TSTP Solution File: NUM844+2 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : NUM844+2 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n027.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 06:26:59 EDT 2022
% Result : Theorem 117.50s 117.94s
% Output : Refutation 117.50s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : NUM844+2 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.12 % Command : bliksem %s
% 0.11/0.33 % Computer : n027.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % DateTime : Tue Jul 5 05:02:56 EDT 2022
% 0.11/0.33 % CPUTime :
% 117.50/117.94 *** allocated 10000 integers for termspace/termends
% 117.50/117.94 *** allocated 10000 integers for clauses
% 117.50/117.94 *** allocated 10000 integers for justifications
% 117.50/117.94 Bliksem 1.12
% 117.50/117.94
% 117.50/117.94
% 117.50/117.94 Automatic Strategy Selection
% 117.50/117.94
% 117.50/117.94
% 117.50/117.94 Clauses:
% 117.50/117.94
% 117.50/117.94 { ! vplus( vmul( vd411, vd413 ), vplus( vd413, vsucc( vd411 ) ) ) = vplus(
% 117.50/117.94 vmul( vd411, vd413 ), vplus( vsucc( vd411 ), vd413 ) ) }.
% 117.50/117.94 { vplus( vplus( vmul( vd411, vd413 ), vd413 ), vsucc( vd411 ) ) = vplus(
% 117.50/117.94 vmul( vd411, vd413 ), vplus( vd413, vsucc( vd411 ) ) ) }.
% 117.50/117.94 { vplus( vmul( vsucc( vd411 ), vd413 ), vsucc( vd411 ) ) = vplus( vplus(
% 117.50/117.94 vmul( vd411, vd413 ), vd413 ), vsucc( vd411 ) ) }.
% 117.50/117.94 { vmul( vsucc( vd411 ), vsucc( vd413 ) ) = vplus( vmul( vsucc( vd411 ),
% 117.50/117.94 vd413 ), vsucc( vd411 ) ) }.
% 117.50/117.94 { vmul( vsucc( vd411 ), vd413 ) = vplus( vmul( vd411, vd413 ), vd413 ) }.
% 117.50/117.94 { vsucc( vmul( vd411, v1 ) ) = vplus( vmul( vd411, v1 ), v1 ) }.
% 117.50/117.94 { vsucc( vd411 ) = vsucc( vmul( vd411, v1 ) ) }.
% 117.50/117.94 { vmul( vsucc( vd411 ), v1 ) = vsucc( vd411 ) }.
% 117.50/117.94 { vmul( v1, X ) = X }.
% 117.50/117.94 { vmul( X, vsucc( Y ) ) = vplus( vmul( X, Y ), X ) }.
% 117.50/117.94 { vmul( X, v1 ) = X }.
% 117.50/117.94 { ! less( X, vplus( Y, v1 ) ), leq( X, Y ) }.
% 117.50/117.94 { ! greater( X, Y ), geq( X, vplus( Y, v1 ) ) }.
% 117.50/117.94 { vplus( Y, X ) = vplus( X, Y ) }.
% 117.50/117.94 { vplus( vsucc( X ), Y ) = vsucc( vplus( X, Y ) ) }.
% 117.50/117.94 { vplus( v1, X ) = vsucc( X ) }.
% 117.50/117.94 { vplus( vplus( X, Y ), Z ) = vplus( X, vplus( Y, Z ) ) }.
% 117.50/117.94 { vplus( X, vsucc( Y ) ) = vsucc( vplus( X, Y ) ) }.
% 117.50/117.94 { vplus( X, v1 ) = vsucc( X ) }.
% 117.50/117.94 { X = v1, X = vsucc( vskolem2( X ) ) }.
% 117.50/117.94 { ! vsucc( X ) = X }.
% 117.50/117.94 { X = Y, ! vsucc( X ) = vsucc( Y ) }.
% 117.50/117.94
% 117.50/117.94 percentage equality = 0.846154, percentage horn = 0.954545
% 117.50/117.94 This is a pure equality problem
% 117.50/117.94
% 117.50/117.94
% 117.50/117.94
% 117.50/117.94 Options Used:
% 117.50/117.94
% 117.50/117.94 useres = 1
% 117.50/117.94 useparamod = 1
% 117.50/117.94 useeqrefl = 1
% 117.50/117.94 useeqfact = 1
% 117.50/117.94 usefactor = 1
% 117.50/117.94 usesimpsplitting = 0
% 117.50/117.94 usesimpdemod = 5
% 117.50/117.94 usesimpres = 3
% 117.50/117.94
% 117.50/117.94 resimpinuse = 1000
% 117.50/117.94 resimpclauses = 20000
% 117.50/117.94 substype = eqrewr
% 117.50/117.94 backwardsubs = 1
% 117.50/117.94 selectoldest = 5
% 117.50/117.94
% 117.50/117.94 litorderings [0] = split
% 117.50/117.94 litorderings [1] = extend the termordering, first sorting on arguments
% 117.50/117.94
% 117.50/117.94 termordering = kbo
% 117.50/117.94
% 117.50/117.94 litapriori = 0
% 117.50/117.94 termapriori = 1
% 117.50/117.94 litaposteriori = 0
% 117.50/117.94 termaposteriori = 0
% 117.50/117.94 demodaposteriori = 0
% 117.50/117.94 ordereqreflfact = 0
% 117.50/117.94
% 117.50/117.94 litselect = negord
% 117.50/117.94
% 117.50/117.94 maxweight = 15
% 117.50/117.94 maxdepth = 30000
% 117.50/117.94 maxlength = 115
% 117.50/117.94 maxnrvars = 195
% 117.50/117.94 excuselevel = 1
% 117.50/117.94 increasemaxweight = 1
% 117.50/117.94
% 117.50/117.94 maxselected = 10000000
% 117.50/117.94 maxnrclauses = 10000000
% 117.50/117.94
% 117.50/117.94 showgenerated = 0
% 117.50/117.94 showkept = 0
% 117.50/117.94 showselected = 0
% 117.50/117.94 showdeleted = 0
% 117.50/117.94 showresimp = 1
% 117.50/117.94 showstatus = 2000
% 117.50/117.94
% 117.50/117.94 prologoutput = 0
% 117.50/117.94 nrgoals = 5000000
% 117.50/117.94 totalproof = 1
% 117.50/117.94
% 117.50/117.94 Symbols occurring in the translation:
% 117.50/117.94
% 117.50/117.94 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 117.50/117.94 . [1, 2] (w:1, o:37, a:1, s:1, b:0),
% 117.50/117.94 ! [4, 1] (w:0, o:30, a:1, s:1, b:0),
% 117.50/117.94 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 117.50/117.94 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 117.50/117.94 vd411 [35, 0] (w:1, o:6, a:1, s:1, b:0),
% 117.50/117.94 vd413 [36, 0] (w:1, o:7, a:1, s:1, b:0),
% 117.50/117.94 vmul [37, 2] (w:1, o:61, a:1, s:1, b:0),
% 117.50/117.94 vsucc [38, 1] (w:1, o:35, a:1, s:1, b:0),
% 117.50/117.94 vplus [39, 2] (w:1, o:62, a:1, s:1, b:0),
% 117.50/117.94 v1 [40, 0] (w:1, o:8, a:1, s:1, b:0),
% 117.50/117.94 less [46, 2] (w:1, o:63, a:1, s:1, b:0),
% 117.50/117.94 leq [47, 2] (w:1, o:64, a:1, s:1, b:0),
% 117.50/117.94 greater [50, 2] (w:1, o:65, a:1, s:1, b:0),
% 117.50/117.94 geq [51, 2] (w:1, o:66, a:1, s:1, b:0),
% 117.50/117.94 vskolem2 [63, 1] (w:1, o:36, a:1, s:1, b:0).
% 117.50/117.94
% 117.50/117.94
% 117.50/117.94 Starting Search:
% 117.50/117.94
% 117.50/117.94 *** allocated 15000 integers for clauses
% 117.50/117.94 *** allocated 22500 integers for clauses
% 117.50/117.94 *** allocated 33750 integers for clauses
% 117.50/117.94 *** allocated 50625 integers for clauses
% 117.50/117.94 *** allocated 15000 integers for termspace/termends
% 117.50/117.94 *** allocated 22500 integers for termspace/termends
% 117.50/117.94 *** allocated 75937 integers for clauses
% 117.50/117.94 Resimplifying inuse:
% 117.50/117.94 Done
% 117.50/117.94
% 117.50/117.94 *** allocated 33750 integers for termspace/termends
% 117.50/117.94 *** allocated 113905 integers for clauses
% 117.50/117.94
% 117.50/117.94 Intermediate Status:
% 117.50/117.94 Generated: 37785
% 117.50/117.94 Kept: 2006
% 117.50/117.94 Inuse: 156
% 117.50/117.94 Deleted: 50
% 117.50/117.94 Deletedinuse: 16
% 117.50/117.94
% 117.50/117.94 Resimplifying inuse:
% 117.50/117.94 Done
% 117.50/117.94
% 117.50/117.94 *** allocated 50625 integers for termspace/termends
% 117.50/117.94 *** allocated 170857 integers for clauses
% 117.50/117.94 Resimplifying inuse:
% 117.50/117.94 Done
% 117.50/117.94
% 117.50/117.94 *** allocated 75937 integers for termspace/termends
% 117.50/117.94 *** allocated 256285 integers for clauses
% 117.50/117.94
% 117.50/117.94 Intermediate Status:
% 117.50/117.94 Generated: 120850
% 117.50/117.94 Kept: 4012
% 117.50/117.94 Inuse: 289
% 117.50/117.94 Deleted: 142
% 117.50/117.94 Deletedinuse: 62
% 117.50/117.94
% 117.50/117.94 Resimplifying inuse:
% 117.50/117.94 Done
% 117.50/117.94
% 117.50/117.94 *** allocated 113905 integers for termspace/termends
% 117.50/117.94 Resimplifying inuse:
% 117.50/117.94 Done
% 117.50/117.94
% 117.50/117.94 *** allocated 384427 integers for clauses
% 117.50/117.94
% 117.50/117.94 Intermediate Status:
% 117.50/117.94 Generated: 215059
% 117.50/117.94 Kept: 6019
% 117.50/117.94 Inuse: 396
% 117.50/117.94 Deleted: 181
% 117.50/117.94 Deletedinuse: 64
% 117.50/117.94
% 117.50/117.94 Resimplifying inuse:
% 117.50/117.94 Done
% 117.50/117.94
% 117.50/117.94 *** allocated 170857 integers for termspace/termends
% 117.50/117.94 Resimplifying inuse:
% 117.50/117.94 Done
% 117.50/117.94
% 117.50/117.94
% 117.50/117.94 Intermediate Status:
% 117.50/117.94 Generated: 274095
% 117.50/117.94 Kept: 8043
% 117.50/117.94 Inuse: 462
% 117.50/117.94 Deleted: 195
% 117.50/117.94 Deletedinuse: 65
% 117.50/117.94
% 117.50/117.94 Resimplifying inuse:
% 117.50/117.94 Done
% 117.50/117.94
% 117.50/117.94 *** allocated 576640 integers for clauses
% 117.50/117.94 Resimplifying inuse:
% 117.50/117.94 Done
% 117.50/117.94
% 117.50/117.94
% 117.50/117.94 Intermediate Status:
% 117.50/117.94 Generated: 405730
% 117.50/117.94 Kept: 10189
% 117.50/117.94 Inuse: 610
% 117.50/117.94 Deleted: 237
% 117.50/117.94 Deletedinuse: 65
% 117.50/117.94
% 117.50/117.94 Resimplifying inuse:
% 117.50/117.94 Done
% 117.50/117.94
% 117.50/117.94 *** allocated 256285 integers for termspace/termends
% 117.50/117.94 Resimplifying inuse:
% 117.50/117.94 Done
% 117.50/117.94
% 117.50/117.94
% 117.50/117.94 Intermediate Status:
% 117.50/117.94 Generated: 478114
% 117.50/117.94 Kept: 12199
% 117.50/117.94 Inuse: 678
% 117.50/117.94 Deleted: 359
% 117.50/117.94 Deletedinuse: 175
% 117.50/117.94
% 117.50/117.94 Resimplifying inuse:
% 117.50/117.94 Done
% 117.50/117.94
% 117.50/117.94 *** allocated 864960 integers for clauses
% 117.50/117.94 Resimplifying inuse:
% 117.50/117.94 Done
% 117.50/117.94
% 117.50/117.94
% 117.50/117.94 Intermediate Status:
% 117.50/117.94 Generated: 620413
% 117.50/117.94 Kept: 14201
% 117.50/117.94 Inuse: 789
% 117.50/117.94 Deleted: 373
% 117.50/117.94 Deletedinuse: 177
% 117.50/117.94
% 117.50/117.94 Resimplifying inuse:
% 117.50/117.94 Done
% 117.50/117.94
% 117.50/117.94 Resimplifying inuse:
% 117.50/117.94 Done
% 117.50/117.94
% 117.50/117.94 *** allocated 384427 integers for termspace/termends
% 117.50/117.94
% 117.50/117.94 Intermediate Status:
% 117.50/117.94 Generated: 730980
% 117.50/117.94 Kept: 16213
% 117.50/117.94 Inuse: 875
% 117.50/117.94 Deleted: 393
% 117.50/117.94 Deletedinuse: 179
% 117.50/117.94
% 117.50/117.94 Resimplifying inuse:
% 117.50/117.94 Done
% 117.50/117.94
% 117.50/117.94 Resimplifying inuse:
% 117.50/117.94 Done
% 117.50/117.94
% 117.50/117.94
% 117.50/117.94 Intermediate Status:
% 117.50/117.94 Generated: 924099
% 117.50/117.94 Kept: 18219
% 117.50/117.94 Inuse: 982
% 117.50/117.94 Deleted: 409
% 117.50/117.94 Deletedinuse: 181
% 117.50/117.94
% 117.50/117.94 Resimplifying inuse:
% 117.50/117.94 Done
% 117.50/117.94
% 117.50/117.94
% 117.50/117.94 Bliksems!, er is een bewijs:
% 117.50/117.94 % SZS status Theorem
% 117.50/117.94 % SZS output start Refutation
% 117.50/117.94
% 117.50/117.94 (0) {G0,W17,D5,L1,V0,M1} I { ! vplus( vmul( vd411, vd413 ), vplus( vd413,
% 117.50/117.94 vsucc( vd411 ) ) ) ==> vplus( vmul( vd411, vd413 ), vplus( vsucc( vd411 )
% 117.50/117.94 , vd413 ) ) }.
% 117.50/117.94 (1) {G0,W17,D5,L1,V0,M1} I { vplus( vmul( vd411, vd413 ), vplus( vd413,
% 117.50/117.94 vsucc( vd411 ) ) ) ==> vplus( vplus( vmul( vd411, vd413 ), vd413 ), vsucc
% 117.50/117.94 ( vd411 ) ) }.
% 117.50/117.94 (2) {G0,W16,D5,L1,V0,M1} I { vplus( vplus( vmul( vd411, vd413 ), vd413 ),
% 117.50/117.94 vsucc( vd411 ) ) ==> vplus( vmul( vsucc( vd411 ), vd413 ), vsucc( vd411 )
% 117.50/117.94 ) }.
% 117.50/117.94 (3) {G0,W13,D5,L1,V0,M1} I { vplus( vmul( vsucc( vd411 ), vd413 ), vsucc(
% 117.50/117.94 vd411 ) ) ==> vmul( vsucc( vd411 ), vsucc( vd413 ) ) }.
% 117.50/117.94 (4) {G0,W10,D4,L1,V0,M1} I { vplus( vmul( vd411, vd413 ), vd413 ) ==> vmul
% 117.50/117.94 ( vsucc( vd411 ), vd413 ) }.
% 117.50/117.94 (8) {G0,W5,D3,L1,V1,M1} I { vmul( v1, X ) ==> X }.
% 117.50/117.94 (9) {G0,W10,D4,L1,V2,M1} I { vplus( vmul( X, Y ), X ) ==> vmul( X, vsucc( Y
% 117.50/117.94 ) ) }.
% 117.50/117.94 (10) {G0,W5,D3,L1,V1,M1} I { vmul( X, v1 ) ==> X }.
% 117.50/117.94 (13) {G0,W7,D3,L1,V2,M1} I { vplus( Y, X ) = vplus( X, Y ) }.
% 117.50/117.94 (14) {G0,W9,D4,L1,V2,M1} I { vplus( vsucc( X ), Y ) ==> vsucc( vplus( X, Y
% 117.50/117.94 ) ) }.
% 117.50/117.94 (16) {G0,W11,D4,L1,V3,M1} I { vplus( X, vplus( Y, Z ) ) ==> vplus( vplus( X
% 117.50/117.94 , Y ), Z ) }.
% 117.50/117.94 (17) {G0,W9,D4,L1,V2,M1} I { vplus( X, vsucc( Y ) ) ==> vsucc( vplus( X, Y
% 117.50/117.94 ) ) }.
% 117.50/117.94 (18) {G0,W6,D3,L1,V1,M1} I { vplus( X, v1 ) ==> vsucc( X ) }.
% 117.50/117.94 (19) {G0,W8,D4,L2,V1,M2} I { X = v1, vsucc( vskolem2( X ) ) ==> X }.
% 117.50/117.94 (20) {G0,W4,D3,L1,V1,M1} I { ! vsucc( X ) ==> X }.
% 117.50/117.94 (21) {G0,W8,D3,L2,V2,M2} I { X = Y, ! vsucc( X ) = vsucc( Y ) }.
% 117.50/117.94 (22) {G1,W13,D6,L1,V0,M1} S(0);d(1);d(2);d(3);d(16);d(17);d(14);d(9) { !
% 117.50/117.94 vsucc( vplus( vmul( vd411, vsucc( vd413 ) ), vd413 ) ) ==> vmul( vsucc(
% 117.50/117.94 vd411 ), vsucc( vd413 ) ) }.
% 117.50/117.94 (27) {G1,W11,D3,L2,V2,M2} P(21,18) { vplus( Y, X ) ==> vsucc( Y ), ! vsucc
% 117.50/117.94 ( v1 ) = vsucc( X ) }.
% 117.50/117.94 (44) {G1,W11,D3,L3,V2,M3} P(21,19);d(19) { X = v1, vsucc( Y ) = X, ! X =
% 117.50/117.94 vsucc( Y ) }.
% 117.50/117.94 (45) {G1,W11,D3,L3,V2,M3} P(19,21) { vskolem2( X ) = Y, ! X = vsucc( Y ), X
% 117.50/117.94 = v1 }.
% 117.50/117.94 (51) {G1,W10,D5,L2,V1,M2} P(19,20) { ! v1 = X, vsucc( vskolem2( vsucc( X )
% 117.50/117.94 ) ) ==> vsucc( X ) }.
% 117.50/117.94 (53) {G2,W7,D5,L1,V0,M1} Q(51) { vsucc( vskolem2( vsucc( v1 ) ) ) ==> vsucc
% 117.50/117.94 ( v1 ) }.
% 117.50/117.94 (54) {G2,W9,D4,L2,V1,M2} Q(45) { vskolem2( vsucc( X ) ) ==> X, vsucc( X )
% 117.50/117.94 ==> v1 }.
% 117.50/117.94 (58) {G2,W8,D3,L2,V1,M2} E(44);f { ! vsucc( X ) ==> v1, vsucc( X ) ==> v1
% 117.50/117.94 }.
% 117.50/117.94 (91) {G3,W10,D4,L2,V1,M2} P(53,21) { vskolem2( vsucc( v1 ) ) = X, ! vsucc(
% 117.50/117.94 v1 ) = vsucc( X ) }.
% 117.50/117.94 (92) {G4,W5,D4,L1,V0,M1} Q(91) { vskolem2( vsucc( v1 ) ) ==> v1 }.
% 117.50/117.94 (96) {G3,W9,D2,L3,V1,M3} P(58,19);d(19) { X = v1, v1 = X, ! X = v1 }.
% 117.50/117.94 (101) {G4,W6,D2,L2,V1,M2} E(96);q { v1 = X, ! X = v1 }.
% 117.50/117.94 (102) {G5,W9,D2,L3,V2,M3} P(101,101) { X = Y, ! Y = X, ! X = v1 }.
% 117.50/117.94 (106) {G5,W11,D4,L3,V2,M3} P(101,19) { Y = X, vsucc( vskolem2( Y ) ) ==> Y
% 117.50/117.94 , ! X = v1 }.
% 117.50/117.94 (113) {G5,W8,D3,L2,V2,M2} P(101,8) { vmul( X, Y ) ==> Y, ! X = v1 }.
% 117.50/117.94 (114) {G5,W8,D3,L2,V2,M2} P(101,10) { vmul( Y, X ) ==> Y, ! X = v1 }.
% 117.50/117.94 (131) {G1,W10,D4,L1,V0,M1} P(4,13) { vplus( vd413, vmul( vd411, vd413 ) )
% 117.50/117.94 ==> vmul( vsucc( vd411 ), vd413 ) }.
% 117.50/117.94 (144) {G6,W9,D2,L3,V2,M3} P(114,113) { X = Y, ! X = v1, ! Y = v1 }.
% 117.50/117.94 (165) {G7,W8,D3,L2,V1,M2} P(144,53);d(92);q { vsucc( X ) = vsucc( v1 ), ! X
% 117.50/117.94 = v1 }.
% 117.50/117.94 (188) {G8,W11,D3,L3,V2,M3} P(165,21) { v1 = Y, ! vsucc( X ) = vsucc( Y ), !
% 117.50/117.94 X = v1 }.
% 117.50/117.94 (214) {G1,W8,D4,L1,V1,M1} P(10,9) { vplus( X, X ) = vmul( X, vsucc( v1 ) )
% 117.50/117.94 }.
% 117.50/117.94 (240) {G2,W11,D5,L1,V1,M1} P(14,214);d(17) { vsucc( vsucc( vplus( X, X ) )
% 117.50/117.94 ) = vmul( vsucc( X ), vsucc( v1 ) ) }.
% 117.50/117.94 (244) {G1,W12,D5,L2,V2,M2} P(19,14) { vsucc( vplus( vskolem2( X ), Y ) )
% 117.50/117.94 ==> vplus( X, Y ), X = v1 }.
% 117.50/117.94 (246) {G1,W9,D4,L1,V2,M1} P(14,13);d(17) { vsucc( vplus( X, Y ) ) = vsucc(
% 117.50/117.94 vplus( Y, X ) ) }.
% 117.50/117.94 (279) {G1,W14,D5,L1,V3,M1} P(9,16) { vplus( vplus( Z, vmul( X, Y ) ), X )
% 117.50/117.94 ==> vplus( Z, vmul( X, vsucc( Y ) ) ) }.
% 117.50/117.94 (320) {G1,W13,D6,L1,V2,M1} P(17,9) { vsucc( vplus( vmul( vsucc( X ), Y ), X
% 117.50/117.94 ) ) ==> vmul( vsucc( X ), vsucc( Y ) ) }.
% 117.50/117.94 (323) {G1,W14,D5,L2,V2,M2} P(19,17);d(18) { vsucc( vskolem2( vsucc( X ) ) )
% 117.50/117.94 ==> vsucc( X ), vsucc( vplus( Y, X ) ) ==> vsucc( Y ) }.
% 117.50/117.94 (403) {G2,W7,D5,L1,V0,M1} P(19,22);d(323);d(10);d(10);q { vsucc( vskolem2(
% 117.50/117.94 vsucc( vd413 ) ) ) ==> vsucc( vd413 ) }.
% 117.50/117.94 (499) {G3,W10,D4,L2,V1,M2} P(403,21) { vskolem2( vsucc( vd413 ) ) = X, !
% 117.50/117.94 vsucc( vd413 ) = vsucc( X ) }.
% 117.50/117.94 (500) {G4,W5,D4,L1,V0,M1} Q(499) { vskolem2( vsucc( vd413 ) ) ==> vd413 }.
% 117.50/117.94 (674) {G3,W12,D4,L3,V2,M3} P(54,21) { X = Y, ! vsucc( Y ) ==> v1, vskolem2
% 117.50/117.94 ( vsucc( X ) ) ==> X }.
% 117.50/117.94 (675) {G4,W10,D4,L2,V1,M2} E(674);q;d(54) { vskolem2( vsucc( X ) ) ==> X, !
% 117.50/117.94 vsucc( vskolem2( v1 ) ) ==> v1 }.
% 117.50/117.94 (1329) {G5,W12,D5,L2,V1,M2} R(675,54) { vskolem2( vsucc( X ) ) ==> X,
% 117.50/117.94 vskolem2( vsucc( vskolem2( v1 ) ) ) ==> vskolem2( v1 ) }.
% 117.50/117.94 (1338) {G6,W7,D5,L1,V0,M1} F(1329) { vskolem2( vsucc( vskolem2( v1 ) ) )
% 117.50/117.94 ==> vskolem2( v1 ) }.
% 117.50/117.94 (1356) {G7,W10,D5,L2,V1,M2} P(102,1338);q { vskolem2( vsucc( vskolem2( X )
% 117.50/117.94 ) ) ==> vskolem2( X ), ! X = v1 }.
% 117.50/117.94 (1371) {G6,W14,D3,L4,V3,M4} R(44,102) { vsucc( X ) = Y, ! Y = vsucc( X ), Y
% 117.50/117.94 = Z, ! Z = Y }.
% 117.50/117.94 (1400) {G7,W8,D3,L2,V2,M2} E(1371);q;f { ! X = vsucc( Y ), vsucc( Y ) = X
% 117.50/117.94 }.
% 117.50/117.94 (1463) {G8,W9,D2,L3,V2,M3} P(19,1400) { ! Y = X, X = Y, X = v1 }.
% 117.50/117.94 (1470) {G8,W7,D3,L2,V2,M2} P(1400,20) { ! Y = X, ! Y = vsucc( X ) }.
% 117.50/117.94 (1473) {G9,W9,D2,L3,V2,M3} E(1463) { ! X = v1, ! X = Y, Y = v1 }.
% 117.50/117.94 (1505) {G10,W11,D3,L3,V2,M3} R(1473,165) { ! X = v1, ! X = Y, vsucc( Y ) =
% 117.50/117.94 vsucc( v1 ) }.
% 117.50/117.94 (1534) {G10,W14,D4,L4,V3,M4} P(1473,19) { Y = X, vsucc( vskolem2( Y ) ) ==>
% 117.50/117.94 Y, ! Z = v1, ! Z = X }.
% 117.50/117.94 (1536) {G11,W13,D4,L3,V2,M3} E(1534);q { vsucc( vskolem2( X ) ) ==> X, ! Y
% 117.50/117.94 = v1, ! Y = vsucc( vskolem2( X ) ) }.
% 117.50/117.94 (1537) {G12,W10,D4,L2,V1,M2} Q(1536) { vsucc( vskolem2( X ) ) ==> X, !
% 117.50/117.94 vsucc( vskolem2( X ) ) ==> v1 }.
% 117.50/117.94 (1550) {G9,W12,D2,L4,V3,M4} R(1463,102) { ! X = Y, Y = X, Y = Z, ! Z = Y
% 117.50/117.94 }.
% 117.50/117.94 (1593) {G10,W6,D2,L2,V2,M2} F(1550);f { ! X = Y, Y = X }.
% 117.50/117.94 (1627) {G2,W14,D3,L4,V2,M4} P(19,45) { vskolem2( Y ) = vskolem2( X ), ! Y =
% 117.50/117.94 X, Y = v1, X = v1 }.
% 117.50/117.94 (1628) {G3,W11,D3,L3,V2,M3} E(1627);f { ! X = Y, vskolem2( X ) = vskolem2(
% 117.50/117.94 Y ), Y = v1 }.
% 117.50/117.94 (1669) {G11,W11,D3,L3,V2,M3} P(1593,19) { X = v1, vsucc( Y ) = X, ! Y =
% 117.50/117.94 vskolem2( X ) }.
% 117.50/117.94 (1672) {G12,W11,D3,L3,V2,M3} E(1669) { ! vsucc( X ) ==> v1, Y = v1, ! X =
% 117.50/117.94 vskolem2( Y ) }.
% 117.50/117.94 (1930) {G13,W11,D4,L3,V2,M3} P(144,1537);r(102) { Y = X, ! Y = v1, ! vsucc
% 117.50/117.94 ( vskolem2( X ) ) ==> v1 }.
% 117.50/117.94 (2204) {G13,W15,D5,L3,V2,M3} R(1672,1356) { ! vsucc( X ) ==> v1, ! X =
% 117.50/117.94 vskolem2( Y ), vskolem2( vsucc( vskolem2( Y ) ) ) ==> vskolem2( Y ) }.
% 117.50/117.94 (2253) {G14,W7,D5,L1,V1,M1} Q(2204);d(54);q { vskolem2( vsucc( vskolem2( X
% 117.50/117.94 ) ) ) ==> vskolem2( X ) }.
% 117.50/117.94 (2262) {G15,W10,D4,L2,V2,M2} P(1593,2253) { vskolem2( Y ) = vskolem2( X ),
% 117.50/117.94 ! Y = vsucc( vskolem2( X ) ) }.
% 117.50/117.94 (2304) {G16,W11,D4,L2,V2,M2} R(2262,1470) { ! X = vsucc( vskolem2( Y ) ), !
% 117.50/117.94 vskolem2( X ) = vsucc( vskolem2( Y ) ) }.
% 117.50/117.94 (3757) {G17,W14,D4,L3,V2,M3} R(2304,106);d(1537) { vsucc( vskolem2( X ) )
% 117.50/117.94 ==> X, ! vsucc( vskolem2( Y ) ) ==> v1, ! vskolem2( X ) = Y }.
% 117.50/117.94 (3777) {G18,W11,D5,L2,V1,M2} Q(3757) { vsucc( vskolem2( X ) ) ==> X, !
% 117.50/117.94 vsucc( vskolem2( vskolem2( X ) ) ) ==> v1 }.
% 117.50/117.94 (5753) {G3,W12,D6,L1,V1,M1} P(214,240) { vsucc( vsucc( vmul( X, vsucc( v1 )
% 117.50/117.94 ) ) ) ==> vmul( vsucc( X ), vsucc( v1 ) ) }.
% 117.50/117.94 (6074) {G19,W13,D5,L3,V2,M3} P(3777,1505);r(1930) { ! Y = v1, X = vsucc( v1
% 117.50/117.94 ), ! vsucc( vskolem2( vskolem2( X ) ) ) ==> v1 }.
% 117.50/117.94 (6088) {G20,W10,D5,L2,V1,M2} Q(6074) { X = vsucc( v1 ), ! vsucc( vskolem2(
% 117.50/117.94 vskolem2( X ) ) ) ==> v1 }.
% 117.50/117.94 (6214) {G21,W13,D6,L2,V2,M2} P(6088,27);q { vplus( Y, X ) ==> vsucc( Y ), !
% 117.50/117.94 vsucc( vskolem2( vskolem2( vsucc( X ) ) ) ) ==> v1 }.
% 117.50/117.94 (6220) {G22,W5,D4,L1,V0,M1} P(6088,22);d(6214);d(500);d(5753);q { ! vsucc(
% 117.50/117.94 vskolem2( vd413 ) ) ==> v1 }.
% 117.50/117.94 (6267) {G23,W10,D5,L2,V1,M2} P(188,6220);q { ! vsucc( X ) = vsucc( vsucc(
% 117.50/117.94 vskolem2( vd413 ) ) ), ! X = v1 }.
% 117.50/117.94 (9990) {G4,W9,D5,L1,V1,M1} P(244,22);d(18);d(5753);q { vsucc( vplus(
% 117.50/117.94 vskolem2( vd413 ), X ) ) ==> vplus( vd413, X ) }.
% 117.50/117.94 (10172) {G5,W9,D5,L1,V1,M1} P(9990,246) { vsucc( vplus( X, vskolem2( vd413
% 117.50/117.94 ) ) ) ==> vplus( vd413, X ) }.
% 117.50/117.94 (10184) {G5,W7,D5,L1,V0,M1} P(18,9990);d(18) { vsucc( vsucc( vskolem2(
% 117.50/117.94 vd413 ) ) ) ==> vsucc( vd413 ) }.
% 117.50/117.94 (10190) {G24,W8,D3,L2,V1,M2} S(6267);d(10184) { ! X = v1, ! vsucc( X ) =
% 117.50/117.94 vsucc( vd413 ) }.
% 117.50/117.94 (10193) {G25,W3,D2,L1,V0,M1} Q(10190) { ! v1 ==> vd413 }.
% 117.50/117.94 (10205) {G26,W8,D4,L2,V1,M2} P(106,10193);q { ! X = vd413, vsucc( vskolem2
% 117.50/117.94 ( X ) ) ==> X }.
% 117.50/117.94 (10206) {G26,W11,D3,L3,V2,M3} P(1628,10193) { ! X = vd413, ! Y = X,
% 117.50/117.94 vskolem2( Y ) = vskolem2( X ) }.
% 117.50/117.94 (10224) {G27,W8,D3,L2,V1,M2} Q(10206) { ! X = vd413, vskolem2( X ) =
% 117.50/117.94 vskolem2( vd413 ) }.
% 117.50/117.94 (11020) {G27,W12,D5,L2,V2,M2} P(10205,17) { vsucc( vplus( Y, vskolem2( X )
% 117.50/117.94 ) ) ==> vplus( Y, X ), ! X = vd413 }.
% 117.50/117.94 (11080) {G28,W10,D3,L2,V2,M2} P(10224,10172);d(11020) { ! X = vd413, vplus
% 117.50/117.94 ( Y, X ) = vplus( vd413, Y ) }.
% 117.50/117.94 (11246) {G29,W12,D3,L2,V2,M2} R(11080,21) { vplus( X, Y ) = vplus( vd413, X
% 117.50/117.94 ), ! vsucc( Y ) = vsucc( vd413 ) }.
% 117.50/117.94 (12948) {G2,W13,D5,L1,V0,M1} P(131,279) { vplus( vd413, vmul( vd411, vsucc
% 117.50/117.94 ( vd413 ) ) ) ==> vplus( vmul( vsucc( vd411 ), vd413 ), vd411 ) }.
% 117.50/117.94 (19152) {G30,W0,D0,L0,V0,M0} P(11246,22);q;d(12948);d(320);q { }.
% 117.50/117.94
% 117.50/117.94
% 117.50/117.94 % SZS output end Refutation
% 117.50/117.94 found a proof!
% 117.50/117.94
% 117.50/117.94
% 117.50/117.94 Unprocessed initial clauses:
% 117.50/117.94
% 117.50/117.94 (19154) {G0,W17,D5,L1,V0,M1} { ! vplus( vmul( vd411, vd413 ), vplus( vd413
% 117.50/117.94 , vsucc( vd411 ) ) ) = vplus( vmul( vd411, vd413 ), vplus( vsucc( vd411 )
% 117.50/117.94 , vd413 ) ) }.
% 117.50/117.94 (19155) {G0,W17,D5,L1,V0,M1} { vplus( vplus( vmul( vd411, vd413 ), vd413 )
% 117.50/117.94 , vsucc( vd411 ) ) = vplus( vmul( vd411, vd413 ), vplus( vd413, vsucc(
% 117.50/117.94 vd411 ) ) ) }.
% 117.50/117.94 (19156) {G0,W16,D5,L1,V0,M1} { vplus( vmul( vsucc( vd411 ), vd413 ), vsucc
% 117.50/117.94 ( vd411 ) ) = vplus( vplus( vmul( vd411, vd413 ), vd413 ), vsucc( vd411 )
% 117.50/117.94 ) }.
% 117.50/117.94 (19157) {G0,W13,D5,L1,V0,M1} { vmul( vsucc( vd411 ), vsucc( vd413 ) ) =
% 117.50/117.94 vplus( vmul( vsucc( vd411 ), vd413 ), vsucc( vd411 ) ) }.
% 117.50/117.94 (19158) {G0,W10,D4,L1,V0,M1} { vmul( vsucc( vd411 ), vd413 ) = vplus( vmul
% 117.50/117.94 ( vd411, vd413 ), vd413 ) }.
% 117.50/117.94 (19159) {G0,W10,D4,L1,V0,M1} { vsucc( vmul( vd411, v1 ) ) = vplus( vmul(
% 117.50/117.94 vd411, v1 ), v1 ) }.
% 117.50/117.94 (19160) {G0,W7,D4,L1,V0,M1} { vsucc( vd411 ) = vsucc( vmul( vd411, v1 ) )
% 117.50/117.94 }.
% 117.50/117.94 (19161) {G0,W7,D4,L1,V0,M1} { vmul( vsucc( vd411 ), v1 ) = vsucc( vd411 )
% 117.50/117.94 }.
% 117.50/117.94 (19162) {G0,W5,D3,L1,V1,M1} { vmul( v1, X ) = X }.
% 117.50/117.94 (19163) {G0,W10,D4,L1,V2,M1} { vmul( X, vsucc( Y ) ) = vplus( vmul( X, Y )
% 117.50/117.94 , X ) }.
% 117.50/117.94 (19164) {G0,W5,D3,L1,V1,M1} { vmul( X, v1 ) = X }.
% 117.50/117.94 (19165) {G0,W8,D3,L2,V2,M2} { ! less( X, vplus( Y, v1 ) ), leq( X, Y ) }.
% 117.50/117.94 (19166) {G0,W8,D3,L2,V2,M2} { ! greater( X, Y ), geq( X, vplus( Y, v1 ) )
% 117.50/117.94 }.
% 117.50/117.94 (19167) {G0,W7,D3,L1,V2,M1} { vplus( Y, X ) = vplus( X, Y ) }.
% 117.50/117.94 (19168) {G0,W9,D4,L1,V2,M1} { vplus( vsucc( X ), Y ) = vsucc( vplus( X, Y
% 117.50/117.94 ) ) }.
% 117.50/117.94 (19169) {G0,W6,D3,L1,V1,M1} { vplus( v1, X ) = vsucc( X ) }.
% 117.50/117.94 (19170) {G0,W11,D4,L1,V3,M1} { vplus( vplus( X, Y ), Z ) = vplus( X, vplus
% 117.50/117.94 ( Y, Z ) ) }.
% 117.50/117.94 (19171) {G0,W9,D4,L1,V2,M1} { vplus( X, vsucc( Y ) ) = vsucc( vplus( X, Y
% 117.50/117.94 ) ) }.
% 117.50/117.94 (19172) {G0,W6,D3,L1,V1,M1} { vplus( X, v1 ) = vsucc( X ) }.
% 117.50/117.94 (19173) {G0,W8,D4,L2,V1,M2} { X = v1, X = vsucc( vskolem2( X ) ) }.
% 117.50/117.94 (19174) {G0,W4,D3,L1,V1,M1} { ! vsucc( X ) = X }.
% 117.50/117.94 (19175) {G0,W8,D3,L2,V2,M2} { X = Y, ! vsucc( X ) = vsucc( Y ) }.
% 117.50/117.94
% 117.50/117.94
% 117.50/117.94 Total Proof:
% 117.50/117.94
% 117.50/117.94 subsumption: (0) {G0,W17,D5,L1,V0,M1} I { ! vplus( vmul( vd411, vd413 ),
% 117.50/117.94 vplus( vd413, vsucc( vd411 ) ) ) ==> vplus( vmul( vd411, vd413 ), vplus(
% 117.50/117.94 vsucc( vd411 ), vd413 ) ) }.
% 117.50/117.94 parent0: (19154) {G0,W17,D5,L1,V0,M1} { ! vplus( vmul( vd411, vd413 ),
% 117.50/117.94 vplus( vd413, vsucc( vd411 ) ) ) = vplus( vmul( vd411, vd413 ), vplus(
% 117.50/117.94 vsucc( vd411 ), vd413 ) ) }.
% 117.50/117.94 substitution0:
% 117.50/117.94 end
% 117.50/117.94 permutation0:
% 117.50/117.94 0 ==> 0
% 117.50/117.94 end
% 117.50/117.94
% 117.50/117.94 eqswap: (19178) {G0,W17,D5,L1,V0,M1} { vplus( vmul( vd411, vd413 ), vplus
% 117.50/117.94 ( vd413, vsucc( vd411 ) ) ) = vplus( vplus( vmul( vd411, vd413 ), vd413 )
% 117.50/117.94 , vsucc( vd411 ) ) }.
% 117.50/117.94 parent0[0]: (19155) {G0,W17,D5,L1,V0,M1} { vplus( vplus( vmul( vd411,
% 117.50/117.94 vd413 ), vd413 ), vsucc( vd411 ) ) = vplus( vmul( vd411, vd413 ), vplus(
% 117.50/117.94 vd413, vsucc( vd411 ) ) ) }.
% 117.50/117.94 substitution0:
% 117.50/117.94 end
% 117.50/117.94
% 117.50/117.94 subsumption: (1) {G0,W17,D5,L1,V0,M1} I { vplus( vmul( vd411, vd413 ),
% 117.50/117.94 vplus( vd413, vsucc( vd411 ) ) ) ==> vplus( vplus( vmul( vd411, vd413 ),
% 117.50/117.94 vd413 ), vsucc( vd411 ) ) }.
% 117.50/117.94 parent0: (19178) {G0,W17,D5,L1,V0,M1} { vplus( vmul( vd411, vd413 ), vplus
% 117.50/117.94 ( vd413, vsucc( vd411 ) ) ) = vplus( vplus( vmul( vd411, vd413 ), vd413 )
% 117.50/117.94 , vsucc( vd411 ) ) }.
% 117.50/117.94 substitution0:
% 117.50/117.94 end
% 117.50/117.94 permutation0:
% 117.50/117.94 0 ==> 0
% 117.50/117.94 end
% 117.50/117.94
% 117.50/117.94 eqswap: (19181) {G0,W16,D5,L1,V0,M1} { vplus( vplus( vmul( vd411, vd413 )
% 117.50/117.94 , vd413 ), vsucc( vd411 ) ) = vplus( vmul( vsucc( vd411 ), vd413 ), vsucc
% 117.50/117.94 ( vd411 ) ) }.
% 117.50/117.94 parent0[0]: (19156) {G0,W16,D5,L1,V0,M1} { vplus( vmul( vsucc( vd411 ),
% 117.50/117.94 vd413 ), vsucc( vd411 ) ) = vplus( vplus( vmul( vd411, vd413 ), vd413 ),
% 117.50/117.94 vsucc( vd411 ) ) }.
% 117.50/117.94 substitution0:
% 117.50/117.94 end
% 117.50/117.94
% 117.50/117.94 subsumption: (2) {G0,W16,D5,L1,V0,M1} I { vplus( vplus( vmul( vd411, vd413
% 117.50/117.94 ), vd413 ), vsucc( vd411 ) ) ==> vplus( vmul( vsucc( vd411 ), vd413 ),
% 117.50/117.94 vsucc( vd411 ) ) }.
% 117.50/117.94 parent0: (19181) {G0,W16,D5,L1,V0,M1} { vplus( vplus( vmul( vd411, vd413 )
% 117.50/117.94 , vd413 ), vsucc( vd411 ) ) = vplus( vmul( vsucc( vd411 ), vd413 ), vsucc
% 117.50/117.94 ( vd411 ) ) }.
% 117.50/117.94 substitution0:
% 117.50/117.94 end
% 117.50/117.94 permutation0:
% 117.50/117.94 0 ==> 0
% 117.50/117.94 end
% 117.50/117.94
% 117.50/117.94 eqswap: (19185) {G0,W13,D5,L1,V0,M1} { vplus( vmul( vsucc( vd411 ), vd413
% 117.50/117.94 ), vsucc( vd411 ) ) = vmul( vsucc( vd411 ), vsucc( vd413 ) ) }.
% 117.50/117.94 parent0[0]: (19157) {G0,W13,D5,L1,V0,M1} { vmul( vsucc( vd411 ), vsucc(
% 117.50/117.94 vd413 ) ) = vplus( vmul( vsucc( vd411 ), vd413 ), vsucc( vd411 ) ) }.
% 117.50/117.94 substitution0:
% 117.50/117.94 end
% 117.50/117.94
% 117.50/117.94 subsumption: (3) {G0,W13,D5,L1,V0,M1} I { vplus( vmul( vsucc( vd411 ),
% 117.50/117.94 vd413 ), vsucc( vd411 ) ) ==> vmul( vsucc( vd411 ), vsucc( vd413 ) ) }.
% 117.50/117.94 parent0: (19185) {G0,W13,D5,L1,V0,M1} { vplus( vmul( vsucc( vd411 ), vd413
% 117.50/117.94 ), vsucc( vd411 ) ) = vmul( vsucc( vd411 ), vsucc( vd413 ) ) }.
% 117.50/117.94 substitution0:
% 117.50/117.94 end
% 117.50/117.94 permutation0:
% 117.50/117.94 0 ==> 0
% 117.50/117.94 end
% 117.50/117.94
% 117.50/117.94 eqswap: (19190) {G0,W10,D4,L1,V0,M1} { vplus( vmul( vd411, vd413 ), vd413
% 117.50/117.94 ) = vmul( vsucc( vd411 ), vd413 ) }.
% 117.50/117.94 parent0[0]: (19158) {G0,W10,D4,L1,V0,M1} { vmul( vsucc( vd411 ), vd413 ) =
% 117.50/117.94 vplus( vmul( vd411, vd413 ), vd413 ) }.
% 117.50/117.94 substitution0:
% 117.50/117.94 end
% 117.50/117.94
% 117.50/117.94 subsumption: (4) {G0,W10,D4,L1,V0,M1} I { vplus( vmul( vd411, vd413 ),
% 117.50/117.94 vd413 ) ==> vmul( vsucc( vd411 ), vd413 ) }.
% 117.50/117.94 parent0: (19190) {G0,W10,D4,L1,V0,M1} { vplus( vmul( vd411, vd413 ), vd413
% 117.50/117.94 ) = vmul( vsucc( vd411 ), vd413 ) }.
% 117.50/117.94 substitution0:
% 117.50/117.94 end
% 117.50/117.94 permutation0:
% 117.50/117.94 0 ==> 0
% 117.50/117.94 end
% 117.50/117.94
% 117.50/117.94 subsumption: (8) {G0,W5,D3,L1,V1,M1} I { vmul( v1, X ) ==> X }.
% 117.50/117.94 parent0: (19162) {G0,W5,D3,L1,V1,M1} { vmul( v1, X ) = X }.
% 117.50/117.94 substitution0:
% 117.50/117.94 X := X
% 117.50/117.94 end
% 117.50/117.94 permutation0:
% 117.50/117.94 0 ==> 0
% 117.50/117.94 end
% 117.50/117.94
% 117.50/117.94 eqswap: (19209) {G0,W10,D4,L1,V2,M1} { vplus( vmul( X, Y ), X ) = vmul( X
% 117.50/117.94 , vsucc( Y ) ) }.
% 117.50/117.94 parent0[0]: (19163) {G0,W10,D4,L1,V2,M1} { vmul( X, vsucc( Y ) ) = vplus(
% 117.50/117.94 vmul( X, Y ), X ) }.
% 117.50/117.94 substitution0:
% 117.50/117.94 X := X
% 117.50/117.94 Y := Y
% 117.50/117.94 end
% 117.50/117.94
% 117.50/117.94 subsumption: (9) {G0,W10,D4,L1,V2,M1} I { vplus( vmul( X, Y ), X ) ==> vmul
% 117.50/117.94 ( X, vsucc( Y ) ) }.
% 117.50/117.94 parent0: (19209) {G0,W10,D4,L1,V2,M1} { vplus( vmul( X, Y ), X ) = vmul( X
% 117.50/117.94 , vsucc( Y ) ) }.
% 117.50/117.94 substitution0:
% 117.50/117.94 X := X
% 117.50/117.94 Y := Y
% 117.50/117.94 end
% 117.50/117.94 permutation0:
% 117.50/117.94 0 ==> 0
% 117.50/117.94 end
% 117.50/117.94
% 117.50/117.94 subsumption: (10) {G0,W5,D3,L1,V1,M1} I { vmul( X, v1 ) ==> X }.
% 117.50/117.94 parent0: (19164) {G0,W5,D3,L1,V1,M1} { vmul( X, v1 ) = X }.
% 117.50/117.94 substitution0:
% 117.50/117.94 X := X
% 117.50/117.94 end
% 117.50/117.94 permutation0:
% 117.50/117.94 0 ==> 0
% 117.50/117.94 end
% 117.50/117.94
% 117.50/117.94 subsumption: (13) {G0,W7,D3,L1,V2,M1} I { vplus( Y, X ) = vplus( X, Y ) }.
% 117.50/117.94 parent0: (19167) {G0,W7,D3,L1,V2,M1} { vplus( Y, X ) = vplus( X, Y ) }.
% 117.50/117.94 substitution0:
% 117.50/117.94 X := X
% 117.50/117.94 Y := Y
% 117.50/117.94 end
% 117.50/117.94 permutation0:
% 117.50/117.94 0 ==> 0
% 117.50/117.94 end
% 117.50/117.94
% 117.50/117.94 subsumption: (14) {G0,W9,D4,L1,V2,M1} I { vplus( vsucc( X ), Y ) ==> vsucc
% 117.50/117.94 ( vplus( X, Y ) ) }.
% 117.50/117.94 parent0: (19168) {G0,W9,D4,L1,V2,M1} { vplus( vsucc( X ), Y ) = vsucc(
% 117.50/117.94 vplus( X, Y ) ) }.
% 117.50/117.94 substitution0:
% 117.50/117.94 X := X
% 117.50/117.94 Y := Y
% 117.50/117.94 end
% 117.50/117.94 permutation0:
% 117.50/117.94 0 ==> 0
% 117.50/117.94 end
% 117.50/117.94
% 117.50/117.94 eqswap: (19257) {G0,W11,D4,L1,V3,M1} { vplus( X, vplus( Y, Z ) ) = vplus(
% 117.50/117.94 vplus( X, Y ), Z ) }.
% 117.50/117.94 parent0[0]: (19170) {G0,W11,D4,L1,V3,M1} { vplus( vplus( X, Y ), Z ) =
% 117.50/117.94 vplus( X, vplus( Y, Z ) ) }.
% 117.50/117.94 substitution0:
% 117.50/117.94 X := X
% 117.50/117.94 Y := Y
% 117.50/117.94 Z := Z
% 117.50/117.94 end
% 117.50/117.94
% 117.50/117.94 subsumption: (16) {G0,W11,D4,L1,V3,M1} I { vplus( X, vplus( Y, Z ) ) ==>
% 117.50/117.94 vplus( vplus( X, Y ), Z ) }.
% 117.50/117.94 parent0: (19257) {G0,W11,D4,L1,V3,M1} { vplus( X, vplus( Y, Z ) ) = vplus
% 117.50/117.94 ( vplus( X, Y ), Z ) }.
% 117.50/117.94 substitution0:
% 117.50/117.94 X := X
% 117.50/117.94 Y := Y
% 117.50/117.94 Z := Z
% 117.50/117.94 end
% 117.50/117.94 permutation0:
% 117.50/117.94 0 ==> 0
% 117.50/117.94 end
% 117.50/117.94
% 117.50/117.94 subsumption: (17) {G0,W9,D4,L1,V2,M1} I { vplus( X, vsucc( Y ) ) ==> vsucc
% 117.50/117.94 ( vplus( X, Y ) ) }.
% 117.50/117.94 parent0: (19171) {G0,W9,D4,L1,V2,M1} { vplus( X, vsucc( Y ) ) = vsucc(
% 117.50/117.94 vplus( X, Y ) ) }.
% 117.50/117.94 substitution0:
% 117.50/117.94 X := X
% 117.50/117.94 Y := Y
% 117.50/117.94 end
% 117.50/117.94 permutation0:
% 117.50/117.94 0 ==> 0
% 117.50/117.94 end
% 117.50/117.94
% 117.50/117.94 subsumption: (18) {G0,W6,D3,L1,V1,M1} I { vplus( X, v1 ) ==> vsucc( X ) }.
% 117.50/117.94 parent0: (19172) {G0,W6,D3,L1,V1,M1} { vplus( X, v1 ) = vsucc( X ) }.
% 117.50/117.94 substitution0:
% 117.50/117.94 X := X
% 117.50/117.94 end
% 117.50/117.94 permutation0:
% 117.50/117.94 0 ==> 0
% 117.50/117.94 end
% 117.50/117.94
% 117.50/117.94 eqswap: (19306) {G0,W8,D4,L2,V1,M2} { vsucc( vskolem2( X ) ) = X, X = v1
% 117.50/117.94 }.
% 117.50/117.94 parent0[1]: (19173) {G0,W8,D4,L2,V1,M2} { X = v1, X = vsucc( vskolem2( X )
% 117.50/117.94 ) }.
% 117.50/117.94 substitution0:
% 117.50/117.94 X := X
% 117.50/117.94 end
% 117.50/117.94
% 117.50/117.94 subsumption: (19) {G0,W8,D4,L2,V1,M2} I { X = v1, vsucc( vskolem2( X ) )
% 117.50/117.94 ==> X }.
% 117.50/117.94 parent0: (19306) {G0,W8,D4,L2,V1,M2} { vsucc( vskolem2( X ) ) = X, X = v1
% 117.50/117.94 }.
% 117.50/117.94 substitution0:
% 117.50/117.94 X := X
% 117.50/117.94 end
% 117.50/117.94 permutation0:
% 117.50/117.94 0 ==> 1
% 117.50/117.94 1 ==> 0
% 117.50/117.94 end
% 117.50/117.94
% 117.50/117.94 subsumption: (20) {G0,W4,D3,L1,V1,M1} I { ! vsucc( X ) ==> X }.
% 117.50/117.94 parent0: (19174) {G0,W4,D3,L1,V1,M1} { ! vsucc( X ) = X }.
% 117.50/117.94 substitution0:
% 117.50/117.94 X := X
% 117.50/117.94 end
% 117.50/117.94 permutation0:
% 117.50/117.94 0 ==> 0
% 117.50/117.94 end
% 117.50/117.94
% 117.50/117.94 subsumption: (21) {G0,W8,D3,L2,V2,M2} I { X = Y, ! vsucc( X ) = vsucc( Y )
% 117.50/117.94 }.
% 117.50/117.94 parent0: (19175) {G0,W8,D3,L2,V2,M2} { X = Y, ! vsucc( X ) = vsucc( Y )
% 117.50/117.94 }.
% 117.50/117.94 substitution0:
% 117.50/117.94 X := X
% 117.50/117.94 Y := Y
% 117.50/117.94 end
% 117.50/117.94 permutation0:
% 117.50/117.94 0 ==> 0
% 117.50/117.94 1 ==> 1
% 117.50/117.94 end
% 117.50/117.94
% 117.50/117.94 paramod: (19357) {G1,W17,D5,L1,V0,M1} { ! vplus( vplus( vmul( vd411, vd413
% 117.50/117.94 ), vd413 ), vsucc( vd411 ) ) ==> vplus( vmul( vd411, vd413 ), vplus(
% 117.50/117.94 vsucc( vd411 ), vd413 ) ) }.
% 117.50/117.94 parent0[0]: (1) {G0,W17,D5,L1,V0,M1} I { vplus( vmul( vd411, vd413 ), vplus
% 117.50/117.94 ( vd413, vsucc( vd411 ) ) ) ==> vplus( vplus( vmul( vd411, vd413 ), vd413
% 117.50/117.94 ), vsucc( vd411 ) ) }.
% 117.50/117.94 parent1[0; 2]: (0) {G0,W17,D5,L1,V0,M1} I { ! vplus( vmul( vd411, vd413 ),
% 117.50/117.94 vplus( vd413, vsucc( vd411 ) ) ) ==> vplus( vmul( vd411, vd413 ), vplus(
% 117.50/117.94 vsucc( vd411 ), vd413 ) ) }.
% 117.50/117.94 substitution0:
% 117.50/117.94 end
% 117.50/117.94 substitution1:
% 117.50/117.94 end
% 117.50/117.94
% 117.50/117.94 paramod: (19358) {G1,W16,D5,L1,V0,M1} { ! vplus( vmul( vsucc( vd411 ),
% 117.50/117.94 vd413 ), vsucc( vd411 ) ) ==> vplus( vmul( vd411, vd413 ), vplus( vsucc(
% 117.50/117.94 vd411 ), vd413 ) ) }.
% 117.50/117.94 parent0[0]: (2) {G0,W16,D5,L1,V0,M1} I { vplus( vplus( vmul( vd411, vd413 )
% 117.50/117.94 , vd413 ), vsucc( vd411 ) ) ==> vplus( vmul( vsucc( vd411 ), vd413 ),
% 117.50/117.94 vsucc( vd411 ) ) }.
% 117.50/117.94 parent1[0; 2]: (19357) {G1,W17,D5,L1,V0,M1} { ! vplus( vplus( vmul( vd411
% 117.50/117.94 , vd413 ), vd413 ), vsucc( vd411 ) ) ==> vplus( vmul( vd411, vd413 ),
% 117.50/117.94 vplus( vsucc( vd411 ), vd413 ) ) }.
% 117.50/117.94 substitution0:
% 117.50/117.94 end
% 117.50/117.94 substitution1:
% 217.86/218.29 end
% 217.86/218.29
% 217.86/218.29 paramod: (19359) {G1,W14,D5,L1,V0,M1} { ! vmul( vsucc( vd411 ), vsucc(
% 217.86/218.29 vd413 ) ) ==> vplus( vmul( vd411, vd413 ), vplus( vsucc( vd411 ), vd413 )
% 217.86/218.29 ) }.
% 217.86/218.29 parent0[0]: (3) {G0,W13,D5,L1,V0,M1} I { vplus( vmul( vsucc( vd411 ), vd413
% 217.86/218.29 ), vsucc( vd411 ) ) ==> vmul( vsucc( vd411 ), vsucc( vd413 ) ) }.
% 217.86/218.29 parent1[0; 2]: (19358) {G1,W16,D5,L1,V0,M1} { ! vplus( vmul( vsucc( vd411
% 217.86/218.29 ), vd413 ), vsucc( vd411 ) ) ==> vplus( vmul( vd411, vd413 ), vplus(
% 217.86/218.29 vsucc( vd411 ), vd413 ) ) }.
% 217.86/218.29 substitution0:
% 217.86/218.29 end
% 217.86/218.29 substitution1:
% 217.86/218.29 end
% 217.86/218.29
% 217.86/218.29 paramod: (19360) {G1,W14,D5,L1,V0,M1} { ! vmul( vsucc( vd411 ), vsucc(
% 217.86/218.29 vd413 ) ) ==> vplus( vplus( vmul( vd411, vd413 ), vsucc( vd411 ) ), vd413
% 217.86/218.29 ) }.
% 217.86/218.29 parent0[0]: (16) {G0,W11,D4,L1,V3,M1} I { vplus( X, vplus( Y, Z ) ) ==>
% 217.86/218.29 vplus( vplus( X, Y ), Z ) }.
% 217.86/218.29 parent1[0; 7]: (19359) {G1,W14,D5,L1,V0,M1} { ! vmul( vsucc( vd411 ),
% 217.86/218.29 vsucc( vd413 ) ) ==> vplus( vmul( vd411, vd413 ), vplus( vsucc( vd411 ),
% 217.86/218.29 vd413 ) ) }.
% 217.86/218.29 substitution0:
% 217.86/218.29 X := vmul( vd411, vd413 )
% 217.86/218.29 Y := vsucc( vd411 )
% 217.86/218.29 Z := vd413
% 217.86/218.29 end
% 217.86/218.29 substitution1:
% 217.86/218.29 end
% 217.86/218.29
% 217.86/218.29 paramod: (19361) {G1,W14,D6,L1,V0,M1} { ! vmul( vsucc( vd411 ), vsucc(
% 217.86/218.29 vd413 ) ) ==> vplus( vsucc( vplus( vmul( vd411, vd413 ), vd411 ) ), vd413
% 217.86/218.29 ) }.
% 217.86/218.29 parent0[0]: (17) {G0,W9,D4,L1,V2,M1} I { vplus( X, vsucc( Y ) ) ==> vsucc(
% 217.86/218.29 vplus( X, Y ) ) }.
% 217.86/218.29 parent1[0; 8]: (19360) {G1,W14,D5,L1,V0,M1} { ! vmul( vsucc( vd411 ),
% 217.86/218.29 vsucc( vd413 ) ) ==> vplus( vplus( vmul( vd411, vd413 ), vsucc( vd411 ) )
% 217.86/218.29 , vd413 ) }.
% 217.86/218.29 substitution0:
% 217.86/218.29 X := vmul( vd411, vd413 )
% 217.86/218.29 Y := vd411
% 217.86/218.29 end
% 217.86/218.29 substitution1:
% 217.86/218.29 end
% 217.86/218.29
% 217.86/218.29 paramod: (19362) {G1,W14,D6,L1,V0,M1} { ! vmul( vsucc( vd411 ), vsucc(
% 217.86/218.29 vd413 ) ) ==> vsucc( vplus( vplus( vmul( vd411, vd413 ), vd411 ), vd413 )
% 217.86/218.29 ) }.
% 217.86/218.29 parent0[0]: (14) {G0,W9,D4,L1,V2,M1} I { vplus( vsucc( X ), Y ) ==> vsucc(
% 217.86/218.29 vplus( X, Y ) ) }.
% 217.86/218.29 parent1[0; 7]: (19361) {G1,W14,D6,L1,V0,M1} { ! vmul( vsucc( vd411 ),
% 217.86/218.29 vsucc( vd413 ) ) ==> vplus( vsucc( vplus( vmul( vd411, vd413 ), vd411 ) )
% 217.86/218.29 , vd413 ) }.
% 217.86/218.29 substitution0:
% 217.86/218.29 X := vplus( vmul( vd411, vd413 ), vd411 )
% 217.86/218.29 Y := vd413
% 217.86/218.29 end
% 217.86/218.29 substitution1:
% 217.86/218.29 end
% 217.86/218.29
% 217.86/218.29 paramod: (19363) {G1,W13,D6,L1,V0,M1} { ! vmul( vsucc( vd411 ), vsucc(
% 217.86/218.29 vd413 ) ) ==> vsucc( vplus( vmul( vd411, vsucc( vd413 ) ), vd413 ) ) }.
% 217.86/218.29 parent0[0]: (9) {G0,W10,D4,L1,V2,M1} I { vplus( vmul( X, Y ), X ) ==> vmul
% 217.86/218.29 ( X, vsucc( Y ) ) }.
% 217.86/218.29 parent1[0; 9]: (19362) {G1,W14,D6,L1,V0,M1} { ! vmul( vsucc( vd411 ),
% 217.86/218.29 vsucc( vd413 ) ) ==> vsucc( vplus( vplus( vmul( vd411, vd413 ), vd411 ),
% 217.86/218.29 vd413 ) ) }.
% 217.86/218.29 substitution0:
% 217.86/218.29 X := vd411
% 217.86/218.29 Y := vd413
% 217.86/218.29 end
% 217.86/218.29 substitution1:
% 217.86/218.29 end
% 217.86/218.29
% 217.86/218.29 eqswap: (19364) {G1,W13,D6,L1,V0,M1} { ! vsucc( vplus( vmul( vd411, vsucc
% 217.86/218.29 ( vd413 ) ), vd413 ) ) ==> vmul( vsucc( vd411 ), vsucc( vd413 ) ) }.
% 217.86/218.29 parent0[0]: (19363) {G1,W13,D6,L1,V0,M1} { ! vmul( vsucc( vd411 ), vsucc(
% 217.86/218.29 vd413 ) ) ==> vsucc( vplus( vmul( vd411, vsucc( vd413 ) ), vd413 ) ) }.
% 217.86/218.29 substitution0:
% 217.86/218.29 end
% 217.86/218.29
% 217.86/218.29 subsumption: (22) {G1,W13,D6,L1,V0,M1} S(0);d(1);d(2);d(3);d(16);d(17);d(14
% 217.86/218.29 );d(9) { ! vsucc( vplus( vmul( vd411, vsucc( vd413 ) ), vd413 ) ) ==>
% 217.86/218.29 vmul( vsucc( vd411 ), vsucc( vd413 ) ) }.
% 217.86/218.29 parent0: (19364) {G1,W13,D6,L1,V0,M1} { ! vsucc( vplus( vmul( vd411, vsucc
% 217.86/218.29 ( vd413 ) ), vd413 ) ) ==> vmul( vsucc( vd411 ), vsucc( vd413 ) ) }.
% 217.86/218.29 substitution0:
% 217.86/218.29 end
% 217.86/218.29 permutation0:
% 217.86/218.29 0 ==> 0
% 217.86/218.29 end
% 217.86/218.29
% 217.86/218.29 *** allocated 15000 integers for justifications
% 217.86/218.29 *** allocated 1297440 integers for clauses
% 217.86/218.29 *** allocated 22500 integers for justifications
% 217.86/218.29 *** allocated 33750 integers for justifications
% 217.86/218.29 *** allocated 50625 integers for justifications
% 217.86/218.29 *** allocated 75937 integers for justifications
% 217.86/218.29 *** allocated 576640 integers for termspace/termends
% 217.86/218.29 *** allocated 113905 integers for justifications
% 217.86/218.29 *** allocated 170857 integers for justifications
% 217.86/218.29 *** allocated 256285 integers for justifications
% 217.86/218.29 *** allocated 864960 integers for termspace/termends
% 217.86/218.29 *** allocated 384427 integers for justifications
% 217.86/218.29 *** allocated 576640 integers for justifications
% 217.86/218.29 *** allocated 1297440 integers for termspace/termends
% 217.86/218.29 *** allocated 864960 integers for justifications
% 217.86/218.29 *** allocated 1946160 integers for clauses
% 217.86/218.29 *** allocated 1946160 integers for termspace/termends
% 217.86/218.29 *** allocatedCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------