TSTP Solution File: NUM851+2 by Bliksem---1.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : NUM851+2 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n023.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 : Mon Jul 18 06:27:04 EDT 2022
% Result : Theorem 23.06s 23.47s
% Output : Refutation 23.06s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : NUM851+2 : TPTP v8.1.0. Released v4.1.0.
% 0.10/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n023.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % DateTime : Tue Jul 5 14:29:42 EDT 2022
% 0.13/0.34 % CPUTime :
% 23.06/23.47 *** allocated 10000 integers for termspace/termends
% 23.06/23.47 *** allocated 10000 integers for clauses
% 23.06/23.47 *** allocated 10000 integers for justifications
% 23.06/23.47 Bliksem 1.12
% 23.06/23.47
% 23.06/23.47
% 23.06/23.47 Automatic Strategy Selection
% 23.06/23.47
% 23.06/23.47
% 23.06/23.47 Clauses:
% 23.06/23.47
% 23.06/23.47 { ! vmul( vplus( vd471, vd473 ), vd469 ) = vplus( vmul( vd471, vd469 ),
% 23.06/23.47 vmul( vd473, vd469 ) ) }.
% 23.06/23.47 { vmul( vd470, vd469 ) = vmul( vplus( vd471, vd473 ), vd469 ) }.
% 23.06/23.47 { vd470 = vplus( vd471, vd473 ) }.
% 23.06/23.47 { greater( vd470, vd471 ) }.
% 23.06/23.47 { vmul( vmul( X, Y ), Z ) = vmul( X, vmul( Y, Z ) ) }.
% 23.06/23.47 { vmul( X, vplus( Y, Z ) ) = vplus( vmul( X, Y ), vmul( X, Z ) ) }.
% 23.06/23.47 { vmul( X, Y ) = vmul( Y, X ) }.
% 23.06/23.47 { vmul( vsucc( X ), Y ) = vplus( vmul( X, Y ), Y ) }.
% 23.06/23.47 { vmul( v1, X ) = X }.
% 23.06/23.47 { vmul( X, vsucc( Y ) ) = vplus( vmul( X, Y ), X ) }.
% 23.06/23.47 { vmul( X, v1 ) = X }.
% 23.06/23.47 { ! less( X, vplus( Y, v1 ) ), leq( X, Y ) }.
% 23.06/23.47 { ! greater( X, Y ), geq( X, vplus( Y, v1 ) ) }.
% 23.06/23.47 { ! greater( Y, X ), Y = vplus( X, skol1( X, Y ) ) }.
% 23.06/23.47 { ! Y = vplus( X, Z ), greater( Y, X ) }.
% 23.06/23.47 { X = Y, X = vplus( Y, skol2( X, Y ) ), Y = vplus( X, skol3( X, Y ) ) }.
% 23.06/23.47 { ! X = Y, ! Y = vplus( X, Z ) }.
% 23.06/23.47 { ! X = vplus( Y, Z ), ! Y = vplus( X, T ) }.
% 23.06/23.47 { ! X = Y, ! X = vplus( Y, Z ) }.
% 23.06/23.47 { X = Y, ! vplus( Z, X ) = vplus( Z, Y ) }.
% 23.06/23.47 { ! Y = vplus( X, Y ) }.
% 23.06/23.47 { vplus( Y, X ) = vplus( X, Y ) }.
% 23.06/23.47 { vplus( vsucc( X ), Y ) = vsucc( vplus( X, Y ) ) }.
% 23.06/23.47 { vplus( v1, X ) = vsucc( X ) }.
% 23.06/23.47 { vplus( vplus( X, Y ), Z ) = vplus( X, vplus( Y, Z ) ) }.
% 23.06/23.47 { vplus( X, vsucc( Y ) ) = vsucc( vplus( X, Y ) ) }.
% 23.06/23.47 { vplus( X, v1 ) = vsucc( X ) }.
% 23.06/23.47 { X = v1, X = vsucc( vskolem2( X ) ) }.
% 23.06/23.47 { ! vsucc( X ) = X }.
% 23.06/23.47 { X = Y, ! vsucc( X ) = vsucc( Y ) }.
% 23.06/23.47
% 23.06/23.47 percentage equality = 0.833333, percentage horn = 0.933333
% 23.06/23.47 This is a pure equality problem
% 23.06/23.47
% 23.06/23.47
% 23.06/23.47
% 23.06/23.47 Options Used:
% 23.06/23.47
% 23.06/23.47 useres = 1
% 23.06/23.47 useparamod = 1
% 23.06/23.47 useeqrefl = 1
% 23.06/23.47 useeqfact = 1
% 23.06/23.47 usefactor = 1
% 23.06/23.47 usesimpsplitting = 0
% 23.06/23.47 usesimpdemod = 5
% 23.06/23.47 usesimpres = 3
% 23.06/23.47
% 23.06/23.47 resimpinuse = 1000
% 23.06/23.47 resimpclauses = 20000
% 23.06/23.47 substype = eqrewr
% 23.06/23.47 backwardsubs = 1
% 23.06/23.47 selectoldest = 5
% 23.06/23.47
% 23.06/23.47 litorderings [0] = split
% 23.06/23.47 litorderings [1] = extend the termordering, first sorting on arguments
% 23.06/23.47
% 23.06/23.47 termordering = kbo
% 23.06/23.47
% 23.06/23.47 litapriori = 0
% 23.06/23.47 termapriori = 1
% 23.06/23.47 litaposteriori = 0
% 23.06/23.47 termaposteriori = 0
% 23.06/23.47 demodaposteriori = 0
% 23.06/23.47 ordereqreflfact = 0
% 23.06/23.47
% 23.06/23.47 litselect = negord
% 23.06/23.47
% 23.06/23.47 maxweight = 15
% 23.06/23.47 maxdepth = 30000
% 23.06/23.47 maxlength = 115
% 23.06/23.47 maxnrvars = 195
% 23.06/23.47 excuselevel = 1
% 23.06/23.47 increasemaxweight = 1
% 23.06/23.47
% 23.06/23.47 maxselected = 10000000
% 23.06/23.47 maxnrclauses = 10000000
% 23.06/23.47
% 23.06/23.47 showgenerated = 0
% 23.06/23.47 showkept = 0
% 23.06/23.47 showselected = 0
% 23.06/23.47 showdeleted = 0
% 23.06/23.47 showresimp = 1
% 23.06/23.47 showstatus = 2000
% 23.06/23.47
% 23.06/23.47 prologoutput = 0
% 23.06/23.47 nrgoals = 5000000
% 23.06/23.47 totalproof = 1
% 23.06/23.47
% 23.06/23.47 Symbols occurring in the translation:
% 23.06/23.47
% 23.06/23.47 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 23.06/23.47 . [1, 2] (w:1, o:61, a:1, s:1, b:0),
% 23.06/23.47 ! [4, 1] (w:0, o:54, a:1, s:1, b:0),
% 23.06/23.47 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 23.06/23.47 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 23.06/23.47 vd471 [35, 0] (w:1, o:8, a:1, s:1, b:0),
% 23.06/23.47 vd473 [36, 0] (w:1, o:9, a:1, s:1, b:0),
% 23.06/23.47 vplus [37, 2] (w:1, o:85, a:1, s:1, b:0),
% 23.06/23.47 vd469 [38, 0] (w:1, o:6, a:1, s:1, b:0),
% 23.06/23.47 vmul [39, 2] (w:1, o:86, a:1, s:1, b:0),
% 23.06/23.47 vd470 [40, 0] (w:1, o:7, a:1, s:1, b:0),
% 23.06/23.47 greater [41, 2] (w:1, o:87, a:1, s:1, b:0),
% 23.06/23.47 vsucc [52, 1] (w:1, o:59, a:1, s:1, b:0),
% 23.06/23.47 v1 [54, 0] (w:1, o:31, a:1, s:1, b:0),
% 23.06/23.47 less [59, 2] (w:1, o:88, a:1, s:1, b:0),
% 23.06/23.47 leq [60, 2] (w:1, o:89, a:1, s:1, b:0),
% 23.06/23.47 geq [63, 2] (w:1, o:90, a:1, s:1, b:0),
% 23.06/23.47 vskolem2 [87, 1] (w:1, o:60, a:1, s:1, b:0),
% 23.06/23.47 skol1 [91, 2] (w:1, o:91, a:1, s:1, b:1),
% 23.06/23.47 skol2 [92, 2] (w:1, o:92, a:1, s:1, b:1),
% 23.06/23.47 skol3 [93, 2] (w:1, o:93, a:1, s:1, b:1).
% 23.06/23.47
% 23.06/23.47
% 23.06/23.47 Starting Search:
% 23.06/23.47
% 23.06/23.47 *** allocated 15000 integers for clauses
% 23.06/23.47 *** allocated 22500 integers for clauses
% 23.06/23.47 *** allocated 33750 integers for clauses
% 23.06/23.47 *** allocated 50625 integers for clauses
% 23.06/23.47 *** allocated 15000 integers for termspace/termends
% 23.06/23.47 *** allocated 75937 integers for clauses
% 23.06/23.47 Resimplifying inuse:
% 23.06/23.47 Done
% 23.06/23.47
% 23.06/23.47 *** allocated 22500 integers for termspace/termends
% 23.06/23.47 *** allocated 113905 integers for clauses
% 23.06/23.47 *** allocated 33750 integers for termspace/termends
% 23.06/23.47 *** allocated 170857 integers for clauses
% 23.06/23.47
% 23.06/23.47 Intermediate Status:
% 23.06/23.47 Generated: 6957
% 23.06/23.47 Kept: 2001
% 23.06/23.47 Inuse: 188
% 23.06/23.47 Deleted: 6
% 23.06/23.47 Deletedinuse: 0
% 23.06/23.47
% 23.06/23.47 Resimplifying inuse:
% 23.06/23.47 Done
% 23.06/23.47
% 23.06/23.47 *** allocated 50625 integers for termspace/termends
% 23.06/23.47 *** allocated 256285 integers for clauses
% 23.06/23.47 Resimplifying inuse:
% 23.06/23.47 Done
% 23.06/23.47
% 23.06/23.47
% 23.06/23.47 Intermediate Status:
% 23.06/23.47 Generated: 15392
% 23.06/23.47 Kept: 4029
% 23.06/23.47 Inuse: 340
% 23.06/23.47 Deleted: 21
% 23.06/23.47 Deletedinuse: 5
% 23.06/23.47
% 23.06/23.47 Resimplifying inuse:
% 23.06/23.47 Done
% 23.06/23.47
% 23.06/23.47 *** allocated 75937 integers for termspace/termends
% 23.06/23.47 *** allocated 384427 integers for clauses
% 23.06/23.47 Resimplifying inuse:
% 23.06/23.47 Done
% 23.06/23.47
% 23.06/23.47
% 23.06/23.47 Intermediate Status:
% 23.06/23.47 Generated: 38964
% 23.06/23.47 Kept: 6134
% 23.06/23.47 Inuse: 450
% 23.06/23.47 Deleted: 129
% 23.06/23.47 Deletedinuse: 98
% 23.06/23.47
% 23.06/23.47 *** allocated 113905 integers for termspace/termends
% 23.06/23.47 Resimplifying inuse:
% 23.06/23.47 Done
% 23.06/23.47
% 23.06/23.47 *** allocated 576640 integers for clauses
% 23.06/23.47 Resimplifying inuse:
% 23.06/23.47 Done
% 23.06/23.47
% 23.06/23.47
% 23.06/23.47 Intermediate Status:
% 23.06/23.47 Generated: 68484
% 23.06/23.47 Kept: 8142
% 23.06/23.47 Inuse: 541
% 23.06/23.47 Deleted: 153
% 23.06/23.47 Deletedinuse: 99
% 23.06/23.47
% 23.06/23.47 Resimplifying inuse:
% 23.06/23.47 Done
% 23.06/23.47
% 23.06/23.47 Resimplifying inuse:
% 23.06/23.47 Done
% 23.06/23.47
% 23.06/23.47 *** allocated 170857 integers for termspace/termends
% 23.06/23.47
% 23.06/23.47 Intermediate Status:
% 23.06/23.47 Generated: 117399
% 23.06/23.47 Kept: 10380
% 23.06/23.47 Inuse: 667
% 23.06/23.47 Deleted: 165
% 23.06/23.47 Deletedinuse: 101
% 23.06/23.47
% 23.06/23.47 Resimplifying inuse:
% 23.06/23.47 Done
% 23.06/23.47
% 23.06/23.47 *** allocated 864960 integers for clauses
% 23.06/23.47 Resimplifying inuse:
% 23.06/23.47 Done
% 23.06/23.47
% 23.06/23.47
% 23.06/23.47 Intermediate Status:
% 23.06/23.47 Generated: 157332
% 23.06/23.47 Kept: 12436
% 23.06/23.47 Inuse: 773
% 23.06/23.47 Deleted: 189
% 23.06/23.47 Deletedinuse: 101
% 23.06/23.47
% 23.06/23.47 Resimplifying inuse:
% 23.06/23.47 Done
% 23.06/23.47
% 23.06/23.47 Resimplifying inuse:
% 23.06/23.47 Done
% 23.06/23.47
% 23.06/23.47 *** allocated 256285 integers for termspace/termends
% 23.06/23.47
% 23.06/23.47 Intermediate Status:
% 23.06/23.47 Generated: 197253
% 23.06/23.47 Kept: 14437
% 23.06/23.47 Inuse: 872
% 23.06/23.47 Deleted: 195
% 23.06/23.47 Deletedinuse: 107
% 23.06/23.47
% 23.06/23.47 Resimplifying inuse:
% 23.06/23.47 Done
% 23.06/23.47
% 23.06/23.47 Resimplifying inuse:
% 23.06/23.47 Done
% 23.06/23.47
% 23.06/23.47
% 23.06/23.47 Intermediate Status:
% 23.06/23.47 Generated: 221152
% 23.06/23.47 Kept: 16448
% 23.06/23.47 Inuse: 947
% 23.06/23.47 Deleted: 196
% 23.06/23.47 Deletedinuse: 107
% 23.06/23.47
% 23.06/23.47 *** allocated 1297440 integers for clauses
% 23.06/23.47 Resimplifying inuse:
% 23.06/23.47 Done
% 23.06/23.47
% 23.06/23.47 Resimplifying inuse:
% 23.06/23.47 Done
% 23.06/23.47
% 23.06/23.47
% 23.06/23.47 Intermediate Status:
% 23.06/23.47 Generated: 264569
% 23.06/23.47 Kept: 18459
% 23.06/23.47 Inuse: 1042
% 23.06/23.47 Deleted: 198
% 23.06/23.47 Deletedinuse: 107
% 23.06/23.47
% 23.06/23.47 Resimplifying inuse:
% 23.06/23.47 Done
% 23.06/23.47
% 23.06/23.47 Resimplifying inuse:
% 23.06/23.47 Done
% 23.06/23.47
% 23.06/23.47 Resimplifying clauses:
% 23.06/23.47 Done
% 23.06/23.47
% 23.06/23.47
% 23.06/23.47 Intermediate Status:
% 23.06/23.47 Generated: 331163
% 23.06/23.47 Kept: 20459
% 23.06/23.47 Inuse: 1139
% 23.06/23.47 Deleted: 2756
% 23.06/23.47 Deletedinuse: 107
% 23.06/23.47
% 23.06/23.47 *** allocated 384427 integers for termspace/termends
% 23.06/23.47 Resimplifying inuse:
% 23.06/23.47 Done
% 23.06/23.47
% 23.06/23.47 Resimplifying inuse:
% 23.06/23.47 Done
% 23.06/23.47
% 23.06/23.47
% 23.06/23.47 Intermediate Status:
% 23.06/23.47 Generated: 389220
% 23.06/23.47 Kept: 22461
% 23.06/23.47 Inuse: 1206
% 23.06/23.47 Deleted: 2915
% 23.06/23.47 Deletedinuse: 226
% 23.06/23.47
% 23.06/23.47 Resimplifying inuse:
% 23.06/23.47 Done
% 23.06/23.47
% 23.06/23.47 Resimplifying inuse:
% 23.06/23.47 Done
% 23.06/23.47
% 23.06/23.47
% 23.06/23.47 Intermediate Status:
% 23.06/23.47 Generated: 417888
% 23.06/23.47 Kept: 24472
% 23.06/23.47 Inuse: 1241
% 23.06/23.47 Deleted: 2982
% 23.06/23.47 Deletedinuse: 226
% 23.06/23.47
% 23.06/23.47 *** allocated 1946160 integers for clauses
% 23.06/23.47 Resimplifying inuse:
% 23.06/23.47 Done
% 23.06/23.47
% 23.06/23.47
% 23.06/23.47 Bliksems!, er is een bewijs:
% 23.06/23.47 % SZS status Theorem
% 23.06/23.47 % SZS output start Refutation
% 23.06/23.47
% 23.06/23.47 (0) {G0,W13,D4,L1,V0,M1} I { ! vplus( vmul( vd471, vd469 ), vmul( vd473,
% 23.06/23.47 vd469 ) ) ==> vmul( vplus( vd471, vd473 ), vd469 ) }.
% 23.06/23.47 (1) {G0,W9,D4,L1,V0,M1} I { vmul( vplus( vd471, vd473 ), vd469 ) ==> vmul(
% 23.06/23.47 vd470, vd469 ) }.
% 23.06/23.47 (2) {G0,W5,D3,L1,V0,M1} I { vplus( vd471, vd473 ) ==> vd470 }.
% 23.06/23.47 (5) {G0,W13,D4,L1,V3,M1} I { vplus( vmul( X, Y ), vmul( X, Z ) ) ==> vmul(
% 23.06/23.47 X, vplus( Y, Z ) ) }.
% 23.06/23.47 (6) {G0,W7,D3,L1,V2,M1} I { vmul( X, Y ) = vmul( Y, X ) }.
% 23.06/23.47 (32) {G1,W11,D4,L1,V0,M1} S(0);d(1) { ! vplus( vmul( vd471, vd469 ), vmul(
% 23.06/23.47 vd473, vd469 ) ) ==> vmul( vd470, vd469 ) }.
% 23.06/23.47 (50) {G1,W13,D4,L1,V3,M1} P(6,5) { vplus( vmul( X, Z ), vmul( Y, X ) ) ==>
% 23.06/23.47 vmul( X, vplus( Z, Y ) ) }.
% 23.06/23.47 (1080) {G2,W7,D3,L1,V0,M1} P(6,32);d(50);d(2) { ! vmul( vd469, vd470 ) ==>
% 23.06/23.47 vmul( vd470, vd469 ) }.
% 23.06/23.47 (25707) {G3,W0,D0,L0,V0,M0} P(6,1080);q { }.
% 23.06/23.47
% 23.06/23.47
% 23.06/23.47 % SZS output end Refutation
% 23.06/23.47 found a proof!
% 23.06/23.47
% 23.06/23.47
% 23.06/23.47 Unprocessed initial clauses:
% 23.06/23.47
% 23.06/23.47 (25709) {G0,W13,D4,L1,V0,M1} { ! vmul( vplus( vd471, vd473 ), vd469 ) =
% 23.06/23.47 vplus( vmul( vd471, vd469 ), vmul( vd473, vd469 ) ) }.
% 23.06/23.47 (25710) {G0,W9,D4,L1,V0,M1} { vmul( vd470, vd469 ) = vmul( vplus( vd471,
% 23.06/23.47 vd473 ), vd469 ) }.
% 23.06/23.47 (25711) {G0,W5,D3,L1,V0,M1} { vd470 = vplus( vd471, vd473 ) }.
% 23.06/23.47 (25712) {G0,W3,D2,L1,V0,M1} { greater( vd470, vd471 ) }.
% 23.06/23.47 (25713) {G0,W11,D4,L1,V3,M1} { vmul( vmul( X, Y ), Z ) = vmul( X, vmul( Y
% 23.06/23.47 , Z ) ) }.
% 23.06/23.47 (25714) {G0,W13,D4,L1,V3,M1} { vmul( X, vplus( Y, Z ) ) = vplus( vmul( X,
% 23.06/23.47 Y ), vmul( X, Z ) ) }.
% 23.06/23.47 (25715) {G0,W7,D3,L1,V2,M1} { vmul( X, Y ) = vmul( Y, X ) }.
% 23.06/23.47 (25716) {G0,W10,D4,L1,V2,M1} { vmul( vsucc( X ), Y ) = vplus( vmul( X, Y )
% 23.06/23.47 , Y ) }.
% 23.06/23.47 (25717) {G0,W5,D3,L1,V1,M1} { vmul( v1, X ) = X }.
% 23.06/23.47 (25718) {G0,W10,D4,L1,V2,M1} { vmul( X, vsucc( Y ) ) = vplus( vmul( X, Y )
% 23.06/23.47 , X ) }.
% 23.06/23.47 (25719) {G0,W5,D3,L1,V1,M1} { vmul( X, v1 ) = X }.
% 23.06/23.47 (25720) {G0,W8,D3,L2,V2,M2} { ! less( X, vplus( Y, v1 ) ), leq( X, Y ) }.
% 23.06/23.47 (25721) {G0,W8,D3,L2,V2,M2} { ! greater( X, Y ), geq( X, vplus( Y, v1 ) )
% 23.06/23.47 }.
% 23.06/23.47 (25722) {G0,W10,D4,L2,V2,M2} { ! greater( Y, X ), Y = vplus( X, skol1( X,
% 23.06/23.47 Y ) ) }.
% 23.06/23.47 (25723) {G0,W8,D3,L2,V3,M2} { ! Y = vplus( X, Z ), greater( Y, X ) }.
% 23.06/23.47 (25724) {G0,W17,D4,L3,V2,M3} { X = Y, X = vplus( Y, skol2( X, Y ) ), Y =
% 23.06/23.47 vplus( X, skol3( X, Y ) ) }.
% 23.06/23.47 (25725) {G0,W8,D3,L2,V3,M2} { ! X = Y, ! Y = vplus( X, Z ) }.
% 23.06/23.47 (25726) {G0,W10,D3,L2,V4,M2} { ! X = vplus( Y, Z ), ! Y = vplus( X, T )
% 23.06/23.47 }.
% 23.06/23.47 (25727) {G0,W8,D3,L2,V3,M2} { ! X = Y, ! X = vplus( Y, Z ) }.
% 23.06/23.47 (25728) {G0,W10,D3,L2,V3,M2} { X = Y, ! vplus( Z, X ) = vplus( Z, Y ) }.
% 23.06/23.47 (25729) {G0,W5,D3,L1,V2,M1} { ! Y = vplus( X, Y ) }.
% 23.06/23.47 (25730) {G0,W7,D3,L1,V2,M1} { vplus( Y, X ) = vplus( X, Y ) }.
% 23.06/23.47 (25731) {G0,W9,D4,L1,V2,M1} { vplus( vsucc( X ), Y ) = vsucc( vplus( X, Y
% 23.06/23.47 ) ) }.
% 23.06/23.47 (25732) {G0,W6,D3,L1,V1,M1} { vplus( v1, X ) = vsucc( X ) }.
% 23.06/23.47 (25733) {G0,W11,D4,L1,V3,M1} { vplus( vplus( X, Y ), Z ) = vplus( X, vplus
% 23.06/23.47 ( Y, Z ) ) }.
% 23.06/23.47 (25734) {G0,W9,D4,L1,V2,M1} { vplus( X, vsucc( Y ) ) = vsucc( vplus( X, Y
% 23.06/23.47 ) ) }.
% 23.06/23.47 (25735) {G0,W6,D3,L1,V1,M1} { vplus( X, v1 ) = vsucc( X ) }.
% 23.06/23.47 (25736) {G0,W8,D4,L2,V1,M2} { X = v1, X = vsucc( vskolem2( X ) ) }.
% 23.06/23.47 (25737) {G0,W4,D3,L1,V1,M1} { ! vsucc( X ) = X }.
% 23.06/23.47 (25738) {G0,W8,D3,L2,V2,M2} { X = Y, ! vsucc( X ) = vsucc( Y ) }.
% 23.06/23.47
% 23.06/23.47
% 23.06/23.47 Total Proof:
% 23.06/23.47
% 23.06/23.47 eqswap: (25739) {G0,W13,D4,L1,V0,M1} { ! vplus( vmul( vd471, vd469 ), vmul
% 23.06/23.47 ( vd473, vd469 ) ) = vmul( vplus( vd471, vd473 ), vd469 ) }.
% 23.06/23.47 parent0[0]: (25709) {G0,W13,D4,L1,V0,M1} { ! vmul( vplus( vd471, vd473 ),
% 23.06/23.47 vd469 ) = vplus( vmul( vd471, vd469 ), vmul( vd473, vd469 ) ) }.
% 23.06/23.47 substitution0:
% 23.06/23.47 end
% 23.06/23.47
% 23.06/23.47 subsumption: (0) {G0,W13,D4,L1,V0,M1} I { ! vplus( vmul( vd471, vd469 ),
% 23.06/23.47 vmul( vd473, vd469 ) ) ==> vmul( vplus( vd471, vd473 ), vd469 ) }.
% 23.06/23.47 parent0: (25739) {G0,W13,D4,L1,V0,M1} { ! vplus( vmul( vd471, vd469 ),
% 23.06/23.47 vmul( vd473, vd469 ) ) = vmul( vplus( vd471, vd473 ), vd469 ) }.
% 23.06/23.47 substitution0:
% 23.06/23.47 end
% 23.06/23.47 permutation0:
% 23.06/23.47 0 ==> 0
% 23.06/23.47 end
% 23.06/23.47
% 23.06/23.47 eqswap: (25741) {G0,W9,D4,L1,V0,M1} { vmul( vplus( vd471, vd473 ), vd469 )
% 23.06/23.47 = vmul( vd470, vd469 ) }.
% 23.06/23.47 parent0[0]: (25710) {G0,W9,D4,L1,V0,M1} { vmul( vd470, vd469 ) = vmul(
% 23.06/23.47 vplus( vd471, vd473 ), vd469 ) }.
% 23.06/23.47 substitution0:
% 23.06/23.47 end
% 23.06/23.47
% 23.06/23.47 subsumption: (1) {G0,W9,D4,L1,V0,M1} I { vmul( vplus( vd471, vd473 ), vd469
% 23.06/23.47 ) ==> vmul( vd470, vd469 ) }.
% 23.06/23.47 parent0: (25741) {G0,W9,D4,L1,V0,M1} { vmul( vplus( vd471, vd473 ), vd469
% 23.06/23.47 ) = vmul( vd470, vd469 ) }.
% 23.06/23.47 substitution0:
% 23.06/23.47 end
% 23.06/23.47 permutation0:
% 23.06/23.47 0 ==> 0
% 23.06/23.47 end
% 23.06/23.47
% 23.06/23.47 eqswap: (25744) {G0,W5,D3,L1,V0,M1} { vplus( vd471, vd473 ) = vd470 }.
% 23.06/23.47 parent0[0]: (25711) {G0,W5,D3,L1,V0,M1} { vd470 = vplus( vd471, vd473 )
% 23.06/23.47 }.
% 23.06/23.47 substitution0:
% 23.06/23.47 end
% 23.06/23.47
% 23.06/23.47 subsumption: (2) {G0,W5,D3,L1,V0,M1} I { vplus( vd471, vd473 ) ==> vd470
% 23.06/23.47 }.
% 23.06/23.47 parent0: (25744) {G0,W5,D3,L1,V0,M1} { vplus( vd471, vd473 ) = vd470 }.
% 23.06/23.47 substitution0:
% 23.06/23.47 end
% 23.06/23.47 permutation0:
% 23.06/23.47 0 ==> 0
% 23.06/23.47 end
% 23.06/23.47
% 23.06/23.47 eqswap: (25749) {G0,W13,D4,L1,V3,M1} { vplus( vmul( X, Y ), vmul( X, Z ) )
% 23.06/23.47 = vmul( X, vplus( Y, Z ) ) }.
% 23.06/23.47 parent0[0]: (25714) {G0,W13,D4,L1,V3,M1} { vmul( X, vplus( Y, Z ) ) =
% 23.06/23.47 vplus( vmul( X, Y ), vmul( X, Z ) ) }.
% 23.06/23.47 substitution0:
% 23.06/23.47 X := X
% 23.06/23.47 Y := Y
% 23.06/23.47 Z := Z
% 23.06/23.47 end
% 23.06/23.47
% 23.06/23.47 subsumption: (5) {G0,W13,D4,L1,V3,M1} I { vplus( vmul( X, Y ), vmul( X, Z )
% 23.06/23.47 ) ==> vmul( X, vplus( Y, Z ) ) }.
% 23.06/23.47 parent0: (25749) {G0,W13,D4,L1,V3,M1} { vplus( vmul( X, Y ), vmul( X, Z )
% 23.06/23.47 ) = vmul( X, vplus( Y, Z ) ) }.
% 23.06/23.47 substitution0:
% 23.06/23.47 X := X
% 23.06/23.47 Y := Y
% 23.06/23.47 Z := Z
% 23.06/23.47 end
% 23.06/23.47 permutation0:
% 23.06/23.47 0 ==> 0
% 23.06/23.47 end
% 23.06/23.47
% 23.06/23.47 subsumption: (6) {G0,W7,D3,L1,V2,M1} I { vmul( X, Y ) = vmul( Y, X ) }.
% 23.06/23.47 parent0: (25715) {G0,W7,D3,L1,V2,M1} { vmul( X, Y ) = vmul( Y, X ) }.
% 23.06/23.47 substitution0:
% 23.06/23.47 X := X
% 23.06/23.47 Y := Y
% 23.06/23.47 end
% 23.06/23.47 permutation0:
% 23.06/23.47 0 ==> 0
% 23.06/23.47 end
% 23.06/23.47
% 23.06/23.47 paramod: (25757) {G1,W11,D4,L1,V0,M1} { ! vplus( vmul( vd471, vd469 ),
% 23.06/23.47 vmul( vd473, vd469 ) ) ==> vmul( vd470, vd469 ) }.
% 23.06/23.47 parent0[0]: (1) {G0,W9,D4,L1,V0,M1} I { vmul( vplus( vd471, vd473 ), vd469
% 23.06/23.47 ) ==> vmul( vd470, vd469 ) }.
% 23.06/23.47 parent1[0; 9]: (0) {G0,W13,D4,L1,V0,M1} I { ! vplus( vmul( vd471, vd469 ),
% 23.06/23.47 vmul( vd473, vd469 ) ) ==> vmul( vplus( vd471, vd473 ), vd469 ) }.
% 23.06/23.47 substitution0:
% 23.06/23.47 end
% 23.06/23.47 substitution1:
% 23.06/23.47 end
% 23.06/23.47
% 23.06/23.47 subsumption: (32) {G1,W11,D4,L1,V0,M1} S(0);d(1) { ! vplus( vmul( vd471,
% 23.06/23.47 vd469 ), vmul( vd473, vd469 ) ) ==> vmul( vd470, vd469 ) }.
% 23.06/23.47 parent0: (25757) {G1,W11,D4,L1,V0,M1} { ! vplus( vmul( vd471, vd469 ),
% 23.06/23.47 vmul( vd473, vd469 ) ) ==> vmul( vd470, vd469 ) }.
% 23.06/23.47 substitution0:
% 23.06/23.47 end
% 23.06/23.47 permutation0:
% 23.06/23.47 0 ==> 0
% 23.06/23.47 end
% 23.06/23.47
% 23.06/23.47 eqswap: (25759) {G0,W13,D4,L1,V3,M1} { vmul( X, vplus( Y, Z ) ) ==> vplus
% 23.06/23.47 ( vmul( X, Y ), vmul( X, Z ) ) }.
% 23.06/23.47 parent0[0]: (5) {G0,W13,D4,L1,V3,M1} I { vplus( vmul( X, Y ), vmul( X, Z )
% 23.06/23.47 ) ==> vmul( X, vplus( Y, Z ) ) }.
% 23.06/23.47 substitution0:
% 23.06/23.47 X := X
% 23.06/23.47 Y := Y
% 23.06/23.47 Z := Z
% 23.06/23.47 end
% 23.06/23.47
% 23.06/23.47 paramod: (25762) {G1,W13,D4,L1,V3,M1} { vmul( X, vplus( Y, Z ) ) ==> vplus
% 23.06/23.47 ( vmul( X, Y ), vmul( Z, X ) ) }.
% 23.06/23.47 parent0[0]: (6) {G0,W7,D3,L1,V2,M1} I { vmul( X, Y ) = vmul( Y, X ) }.
% 23.06/23.47 parent1[0; 10]: (25759) {G0,W13,D4,L1,V3,M1} { vmul( X, vplus( Y, Z ) )
% 23.06/23.47 ==> vplus( vmul( X, Y ), vmul( X, Z ) ) }.
% 23.06/23.47 substitution0:
% 23.06/23.47 X := X
% 23.06/23.47 Y := Z
% 23.06/23.47 end
% 23.06/23.47 substitution1:
% 23.06/23.47 X := X
% 23.06/23.47 Y := Y
% 23.06/23.47 Z := Z
% 23.06/23.47 end
% 23.06/23.47
% 23.06/23.47 eqswap: (25775) {G1,W13,D4,L1,V3,M1} { vplus( vmul( X, Y ), vmul( Z, X ) )
% 23.06/23.47 ==> vmul( X, vplus( Y, Z ) ) }.
% 23.06/23.47 parent0[0]: (25762) {G1,W13,D4,L1,V3,M1} { vmul( X, vplus( Y, Z ) ) ==>
% 23.06/23.47 vplus( vmul( X, Y ), vmul( Z, X ) ) }.
% 23.06/23.47 substitution0:
% 23.06/23.47 X := X
% 23.06/23.47 Y := Y
% 23.06/23.47 Z := Z
% 23.06/23.47 end
% 23.06/23.47
% 23.06/23.47 subsumption: (50) {G1,W13,D4,L1,V3,M1} P(6,5) { vplus( vmul( X, Z ), vmul(
% 23.06/23.47 Y, X ) ) ==> vmul( X, vplus( Z, Y ) ) }.
% 23.06/23.47 parent0: (25775) {G1,W13,D4,L1,V3,M1} { vplus( vmul( X, Y ), vmul( Z, X )
% 23.06/23.47 ) ==> vmul( X, vplus( Y, Z ) ) }.
% 23.06/23.47 substitution0:
% 23.06/23.47 X := X
% 23.06/23.47 Y := Z
% 23.06/23.47 Z := Y
% 23.06/23.47 end
% 23.06/23.47 permutation0:
% 23.06/23.47 0 ==> 0
% 23.06/23.47 end
% 23.06/23.47
% 23.06/23.47 eqswap: (25776) {G1,W11,D4,L1,V0,M1} { ! vmul( vd470, vd469 ) ==> vplus(
% 23.06/23.47 vmul( vd471, vd469 ), vmul( vd473, vd469 ) ) }.
% 23.06/23.47 parent0[0]: (32) {G1,W11,D4,L1,V0,M1} S(0);d(1) { ! vplus( vmul( vd471,
% 23.06/23.47 vd469 ), vmul( vd473, vd469 ) ) ==> vmul( vd470, vd469 ) }.
% 23.06/23.47 substitution0:
% 23.06/23.47 end
% 23.06/23.47
% 23.06/23.47 paramod: (25780) {G1,W11,D4,L1,V0,M1} { ! vmul( vd470, vd469 ) ==> vplus(
% 23.06/23.47 vmul( vd469, vd471 ), vmul( vd473, vd469 ) ) }.
% 23.06/23.47 parent0[0]: (6) {G0,W7,D3,L1,V2,M1} I { vmul( X, Y ) = vmul( Y, X ) }.
% 23.06/23.47 parent1[0; 6]: (25776) {G1,W11,D4,L1,V0,M1} { ! vmul( vd470, vd469 ) ==>
% 23.06/23.47 vplus( vmul( vd471, vd469 ), vmul( vd473, vd469 ) ) }.
% 23.06/23.47 substitution0:
% 23.06/23.47 X := vd471
% 23.06/23.47 Y := vd469
% 23.06/23.47 end
% 23.06/23.47 substitution1:
% 23.06/23.47 end
% 23.06/23.47
% 23.06/23.47 paramod: (25789) {G2,W9,D4,L1,V0,M1} { ! vmul( vd470, vd469 ) ==> vmul(
% 23.06/23.47 vd469, vplus( vd471, vd473 ) ) }.
% 23.06/23.47 parent0[0]: (50) {G1,W13,D4,L1,V3,M1} P(6,5) { vplus( vmul( X, Z ), vmul( Y
% 23.06/23.47 , X ) ) ==> vmul( X, vplus( Z, Y ) ) }.
% 23.06/23.47 parent1[0; 5]: (25780) {G1,W11,D4,L1,V0,M1} { ! vmul( vd470, vd469 ) ==>
% 23.06/23.47 vplus( vmul( vd469, vd471 ), vmul( vd473, vd469 ) ) }.
% 23.06/23.47 substitution0:
% 23.06/23.47 X := vd469
% 23.06/23.47 Y := vd473
% 23.06/23.47 Z := vd471
% 23.06/23.47 end
% 23.06/23.47 substitution1:
% 23.06/23.47 end
% 23.06/23.47
% 23.06/23.47 paramod: (25790) {G1,W7,D3,L1,V0,M1} { ! vmul( vd470, vd469 ) ==> vmul(
% 23.06/23.47 vd469, vd470 ) }.
% 23.06/23.47 parent0[0]: (2) {G0,W5,D3,L1,V0,M1} I { vplus( vd471, vd473 ) ==> vd470 }.
% 23.06/23.47 parent1[0; 7]: (25789) {G2,W9,D4,L1,V0,M1} { ! vmul( vd470, vd469 ) ==>
% 23.06/23.47 vmul( vd469, vplus( vd471, vd473 ) ) }.
% 23.06/23.47 substitution0:
% 23.06/23.47 end
% 23.06/23.47 substitution1:
% 23.06/23.47 end
% 23.06/23.47
% 23.06/23.47 eqswap: (25791) {G1,W7,D3,L1,V0,M1} { ! vmul( vd469, vd470 ) ==> vmul(
% 23.06/23.47 vd470, vd469 ) }.
% 23.06/23.47 parent0[0]: (25790) {G1,W7,D3,L1,V0,M1} { ! vmul( vd470, vd469 ) ==> vmul
% 23.06/23.47 ( vd469, vd470 ) }.
% 23.06/23.47 substitution0:
% 23.06/23.47 end
% 23.06/23.47
% 23.06/23.47 subsumption: (1080) {G2,W7,D3,L1,V0,M1} P(6,32);d(50);d(2) { ! vmul( vd469
% 23.06/23.47 , vd470 ) ==> vmul( vd470, vd469 ) }.
% 23.06/23.47 parent0: (25791) {G1,W7,D3,L1,V0,M1} { ! vmul( vd469, vd470 ) ==> vmul(
% 23.06/23.47 vd470, vd469 ) }.
% 23.06/23.47 substitution0:
% 23.06/23.47 end
% 23.06/23.47 permutation0:
% 23.06/23.47 0 ==> 0
% 23.06/23.47 end
% 23.06/23.47
% 23.06/23.47 eqswap: (25792) {G2,W7,D3,L1,V0,M1} { ! vmul( vd470, vd469 ) ==> vmul(
% 23.06/23.47 vd469, vd470 ) }.
% 23.06/23.47 parent0[0]: (1080) {G2,W7,D3,L1,V0,M1} P(6,32);d(50);d(2) { ! vmul( vd469,
% 23.06/23.47 vd470 ) ==> vmul( vd470, vd469 ) }.
% 23.06/23.47 substitution0:
% 23.06/23.47 end
% 23.06/23.47
% 23.06/23.47 paramod: (25794) {G1,W7,D3,L1,V0,M1} { ! vmul( vd470, vd469 ) ==> vmul(
% 23.06/23.47 vd470, vd469 ) }.
% 23.06/23.47 parent0[0]: (6) {G0,W7,D3,L1,V2,M1} I { vmul( X, Y ) = vmul( Y, X ) }.
% 23.06/23.47 parent1[0; 5]: (25792) {G2,W7,D3,L1,V0,M1} { ! vmul( vd470, vd469 ) ==>
% 23.06/23.47 vmul( vd469, vd470 ) }.
% 23.06/23.47 substitution0:
% 23.06/23.47 X := vd469
% 23.06/23.47 Y := vd470
% 23.06/23.47 end
% 23.06/23.47 substitution1:
% 23.06/23.47 end
% 23.06/23.47
% 23.06/23.47 eqrefl: (25797) {G0,W0,D0,L0,V0,M0} { }.
% 23.06/23.47 parent0[0]: (25794) {G1,W7,D3,L1,V0,M1} { ! vmul( vd470, vd469 ) ==> vmul
% 23.06/23.47 ( vd470, vd469 ) }.
% 23.06/23.47 substitution0:
% 23.06/23.47 end
% 23.06/23.47
% 23.06/23.47 subsumption: (25707) {G3,W0,D0,L0,V0,M0} P(6,1080);q { }.
% 23.06/23.47 parent0: (25797) {G0,W0,D0,L0,V0,M0} { }.
% 23.06/23.47 substitution0:
% 23.06/23.47 end
% 23.06/23.47 permutation0:
% 23.06/23.47 end
% 23.06/23.47
% 23.06/23.47 Proof check complete!
% 23.06/23.47
% 23.06/23.47 Memory use:
% 23.06/23.47
% 23.06/23.47 space for terms: 329261
% 23.06/23.47 space for clauses: 1313964
% 23.06/23.47
% 23.06/23.47
% 23.06/23.47 clauses generated: 428876
% 23.06/23.47 clauses kept: 25708
% 23.06/23.47 clauses selected: 1246
% 23.06/23.47 clauses deleted: 2999
% 23.06/23.47 clauses inuse deleted: 226
% 23.06/23.47
% 23.06/23.47 subsentry: 1174041
% 23.06/23.47 literals s-matched: 635364
% 23.06/23.47 literals matched: 597074
% 23.06/23.47 full subsumption: 396520
% 23.06/23.47
% 23.06/23.47 checksum: -1851984247
% 23.06/23.47
% 23.06/23.47
% 23.06/23.47 Bliksem ended
%------------------------------------------------------------------------------