TSTP Solution File: ANA019-2 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : ANA019-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n021.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 18:38:18 EDT 2022
% Result : Unsatisfiable 0.88s 1.24s
% Output : Refutation 0.88s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ANA019-2 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12 % Command : bliksem %s
% 0.13/0.33 % Computer : n021.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % DateTime : Fri Jul 8 02:51:20 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.86/1.24 *** allocated 10000 integers for termspace/termends
% 0.86/1.24 *** allocated 10000 integers for clauses
% 0.86/1.24 *** allocated 10000 integers for justifications
% 0.86/1.24 Bliksem 1.12
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 Automatic Strategy Selection
% 0.86/1.24
% 0.86/1.24 Clauses:
% 0.86/1.24 [
% 0.86/1.24 [ =( 'v_f'( 'c_0' ), 'c_0' ) ],
% 0.86/1.24 [ 'c_less'( 'c_0', 'v_x', 't_a' ) ],
% 0.86/1.24 [ 'c_lessequals'( 'c_HOL_Oabs'( 'v_f'( 'c_Suc'( X ) ), 't_a' ),
% 0.86/1.24 'c_times'( 'v_x', 'c_HOL_Oabs'( 'v_h'( 'c_Suc'( X ) ), 't_a' ), 't_a' ),
% 0.86/1.24 't_a' ) ],
% 0.86/1.24 [ ~( 'c_lessequals'( 'c_HOL_Oabs'( 'v_f'( 'v_xa'( X ) ), 't_a' ),
% 0.86/1.24 'c_times'( X, 'c_HOL_Oabs'( 'v_h'( 'v_xa'( X ) ), 't_a' ), 't_a' ), 't_a'
% 0.86/1.24 ) ), ~( 'c_less'( 'c_0', X, 't_a' ) ) ],
% 0.86/1.24 [ 'class_Ring__and__Field_Oordered__idom'( 't_a' ) ],
% 0.86/1.24 [ ~( 'c_less'( 'c_0', X, 'tc_nat' ) ), =( X, 'c_Suc'( 'c_minus'( X,
% 0.86/1.24 'c_1', 'tc_nat' ) ) ) ],
% 0.86/1.24 [ 'c_less'( 'c_0', X, 'tc_nat' ), =( X, 'c_0' ) ],
% 0.86/1.24 [ ~( 'class_OrderedGroup_Olordered__ab__group__abs'( X ) ), =(
% 0.86/1.24 'c_HOL_Oabs'( 'c_0', X ), 'c_0' ) ],
% 0.86/1.24 [ ~( 'class_OrderedGroup_Olordered__ab__group__abs'( X ) ),
% 0.86/1.24 'c_lessequals'( 'c_0', 'c_HOL_Oabs'( Y, X ), X ) ],
% 0.86/1.24 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_less'( Y, Z, X ) ),
% 0.86/1.24 'c_lessequals'( Y, Z, X ) ],
% 0.86/1.24 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ), ~(
% 0.86/1.24 'c_lessequals'( 'c_0', Y, X ) ), ~( 'c_lessequals'( 'c_0', Z, X ) ),
% 0.86/1.24 'c_lessequals'( 'c_0', 'c_times'( Z, Y, X ), X ) ],
% 0.86/1.24 [ ~( 'class_LOrder_Ojoin__semilorder'( X ) ), 'class_Orderings_Oorder'(
% 0.86/1.24 X ) ],
% 0.86/1.24 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.86/1.24 'class_LOrder_Ojoin__semilorder'( X ) ],
% 0.86/1.24 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.86/1.24 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ],
% 0.86/1.24 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.86/1.24 'class_OrderedGroup_Olordered__ab__group__abs'( X ) ]
% 0.86/1.24 ] .
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 percentage equality = 0.137931, percentage horn = 0.933333
% 0.86/1.24 This is a problem with some equality
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 Options Used:
% 0.86/1.24
% 0.86/1.24 useres = 1
% 0.86/1.24 useparamod = 1
% 0.86/1.24 useeqrefl = 1
% 0.86/1.24 useeqfact = 1
% 0.86/1.24 usefactor = 1
% 0.86/1.24 usesimpsplitting = 0
% 0.86/1.24 usesimpdemod = 5
% 0.86/1.24 usesimpres = 3
% 0.86/1.24
% 0.86/1.24 resimpinuse = 1000
% 0.86/1.24 resimpclauses = 20000
% 0.86/1.24 substype = eqrewr
% 0.86/1.24 backwardsubs = 1
% 0.86/1.24 selectoldest = 5
% 0.86/1.24
% 0.86/1.24 litorderings [0] = split
% 0.86/1.24 litorderings [1] = extend the termordering, first sorting on arguments
% 0.86/1.24
% 0.86/1.24 termordering = kbo
% 0.86/1.24
% 0.86/1.24 litapriori = 0
% 0.86/1.24 termapriori = 1
% 0.86/1.24 litaposteriori = 0
% 0.86/1.24 termaposteriori = 0
% 0.86/1.24 demodaposteriori = 0
% 0.86/1.24 ordereqreflfact = 0
% 0.86/1.24
% 0.86/1.24 litselect = negord
% 0.86/1.24
% 0.86/1.24 maxweight = 15
% 0.86/1.24 maxdepth = 30000
% 0.86/1.24 maxlength = 115
% 0.86/1.24 maxnrvars = 195
% 0.86/1.24 excuselevel = 1
% 0.86/1.24 increasemaxweight = 1
% 0.86/1.24
% 0.86/1.24 maxselected = 10000000
% 0.86/1.24 maxnrclauses = 10000000
% 0.86/1.24
% 0.86/1.24 showgenerated = 0
% 0.86/1.24 showkept = 0
% 0.86/1.24 showselected = 0
% 0.86/1.24 showdeleted = 0
% 0.86/1.24 showresimp = 1
% 0.86/1.24 showstatus = 2000
% 0.86/1.24
% 0.86/1.24 prologoutput = 1
% 0.86/1.24 nrgoals = 5000000
% 0.86/1.24 totalproof = 1
% 0.86/1.24
% 0.86/1.24 Symbols occurring in the translation:
% 0.86/1.24
% 0.86/1.24 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.86/1.24 . [1, 2] (w:1, o:36, a:1, s:1, b:0),
% 0.86/1.24 ! [4, 1] (w:0, o:22, a:1, s:1, b:0),
% 0.86/1.24 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.88/1.24 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.88/1.24 'c_0' [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.88/1.24 'v_f' [40, 1] (w:1, o:27, a:1, s:1, b:0),
% 0.88/1.24 'v_x' [41, 0] (w:1, o:10, a:1, s:1, b:0),
% 0.88/1.24 't_a' [42, 0] (w:1, o:11, a:1, s:1, b:0),
% 0.88/1.24 'c_less' [43, 3] (w:1, o:62, a:1, s:1, b:0),
% 0.88/1.24 'c_Suc' [45, 1] (w:1, o:28, a:1, s:1, b:0),
% 0.88/1.24 'c_HOL_Oabs' [46, 2] (w:1, o:61, a:1, s:1, b:0),
% 0.88/1.24 'v_h' [47, 1] (w:1, o:29, a:1, s:1, b:0),
% 0.88/1.24 'c_times' [48, 3] (w:1, o:63, a:1, s:1, b:0),
% 0.88/1.24 'c_lessequals' [49, 3] (w:1, o:64, a:1, s:1, b:0),
% 0.88/1.24 'v_xa' [50, 1] (w:1, o:30, a:1, s:1, b:0),
% 0.88/1.24 'class_Ring__and__Field_Oordered__idom' [51, 1] (w:1, o:31, a:1, s:1
% 0.88/1.24 , b:0),
% 0.88/1.24 'tc_nat' [53, 0] (w:1, o:14, a:1, s:1, b:0),
% 0.88/1.24 'c_1' [54, 0] (w:1, o:15, a:1, s:1, b:0),
% 0.88/1.24 'c_minus' [55, 3] (w:1, o:65, a:1, s:1, b:0),
% 0.88/1.24 'class_OrderedGroup_Olordered__ab__group__abs' [58, 1] (w:1, o:32, a:
% 0.88/1.24 1, s:1, b:0),
% 0.88/1.24 'class_Orderings_Oorder' [60, 1] (w:1, o:33, a:1, s:1, b:0),
% 0.88/1.24 'class_Ring__and__Field_Opordered__cancel__semiring' [62, 1] (w:1, o:
% 0.88/1.24 34, a:1, s:1, b:0),
% 0.88/1.24 'class_LOrder_Ojoin__semilorder' [65, 1] (w:1, o:35, a:1, s:1, b:0)
% 0.88/1.24 .
% 0.88/1.24
% 0.88/1.24
% 0.88/1.24 Starting Search:
% 0.88/1.24
% 0.88/1.24 Resimplifying inuse:
% 0.88/1.24 Done
% 0.88/1.24
% 0.88/1.24
% 0.88/1.24 Bliksems!, er is een bewijs:
% 0.88/1.24 % SZS status Unsatisfiable
% 0.88/1.24 % SZS output start Refutation
% 0.88/1.24
% 0.88/1.24 clause( 0, [ =( 'v_f'( 'c_0' ), 'c_0' ) ] )
% 0.88/1.24 .
% 0.88/1.24 clause( 1, [ 'c_less'( 'c_0', 'v_x', 't_a' ) ] )
% 0.88/1.24 .
% 0.88/1.24 clause( 2, [ 'c_lessequals'( 'c_HOL_Oabs'( 'v_f'( 'c_Suc'( X ) ), 't_a' ),
% 0.88/1.24 'c_times'( 'v_x', 'c_HOL_Oabs'( 'v_h'( 'c_Suc'( X ) ), 't_a' ), 't_a' ),
% 0.88/1.24 't_a' ) ] )
% 0.88/1.24 .
% 0.88/1.24 clause( 3, [ ~( 'c_lessequals'( 'c_HOL_Oabs'( 'v_f'( 'v_xa'( X ) ), 't_a' )
% 0.88/1.24 , 'c_times'( X, 'c_HOL_Oabs'( 'v_h'( 'v_xa'( X ) ), 't_a' ), 't_a' ),
% 0.88/1.24 't_a' ) ), ~( 'c_less'( 'c_0', X, 't_a' ) ) ] )
% 0.88/1.24 .
% 0.88/1.24 clause( 4, [ 'class_Ring__and__Field_Oordered__idom'( 't_a' ) ] )
% 0.88/1.24 .
% 0.88/1.24 clause( 5, [ ~( 'c_less'( 'c_0', X, 'tc_nat' ) ), =( 'c_Suc'( 'c_minus'( X
% 0.88/1.24 , 'c_1', 'tc_nat' ) ), X ) ] )
% 0.88/1.24 .
% 0.88/1.24 clause( 6, [ 'c_less'( 'c_0', X, 'tc_nat' ), =( X, 'c_0' ) ] )
% 0.88/1.24 .
% 0.88/1.24 clause( 7, [ ~( 'class_OrderedGroup_Olordered__ab__group__abs'( X ) ), =(
% 0.88/1.24 'c_HOL_Oabs'( 'c_0', X ), 'c_0' ) ] )
% 0.88/1.24 .
% 0.88/1.24 clause( 8, [ ~( 'class_OrderedGroup_Olordered__ab__group__abs'( X ) ),
% 0.88/1.24 'c_lessequals'( 'c_0', 'c_HOL_Oabs'( Y, X ), X ) ] )
% 0.88/1.24 .
% 0.88/1.24 clause( 9, [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_less'( Y, Z, X ) ),
% 0.88/1.24 'c_lessequals'( Y, Z, X ) ] )
% 0.88/1.24 .
% 0.88/1.24 clause( 10, [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X )
% 0.88/1.24 ), ~( 'c_lessequals'( 'c_0', Y, X ) ), ~( 'c_lessequals'( 'c_0', Z, X )
% 0.88/1.24 ), 'c_lessequals'( 'c_0', 'c_times'( Z, Y, X ), X ) ] )
% 0.88/1.24 .
% 0.88/1.24 clause( 11, [ ~( 'class_LOrder_Ojoin__semilorder'( X ) ),
% 0.88/1.24 'class_Orderings_Oorder'( X ) ] )
% 0.88/1.24 .
% 0.88/1.24 clause( 12, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.88/1.24 'class_LOrder_Ojoin__semilorder'( X ) ] )
% 0.88/1.24 .
% 0.88/1.24 clause( 13, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.88/1.24 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ] )
% 0.88/1.24 .
% 0.88/1.24 clause( 14, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.88/1.24 'class_OrderedGroup_Olordered__ab__group__abs'( X ) ] )
% 0.88/1.24 .
% 0.88/1.24 clause( 16, [ 'class_OrderedGroup_Olordered__ab__group__abs'( 't_a' ) ] )
% 0.88/1.24 .
% 0.88/1.24 clause( 17, [ 'class_Ring__and__Field_Opordered__cancel__semiring'( 't_a' )
% 0.88/1.24 ] )
% 0.88/1.24 .
% 0.88/1.24 clause( 18, [ 'class_LOrder_Ojoin__semilorder'( 't_a' ) ] )
% 0.88/1.24 .
% 0.88/1.24 clause( 19, [ 'class_Orderings_Oorder'( 't_a' ) ] )
% 0.88/1.24 .
% 0.88/1.24 clause( 42, [ ~( 'c_lessequals'( 'c_HOL_Oabs'( 'v_f'( 'v_xa'( 'v_x' ) ),
% 0.88/1.24 't_a' ), 'c_times'( 'v_x', 'c_HOL_Oabs'( 'v_h'( 'v_xa'( 'v_x' ) ), 't_a'
% 0.88/1.24 ), 't_a' ), 't_a' ) ) ] )
% 0.88/1.24 .
% 0.88/1.24 clause( 69, [ 'c_lessequals'( 'c_HOL_Oabs'( 'v_f'( X ), 't_a' ), 'c_times'(
% 0.88/1.24 'v_x', 'c_HOL_Oabs'( 'v_h'( X ), 't_a' ), 't_a' ), 't_a' ), ~( 'c_less'(
% 0.88/1.24 'c_0', X, 'tc_nat' ) ) ] )
% 0.88/1.24 .
% 0.88/1.24 clause( 71, [ =( 'c_HOL_Oabs'( 'c_0', 't_a' ), 'c_0' ) ] )
% 0.88/1.24 .
% 0.88/1.24 clause( 84, [ 'c_lessequals'( 'c_0', 'c_HOL_Oabs'( X, 't_a' ), 't_a' ) ] )
% 0.88/1.24 .
% 0.88/1.24 clause( 107, [ 'c_lessequals'( 'c_0', 'v_x', 't_a' ) ] )
% 0.88/1.24 .
% 0.88/1.24 clause( 132, [ ~( 'c_lessequals'( 'c_0', X, 't_a' ) ), 'c_lessequals'(
% 0.88/1.24 'c_0', 'c_times'( 'v_x', X, 't_a' ), 't_a' ) ] )
% 0.88/1.24 .
% 0.88/1.24 clause( 1481, [ ~( 'c_less'( 'c_0', 'v_xa'( 'v_x' ), 'tc_nat' ) ) ] )
% 0.88/1.24 .
% 0.88/1.24 clause( 1508, [ =( 'v_xa'( 'v_x' ), 'c_0' ) ] )
% 0.88/1.24 .
% 0.88/1.24 clause( 1539, [ ~( 'c_lessequals'( 'c_0', 'c_times'( 'v_x', 'c_HOL_Oabs'(
% 0.88/1.24 'v_h'( 'c_0' ), 't_a' ), 't_a' ), 't_a' ) ) ] )
% 0.88/1.24 .
% 0.88/1.24 clause( 1912, [] )
% 0.88/1.24 .
% 0.88/1.24
% 0.88/1.24
% 0.88/1.24 % SZS output end Refutation
% 0.88/1.24 found a proof!
% 0.88/1.24
% 0.88/1.24 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.88/1.24
% 0.88/1.24 initialclauses(
% 0.88/1.24 [ clause( 1914, [ =( 'v_f'( 'c_0' ), 'c_0' ) ] )
% 0.88/1.24 , clause( 1915, [ 'c_less'( 'c_0', 'v_x', 't_a' ) ] )
% 0.88/1.24 , clause( 1916, [ 'c_lessequals'( 'c_HOL_Oabs'( 'v_f'( 'c_Suc'( X ) ),
% 0.88/1.24 't_a' ), 'c_times'( 'v_x', 'c_HOL_Oabs'( 'v_h'( 'c_Suc'( X ) ), 't_a' ),
% 0.88/1.24 't_a' ), 't_a' ) ] )
% 0.88/1.24 , clause( 1917, [ ~( 'c_lessequals'( 'c_HOL_Oabs'( 'v_f'( 'v_xa'( X ) ),
% 0.88/1.24 't_a' ), 'c_times'( X, 'c_HOL_Oabs'( 'v_h'( 'v_xa'( X ) ), 't_a' ), 't_a'
% 0.88/1.24 ), 't_a' ) ), ~( 'c_less'( 'c_0', X, 't_a' ) ) ] )
% 0.88/1.24 , clause( 1918, [ 'class_Ring__and__Field_Oordered__idom'( 't_a' ) ] )
% 0.88/1.24 , clause( 1919, [ ~( 'c_less'( 'c_0', X, 'tc_nat' ) ), =( X, 'c_Suc'(
% 0.88/1.24 'c_minus'( X, 'c_1', 'tc_nat' ) ) ) ] )
% 0.88/1.24 , clause( 1920, [ 'c_less'( 'c_0', X, 'tc_nat' ), =( X, 'c_0' ) ] )
% 0.88/1.25 , clause( 1921, [ ~( 'class_OrderedGroup_Olordered__ab__group__abs'( X ) )
% 0.88/1.25 , =( 'c_HOL_Oabs'( 'c_0', X ), 'c_0' ) ] )
% 0.88/1.25 , clause( 1922, [ ~( 'class_OrderedGroup_Olordered__ab__group__abs'( X ) )
% 0.88/1.25 , 'c_lessequals'( 'c_0', 'c_HOL_Oabs'( Y, X ), X ) ] )
% 0.88/1.25 , clause( 1923, [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_less'( Y, Z, X
% 0.88/1.25 ) ), 'c_lessequals'( Y, Z, X ) ] )
% 0.88/1.25 , clause( 1924, [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 0.88/1.25 X ) ), ~( 'c_lessequals'( 'c_0', Y, X ) ), ~( 'c_lessequals'( 'c_0', Z, X
% 0.88/1.25 ) ), 'c_lessequals'( 'c_0', 'c_times'( Z, Y, X ), X ) ] )
% 0.88/1.25 , clause( 1925, [ ~( 'class_LOrder_Ojoin__semilorder'( X ) ),
% 0.88/1.25 'class_Orderings_Oorder'( X ) ] )
% 0.88/1.25 , clause( 1926, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.88/1.25 'class_LOrder_Ojoin__semilorder'( X ) ] )
% 0.88/1.25 , clause( 1927, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.88/1.25 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ] )
% 0.88/1.25 , clause( 1928, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.88/1.25 'class_OrderedGroup_Olordered__ab__group__abs'( X ) ] )
% 0.88/1.25 ] ).
% 0.88/1.25
% 0.88/1.25
% 0.88/1.25
% 0.88/1.25 subsumption(
% 0.88/1.25 clause( 0, [ =( 'v_f'( 'c_0' ), 'c_0' ) ] )
% 0.88/1.25 , clause( 1914, [ =( 'v_f'( 'c_0' ), 'c_0' ) ] )
% 0.88/1.25 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.88/1.25
% 0.88/1.25
% 0.88/1.25 subsumption(
% 0.88/1.25 clause( 1, [ 'c_less'( 'c_0', 'v_x', 't_a' ) ] )
% 0.88/1.25 , clause( 1915, [ 'c_less'( 'c_0', 'v_x', 't_a' ) ] )
% 0.88/1.25 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.88/1.25
% 0.88/1.25
% 0.88/1.25 subsumption(
% 0.88/1.25 clause( 2, [ 'c_lessequals'( 'c_HOL_Oabs'( 'v_f'( 'c_Suc'( X ) ), 't_a' ),
% 0.88/1.25 'c_times'( 'v_x', 'c_HOL_Oabs'( 'v_h'( 'c_Suc'( X ) ), 't_a' ), 't_a' ),
% 0.88/1.25 't_a' ) ] )
% 0.88/1.25 , clause( 1916, [ 'c_lessequals'( 'c_HOL_Oabs'( 'v_f'( 'c_Suc'( X ) ),
% 0.88/1.25 't_a' ), 'c_times'( 'v_x', 'c_HOL_Oabs'( 'v_h'( 'c_Suc'( X ) ), 't_a' ),
% 0.88/1.25 't_a' ), 't_a' ) ] )
% 0.88/1.25 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.88/1.25
% 0.88/1.25
% 0.88/1.25 subsumption(
% 0.88/1.25 clause( 3, [ ~( 'c_lessequals'( 'c_HOL_Oabs'( 'v_f'( 'v_xa'( X ) ), 't_a' )
% 0.88/1.25 , 'c_times'( X, 'c_HOL_Oabs'( 'v_h'( 'v_xa'( X ) ), 't_a' ), 't_a' ),
% 0.88/1.25 't_a' ) ), ~( 'c_less'( 'c_0', X, 't_a' ) ) ] )
% 0.88/1.25 , clause( 1917, [ ~( 'c_lessequals'( 'c_HOL_Oabs'( 'v_f'( 'v_xa'( X ) ),
% 0.88/1.25 't_a' ), 'c_times'( X, 'c_HOL_Oabs'( 'v_h'( 'v_xa'( X ) ), 't_a' ), 't_a'
% 0.88/1.25 ), 't_a' ) ), ~( 'c_less'( 'c_0', X, 't_a' ) ) ] )
% 0.88/1.25 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 0.88/1.25 1 )] ) ).
% 0.88/1.25
% 0.88/1.25
% 0.88/1.25 subsumption(
% 0.88/1.25 clause( 4, [ 'class_Ring__and__Field_Oordered__idom'( 't_a' ) ] )
% 0.88/1.25 , clause( 1918, [ 'class_Ring__and__Field_Oordered__idom'( 't_a' ) ] )
% 0.88/1.25 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.88/1.25
% 0.88/1.25
% 0.88/1.25 eqswap(
% 0.88/1.25 clause( 1935, [ =( 'c_Suc'( 'c_minus'( X, 'c_1', 'tc_nat' ) ), X ), ~(
% 0.88/1.25 'c_less'( 'c_0', X, 'tc_nat' ) ) ] )
% 0.88/1.25 , clause( 1919, [ ~( 'c_less'( 'c_0', X, 'tc_nat' ) ), =( X, 'c_Suc'(
% 0.88/1.25 'c_minus'( X, 'c_1', 'tc_nat' ) ) ) ] )
% 0.88/1.25 , 1, substitution( 0, [ :=( X, X )] )).
% 0.88/1.25
% 0.88/1.25
% 0.88/1.25 subsumption(
% 0.88/1.25 clause( 5, [ ~( 'c_less'( 'c_0', X, 'tc_nat' ) ), =( 'c_Suc'( 'c_minus'( X
% 0.88/1.25 , 'c_1', 'tc_nat' ) ), X ) ] )
% 0.88/1.25 , clause( 1935, [ =( 'c_Suc'( 'c_minus'( X, 'c_1', 'tc_nat' ) ), X ), ~(
% 0.88/1.25 'c_less'( 'c_0', X, 'tc_nat' ) ) ] )
% 0.88/1.25 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 1 ), ==>( 1,
% 0.88/1.25 0 )] ) ).
% 0.88/1.25
% 0.88/1.25
% 0.88/1.25 subsumption(
% 0.88/1.25 clause( 6, [ 'c_less'( 'c_0', X, 'tc_nat' ), =( X, 'c_0' ) ] )
% 0.88/1.25 , clause( 1920, [ 'c_less'( 'c_0', X, 'tc_nat' ), =( X, 'c_0' ) ] )
% 0.88/1.25 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 0.88/1.25 1 )] ) ).
% 0.88/1.25
% 0.88/1.25
% 0.88/1.25 subsumption(
% 0.88/1.25 clause( 7, [ ~( 'class_OrderedGroup_Olordered__ab__group__abs'( X ) ), =(
% 0.88/1.25 'c_HOL_Oabs'( 'c_0', X ), 'c_0' ) ] )
% 0.88/1.25 , clause( 1921, [ ~( 'class_OrderedGroup_Olordered__ab__group__abs'( X ) )
% 0.88/1.25 , =( 'c_HOL_Oabs'( 'c_0', X ), 'c_0' ) ] )
% 0.88/1.25 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 0.88/1.25 1 )] ) ).
% 0.88/1.25
% 0.88/1.25
% 0.88/1.25 subsumption(
% 0.88/1.25 clause( 8, [ ~( 'class_OrderedGroup_Olordered__ab__group__abs'( X ) ),
% 0.88/1.25 'c_lessequals'( 'c_0', 'c_HOL_Oabs'( Y, X ), X ) ] )
% 0.88/1.25 , clause( 1922, [ ~( 'class_OrderedGroup_Olordered__ab__group__abs'( X ) )
% 0.88/1.25 , 'c_lessequals'( 'c_0', 'c_HOL_Oabs'( Y, X ), X ) ] )
% 0.88/1.25 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.88/1.25 ), ==>( 1, 1 )] ) ).
% 0.88/1.25
% 0.88/1.25
% 0.88/1.25 subsumption(
% 0.88/1.25 clause( 9, [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_less'( Y, Z, X ) ),
% 0.88/1.25 'c_lessequals'( Y, Z, X ) ] )
% 0.88/1.25 , clause( 1923, [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_less'( Y, Z, X
% 0.88/1.25 ) ), 'c_lessequals'( Y, Z, X ) ] )
% 0.88/1.25 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.88/1.25 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 0.88/1.25
% 0.88/1.25
% 0.88/1.25 subsumption(
% 0.88/1.25 clause( 10, [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X )
% 0.88/1.25 ), ~( 'c_lessequals'( 'c_0', Y, X ) ), ~( 'c_lessequals'( 'c_0', Z, X )
% 0.88/1.25 ), 'c_lessequals'( 'c_0', 'c_times'( Z, Y, X ), X ) ] )
% 0.88/1.25 , clause( 1924, [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 0.88/1.25 X ) ), ~( 'c_lessequals'( 'c_0', Y, X ) ), ~( 'c_lessequals'( 'c_0', Z, X
% 0.88/1.25 ) ), 'c_lessequals'( 'c_0', 'c_times'( Z, Y, X ), X ) ] )
% 0.88/1.25 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.88/1.25 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 ), ==>( 3, 3 )] )
% 0.88/1.25 ).
% 0.88/1.25
% 0.88/1.25
% 0.88/1.25 subsumption(
% 0.88/1.25 clause( 11, [ ~( 'class_LOrder_Ojoin__semilorder'( X ) ),
% 0.88/1.25 'class_Orderings_Oorder'( X ) ] )
% 0.88/1.25 , clause( 1925, [ ~( 'class_LOrder_Ojoin__semilorder'( X ) ),
% 0.88/1.25 'class_Orderings_Oorder'( X ) ] )
% 0.88/1.25 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 0.88/1.25 1 )] ) ).
% 0.88/1.25
% 0.88/1.25
% 0.88/1.25 subsumption(
% 0.88/1.25 clause( 12, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.88/1.25 'class_LOrder_Ojoin__semilorder'( X ) ] )
% 0.88/1.25 , clause( 1926, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.88/1.25 'class_LOrder_Ojoin__semilorder'( X ) ] )
% 0.88/1.25 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 0.88/1.25 1 )] ) ).
% 0.88/1.25
% 0.88/1.25
% 0.88/1.25 subsumption(
% 0.88/1.25 clause( 13, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.88/1.25 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ] )
% 0.88/1.25 , clause( 1927, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.88/1.25 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ] )
% 0.88/1.25 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 0.88/1.25 1 )] ) ).
% 0.88/1.25
% 0.88/1.25
% 0.88/1.25 subsumption(
% 0.88/1.25 clause( 14, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.88/1.25 'class_OrderedGroup_Olordered__ab__group__abs'( X ) ] )
% 0.88/1.25 , clause( 1928, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.88/1.25 'class_OrderedGroup_Olordered__ab__group__abs'( X ) ] )
% 0.88/1.25 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 0.88/1.25 1 )] ) ).
% 0.88/1.25
% 0.88/1.25
% 0.88/1.25 resolution(
% 0.88/1.25 clause( 1976, [ 'class_OrderedGroup_Olordered__ab__group__abs'( 't_a' ) ]
% 0.88/1.25 )
% 0.88/1.25 , clause( 14, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.88/1.25 'class_OrderedGroup_Olordered__ab__group__abs'( X ) ] )
% 0.88/1.25 , 0, clause( 4, [ 'class_Ring__and__Field_Oordered__idom'( 't_a' ) ] )
% 0.88/1.25 , 0, substitution( 0, [ :=( X, 't_a' )] ), substitution( 1, [] )).
% 0.88/1.25
% 0.88/1.25
% 0.88/1.25 subsumption(
% 0.88/1.25 clause( 16, [ 'class_OrderedGroup_Olordered__ab__group__abs'( 't_a' ) ] )
% 0.88/1.25 , clause( 1976, [ 'class_OrderedGroup_Olordered__ab__group__abs'( 't_a' ) ]
% 0.88/1.25 )
% 0.88/1.25 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.88/1.25
% 0.88/1.25
% 0.88/1.25 resolution(
% 0.88/1.25 clause( 1977, [ 'class_Ring__and__Field_Opordered__cancel__semiring'( 't_a'
% 0.88/1.25 ) ] )
% 0.88/1.25 , clause( 13, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.88/1.25 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ] )
% 0.88/1.25 , 0, clause( 4, [ 'class_Ring__and__Field_Oordered__idom'( 't_a' ) ] )
% 0.88/1.25 , 0, substitution( 0, [ :=( X, 't_a' )] ), substitution( 1, [] )).
% 0.88/1.25
% 0.88/1.25
% 0.88/1.25 subsumption(
% 0.88/1.25 clause( 17, [ 'class_Ring__and__Field_Opordered__cancel__semiring'( 't_a' )
% 0.88/1.25 ] )
% 0.88/1.25 , clause( 1977, [ 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 0.88/1.25 't_a' ) ] )
% 0.88/1.25 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.88/1.25
% 0.88/1.25
% 0.88/1.25 resolution(
% 0.88/1.25 clause( 1978, [ 'class_LOrder_Ojoin__semilorder'( 't_a' ) ] )
% 0.88/1.25 , clause( 12, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.88/1.25 'class_LOrder_Ojoin__semilorder'( X ) ] )
% 0.88/1.25 , 0, clause( 4, [ 'class_Ring__and__Field_Oordered__idom'( 't_a' ) ] )
% 0.88/1.25 , 0, substitution( 0, [ :=( X, 't_a' )] ), substitution( 1, [] )).
% 0.88/1.25
% 0.88/1.25
% 0.88/1.25 subsumption(
% 0.88/1.25 clause( 18, [ 'class_LOrder_Ojoin__semilorder'( 't_a' ) ] )
% 0.88/1.25 , clause( 1978, [ 'class_LOrder_Ojoin__semilorder'( 't_a' ) ] )
% 0.88/1.25 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.88/1.25
% 0.88/1.25
% 0.88/1.25 resolution(
% 0.88/1.25 clause( 1979, [ 'class_Orderings_Oorder'( 't_a' ) ] )
% 0.88/1.25 , clause( 11, [ ~( 'class_LOrder_Ojoin__semilorder'( X ) ),
% 0.88/1.25 'class_Orderings_Oorder'( X ) ] )
% 0.88/1.25 , 0, clause( 18, [ 'class_LOrder_Ojoin__semilorder'( 't_a' ) ] )
% 0.88/1.25 , 0, substitution( 0, [ :=( X, 't_a' )] ), substitution( 1, [] )).
% 0.88/1.25
% 0.88/1.25
% 0.88/1.25 subsumption(
% 0.88/1.25 clause( 19, [ 'class_Orderings_Oorder'( 't_a' ) ] )
% 0.88/1.25 , clause( 1979, [ 'class_Orderings_Oorder'( 't_a' ) ] )
% 0.88/1.25 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.88/1.25
% 0.88/1.25
% 0.88/1.25 resolution(
% 0.88/1.25 clause( 1980, [ ~( 'c_lessequals'( 'c_HOL_Oabs'( 'v_f'( 'v_xa'( 'v_x' ) ),
% 0.88/1.25 't_a' ), 'c_times'( 'v_x', 'c_HOL_Oabs'( 'v_h'( 'v_xa'( 'v_x' ) ), 't_a'
% 0.88/1.25 ), 't_a' ), 't_a' ) ) ] )
% 0.88/1.25 , clause( 3, [ ~( 'c_lessequals'( 'c_HOL_Oabs'( 'v_f'( 'v_xa'( X ) ), 't_a'
% 0.88/1.25 ), 'c_times'( X, 'c_HOL_Oabs'( 'v_h'( 'v_xa'( X ) ), 't_a' ), 't_a' ),
% 0.88/1.25 't_a' ) ), ~( 'c_less'( 'c_0', X, 't_a' ) ) ] )
% 0.88/1.25 , 1, clause( 1, [ 'c_less'( 'c_0', 'v_x', 't_a' ) ] )
% 0.88/1.25 , 0, substitution( 0, [ :=( X, 'v_x' )] ), substitution( 1, [] )).
% 0.88/1.25
% 0.88/1.25
% 0.88/1.25 subsumption(
% 0.88/1.25 clause( 42, [ ~( 'c_lessequals'( 'c_HOL_Oabs'( 'v_f'( 'v_xa'( 'v_x' ) ),
% 0.88/1.25 't_a' ), 'c_times'( 'v_x', 'c_HOL_Oabs'( 'v_h'( 'v_xa'( 'v_x' ) ), 't_a'
% 0.88/1.25 ), 't_a' ), 't_a' ) ) ] )
% 0.88/1.25 , clause( 1980, [ ~( 'c_lessequals'( 'c_HOL_Oabs'( 'v_f'( 'v_xa'( 'v_x' ) )
% 0.88/1.25 , 't_a' ), 'c_times'( 'v_x', 'c_HOL_Oabs'( 'v_h'( 'v_xa'( 'v_x' ) ),
% 0.88/1.25 't_a' ), 't_a' ), 't_a' ) ) ] )
% 0.88/1.25 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.88/1.25
% 0.88/1.25
% 0.88/1.25 paramod(
% 0.88/1.25 clause( 1983, [ 'c_lessequals'( 'c_HOL_Oabs'( 'v_f'( 'c_Suc'( 'c_minus'( X
% 0.88/1.25 , 'c_1', 'tc_nat' ) ) ), 't_a' ), 'c_times'( 'v_x', 'c_HOL_Oabs'( 'v_h'(
% 0.88/1.25 X ), 't_a' ), 't_a' ), 't_a' ), ~( 'c_less'( 'c_0', X, 'tc_nat' ) ) ] )
% 0.88/1.25 , clause( 5, [ ~( 'c_less'( 'c_0', X, 'tc_nat' ) ), =( 'c_Suc'( 'c_minus'(
% 0.88/1.25 X, 'c_1', 'tc_nat' ) ), X ) ] )
% 0.88/1.25 , 1, clause( 2, [ 'c_lessequals'( 'c_HOL_Oabs'( 'v_f'( 'c_Suc'( X ) ),
% 0.88/1.25 't_a' ), 'c_times'( 'v_x', 'c_HOL_Oabs'( 'v_h'( 'c_Suc'( X ) ), 't_a' ),
% 0.88/1.25 't_a' ), 't_a' ) ] )
% 0.88/1.25 , 0, 13, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X,
% 0.88/1.25 'c_minus'( X, 'c_1', 'tc_nat' ) )] )).
% 0.88/1.25
% 0.88/1.25
% 0.88/1.25 paramod(
% 0.88/1.25 clause( 1984, [ 'c_lessequals'( 'c_HOL_Oabs'( 'v_f'( X ), 't_a' ),
% 0.88/1.25 'c_times'( 'v_x', 'c_HOL_Oabs'( 'v_h'( X ), 't_a' ), 't_a' ), 't_a' ),
% 0.88/1.25 ~( 'c_less'( 'c_0', X, 'tc_nat' ) ), ~( 'c_less'( 'c_0', X, 'tc_nat' ) )
% 0.88/1.25 ] )
% 0.88/1.25 , clause( 5, [ ~( 'c_less'( 'c_0', X, 'tc_nat' ) ), =( 'c_Suc'( 'c_minus'(
% 0.88/1.25 X, 'c_1', 'tc_nat' ) ), X ) ] )
% 0.88/1.25 , 1, clause( 1983, [ 'c_lessequals'( 'c_HOL_Oabs'( 'v_f'( 'c_Suc'(
% 0.88/1.25 'c_minus'( X, 'c_1', 'tc_nat' ) ) ), 't_a' ), 'c_times'( 'v_x',
% 0.88/1.25 'c_HOL_Oabs'( 'v_h'( X ), 't_a' ), 't_a' ), 't_a' ), ~( 'c_less'( 'c_0',
% 0.88/1.25 X, 'tc_nat' ) ) ] )
% 0.88/1.25 , 0, 3, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 0.88/1.25 ).
% 0.88/1.25
% 0.88/1.25
% 0.88/1.25 factor(
% 0.88/1.25 clause( 1985, [ 'c_lessequals'( 'c_HOL_Oabs'( 'v_f'( X ), 't_a' ),
% 0.88/1.25 'c_times'( 'v_x', 'c_HOL_Oabs'( 'v_h'( X ), 't_a' ), 't_a' ), 't_a' ),
% 0.88/1.25 ~( 'c_less'( 'c_0', X, 'tc_nat' ) ) ] )
% 0.88/1.25 , clause( 1984, [ 'c_lessequals'( 'c_HOL_Oabs'( 'v_f'( X ), 't_a' ),
% 0.88/1.25 'c_times'( 'v_x', 'c_HOL_Oabs'( 'v_h'( X ), 't_a' ), 't_a' ), 't_a' ),
% 0.88/1.25 ~( 'c_less'( 'c_0', X, 'tc_nat' ) ), ~( 'c_less'( 'c_0', X, 'tc_nat' ) )
% 0.88/1.25 ] )
% 0.88/1.25 , 1, 2, substitution( 0, [ :=( X, X )] )).
% 0.88/1.25
% 0.88/1.25
% 0.88/1.25 subsumption(
% 0.88/1.25 clause( 69, [ 'c_lessequals'( 'c_HOL_Oabs'( 'v_f'( X ), 't_a' ), 'c_times'(
% 0.88/1.25 'v_x', 'c_HOL_Oabs'( 'v_h'( X ), 't_a' ), 't_a' ), 't_a' ), ~( 'c_less'(
% 0.88/1.25 'c_0', X, 'tc_nat' ) ) ] )
% 0.88/1.25 , clause( 1985, [ 'c_lessequals'( 'c_HOL_Oabs'( 'v_f'( X ), 't_a' ),
% 0.88/1.25 'c_times'( 'v_x', 'c_HOL_Oabs'( 'v_h'( X ), 't_a' ), 't_a' ), 't_a' ),
% 0.88/1.25 ~( 'c_less'( 'c_0', X, 'tc_nat' ) ) ] )
% 0.88/1.25 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 0.88/1.25 1 )] ) ).
% 0.88/1.25
% 0.88/1.25
% 0.88/1.25 eqswap(
% 0.88/1.25 clause( 1986, [ =( 'c_0', 'c_HOL_Oabs'( 'c_0', X ) ), ~(
% 0.88/1.25 'class_OrderedGroup_Olordered__ab__group__abs'( X ) ) ] )
% 0.88/1.25 , clause( 7, [ ~( 'class_OrderedGroup_Olordered__ab__group__abs'( X ) ),
% 0.88/1.25 =( 'c_HOL_Oabs'( 'c_0', X ), 'c_0' ) ] )
% 0.88/1.25 , 1, substitution( 0, [ :=( X, X )] )).
% 0.88/1.25
% 0.88/1.25
% 0.88/1.25 resolution(
% 0.88/1.25 clause( 1987, [ =( 'c_0', 'c_HOL_Oabs'( 'c_0', 't_a' ) ) ] )
% 0.88/1.25 , clause( 1986, [ =( 'c_0', 'c_HOL_Oabs'( 'c_0', X ) ), ~(
% 0.88/1.25 'class_OrderedGroup_Olordered__ab__group__abs'( X ) ) ] )
% 0.88/1.25 , 1, clause( 16, [ 'class_OrderedGroup_Olordered__ab__group__abs'( 't_a' )
% 0.88/1.25 ] )
% 0.88/1.25 , 0, substitution( 0, [ :=( X, 't_a' )] ), substitution( 1, [] )).
% 0.88/1.25
% 0.88/1.25
% 0.88/1.25 eqswap(
% 0.88/1.25 clause( 1988, [ =( 'c_HOL_Oabs'( 'c_0', 't_a' ), 'c_0' ) ] )
% 0.88/1.25 , clause( 1987, [ =( 'c_0', 'c_HOL_Oabs'( 'c_0', 't_a' ) ) ] )
% 0.88/1.25 , 0, substitution( 0, [] )).
% 0.88/1.25
% 0.88/1.25
% 0.88/1.25 subsumption(
% 0.88/1.25 clause( 71, [ =( 'c_HOL_Oabs'( 'c_0', 't_a' ), 'c_0' ) ] )
% 0.88/1.25 , clause( 1988, [ =( 'c_HOL_Oabs'( 'c_0', 't_a' ), 'c_0' ) ] )
% 0.88/1.25 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.88/1.25
% 0.88/1.25
% 0.88/1.25 resolution(
% 0.88/1.25 clause( 1989, [ 'c_lessequals'( 'c_0', 'c_HOL_Oabs'( X, 't_a' ), 't_a' ) ]
% 0.88/1.25 )
% 0.88/1.25 , clause( 8, [ ~( 'class_OrderedGroup_Olordered__ab__group__abs'( X ) ),
% 0.88/1.25 'c_lessequals'( 'c_0', 'c_HOL_Oabs'( Y, X ), X ) ] )
% 0.88/1.25 , 0, clause( 16, [ 'class_OrderedGroup_Olordered__ab__group__abs'( 't_a' )
% 0.88/1.25 ] )
% 0.88/1.25 , 0, substitution( 0, [ :=( X, 't_a' ), :=( Y, X )] ), substitution( 1, [] )
% 0.88/1.25 ).
% 0.88/1.25
% 0.88/1.25
% 0.88/1.25 subsumption(
% 0.88/1.25 clause( 84, [ 'c_lessequals'( 'c_0', 'c_HOL_Oabs'( X, 't_a' ), 't_a' ) ] )
% 0.88/1.25 , clause( 1989, [ 'c_lessequals'( 'c_0', 'c_HOL_Oabs'( X, 't_a' ), 't_a' )
% 0.88/1.25 ] )
% 0.88/1.25 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.88/1.25
% 0.88/1.25
% 0.88/1.25 resolution(
% 0.88/1.25 clause( 1990, [ ~( 'class_Orderings_Oorder'( 't_a' ) ), 'c_lessequals'(
% 0.88/1.25 'c_0', 'v_x', 't_a' ) ] )
% 0.88/1.25 , clause( 9, [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_less'( Y, Z, X ) )
% 0.88/1.25 , 'c_lessequals'( Y, Z, X ) ] )
% 0.88/1.25 , 1, clause( 1, [ 'c_less'( 'c_0', 'v_x', 't_a' ) ] )
% 0.88/1.25 , 0, substitution( 0, [ :=( X, 't_a' ), :=( Y, 'c_0' ), :=( Z, 'v_x' )] ),
% 0.88/1.25 substitution( 1, [] )).
% 0.88/1.25
% 0.88/1.25
% 0.88/1.25 resolution(
% 0.88/1.25 clause( 1991, [ 'c_lessequals'( 'c_0', 'v_x', 't_a' ) ] )
% 0.88/1.25 , clause( 1990, [ ~( 'class_Orderings_Oorder'( 't_a' ) ), 'c_lessequals'(
% 0.88/1.25 'c_0', 'v_x', 't_a' ) ] )
% 0.88/1.25 , 0, clause( 19, [ 'class_Orderings_Oorder'( 't_a' ) ] )
% 0.88/1.25 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 0.88/1.25
% 0.88/1.25
% 0.88/1.25 subsumption(
% 0.88/1.25 clause( 107, [ 'c_lessequals'( 'c_0', 'v_x', 't_a' ) ] )
% 0.88/1.25 , clause( 1991, [ 'c_lessequals'( 'c_0', 'v_x', 't_a' ) ] )
% 0.88/1.25 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.88/1.25
% 0.88/1.25
% 0.88/1.25 resolution(
% 0.88/1.25 clause( 1993, [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 0.88/1.25 't_a' ) ), ~( 'c_lessequals'( 'c_0', X, 't_a' ) ), 'c_lessequals'( 'c_0'
% 0.88/1.25 , 'c_times'( 'v_x', X, 't_a' ), 't_a' ) ] )
% 0.88/1.25 , clause( 10, [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X
% 0.88/1.25 ) ), ~( 'c_lessequals'( 'c_0', Y, X ) ), ~( 'c_lessequals'( 'c_0', Z, X
% 0.88/1.25 ) ), 'c_lessequals'( 'c_0', 'c_times'( Z, Y, X ), X ) ] )
% 0.88/1.25 , 2, clause( 107, [ 'c_lessequals'( 'c_0', 'v_x', 't_a' ) ] )
% 0.88/1.25 , 0, substitution( 0, [ :=( X, 't_a' ), :=( Y, X ), :=( Z, 'v_x' )] ),
% 0.88/1.25 substitution( 1, [] )).
% 0.88/1.25
% 0.88/1.25
% 0.88/1.25 resolution(
% 0.88/1.25 clause( 1995, [ ~( 'c_lessequals'( 'c_0', X, 't_a' ) ), 'c_lessequals'(
% 0.88/1.25 'c_0', 'c_times'( 'v_x', X, 't_a' ), 't_a' ) ] )
% 0.88/1.25 , clause( 1993, [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 0.88/1.25 't_a' ) ), ~( 'c_lessequals'( 'c_0', X, 't_a' ) ), 'c_lessequals'( 'c_0'
% 0.88/1.25 , 'c_times'( 'v_x', X, 't_a' ), 't_a' ) ] )
% 0.88/1.25 , 0, clause( 17, [ 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 0.88/1.25 't_a' ) ] )
% 0.88/1.25 , 0, substitution( 0, [ :=( X, X )] ), substitution( 1, [] )).
% 0.88/1.25
% 0.88/1.25
% 0.88/1.25 subsumption(
% 0.88/1.25 clause( 132, [ ~( 'c_lessequals'( 'c_0', X, 't_a' ) ), 'c_lessequals'(
% 0.88/1.25 'c_0', 'c_times'( 'v_x', X, 't_a' ), 't_a' ) ] )
% 0.88/1.25 , clause( 1995, [ ~( 'c_lessequals'( 'c_0', X, 't_a' ) ), 'c_lessequals'(
% 0.88/1.25 'c_0', 'c_times'( 'v_x', X, 't_a' ), 't_a' ) ] )
% 0.88/1.25 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 0.88/1.25 1 )] ) ).
% 0.88/1.25
% 0.88/1.25
% 0.88/1.25 resolution(
% 0.88/1.25 clause( 1996, [ ~( 'c_less'( 'c_0', 'v_xa'( 'v_x' ), 'tc_nat' ) ) ] )
% 0.88/1.25 , clause( 42, [ ~( 'c_lessequals'( 'c_HOL_Oabs'( 'v_f'( 'v_xa'( 'v_x' ) ),
% 0.88/1.25 't_a' ), 'c_times'( 'v_x', 'c_HOL_Oabs'( 'v_h'( 'v_xa'( 'v_x' ) ), 't_a'
% 0.88/1.25 ), 't_a' ), 't_a' ) ) ] )
% 0.88/1.25 , 0, clause( 69, [ 'c_lessequals'( 'c_HOL_Oabs'( 'v_f'( X ), 't_a' ),
% 0.88/1.25 'c_times'( 'v_x', 'c_HOL_Oabs'( 'v_h'( X ), 't_a' ), 't_a' ), 't_a' ),
% 0.88/1.25 ~( 'c_less'( 'c_0', X, 'tc_nat' ) ) ] )
% 0.88/1.25 , 0, substitution( 0, [] ), substitution( 1, [ :=( X, 'v_xa'( 'v_x' ) )] )
% 0.88/1.25 ).
% 0.88/1.25
% 0.88/1.25
% 0.88/1.25 subsumption(
% 0.88/1.25 clause( 1481, [ ~( 'c_less'( 'c_0', 'v_xa'( 'v_x' ), 'tc_nat' ) ) ] )
% 0.88/1.25 , clause( 1996, [ ~( 'c_less'( 'c_0', 'v_xa'( 'v_x' ), 'tc_nat' ) ) ] )
% 0.88/1.25 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.88/1.25
% 0.88/1.25
% 0.88/1.25 eqswap(
% 0.88/1.25 clause( 1997, [ =( 'c_0', X ), 'c_less'( 'c_0', X, 'tc_nat' ) ] )
% 0.88/1.25 , clause( 6, [ 'c_less'( 'c_0', X, 'tc_nat' ), =( X, 'c_0' ) ] )
% 0.88/1.25 , 1, substitution( 0, [ :=( X, X )] )).
% 0.88/1.25
% 0.88/1.25
% 0.88/1.25 resolution(
% 0.88/1.25 clause( 1998, [ =( 'c_0', 'v_xa'( 'v_x' ) ) ] )
% 0.88/1.25 , clause( 1481, [ ~( 'c_less'( 'c_0', 'v_xa'( 'v_x' ), 'tc_nat' ) ) ] )
% 0.88/1.25 , 0, clause( 1997, [ =( 'c_0', X ), 'c_less'( 'c_0', X, 'tc_nat' ) ] )
% 0.88/1.25 , 1, substitution( 0, [] ), substitution( 1, [ :=( X, 'v_xa'( 'v_x' ) )] )
% 0.88/1.25 ).
% 0.88/1.25
% 0.88/1.25
% 0.88/1.25 eqswap(
% 0.88/1.25 clause( 1999, [ =( 'v_xa'( 'v_x' ), 'c_0' ) ] )
% 0.88/1.25 , clause( 1998, [ =( 'c_0', 'v_xa'( 'v_x' ) ) ] )
% 0.88/1.25 , 0, substitution( 0, [] )).
% 0.88/1.25
% 0.88/1.25
% 0.88/1.25 subsumption(
% 0.88/1.25 clause( 1508, [ =( 'v_xa'( 'v_x' ), 'c_0' ) ] )
% 0.88/1.25 , clause( 1999, [ =( 'v_xa'( 'v_x' ), 'c_0' ) ] )
% 0.88/1.25 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.88/1.25
% 0.88/1.25
% 0.88/1.25 paramod(
% 0.88/1.25 clause( 2004, [ ~( 'c_lessequals'( 'c_HOL_Oabs'( 'v_f'( 'v_xa'( 'v_x' ) ),
% 0.88/1.25 't_a' ), 'c_times'( 'v_x', 'c_HOL_Oabs'( 'v_h'( 'c_0' ), 't_a' ), 't_a' )
% 0.88/1.25 , 't_a' ) ) ] )
% 0.88/1.25 , clause( 1508, [ =( 'v_xa'( 'v_x' ), 'c_0' ) ] )
% 0.88/1.25 , 0, clause( 42, [ ~( 'c_lessequals'( 'c_HOL_Oabs'( 'v_f'( 'v_xa'( 'v_x' )
% 0.88/1.25 ), 't_a' ), 'c_times'( 'v_x', 'c_HOL_Oabs'( 'v_h'( 'v_xa'( 'v_x' ) ),
% 0.88/1.25 't_a' ), 't_a' ), 't_a' ) ) ] )
% 0.88/1.25 , 0, 11, substitution( 0, [] ), substitution( 1, [] )).
% 0.88/1.25
% 0.88/1.25
% 0.88/1.25 paramod(
% 0.88/1.25 clause( 2005, [ ~( 'c_lessequals'( 'c_HOL_Oabs'( 'v_f'( 'c_0' ), 't_a' ),
% 0.88/1.25 'c_times'( 'v_x', 'c_HOL_Oabs'( 'v_h'( 'c_0' ), 't_a' ), 't_a' ), 't_a' )
% 0.88/1.25 ) ] )
% 0.88/1.25 , clause( 1508, [ =( 'v_xa'( 'v_x' ), 'c_0' ) ] )
% 0.88/1.25 , 0, clause( 2004, [ ~( 'c_lessequals'( 'c_HOL_Oabs'( 'v_f'( 'v_xa'( 'v_x'
% 0.88/1.25 ) ), 't_a' ), 'c_times'( 'v_x', 'c_HOL_Oabs'( 'v_h'( 'c_0' ), 't_a' ),
% 0.88/1.25 't_a' ), 't_a' ) ) ] )
% 0.88/1.25 , 0, 4, substitution( 0, [] ), substitution( 1, [] )).
% 0.88/1.25
% 0.88/1.25
% 0.88/1.25 paramod(
% 0.88/1.25 clause( 2006, [ ~( 'c_lessequals'( 'c_HOL_Oabs'( 'c_0', 't_a' ), 'c_times'(
% 0.88/1.25 'v_x', 'c_HOL_Oabs'( 'v_h'( 'c_0' ), 't_a' ), 't_a' ), 't_a' ) ) ] )
% 0.88/1.25 , clause( 0, [ =( 'v_f'( 'c_0' ), 'c_0' ) ] )
% 0.88/1.25 , 0, clause( 2005, [ ~( 'c_lessequals'( 'c_HOL_Oabs'( 'v_f'( 'c_0' ), 't_a'
% 0.88/1.25 ), 'c_times'( 'v_x', 'c_HOL_Oabs'( 'v_h'( 'c_0' ), 't_a' ), 't_a' ),
% 0.88/1.25 't_a' ) ) ] )
% 0.88/1.25 , 0, 3, substitution( 0, [] ), substitution( 1, [] )).
% 0.88/1.25
% 0.88/1.25
% 0.88/1.25 paramod(
% 0.88/1.25 clause( 2007, [ ~( 'c_lessequals'( 'c_0', 'c_times'( 'v_x', 'c_HOL_Oabs'(
% 0.88/1.25 'v_h'( 'c_0' ), 't_a' ), 't_a' ), 't_a' ) ) ] )
% 0.88/1.25 , clause( 71, [ =( 'c_HOL_Oabs'( 'c_0', 't_a' ), 'c_0' ) ] )
% 0.88/1.25 , 0, clause( 2006, [ ~( 'c_lessequals'( 'c_HOL_Oabs'( 'c_0', 't_a' ),
% 0.88/1.25 'c_times'( 'v_x', 'c_HOL_Oabs'( 'v_h'( 'c_0' ), 't_a' ), 't_a' ), 't_a' )
% 0.88/1.25 ) ] )
% 0.88/1.25 , 0, 2, substitution( 0, [] ), substitution( 1, [] )).
% 0.88/1.25
% 0.88/1.25
% 0.88/1.25 subsumption(
% 0.88/1.25 clause( 1539, [ ~( 'c_lessequals'( 'c_0', 'c_times'( 'v_x', 'c_HOL_Oabs'(
% 0.88/1.25 'v_h'( 'c_0' ), 't_a' ), 't_a' ), 't_a' ) ) ] )
% 0.88/1.25 , clause( 2007, [ ~( 'c_lessequals'( 'c_0', 'c_times'( 'v_x', 'c_HOL_Oabs'(
% 0.88/1.25 'v_h'( 'c_0' ), 't_a' ), 't_a' ), 't_a' ) ) ] )
% 0.88/1.25 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.88/1.25
% 0.88/1.25
% 0.88/1.25 resolution(
% 0.88/1.25 clause( 2008, [ ~( 'c_lessequals'( 'c_0', 'c_HOL_Oabs'( 'v_h'( 'c_0' ),
% 0.88/1.25 't_a' ), 't_a' ) ) ] )
% 0.88/1.25 , clause( 1539, [ ~( 'c_lessequals'( 'c_0', 'c_times'( 'v_x', 'c_HOL_Oabs'(
% 0.88/1.25 'v_h'( 'c_0' ), 't_a' ), 't_a' ), 't_a' ) ) ] )
% 0.88/1.25 , 0, clause( 132, [ ~( 'c_lessequals'( 'c_0', X, 't_a' ) ), 'c_lessequals'(
% 0.88/1.25 'c_0', 'c_times'( 'v_x', X, 't_a' ), 't_a' ) ] )
% 0.88/1.25 , 1, substitution( 0, [] ), substitution( 1, [ :=( X, 'c_HOL_Oabs'( 'v_h'(
% 0.88/1.25 'c_0' ), 't_a' ) )] )).
% 0.88/1.25
% 0.88/1.25
% 0.88/1.25 resolution(
% 0.88/1.25 clause( 2009, [] )
% 0.88/1.25 , clause( 2008, [ ~( 'c_lessequals'( 'c_0', 'c_HOL_Oabs'( 'v_h'( 'c_0' ),
% 0.88/1.25 't_a' ), 't_a' ) ) ] )
% 0.88/1.25 , 0, clause( 84, [ 'c_lessequals'( 'c_0', 'c_HOL_Oabs'( X, 't_a' ), 't_a' )
% 0.88/1.25 ] )
% 0.88/1.25 , 0, substitution( 0, [] ), substitution( 1, [ :=( X, 'v_h'( 'c_0' ) )] )
% 0.88/1.25 ).
% 0.88/1.25
% 0.88/1.25
% 0.88/1.25 subsumption(
% 0.88/1.25 clause( 1912, [] )
% 0.88/1.25 , clause( 2009, [] )
% 0.88/1.25 , substitution( 0, [] ), permutation( 0, [] ) ).
% 0.88/1.25
% 0.88/1.25
% 0.88/1.25 end.
% 0.88/1.25
% 0.88/1.25 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.88/1.25
% 0.88/1.25 Memory use:
% 0.88/1.25
% 0.88/1.25 space for terms: 27020
% 0.88/1.25 space for clauses: 81940
% 0.88/1.25
% 0.88/1.25
% 0.88/1.25 clauses generated: 21528
% 0.88/1.25 clauses kept: 1913
% 0.88/1.25 clauses selected: 261
% 0.88/1.25 clauses deleted: 41
% 0.88/1.25 clauses inuse deleted: 0
% 0.88/1.25
% 0.88/1.25 subsentry: 14852
% 0.88/1.25 literals s-matched: 11083
% 0.88/1.25 literals matched: 9724
% 0.88/1.25 full subsumption: 1591
% 0.88/1.25
% 0.88/1.25 checksum: -1506032276
% 0.88/1.25
% 0.88/1.25
% 0.88/1.25 Bliksem ended
%------------------------------------------------------------------------------