TSTP Solution File: NUM835+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : NUM835+1 : 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 06:26:52 EDT 2022
% Result : Theorem 0.72s 1.36s
% Output : Refutation 0.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM835+1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.13 % Command : bliksem %s
% 0.12/0.34 % Computer : n027.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % DateTime : Wed Jul 6 10:04:28 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.72/1.36 *** allocated 10000 integers for termspace/termends
% 0.72/1.36 *** allocated 10000 integers for clauses
% 0.72/1.36 *** allocated 10000 integers for justifications
% 0.72/1.36 Bliksem 1.12
% 0.72/1.36
% 0.72/1.36
% 0.72/1.36 Automatic Strategy Selection
% 0.72/1.36
% 0.72/1.36
% 0.72/1.36 Clauses:
% 0.72/1.36
% 0.72/1.36 { ! vd165 = vplus( vd151, X ) }.
% 0.72/1.36 { ! vd151 = vplus( vd165, X ) }.
% 0.72/1.36 { ! vd151 = vd165 }.
% 0.72/1.36 { ! vd165 = vplus( vd151, X ), m( vsucc( vd165 ) ) }.
% 0.72/1.36 { ! vd165 = vplus( vd151, X ), vsucc( vplus( vd151, X ) ) = vplus( vd151,
% 0.72/1.36 vsucc( X ) ) }.
% 0.72/1.36 { ! vd165 = vplus( vd151, X ), vsucc( vd165 ) = vsucc( vplus( vd151, X ) )
% 0.72/1.36 }.
% 0.72/1.36 { ! vd151 = vplus( vd165, X ), X = v1, m( vsucc( vd165 ) ) }.
% 0.72/1.36 { ! vd151 = vplus( vd165, X ), X = v1, vplus( vplus( vd165, v1 ), vskolem3
% 0.72/1.36 ) = vplus( vsucc( vd165 ), vskolem3 ) }.
% 0.72/1.36 { ! vd151 = vplus( vd165, X ), X = v1, vplus( vd165, vplus( v1, vskolem3 )
% 0.72/1.36 ) = vplus( vplus( vd165, v1 ), vskolem3 ) }.
% 0.72/1.36 { ! vd151 = vplus( vd165, X ), X = v1, vd151 = vplus( vd165, vplus( v1,
% 0.72/1.36 vskolem3 ) ) }.
% 0.72/1.36 { ! vd151 = vplus( vd165, X ), X = v1, vsucc( vskolem3 ) = vplus( v1,
% 0.72/1.36 vskolem3 ) }.
% 0.72/1.36 { ! vd151 = vplus( vd165, X ), X = v1, X = vsucc( vskolem3 ) }.
% 0.72/1.36 { ! vd151 = vplus( vd165, X ), ! X = v1, m( vsucc( vd165 ) ) }.
% 0.72/1.36 { ! vd151 = vplus( vd165, X ), ! X = v1, vplus( vd165, v1 ) = vsucc( vd165
% 0.72/1.36 ) }.
% 0.72/1.36 { ! vd151 = vplus( vd165, X ), ! X = v1, vd151 = vplus( vd165, v1 ) }.
% 0.72/1.36 { ! vd151 = vd165, m( vsucc( vd165 ) ) }.
% 0.72/1.36 { ! vd151 = vd165, vplus( vd165, v1 ) = vplus( vd151, v1 ) }.
% 0.72/1.36 { ! vd151 = vd165, vsucc( vd165 ) = vplus( vd165, v1 ) }.
% 0.72/1.36 { m( vd165 ) }.
% 0.72/1.36 { m( v1 ) }.
% 0.72/1.36 { alpha2( X ), vsucc( skol1( Y ) ) = vplus( v1, skol1( Y ) ) }.
% 0.72/1.36 { alpha2( X ), vd151 = vsucc( skol1( Y ) ) }.
% 0.72/1.36 { alpha2( X ), vplus( v1, skol1( X ) ) = vplus( X, skol1( X ) ) }.
% 0.72/1.36 { ! alpha2( X ), ! X = v1, v1 = X }.
% 0.72/1.36 { ! alpha2( X ), ! X = v1, vd151 = v1 }.
% 0.72/1.36 { X = v1, alpha2( X ) }.
% 0.72/1.36 { ! v1 = X, ! vd151 = v1, alpha2( X ) }.
% 0.72/1.36 { ! m( Y ), X = Y, alpha1( X, Y ) }.
% 0.72/1.36 { ! X = Y, m( Y ) }.
% 0.72/1.36 { ! alpha1( X, Y ), m( Y ) }.
% 0.72/1.36 { ! alpha1( X, Y ), X = vplus( Y, skol2( X, Y ) ), Y = vplus( X, skol3( X,
% 0.72/1.36 Y ) ) }.
% 0.72/1.36 { ! X = vplus( Y, Z ), alpha1( X, Y ) }.
% 0.72/1.36 { ! Y = vplus( X, Z ), alpha1( X, Y ) }.
% 0.72/1.36 { ! X = Y, ! Y = vplus( X, Z ) }.
% 0.72/1.36 { ! X = vplus( Y, Z ), ! Y = vplus( X, T ) }.
% 0.72/1.36 { ! X = Y, ! X = vplus( Y, Z ) }.
% 0.72/1.36 { ! Y = vplus( X, Z ), ! X = vplus( Y, T ) }.
% 0.72/1.36 { ! Y = vplus( X, T ), ! X = vplus( Y, Z ) }.
% 0.72/1.36 { ! Y = vplus( X, Z ), ! X = Y }.
% 0.72/1.36 { ! X = vplus( Y, Z ), ! X = Y }.
% 0.72/1.36 { X = Y, ! vplus( Z, X ) = vplus( Z, Y ) }.
% 0.72/1.36 { ! Y = vplus( X, Y ) }.
% 0.72/1.36 { vplus( Y, X ) = vplus( X, Y ) }.
% 0.72/1.36 { vplus( vsucc( X ), Y ) = vsucc( vplus( X, Y ) ) }.
% 0.72/1.36 { vplus( v1, X ) = vsucc( X ) }.
% 0.72/1.36 { vplus( vplus( X, Y ), Z ) = vplus( X, vplus( Y, Z ) ) }.
% 0.72/1.36 { vplus( X, vsucc( Y ) ) = vsucc( vplus( X, Y ) ) }.
% 0.72/1.36 { vplus( X, v1 ) = vsucc( X ) }.
% 0.72/1.36 { X = v1, X = vsucc( vskolem2( X ) ) }.
% 0.72/1.36 { ! vsucc( X ) = X }.
% 0.72/1.36 { X = Y, ! vsucc( X ) = vsucc( Y ) }.
% 0.72/1.36 { ! vsucc( X ) = vsucc( Y ), X = Y }.
% 0.72/1.36 { ! vsucc( X ) = v1 }.
% 0.72/1.36
% 0.72/1.36 percentage equality = 0.701754, percentage horn = 0.787879
% 0.72/1.36 This is a problem with some equality
% 0.72/1.36
% 0.72/1.36
% 0.72/1.36
% 0.72/1.36 Options Used:
% 0.72/1.36
% 0.72/1.36 useres = 1
% 0.72/1.36 useparamod = 1
% 0.72/1.36 useeqrefl = 1
% 0.72/1.36 useeqfact = 1
% 0.72/1.36 usefactor = 1
% 0.72/1.36 usesimpsplitting = 0
% 0.72/1.36 usesimpdemod = 5
% 0.72/1.36 usesimpres = 3
% 0.72/1.36
% 0.72/1.36 resimpinuse = 1000
% 0.72/1.36 resimpclauses = 20000
% 0.72/1.36 substype = eqrewr
% 0.72/1.36 backwardsubs = 1
% 0.72/1.36 selectoldest = 5
% 0.72/1.36
% 0.72/1.36 litorderings [0] = split
% 0.72/1.36 litorderings [1] = extend the termordering, first sorting on arguments
% 0.72/1.36
% 0.72/1.36 termordering = kbo
% 0.72/1.36
% 0.72/1.36 litapriori = 0
% 0.72/1.36 termapriori = 1
% 0.72/1.36 litaposteriori = 0
% 0.72/1.36 termaposteriori = 0
% 0.72/1.36 demodaposteriori = 0
% 0.72/1.36 ordereqreflfact = 0
% 0.72/1.36
% 0.72/1.36 litselect = negord
% 0.72/1.36
% 0.72/1.36 maxweight = 15
% 0.72/1.36 maxdepth = 30000
% 0.72/1.36 maxlength = 115
% 0.72/1.36 maxnrvars = 195
% 0.72/1.36 excuselevel = 1
% 0.72/1.36 increasemaxweight = 1
% 0.72/1.36
% 0.72/1.36 maxselected = 10000000
% 0.72/1.36 maxnrclauses = 10000000
% 0.72/1.36
% 0.72/1.36 showgenerated = 0
% 0.72/1.36 showkept = 0
% 0.72/1.36 showselected = 0
% 0.72/1.36 showdeleted = 0
% 0.72/1.36 showresimp = 1
% 0.72/1.36 showstatus = 2000
% 0.72/1.36
% 0.72/1.36 prologoutput = 0
% 0.72/1.36 nrgoals = 5000000
% 0.72/1.36 totalproof = 1
% 0.72/1.36
% 0.72/1.36 Symbols occurring in the translation:
% 0.72/1.36
% 0.72/1.36 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.72/1.36 . [1, 2] (w:1, o:62, a:1, s:1, b:0),
% 0.72/1.36 ! [4, 1] (w:0, o:52, a:1, s:1, b:0),
% 0.72/1.36 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.72/1.36 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.72/1.36 vd165 [36, 0] (w:1, o:25, a:1, s:1, b:0),
% 0.72/1.36 vd151 [37, 0] (w:1, o:24, a:1, s:1, b:0),
% 0.72/1.36 vplus [38, 2] (w:1, o:86, a:1, s:1, b:0),
% 0.72/1.36 vsucc [40, 1] (w:1, o:57, a:1, s:1, b:0),
% 0.72/1.36 m [41, 1] (w:1, o:58, a:1, s:1, b:0),
% 0.72/1.36 v1 [42, 0] (w:1, o:26, a:1, s:1, b:0),
% 0.72/1.36 vskolem3 [43, 0] (w:1, o:27, a:1, s:1, b:0),
% 0.72/1.36 vskolem2 [78, 1] (w:1, o:59, a:1, s:1, b:0),
% 0.72/1.36 alpha1 [85, 2] (w:1, o:87, a:1, s:1, b:1),
% 0.72/1.36 alpha2 [86, 1] (w:1, o:60, a:1, s:1, b:1),
% 0.72/1.36 skol1 [87, 1] (w:1, o:61, a:1, s:1, b:1),
% 0.72/1.36 skol2 [88, 2] (w:1, o:88, a:1, s:1, b:1),
% 0.72/1.36 skol3 [89, 2] (w:1, o:89, a:1, s:1, b:1).
% 0.72/1.36
% 0.72/1.36
% 0.72/1.36 Starting Search:
% 0.72/1.36
% 0.72/1.36 *** allocated 15000 integers for clauses
% 0.72/1.36 *** allocated 22500 integers for clauses
% 0.72/1.36 *** allocated 33750 integers for clauses
% 0.72/1.36 *** allocated 50625 integers for clauses
% 0.72/1.36 *** allocated 15000 integers for termspace/termends
% 0.72/1.36 Resimplifying inuse:
% 0.72/1.36 Done
% 0.72/1.36
% 0.72/1.36 *** allocated 75937 integers for clauses
% 0.72/1.36 *** allocated 22500 integers for termspace/termends
% 0.72/1.36 *** allocated 113905 integers for clauses
% 0.72/1.36 *** allocated 33750 integers for termspace/termends
% 0.72/1.36
% 0.72/1.36 Intermediate Status:
% 0.72/1.36 Generated: 9214
% 0.72/1.36 Kept: 2012
% 0.72/1.36 Inuse: 301
% 0.72/1.36 Deleted: 68
% 0.72/1.36 Deletedinuse: 15
% 0.72/1.36
% 0.72/1.36 Resimplifying inuse:
% 0.72/1.36 Done
% 0.72/1.36
% 0.72/1.36 *** allocated 170857 integers for clauses
% 0.72/1.36 *** allocated 50625 integers for termspace/termends
% 0.72/1.36 Resimplifying inuse:
% 0.72/1.36 Done
% 0.72/1.36
% 0.72/1.36
% 0.72/1.36 Bliksems!, er is een bewijs:
% 0.72/1.36 % SZS status Theorem
% 0.72/1.36 % SZS output start Refutation
% 0.72/1.36
% 0.72/1.36 (0) {G0,W5,D3,L1,V1,M1} I { ! vplus( vd151, X ) ==> vd165 }.
% 0.72/1.36 (1) {G0,W5,D3,L1,V1,M1} I { ! vplus( vd165, X ) ==> vd151 }.
% 0.72/1.36 (2) {G0,W3,D2,L1,V0,M1} I { ! vd165 ==> vd151 }.
% 0.72/1.36 (12) {G0,W8,D2,L3,V2,M3} I { ! m( Y ), X = Y, alpha1( X, Y ) }.
% 0.72/1.36 (13) {G0,W5,D2,L2,V2,M2} I { ! X = Y, m( Y ) }.
% 0.72/1.36 (15) {G0,W17,D4,L3,V2,M3} I { ! alpha1( X, Y ), vplus( Y, skol2( X, Y ) )
% 0.72/1.36 ==> X, vplus( X, skol3( X, Y ) ) ==> Y }.
% 0.72/1.36 (30) {G0,W8,D3,L2,V2,M2} I { X = Y, ! vsucc( X ) = vsucc( Y ) }.
% 0.72/1.36 (34) {G1,W2,D2,L1,V1,M1} Q(13) { m( X ) }.
% 0.72/1.36 (107) {G2,W6,D2,L2,V2,M2} S(12);r(34) { X = Y, alpha1( X, Y ) }.
% 0.72/1.36 (163) {G3,W6,D2,L2,V1,M2} P(107,2) { ! X = vd151, alpha1( X, vd165 ) }.
% 0.72/1.36 (164) {G4,W3,D2,L1,V0,M1} Q(163) { alpha1( vd151, vd165 ) }.
% 0.72/1.36 (571) {G1,W10,D3,L2,V2,M2} P(30,1) { ! vplus( X, Y ) ==> vd151, ! vsucc(
% 0.72/1.36 vd165 ) = vsucc( X ) }.
% 0.72/1.36 (574) {G1,W10,D4,L2,V2,M2} P(30,0) { ! Y = vd165, ! vsucc( vplus( vd151, X
% 0.72/1.36 ) ) = vsucc( Y ) }.
% 0.72/1.36 (580) {G2,W7,D4,L1,V1,M1} Q(574) { ! vsucc( vplus( vd151, X ) ) ==> vsucc(
% 0.72/1.36 vd165 ) }.
% 0.72/1.36 (3218) {G3,W8,D3,L2,V1,M2} P(15,580);r(571) { ! vsucc( X ) = vsucc( vd165 )
% 0.72/1.36 , ! alpha1( vd151, X ) }.
% 0.72/1.36 (3227) {G5,W0,D0,L0,V0,M0} Q(3218);r(164) { }.
% 0.72/1.36
% 0.72/1.36
% 0.72/1.36 % SZS output end Refutation
% 0.72/1.36 found a proof!
% 0.72/1.36
% 0.72/1.36
% 0.72/1.36 Unprocessed initial clauses:
% 0.72/1.36
% 0.72/1.36 (3229) {G0,W5,D3,L1,V1,M1} { ! vd165 = vplus( vd151, X ) }.
% 0.72/1.36 (3230) {G0,W5,D3,L1,V1,M1} { ! vd151 = vplus( vd165, X ) }.
% 0.72/1.36 (3231) {G0,W3,D2,L1,V0,M1} { ! vd151 = vd165 }.
% 0.72/1.36 (3232) {G0,W8,D3,L2,V1,M2} { ! vd165 = vplus( vd151, X ), m( vsucc( vd165
% 0.72/1.36 ) ) }.
% 0.72/1.36 (3233) {G0,W14,D4,L2,V1,M2} { ! vd165 = vplus( vd151, X ), vsucc( vplus(
% 0.72/1.36 vd151, X ) ) = vplus( vd151, vsucc( X ) ) }.
% 0.72/1.36 (3234) {G0,W12,D4,L2,V1,M2} { ! vd165 = vplus( vd151, X ), vsucc( vd165 )
% 0.72/1.36 = vsucc( vplus( vd151, X ) ) }.
% 0.72/1.36 (3235) {G0,W11,D3,L3,V1,M3} { ! vd151 = vplus( vd165, X ), X = v1, m(
% 0.72/1.36 vsucc( vd165 ) ) }.
% 0.72/1.36 (3236) {G0,W18,D4,L3,V1,M3} { ! vd151 = vplus( vd165, X ), X = v1, vplus(
% 0.72/1.36 vplus( vd165, v1 ), vskolem3 ) = vplus( vsucc( vd165 ), vskolem3 ) }.
% 0.72/1.36 (3237) {G0,W19,D4,L3,V1,M3} { ! vd151 = vplus( vd165, X ), X = v1, vplus(
% 0.72/1.36 vd165, vplus( v1, vskolem3 ) ) = vplus( vplus( vd165, v1 ), vskolem3 )
% 0.72/1.36 }.
% 0.72/1.36 (3238) {G0,W15,D4,L3,V1,M3} { ! vd151 = vplus( vd165, X ), X = v1, vd151 =
% 0.72/1.36 vplus( vd165, vplus( v1, vskolem3 ) ) }.
% 0.72/1.36 (3239) {G0,W14,D3,L3,V1,M3} { ! vd151 = vplus( vd165, X ), X = v1, vsucc(
% 0.72/1.36 vskolem3 ) = vplus( v1, vskolem3 ) }.
% 0.72/1.36 (3240) {G0,W12,D3,L3,V1,M3} { ! vd151 = vplus( vd165, X ), X = v1, X =
% 0.72/1.36 vsucc( vskolem3 ) }.
% 0.72/1.36 (3241) {G0,W11,D3,L3,V1,M3} { ! vd151 = vplus( vd165, X ), ! X = v1, m(
% 0.72/1.36 vsucc( vd165 ) ) }.
% 0.72/1.36 (3242) {G0,W14,D3,L3,V1,M3} { ! vd151 = vplus( vd165, X ), ! X = v1, vplus
% 0.72/1.36 ( vd165, v1 ) = vsucc( vd165 ) }.
% 0.72/1.36 (3243) {G0,W13,D3,L3,V1,M3} { ! vd151 = vplus( vd165, X ), ! X = v1, vd151
% 0.72/1.36 = vplus( vd165, v1 ) }.
% 0.72/1.36 (3244) {G0,W6,D3,L2,V0,M2} { ! vd151 = vd165, m( vsucc( vd165 ) ) }.
% 0.72/1.36 (3245) {G0,W10,D3,L2,V0,M2} { ! vd151 = vd165, vplus( vd165, v1 ) = vplus
% 0.72/1.36 ( vd151, v1 ) }.
% 0.72/1.36 (3246) {G0,W9,D3,L2,V0,M2} { ! vd151 = vd165, vsucc( vd165 ) = vplus(
% 0.72/1.36 vd165, v1 ) }.
% 0.72/1.36 (3247) {G0,W2,D2,L1,V0,M1} { m( vd165 ) }.
% 0.72/1.36 (3248) {G0,W2,D2,L1,V0,M1} { m( v1 ) }.
% 0.72/1.36 (3249) {G0,W10,D4,L2,V2,M2} { alpha2( X ), vsucc( skol1( Y ) ) = vplus( v1
% 0.72/1.36 , skol1( Y ) ) }.
% 0.72/1.36 (3250) {G0,W7,D4,L2,V2,M2} { alpha2( X ), vd151 = vsucc( skol1( Y ) ) }.
% 0.72/1.36 (3251) {G0,W11,D4,L2,V1,M2} { alpha2( X ), vplus( v1, skol1( X ) ) = vplus
% 0.72/1.36 ( X, skol1( X ) ) }.
% 0.72/1.36 (3252) {G0,W8,D2,L3,V1,M3} { ! alpha2( X ), ! X = v1, v1 = X }.
% 0.72/1.36 (3253) {G0,W8,D2,L3,V1,M3} { ! alpha2( X ), ! X = v1, vd151 = v1 }.
% 0.72/1.36 (3254) {G0,W5,D2,L2,V1,M2} { X = v1, alpha2( X ) }.
% 0.72/1.36 (3255) {G0,W8,D2,L3,V1,M3} { ! v1 = X, ! vd151 = v1, alpha2( X ) }.
% 0.72/1.36 (3256) {G0,W8,D2,L3,V2,M3} { ! m( Y ), X = Y, alpha1( X, Y ) }.
% 0.72/1.36 (3257) {G0,W5,D2,L2,V2,M2} { ! X = Y, m( Y ) }.
% 0.72/1.36 (3258) {G0,W5,D2,L2,V2,M2} { ! alpha1( X, Y ), m( Y ) }.
% 0.72/1.36 (3259) {G0,W17,D4,L3,V2,M3} { ! alpha1( X, Y ), X = vplus( Y, skol2( X, Y
% 0.72/1.36 ) ), Y = vplus( X, skol3( X, Y ) ) }.
% 0.72/1.36 (3260) {G0,W8,D3,L2,V3,M2} { ! X = vplus( Y, Z ), alpha1( X, Y ) }.
% 0.72/1.36 (3261) {G0,W8,D3,L2,V3,M2} { ! Y = vplus( X, Z ), alpha1( X, Y ) }.
% 0.72/1.36 (3262) {G0,W8,D3,L2,V3,M2} { ! X = Y, ! Y = vplus( X, Z ) }.
% 0.72/1.36 (3263) {G0,W10,D3,L2,V4,M2} { ! X = vplus( Y, Z ), ! Y = vplus( X, T ) }.
% 0.72/1.36 (3264) {G0,W8,D3,L2,V3,M2} { ! X = Y, ! X = vplus( Y, Z ) }.
% 0.72/1.36 (3265) {G0,W10,D3,L2,V4,M2} { ! Y = vplus( X, Z ), ! X = vplus( Y, T ) }.
% 0.72/1.36 (3266) {G0,W10,D3,L2,V4,M2} { ! Y = vplus( X, T ), ! X = vplus( Y, Z ) }.
% 0.72/1.36 (3267) {G0,W8,D3,L2,V3,M2} { ! Y = vplus( X, Z ), ! X = Y }.
% 0.72/1.36 (3268) {G0,W8,D3,L2,V3,M2} { ! X = vplus( Y, Z ), ! X = Y }.
% 0.72/1.36 (3269) {G0,W10,D3,L2,V3,M2} { X = Y, ! vplus( Z, X ) = vplus( Z, Y ) }.
% 0.72/1.36 (3270) {G0,W5,D3,L1,V2,M1} { ! Y = vplus( X, Y ) }.
% 0.72/1.36 (3271) {G0,W7,D3,L1,V2,M1} { vplus( Y, X ) = vplus( X, Y ) }.
% 0.72/1.36 (3272) {G0,W9,D4,L1,V2,M1} { vplus( vsucc( X ), Y ) = vsucc( vplus( X, Y )
% 0.72/1.36 ) }.
% 0.72/1.36 (3273) {G0,W6,D3,L1,V1,M1} { vplus( v1, X ) = vsucc( X ) }.
% 0.72/1.36 (3274) {G0,W11,D4,L1,V3,M1} { vplus( vplus( X, Y ), Z ) = vplus( X, vplus
% 0.72/1.36 ( Y, Z ) ) }.
% 0.72/1.36 (3275) {G0,W9,D4,L1,V2,M1} { vplus( X, vsucc( Y ) ) = vsucc( vplus( X, Y )
% 0.72/1.36 ) }.
% 0.72/1.36 (3276) {G0,W6,D3,L1,V1,M1} { vplus( X, v1 ) = vsucc( X ) }.
% 0.72/1.36 (3277) {G0,W8,D4,L2,V1,M2} { X = v1, X = vsucc( vskolem2( X ) ) }.
% 0.72/1.36 (3278) {G0,W4,D3,L1,V1,M1} { ! vsucc( X ) = X }.
% 0.72/1.36 (3279) {G0,W8,D3,L2,V2,M2} { X = Y, ! vsucc( X ) = vsucc( Y ) }.
% 0.72/1.36 (3280) {G0,W8,D3,L2,V2,M2} { ! vsucc( X ) = vsucc( Y ), X = Y }.
% 0.72/1.36 (3281) {G0,W4,D3,L1,V1,M1} { ! vsucc( X ) = v1 }.
% 0.72/1.36
% 0.72/1.36
% 0.72/1.36 Total Proof:
% 0.72/1.36
% 0.72/1.36 eqswap: (3282) {G0,W5,D3,L1,V1,M1} { ! vplus( vd151, X ) = vd165 }.
% 0.72/1.36 parent0[0]: (3229) {G0,W5,D3,L1,V1,M1} { ! vd165 = vplus( vd151, X ) }.
% 0.72/1.36 substitution0:
% 0.72/1.36 X := X
% 0.72/1.36 end
% 0.72/1.36
% 0.72/1.36 subsumption: (0) {G0,W5,D3,L1,V1,M1} I { ! vplus( vd151, X ) ==> vd165 }.
% 0.72/1.36 parent0: (3282) {G0,W5,D3,L1,V1,M1} { ! vplus( vd151, X ) = vd165 }.
% 0.72/1.36 substitution0:
% 0.72/1.36 X := X
% 0.72/1.36 end
% 0.72/1.36 permutation0:
% 0.72/1.36 0 ==> 0
% 0.72/1.36 end
% 0.72/1.36
% 0.72/1.36 eqswap: (3284) {G0,W5,D3,L1,V1,M1} { ! vplus( vd165, X ) = vd151 }.
% 0.72/1.36 parent0[0]: (3230) {G0,W5,D3,L1,V1,M1} { ! vd151 = vplus( vd165, X ) }.
% 0.72/1.36 substitution0:
% 0.72/1.36 X := X
% 0.72/1.36 end
% 0.72/1.36
% 0.72/1.36 subsumption: (1) {G0,W5,D3,L1,V1,M1} I { ! vplus( vd165, X ) ==> vd151 }.
% 0.72/1.36 parent0: (3284) {G0,W5,D3,L1,V1,M1} { ! vplus( vd165, X ) = vd151 }.
% 0.72/1.36 substitution0:
% 0.72/1.36 X := X
% 0.72/1.36 end
% 0.72/1.36 permutation0:
% 0.72/1.36 0 ==> 0
% 0.72/1.36 end
% 0.72/1.36
% 0.72/1.36 eqswap: (3287) {G0,W3,D2,L1,V0,M1} { ! vd165 = vd151 }.
% 0.72/1.36 parent0[0]: (3231) {G0,W3,D2,L1,V0,M1} { ! vd151 = vd165 }.
% 0.72/1.36 substitution0:
% 0.72/1.36 end
% 0.72/1.36
% 0.72/1.36 subsumption: (2) {G0,W3,D2,L1,V0,M1} I { ! vd165 ==> vd151 }.
% 0.72/1.36 parent0: (3287) {G0,W3,D2,L1,V0,M1} { ! vd165 = vd151 }.
% 0.72/1.36 substitution0:
% 0.72/1.36 end
% 0.72/1.36 permutation0:
% 0.72/1.36 0 ==> 0
% 0.72/1.36 end
% 0.72/1.36
% 0.72/1.36 subsumption: (12) {G0,W8,D2,L3,V2,M3} I { ! m( Y ), X = Y, alpha1( X, Y )
% 0.72/1.36 }.
% 0.72/1.36 parent0: (3256) {G0,W8,D2,L3,V2,M3} { ! m( Y ), X = Y, alpha1( X, Y ) }.
% 0.72/1.36 substitution0:
% 0.72/1.36 X := X
% 0.72/1.36 Y := Y
% 0.72/1.36 end
% 0.72/1.36 permutation0:
% 0.72/1.36 0 ==> 0
% 0.72/1.36 1 ==> 1
% 66.20/66.60 2 ==> 2
% 66.20/66.60 end
% 66.20/66.60
% 66.20/66.60 subsumption: (13) {G0,W5,D2,L2,V2,M2} I { ! X = Y, m( Y ) }.
% 66.20/66.60 parent0: (3257) {G0,W5,D2,L2,V2,M2} { ! X = Y, m( Y ) }.
% 66.20/66.60 substitution0:
% 66.20/66.60 X := X
% 66.20/66.60 Y := Y
% 66.20/66.60 end
% 66.20/66.60 permutation0:
% 66.20/66.60 0 ==> 0
% 66.20/66.60 1 ==> 1
% 66.20/66.60 end
% 66.20/66.60
% 66.20/66.60 eqswap: (3555) {G0,W17,D4,L3,V2,M3} { vplus( Y, skol3( Y, X ) ) = X, !
% 66.20/66.60 alpha1( Y, X ), Y = vplus( X, skol2( Y, X ) ) }.
% 66.20/66.60 parent0[2]: (3259) {G0,W17,D4,L3,V2,M3} { ! alpha1( X, Y ), X = vplus( Y,
% 66.20/66.60 skol2( X, Y ) ), Y = vplus( X, skol3( X, Y ) ) }.
% 66.20/66.60 substitution0:
% 66.20/66.60 X := Y
% 66.20/66.60 Y := X
% 66.20/66.60 end
% 66.20/66.60
% 66.20/66.60 eqswap: (3556) {G0,W17,D4,L3,V2,M3} { vplus( Y, skol2( X, Y ) ) = X, vplus
% 66.20/66.60 ( X, skol3( X, Y ) ) = Y, ! alpha1( X, Y ) }.
% 66.20/66.60 parent0[2]: (3555) {G0,W17,D4,L3,V2,M3} { vplus( Y, skol3( Y, X ) ) = X, !
% 66.20/66.60 alpha1( Y, X ), Y = vplus( X, skol2( Y, X ) ) }.
% 66.20/66.60 substitution0:
% 66.20/66.60 X := Y
% 66.20/66.60 Y := X
% 66.20/66.60 end
% 66.20/66.60
% 66.20/66.60 subsumption: (15) {G0,W17,D4,L3,V2,M3} I { ! alpha1( X, Y ), vplus( Y,
% 66.20/66.60 skol2( X, Y ) ) ==> X, vplus( X, skol3( X, Y ) ) ==> Y }.
% 66.20/66.60 parent0: (3556) {G0,W17,D4,L3,V2,M3} { vplus( Y, skol2( X, Y ) ) = X,
% 66.20/66.60 vplus( X, skol3( X, Y ) ) = Y, ! alpha1( X, Y ) }.
% 66.20/66.60 substitution0:
% 66.20/66.60 X := X
% 66.20/66.60 Y := Y
% 66.20/66.60 end
% 66.20/66.60 permutation0:
% 66.20/66.60 0 ==> 1
% 66.20/66.60 1 ==> 2
% 66.20/66.60 2 ==> 0
% 66.20/66.60 end
% 66.20/66.60
% 66.20/66.60 subsumption: (30) {G0,W8,D3,L2,V2,M2} I { X = Y, ! vsucc( X ) = vsucc( Y )
% 66.20/66.60 }.
% 66.20/66.60 parent0: (3279) {G0,W8,D3,L2,V2,M2} { X = Y, ! vsucc( X ) = vsucc( Y ) }.
% 66.20/66.60 substitution0:
% 66.20/66.60 X := X
% 66.20/66.60 Y := Y
% 66.20/66.60 end
% 66.20/66.60 permutation0:
% 66.20/66.60 0 ==> 0
% 66.20/66.60 1 ==> 1
% 66.20/66.60 end
% 66.20/66.60
% 66.20/66.60 eqswap: (3687) {G0,W5,D2,L2,V2,M2} { ! Y = X, m( Y ) }.
% 66.20/66.60 parent0[0]: (13) {G0,W5,D2,L2,V2,M2} I { ! X = Y, m( Y ) }.
% 66.20/66.60 substitution0:
% 66.20/66.60 X := X
% 66.20/66.60 Y := Y
% 66.20/66.60 end
% 66.20/66.60
% 66.20/66.60 eqrefl: (3688) {G0,W2,D2,L1,V1,M1} { m( X ) }.
% 66.20/66.60 parent0[0]: (3687) {G0,W5,D2,L2,V2,M2} { ! Y = X, m( Y ) }.
% 66.20/66.60 substitution0:
% 66.20/66.60 X := X
% 66.20/66.60 Y := X
% 66.20/66.60 end
% 66.20/66.60
% 66.20/66.60 subsumption: (34) {G1,W2,D2,L1,V1,M1} Q(13) { m( X ) }.
% 66.20/66.60 parent0: (3688) {G0,W2,D2,L1,V1,M1} { m( X ) }.
% 66.20/66.60 substitution0:
% 66.20/66.60 X := X
% 66.20/66.60 end
% 66.20/66.60 permutation0:
% 66.20/66.60 0 ==> 0
% 66.20/66.60 end
% 66.20/66.60
% 66.20/66.60 resolution: (3690) {G1,W6,D2,L2,V2,M2} { Y = X, alpha1( Y, X ) }.
% 66.20/66.60 parent0[0]: (12) {G0,W8,D2,L3,V2,M3} I { ! m( Y ), X = Y, alpha1( X, Y )
% 66.20/66.60 }.
% 66.20/66.60 parent1[0]: (34) {G1,W2,D2,L1,V1,M1} Q(13) { m( X ) }.
% 66.20/66.60 substitution0:
% 66.20/66.60 X := Y
% 66.20/66.60 Y := X
% 66.20/66.60 end
% 66.20/66.60 substitution1:
% 66.20/66.60 X := X
% 66.20/66.60 end
% 66.20/66.60
% 66.20/66.60 subsumption: (107) {G2,W6,D2,L2,V2,M2} S(12);r(34) { X = Y, alpha1( X, Y )
% 66.20/66.60 }.
% 66.20/66.60 parent0: (3690) {G1,W6,D2,L2,V2,M2} { Y = X, alpha1( Y, X ) }.
% 66.20/66.60 substitution0:
% 66.20/66.60 X := Y
% 66.20/66.60 Y := X
% 66.20/66.60 end
% 66.20/66.60 permutation0:
% 66.20/66.60 0 ==> 0
% 66.20/66.60 1 ==> 1
% 66.20/66.60 end
% 66.20/66.60
% 66.20/66.60 *** allocated 15000 integers for justifications
% 66.20/66.60 *** allocated 75937 integers for termspace/termends
% 66.20/66.60 *** allocated 22500 integers for justifications
% 66.20/66.60 *** allocated 256285 integers for clauses
% 66.20/66.60 *** allocated 33750 integers for justifications
% 66.20/66.60 *** allocated 50625 integers for justifications
% 66.20/66.60 *** allocated 113905 integers for termspace/termends
% 66.20/66.60 *** allocated 75937 integers for justifications
% 66.20/66.60 *** allocated 113905 integers for justifications
% 66.20/66.60 *** allocated 170857 integers for termspace/termends
% 66.20/66.60 *** allocated 170857 integers for justifications
% 66.20/66.60 *** allocated 384427 integers for clauses
% 66.20/66.60 *** allocated 256285 integers for justifications
% 66.20/66.60 *** allocated 256285 integers for termspace/termends
% 66.20/66.60 *** allocated 384427 integers for justifications
% 66.20/66.60 *** allocated 384427 integers for termspace/termends
% 66.20/66.60 *** allocated 576640 integers for clauses
% 66.20/66.60 *** allocated 576640 integers for justifications
% 66.20/66.60 eqswap: (3692) {G2,W6,D2,L2,V2,M2} { Y = X, alpha1( X, Y ) }.
% 66.20/66.60 parent0[0]: (107) {G2,W6,D2,L2,V2,M2} S(12);r(34) { X = Y, alpha1( X, Y )
% 66.20/66.60 }.
% 66.20/66.60 substitution0:
% 66.20/66.60 X := X
% 66.20/66.60 Y := Y
% 66.20/66.60 end
% 66.20/66.60
% 66.20/66.60 eqswap: (3693) {G0,W3,D2,L1,V0,M1} { ! vd151 ==> vd165 }.
% 66.20/66.60 parent0[0]: (2) {G0,W3,D2,L1,V0,M1} I { ! vd165 ==> vd151 }.
% 66.20/66.60 substitution0:
% 66.20/66.60 end
% 66.20/66.60
% 66.20/66.60 paramod: (3695) {G1,W6,D2,L2,V1,M2} { ! vd151 ==> X, alpha1( X, vd165 )
% 66.20/66.60 }.
% 66.20/66.60 parent0[0]: (3692) {G2,W6,D2,L2,V2,M2} { Y = X, alpha1( X, Y ) }.
% 66.20/66.60 parent1[0; 3]: (3693) {G0,W3,D2,L1,V0,M1} { ! vd151 ==> vd165 }.
% 66.20/66.60 substitution0:
% 66.20/66.60 X := X
% 66.20/66.60 Y := vd165
% 66.20/66.60 end
% 66.20/66.60 substitution1:
% 66.20/66.60 end
% 66.20/66.60
% 66.20/66.60 eqswap: (3737) {G1,W6,D2,L2,V1,M2} { ! X ==> vd151, alpha1( X, vd165 ) }.
% 66.20/66.60 parent0[0]: (3695) {G1,W6,D2,L2,V1,M2} { ! vd151 ==> X, alpha1( X, vd165 )
% 66.20/66.60 }.
% 66.20/66.60 substitution0:
% 66.20/66.60 X := X
% 66.20/66.60 end
% 66.20/66.60
% 66.20/66.60 subsumption: (163) {G3,W6,D2,L2,V1,M2} P(107,2) { ! X = vd151, alpha1( X,
% 66.20/66.60 vd165Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------