%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWX190+1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n011.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 : Tue May 5 06:56:45 PM UTC 2026
% Result : Theorem 89.92s 90.34s
% Output : Refutation 89.92s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWX190+1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.12 % Command : bliksem %s
% 0.15/0.33 % Computer : n011.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % DateTime : Tue May 5 09:52:02 EDT 2026
% 0.15/0.33 % CPUTime :
% 39.75/40.17 *** allocated 10000 integers for termspace/termends
% 39.75/40.17 *** allocated 10000 integers for clauses
% 39.75/40.17 *** allocated 10000 integers for justifications
% 39.75/40.17 Bliksem 1.12
% 39.75/40.17
% 39.75/40.17
% 39.75/40.17 Automatic Strategy Selection
% 39.75/40.17
% 39.75/40.17
% 39.75/40.17 Clauses:
% 39.75/40.17
% 39.75/40.17 { proj1S( s( X ) ) = X }.
% 39.75/40.17 { ! s( X ) = z }.
% 39.75/40.17 { proj1N( n( X ) ) = X }.
% 39.75/40.17 { proj1( x( X, Y ) ) = X }.
% 39.75/40.17 { proj2( x( X, Y ) ) = Y }.
% 39.75/40.17 { proj12( y( X, Y ) ) = X }.
% 39.75/40.17 { proj22( y( X, Y ) ) = Y }.
% 39.75/40.17 { ! n( X ) = x( Y, Z ) }.
% 39.75/40.17 { ! n( X ) = y( Y, Z ) }.
% 39.75/40.17 { ! n( X ) = x2 }.
% 39.75/40.17 { ! x( X, Y ) = y( Z, T ) }.
% 39.75/40.17 { ! x( X, Y ) = x2 }.
% 39.75/40.17 { ! y( X, Y ) = x2 }.
% 39.75/40.17 { ! X = Y, fail2( X, Y ) = y( n( s( s( z ) ) ), opt( X ) ) }.
% 39.75/40.17 { X = Y, X = x( proj1( X ), proj2( X ) ), fail2( X, Y ) = x( opt( X ), opt
% 39.75/40.17 ( Y ) ) }.
% 39.75/40.17 { x( Y, Z ) = X, fail2( x( Y, Z ), X ) = opt( x( Y, x( Z, X ) ) ) }.
% 39.75/40.17 { X = n( proj1N( X ) ), fail1( X, Y ) = fail2( X, Y ) }.
% 39.75/40.17 { X = n( proj1N( X ) ), fail1( n( Y ), X ) = fail2( n( Y ), X ) }.
% 39.75/40.17 { fail1( n( X ), n( Y ) ) = n( addNat( X, Y ) ) }.
% 39.75/40.17 { X = n( proj1N( X ) ), fail( Y, X ) = fail1( Y, X ) }.
% 39.75/40.17 { fail( X, n( s( Y ) ) ) = fail1( X, n( s( Y ) ) ) }.
% 39.75/40.17 { fail( X, n( z ) ) = X }.
% 39.75/40.17 { fail4( X, Y ) = y( opt( X ), opt( Y ) ) }.
% 39.75/40.17 { X = n( proj1N( X ) ), X = y( proj12( X ), proj22( X ) ), fail32( X, Y ) =
% 39.75/40.17 fail4( X, Y ) }.
% 39.75/40.17 { X = n( proj1N( X ) ), fail32( n( Y ), X ) = fail4( n( Y ), X ) }.
% 39.75/40.17 { fail32( n( X ), n( Y ) ) = n( mulNat( X, Y ) ) }.
% 39.75/40.17 { fail32( y( Y, Z ), X ) = opt( y( Y, y( Z, X ) ) ) }.
% 39.75/40.17 { X = n( proj1N( X ) ), fail22( Y, X ) = fail32( Y, X ) }.
% 39.75/40.17 { fail22( X, n( s( s( Y ) ) ) ) = fail32( X, n( s( s( Y ) ) ) ) }.
% 39.75/40.17 { fail22( X, n( s( z ) ) ) = X }.
% 39.75/40.17 { fail22( X, n( z ) ) = fail32( X, n( z ) ) }.
% 39.75/40.17 { X = n( proj1N( X ) ), fail12( X, Y ) = fail22( X, Y ) }.
% 39.75/40.17 { fail12( n( s( s( Y ) ) ), X ) = fail22( n( s( s( Y ) ) ), X ) }.
% 39.75/40.17 { fail12( n( s( z ) ), X ) = X }.
% 39.75/40.17 { fail12( n( z ), X ) = fail22( n( z ), X ) }.
% 39.75/40.17 { X = n( proj1N( X ) ), fail3( Y, X ) = fail12( Y, X ) }.
% 39.75/40.17 { fail3( X, n( s( Y ) ) ) = fail12( X, n( s( Y ) ) ) }.
% 39.75/40.17 { fail3( X, n( z ) ) = n( z ) }.
% 39.75/40.17 { d( n( X ) ) = n( z ) }.
% 39.75/40.17 { d( x( X, Y ) ) = x( d( X ), d( Y ) ) }.
% 39.75/40.17 { d( y( X, Y ) ) = x( y( d( X ), Y ), y( X, d( Y ) ) ) }.
% 39.75/40.17 { d( x2 ) = n( s( z ) ) }.
% 39.75/40.17 { addNat( s( Y ), X ) = s( addNat( Y, X ) ) }.
% 39.75/40.17 { addNat( z, X ) = X }.
% 39.75/40.17 { mulNat( s( Y ), X ) = addNat( X, mulNat( Y, X ) ) }.
% 39.75/40.17 { mulNat( z, X ) = z }.
% 39.75/40.17 { X = x( proj1( X ), proj2( X ) ), X = y( proj12( X ), proj22( X ) ), opt(
% 39.75/40.17 X ) = X }.
% 39.75/40.17 { X = n( proj1N( X ) ), opt( x( X, Y ) ) = fail( X, Y ) }.
% 39.75/40.17 { opt( x( n( s( Y ) ), X ) ) = fail( n( s( Y ) ), X ) }.
% 39.75/40.17 { opt( x( n( z ), X ) ) = X }.
% 39.75/40.17 { X = n( proj1N( X ) ), opt( y( X, Y ) ) = fail3( X, Y ) }.
% 39.75/40.17 { opt( y( n( s( Y ) ), X ) ) = fail3( n( s( Y ) ), X ) }.
% 39.75/40.17 { opt( y( n( z ), X ) ) = n( z ) }.
% 39.75/40.17 { opt( d( X ) ) = opt( d( opt( X ) ) ) }.
% 39.75/40.17
% 39.75/40.17 percentage equality = 1.000000, percentage horn = 0.759259
% 39.75/40.17 This is a pure equality problem
% 39.75/40.17
% 39.75/40.17
% 39.75/40.17
% 39.75/40.17 Options Used:
% 39.75/40.17
% 39.75/40.17 useres = 1
% 39.75/40.17 useparamod = 1
% 39.75/40.17 useeqrefl = 1
% 39.75/40.17 useeqfact = 1
% 39.75/40.17 usefactor = 1
% 39.75/40.17 usesimpsplitting = 0
% 39.75/40.17 usesimpdemod = 5
% 39.75/40.17 usesimpres = 3
% 39.75/40.17
% 39.75/40.17 resimpinuse = 1000
% 39.75/40.17 resimpclauses = 20000
% 39.75/40.17 substype = eqrewr
% 39.75/40.17 backwardsubs = 1
% 39.75/40.17 selectoldest = 5
% 39.75/40.17
% 39.75/40.17 litorderings [0] = split
% 39.75/40.17 litorderings [1] = extend the termordering, first sorting on arguments
% 39.75/40.17
% 39.75/40.17 termordering = kbo
% 39.75/40.17
% 39.75/40.17 litapriori = 0
% 39.75/40.17 termapriori = 1
% 39.75/40.17 litaposteriori = 0
% 39.75/40.17 termaposteriori = 0
% 39.75/40.17 demodaposteriori = 0
% 39.75/40.17 ordereqreflfact = 0
% 39.75/40.17
% 39.75/40.17 litselect = negord
% 39.75/40.17
% 39.75/40.17 maxweight = 15
% 39.75/40.17 maxdepth = 30000
% 39.75/40.17 maxlength = 115
% 39.75/40.17 maxnrvars = 195
% 39.75/40.17 excuselevel = 1
% 39.75/40.17 increasemaxweight = 1
% 39.75/40.17
% 39.75/40.17 maxselected = 10000000
% 39.75/40.17 maxnrclauses = 10000000
% 39.75/40.17
% 39.75/40.17 showgenerated = 0
% 39.75/40.17 showkept = 0
% 39.75/40.17 showselected = 0
% 39.75/40.17 showdeleted = 0
% 39.75/40.17 showresimp = 1
% 39.75/40.17 showstatus = 2000
% 39.75/40.17
% 39.75/40.17 prologoutput = 0
% 39.75/40.17 nrgoals = 5000000
% 39.75/40.17 totalproof = 1
% 39.75/40.17
% 39.75/40.17 Symbols occurring in the translation:
% 39.75/40.17
% 39.75/40.17 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 39.75/40.17 . [1, 2] (w:1, o:48, a:1, s:1, b:0),
% 39.75/40.17 ! [4, 1] (w:0, o:33, a:1, s:1, b:0),
% 39.75/40.17 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 39.75/40.17 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 39.75/40.17 s [36, 1] (w:1, o:38, a:1, s:1, b:0),
% 39.75/40.17 proj1S [37, 1] (w:1, o:40, a:1, s:1, b:0),
% 89.92/90.34 z [38, 0] (w:1, o:7, a:1, s:1, b:0),
% 89.92/90.34 n [39, 1] (w:1, o:41, a:1, s:1, b:0),
% 89.92/90.34 proj1N [40, 1] (w:1, o:42, a:1, s:1, b:0),
% 89.92/90.34 x [42, 2] (w:1, o:72, a:1, s:1, b:0),
% 89.92/90.34 proj1 [43, 1] (w:1, o:43, a:1, s:1, b:0),
% 89.92/90.34 proj2 [44, 1] (w:1, o:45, a:1, s:1, b:0),
% 89.92/90.34 y [45, 2] (w:1, o:73, a:1, s:1, b:0),
% 89.92/90.34 proj12 [46, 1] (w:1, o:44, a:1, s:1, b:0),
% 89.92/90.34 proj22 [47, 1] (w:1, o:46, a:1, s:1, b:0),
% 89.92/90.34 x2 [49, 0] (w:1, o:13, a:1, s:1, b:0),
% 89.92/90.34 fail2 [53, 2] (w:1, o:76, a:1, s:1, b:0),
% 89.92/90.34 opt [54, 1] (w:1, o:39, a:1, s:1, b:0),
% 89.92/90.34 fail1 [57, 2] (w:1, o:74, a:1, s:1, b:0),
% 89.92/90.34 addNat [60, 2] (w:1, o:77, a:1, s:1, b:0),
% 89.92/90.34 fail [61, 2] (w:1, o:78, a:1, s:1, b:0),
% 89.92/90.34 fail4 [64, 2] (w:1, o:82, a:1, s:1, b:0),
% 89.92/90.34 fail32 [65, 2] (w:1, o:80, a:1, s:1, b:0),
% 89.92/90.34 mulNat [68, 2] (w:1, o:83, a:1, s:1, b:0),
% 89.92/90.34 fail22 [71, 2] (w:1, o:79, a:1, s:1, b:0),
% 89.92/90.34 fail12 [73, 2] (w:1, o:75, a:1, s:1, b:0),
% 89.92/90.34 fail3 [75, 2] (w:1, o:81, a:1, s:1, b:0),
% 89.92/90.34 d [77, 1] (w:1, o:47, a:1, s:1, b:0).
% 89.92/90.34
% 89.92/90.34
% 89.92/90.34 Starting Search:
% 89.92/90.34
% 89.92/90.34 *** allocated 15000 integers for clauses
% 89.92/90.34 *** allocated 22500 integers for clauses
% 89.92/90.34 *** allocated 33750 integers for clauses
% 89.92/90.34 *** allocated 50625 integers for clauses
% 89.92/90.34 *** allocated 15000 integers for termspace/termends
% 89.92/90.34 *** allocated 75937 integers for clauses
% 89.92/90.34 *** allocated 22500 integers for termspace/termends
% 89.92/90.34 *** allocated 113905 integers for clauses
% 89.92/90.34 Resimplifying inuse:
% 89.92/90.34 Done
% 89.92/90.34
% 89.92/90.34 *** allocated 33750 integers for termspace/termends
% 89.92/90.34 *** allocated 170857 integers for clauses
% 89.92/90.34
% 89.92/90.34 Intermediate Status:
% 89.92/90.34 Generated: 73306
% 89.92/90.34 Kept: 2069
% 89.92/90.34 Inuse: 402
% 89.92/90.34 Deleted: 57
% 89.92/90.34 Deletedinuse: 18
% 89.92/90.34
% 89.92/90.34 Resimplifying inuse:
% 89.92/90.34 Done
% 89.92/90.34
% 89.92/90.34 *** allocated 50625 integers for termspace/termends
% 89.92/90.34 *** allocated 256285 integers for clauses
% 89.92/90.34 Resimplifying inuse:
% 89.92/90.34 Done
% 89.92/90.34
% 89.92/90.34 *** allocated 75937 integers for termspace/termends
% 89.92/90.34 *** allocated 384427 integers for clauses
% 89.92/90.34
% 89.92/90.34 Intermediate Status:
% 89.92/90.34 Generated: 159683
% 89.92/90.34 Kept: 4228
% 89.92/90.34 Inuse: 559
% 89.92/90.34 Deleted: 109
% 89.92/90.34 Deletedinuse: 46
% 89.92/90.34
% 89.92/90.34 Resimplifying inuse:
% 89.92/90.34 Done
% 89.92/90.34
% 89.92/90.34 *** allocated 113905 integers for termspace/termends
% 89.92/90.34 Resimplifying inuse:
% 89.92/90.34 Done
% 89.92/90.34
% 89.92/90.34
% 89.92/90.34 Intermediate Status:
% 89.92/90.34 Generated: 177910
% 89.92/90.34 Kept: 6788
% 89.92/90.34 Inuse: 601
% 89.92/90.34 Deleted: 137
% 89.92/90.34 Deletedinuse: 64
% 89.92/90.34
% 89.92/90.34 Resimplifying inuse:
% 89.92/90.34 Done
% 89.92/90.34
% 89.92/90.34 *** allocated 576640 integers for clauses
% 89.92/90.34 *** allocated 170857 integers for termspace/termends
% 89.92/90.34 Resimplifying inuse:
% 89.92/90.34 Done
% 89.92/90.34
% 89.92/90.34
% 89.92/90.34 Intermediate Status:
% 89.92/90.34 Generated: 248692
% 89.92/90.34 Kept: 8798
% 89.92/90.34 Inuse: 727
% 89.92/90.34 Deleted: 181
% 89.92/90.34 Deletedinuse: 68
% 89.92/90.34
% 89.92/90.34 Resimplifying inuse:
% 89.92/90.34 Done
% 89.92/90.34
% 89.92/90.34 Resimplifying inuse:
% 89.92/90.34 Done
% 89.92/90.34
% 89.92/90.34 *** allocated 864960 integers for clauses
% 89.92/90.34
% 89.92/90.34 Intermediate Status:
% 89.92/90.34 Generated: 288090
% 89.92/90.34 Kept: 10814
% 89.92/90.34 Inuse: 800
% 89.92/90.34 Deleted: 217
% 89.92/90.34 Deletedinuse: 80
% 89.92/90.34
% 89.92/90.34 Resimplifying inuse:
% 89.92/90.34 Done
% 89.92/90.34
% 89.92/90.34 *** allocated 256285 integers for termspace/termends
% 89.92/90.34 Resimplifying inuse:
% 89.92/90.34 Done
% 89.92/90.34
% 89.92/90.34
% 89.92/90.34 Intermediate Status:
% 89.92/90.34 Generated: 353345
% 89.92/90.34 Kept: 12879
% 89.92/90.34 Inuse: 879
% 89.92/90.34 Deleted: 231
% 89.92/90.34 Deletedinuse: 89
% 89.92/90.34
% 89.92/90.34 Resimplifying inuse:
% 89.92/90.34 Done
% 89.92/90.34
% 89.92/90.34 Resimplifying inuse:
% 89.92/90.34 Done
% 89.92/90.34
% 89.92/90.34
% 89.92/90.34 Intermediate Status:
% 89.92/90.34 Generated: 426331
% 89.92/90.34 Kept: 14882
% 89.92/90.34 Inuse: 967
% 89.92/90.34 Deleted: 269
% 89.92/90.34 Deletedinuse: 102
% 89.92/90.34
% 89.92/90.34 Resimplifying inuse:
% 89.92/90.34 Done
% 89.92/90.34
% 89.92/90.34 Resimplifying inuse:
% 89.92/90.34 Done
% 89.92/90.34
% 89.92/90.34 *** allocated 1297440 integers for clauses
% 89.92/90.34 *** allocated 384427 integers for termspace/termends
% 89.92/90.34
% 89.92/90.34 Intermediate Status:
% 89.92/90.34 Generated: 479455
% 89.92/90.34 Kept: 16907
% 89.92/90.34 Inuse: 1065
% 89.92/90.34 Deleted: 306
% 89.92/90.34 Deletedinuse: 125
% 89.92/90.34
% 89.92/90.34 Resimplifying inuse:
% 89.92/90.34 Done
% 89.92/90.34
% 89.92/90.34 Resimplifying inuse:
% 89.92/90.34 Done
% 89.92/90.34
% 89.92/90.34
% 89.92/90.34 Intermediate Status:
% 89.92/90.34 Generated: 594669
% 89.92/90.34 Kept: 18922
% 89.92/90.34 Inuse: 1196
% 89.92/90.34 Deleted: 320
% 89.92/90.34 Deletedinuse: 126
% 89.92/90.34
% 89.92/90.34 Resimplifying inuse:
% 89.92/90.34 Done
% 89.92/90.34
% 89.92/90.34 Resimplifying clauses:
% 89.92/90.34 Done
% 89.92/90.34
% 89.92/90.34 Resimplifying inuse:
% 89.92/90.34 Done
% 89.92/90.34
% 89.92/90.34
% 89.92/90.34 Intermediate Status:
% 89.92/90.34 Generated: 666745
% 89.92/90.34 Kept: 20927
% 89.92/90.34 Inuse: 1320
% 89.92/90.34 Deleted: 2090
% 89.92/90.34 Deletedinuse: 139
% 89.92/90.34
% 89.92/90.34 Resimplifying inuse:
% 89.92/90.34 Done
% 89.92/90.34
% 89.92/90.34 Resimplifying inuse:
% 89.92/90.34 Done
% 89.92/90.34
% 89.92/90.34
% 89.92/90.34 Intermediate Status:
% 89.92/90.34 Generated: 770498
% 89.92/90.34 Kept: 22950
% 89.92/90.34 Inuse: 1413
% 89.92/90.34 Deleted: 2098
% 89.92/90.34 Deletedinuse: 139
% 89.92/90.34
% 89.92/90.34 Resimplifying inuse:
% 89.92/90.34 Done
% 89.92/90.34
% 89.92/90.34 Resimplifying inuse:
% 89.92/90.34 Done
% 89.92/90.34
% 89.92/90.34 *** allocated 1946160 integers for clauses
% 89.92/90.34
% 89.92/90.34 Intermediate Status:
% 89.92/90.34 Generated: 816749
% 89.92/90.34 Kept: 24973
% 89.92/90.34 Inuse: 1480
% 89.92/90.34 Deleted: 2100
% 89.92/90.34 Deletedinuse: 140
% 89.92/90.34
% 89.92/90.34 *** allocated 576640 integers for termspace/termends
% 89.92/90.34 Resimplifying inuse:
% 89.92/90.34 Done
% 89.92/90.34
% 89.92/90.34 Resimplifying inuse:
% 89.92/90.34 Done
% 89.92/90.34
% 89.92/90.34
% 89.92/90.34 Intermediate Status:
% 89.92/90.34 Generated: 858564
% 89.92/90.34 Kept: 26982
% 89.92/90.34 Inuse: 1551
% 89.92/90.34 Deleted: 2100
% 89.92/90.34 Deletedinuse: 140
% 89.92/90.34
% 89.92/90.34 Resimplifying inuse:
% 89.92/90.34 Done
% 89.92/90.34
% 89.92/90.34 Resimplifying inuse:
% 89.92/90.34 Done
% 89.92/90.34
% 89.92/90.34
% 89.92/90.34 Intermediate Status:
% 89.92/90.34 Generated: 936156
% 89.92/90.34 Kept: 28997
% 89.92/90.34 Inuse: 1596
% 89.92/90.34 Deleted: 2106
% 89.92/90.34 Deletedinuse: 141
% 89.92/90.34
% 89.92/90.34 Resimplifying inuse:
% 89.92/90.34 Done
% 89.92/90.34
% 89.92/90.34 Resimplifying inuse:
% 89.92/90.34 Done
% 89.92/90.34
% 89.92/90.34
% 89.92/90.34 Intermediate Status:
% 89.92/90.34 Generated: 1023389
% 89.92/90.34 Kept: 31339
% 89.92/90.34 Inuse: 1711
% 89.92/90.34 Deleted: 2114
% 89.92/90.34 Deletedinuse: 141
% 89.92/90.34
% 89.92/90.34 Resimplifying inuse:
% 89.92/90.34 Done
% 89.92/90.34
% 89.92/90.34 Resimplifying inuse:
% 89.92/90.34 Done
% 89.92/90.34
% 89.92/90.34
% 89.92/90.34 Intermediate Status:
% 89.92/90.34 Generated: 1165750
% 89.92/90.34 Kept: 33400
% 89.92/90.34 Inuse: 1829
% 89.92/90.34 Deleted: 2121
% 89.92/90.34 Deletedinuse: 141
% 89.92/90.34
% 89.92/90.34 Resimplifying inuse:
% 89.92/90.34 Done
% 89.92/90.34
% 89.92/90.34 Resimplifying inuse:
% 89.92/90.34 Done
% 89.92/90.34
% 89.92/90.34
% 89.92/90.34 Intermediate Status:
% 89.92/90.34 Generated: 1321742
% 89.92/90.34 Kept: 35405
% 89.92/90.34 Inuse: 1959
% 89.92/90.34 Deleted: 2127
% 89.92/90.34 Deletedinuse: 141
% 89.92/90.34
% 89.92/90.34 Resimplifying inuse:
% 89.92/90.34 Done
% 89.92/90.34
% 89.92/90.34
% 89.92/90.34 Bliksems!, er is een bewijs:
% 89.92/90.34 % SZS status Theorem
% 89.92/90.34 % SZS output start Refutation
% 89.92/90.34
% 89.92/90.34 (7) {G0,W6,D3,L1,V3,M1} I { ! n( X ) = x( Y, Z ) }.
% 89.92/90.34 (21) {G0,W6,D4,L1,V1,M1} I { fail( X, n( z ) ) ==> X }.
% 89.92/90.34 (38) {G0,W6,D4,L1,V1,M1} I { d( n( X ) ) ==> n( z ) }.
% 89.92/90.34 (39) {G0,W10,D4,L1,V2,M1} I { x( d( X ), d( Y ) ) ==> d( x( X, Y ) ) }.
% 89.92/90.34 (41) {G0,W6,D4,L1,V0,M1} I { n( s( z ) ) ==> d( x2 ) }.
% 89.92/90.34 (48) {G0,W12,D6,L1,V2,M1} I { opt( x( n( s( Y ) ), X ) ) ==> fail( n( s( Y
% 89.92/90.34 ) ), X ) }.
% 89.92/90.34 (49) {G0,W7,D5,L1,V1,M1} I { opt( x( n( z ), X ) ) ==> X }.
% 89.92/90.34 (53) {G0,W8,D5,L1,V1,M1} I { opt( d( opt( X ) ) ) ==> opt( d( X ) ) }.
% 89.92/90.34 (56) {G1,W6,D4,L1,V0,M1} P(41,38) { d( d( x2 ) ) ==> n( z ) }.
% 89.92/90.34 (57) {G1,W6,D3,L1,V2,M1} P(41,7) { ! x( X, Y ) ==> d( x2 ) }.
% 89.92/90.34 (299) {G1,W10,D6,L1,V1,M1} P(49,53) { opt( d( x( n( z ), X ) ) ) ==> opt( d
% 89.92/90.34 ( X ) ) }.
% 89.92/90.34 (656) {G2,W11,D5,L1,V1,M1} P(56,39) { x( n( z ), d( X ) ) ==> d( x( d( x2 )
% 89.92/90.34 , X ) ) }.
% 89.92/90.34 (657) {G2,W11,D5,L1,V1,M1} P(56,39) { x( d( X ), n( z ) ) ==> d( x( X, d(
% 89.92/90.34 x2 ) ) ) }.
% 89.92/90.34 (662) {G2,W7,D4,L1,V2,M1} P(39,57) { ! d( x( X, Y ) ) ==> d( x2 ) }.
% 89.92/90.34 (664) {G3,W11,D5,L1,V2,M1} P(38,39);d(656) { d( x( d( x2 ), Y ) ) = d( x( n
% 89.92/90.34 ( X ), Y ) ) }.
% 89.92/90.34 (903) {G1,W10,D5,L1,V1,M1} P(41,48) { opt( x( d( x2 ), X ) ) ==> fail( d(
% 89.92/90.34 x2 ), X ) }.
% 89.92/90.34 (35956) {G3,W9,D6,L1,V1,M1} P(656,49) { opt( d( x( d( x2 ), X ) ) ) ==> d(
% 89.92/90.34 X ) }.
% 89.92/90.34 (36020) {G3,W9,D6,L1,V0,M1} P(657,903);d(21) { opt( d( x( x2, d( x2 ) ) ) )
% 89.92/90.34 ==> d( x2 ) }.
% 89.92/90.34 (36330) {G4,W6,D4,L1,V1,M1} P(664,299);d(35956) { opt( d( X ) ) ==> d( X )
% 89.92/90.34 }.
% 89.92/90.34 (36343) {G5,W0,D0,L0,V0,M0} P(36330,36020);r(662) { }.
% 89.92/90.34
% 89.92/90.34
% 89.92/90.34 % SZS output end Refutation
% 89.92/90.34 found a proof!
% 89.92/90.34
% 89.92/90.34
% 89.92/90.34 Unprocessed initial clauses:
% 89.92/90.34
% 89.92/90.34 (36345) {G0,W5,D4,L1,V1,M1} { proj1S( s( X ) ) = X }.
% 89.92/90.34 (36346) {G0,W4,D3,L1,V1,M1} { ! s( X ) = z }.
% 89.92/90.34 (36347) {G0,W5,D4,L1,V1,M1} { proj1N( n( X ) ) = X }.
% 89.92/90.34 (36348) {G0,W6,D4,L1,V2,M1} { proj1( x( X, Y ) ) = X }.
% 89.92/90.34 (36349) {G0,W6,D4,L1,V2,M1} { proj2( x( X, Y ) ) = Y }.
% 89.92/90.34 (36350) {G0,W6,D4,L1,V2,M1} { proj12( y( X, Y ) ) = X }.
% 89.92/90.34 (36351) {G0,W6,D4,L1,V2,M1} { proj22( y( X, Y ) ) = Y }.
% 89.92/90.34 (36352) {G0,W6,D3,L1,V3,M1} { ! n( X ) = x( Y, Z ) }.
% 89.92/90.34 (36353) {G0,W6,D3,L1,V3,M1} { ! n( X ) = y( Y, Z ) }.
% 89.92/90.34 (36354) {G0,W4,D3,L1,V1,M1} { ! n( X ) = x2 }.
% 89.92/90.34 (36355) {G0,W7,D3,L1,V4,M1} { ! x( X, Y ) = y( Z, T ) }.
% 89.92/90.34 (36356) {G0,W5,D3,L1,V2,M1} { ! x( X, Y ) = x2 }.
% 89.92/90.34 (36357) {G0,W5,D3,L1,V2,M1} { ! y( X, Y ) = x2 }.
% 89.92/90.34 (36358) {G0,W14,D6,L2,V2,M2} { ! X = Y, fail2( X, Y ) = y( n( s( s( z ) )
% 89.92/90.34 ), opt( X ) ) }.
% 89.92/90.34 (36359) {G0,W19,D4,L3,V2,M3} { X = Y, X = x( proj1( X ), proj2( X ) ),
% 89.92/90.34 fail2( X, Y ) = x( opt( X ), opt( Y ) ) }.
% 89.92/90.34 (36360) {G0,W17,D5,L2,V3,M2} { x( Y, Z ) = X, fail2( x( Y, Z ), X ) = opt
% 89.92/90.34 ( x( Y, x( Z, X ) ) ) }.
% 89.92/90.34 (36361) {G0,W12,D4,L2,V2,M2} { X = n( proj1N( X ) ), fail1( X, Y ) = fail2
% 89.92/90.34 ( X, Y ) }.
% 89.92/90.34 (36362) {G0,W14,D4,L2,V2,M2} { X = n( proj1N( X ) ), fail1( n( Y ), X ) =
% 89.92/90.34 fail2( n( Y ), X ) }.
% 89.92/90.34 (36363) {G0,W10,D4,L1,V2,M1} { fail1( n( X ), n( Y ) ) = n( addNat( X, Y )
% 89.92/90.34 ) }.
% 89.92/90.34 (36364) {G0,W12,D4,L2,V2,M2} { X = n( proj1N( X ) ), fail( Y, X ) = fail1
% 89.92/90.34 ( Y, X ) }.
% 89.92/90.34 (36365) {G0,W11,D5,L1,V2,M1} { fail( X, n( s( Y ) ) ) = fail1( X, n( s( Y
% 89.92/90.35 ) ) ) }.
% 89.92/90.35 (36366) {G0,W6,D4,L1,V1,M1} { fail( X, n( z ) ) = X }.
% 89.92/90.35 (36367) {G0,W9,D4,L1,V2,M1} { fail4( X, Y ) = y( opt( X ), opt( Y ) ) }.
% 89.92/90.35 (36368) {G0,W19,D4,L3,V2,M3} { X = n( proj1N( X ) ), X = y( proj12( X ),
% 89.92/90.35 proj22( X ) ), fail32( X, Y ) = fail4( X, Y ) }.
% 89.92/90.35 (36369) {G0,W14,D4,L2,V2,M2} { X = n( proj1N( X ) ), fail32( n( Y ), X ) =
% 89.92/90.35 fail4( n( Y ), X ) }.
% 89.92/90.35 (36370) {G0,W10,D4,L1,V2,M1} { fail32( n( X ), n( Y ) ) = n( mulNat( X, Y
% 89.92/90.35 ) ) }.
% 89.92/90.35 (36371) {G0,W12,D5,L1,V3,M1} { fail32( y( Y, Z ), X ) = opt( y( Y, y( Z, X
% 89.92/90.35 ) ) ) }.
% 89.92/90.35 (36372) {G0,W12,D4,L2,V2,M2} { X = n( proj1N( X ) ), fail22( Y, X ) =
% 89.92/90.35 fail32( Y, X ) }.
% 89.92/90.35 (36373) {G0,W13,D6,L1,V2,M1} { fail22( X, n( s( s( Y ) ) ) ) = fail32( X,
% 89.92/90.35 n( s( s( Y ) ) ) ) }.
% 89.92/90.35 (36374) {G0,W7,D5,L1,V1,M1} { fail22( X, n( s( z ) ) ) = X }.
% 89.92/90.35 (36375) {G0,W9,D4,L1,V1,M1} { fail22( X, n( z ) ) = fail32( X, n( z ) )
% 89.92/90.35 }.
% 89.92/90.35 (36376) {G0,W12,D4,L2,V2,M2} { X = n( proj1N( X ) ), fail12( X, Y ) =
% 89.92/90.35 fail22( X, Y ) }.
% 89.92/90.35 (36377) {G0,W13,D6,L1,V2,M1} { fail12( n( s( s( Y ) ) ), X ) = fail22( n(
% 89.92/90.35 s( s( Y ) ) ), X ) }.
% 89.92/90.35 (36378) {G0,W7,D5,L1,V1,M1} { fail12( n( s( z ) ), X ) = X }.
% 89.92/90.35 (36379) {G0,W9,D4,L1,V1,M1} { fail12( n( z ), X ) = fail22( n( z ), X )
% 89.92/90.35 }.
% 89.92/90.35 (36380) {G0,W12,D4,L2,V2,M2} { X = n( proj1N( X ) ), fail3( Y, X ) =
% 89.92/90.35 fail12( Y, X ) }.
% 89.92/90.35 (36381) {G0,W11,D5,L1,V2,M1} { fail3( X, n( s( Y ) ) ) = fail12( X, n( s(
% 89.92/90.35 Y ) ) ) }.
% 89.92/90.35 (36382) {G0,W7,D4,L1,V1,M1} { fail3( X, n( z ) ) = n( z ) }.
% 89.92/90.35 (36383) {G0,W6,D4,L1,V1,M1} { d( n( X ) ) = n( z ) }.
% 89.92/90.35 (36384) {G0,W10,D4,L1,V2,M1} { d( x( X, Y ) ) = x( d( X ), d( Y ) ) }.
% 89.92/90.35 (36385) {G0,W14,D5,L1,V2,M1} { d( y( X, Y ) ) = x( y( d( X ), Y ), y( X, d
% 89.92/90.35 ( Y ) ) ) }.
% 89.92/90.35 (36386) {G0,W6,D4,L1,V0,M1} { d( x2 ) = n( s( z ) ) }.
% 89.92/90.35 (36387) {G0,W9,D4,L1,V2,M1} { addNat( s( Y ), X ) = s( addNat( Y, X ) )
% 89.92/90.35 }.
% 89.92/90.35 (36388) {G0,W5,D3,L1,V1,M1} { addNat( z, X ) = X }.
% 89.92/90.35 (36389) {G0,W10,D4,L1,V2,M1} { mulNat( s( Y ), X ) = addNat( X, mulNat( Y
% 89.92/90.35 , X ) ) }.
% 89.92/90.35 (36390) {G0,W5,D3,L1,V1,M1} { mulNat( z, X ) = z }.
% 89.92/90.35 (36391) {G0,W18,D4,L3,V1,M3} { X = x( proj1( X ), proj2( X ) ), X = y(
% 89.92/90.35 proj12( X ), proj22( X ) ), opt( X ) = X }.
% 89.92/90.35 (36392) {G0,W13,D4,L2,V2,M2} { X = n( proj1N( X ) ), opt( x( X, Y ) ) =
% 89.92/90.35 fail( X, Y ) }.
% 89.92/90.35 (36393) {G0,W12,D6,L1,V2,M1} { opt( x( n( s( Y ) ), X ) ) = fail( n( s( Y
% 89.92/90.35 ) ), X ) }.
% 89.92/90.35 (36394) {G0,W7,D5,L1,V1,M1} { opt( x( n( z ), X ) ) = X }.
% 89.92/90.35 (36395) {G0,W13,D4,L2,V2,M2} { X = n( proj1N( X ) ), opt( y( X, Y ) ) =
% 89.92/90.35 fail3( X, Y ) }.
% 89.92/90.35 (36396) {G0,W12,D6,L1,V2,M1} { opt( y( n( s( Y ) ), X ) ) = fail3( n( s( Y
% 89.92/90.35 ) ), X ) }.
% 89.92/90.35 (36397) {G0,W8,D5,L1,V1,M1} { opt( y( n( z ), X ) ) = n( z ) }.
% 89.92/90.35 (36398) {G0,W8,D5,L1,V1,M1} { opt( d( X ) ) = opt( d( opt( X ) ) ) }.
% 89.92/90.35
% 89.92/90.35
% 89.92/90.35 Total Proof:
% 89.92/90.35
% 89.92/90.35 subsumption: (7) {G0,W6,D3,L1,V3,M1} I { ! n( X ) = x( Y, Z ) }.
% 89.92/90.35 parent0: (36352) {G0,W6,D3,L1,V3,M1} { ! n( X ) = x( Y, Z ) }.
% 89.92/90.35 substitution0:
% 89.92/90.35 X := X
% 89.92/90.35 Y := Y
% 89.92/90.35 Z := Z
% 89.92/90.35 end
% 89.92/90.35 permutation0:
% 89.92/90.35 0 ==> 0
% 89.92/90.35 end
% 89.92/90.35
% 89.92/90.35 subsumption: (21) {G0,W6,D4,L1,V1,M1} I { fail( X, n( z ) ) ==> X }.
% 89.92/90.35 parent0: (36366) {G0,W6,D4,L1,V1,M1} { fail( X, n( z ) ) = X }.
% 89.92/90.35 substitution0:
% 89.92/90.35 X := X
% 89.92/90.35 end
% 89.92/90.35 permutation0:
% 89.92/90.35 0 ==> 0
% 89.92/90.35 end
% 89.92/90.35
% 89.92/90.35 subsumption: (38) {G0,W6,D4,L1,V1,M1} I { d( n( X ) ) ==> n( z ) }.
% 89.92/90.35 parent0: (36383) {G0,W6,D4,L1,V1,M1} { d( n( X ) ) = n( z ) }.
% 89.92/90.35 substitution0:
% 89.92/90.35 X := X
% 89.92/90.35 end
% 89.92/90.35 permutation0:
% 89.92/90.35 0 ==> 0
% 89.92/90.35 end
% 89.92/90.35
% 89.92/90.35 eqswap: (36595) {G0,W10,D4,L1,V2,M1} { x( d( X ), d( Y ) ) = d( x( X, Y )
% 89.92/90.35 ) }.
% 89.92/90.35 parent0[0]: (36384) {G0,W10,D4,L1,V2,M1} { d( x( X, Y ) ) = x( d( X ), d(
% 89.92/90.35 Y ) ) }.
% 89.92/90.35 substitution0:
% 89.92/90.35 X := X
% 89.92/90.35 Y := Y
% 89.92/90.35 end
% 89.92/90.35
% 89.92/90.35 subsumption: (39) {G0,W10,D4,L1,V2,M1} I { x( d( X ), d( Y ) ) ==> d( x( X
% 89.92/90.35 , Y ) ) }.
% 89.92/90.35 parent0: (36595) {G0,W10,D4,L1,V2,M1} { x( d( X ), d( Y ) ) = d( x( X, Y )
% 89.92/90.35 ) }.
% 89.92/90.35 substitution0:
% 89.92/90.35 X := X
% 89.92/90.35 Y := Y
% 89.92/90.35 end
% 89.92/90.35 permutation0:
% 89.92/90.35 0 ==> 0
% 89.92/90.35 end
% 89.92/90.35
% 89.92/90.35 eqswap: (36671) {G0,W6,D4,L1,V0,M1} { n( s( z ) ) = d( x2 ) }.
% 89.92/90.35 parent0[0]: (36386) {G0,W6,D4,L1,V0,M1} { d( x2 ) = n( s( z ) ) }.
% 89.92/90.35 substitution0:
% 89.92/90.35 end
% 89.92/90.35
% 89.92/90.35 subsumption: (41) {G0,W6,D4,L1,V0,M1} I { n( s( z ) ) ==> d( x2 ) }.
% 89.92/90.35 parent0: (36671) {G0,W6,D4,L1,V0,M1} { n( s( z ) ) = d( x2 ) }.
% 89.92/90.35 substitution0:
% 89.92/90.35 end
% 89.92/90.35 permutation0:
% 89.92/90.35 0 ==> 0
% 89.92/90.35 end
% 89.92/90.35
% 89.92/90.35 subsumption: (48) {G0,W12,D6,L1,V2,M1} I { opt( x( n( s( Y ) ), X ) ) ==>
% 89.92/90.35 fail( n( s( Y ) ), X ) }.
% 89.92/90.35 parent0: (36393) {G0,W12,D6,L1,V2,M1} { opt( x( n( s( Y ) ), X ) ) = fail
% 89.92/90.35 ( n( s( Y ) ), X ) }.
% 89.92/90.35 substitution0:
% 89.92/90.35 X := X
% 89.92/90.35 Y := Y
% 89.92/90.35 end
% 89.92/90.35 permutation0:
% 89.92/90.35 0 ==> 0
% 89.92/90.35 end
% 89.92/90.35
% 89.92/90.35 subsumption: (49) {G0,W7,D5,L1,V1,M1} I { opt( x( n( z ), X ) ) ==> X }.
% 89.92/90.35 parent0: (36394) {G0,W7,D5,L1,V1,M1} { opt( x( n( z ), X ) ) = X }.
% 89.92/90.35 substitution0:
% 89.92/90.35 X := X
% 89.92/90.35 end
% 89.92/90.35 permutation0:
% 89.92/90.35 0 ==> 0
% 89.92/90.35 end
% 89.92/90.35
% 89.92/90.35 eqswap: (36952) {G0,W8,D5,L1,V1,M1} { opt( d( opt( X ) ) ) = opt( d( X ) )
% 89.92/90.35 }.
% 89.92/90.35 parent0[0]: (36398) {G0,W8,D5,L1,V1,M1} { opt( d( X ) ) = opt( d( opt( X )
% 89.92/90.35 ) ) }.
% 89.92/90.35 substitution0:
% 89.92/90.35 X := X
% 89.92/90.35 end
% 89.92/90.35
% 89.92/90.35 subsumption: (53) {G0,W8,D5,L1,V1,M1} I { opt( d( opt( X ) ) ) ==> opt( d(
% 89.92/90.35 X ) ) }.
% 89.92/90.35 parent0: (36952) {G0,W8,D5,L1,V1,M1} { opt( d( opt( X ) ) ) = opt( d( X )
% 89.92/90.35 ) }.
% 89.92/90.35 substitution0:
% 89.92/90.35 X := X
% 89.92/90.35 end
% 89.92/90.35 permutation0:
% 89.92/90.35 0 ==> 0
% 89.92/90.35 end
% 89.92/90.35
% 89.92/90.35 eqswap: (36954) {G0,W6,D4,L1,V1,M1} { n( z ) ==> d( n( X ) ) }.
% 89.92/90.35 parent0[0]: (38) {G0,W6,D4,L1,V1,M1} I { d( n( X ) ) ==> n( z ) }.
% 89.92/90.35 substitution0:
% 89.92/90.35 X := X
% 89.92/90.35 end
% 89.92/90.35
% 89.92/90.35 paramod: (36955) {G1,W6,D4,L1,V0,M1} { n( z ) ==> d( d( x2 ) ) }.
% 89.92/90.35 parent0[0]: (41) {G0,W6,D4,L1,V0,M1} I { n( s( z ) ) ==> d( x2 ) }.
% 89.92/90.35 parent1[0; 4]: (36954) {G0,W6,D4,L1,V1,M1} { n( z ) ==> d( n( X ) ) }.
% 89.92/90.35 substitution0:
% 89.92/90.35 end
% 89.92/90.35 substitution1:
% 89.92/90.35 X := s( z )
% 89.92/90.35 end
% 89.92/90.35
% 89.92/90.35 eqswap: (36956) {G1,W6,D4,L1,V0,M1} { d( d( x2 ) ) ==> n( z ) }.
% 89.92/90.35 parent0[0]: (36955) {G1,W6,D4,L1,V0,M1} { n( z ) ==> d( d( x2 ) ) }.
% 89.92/90.35 substitution0:
% 89.92/90.35 end
% 89.92/90.35
% 89.92/90.35 subsumption: (56) {G1,W6,D4,L1,V0,M1} P(41,38) { d( d( x2 ) ) ==> n( z )
% 89.92/90.35 }.
% 89.92/90.35 parent0: (36956) {G1,W6,D4,L1,V0,M1} { d( d( x2 ) ) ==> n( z ) }.
% 89.92/90.35 substitution0:
% 89.92/90.35 end
% 89.92/90.35 permutation0:
% 89.92/90.35 0 ==> 0
% 89.92/90.35 end
% 89.92/90.35
% 89.92/90.35 eqswap: (36958) {G0,W6,D3,L1,V3,M1} { ! x( Y, Z ) = n( X ) }.
% 89.92/90.35 parent0[0]: (7) {G0,W6,D3,L1,V3,M1} I { ! n( X ) = x( Y, Z ) }.
% 89.92/90.35 substitution0:
% 89.92/90.35 X := X
% 89.92/90.35 Y := Y
% 89.92/90.35 Z := Z
% 89.92/90.35 end
% 89.92/90.35
% 89.92/90.35 paramod: (36959) {G1,W6,D3,L1,V2,M1} { ! x( X, Y ) = d( x2 ) }.
% 89.92/90.35 parent0[0]: (41) {G0,W6,D4,L1,V0,M1} I { n( s( z ) ) ==> d( x2 ) }.
% 89.92/90.35 parent1[0; 5]: (36958) {G0,W6,D3,L1,V3,M1} { ! x( Y, Z ) = n( X ) }.
% 89.92/90.35 substitution0:
% 89.92/90.35 end
% 89.92/90.35 substitution1:
% 89.92/90.35 X := s( z )
% 89.92/90.35 Y := X
% 89.92/90.35 Z := Y
% 89.92/90.35 end
% 89.92/90.35
% 89.92/90.35 subsumption: (57) {G1,W6,D3,L1,V2,M1} P(41,7) { ! x( X, Y ) ==> d( x2 ) }.
% 89.92/90.35 parent0: (36959) {G1,W6,D3,L1,V2,M1} { ! x( X, Y ) = d( x2 ) }.
% 89.92/90.35 substitution0:
% 89.92/90.35 X := X
% 89.92/90.35 Y := Y
% 89.92/90.35 end
% 89.92/90.35 permutation0:
% 89.92/90.35 0 ==> 0
% 89.92/90.35 end
% 89.92/90.35
% 89.92/90.35 eqswap: (36962) {G0,W8,D5,L1,V1,M1} { opt( d( X ) ) ==> opt( d( opt( X ) )
% 89.92/90.35 ) }.
% 89.92/90.35 parent0[0]: (53) {G0,W8,D5,L1,V1,M1} I { opt( d( opt( X ) ) ) ==> opt( d( X
% 89.92/90.35 ) ) }.
% 89.92/90.35 substitution0:
% 89.92/90.35 X := X
% 89.92/90.35 end
% 89.92/90.35
% 89.92/90.35 paramod: (36963) {G1,W10,D6,L1,V1,M1} { opt( d( x( n( z ), X ) ) ) ==> opt
% 89.92/90.35 ( d( X ) ) }.
% 89.92/90.35 parent0[0]: (49) {G0,W7,D5,L1,V1,M1} I { opt( x( n( z ), X ) ) ==> X }.
% 89.92/90.35 parent1[0; 9]: (36962) {G0,W8,D5,L1,V1,M1} { opt( d( X ) ) ==> opt( d( opt
% 89.92/90.35 ( X ) ) ) }.
% 89.92/90.35 substitution0:
% 89.92/90.35 X := X
% 89.92/90.35 end
% 89.92/90.35 substitution1:
% 89.92/90.35 X := x( n( z ), X )
% 89.92/90.35 end
% 89.92/90.35
% 89.92/90.35 subsumption: (299) {G1,W10,D6,L1,V1,M1} P(49,53) { opt( d( x( n( z ), X ) )
% 89.92/90.35 ) ==> opt( d( X ) ) }.
% 89.92/90.35 parent0: (36963) {G1,W10,D6,L1,V1,M1} { opt( d( x( n( z ), X ) ) ) ==> opt
% 89.92/90.35 ( d( X ) ) }.
% 89.92/90.35 substitution0:
% 89.92/90.35 X := X
% 89.92/90.35 end
% 89.92/90.35 permutation0:
% 89.92/90.35 0 ==> 0
% 89.92/90.35 end
% 89.92/90.35
% 89.92/90.35 eqswap: (36966) {G0,W10,D4,L1,V2,M1} { d( x( X, Y ) ) ==> x( d( X ), d( Y
% 89.92/90.35 ) ) }.
% 89.92/90.35 parent0[0]: (39) {G0,W10,D4,L1,V2,M1} I { x( d( X ), d( Y ) ) ==> d( x( X,
% 89.92/90.35 Y ) ) }.
% 89.92/90.35 substitution0:
% 89.92/90.35 X := X
% 89.92/90.35 Y := Y
% 89.92/90.35 end
% 89.92/90.35
% 89.92/90.35 paramod: (36967) {G1,W11,D5,L1,V1,M1} { d( x( d( x2 ), X ) ) ==> x( n( z )
% 89.92/90.35 , d( X ) ) }.
% 89.92/90.35 parent0[0]: (56) {G1,W6,D4,L1,V0,M1} P(41,38) { d( d( x2 ) ) ==> n( z ) }.
% 89.92/90.35 parent1[0; 7]: (36966) {G0,W10,D4,L1,V2,M1} { d( x( X, Y ) ) ==> x( d( X )
% 89.92/90.35 , d( Y ) ) }.
% 89.92/90.35 substitution0:
% 89.92/90.35 end
% 89.92/90.35 substitution1:
% 89.92/90.35 X := d( x2 )
% 89.92/90.35 Y := X
% 89.92/90.35 end
% 89.92/90.35
% 89.92/90.35 eqswap: (36969) {G1,W11,D5,L1,V1,M1} { x( n( z ), d( X ) ) ==> d( x( d( x2
% 89.92/90.35 ), X ) ) }.
% 89.92/90.35 parent0[0]: (36967) {G1,W11,D5,L1,V1,M1} { d( x( d( x2 ), X ) ) ==> x( n(
% 89.92/90.35 z ), d( X ) ) }.
% 89.92/90.35 substitution0:
% 89.92/90.35 X := X
% 89.92/90.35 end
% 89.92/90.35
% 89.92/90.35 subsumption: (656) {G2,W11,D5,L1,V1,M1} P(56,39) { x( n( z ), d( X ) ) ==>
% 89.92/90.35 d( x( d( x2 ), X ) ) }.
% 89.92/90.35 parent0: (36969) {G1,W11,D5,L1,V1,M1} { x( n( z ), d( X ) ) ==> d( x( d(
% 89.92/90.35 x2 ), X ) ) }.
% 89.92/90.35 substitution0:
% 89.92/90.35 X := X
% 89.92/90.35 end
% 89.92/90.35 permutation0:
% 89.92/90.35 0 ==> 0
% 89.92/90.35 end
% 89.92/90.35
% 89.92/90.35 eqswap: (36972) {G0,W10,D4,L1,V2,M1} { d( x( X, Y ) ) ==> x( d( X ), d( Y
% 89.92/90.35 ) ) }.
% 89.92/90.35 parent0[0]: (39) {G0,W10,D4,L1,V2,M1} I { x( d( X ), d( Y ) ) ==> d( x( X,
% 89.92/90.35 Y ) ) }.
% 89.92/90.35 substitution0:
% 89.92/90.35 X := X
% 89.92/90.35 Y := Y
% 89.92/90.35 end
% 89.92/90.35
% 89.92/90.35 paramod: (36974) {G1,W11,D5,L1,V1,M1} { d( x( X, d( x2 ) ) ) ==> x( d( X )
% 89.92/90.35 , n( z ) ) }.
% 89.92/90.35 parent0[0]: (56) {G1,W6,D4,L1,V0,M1} P(41,38) { d( d( x2 ) ) ==> n( z ) }.
% 89.92/90.35 parent1[0; 9]: (36972) {G0,W10,D4,L1,V2,M1} { d( x( X, Y ) ) ==> x( d( X )
% 89.92/90.35 , d( Y ) ) }.
% 89.92/90.35 substitution0:
% 89.92/90.35 end
% 89.92/90.35 substitution1:
% 89.92/90.35 X := X
% 89.92/90.35 Y := d( x2 )
% 89.92/90.35 end
% 89.92/90.35
% 89.92/90.35 eqswap: (36976) {G1,W11,D5,L1,V1,M1} { x( d( X ), n( z ) ) ==> d( x( X, d
% 89.92/90.35 ( x2 ) ) ) }.
% 89.92/90.35 parent0[0]: (36974) {G1,W11,D5,L1,V1,M1} { d( x( X, d( x2 ) ) ) ==> x( d(
% 89.92/90.35 X ), n( z ) ) }.
% 89.92/90.35 substitution0:
% 89.92/90.35 X := X
% 89.92/90.35 end
% 89.92/90.35
% 89.92/90.35 subsumption: (657) {G2,W11,D5,L1,V1,M1} P(56,39) { x( d( X ), n( z ) ) ==>
% 89.92/90.35 d( x( X, d( x2 ) ) ) }.
% 89.92/90.35 parent0: (36976) {G1,W11,D5,L1,V1,M1} { x( d( X ), n( z ) ) ==> d( x( X, d
% 89.92/90.35 ( x2 ) ) ) }.
% 89.92/90.35 substitution0:
% 89.92/90.35 X := X
% 89.92/90.35 end
% 89.92/90.35 permutation0:
% 89.92/90.35 0 ==> 0
% 89.92/90.35 end
% 89.92/90.35
% 89.92/90.35 eqswap: (36978) {G1,W6,D3,L1,V2,M1} { ! d( x2 ) ==> x( X, Y ) }.
% 89.92/90.35 parent0[0]: (57) {G1,W6,D3,L1,V2,M1} P(41,7) { ! x( X, Y ) ==> d( x2 ) }.
% 89.92/90.35 substitution0:
% 89.92/90.35 X := X
% 89.92/90.35 Y := Y
% 89.92/90.35 end
% 89.92/90.35
% 89.92/90.35 paramod: (36979) {G1,W7,D4,L1,V2,M1} { ! d( x2 ) ==> d( x( X, Y ) ) }.
% 89.92/90.35 parent0[0]: (39) {G0,W10,D4,L1,V2,M1} I { x( d( X ), d( Y ) ) ==> d( x( X,
% 89.92/90.35 Y ) ) }.
% 89.92/90.35 parent1[0; 4]: (36978) {G1,W6,D3,L1,V2,M1} { ! d( x2 ) ==> x( X, Y ) }.
% 89.92/90.35 substitution0:
% 89.92/90.35 X := X
% 89.92/90.35 Y := Y
% 89.92/90.35 end
% 89.92/90.35 substitution1:
% 89.92/90.35 X := d( X )
% 89.92/90.35 Y := d( Y )
% 89.92/90.35 end
% 89.92/90.35
% 89.92/90.35 eqswap: (36980) {G1,W7,D4,L1,V2,M1} { ! d( x( X, Y ) ) ==> d( x2 ) }.
% 89.92/90.35 parent0[0]: (36979) {G1,W7,D4,L1,V2,M1} { ! d( x2 ) ==> d( x( X, Y ) ) }.
% 89.92/90.35 substitution0:
% 89.92/90.35 X := X
% 89.92/90.35 Y := Y
% 89.92/90.35 end
% 89.92/90.35
% 89.92/90.35 subsumption: (662) {G2,W7,D4,L1,V2,M1} P(39,57) { ! d( x( X, Y ) ) ==> d(
% 89.92/90.35 x2 ) }.
% 89.92/90.35 parent0: (36980) {G1,W7,D4,L1,V2,M1} { ! d( x( X, Y ) ) ==> d( x2 ) }.
% 89.92/90.35 substitution0:
% 89.92/90.35 X := X
% 89.92/90.35 Y := Y
% 89.92/90.35 end
% 89.92/90.35 permutation0:
% 89.92/90.35 0 ==> 0
% 89.92/90.35 end
% 89.92/90.35
% 89.92/90.35 eqswap: (36982) {G0,W10,D4,L1,V2,M1} { d( x( X, Y ) ) ==> x( d( X ), d( Y
% 89.92/90.35 ) ) }.
% 89.92/90.35 parent0[0]: (39) {G0,W10,D4,L1,V2,M1} I { x( d( X ), d( Y ) ) ==> d( x( X,
% 89.92/90.35 Y ) ) }.
% 89.92/90.35 substitution0:
% 89.92/90.35 X := X
% 89.92/90.35 Y := Y
% 89.92/90.35 end
% 89.92/90.35
% 89.92/90.35 paramod: (36984) {G1,W11,D5,L1,V2,M1} { d( x( n( X ), Y ) ) ==> x( n( z )
% 89.92/90.35 , d( Y ) ) }.
% 89.92/90.35 parent0[0]: (38) {G0,W6,D4,L1,V1,M1} I { d( n( X ) ) ==> n( z ) }.
% 89.92/90.35 parent1[0; 7]: (36982) {G0,W10,D4,L1,V2,M1} { d( x( X, Y ) ) ==> x( d( X )
% 89.92/90.35 , d( Y ) ) }.
% 89.92/90.35 substitution0:
% 89.92/90.35 X := X
% 89.92/90.35 end
% 89.92/90.35 substitution1:
% 89.92/90.35 X := n( X )
% 89.92/90.35 Y := Y
% 89.92/90.35 end
% 89.92/90.35
% 89.92/90.35 paramod: (36986) {G2,W11,D5,L1,V2,M1} { d( x( n( X ), Y ) ) ==> d( x( d(
% 89.92/90.35 x2 ), Y ) ) }.
% 89.92/90.35 parent0[0]: (656) {G2,W11,D5,L1,V1,M1} P(56,39) { x( n( z ), d( X ) ) ==> d
% 89.92/90.35 ( x( d( x2 ), X ) ) }.
% 89.92/90.35 parent1[0; 6]: (36984) {G1,W11,D5,L1,V2,M1} { d( x( n( X ), Y ) ) ==> x( n
% 89.92/90.35 ( z ), d( Y ) ) }.
% 89.92/90.35 substitution0:
% 89.92/90.35 X := Y
% 89.92/90.35 end
% 89.92/90.35 substitution1:
% 89.92/90.35 X := X
% 89.92/90.35 Y := Y
% 89.92/90.35 end
% 89.92/90.35
% 89.92/90.35 eqswap: (36987) {G2,W11,D5,L1,V2,M1} { d( x( d( x2 ), Y ) ) ==> d( x( n( X
% 89.92/90.35 ), Y ) ) }.
% 89.92/90.35 parent0[0]: (36986) {G2,W11,D5,L1,V2,M1} { d( x( n( X ), Y ) ) ==> d( x( d
% 89.92/90.35 ( x2 ), Y ) ) }.
% 89.92/90.35 substitution0:
% 89.92/90.35 X := X
% 89.92/90.35 Y := Y
% 89.92/90.35 end
% 89.92/90.35
% 89.92/90.35 subsumption: (664) {G3,W11,D5,L1,V2,M1} P(38,39);d(656) { d( x( d( x2 ), Y
% 89.92/90.35 ) ) = d( x( n( X ), Y ) ) }.
% 89.92/90.35 parent0: (36987) {G2,W11,D5,L1,V2,M1} { d( x( d( x2 ), Y ) ) ==> d( x( n(
% 89.92/90.35 X ), Y ) ) }.
% 89.92/90.35 substitution0:
% 89.92/90.35 X := X
% 89.92/90.35 Y := Y
% 89.92/90.35 end
% 89.92/90.35 permutation0:
% 89.92/90.35 0 ==> 0
% 89.92/90.35 end
% 89.92/90.35
% 89.92/90.35 eqswap: (36989) {G0,W12,D6,L1,V2,M1} { fail( n( s( X ) ), Y ) ==> opt( x(
% 89.92/90.35 n( s( X ) ), Y ) ) }.
% 89.92/90.35 parent0[0]: (48) {G0,W12,D6,L1,V2,M1} I { opt( x( n( s( Y ) ), X ) ) ==>
% 89.92/90.35 fail( n( s( Y ) ), X ) }.
% 89.92/90.35 substitution0:
% 89.92/90.35 X := Y
% 89.92/90.35 Y := X
% 89.92/90.35 end
% 89.92/90.35
% 89.92/90.35 paramod: (36991) {G1,W11,D5,L1,V1,M1} { fail( n( s( z ) ), X ) ==> opt( x
% 89.92/90.35 ( d( x2 ), X ) ) }.
% 89.92/90.35 parent0[0]: (41) {G0,W6,D4,L1,V0,M1} I { n( s( z ) ) ==> d( x2 ) }.
% 89.92/90.35 parent1[0; 8]: (36989) {G0,W12,D6,L1,V2,M1} { fail( n( s( X ) ), Y ) ==>
% 89.92/90.35 opt( x( n( s( X ) ), Y ) ) }.
% 89.92/90.35 substitution0:
% 89.92/90.35 end
% 89.92/90.35 substitution1:
% 89.92/90.35 X := z
% 89.92/90.35 Y := X
% 89.92/90.35 end
% 89.92/90.35
% 89.92/90.35 paramod: (36992) {G1,W10,D5,L1,V1,M1} { fail( d( x2 ), X ) ==> opt( x( d(
% 89.92/90.35 x2 ), X ) ) }.
% 89.92/90.35 parent0[0]: (41) {G0,W6,D4,L1,V0,M1} I { n( s( z ) ) ==> d( x2 ) }.
% 89.92/90.35 parent1[0; 2]: (36991) {G1,W11,D5,L1,V1,M1} { fail( n( s( z ) ), X ) ==>
% 89.92/90.35 opt( x( d( x2 ), X ) ) }.
% 89.92/90.35 substitution0:
% 89.92/90.35 end
% 89.92/90.35 substitution1:
% 89.92/90.35 X := X
% 89.92/90.35 end
% 89.92/90.35
% 89.92/90.35 eqswap: (36994) {G1,W10,D5,L1,V1,M1} { opt( x( d( x2 ), X ) ) ==> fail( d
% 89.92/90.35 ( x2 ), X ) }.
% 89.92/90.35 parent0[0]: (36992) {G1,W10,D5,L1,V1,M1} { fail( d( x2 ), X ) ==> opt( x(
% 89.92/90.35 d( x2 ), X ) ) }.
% 89.92/90.35 substitution0:
% 89.92/90.35 X := X
% 89.92/90.35 end
% 89.92/90.35
% 89.92/90.35 subsumption: (903) {G1,W10,D5,L1,V1,M1} P(41,48) { opt( x( d( x2 ), X ) )
% 89.92/90.35 ==> fail( d( x2 ), X ) }.
% 89.92/90.35 parent0: (36994) {G1,W10,D5,L1,V1,M1} { opt( x( d( x2 ), X ) ) ==> fail( d
% 89.92/90.35 ( x2 ), X ) }.
% 89.92/90.35 substitution0:
% 89.92/90.35 X := X
% 89.92/90.35 end
% 89.92/90.35 permutation0:
% 89.92/90.35 0 ==> 0
% 89.92/90.35 end
% 89.92/90.35
% 89.92/90.35 eqswap: (36997) {G0,W7,D5,L1,V1,M1} { X ==> opt( x( n( z ), X ) ) }.
% 89.92/90.35 parent0[0]: (49) {G0,W7,D5,L1,V1,M1} I { opt( x( n( z ), X ) ) ==> X }.
% 89.92/90.35 substitution0:
% 89.92/90.35 X := X
% 89.92/90.35 end
% 89.92/90.35
% 89.92/90.35 paramod: (36998) {G1,W9,D6,L1,V1,M1} { d( X ) ==> opt( d( x( d( x2 ), X )
% 89.92/90.35 ) ) }.
% 89.92/90.35 parent0[0]: (656) {G2,W11,D5,L1,V1,M1} P(56,39) { x( n( z ), d( X ) ) ==> d
% 89.92/90.35 ( x( d( x2 ), X ) ) }.
% 89.92/90.35 parent1[0; 4]: (36997) {G0,W7,D5,L1,V1,M1} { X ==> opt( x( n( z ), X ) )
% 89.92/90.35 }.
% 89.92/90.35 substitution0:
% 89.92/90.35 X := X
% 89.92/90.35 end
% 89.92/90.35 substitution1:
% 89.92/90.35 X := d( X )
% 89.92/90.35 end
% 89.92/90.35
% 89.92/90.35 eqswap: (36999) {G1,W9,D6,L1,V1,M1} { opt( d( x( d( x2 ), X ) ) ) ==> d( X
% 89.92/90.35 ) }.
% 89.92/90.35 parent0[0]: (36998) {G1,W9,D6,L1,V1,M1} { d( X ) ==> opt( d( x( d( x2 ), X
% 89.92/90.35 ) ) ) }.
% 89.92/90.35 substitution0:
% 89.92/90.35 X := X
% 89.92/90.35 end
% 89.92/90.35
% 89.92/90.35 subsumption: (35956) {G3,W9,D6,L1,V1,M1} P(656,49) { opt( d( x( d( x2 ), X
% 89.92/90.35 ) ) ) ==> d( X ) }.
% 89.92/90.35 parent0: (36999) {G1,W9,D6,L1,V1,M1} { opt( d( x( d( x2 ), X ) ) ) ==> d(
% 89.92/90.35 X ) }.
% 89.92/90.35 substitution0:
% 89.92/90.35 X := X
% 89.92/90.35 end
% 89.92/90.35 permutation0:
% 89.92/90.35 0 ==> 0
% 89.92/90.35 end
% 89.92/90.35
% 89.92/90.35 eqswap: (37001) {G1,W10,D5,L1,V1,M1} { fail( d( x2 ), X ) ==> opt( x( d(
% 89.92/90.35 x2 ), X ) ) }.
% 89.92/90.35 parent0[0]: (903) {G1,W10,D5,L1,V1,M1} P(41,48) { opt( x( d( x2 ), X ) )
% 89.92/90.35 ==> fail( d( x2 ), X ) }.
% 89.92/90.35 substitution0:
% 89.92/90.35 X := X
% 89.92/90.35 end
% 89.92/90.35
% 89.92/90.35 paramod: (37003) {G2,W12,D6,L1,V0,M1} { fail( d( x2 ), n( z ) ) ==> opt( d
% 89.92/90.35 ( x( x2, d( x2 ) ) ) ) }.
% 89.92/90.35 parent0[0]: (657) {G2,W11,D5,L1,V1,M1} P(56,39) { x( d( X ), n( z ) ) ==> d
% 89.92/90.35 ( x( X, d( x2 ) ) ) }.
% 89.92/90.35 parent1[0; 7]: (37001) {G1,W10,D5,L1,V1,M1} { fail( d( x2 ), X ) ==> opt(
% 89.92/90.35 x( d( x2 ), X ) ) }.
% 89.92/90.35 substitution0:
% 89.92/90.35 X := x2
% 89.92/90.35 end
% 89.92/90.35 substitution1:
% 89.92/90.35 X := n( z )
% 89.92/90.35 end
% 89.92/90.35
% 89.92/90.35 paramod: (37004) {G1,W9,D6,L1,V0,M1} { d( x2 ) ==> opt( d( x( x2, d( x2 )
% 89.92/90.35 ) ) ) }.
% 89.92/90.35 parent0[0]: (21) {G0,W6,D4,L1,V1,M1} I { fail( X, n( z ) ) ==> X }.
% 89.92/90.35 parent1[0; 1]: (37003) {G2,W12,D6,L1,V0,M1} { fail( d( x2 ), n( z ) ) ==>
% 89.92/90.35 opt( d( x( x2, d( x2 ) ) ) ) }.
% 89.92/90.35 substitution0:
% 89.92/90.35 X := d( x2 )
% 89.92/90.35 end
% 89.92/90.35 substitution1:
% 89.92/90.35 end
% 89.92/90.35
% 89.92/90.35 eqswap: (37005) {G1,W9,D6,L1,V0,M1} { opt( d( x( x2, d( x2 ) ) ) ) ==> d(
% 89.92/90.35 x2 ) }.
% 89.92/90.35 parent0[0]: (37004) {G1,W9,D6,L1,V0,M1} { d( x2 ) ==> opt( d( x( x2, d( x2
% 89.92/90.35 ) ) ) ) }.
% 89.92/90.35 substitution0:
% 89.92/90.35 end
% 89.92/90.35
% 89.92/90.35 subsumption: (36020) {G3,W9,D6,L1,V0,M1} P(657,903);d(21) { opt( d( x( x2,
% 89.92/90.35 d( x2 ) ) ) ) ==> d( x2 ) }.
% 89.92/90.35 parent0: (37005) {G1,W9,D6,L1,V0,M1} { opt( d( x( x2, d( x2 ) ) ) ) ==> d
% 89.92/90.35 ( x2 ) }.
% 89.92/90.35 substitution0:
% 89.92/90.35 end
% 89.92/90.35 permutation0:
% 89.92/90.35 0 ==> 0
% 89.92/90.35 end
% 89.92/90.35
% 89.92/90.35 eqswap: (37006) {G3,W11,D5,L1,V2,M1} { d( x( n( Y ), X ) ) = d( x( d( x2 )
% 89.92/90.35 , X ) ) }.
% 89.92/90.35 parent0[0]: (664) {G3,W11,D5,L1,V2,M1} P(38,39);d(656) { d( x( d( x2 ), Y )
% 89.92/90.35 ) = d( x( n( X ), Y ) ) }.
% 89.92/90.35 substitution0:
% 89.92/90.35 X := Y
% 89.92/90.35 Y := X
% 89.92/90.35 end
% 89.92/90.35
% 89.92/90.35 eqswap: (37007) {G1,W10,D6,L1,V1,M1} { opt( d( X ) ) ==> opt( d( x( n( z )
% 89.92/90.35 , X ) ) ) }.
% 89.92/90.35 parent0[0]: (299) {G1,W10,D6,L1,V1,M1} P(49,53) { opt( d( x( n( z ), X ) )
% 89.92/90.35 ) ==> opt( d( X ) ) }.
% 89.92/90.35 substitution0:
% 89.92/90.35 X := X
% 89.92/90.35 end
% 89.92/90.35
% 89.92/90.35 paramod: (37010) {G2,W10,D6,L1,V1,M1} { opt( d( X ) ) ==> opt( d( x( d( x2
% 89.92/90.35 ), X ) ) ) }.
% 89.92/90.35 parent0[0]: (37006) {G3,W11,D5,L1,V2,M1} { d( x( n( Y ), X ) ) = d( x( d(
% 89.92/90.35 x2 ), X ) ) }.
% 89.92/90.35 parent1[0; 5]: (37007) {G1,W10,D6,L1,V1,M1} { opt( d( X ) ) ==> opt( d( x
% 89.92/90.35 ( n( z ), X ) ) ) }.
% 89.92/90.35 substitution0:
% 89.92/90.35 X := X
% 89.92/90.35 Y := z
% 89.92/90.35 end
% 89.92/90.35 substitution1:
% 89.92/90.35 X := X
% 89.92/90.35 end
% 89.92/90.35
% 89.92/90.35 paramod: (37012) {G3,W6,D4,L1,V1,M1} { opt( d( X ) ) ==> d( X ) }.
% 89.92/90.35 parent0[0]: (35956) {G3,W9,D6,L1,V1,M1} P(656,49) { opt( d( x( d( x2 ), X )
% 89.92/90.35 ) ) ==> d( X ) }.
% 89.92/90.35 parent1[0; 4]: (37010) {G2,W10,D6,L1,V1,M1} { opt( d( X ) ) ==> opt( d( x
% 89.92/90.35 ( d( x2 ), X ) ) ) }.
% 89.92/90.35 substitution0:
% 89.92/90.35 X := X
% 89.92/90.35 end
% 89.92/90.35 substitution1:
% 89.92/90.35 X := X
% 89.92/90.35 end
% 89.92/90.35
% 89.92/90.35 subsumption: (36330) {G4,W6,D4,L1,V1,M1} P(664,299);d(35956) { opt( d( X )
% 89.92/90.35 ) ==> d( X ) }.
% 89.92/90.35 parent0: (37012) {G3,W6,D4,L1,V1,M1} { opt( d( X ) ) ==> d( X ) }.
% 89.92/90.35 substitution0:
% 89.92/90.35 X := X
% 89.92/90.35 end
% 89.92/90.35 permutation0:
% 89.92/90.35 0 ==> 0
% 89.92/90.35 end
% 89.92/90.35
% 89.92/90.35 eqswap: (37014) {G4,W6,D4,L1,V1,M1} { d( X ) ==> opt( d( X ) ) }.
% 89.92/90.35 parent0[0]: (36330) {G4,W6,D4,L1,V1,M1} P(664,299);d(35956) { opt( d( X ) )
% 89.92/90.35 ==> d( X ) }.
% 89.92/90.35 substitution0:
% 89.92/90.35 X := X
% 89.92/90.35 end
% 89.92/90.35
% 89.92/90.35 paramod: (37017) {G4,W8,D5,L1,V0,M1} { d( x( x2, d( x2 ) ) ) ==> d( x2 )
% 89.92/90.35 }.
% 89.92/90.35 parent0[0]: (36020) {G3,W9,D6,L1,V0,M1} P(657,903);d(21) { opt( d( x( x2, d
% 89.92/90.35 ( x2 ) ) ) ) ==> d( x2 ) }.
% 89.92/90.35 parent1[0; 6]: (37014) {G4,W6,D4,L1,V1,M1} { d( X ) ==> opt( d( X ) ) }.
% 89.92/90.35 substitution0:
% 89.92/90.35 end
% 89.92/90.35 substitution1:
% 89.92/90.35 X := x( x2, d( x2 ) )
% 89.92/90.35 end
% 89.92/90.35
% 89.92/90.35 resolution: (37018) {G3,W0,D0,L0,V0,M0} { }.
% 89.92/90.35 parent0[0]: (662) {G2,W7,D4,L1,V2,M1} P(39,57) { ! d( x( X, Y ) ) ==> d( x2
% 89.92/90.35 ) }.
% 89.92/90.35 parent1[0]: (37017) {G4,W8,D5,L1,V0,M1} { d( x( x2, d( x2 ) ) ) ==> d( x2
% 89.92/90.35 ) }.
% 89.92/90.35 substitution0:
% 89.92/90.35 X := x2
% 89.92/90.35 Y := d( x2 )
% 89.92/90.35 end
% 89.92/90.35 substitution1:
% 89.92/90.35 end
% 89.92/90.35
% 89.92/90.35 subsumption: (36343) {G5,W0,D0,L0,V0,M0} P(36330,36020);r(662) { }.
% 89.92/90.35 parent0: (37018) {G3,W0,D0,L0,V0,M0} { }.
% 89.92/90.35 substitution0:
% 89.92/90.35 end
% 89.92/90.35 permutation0:
% 89.92/90.35 end
% 89.92/90.35
% 89.92/90.35 Proof check complete!
% 89.92/90.35
% 89.92/90.35 Memory use:
% 89.92/90.35
% 89.92/90.35 space for terms: 555369
% 89.92/90.35 space for clauses: 1911545
% 89.92/90.35
% 89.92/90.35
% 89.92/90.35 clauses generated: 1377474
% 89.92/90.35 clauses kept: 36344
% 89.92/90.35 clauses selected: 2021
% 89.92/90.35 clauses deleted: 2320
% 89.92/90.35 clauses inuse deleted: 326
% 89.92/90.35
% 89.92/90.35 subsentry: 1145318
% 89.92/90.35 literals s-matched: 245324
% 89.92/90.35 literals matched: 212439
% 89.92/90.35 full subsumption: 68432
% 89.92/90.35
% 89.92/90.35 checksum: 133652287
% 89.92/90.35
% 89.92/90.35
% 89.92/90.35 Bliksem ended
%------------------------------------------------------------------------------