), ~( 'class_OrderedGroup_Oab__group__add'( Y ) ), ~(
% 1.43/1.78 'class_OrderedGroup_Oab__group__add'( Y ) ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.43/1.78 , 1, 2, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 paramod(
% 1.43/1.78 clause( 5240, [ =( 'c_uminus'( X, Y ), 'c_minus'( 'c_0', X, Y ) ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ), ~(
% 1.43/1.78 'class_OrderedGroup_Oab__group__add'( Y ) ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.43/1.78 , clause( 53, [ =( 'c_plus'( 'c_0', X, Y ), X ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.43/1.78 , 0, clause( 5239, [ =( 'c_uminus'( 'c_plus'( 'c_0', X, Y ), Y ), 'c_minus'(
% 1.43/1.78 'c_0', X, Y ) ), ~( 'class_OrderedGroup_Oab__group__add'( Y ) ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.43/1.78 , 0, 2, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 1.43/1.78 :=( X, X ), :=( Y, Y )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 factor(
% 1.43/1.78 clause( 5241, [ =( 'c_uminus'( X, Y ), 'c_minus'( 'c_0', X, Y ) ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ), ~(
% 1.43/1.78 'class_OrderedGroup_Oab__group__add'( Y ) ) ] )
% 1.43/1.78 , clause( 5240, [ =( 'c_uminus'( X, Y ), 'c_minus'( 'c_0', X, Y ) ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ), ~(
% 1.43/1.78 'class_OrderedGroup_Oab__group__add'( Y ) ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.43/1.78 , 1, 3, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 resolution(
% 1.43/1.78 clause( 5242, [ =( 'c_uminus'( X, Y ), 'c_minus'( 'c_0', X, Y ) ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.43/1.78 , clause( 5241, [ =( 'c_uminus'( X, Y ), 'c_minus'( 'c_0', X, Y ) ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ), ~(
% 1.43/1.78 'class_OrderedGroup_Oab__group__add'( Y ) ) ] )
% 1.43/1.78 , 2, clause( 25, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.43/1.78 'class_OrderedGroup_Oab__group__add'( X ) ] )
% 1.43/1.78 , 1, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [ :=( X
% 1.43/1.78 , Y )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 eqswap(
% 1.43/1.78 clause( 5243, [ =( 'c_minus'( 'c_0', X, Y ), 'c_uminus'( X, Y ) ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.43/1.78 , clause( 5242, [ =( 'c_uminus'( X, Y ), 'c_minus'( 'c_0', X, Y ) ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.43/1.78 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 factor(
% 1.43/1.78 clause( 5244, [ =( 'c_minus'( 'c_0', X, Y ), 'c_uminus'( X, Y ) ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.43/1.78 , clause( 5243, [ =( 'c_minus'( 'c_0', X, Y ), 'c_uminus'( X, Y ) ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.43/1.78 , 1, 2, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 subsumption(
% 1.43/1.78 clause( 1042, [ ~( 'class_Ring__and__Field_Oordered__idom'( Y ) ), =(
% 1.43/1.78 'c_minus'( 'c_0', X, Y ), 'c_uminus'( X, Y ) ) ] )
% 1.43/1.78 , clause( 5244, [ =( 'c_minus'( 'c_0', X, Y ), 'c_uminus'( X, Y ) ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.43/1.78 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 1
% 1.43/1.78 ), ==>( 1, 0 )] ) ).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 eqswap(
% 1.43/1.78 clause( 5247, [ =( 'c_minus'( Y, X, Z ), 'c_uminus'( 'c_minus'( X, Y, Z ),
% 1.43/1.78 Z ) ), ~( 'class_OrderedGroup_Oab__group__add'( Z ) ) ] )
% 1.43/1.78 , clause( 14, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.43/1.78 'c_uminus'( 'c_minus'( Y, Z, X ), X ), 'c_minus'( Z, Y, X ) ) ] )
% 1.43/1.78 , 1, substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 paramod(
% 1.43/1.78 clause( 5254, [ =( 'c_minus'( X, 'c_0', Y ), 'c_uminus'( 'c_uminus'( X, Y )
% 1.43/1.78 , Y ) ), ~( 'class_Ring__and__Field_Oordered__idom'( Y ) ), ~(
% 1.43/1.78 'class_OrderedGroup_Oab__group__add'( Y ) ) ] )
% 1.43/1.78 , clause( 1042, [ ~( 'class_Ring__and__Field_Oordered__idom'( Y ) ), =(
% 1.43/1.78 'c_minus'( 'c_0', X, Y ), 'c_uminus'( X, Y ) ) ] )
% 1.43/1.78 , 1, clause( 5247, [ =( 'c_minus'( Y, X, Z ), 'c_uminus'( 'c_minus'( X, Y,
% 1.43/1.78 Z ), Z ) ), ~( 'class_OrderedGroup_Oab__group__add'( Z ) ) ] )
% 1.43/1.78 , 0, 6, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 1.43/1.78 :=( X, 'c_0' ), :=( Y, X ), :=( Z, Y )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 resolution(
% 1.43/1.78 clause( 5255, [ =( 'c_minus'( X, 'c_0', Y ), 'c_uminus'( 'c_uminus'( X, Y )
% 1.43/1.78 , Y ) ), ~( 'class_Ring__and__Field_Oordered__idom'( Y ) ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.43/1.78 , clause( 5254, [ =( 'c_minus'( X, 'c_0', Y ), 'c_uminus'( 'c_uminus'( X, Y
% 1.43/1.78 ), Y ) ), ~( 'class_Ring__and__Field_Oordered__idom'( Y ) ), ~(
% 1.43/1.78 'class_OrderedGroup_Oab__group__add'( Y ) ) ] )
% 1.43/1.78 , 2, clause( 25, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.43/1.78 'class_OrderedGroup_Oab__group__add'( X ) ] )
% 1.43/1.78 , 1, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [ :=( X
% 1.43/1.78 , Y )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 eqswap(
% 1.43/1.78 clause( 5256, [ =( 'c_uminus'( 'c_uminus'( X, Y ), Y ), 'c_minus'( X, 'c_0'
% 1.43/1.78 , Y ) ), ~( 'class_Ring__and__Field_Oordered__idom'( Y ) ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.43/1.78 , clause( 5255, [ =( 'c_minus'( X, 'c_0', Y ), 'c_uminus'( 'c_uminus'( X, Y
% 1.43/1.78 ), Y ) ), ~( 'class_Ring__and__Field_Oordered__idom'( Y ) ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.43/1.78 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 factor(
% 1.43/1.78 clause( 5257, [ =( 'c_uminus'( 'c_uminus'( X, Y ), Y ), 'c_minus'( X, 'c_0'
% 1.43/1.78 , Y ) ), ~( 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.43/1.78 , clause( 5256, [ =( 'c_uminus'( 'c_uminus'( X, Y ), Y ), 'c_minus'( X,
% 1.43/1.78 'c_0', Y ) ), ~( 'class_Ring__and__Field_Oordered__idom'( Y ) ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.43/1.78 , 1, 2, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 subsumption(
% 1.43/1.78 clause( 1046, [ =( 'c_uminus'( 'c_uminus'( X, Y ), Y ), 'c_minus'( X, 'c_0'
% 1.43/1.78 , Y ) ), ~( 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.43/1.78 , clause( 5257, [ =( 'c_uminus'( 'c_uminus'( X, Y ), Y ), 'c_minus'( X,
% 1.43/1.78 'c_0', Y ) ), ~( 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.43/1.78 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.43/1.78 ), ==>( 1, 1 )] ) ).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 eqswap(
% 1.43/1.78 clause( 5259, [ =( 'c_uminus'( X, Y ), 'c_minus'( 'c_0', X, Y ) ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.43/1.78 , clause( 1042, [ ~( 'class_Ring__and__Field_Oordered__idom'( Y ) ), =(
% 1.43/1.78 'c_minus'( 'c_0', X, Y ), 'c_uminus'( X, Y ) ) ] )
% 1.43/1.78 , 1, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 paramod(
% 1.43/1.78 clause( 5263, [ =( 'c_uminus'( 'c_uminus'( X, Y ), Y ), 'c_plus'( 'c_0', X
% 1.43/1.78 , Y ) ), ~( 'class_OrderedGroup_Oab__group__add'( Y ) ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.43/1.78 , clause( 12, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.43/1.78 'c_minus'( Y, 'c_uminus'( Z, X ), X ), 'c_plus'( Y, Z, X ) ) ] )
% 1.43/1.78 , 1, clause( 5259, [ =( 'c_uminus'( X, Y ), 'c_minus'( 'c_0', X, Y ) ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.43/1.78 , 0, 6, substitution( 0, [ :=( X, Y ), :=( Y, 'c_0' ), :=( Z, X )] ),
% 1.43/1.78 substitution( 1, [ :=( X, 'c_uminus'( X, Y ) ), :=( Y, Y )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 paramod(
% 1.43/1.78 clause( 5264, [ =( 'c_minus'( X, 'c_0', Y ), 'c_plus'( 'c_0', X, Y ) ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ), ~(
% 1.43/1.78 'class_OrderedGroup_Oab__group__add'( Y ) ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.43/1.78 , clause( 1046, [ =( 'c_uminus'( 'c_uminus'( X, Y ), Y ), 'c_minus'( X,
% 1.43/1.78 'c_0', Y ) ), ~( 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.43/1.78 , 0, clause( 5263, [ =( 'c_uminus'( 'c_uminus'( X, Y ), Y ), 'c_plus'(
% 1.43/1.78 'c_0', X, Y ) ), ~( 'class_OrderedGroup_Oab__group__add'( Y ) ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.43/1.78 , 0, 1, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 1.43/1.78 :=( X, X ), :=( Y, Y )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 factor(
% 1.43/1.78 clause( 5265, [ =( 'c_minus'( X, 'c_0', Y ), 'c_plus'( 'c_0', X, Y ) ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ), ~(
% 1.43/1.78 'class_OrderedGroup_Oab__group__add'( Y ) ) ] )
% 1.43/1.78 , clause( 5264, [ =( 'c_minus'( X, 'c_0', Y ), 'c_plus'( 'c_0', X, Y ) ),
% 1.43/1.78 ~( 'class_Ring__and__Field_Oordered__idom'( Y ) ), ~(
% 1.43/1.78 'class_OrderedGroup_Oab__group__add'( Y ) ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.43/1.78 , 1, 3, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 paramod(
% 1.43/1.78 clause( 5266, [ =( 'c_minus'( X, 'c_0', Y ), X ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ), ~(
% 1.43/1.78 'class_OrderedGroup_Oab__group__add'( Y ) ) ] )
% 1.43/1.78 , clause( 53, [ =( 'c_plus'( 'c_0', X, Y ), X ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.43/1.78 , 0, clause( 5265, [ =( 'c_minus'( X, 'c_0', Y ), 'c_plus'( 'c_0', X, Y ) )
% 1.43/1.78 , ~( 'class_Ring__and__Field_Oordered__idom'( Y ) ), ~(
% 1.43/1.78 'class_OrderedGroup_Oab__group__add'( Y ) ) ] )
% 1.43/1.78 , 0, 5, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 1.43/1.78 :=( X, X ), :=( Y, Y )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 factor(
% 1.43/1.78 clause( 5267, [ =( 'c_minus'( X, 'c_0', Y ), X ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ), ~(
% 1.43/1.78 'class_OrderedGroup_Oab__group__add'( Y ) ) ] )
% 1.43/1.78 , clause( 5266, [ =( 'c_minus'( X, 'c_0', Y ), X ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ), ~(
% 1.43/1.78 'class_OrderedGroup_Oab__group__add'( Y ) ) ] )
% 1.43/1.78 , 1, 2, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 resolution(
% 1.43/1.78 clause( 5268, [ =( 'c_minus'( X, 'c_0', Y ), X ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.43/1.78 , clause( 5267, [ =( 'c_minus'( X, 'c_0', Y ), X ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ), ~(
% 1.43/1.78 'class_OrderedGroup_Oab__group__add'( Y ) ) ] )
% 1.43/1.78 , 2, clause( 25, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.43/1.78 'class_OrderedGroup_Oab__group__add'( X ) ] )
% 1.43/1.78 , 1, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [ :=( X
% 1.43/1.78 , Y )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 factor(
% 1.43/1.78 clause( 5271, [ =( 'c_minus'( X, 'c_0', Y ), X ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.43/1.78 , clause( 5268, [ =( 'c_minus'( X, 'c_0', Y ), X ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.43/1.78 , 1, 2, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 subsumption(
% 1.43/1.78 clause( 1047, [ ~( 'class_Ring__and__Field_Oordered__idom'( Y ) ), =(
% 1.43/1.78 'c_minus'( X, 'c_0', Y ), X ) ] )
% 1.43/1.78 , clause( 5271, [ =( 'c_minus'( X, 'c_0', Y ), X ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.43/1.78 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 1
% 1.43/1.78 ), ==>( 1, 0 )] ) ).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 eqswap(
% 1.43/1.78 clause( 5272, [ =( 'c_HOL_Oabs'( X, Y ), 'c_uminus'( X, Y ) ), ~(
% 1.43/1.78 'c_lessequals'( X, 'c_0', Y ) ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.43/1.78 , clause( 44, [ ~( 'c_lessequals'( X, 'c_0', Y ) ), =( 'c_uminus'( X, Y ),
% 1.43/1.78 'c_HOL_Oabs'( X, Y ) ), ~( 'class_Ring__and__Field_Oordered__idom'( Y ) )
% 1.43/1.78 ] )
% 1.43/1.78 , 1, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 resolution(
% 1.43/1.78 clause( 5274, [ =( 'c_HOL_Oabs'( 'c_minus'( X, Y, 't_b' ), 't_b' ),
% 1.43/1.78 'c_uminus'( 'c_minus'( X, Y, 't_b' ), 't_b' ) ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( 't_b' ) ), 'c_lessequals'( Y, X
% 1.43/1.78 , 't_b' ) ] )
% 1.43/1.78 , clause( 5272, [ =( 'c_HOL_Oabs'( X, Y ), 'c_uminus'( X, Y ) ), ~(
% 1.43/1.78 'c_lessequals'( X, 'c_0', Y ) ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.43/1.78 , 1, clause( 126, [ 'c_lessequals'( 'c_minus'( X, Y, 't_b' ), 'c_0', 't_b'
% 1.43/1.78 ), 'c_lessequals'( Y, X, 't_b' ) ] )
% 1.43/1.78 , 0, substitution( 0, [ :=( X, 'c_minus'( X, Y, 't_b' ) ), :=( Y, 't_b' )] )
% 1.43/1.78 , substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 paramod(
% 1.43/1.78 clause( 5276, [ =( 'c_HOL_Oabs'( 'c_minus'( X, Y, 't_b' ), 't_b' ),
% 1.43/1.78 'c_minus'( Y, X, 't_b' ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 1.43/1.78 't_b' ) ), ~( 'class_Ring__and__Field_Oordered__idom'( 't_b' ) ),
% 1.43/1.78 'c_lessequals'( Y, X, 't_b' ) ] )
% 1.43/1.78 , clause( 175, [ =( 'c_uminus'( 'c_minus'( X, Y, Z ), Z ), 'c_minus'( Y, X
% 1.43/1.78 , Z ) ), ~( 'class_Ring__and__Field_Oordered__idom'( Z ) ) ] )
% 1.43/1.78 , 0, clause( 5274, [ =( 'c_HOL_Oabs'( 'c_minus'( X, Y, 't_b' ), 't_b' ),
% 1.43/1.78 'c_uminus'( 'c_minus'( X, Y, 't_b' ), 't_b' ) ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( 't_b' ) ), 'c_lessequals'( Y, X
% 1.43/1.78 , 't_b' ) ] )
% 1.43/1.78 , 0, 7, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, 't_b' )] ),
% 1.43/1.78 substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 factor(
% 1.43/1.78 clause( 5277, [ =( 'c_HOL_Oabs'( 'c_minus'( X, Y, 't_b' ), 't_b' ),
% 1.43/1.78 'c_minus'( Y, X, 't_b' ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 1.43/1.78 't_b' ) ), 'c_lessequals'( Y, X, 't_b' ) ] )
% 1.43/1.78 , clause( 5276, [ =( 'c_HOL_Oabs'( 'c_minus'( X, Y, 't_b' ), 't_b' ),
% 1.43/1.78 'c_minus'( Y, X, 't_b' ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 1.43/1.78 't_b' ) ), ~( 'class_Ring__and__Field_Oordered__idom'( 't_b' ) ),
% 1.43/1.78 'c_lessequals'( Y, X, 't_b' ) ] )
% 1.43/1.78 , 1, 2, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 resolution(
% 1.43/1.78 clause( 5278, [ =( 'c_HOL_Oabs'( 'c_minus'( X, Y, 't_b' ), 't_b' ),
% 1.43/1.78 'c_minus'( Y, X, 't_b' ) ), 'c_lessequals'( Y, X, 't_b' ) ] )
% 1.43/1.78 , clause( 5277, [ =( 'c_HOL_Oabs'( 'c_minus'( X, Y, 't_b' ), 't_b' ),
% 1.43/1.78 'c_minus'( Y, X, 't_b' ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 1.43/1.78 't_b' ) ), 'c_lessequals'( Y, X, 't_b' ) ] )
% 1.43/1.78 , 1, clause( 2, [ 'class_Ring__and__Field_Oordered__idom'( 't_b' ) ] )
% 1.43/1.78 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [] )
% 1.43/1.78 ).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 subsumption(
% 1.43/1.78 clause( 1336, [ 'c_lessequals'( X, Y, 't_b' ), =( 'c_HOL_Oabs'( 'c_minus'(
% 1.43/1.78 Y, X, 't_b' ), 't_b' ), 'c_minus'( X, Y, 't_b' ) ) ] )
% 1.43/1.78 , clause( 5278, [ =( 'c_HOL_Oabs'( 'c_minus'( X, Y, 't_b' ), 't_b' ),
% 1.43/1.78 'c_minus'( Y, X, 't_b' ) ), 'c_lessequals'( Y, X, 't_b' ) ] )
% 1.43/1.78 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 1
% 1.43/1.78 ), ==>( 1, 0 )] ) ).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 eqswap(
% 1.43/1.78 clause( 5280, [ =( 'c_HOL_Oabs'( X, 't_b' ), 'c_uminus'( X, 't_b' ) ), ~(
% 1.43/1.78 'c_less'( X, 'c_0', 't_b' ) ) ] )
% 1.43/1.78 , clause( 72, [ ~( 'c_less'( X, 'c_0', 't_b' ) ), =( 'c_uminus'( X, 't_b' )
% 1.43/1.78 , 'c_HOL_Oabs'( X, 't_b' ) ) ] )
% 1.43/1.78 , 1, substitution( 0, [ :=( X, X )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 eqswap(
% 1.43/1.78 clause( 5283, [ =( X, 'c_HOL_Oabs'( X, 't_b' ) ), =( 'c_uminus'( X, 't_b' )
% 1.43/1.78 , 'c_HOL_Oabs'( X, 't_b' ) ) ] )
% 1.43/1.78 , clause( 478, [ =( 'c_HOL_Oabs'( X, 't_b' ), X ), =( 'c_uminus'( X, 't_b'
% 1.43/1.78 ), 'c_HOL_Oabs'( X, 't_b' ) ) ] )
% 1.43/1.78 , 0, substitution( 0, [ :=( X, X )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 paramod(
% 1.43/1.78 clause( 5286, [ =( 'c_HOL_Oabs'( 'c_uminus'( X, 't_b' ), 't_b' ), X ), ~(
% 1.43/1.78 'c_less'( 'c_uminus'( X, 't_b' ), 'c_0', 't_b' ) ) ] )
% 1.43/1.78 , clause( 188, [ =( 'c_uminus'( 'c_uminus'( X, 't_b' ), 't_b' ), X ) ] )
% 1.43/1.78 , 0, clause( 5280, [ =( 'c_HOL_Oabs'( X, 't_b' ), 'c_uminus'( X, 't_b' ) )
% 1.43/1.78 , ~( 'c_less'( X, 'c_0', 't_b' ) ) ] )
% 1.43/1.78 , 0, 6, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X,
% 1.43/1.78 'c_uminus'( X, 't_b' ) )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 paramod(
% 1.43/1.78 clause( 5287, [ =( 'c_HOL_Oabs'( X, 't_b' ), X ), ~( 'c_less'( 'c_uminus'(
% 1.43/1.78 X, 't_b' ), 'c_0', 't_b' ) ) ] )
% 1.43/1.78 , clause( 39, [ =( 'c_HOL_Oabs'( 'c_uminus'( X, 't_b' ), 't_b' ),
% 1.43/1.78 'c_HOL_Oabs'( X, 't_b' ) ) ] )
% 1.43/1.78 , 0, clause( 5286, [ =( 'c_HOL_Oabs'( 'c_uminus'( X, 't_b' ), 't_b' ), X )
% 1.43/1.78 , ~( 'c_less'( 'c_uminus'( X, 't_b' ), 'c_0', 't_b' ) ) ] )
% 1.43/1.78 , 0, 1, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 1.43/1.78 ).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 paramod(
% 1.43/1.78 clause( 5288, [ ~( 'c_less'( 'c_HOL_Oabs'( X, 't_b' ), 'c_0', 't_b' ) ),
% 1.43/1.78 =( X, 'c_HOL_Oabs'( X, 't_b' ) ), =( 'c_HOL_Oabs'( X, 't_b' ), X ) ] )
% 1.43/1.78 , clause( 5283, [ =( X, 'c_HOL_Oabs'( X, 't_b' ) ), =( 'c_uminus'( X, 't_b'
% 1.43/1.78 ), 'c_HOL_Oabs'( X, 't_b' ) ) ] )
% 1.43/1.78 , 1, clause( 5287, [ =( 'c_HOL_Oabs'( X, 't_b' ), X ), ~( 'c_less'(
% 1.43/1.78 'c_uminus'( X, 't_b' ), 'c_0', 't_b' ) ) ] )
% 1.43/1.78 , 1, 2, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 1.43/1.78 ).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 eqswap(
% 1.43/1.78 clause( 5289, [ =( 'c_HOL_Oabs'( X, 't_b' ), X ), ~( 'c_less'( 'c_HOL_Oabs'(
% 1.43/1.78 X, 't_b' ), 'c_0', 't_b' ) ), =( 'c_HOL_Oabs'( X, 't_b' ), X ) ] )
% 1.43/1.78 , clause( 5288, [ ~( 'c_less'( 'c_HOL_Oabs'( X, 't_b' ), 'c_0', 't_b' ) ),
% 1.43/1.78 =( X, 'c_HOL_Oabs'( X, 't_b' ) ), =( 'c_HOL_Oabs'( X, 't_b' ), X ) ] )
% 1.43/1.78 , 1, substitution( 0, [ :=( X, X )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 factor(
% 1.43/1.78 clause( 5291, [ =( 'c_HOL_Oabs'( X, 't_b' ), X ), ~( 'c_less'( 'c_HOL_Oabs'(
% 1.43/1.78 X, 't_b' ), 'c_0', 't_b' ) ) ] )
% 1.43/1.78 , clause( 5289, [ =( 'c_HOL_Oabs'( X, 't_b' ), X ), ~( 'c_less'(
% 1.43/1.78 'c_HOL_Oabs'( X, 't_b' ), 'c_0', 't_b' ) ), =( 'c_HOL_Oabs'( X, 't_b' ),
% 1.43/1.78 X ) ] )
% 1.43/1.78 , 0, 2, substitution( 0, [ :=( X, X )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 subsumption(
% 1.43/1.78 clause( 1344, [ =( 'c_HOL_Oabs'( X, 't_b' ), X ), ~( 'c_less'( 'c_HOL_Oabs'(
% 1.43/1.78 X, 't_b' ), 'c_0', 't_b' ) ) ] )
% 1.43/1.78 , clause( 5291, [ =( 'c_HOL_Oabs'( X, 't_b' ), X ), ~( 'c_less'(
% 1.43/1.78 'c_HOL_Oabs'( X, 't_b' ), 'c_0', 't_b' ) ) ] )
% 1.43/1.78 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 1.43/1.78 1 )] ) ).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 paramod(
% 1.43/1.78 clause( 5294, [ 'c_lessequals'( 'c_0', X, 't_b' ), ~( 'c_less'(
% 1.43/1.78 'c_HOL_Oabs'( X, 't_b' ), 'c_0', 't_b' ) ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( 't_b' ) ) ] )
% 1.43/1.78 , clause( 1344, [ =( 'c_HOL_Oabs'( X, 't_b' ), X ), ~( 'c_less'(
% 1.43/1.78 'c_HOL_Oabs'( X, 't_b' ), 'c_0', 't_b' ) ) ] )
% 1.43/1.78 , 0, clause( 36, [ 'c_lessequals'( 'c_0', 'c_HOL_Oabs'( X, Y ), Y ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.43/1.78 , 0, 2, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ),
% 1.43/1.78 :=( Y, 't_b' )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 resolution(
% 1.43/1.78 clause( 5305, [ 'c_lessequals'( 'c_0', X, 't_b' ), ~( 'c_less'(
% 1.43/1.78 'c_HOL_Oabs'( X, 't_b' ), 'c_0', 't_b' ) ) ] )
% 1.43/1.78 , clause( 5294, [ 'c_lessequals'( 'c_0', X, 't_b' ), ~( 'c_less'(
% 1.43/1.78 'c_HOL_Oabs'( X, 't_b' ), 'c_0', 't_b' ) ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( 't_b' ) ) ] )
% 1.43/1.78 , 2, clause( 2, [ 'class_Ring__and__Field_Oordered__idom'( 't_b' ) ] )
% 1.43/1.78 , 0, substitution( 0, [ :=( X, X )] ), substitution( 1, [] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 subsumption(
% 1.43/1.78 clause( 1393, [ 'c_lessequals'( 'c_0', X, 't_b' ), ~( 'c_less'(
% 1.43/1.78 'c_HOL_Oabs'( X, 't_b' ), 'c_0', 't_b' ) ) ] )
% 1.43/1.78 , clause( 5305, [ 'c_lessequals'( 'c_0', X, 't_b' ), ~( 'c_less'(
% 1.43/1.78 'c_HOL_Oabs'( X, 't_b' ), 'c_0', 't_b' ) ) ] )
% 1.43/1.78 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 1.43/1.78 1 )] ) ).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 eqswap(
% 1.43/1.78 clause( 5307, [ =( X, 'c_HOL_Oabs'( X, 't_b' ) ), =( 'c_uminus'( X, 't_b' )
% 1.43/1.78 , 'c_HOL_Oabs'( X, 't_b' ) ) ] )
% 1.43/1.78 , clause( 478, [ =( 'c_HOL_Oabs'( X, 't_b' ), X ), =( 'c_uminus'( X, 't_b'
% 1.43/1.78 ), 'c_HOL_Oabs'( X, 't_b' ) ) ] )
% 1.43/1.78 , 0, substitution( 0, [ :=( X, X )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 paramod(
% 1.43/1.78 clause( 5310, [ ~( 'c_lessequals'( 'c_HOL_Oabs'( X, 't_b' ), 'c_0', 't_b' )
% 1.43/1.78 ), =( X, 'c_HOL_Oabs'( X, 't_b' ) ), =( 'c_HOL_Oabs'( X, 't_b' ), X ) ]
% 1.43/1.78 )
% 1.43/1.78 , clause( 5307, [ =( X, 'c_HOL_Oabs'( X, 't_b' ) ), =( 'c_uminus'( X, 't_b'
% 1.43/1.78 ), 'c_HOL_Oabs'( X, 't_b' ) ) ] )
% 1.43/1.78 , 1, clause( 236, [ ~( 'c_lessequals'( 'c_uminus'( X, 't_b' ), 'c_0', 't_b'
% 1.43/1.78 ) ), =( 'c_HOL_Oabs'( X, 't_b' ), X ) ] )
% 1.43/1.78 , 0, 2, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 1.43/1.78 ).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 eqswap(
% 1.43/1.78 clause( 5311, [ =( 'c_HOL_Oabs'( X, 't_b' ), X ), ~( 'c_lessequals'(
% 1.43/1.78 'c_HOL_Oabs'( X, 't_b' ), 'c_0', 't_b' ) ), =( 'c_HOL_Oabs'( X, 't_b' ),
% 1.43/1.78 X ) ] )
% 1.43/1.78 , clause( 5310, [ ~( 'c_lessequals'( 'c_HOL_Oabs'( X, 't_b' ), 'c_0', 't_b'
% 1.43/1.78 ) ), =( X, 'c_HOL_Oabs'( X, 't_b' ) ), =( 'c_HOL_Oabs'( X, 't_b' ), X )
% 1.43/1.78 ] )
% 1.43/1.78 , 1, substitution( 0, [ :=( X, X )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 factor(
% 1.43/1.78 clause( 5313, [ =( 'c_HOL_Oabs'( X, 't_b' ), X ), ~( 'c_lessequals'(
% 1.43/1.78 'c_HOL_Oabs'( X, 't_b' ), 'c_0', 't_b' ) ) ] )
% 1.43/1.78 , clause( 5311, [ =( 'c_HOL_Oabs'( X, 't_b' ), X ), ~( 'c_lessequals'(
% 1.43/1.78 'c_HOL_Oabs'( X, 't_b' ), 'c_0', 't_b' ) ), =( 'c_HOL_Oabs'( X, 't_b' ),
% 1.43/1.78 X ) ] )
% 1.43/1.78 , 0, 2, substitution( 0, [ :=( X, X )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 subsumption(
% 1.43/1.78 clause( 1515, [ =( 'c_HOL_Oabs'( X, 't_b' ), X ), ~( 'c_lessequals'(
% 1.43/1.78 'c_HOL_Oabs'( X, 't_b' ), 'c_0', 't_b' ) ) ] )
% 1.43/1.78 , clause( 5313, [ =( 'c_HOL_Oabs'( X, 't_b' ), X ), ~( 'c_lessequals'(
% 1.43/1.78 'c_HOL_Oabs'( X, 't_b' ), 'c_0', 't_b' ) ) ] )
% 1.43/1.78 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 1.43/1.78 1 )] ) ).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 paramod(
% 1.43/1.78 clause( 5316, [ ~( 'c_less'( X, 'c_0', 't_b' ) ), ~( 'c_lessequals'(
% 1.43/1.78 'c_HOL_Oabs'( X, 't_b' ), 'c_0', 't_b' ) ), 'c_lessequals'( 'c_0', X,
% 1.43/1.78 't_b' ) ] )
% 1.43/1.78 , clause( 1515, [ =( 'c_HOL_Oabs'( X, 't_b' ), X ), ~( 'c_lessequals'(
% 1.43/1.78 'c_HOL_Oabs'( X, 't_b' ), 'c_0', 't_b' ) ) ] )
% 1.43/1.78 , 0, clause( 1393, [ 'c_lessequals'( 'c_0', X, 't_b' ), ~( 'c_less'(
% 1.43/1.78 'c_HOL_Oabs'( X, 't_b' ), 'c_0', 't_b' ) ) ] )
% 1.43/1.78 , 1, 2, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 1.43/1.78 ).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 resolution(
% 1.43/1.78 clause( 5327, [ ~( 'c_lessequals'( 'c_HOL_Oabs'( X, 't_b' ), 'c_0', 't_b' )
% 1.43/1.78 ), 'c_lessequals'( 'c_0', X, 't_b' ), 'c_lessequals'( 'c_0', X, 't_b' )
% 1.43/1.78 ] )
% 1.43/1.78 , clause( 5316, [ ~( 'c_less'( X, 'c_0', 't_b' ) ), ~( 'c_lessequals'(
% 1.43/1.78 'c_HOL_Oabs'( X, 't_b' ), 'c_0', 't_b' ) ), 'c_lessequals'( 'c_0', X,
% 1.43/1.78 't_b' ) ] )
% 1.43/1.78 , 0, clause( 94, [ 'c_less'( X, Y, 't_b' ), 'c_lessequals'( Y, X, 't_b' ) ]
% 1.43/1.78 )
% 1.43/1.78 , 0, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ), :=( Y
% 1.43/1.78 , 'c_0' )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 factor(
% 1.43/1.78 clause( 5329, [ ~( 'c_lessequals'( 'c_HOL_Oabs'( X, 't_b' ), 'c_0', 't_b' )
% 1.43/1.78 ), 'c_lessequals'( 'c_0', X, 't_b' ) ] )
% 1.43/1.78 , clause( 5327, [ ~( 'c_lessequals'( 'c_HOL_Oabs'( X, 't_b' ), 'c_0', 't_b'
% 1.43/1.78 ) ), 'c_lessequals'( 'c_0', X, 't_b' ), 'c_lessequals'( 'c_0', X, 't_b'
% 1.43/1.78 ) ] )
% 1.43/1.78 , 1, 2, substitution( 0, [ :=( X, X )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 subsumption(
% 1.43/1.78 clause( 1539, [ 'c_lessequals'( 'c_0', X, 't_b' ), ~( 'c_lessequals'(
% 1.43/1.78 'c_HOL_Oabs'( X, 't_b' ), 'c_0', 't_b' ) ) ] )
% 1.43/1.78 , clause( 5329, [ ~( 'c_lessequals'( 'c_HOL_Oabs'( X, 't_b' ), 'c_0', 't_b'
% 1.43/1.78 ) ), 'c_lessequals'( 'c_0', X, 't_b' ) ] )
% 1.43/1.78 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 1 ), ==>( 1,
% 1.43/1.78 0 )] ) ).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 paramod(
% 1.43/1.78 clause( 5332, [ ~( 'c_lessequals'( 'c_0', 'c_plus'( Y, 'c_uminus'( X, 't_b'
% 1.43/1.78 ), 't_b' ), 't_b' ) ), ~( 'class_OrderedGroup_Oab__group__add'( 't_b' )
% 1.43/1.78 ), 'c_lessequals'( X, Y, 't_b' ) ] )
% 1.43/1.78 , clause( 162, [ ~( 'class_OrderedGroup_Oab__group__add'( Y ) ), =(
% 1.43/1.78 'c_plus'( 'c_uminus'( X, Y ), X, Y ), 'c_0' ) ] )
% 1.43/1.78 , 1, clause( 111, [ ~( 'c_lessequals'( 'c_plus'( X, Y, 't_b' ), 'c_plus'( Z
% 1.43/1.78 , X, 't_b' ), 't_b' ) ), 'c_lessequals'( Y, Z, 't_b' ) ] )
% 1.43/1.78 , 0, 2, substitution( 0, [ :=( X, X ), :=( Y, 't_b' )] ), substitution( 1
% 1.43/1.78 , [ :=( X, 'c_uminus'( X, 't_b' ) ), :=( Y, X ), :=( Z, Y )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 paramod(
% 1.43/1.78 clause( 5334, [ ~( 'c_lessequals'( 'c_0', 'c_minus'( X, Y, 't_b' ), 't_b' )
% 1.43/1.78 ), ~( 'class_OrderedGroup_Oab__group__add'( 't_b' ) ), 'c_lessequals'( Y
% 1.43/1.78 , X, 't_b' ) ] )
% 1.43/1.78 , clause( 192, [ =( 'c_plus'( Y, 'c_uminus'( X, 't_b' ), 't_b' ), 'c_minus'(
% 1.43/1.78 Y, X, 't_b' ) ) ] )
% 1.43/1.78 , 0, clause( 5332, [ ~( 'c_lessequals'( 'c_0', 'c_plus'( Y, 'c_uminus'( X,
% 1.43/1.78 't_b' ), 't_b' ), 't_b' ) ), ~( 'class_OrderedGroup_Oab__group__add'(
% 1.43/1.78 't_b' ) ), 'c_lessequals'( X, Y, 't_b' ) ] )
% 1.43/1.78 , 0, 3, substitution( 0, [ :=( X, Y ), :=( Y, X )] ), substitution( 1, [
% 1.43/1.78 :=( X, Y ), :=( Y, X )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 resolution(
% 1.43/1.78 clause( 5335, [ ~( 'c_lessequals'( 'c_0', 'c_minus'( X, Y, 't_b' ), 't_b' )
% 1.43/1.78 ), 'c_lessequals'( Y, X, 't_b' ) ] )
% 1.43/1.78 , clause( 5334, [ ~( 'c_lessequals'( 'c_0', 'c_minus'( X, Y, 't_b' ), 't_b'
% 1.43/1.78 ) ), ~( 'class_OrderedGroup_Oab__group__add'( 't_b' ) ), 'c_lessequals'(
% 1.43/1.78 Y, X, 't_b' ) ] )
% 1.43/1.78 , 1, clause( 29, [ 'class_OrderedGroup_Oab__group__add'( 't_b' ) ] )
% 1.43/1.78 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [] )
% 1.43/1.78 ).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 subsumption(
% 1.43/1.78 clause( 2641, [ 'c_lessequals'( X, Y, 't_b' ), ~( 'c_lessequals'( 'c_0',
% 1.43/1.78 'c_minus'( Y, X, 't_b' ), 't_b' ) ) ] )
% 1.43/1.78 , clause( 5335, [ ~( 'c_lessequals'( 'c_0', 'c_minus'( X, Y, 't_b' ), 't_b'
% 1.43/1.78 ) ), 'c_lessequals'( Y, X, 't_b' ) ] )
% 1.43/1.78 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 1
% 1.43/1.78 ), ==>( 1, 0 )] ) ).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 resolution(
% 1.43/1.78 clause( 5337, [ 'c_lessequals'( X, Y, 't_b' ), ~( 'c_lessequals'(
% 1.43/1.78 'c_HOL_Oabs'( 'c_minus'( Y, X, 't_b' ), 't_b' ), 'c_0', 't_b' ) ) ] )
% 1.43/1.78 , clause( 2641, [ 'c_lessequals'( X, Y, 't_b' ), ~( 'c_lessequals'( 'c_0',
% 1.43/1.78 'c_minus'( Y, X, 't_b' ), 't_b' ) ) ] )
% 1.43/1.78 , 1, clause( 1539, [ 'c_lessequals'( 'c_0', X, 't_b' ), ~( 'c_lessequals'(
% 1.43/1.78 'c_HOL_Oabs'( X, 't_b' ), 'c_0', 't_b' ) ) ] )
% 1.43/1.78 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [ :=( X
% 1.43/1.78 , 'c_minus'( Y, X, 't_b' ) )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 paramod(
% 1.43/1.78 clause( 5338, [ ~( 'c_lessequals'( 'c_minus'( Y, X, 't_b' ), 'c_0', 't_b' )
% 1.43/1.78 ), 'c_lessequals'( Y, X, 't_b' ), 'c_lessequals'( Y, X, 't_b' ) ] )
% 1.43/1.78 , clause( 1336, [ 'c_lessequals'( X, Y, 't_b' ), =( 'c_HOL_Oabs'( 'c_minus'(
% 1.43/1.78 Y, X, 't_b' ), 't_b' ), 'c_minus'( X, Y, 't_b' ) ) ] )
% 1.43/1.78 , 1, clause( 5337, [ 'c_lessequals'( X, Y, 't_b' ), ~( 'c_lessequals'(
% 1.43/1.78 'c_HOL_Oabs'( 'c_minus'( Y, X, 't_b' ), 't_b' ), 'c_0', 't_b' ) ) ] )
% 1.43/1.78 , 1, 2, substitution( 0, [ :=( X, Y ), :=( Y, X )] ), substitution( 1, [
% 1.43/1.78 :=( X, Y ), :=( Y, X )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 factor(
% 1.43/1.78 clause( 5339, [ ~( 'c_lessequals'( 'c_minus'( X, Y, 't_b' ), 'c_0', 't_b' )
% 1.43/1.78 ), 'c_lessequals'( X, Y, 't_b' ) ] )
% 1.43/1.78 , clause( 5338, [ ~( 'c_lessequals'( 'c_minus'( Y, X, 't_b' ), 'c_0', 't_b'
% 1.43/1.78 ) ), 'c_lessequals'( Y, X, 't_b' ), 'c_lessequals'( Y, X, 't_b' ) ] )
% 1.43/1.78 , 1, 2, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 subsumption(
% 1.43/1.78 clause( 2780, [ 'c_lessequals'( X, Y, 't_b' ), ~( 'c_lessequals'( 'c_minus'(
% 1.43/1.78 X, Y, 't_b' ), 'c_0', 't_b' ) ) ] )
% 1.43/1.78 , clause( 5339, [ ~( 'c_lessequals'( 'c_minus'( X, Y, 't_b' ), 'c_0', 't_b'
% 1.43/1.78 ) ), 'c_lessequals'( X, Y, 't_b' ) ] )
% 1.43/1.78 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 1
% 1.43/1.78 ), ==>( 1, 0 )] ) ).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 resolution(
% 1.43/1.78 clause( 5341, [ 'c_lessequals'( X, Y, 't_b' ), ~( 'c_less'( 'c_HOL_Oabs'(
% 1.43/1.78 'c_minus'( Y, X, 't_b' ), 't_b' ), 'c_0', 't_b' ) ) ] )
% 1.43/1.78 , clause( 2641, [ 'c_lessequals'( X, Y, 't_b' ), ~( 'c_lessequals'( 'c_0',
% 1.43/1.78 'c_minus'( Y, X, 't_b' ), 't_b' ) ) ] )
% 1.43/1.78 , 1, clause( 1393, [ 'c_lessequals'( 'c_0', X, 't_b' ), ~( 'c_less'(
% 1.43/1.78 'c_HOL_Oabs'( X, 't_b' ), 'c_0', 't_b' ) ) ] )
% 1.43/1.78 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [ :=( X
% 1.43/1.78 , 'c_minus'( Y, X, 't_b' ) )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 paramod(
% 1.43/1.78 clause( 5342, [ ~( 'c_less'( 'c_minus'( Y, X, 't_b' ), 'c_0', 't_b' ) ),
% 1.43/1.78 'c_lessequals'( Y, X, 't_b' ), 'c_lessequals'( Y, X, 't_b' ) ] )
% 1.43/1.78 , clause( 1336, [ 'c_lessequals'( X, Y, 't_b' ), =( 'c_HOL_Oabs'( 'c_minus'(
% 1.43/1.78 Y, X, 't_b' ), 't_b' ), 'c_minus'( X, Y, 't_b' ) ) ] )
% 1.43/1.78 , 1, clause( 5341, [ 'c_lessequals'( X, Y, 't_b' ), ~( 'c_less'(
% 1.43/1.78 'c_HOL_Oabs'( 'c_minus'( Y, X, 't_b' ), 't_b' ), 'c_0', 't_b' ) ) ] )
% 1.43/1.78 , 1, 2, substitution( 0, [ :=( X, Y ), :=( Y, X )] ), substitution( 1, [
% 1.43/1.78 :=( X, Y ), :=( Y, X )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 factor(
% 1.43/1.78 clause( 5343, [ ~( 'c_less'( 'c_minus'( X, Y, 't_b' ), 'c_0', 't_b' ) ),
% 1.43/1.78 'c_lessequals'( X, Y, 't_b' ) ] )
% 1.43/1.78 , clause( 5342, [ ~( 'c_less'( 'c_minus'( Y, X, 't_b' ), 'c_0', 't_b' ) ),
% 1.43/1.78 'c_lessequals'( Y, X, 't_b' ), 'c_lessequals'( Y, X, 't_b' ) ] )
% 1.43/1.78 , 1, 2, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 subsumption(
% 1.43/1.78 clause( 2781, [ 'c_lessequals'( X, Y, 't_b' ), ~( 'c_less'( 'c_minus'( X, Y
% 1.43/1.78 , 't_b' ), 'c_0', 't_b' ) ) ] )
% 1.43/1.78 , clause( 5343, [ ~( 'c_less'( 'c_minus'( X, Y, 't_b' ), 'c_0', 't_b' ) ),
% 1.43/1.78 'c_lessequals'( X, Y, 't_b' ) ] )
% 1.43/1.78 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 1
% 1.43/1.78 ), ==>( 1, 0 )] ) ).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 paramod(
% 1.43/1.78 clause( 5346, [ ~( 'c_lessequals'( 'c_plus'( 'c_0', Y, 't_b' ), 'c_0',
% 1.43/1.78 't_b' ) ), ~( 'class_OrderedGroup_Oab__group__add'( 't_b' ) ),
% 1.43/1.78 'c_lessequals'( 'c_plus'( X, Y, 't_b' ), X, 't_b' ) ] )
% 1.43/1.78 , clause( 82, [ ~( 'class_OrderedGroup_Oab__group__add'( Y ) ), =(
% 1.43/1.78 'c_minus'( 'c_plus'( X, Z, Y ), X, Y ), 'c_plus'( 'c_0', Z, Y ) ) ] )
% 1.43/1.78 , 1, clause( 2780, [ 'c_lessequals'( X, Y, 't_b' ), ~( 'c_lessequals'(
% 1.43/1.78 'c_minus'( X, Y, 't_b' ), 'c_0', 't_b' ) ) ] )
% 1.43/1.78 , 1, 2, substitution( 0, [ :=( X, X ), :=( Y, 't_b' ), :=( Z, Y )] ),
% 1.43/1.78 substitution( 1, [ :=( X, 'c_plus'( X, Y, 't_b' ) ), :=( Y, X )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 paramod(
% 1.43/1.78 clause( 5347, [ ~( 'c_lessequals'( X, 'c_0', 't_b' ) ), ~(
% 1.43/1.78 'class_OrderedGroup_Oab__group__add'( 't_b' ) ), 'c_lessequals'( 'c_plus'(
% 1.43/1.78 Y, X, 't_b' ), Y, 't_b' ) ] )
% 1.43/1.78 , clause( 52, [ =( 'c_plus'( 'c_0', X, 't_b' ), X ) ] )
% 1.43/1.78 , 0, clause( 5346, [ ~( 'c_lessequals'( 'c_plus'( 'c_0', Y, 't_b' ), 'c_0'
% 1.43/1.78 , 't_b' ) ), ~( 'class_OrderedGroup_Oab__group__add'( 't_b' ) ),
% 1.43/1.78 'c_lessequals'( 'c_plus'( X, Y, 't_b' ), X, 't_b' ) ] )
% 1.43/1.78 , 0, 2, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, Y ),
% 1.43/1.78 :=( Y, X )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 resolution(
% 1.43/1.78 clause( 5348, [ ~( 'c_lessequals'( X, 'c_0', 't_b' ) ), 'c_lessequals'(
% 1.43/1.78 'c_plus'( Y, X, 't_b' ), Y, 't_b' ) ] )
% 1.43/1.78 , clause( 5347, [ ~( 'c_lessequals'( X, 'c_0', 't_b' ) ), ~(
% 1.43/1.78 'class_OrderedGroup_Oab__group__add'( 't_b' ) ), 'c_lessequals'( 'c_plus'(
% 1.43/1.78 Y, X, 't_b' ), Y, 't_b' ) ] )
% 1.43/1.78 , 1, clause( 29, [ 'class_OrderedGroup_Oab__group__add'( 't_b' ) ] )
% 1.43/1.78 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [] )
% 1.43/1.78 ).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 subsumption(
% 1.43/1.78 clause( 2908, [ 'c_lessequals'( 'c_plus'( X, Y, 't_b' ), X, 't_b' ), ~(
% 1.43/1.78 'c_lessequals'( Y, 'c_0', 't_b' ) ) ] )
% 1.43/1.78 , clause( 5348, [ ~( 'c_lessequals'( X, 'c_0', 't_b' ) ), 'c_lessequals'(
% 1.43/1.78 'c_plus'( Y, X, 't_b' ), Y, 't_b' ) ] )
% 1.43/1.78 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 1
% 1.43/1.78 ), ==>( 1, 0 )] ) ).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 resolution(
% 1.43/1.78 clause( 5350, [ 'c_lessequals'( 'c_plus'( X, 'c_minus'( 'v_k'( Y ), 'v_f'(
% 1.43/1.78 Y ), 't_b' ), 't_b' ), X, 't_b' ) ] )
% 1.43/1.78 , clause( 2908, [ 'c_lessequals'( 'c_plus'( X, Y, 't_b' ), X, 't_b' ), ~(
% 1.43/1.78 'c_lessequals'( Y, 'c_0', 't_b' ) ) ] )
% 1.43/1.78 , 1, clause( 139, [ 'c_lessequals'( 'c_minus'( 'v_k'( X ), 'v_f'( X ),
% 1.43/1.78 't_b' ), 'c_0', 't_b' ) ] )
% 1.43/1.78 , 0, substitution( 0, [ :=( X, X ), :=( Y, 'c_minus'( 'v_k'( Y ), 'v_f'( Y
% 1.43/1.78 ), 't_b' ) )] ), substitution( 1, [ :=( X, Y )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 paramod(
% 1.43/1.78 clause( 5351, [ 'c_lessequals'( 'c_minus'( 'c_plus'( X, 'v_k'( Y ), 't_b' )
% 1.43/1.78 , 'v_f'( Y ), 't_b' ), X, 't_b' ) ] )
% 1.43/1.78 , clause( 60, [ =( 'c_plus'( X, 'c_minus'( Y, Z, 't_b' ), 't_b' ),
% 1.43/1.78 'c_minus'( 'c_plus'( X, Y, 't_b' ), Z, 't_b' ) ) ] )
% 1.43/1.78 , 0, clause( 5350, [ 'c_lessequals'( 'c_plus'( X, 'c_minus'( 'v_k'( Y ),
% 1.43/1.78 'v_f'( Y ), 't_b' ), 't_b' ), X, 't_b' ) ] )
% 1.43/1.78 , 0, 1, substitution( 0, [ :=( X, X ), :=( Y, 'v_k'( Y ) ), :=( Z, 'v_f'( Y
% 1.43/1.78 ) )] ), substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 subsumption(
% 1.43/1.78 clause( 3395, [ 'c_lessequals'( 'c_minus'( 'c_plus'( X, 'v_k'( Y ), 't_b' )
% 1.43/1.78 , 'v_f'( Y ), 't_b' ), X, 't_b' ) ] )
% 1.43/1.78 , clause( 5351, [ 'c_lessequals'( 'c_minus'( 'c_plus'( X, 'v_k'( Y ), 't_b'
% 1.43/1.78 ), 'v_f'( Y ), 't_b' ), X, 't_b' ) ] )
% 1.43/1.78 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.43/1.78 )] ) ).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 eqswap(
% 1.43/1.78 clause( 5352, [ =( 'c_HOL_Oabs'( 'c_minus'( X, Y, Z ), Z ), 'c_uminus'(
% 1.43/1.78 'c_minus'( X, Y, Z ), Z ) ), ~( 'c_lessequals'( X, Y, Z ) ), ~(
% 1.43/1.78 'class_OrderedGroup_Olordered__ab__group__abs'( Z ) ) ] )
% 1.43/1.78 , clause( 135, [ ~( 'c_lessequals'( Y, Z, X ) ), ~(
% 1.43/1.78 'class_OrderedGroup_Olordered__ab__group__abs'( X ) ), =( 'c_uminus'(
% 1.43/1.78 'c_minus'( Y, Z, X ), X ), 'c_HOL_Oabs'( 'c_minus'( Y, Z, X ), X ) ) ] )
% 1.43/1.78 , 2, substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 resolution(
% 1.43/1.78 clause( 5358, [ =( 'c_HOL_Oabs'( 'c_minus'( 'c_uminus'( X, Y ), 'c_0', Y )
% 1.43/1.78 , Y ), 'c_uminus'( 'c_minus'( 'c_uminus'( X, Y ), 'c_0', Y ), Y ) ), ~(
% 1.43/1.78 'class_OrderedGroup_Olordered__ab__group__abs'( Y ) ), ~( 'c_lessequals'(
% 1.43/1.78 'c_0', X, Y ) ), ~( 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.43/1.78 , clause( 5352, [ =( 'c_HOL_Oabs'( 'c_minus'( X, Y, Z ), Z ), 'c_uminus'(
% 1.43/1.78 'c_minus'( X, Y, Z ), Z ) ), ~( 'c_lessequals'( X, Y, Z ) ), ~(
% 1.43/1.78 'class_OrderedGroup_Olordered__ab__group__abs'( Z ) ) ] )
% 1.43/1.78 , 1, clause( 895, [ ~( 'c_lessequals'( 'c_0', X, Y ) ), 'c_lessequals'(
% 1.43/1.78 'c_uminus'( X, Y ), 'c_0', Y ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.43/1.78 , 1, substitution( 0, [ :=( X, 'c_uminus'( X, Y ) ), :=( Y, 'c_0' ), :=( Z
% 1.43/1.78 , Y )] ), substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 paramod(
% 1.43/1.78 clause( 5359, [ =( 'c_HOL_Oabs'( 'c_minus'( 'c_uminus'( X, Y ), 'c_0', Y )
% 1.43/1.78 , Y ), 'c_minus'( 'c_0', 'c_uminus'( X, Y ), Y ) ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ), ~(
% 1.43/1.78 'class_OrderedGroup_Olordered__ab__group__abs'( Y ) ), ~( 'c_lessequals'(
% 1.43/1.78 'c_0', X, Y ) ), ~( 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.43/1.78 , clause( 175, [ =( 'c_uminus'( 'c_minus'( X, Y, Z ), Z ), 'c_minus'( Y, X
% 1.43/1.78 , Z ) ), ~( 'class_Ring__and__Field_Oordered__idom'( Z ) ) ] )
% 1.43/1.78 , 0, clause( 5358, [ =( 'c_HOL_Oabs'( 'c_minus'( 'c_uminus'( X, Y ), 'c_0'
% 1.43/1.78 , Y ), Y ), 'c_uminus'( 'c_minus'( 'c_uminus'( X, Y ), 'c_0', Y ), Y ) )
% 1.43/1.78 , ~( 'class_OrderedGroup_Olordered__ab__group__abs'( Y ) ), ~(
% 1.43/1.78 'c_lessequals'( 'c_0', X, Y ) ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.43/1.78 , 0, 9, substitution( 0, [ :=( X, 'c_uminus'( X, Y ) ), :=( Y, 'c_0' ),
% 1.43/1.78 :=( Z, Y )] ), substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 factor(
% 1.43/1.78 clause( 5360, [ =( 'c_HOL_Oabs'( 'c_minus'( 'c_uminus'( X, Y ), 'c_0', Y )
% 1.43/1.78 , Y ), 'c_minus'( 'c_0', 'c_uminus'( X, Y ), Y ) ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ), ~(
% 1.43/1.78 'class_OrderedGroup_Olordered__ab__group__abs'( Y ) ), ~( 'c_lessequals'(
% 1.43/1.78 'c_0', X, Y ) ) ] )
% 1.43/1.78 , clause( 5359, [ =( 'c_HOL_Oabs'( 'c_minus'( 'c_uminus'( X, Y ), 'c_0', Y
% 1.43/1.78 ), Y ), 'c_minus'( 'c_0', 'c_uminus'( X, Y ), Y ) ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ), ~(
% 1.43/1.78 'class_OrderedGroup_Olordered__ab__group__abs'( Y ) ), ~( 'c_lessequals'(
% 1.43/1.78 'c_0', X, Y ) ), ~( 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.43/1.78 , 1, 4, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 paramod(
% 1.43/1.78 clause( 5361, [ =( 'c_HOL_Oabs'( 'c_minus'( 'c_uminus'( X, Y ), 'c_0', Y )
% 1.43/1.78 , Y ), 'c_plus'( 'c_0', X, Y ) ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ), ~(
% 1.43/1.78 'class_OrderedGroup_Olordered__ab__group__abs'( Y ) ), ~( 'c_lessequals'(
% 1.43/1.78 'c_0', X, Y ) ) ] )
% 1.43/1.78 , clause( 153, [ =( 'c_minus'( X, 'c_uminus'( Y, Z ), Z ), 'c_plus'( X, Y,
% 1.43/1.78 Z ) ), ~( 'class_Ring__and__Field_Oordered__idom'( Z ) ) ] )
% 1.43/1.78 , 0, clause( 5360, [ =( 'c_HOL_Oabs'( 'c_minus'( 'c_uminus'( X, Y ), 'c_0'
% 1.43/1.78 , Y ), Y ), 'c_minus'( 'c_0', 'c_uminus'( X, Y ), Y ) ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ), ~(
% 1.43/1.78 'class_OrderedGroup_Olordered__ab__group__abs'( Y ) ), ~( 'c_lessequals'(
% 1.43/1.78 'c_0', X, Y ) ) ] )
% 1.43/1.78 , 0, 9, substitution( 0, [ :=( X, 'c_0' ), :=( Y, X ), :=( Z, Y )] ),
% 1.43/1.78 substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 factor(
% 1.43/1.78 clause( 5362, [ =( 'c_HOL_Oabs'( 'c_minus'( 'c_uminus'( X, Y ), 'c_0', Y )
% 1.43/1.78 , Y ), 'c_plus'( 'c_0', X, Y ) ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ), ~(
% 1.43/1.78 'class_OrderedGroup_Olordered__ab__group__abs'( Y ) ), ~( 'c_lessequals'(
% 1.43/1.78 'c_0', X, Y ) ) ] )
% 1.43/1.78 , clause( 5361, [ =( 'c_HOL_Oabs'( 'c_minus'( 'c_uminus'( X, Y ), 'c_0', Y
% 1.43/1.78 ), Y ), 'c_plus'( 'c_0', X, Y ) ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ), ~(
% 1.43/1.78 'class_OrderedGroup_Olordered__ab__group__abs'( Y ) ), ~( 'c_lessequals'(
% 1.43/1.78 'c_0', X, Y ) ) ] )
% 1.43/1.78 , 1, 2, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 paramod(
% 1.43/1.78 clause( 5363, [ =( 'c_HOL_Oabs'( 'c_minus'( 'c_uminus'( X, Y ), 'c_0', Y )
% 1.43/1.78 , Y ), X ), ~( 'class_Ring__and__Field_Oordered__idom'( Y ) ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ), ~(
% 1.43/1.78 'class_OrderedGroup_Olordered__ab__group__abs'( Y ) ), ~( 'c_lessequals'(
% 1.43/1.78 'c_0', X, Y ) ) ] )
% 1.43/1.78 , clause( 53, [ =( 'c_plus'( 'c_0', X, Y ), X ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.43/1.78 , 0, clause( 5362, [ =( 'c_HOL_Oabs'( 'c_minus'( 'c_uminus'( X, Y ), 'c_0'
% 1.43/1.78 , Y ), Y ), 'c_plus'( 'c_0', X, Y ) ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ), ~(
% 1.43/1.78 'class_OrderedGroup_Olordered__ab__group__abs'( Y ) ), ~( 'c_lessequals'(
% 1.43/1.78 'c_0', X, Y ) ) ] )
% 1.43/1.78 , 0, 9, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 1.43/1.78 :=( X, X ), :=( Y, Y )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 factor(
% 1.43/1.78 clause( 5364, [ =( 'c_HOL_Oabs'( 'c_minus'( 'c_uminus'( X, Y ), 'c_0', Y )
% 1.43/1.78 , Y ), X ), ~( 'class_Ring__and__Field_Oordered__idom'( Y ) ), ~(
% 1.43/1.78 'class_OrderedGroup_Olordered__ab__group__abs'( Y ) ), ~( 'c_lessequals'(
% 1.43/1.78 'c_0', X, Y ) ) ] )
% 1.43/1.78 , clause( 5363, [ =( 'c_HOL_Oabs'( 'c_minus'( 'c_uminus'( X, Y ), 'c_0', Y
% 1.43/1.78 ), Y ), X ), ~( 'class_Ring__and__Field_Oordered__idom'( Y ) ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ), ~(
% 1.43/1.78 'class_OrderedGroup_Olordered__ab__group__abs'( Y ) ), ~( 'c_lessequals'(
% 1.43/1.78 'c_0', X, Y ) ) ] )
% 1.43/1.78 , 1, 2, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 paramod(
% 1.43/1.78 clause( 5365, [ =( 'c_HOL_Oabs'( 'c_uminus'( X, Y ), Y ), X ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ), ~(
% 1.43/1.78 'class_OrderedGroup_Olordered__ab__group__abs'( Y ) ), ~( 'c_lessequals'(
% 1.43/1.78 'c_0', X, Y ) ) ] )
% 1.43/1.78 , clause( 1047, [ ~( 'class_Ring__and__Field_Oordered__idom'( Y ) ), =(
% 1.43/1.78 'c_minus'( X, 'c_0', Y ), X ) ] )
% 1.43/1.78 , 1, clause( 5364, [ =( 'c_HOL_Oabs'( 'c_minus'( 'c_uminus'( X, Y ), 'c_0'
% 1.43/1.78 , Y ), Y ), X ), ~( 'class_Ring__and__Field_Oordered__idom'( Y ) ), ~(
% 1.43/1.78 'class_OrderedGroup_Olordered__ab__group__abs'( Y ) ), ~( 'c_lessequals'(
% 1.43/1.78 'c_0', X, Y ) ) ] )
% 1.43/1.78 , 0, 2, substitution( 0, [ :=( X, 'c_uminus'( X, Y ) ), :=( Y, Y )] ),
% 1.43/1.78 substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 factor(
% 1.43/1.78 clause( 5366, [ =( 'c_HOL_Oabs'( 'c_uminus'( X, Y ), Y ), X ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ), ~(
% 1.43/1.78 'class_OrderedGroup_Olordered__ab__group__abs'( Y ) ), ~( 'c_lessequals'(
% 1.43/1.78 'c_0', X, Y ) ) ] )
% 1.43/1.78 , clause( 5365, [ =( 'c_HOL_Oabs'( 'c_uminus'( X, Y ), Y ), X ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ), ~(
% 1.43/1.78 'class_OrderedGroup_Olordered__ab__group__abs'( Y ) ), ~( 'c_lessequals'(
% 1.43/1.78 'c_0', X, Y ) ) ] )
% 1.43/1.78 , 1, 2, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 paramod(
% 1.43/1.78 clause( 5367, [ =( 'c_HOL_Oabs'( X, Y ), X ), ~(
% 1.43/1.78 'class_OrderedGroup_Olordered__ab__group__abs'( Y ) ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ), ~(
% 1.43/1.78 'class_OrderedGroup_Olordered__ab__group__abs'( Y ) ), ~( 'c_lessequals'(
% 1.43/1.78 'c_0', X, Y ) ) ] )
% 1.43/1.78 , clause( 4, [ ~( 'class_OrderedGroup_Olordered__ab__group__abs'( X ) ),
% 1.43/1.78 =( 'c_HOL_Oabs'( 'c_uminus'( Y, X ), X ), 'c_HOL_Oabs'( Y, X ) ) ] )
% 1.43/1.78 , 1, clause( 5366, [ =( 'c_HOL_Oabs'( 'c_uminus'( X, Y ), Y ), X ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ), ~(
% 1.43/1.78 'class_OrderedGroup_Olordered__ab__group__abs'( Y ) ), ~( 'c_lessequals'(
% 1.43/1.78 'c_0', X, Y ) ) ] )
% 1.43/1.78 , 0, 1, substitution( 0, [ :=( X, Y ), :=( Y, X )] ), substitution( 1, [
% 1.43/1.78 :=( X, X ), :=( Y, Y )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 factor(
% 1.43/1.78 clause( 5368, [ =( 'c_HOL_Oabs'( X, Y ), X ), ~(
% 1.43/1.78 'class_OrderedGroup_Olordered__ab__group__abs'( Y ) ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ), ~( 'c_lessequals'( 'c_0'
% 1.43/1.78 , X, Y ) ) ] )
% 1.43/1.78 , clause( 5367, [ =( 'c_HOL_Oabs'( X, Y ), X ), ~(
% 1.43/1.78 'class_OrderedGroup_Olordered__ab__group__abs'( Y ) ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ), ~(
% 1.43/1.78 'class_OrderedGroup_Olordered__ab__group__abs'( Y ) ), ~( 'c_lessequals'(
% 1.43/1.78 'c_0', X, Y ) ) ] )
% 1.43/1.78 , 1, 3, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 resolution(
% 1.43/1.78 clause( 5369, [ =( 'c_HOL_Oabs'( X, Y ), X ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ), ~( 'c_lessequals'( 'c_0'
% 1.43/1.78 , X, Y ) ), ~( 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.43/1.78 , clause( 5368, [ =( 'c_HOL_Oabs'( X, Y ), X ), ~(
% 1.43/1.78 'class_OrderedGroup_Olordered__ab__group__abs'( Y ) ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ), ~( 'c_lessequals'( 'c_0'
% 1.43/1.78 , X, Y ) ) ] )
% 1.43/1.78 , 1, clause( 26, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.43/1.78 'class_OrderedGroup_Olordered__ab__group__abs'( X ) ] )
% 1.43/1.78 , 1, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [ :=( X
% 1.43/1.78 , Y )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 factor(
% 1.43/1.78 clause( 5372, [ =( 'c_HOL_Oabs'( X, Y ), X ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ), ~( 'c_lessequals'( 'c_0'
% 1.43/1.78 , X, Y ) ) ] )
% 1.43/1.78 , clause( 5369, [ =( 'c_HOL_Oabs'( X, Y ), X ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ), ~( 'c_lessequals'( 'c_0'
% 1.43/1.78 , X, Y ) ), ~( 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.43/1.78 , 1, 3, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 subsumption(
% 1.43/1.78 clause( 4069, [ ~( 'c_lessequals'( 'c_0', X, Y ) ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ), =( 'c_HOL_Oabs'( X, Y ),
% 1.43/1.78 X ) ] )
% 1.43/1.78 , clause( 5372, [ =( 'c_HOL_Oabs'( X, Y ), X ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ), ~( 'c_lessequals'( 'c_0'
% 1.43/1.78 , X, Y ) ) ] )
% 1.43/1.78 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 2
% 1.43/1.78 ), ==>( 1, 1 ), ==>( 2, 0 )] ) ).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 eqswap(
% 1.43/1.78 clause( 5373, [ =( X, 'c_HOL_Oabs'( X, Y ) ), ~( 'c_lessequals'( 'c_0', X,
% 1.43/1.78 Y ) ), ~( 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.43/1.78 , clause( 4069, [ ~( 'c_lessequals'( 'c_0', X, Y ) ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ), =( 'c_HOL_Oabs'( X, Y ),
% 1.43/1.78 X ) ] )
% 1.43/1.78 , 2, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 resolution(
% 1.43/1.78 clause( 5374, [ =( X, 'c_HOL_Oabs'( X, Y ) ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ), 'c_less'( X, 'c_0', Y ),
% 1.43/1.78 ~( 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.43/1.78 , clause( 5373, [ =( X, 'c_HOL_Oabs'( X, Y ) ), ~( 'c_lessequals'( 'c_0', X
% 1.43/1.78 , Y ) ), ~( 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.43/1.78 , 1, clause( 95, [ 'c_less'( X, Y, Z ), 'c_lessequals'( Y, X, Z ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Z ) ) ] )
% 1.43/1.78 , 1, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [ :=( X
% 1.43/1.78 , X ), :=( Y, 'c_0' ), :=( Z, Y )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 factor(
% 1.43/1.78 clause( 5375, [ =( X, 'c_HOL_Oabs'( X, Y ) ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ), 'c_less'( X, 'c_0', Y ) ]
% 1.43/1.78 )
% 1.43/1.78 , clause( 5374, [ =( X, 'c_HOL_Oabs'( X, Y ) ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ), 'c_less'( X, 'c_0', Y ),
% 1.43/1.78 ~( 'class_Ring__and__Field_Oordered__idom'( Y ) ) ] )
% 1.43/1.78 , 1, 3, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 eqswap(
% 1.43/1.78 clause( 5376, [ =( 'c_HOL_Oabs'( X, Y ), X ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ), 'c_less'( X, 'c_0', Y ) ]
% 1.43/1.78 )
% 1.43/1.78 , clause( 5375, [ =( X, 'c_HOL_Oabs'( X, Y ) ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ), 'c_less'( X, 'c_0', Y ) ]
% 1.43/1.78 )
% 1.43/1.78 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 subsumption(
% 1.43/1.78 clause( 4073, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.43/1.78 'c_HOL_Oabs'( Y, X ), Y ), 'c_less'( Y, 'c_0', X ) ] )
% 1.43/1.78 , clause( 5376, [ =( 'c_HOL_Oabs'( X, Y ), X ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ), 'c_less'( X, 'c_0', Y ) ]
% 1.43/1.78 )
% 1.43/1.78 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 1
% 1.43/1.78 ), ==>( 1, 0 ), ==>( 2, 2 )] ) ).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 paramod(
% 1.43/1.78 clause( 5379, [ 'c_lessequals'( 'c_plus'( Y, 'v_k'( X ), 't_b' ), 'c_plus'(
% 1.43/1.78 'v_f'( X ), Y, 't_b' ), 't_b' ) ] )
% 1.43/1.78 , clause( 83, [ =( 'c_minus'( 'c_plus'( 'c_plus'( X, Y, 't_b' ), Z, 't_b' )
% 1.43/1.78 , X, 't_b' ), 'c_plus'( Y, Z, 't_b' ) ) ] )
% 1.43/1.78 , 0, clause( 3395, [ 'c_lessequals'( 'c_minus'( 'c_plus'( X, 'v_k'( Y ),
% 1.43/1.78 't_b' ), 'v_f'( Y ), 't_b' ), X, 't_b' ) ] )
% 1.43/1.78 , 0, 1, substitution( 0, [ :=( X, 'v_f'( X ) ), :=( Y, Y ), :=( Z, 'v_k'( X
% 1.43/1.78 ) )] ), substitution( 1, [ :=( X, 'c_plus'( 'v_f'( X ), Y, 't_b' ) ),
% 1.43/1.78 :=( Y, X )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 subsumption(
% 1.43/1.78 clause( 4406, [ 'c_lessequals'( 'c_plus'( Y, 'v_k'( X ), 't_b' ), 'c_plus'(
% 1.43/1.78 'v_f'( X ), Y, 't_b' ), 't_b' ) ] )
% 1.43/1.78 , clause( 5379, [ 'c_lessequals'( 'c_plus'( Y, 'v_k'( X ), 't_b' ),
% 1.43/1.78 'c_plus'( 'v_f'( X ), Y, 't_b' ), 't_b' ) ] )
% 1.43/1.78 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.43/1.78 )] ) ).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 paramod(
% 1.43/1.78 clause( 5382, [ 'c_lessequals'( 'c_plus'( 'c_uminus'( X, 't_b' ), 'v_k'( Y
% 1.43/1.78 ), 't_b' ), 'c_minus'( 'v_f'( Y ), X, 't_b' ), 't_b' ) ] )
% 1.43/1.78 , clause( 192, [ =( 'c_plus'( Y, 'c_uminus'( X, 't_b' ), 't_b' ), 'c_minus'(
% 1.43/1.78 Y, X, 't_b' ) ) ] )
% 1.43/1.78 , 0, clause( 4406, [ 'c_lessequals'( 'c_plus'( Y, 'v_k'( X ), 't_b' ),
% 1.43/1.78 'c_plus'( 'v_f'( X ), Y, 't_b' ), 't_b' ) ] )
% 1.43/1.78 , 0, 8, substitution( 0, [ :=( X, X ), :=( Y, 'v_f'( Y ) )] ),
% 1.43/1.78 substitution( 1, [ :=( X, Y ), :=( Y, 'c_uminus'( X, 't_b' ) )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 paramod(
% 1.43/1.78 clause( 5383, [ 'c_lessequals'( 'c_minus'( 'v_k'( Y ), X, 't_b' ),
% 1.43/1.78 'c_minus'( 'v_f'( Y ), X, 't_b' ), 't_b' ) ] )
% 1.43/1.78 , clause( 191, [ =( 'c_plus'( 'c_uminus'( X, 't_b' ), Y, 't_b' ), 'c_minus'(
% 1.43/1.78 Y, X, 't_b' ) ) ] )
% 1.43/1.78 , 0, clause( 5382, [ 'c_lessequals'( 'c_plus'( 'c_uminus'( X, 't_b' ),
% 1.43/1.78 'v_k'( Y ), 't_b' ), 'c_minus'( 'v_f'( Y ), X, 't_b' ), 't_b' ) ] )
% 1.43/1.78 , 0, 1, substitution( 0, [ :=( X, X ), :=( Y, 'v_k'( Y ) )] ),
% 1.43/1.78 substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 subsumption(
% 1.43/1.78 clause( 4432, [ 'c_lessequals'( 'c_minus'( 'v_k'( X ), Y, 't_b' ),
% 1.43/1.78 'c_minus'( 'v_f'( X ), Y, 't_b' ), 't_b' ) ] )
% 1.43/1.78 , clause( 5383, [ 'c_lessequals'( 'c_minus'( 'v_k'( Y ), X, 't_b' ),
% 1.43/1.78 'c_minus'( 'v_f'( Y ), X, 't_b' ), 't_b' ) ] )
% 1.43/1.78 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 1.43/1.78 )] ) ).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 resolution(
% 1.43/1.78 clause( 5384, [ ~( 'c_lessequals'( 'c_minus'( 'v_k'( 'v_x' ), 'v_g'( 'v_x'
% 1.43/1.78 ), 't_b' ), 'c_0', 't_b' ) ) ] )
% 1.43/1.78 , clause( 304, [ ~( 'c_lessequals'( 'c_Orderings_Omax'( 'c_minus'( 'v_k'(
% 1.43/1.78 'v_x' ), 'v_g'( 'v_x' ), 't_b' ), 'c_0', 't_b' ), 'c_0', 't_b' ) ) ] )
% 1.43/1.78 , 0, clause( 215, [ ~( 'c_lessequals'( X, Y, 't_b' ) ), 'c_lessequals'(
% 1.43/1.78 'c_Orderings_Omax'( X, Y, 't_b' ), Y, 't_b' ) ] )
% 1.43/1.78 , 1, substitution( 0, [] ), substitution( 1, [ :=( X, 'c_minus'( 'v_k'(
% 1.43/1.78 'v_x' ), 'v_g'( 'v_x' ), 't_b' ) ), :=( Y, 'c_0' )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 subsumption(
% 1.43/1.78 clause( 4493, [ ~( 'c_lessequals'( 'c_minus'( 'v_k'( 'v_x' ), 'v_g'( 'v_x'
% 1.43/1.78 ), 't_b' ), 'c_0', 't_b' ) ) ] )
% 1.43/1.78 , clause( 5384, [ ~( 'c_lessequals'( 'c_minus'( 'v_k'( 'v_x' ), 'v_g'(
% 1.43/1.78 'v_x' ), 't_b' ), 'c_0', 't_b' ) ) ] )
% 1.43/1.78 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 resolution(
% 1.43/1.78 clause( 5385, [ ~( 'c_lessequals'( 'v_k'( 'v_x' ), 'v_g'( 'v_x' ), 't_b' )
% 1.43/1.78 ), ~( 'class_OrderedGroup_Olordered__ab__group__abs'( 't_b' ) ) ] )
% 1.43/1.78 , clause( 4493, [ ~( 'c_lessequals'( 'c_minus'( 'v_k'( 'v_x' ), 'v_g'(
% 1.43/1.78 'v_x' ), 't_b' ), 'c_0', 't_b' ) ) ] )
% 1.43/1.78 , 0, clause( 137, [ ~( 'c_lessequals'( X, Y, Z ) ), 'c_lessequals'(
% 1.43/1.78 'c_minus'( X, Y, Z ), 'c_0', Z ), ~(
% 1.43/1.78 'class_OrderedGroup_Olordered__ab__group__abs'( Z ) ) ] )
% 1.43/1.78 , 1, substitution( 0, [] ), substitution( 1, [ :=( X, 'v_k'( 'v_x' ) ),
% 1.43/1.78 :=( Y, 'v_g'( 'v_x' ) ), :=( Z, 't_b' )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 resolution(
% 1.43/1.78 clause( 5386, [ ~( 'c_lessequals'( 'v_k'( 'v_x' ), 'v_g'( 'v_x' ), 't_b' )
% 1.43/1.78 ) ] )
% 1.43/1.78 , clause( 5385, [ ~( 'c_lessequals'( 'v_k'( 'v_x' ), 'v_g'( 'v_x' ), 't_b'
% 1.43/1.78 ) ), ~( 'class_OrderedGroup_Olordered__ab__group__abs'( 't_b' ) ) ] )
% 1.43/1.78 , 1, clause( 28, [ 'class_OrderedGroup_Olordered__ab__group__abs'( 't_b' )
% 1.43/1.78 ] )
% 1.43/1.78 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 subsumption(
% 1.43/1.78 clause( 4587, [ ~( 'c_lessequals'( 'v_k'( 'v_x' ), 'v_g'( 'v_x' ), 't_b' )
% 1.43/1.78 ) ] )
% 1.43/1.78 , clause( 5386, [ ~( 'c_lessequals'( 'v_k'( 'v_x' ), 'v_g'( 'v_x' ), 't_b'
% 1.43/1.78 ) ) ] )
% 1.43/1.78 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 resolution(
% 1.43/1.78 clause( 5387, [ ~( 'c_lessequals'( 'v_f'( 'v_x' ), 'v_g'( 'v_x' ), 't_b' )
% 1.43/1.78 ) ] )
% 1.43/1.78 , clause( 4587, [ ~( 'c_lessequals'( 'v_k'( 'v_x' ), 'v_g'( 'v_x' ), 't_b'
% 1.43/1.78 ) ) ] )
% 1.43/1.78 , 0, clause( 285, [ ~( 'c_lessequals'( 'v_f'( X ), Y, 't_b' ) ),
% 1.43/1.78 'c_lessequals'( 'v_k'( X ), Y, 't_b' ) ] )
% 1.43/1.78 , 1, substitution( 0, [] ), substitution( 1, [ :=( X, 'v_x' ), :=( Y, 'v_g'(
% 1.43/1.78 'v_x' ) )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 subsumption(
% 1.43/1.78 clause( 4650, [ ~( 'c_lessequals'( 'v_f'( 'v_x' ), 'v_g'( 'v_x' ), 't_b' )
% 1.43/1.78 ) ] )
% 1.43/1.78 , clause( 5387, [ ~( 'c_lessequals'( 'v_f'( 'v_x' ), 'v_g'( 'v_x' ), 't_b'
% 1.43/1.78 ) ) ] )
% 1.43/1.78 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 resolution(
% 1.43/1.78 clause( 5388, [ ~( 'c_less'( 'c_minus'( 'v_f'( 'v_x' ), 'v_g'( 'v_x' ),
% 1.43/1.78 't_b' ), 'c_0', 't_b' ) ) ] )
% 1.43/1.78 , clause( 4650, [ ~( 'c_lessequals'( 'v_f'( 'v_x' ), 'v_g'( 'v_x' ), 't_b'
% 1.43/1.78 ) ) ] )
% 1.43/1.78 , 0, clause( 2781, [ 'c_lessequals'( X, Y, 't_b' ), ~( 'c_less'( 'c_minus'(
% 1.43/1.78 X, Y, 't_b' ), 'c_0', 't_b' ) ) ] )
% 1.43/1.78 , 0, substitution( 0, [] ), substitution( 1, [ :=( X, 'v_f'( 'v_x' ) ),
% 1.43/1.78 :=( Y, 'v_g'( 'v_x' ) )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 subsumption(
% 1.43/1.78 clause( 4655, [ ~( 'c_less'( 'c_minus'( 'v_f'( 'v_x' ), 'v_g'( 'v_x' ),
% 1.43/1.78 't_b' ), 'c_0', 't_b' ) ) ] )
% 1.43/1.78 , clause( 5388, [ ~( 'c_less'( 'c_minus'( 'v_f'( 'v_x' ), 'v_g'( 'v_x' ),
% 1.43/1.78 't_b' ), 'c_0', 't_b' ) ) ] )
% 1.43/1.78 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 eqswap(
% 1.43/1.78 clause( 5389, [ =( X, 'c_HOL_Oabs'( X, Y ) ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ), 'c_less'( X, 'c_0', Y ) ]
% 1.43/1.78 )
% 1.43/1.78 , clause( 4073, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.43/1.78 'c_HOL_Oabs'( Y, X ), Y ), 'c_less'( Y, 'c_0', X ) ] )
% 1.43/1.78 , 1, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 resolution(
% 1.43/1.78 clause( 5390, [ =( 'c_minus'( 'v_f'( 'v_x' ), 'v_g'( 'v_x' ), 't_b' ),
% 1.43/1.78 'c_HOL_Oabs'( 'c_minus'( 'v_f'( 'v_x' ), 'v_g'( 'v_x' ), 't_b' ), 't_b' )
% 1.43/1.78 ), ~( 'class_Ring__and__Field_Oordered__idom'( 't_b' ) ) ] )
% 1.43/1.78 , clause( 4655, [ ~( 'c_less'( 'c_minus'( 'v_f'( 'v_x' ), 'v_g'( 'v_x' ),
% 1.43/1.78 't_b' ), 'c_0', 't_b' ) ) ] )
% 1.43/1.78 , 0, clause( 5389, [ =( X, 'c_HOL_Oabs'( X, Y ) ), ~(
% 1.43/1.78 'class_Ring__and__Field_Oordered__idom'( Y ) ), 'c_less'( X, 'c_0', Y ) ]
% 1.43/1.78 )
% 1.43/1.78 , 2, substitution( 0, [] ), substitution( 1, [ :=( X, 'c_minus'( 'v_f'(
% 1.43/1.78 'v_x' ), 'v_g'( 'v_x' ), 't_b' ) ), :=( Y, 't_b' )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 resolution(
% 1.43/1.78 clause( 5391, [ =( 'c_minus'( 'v_f'( 'v_x' ), 'v_g'( 'v_x' ), 't_b' ),
% 1.43/1.78 'c_HOL_Oabs'( 'c_minus'( 'v_f'( 'v_x' ), 'v_g'( 'v_x' ), 't_b' ), 't_b' )
% 1.43/1.78 ) ] )
% 1.43/1.78 , clause( 5390, [ =( 'c_minus'( 'v_f'( 'v_x' ), 'v_g'( 'v_x' ), 't_b' ),
% 1.43/1.78 'c_HOL_Oabs'( 'c_minus'( 'v_f'( 'v_x' ), 'v_g'( 'v_x' ), 't_b' ), 't_b' )
% 1.43/1.78 ), ~( 'class_Ring__and__Field_Oordered__idom'( 't_b' ) ) ] )
% 1.43/1.78 , 1, clause( 2, [ 'class_Ring__and__Field_Oordered__idom'( 't_b' ) ] )
% 1.43/1.78 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 eqswap(
% 1.43/1.78 clause( 5392, [ =( 'c_HOL_Oabs'( 'c_minus'( 'v_f'( 'v_x' ), 'v_g'( 'v_x' )
% 1.43/1.78 , 't_b' ), 't_b' ), 'c_minus'( 'v_f'( 'v_x' ), 'v_g'( 'v_x' ), 't_b' ) )
% 1.43/1.78 ] )
% 1.43/1.78 , clause( 5391, [ =( 'c_minus'( 'v_f'( 'v_x' ), 'v_g'( 'v_x' ), 't_b' ),
% 1.43/1.78 'c_HOL_Oabs'( 'c_minus'( 'v_f'( 'v_x' ), 'v_g'( 'v_x' ), 't_b' ), 't_b' )
% 1.43/1.78 ) ] )
% 1.43/1.78 , 0, substitution( 0, [] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 subsumption(
% 1.43/1.78 clause( 4696, [ =( 'c_HOL_Oabs'( 'c_minus'( 'v_f'( 'v_x' ), 'v_g'( 'v_x' )
% 1.43/1.78 , 't_b' ), 't_b' ), 'c_minus'( 'v_f'( 'v_x' ), 'v_g'( 'v_x' ), 't_b' ) )
% 1.43/1.78 ] )
% 1.43/1.78 , clause( 5392, [ =( 'c_HOL_Oabs'( 'c_minus'( 'v_f'( 'v_x' ), 'v_g'( 'v_x'
% 1.43/1.78 ), 't_b' ), 't_b' ), 'c_minus'( 'v_f'( 'v_x' ), 'v_g'( 'v_x' ), 't_b' )
% 1.43/1.78 ) ] )
% 1.43/1.78 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 resolution(
% 1.43/1.78 clause( 5395, [ ~( 'c_lessequals'( 'c_minus'( 'v_k'( 'v_x' ), 'v_g'( 'v_x'
% 1.43/1.78 ), 't_b' ), 'c_HOL_Oabs'( 'c_minus'( 'v_f'( 'v_x' ), 'v_g'( 'v_x' ),
% 1.43/1.78 't_b' ), 't_b' ), 't_b' ) ), 'c_less'( 'c_HOL_Oabs'( 'c_minus'( 'v_f'(
% 1.43/1.78 'v_x' ), 'v_g'( 'v_x' ), 't_b' ), 't_b' ), 'c_0', 't_b' ) ] )
% 1.43/1.78 , clause( 1, [ ~( 'c_lessequals'( 'c_Orderings_Omax'( 'c_minus'( 'v_k'(
% 1.43/1.78 'v_x' ), 'v_g'( 'v_x' ), 't_b' ), 'c_0', 't_b' ), 'c_HOL_Oabs'( 'c_minus'(
% 1.43/1.78 'v_f'( 'v_x' ), 'v_g'( 'v_x' ), 't_b' ), 't_b' ), 't_b' ) ) ] )
% 1.43/1.78 , 0, clause( 201, [ ~( 'c_lessequals'( X, Y, 't_b' ) ), 'c_lessequals'(
% 1.43/1.78 'c_Orderings_Omax'( X, Z, 't_b' ), Y, 't_b' ), 'c_less'( Y, Z, 't_b' ) ]
% 1.43/1.78 )
% 1.43/1.78 , 1, substitution( 0, [] ), substitution( 1, [ :=( X, 'c_minus'( 'v_k'(
% 1.43/1.78 'v_x' ), 'v_g'( 'v_x' ), 't_b' ) ), :=( Y, 'c_HOL_Oabs'( 'c_minus'( 'v_f'(
% 1.43/1.78 'v_x' ), 'v_g'( 'v_x' ), 't_b' ), 't_b' ) ), :=( Z, 'c_0' )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 paramod(
% 1.43/1.78 clause( 5397, [ 'c_less'( 'c_minus'( 'v_f'( 'v_x' ), 'v_g'( 'v_x' ), 't_b'
% 1.43/1.78 ), 'c_0', 't_b' ), ~( 'c_lessequals'( 'c_minus'( 'v_k'( 'v_x' ), 'v_g'(
% 1.43/1.78 'v_x' ), 't_b' ), 'c_HOL_Oabs'( 'c_minus'( 'v_f'( 'v_x' ), 'v_g'( 'v_x' )
% 1.43/1.78 , 't_b' ), 't_b' ), 't_b' ) ) ] )
% 1.43/1.78 , clause( 4696, [ =( 'c_HOL_Oabs'( 'c_minus'( 'v_f'( 'v_x' ), 'v_g'( 'v_x'
% 1.43/1.78 ), 't_b' ), 't_b' ), 'c_minus'( 'v_f'( 'v_x' ), 'v_g'( 'v_x' ), 't_b' )
% 1.43/1.78 ) ] )
% 1.43/1.78 , 0, clause( 5395, [ ~( 'c_lessequals'( 'c_minus'( 'v_k'( 'v_x' ), 'v_g'(
% 1.43/1.78 'v_x' ), 't_b' ), 'c_HOL_Oabs'( 'c_minus'( 'v_f'( 'v_x' ), 'v_g'( 'v_x' )
% 1.43/1.78 , 't_b' ), 't_b' ), 't_b' ) ), 'c_less'( 'c_HOL_Oabs'( 'c_minus'( 'v_f'(
% 1.43/1.78 'v_x' ), 'v_g'( 'v_x' ), 't_b' ), 't_b' ), 'c_0', 't_b' ) ] )
% 1.43/1.78 , 1, 1, substitution( 0, [] ), substitution( 1, [] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 paramod(
% 1.43/1.78 clause( 5399, [ ~( 'c_lessequals'( 'c_minus'( 'v_k'( 'v_x' ), 'v_g'( 'v_x'
% 1.43/1.78 ), 't_b' ), 'c_minus'( 'v_f'( 'v_x' ), 'v_g'( 'v_x' ), 't_b' ), 't_b' )
% 1.43/1.78 ), 'c_less'( 'c_minus'( 'v_f'( 'v_x' ), 'v_g'( 'v_x' ), 't_b' ), 'c_0',
% 1.43/1.78 't_b' ) ] )
% 1.43/1.78 , clause( 4696, [ =( 'c_HOL_Oabs'( 'c_minus'( 'v_f'( 'v_x' ), 'v_g'( 'v_x'
% 1.43/1.78 ), 't_b' ), 't_b' ), 'c_minus'( 'v_f'( 'v_x' ), 'v_g'( 'v_x' ), 't_b' )
% 1.43/1.78 ) ] )
% 1.43/1.78 , 0, clause( 5397, [ 'c_less'( 'c_minus'( 'v_f'( 'v_x' ), 'v_g'( 'v_x' ),
% 1.43/1.78 't_b' ), 'c_0', 't_b' ), ~( 'c_lessequals'( 'c_minus'( 'v_k'( 'v_x' ),
% 1.43/1.78 'v_g'( 'v_x' ), 't_b' ), 'c_HOL_Oabs'( 'c_minus'( 'v_f'( 'v_x' ), 'v_g'(
% 1.43/1.78 'v_x' ), 't_b' ), 't_b' ), 't_b' ) ) ] )
% 1.43/1.78 , 1, 8, substitution( 0, [] ), substitution( 1, [] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 resolution(
% 1.43/1.78 clause( 5400, [ 'c_less'( 'c_minus'( 'v_f'( 'v_x' ), 'v_g'( 'v_x' ), 't_b'
% 1.43/1.78 ), 'c_0', 't_b' ) ] )
% 1.43/1.78 , clause( 5399, [ ~( 'c_lessequals'( 'c_minus'( 'v_k'( 'v_x' ), 'v_g'(
% 1.43/1.78 'v_x' ), 't_b' ), 'c_minus'( 'v_f'( 'v_x' ), 'v_g'( 'v_x' ), 't_b' ),
% 1.43/1.78 't_b' ) ), 'c_less'( 'c_minus'( 'v_f'( 'v_x' ), 'v_g'( 'v_x' ), 't_b' ),
% 1.43/1.78 'c_0', 't_b' ) ] )
% 1.43/1.78 , 0, clause( 4432, [ 'c_lessequals'( 'c_minus'( 'v_k'( X ), Y, 't_b' ),
% 1.43/1.78 'c_minus'( 'v_f'( X ), Y, 't_b' ), 't_b' ) ] )
% 1.43/1.78 , 0, substitution( 0, [] ), substitution( 1, [ :=( X, 'v_x' ), :=( Y, 'v_g'(
% 1.43/1.78 'v_x' ) )] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 subsumption(
% 1.43/1.78 clause( 4778, [ 'c_less'( 'c_minus'( 'v_f'( 'v_x' ), 'v_g'( 'v_x' ), 't_b'
% 1.43/1.78 ), 'c_0', 't_b' ) ] )
% 1.43/1.78 , clause( 5400, [ 'c_less'( 'c_minus'( 'v_f'( 'v_x' ), 'v_g'( 'v_x' ),
% 1.43/1.78 't_b' ), 'c_0', 't_b' ) ] )
% 1.43/1.78 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 resolution(
% 1.43/1.78 clause( 5401, [] )
% 1.43/1.78 , clause( 4655, [ ~( 'c_less'( 'c_minus'( 'v_f'( 'v_x' ), 'v_g'( 'v_x' ),
% 1.43/1.78 't_b' ), 'c_0', 't_b' ) ) ] )
% 1.43/1.78 , 0, clause( 4778, [ 'c_less'( 'c_minus'( 'v_f'( 'v_x' ), 'v_g'( 'v_x' ),
% 1.43/1.78 't_b' ), 'c_0', 't_b' ) ] )
% 1.43/1.78 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 1.43/1.78
% 1.43/1.78
% 1.43/1.78 subsumption(
% 1.43/1.78 clause( 4780, [] )
% 1.43/1.78 , clause( 5401, [] )
% 1.43/1.78 , substitution( 0, [] ), permutation( 0, [] ) ).
% 1.43/1.79
% 1.43/1.79
% 1.43/1.79 end.
% 1.43/1.79
% 1.43/1.79 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 1.43/1.79
% 1.43/1.79 Memory use:
% 1.43/1.79
% 1.43/1.79 space for terms: 71286
% 1.43/1.79 space for clauses: 254990
% 1.43/1.79
% 1.43/1.79
% 1.43/1.79 clauses generated: 55076
% 1.43/1.79 clauses kept: 4781
% 1.43/1.79 clauses selected: 534
% 1.43/1.79 clauses deleted: 82
% 1.43/1.79 clauses inuse deleted: 19
% 1.43/1.79
% 1.43/1.79 subsentry: 154030
% 1.43/1.79 literals s-matched: 89033
% 1.43/1.79 literals matched: 86310
% 1.43/1.79 full subsumption: 21326
% 1.43/1.79
% 1.43/1.79 checksum: 2122839540
% 1.43/1.79
% 1.43/1.79
% 1.43/1.79 Bliksem ended
%------------------------------------------------------------------------------