TSTP Solution File: NUN080+2 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : NUN080+2 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n028.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 16:19:16 EDT 2022
% Result : Theorem 2.16s 2.58s
% Output : Refutation 2.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUN080+2 : TPTP v8.1.0. Released v7.3.0.
% 0.03/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n028.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % DateTime : Thu Jun 2 03:00:23 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.16/2.58 *** allocated 10000 integers for termspace/termends
% 2.16/2.58 *** allocated 10000 integers for clauses
% 2.16/2.58 *** allocated 10000 integers for justifications
% 2.16/2.58 Bliksem 1.12
% 2.16/2.58
% 2.16/2.58
% 2.16/2.58 Automatic Strategy Selection
% 2.16/2.58
% 2.16/2.58
% 2.16/2.58 Clauses:
% 2.16/2.58
% 2.16/2.58 { alpha1( skol1, X ), r1( X ) }.
% 2.16/2.58 { alpha1( skol1, X ), X = skol1 }.
% 2.16/2.58 { ! alpha1( X, Y ), ! r1( Y ) }.
% 2.16/2.58 { ! alpha1( X, Y ), ! Y = X }.
% 2.16/2.58 { r1( Y ), Y = X, alpha1( X, Y ) }.
% 2.16/2.58 { alpha2( X, skol2( X ), Y ), r2( X, Y ) }.
% 2.16/2.58 { alpha2( X, skol2( X ), Y ), Y = skol2( X ) }.
% 2.16/2.58 { ! alpha2( X, Y, Z ), ! r2( X, Z ) }.
% 2.16/2.58 { ! alpha2( X, Y, Z ), ! Z = Y }.
% 2.16/2.58 { r2( X, Z ), Z = Y, alpha2( X, Y, Z ) }.
% 2.16/2.58 { alpha3( X, Y, skol3( X, Y ), Z ), r3( X, Y, Z ) }.
% 2.16/2.58 { alpha3( X, Y, skol3( X, Y ), Z ), Z = skol3( X, Y ) }.
% 2.16/2.58 { ! alpha3( X, Y, Z, T ), ! r3( X, Y, T ) }.
% 2.16/2.58 { ! alpha3( X, Y, Z, T ), ! T = Z }.
% 2.16/2.58 { r3( X, Y, T ), T = Z, alpha3( X, Y, Z, T ) }.
% 2.16/2.58 { alpha4( X, Y, skol4( X, Y ), Z ), r4( X, Y, Z ) }.
% 2.16/2.58 { alpha4( X, Y, skol4( X, Y ), Z ), Z = skol4( X, Y ) }.
% 2.16/2.58 { ! alpha4( X, Y, Z, T ), ! r4( X, Y, T ) }.
% 2.16/2.58 { ! alpha4( X, Y, Z, T ), ! T = Z }.
% 2.16/2.58 { r4( X, Y, T ), T = Z, alpha4( X, Y, Z, T ) }.
% 2.16/2.58 { r2( Y, skol16( Z, Y ) ) }.
% 2.16/2.58 { r3( X, skol16( X, Y ), skol11( X, Y ) ) }.
% 2.16/2.58 { skol11( X, Y ) = skol5( X, Y ) }.
% 2.16/2.58 { r2( skol19( X, Y ), skol5( X, Y ) ) }.
% 2.16/2.58 { r3( X, Y, skol19( X, Y ) ) }.
% 2.16/2.58 { r2( Y, skol17( Z, Y ) ) }.
% 2.16/2.58 { r4( X, skol17( X, Y ), skol12( X, Y ) ) }.
% 2.16/2.58 { skol12( X, Y ) = skol6( X, Y ) }.
% 2.16/2.58 { r3( skol20( X, Y ), X, skol6( X, Y ) ) }.
% 2.16/2.58 { r4( X, Y, skol20( X, Y ) ) }.
% 2.16/2.58 { ! r2( X, T ), ! T = Z, ! r2( Y, Z ), X = Y }.
% 2.16/2.58 { r1( skol13( Y ) ) }.
% 2.16/2.58 { r3( X, skol13( X ), skol7( X ) ) }.
% 2.16/2.58 { skol7( X ) = X }.
% 2.16/2.58 { r1( skol14( Z ) ) }.
% 2.16/2.58 { skol8( Y ) = skol14( Y ) }.
% 2.16/2.58 { r1( skol18( Y ) ) }.
% 2.16/2.58 { r4( X, skol18( X ), skol8( X ) ) }.
% 2.16/2.58 { alpha5( X ), r2( skol15( Y ), skol9( Y ) ) }.
% 2.16/2.58 { alpha5( X ), X = skol9( X ) }.
% 2.16/2.58 { ! alpha5( X ), r1( skol10( Y ) ) }.
% 2.16/2.58 { ! alpha5( X ), X = skol10( X ) }.
% 2.16/2.58 { ! r1( Y ), ! X = Y, alpha5( X ) }.
% 2.16/2.58 { ! r1( Y ), ! Y = X, ! r2( Z, X ) }.
% 2.16/2.58 { ! X = Y, ! r3( T, Z, X ), ! r2( U, Z ), ! r1( W ), ! r2( W, U ) }.
% 2.16/2.58
% 2.16/2.58 percentage equality = 0.273810, percentage horn = 0.688889
% 2.16/2.58 This is a problem with some equality
% 2.16/2.58
% 2.16/2.58
% 2.16/2.58
% 2.16/2.58 Options Used:
% 2.16/2.58
% 2.16/2.58 useres = 1
% 2.16/2.58 useparamod = 1
% 2.16/2.58 useeqrefl = 1
% 2.16/2.58 useeqfact = 1
% 2.16/2.58 usefactor = 1
% 2.16/2.58 usesimpsplitting = 0
% 2.16/2.58 usesimpdemod = 5
% 2.16/2.58 usesimpres = 3
% 2.16/2.58
% 2.16/2.58 resimpinuse = 1000
% 2.16/2.58 resimpclauses = 20000
% 2.16/2.58 substype = eqrewr
% 2.16/2.58 backwardsubs = 1
% 2.16/2.58 selectoldest = 5
% 2.16/2.58
% 2.16/2.58 litorderings [0] = split
% 2.16/2.58 litorderings [1] = extend the termordering, first sorting on arguments
% 2.16/2.58
% 2.16/2.58 termordering = kbo
% 2.16/2.58
% 2.16/2.58 litapriori = 0
% 2.16/2.58 termapriori = 1
% 2.16/2.58 litaposteriori = 0
% 2.16/2.58 termaposteriori = 0
% 2.16/2.58 demodaposteriori = 0
% 2.16/2.58 ordereqreflfact = 0
% 2.16/2.58
% 2.16/2.58 litselect = negord
% 2.16/2.58
% 2.16/2.58 maxweight = 15
% 2.16/2.58 maxdepth = 30000
% 2.16/2.58 maxlength = 115
% 2.16/2.58 maxnrvars = 195
% 2.16/2.58 excuselevel = 1
% 2.16/2.58 increasemaxweight = 1
% 2.16/2.58
% 2.16/2.58 maxselected = 10000000
% 2.16/2.58 maxnrclauses = 10000000
% 2.16/2.58
% 2.16/2.58 showgenerated = 0
% 2.16/2.58 showkept = 0
% 2.16/2.58 showselected = 0
% 2.16/2.58 showdeleted = 0
% 2.16/2.58 showresimp = 1
% 2.16/2.58 showstatus = 2000
% 2.16/2.58
% 2.16/2.58 prologoutput = 0
% 2.16/2.58 nrgoals = 5000000
% 2.16/2.58 totalproof = 1
% 2.16/2.58
% 2.16/2.58 Symbols occurring in the translation:
% 2.16/2.58
% 2.16/2.58 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 2.16/2.58 . [1, 2] (w:1, o:66, a:1, s:1, b:0),
% 2.16/2.58 ! [4, 1] (w:0, o:50, a:1, s:1, b:0),
% 2.16/2.58 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 2.16/2.58 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 2.16/2.58 r1 [37, 1] (w:1, o:55, a:1, s:1, b:0),
% 2.16/2.58 r2 [41, 2] (w:1, o:90, a:1, s:1, b:0),
% 2.16/2.58 r3 [46, 3] (w:1, o:102, a:1, s:1, b:0),
% 2.16/2.58 r4 [51, 3] (w:1, o:103, a:1, s:1, b:0),
% 2.16/2.58 alpha1 [82, 2] (w:1, o:91, a:1, s:1, b:1),
% 2.16/2.58 alpha2 [83, 3] (w:1, o:104, a:1, s:1, b:1),
% 2.16/2.58 alpha3 [84, 4] (w:1, o:105, a:1, s:1, b:1),
% 2.16/2.58 alpha4 [85, 4] (w:1, o:106, a:1, s:1, b:1),
% 2.16/2.58 alpha5 [86, 1] (w:1, o:56, a:1, s:1, b:1),
% 2.16/2.58 skol1 [87, 0] (w:1, o:49, a:1, s:1, b:1),
% 2.16/2.58 skol2 [88, 1] (w:1, o:62, a:1, s:1, b:1),
% 2.16/2.58 skol3 [89, 2] (w:1, o:93, a:1, s:1, b:1),
% 2.16/2.58 skol4 [90, 2] (w:1, o:94, a:1, s:1, b:1),
% 2.16/2.58 skol5 [91, 2] (w:1, o:95, a:1, s:1, b:1),
% 2.16/2.58 skol6 [92, 2] (w:1, o:96, a:1, s:1, b:1),
% 2.16/2.58 skol7 [93, 1] (w:1, o:63, a:1, s:1, b:1),
% 2.16/2.58 skol8 [94, 1] (w:1, o:64, a:1, s:1, b:1),
% 2.16/2.58 skol9 [95, 1] (w:1, o:65, a:1, s:1, b:1),
% 2.16/2.58 skol10 [96, 1] (w:1, o:57, a:1, s:1, b:1),
% 2.16/2.58 skol11 [97, 2] (w:1, o:97, a:1, s:1, b:1),
% 2.16/2.58 skol12 [98, 2] (w:1, o:98, a:1, s:1, b:1),
% 2.16/2.58 skol13 [99, 1] (w:1, o:58, a:1, s:1, b:1),
% 2.16/2.58 skol14 [100, 1] (w:1, o:59, a:1, s:1, b:1),
% 2.16/2.58 skol15 [101, 1] (w:1, o:60, a:1, s:1, b:1),
% 2.16/2.58 skol16 [102, 2] (w:1, o:99, a:1, s:1, b:1),
% 2.16/2.58 skol17 [103, 2] (w:1, o:100, a:1, s:1, b:1),
% 2.16/2.58 skol18 [104, 1] (w:1, o:61, a:1, s:1, b:1),
% 2.16/2.58 skol19 [105, 2] (w:1, o:101, a:1, s:1, b:1),
% 2.16/2.58 skol20 [106, 2] (w:1, o:92, a:1, s:1, b:1).
% 2.16/2.58
% 2.16/2.58
% 2.16/2.58 Starting Search:
% 2.16/2.58
% 2.16/2.58 *** allocated 15000 integers for clauses
% 2.16/2.58 *** allocated 22500 integers for clauses
% 2.16/2.58 *** allocated 33750 integers for clauses
% 2.16/2.58 *** allocated 50625 integers for clauses
% 2.16/2.58 *** allocated 15000 integers for termspace/termends
% 2.16/2.58 Resimplifying inuse:
% 2.16/2.58 Done
% 2.16/2.58
% 2.16/2.58 *** allocated 75937 integers for clauses
% 2.16/2.58 *** allocated 22500 integers for termspace/termends
% 2.16/2.58 *** allocated 113905 integers for clauses
% 2.16/2.58 *** allocated 33750 integers for termspace/termends
% 2.16/2.58
% 2.16/2.58 Intermediate Status:
% 2.16/2.58 Generated: 7096
% 2.16/2.58 Kept: 2002
% 2.16/2.58 Inuse: 209
% 2.16/2.58 Deleted: 44
% 2.16/2.58 Deletedinuse: 25
% 2.16/2.58
% 2.16/2.58 Resimplifying inuse:
% 2.16/2.58 Done
% 2.16/2.58
% 2.16/2.58 *** allocated 170857 integers for clauses
% 2.16/2.58 *** allocated 50625 integers for termspace/termends
% 2.16/2.58 Resimplifying inuse:
% 2.16/2.58 Done
% 2.16/2.58
% 2.16/2.58 *** allocated 75937 integers for termspace/termends
% 2.16/2.58
% 2.16/2.58 Intermediate Status:
% 2.16/2.58 Generated: 16862
% 2.16/2.58 Kept: 4007
% 2.16/2.58 Inuse: 289
% 2.16/2.58 Deleted: 74
% 2.16/2.58 Deletedinuse: 44
% 2.16/2.58
% 2.16/2.58 *** allocated 256285 integers for clauses
% 2.16/2.58 Resimplifying inuse:
% 2.16/2.58 Done
% 2.16/2.58
% 2.16/2.58 Resimplifying inuse:
% 2.16/2.58 Done
% 2.16/2.58
% 2.16/2.58 *** allocated 113905 integers for termspace/termends
% 2.16/2.58
% 2.16/2.58 Intermediate Status:
% 2.16/2.58 Generated: 25121
% 2.16/2.58 Kept: 6034
% 2.16/2.58 Inuse: 345
% 2.16/2.58 Deleted: 87
% 2.16/2.58 Deletedinuse: 49
% 2.16/2.58
% 2.16/2.58 *** allocated 384427 integers for clauses
% 2.16/2.58 Resimplifying inuse:
% 2.16/2.58 Done
% 2.16/2.58
% 2.16/2.58 Resimplifying inuse:
% 2.16/2.58 Done
% 2.16/2.58
% 2.16/2.58
% 2.16/2.58 Intermediate Status:
% 2.16/2.58 Generated: 36912
% 2.16/2.58 Kept: 8053
% 2.16/2.58 Inuse: 418
% 2.16/2.58 Deleted: 107
% 2.16/2.58 Deletedinuse: 49
% 2.16/2.58
% 2.16/2.58 Resimplifying inuse:
% 2.16/2.58 Done
% 2.16/2.58
% 2.16/2.58 *** allocated 170857 integers for termspace/termends
% 2.16/2.58 *** allocated 576640 integers for clauses
% 2.16/2.58 Resimplifying inuse:
% 2.16/2.58 Done
% 2.16/2.58
% 2.16/2.58
% 2.16/2.58 Intermediate Status:
% 2.16/2.58 Generated: 44790
% 2.16/2.58 Kept: 10067
% 2.16/2.58 Inuse: 458
% 2.16/2.58 Deleted: 109
% 2.16/2.58 Deletedinuse: 50
% 2.16/2.58
% 2.16/2.58 Resimplifying inuse:
% 2.16/2.58 Done
% 2.16/2.58
% 2.16/2.58 Resimplifying inuse:
% 2.16/2.58 Done
% 2.16/2.58
% 2.16/2.58
% 2.16/2.58 Intermediate Status:
% 2.16/2.58 Generated: 54678
% 2.16/2.58 Kept: 12129
% 2.16/2.58 Inuse: 509
% 2.16/2.58 Deleted: 122
% 2.16/2.58 Deletedinuse: 53
% 2.16/2.58
% 2.16/2.58 Resimplifying inuse:
% 2.16/2.58 Done
% 2.16/2.58
% 2.16/2.58 *** allocated 256285 integers for termspace/termends
% 2.16/2.58 Resimplifying inuse:
% 2.16/2.58 Done
% 2.16/2.58
% 2.16/2.58
% 2.16/2.58 Intermediate Status:
% 2.16/2.58 Generated: 71110
% 2.16/2.58 Kept: 14129
% 2.16/2.58 Inuse: 571
% 2.16/2.58 Deleted: 137
% 2.16/2.58 Deletedinuse: 53
% 2.16/2.58
% 2.16/2.58 *** allocated 864960 integers for clauses
% 2.16/2.58
% 2.16/2.58 Bliksems!, er is een bewijs:
% 2.16/2.58 % SZS status Theorem
% 2.16/2.58 % SZS output start Refutation
% 2.16/2.58
% 2.16/2.58 (0) {G0,W5,D2,L2,V1,M2} I { alpha1( skol1, X ), r1( X ) }.
% 2.16/2.58 (1) {G0,W6,D2,L2,V1,M2} I { alpha1( skol1, X ), X = skol1 }.
% 2.16/2.58 (2) {G0,W5,D2,L2,V2,M2} I { ! alpha1( X, Y ), ! r1( Y ) }.
% 2.16/2.58 (3) {G0,W6,D2,L2,V2,M2} I { ! alpha1( X, Y ), ! Y = X }.
% 2.16/2.58 (5) {G0,W8,D3,L2,V2,M2} I { alpha2( X, skol2( X ), Y ), r2( X, Y ) }.
% 2.16/2.58 (8) {G0,W7,D2,L2,V3,M2} I { ! alpha2( X, Y, Z ), ! Z = Y }.
% 2.16/2.58 (23) {G0,W7,D3,L1,V2,M1} I { r2( skol19( X, Y ), skol5( X, Y ) ) }.
% 2.16/2.58 (28) {G0,W8,D3,L1,V2,M1} I { r3( skol20( X, Y ), X, skol6( X, Y ) ) }.
% 2.16/2.58 (30) {G0,W12,D2,L4,V4,M4} I { ! r2( X, T ), ! T = Z, ! r2( Y, Z ), X = Y
% 2.16/2.58 }.
% 2.16/2.58 (36) {G0,W3,D3,L1,V1,M1} I { r1( skol18( Y ) ) }.
% 2.16/2.58 (38) {G0,W7,D3,L2,V2,M2} I { alpha5( X ), r2( skol15( Y ), skol9( Y ) ) }.
% 2.16/2.58 (39) {G0,W6,D3,L2,V1,M2} I { alpha5( X ), skol9( X ) ==> X }.
% 2.16/2.58 (40) {G0,W5,D3,L2,V2,M2} I { ! alpha5( X ), r1( skol10( Y ) ) }.
% 2.16/2.58 (41) {G0,W6,D3,L2,V1,M2} I { ! alpha5( X ), skol10( X ) ==> X }.
% 2.16/2.58 (42) {G0,W7,D2,L3,V2,M3} I { ! r1( Y ), ! X = Y, alpha5( X ) }.
% 2.16/2.58 (43) {G0,W8,D2,L3,V3,M3} I { ! r1( Y ), ! Y = X, ! r2( Z, X ) }.
% 2.16/2.58 (44) {G0,W15,D2,L5,V6,M5} I { ! X = Y, ! r3( T, Z, X ), ! r2( U, Z ), ! r1
% 2.16/2.58 ( W ), ! r2( W, U ) }.
% 2.16/2.58 (45) {G1,W3,D2,L1,V1,M1} Q(3) { ! alpha1( X, X ) }.
% 2.16/2.58 (46) {G1,W4,D2,L1,V2,M1} Q(8) { ! alpha2( X, Y, Y ) }.
% 2.16/2.58 (50) {G1,W4,D2,L2,V1,M2} Q(42) { ! r1( X ), alpha5( X ) }.
% 2.16/2.58 (51) {G1,W5,D2,L2,V2,M2} Q(43) { ! r1( X ), ! r2( Y, X ) }.
% 2.16/2.58 (52) {G1,W12,D2,L4,V5,M4} Q(44) { ! r3( X, Y, Z ), ! r2( T, Y ), ! r1( U )
% 2.16/2.58 , ! r2( U, T ) }.
% 2.16/2.58 (53) {G2,W2,D2,L1,V0,M1} R(0,45) { r1( skol1 ) }.
% 2.16/2.58 (58) {G2,W3,D3,L1,V1,M1} R(50,36) { alpha5( skol18( X ) ) }.
% 2.16/2.58 (60) {G1,W5,D2,L2,V1,M2} R(2,1) { ! r1( X ), X = skol1 }.
% 2.16/2.58 (69) {G1,W5,D2,L2,V1,M2} R(3,0) { ! X = skol1, r1( X ) }.
% 2.16/2.58 (73) {G3,W3,D2,L1,V1,M1} R(51,53) { ! r2( X, skol1 ) }.
% 2.16/2.58 (82) {G2,W4,D3,L1,V1,M1} R(5,46) { r2( X, skol2( X ) ) }.
% 2.16/2.58 (186) {G3,W3,D3,L1,V1,M1} R(40,58) { r1( skol10( X ) ) }.
% 2.16/2.58 (193) {G4,W4,D3,L1,V1,M1} R(186,60) { skol10( X ) ==> skol1 }.
% 2.16/2.58 (474) {G5,W5,D2,L2,V1,M2} S(41);d(193) { ! alpha5( X ), skol1 = X }.
% 2.16/2.58 (503) {G6,W5,D2,L2,V2,M2} P(474,73) { ! r2( Y, X ), ! alpha5( X ) }.
% 2.16/2.58 (506) {G6,W4,D2,L2,V1,M2} P(474,53) { r1( X ), ! alpha5( X ) }.
% 2.16/2.58 (520) {G7,W4,D3,L1,V2,M1} R(23,503) { ! alpha5( skol5( X, Y ) ) }.
% 2.16/2.58 (619) {G7,W6,D3,L2,V1,M2} R(39,506) { skol9( X ) ==> X, r1( X ) }.
% 2.16/2.58 (833) {G8,W5,D3,L1,V1,M1} R(38,520) { r2( skol15( X ), skol9( X ) ) }.
% 2.16/2.58 (885) {G9,W6,D3,L2,V1,M2} P(619,833) { r2( skol15( X ), X ), r1( X ) }.
% 2.16/2.58 (1041) {G10,W7,D3,L2,V2,M2} R(885,51) { r2( skol15( X ), X ), ! r2( Y, X )
% 2.16/2.58 }.
% 2.16/2.58 (1119) {G2,W8,D2,L3,V3,M3} R(52,28) { ! r2( X, Y ), ! r1( Z ), ! r2( Z, X )
% 2.16/2.58 }.
% 2.16/2.58 (2326) {G11,W13,D3,L4,V4,M4} R(1041,30) { ! r2( X, Y ), ! Y = Z, ! r2( T, Z
% 2.16/2.58 ), skol15( Y ) = T }.
% 2.16/2.58 (2355) {G12,W7,D3,L2,V2,M2} F(2326);q { ! r2( X, Y ), skol15( Y ) = X }.
% 2.16/2.58 (2494) {G13,W5,D4,L1,V1,M1} R(2355,82) { skol15( skol2( X ) ) ==> X }.
% 2.16/2.58 (2497) {G13,W6,D3,L2,V1,M2} R(2355,69) { ! r2( skol1, X ), r1( skol15( X )
% 2.16/2.58 ) }.
% 2.16/2.58 (2727) {G14,W6,D3,L2,V1,M2} P(2494,2497) { ! r2( skol1, skol2( X ) ), r1( X
% 2.16/2.58 ) }.
% 2.16/2.58 (14808) {G15,W10,D3,L3,V3,M3} R(1119,2727) { ! r2( X, Y ), ! r2( Z, X ), !
% 2.16/2.58 r2( skol1, skol2( Z ) ) }.
% 2.16/2.58 (14844) {G16,W4,D3,L1,V1,M1} F(14808);r(82) { ! r2( skol2( skol1 ), X ) }.
% 2.16/2.58 (14885) {G17,W0,D0,L0,V0,M0} R(14844,82) { }.
% 2.16/2.58
% 2.16/2.58
% 2.16/2.58 % SZS output end Refutation
% 2.16/2.58 found a proof!
% 2.16/2.58
% 2.16/2.58
% 2.16/2.58 Unprocessed initial clauses:
% 2.16/2.58
% 2.16/2.58 (14887) {G0,W5,D2,L2,V1,M2} { alpha1( skol1, X ), r1( X ) }.
% 2.16/2.58 (14888) {G0,W6,D2,L2,V1,M2} { alpha1( skol1, X ), X = skol1 }.
% 2.16/2.58 (14889) {G0,W5,D2,L2,V2,M2} { ! alpha1( X, Y ), ! r1( Y ) }.
% 2.16/2.58 (14890) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), ! Y = X }.
% 2.16/2.58 (14891) {G0,W8,D2,L3,V2,M3} { r1( Y ), Y = X, alpha1( X, Y ) }.
% 2.16/2.58 (14892) {G0,W8,D3,L2,V2,M2} { alpha2( X, skol2( X ), Y ), r2( X, Y ) }.
% 2.16/2.58 (14893) {G0,W9,D3,L2,V2,M2} { alpha2( X, skol2( X ), Y ), Y = skol2( X )
% 2.16/2.58 }.
% 2.16/2.58 (14894) {G0,W7,D2,L2,V3,M2} { ! alpha2( X, Y, Z ), ! r2( X, Z ) }.
% 2.16/2.58 (14895) {G0,W7,D2,L2,V3,M2} { ! alpha2( X, Y, Z ), ! Z = Y }.
% 2.16/2.58 (14896) {G0,W10,D2,L3,V3,M3} { r2( X, Z ), Z = Y, alpha2( X, Y, Z ) }.
% 2.16/2.58 (14897) {G0,W11,D3,L2,V3,M2} { alpha3( X, Y, skol3( X, Y ), Z ), r3( X, Y
% 2.16/2.58 , Z ) }.
% 2.16/2.58 (14898) {G0,W12,D3,L2,V3,M2} { alpha3( X, Y, skol3( X, Y ), Z ), Z = skol3
% 2.16/2.58 ( X, Y ) }.
% 2.16/2.58 (14899) {G0,W9,D2,L2,V4,M2} { ! alpha3( X, Y, Z, T ), ! r3( X, Y, T ) }.
% 2.16/2.58 (14900) {G0,W8,D2,L2,V4,M2} { ! alpha3( X, Y, Z, T ), ! T = Z }.
% 2.16/2.58 (14901) {G0,W12,D2,L3,V4,M3} { r3( X, Y, T ), T = Z, alpha3( X, Y, Z, T )
% 2.16/2.58 }.
% 2.16/2.58 (14902) {G0,W11,D3,L2,V3,M2} { alpha4( X, Y, skol4( X, Y ), Z ), r4( X, Y
% 2.16/2.58 , Z ) }.
% 2.16/2.58 (14903) {G0,W12,D3,L2,V3,M2} { alpha4( X, Y, skol4( X, Y ), Z ), Z = skol4
% 2.16/2.58 ( X, Y ) }.
% 2.16/2.58 (14904) {G0,W9,D2,L2,V4,M2} { ! alpha4( X, Y, Z, T ), ! r4( X, Y, T ) }.
% 2.16/2.58 (14905) {G0,W8,D2,L2,V4,M2} { ! alpha4( X, Y, Z, T ), ! T = Z }.
% 2.16/2.58 (14906) {G0,W12,D2,L3,V4,M3} { r4( X, Y, T ), T = Z, alpha4( X, Y, Z, T )
% 2.16/2.58 }.
% 2.16/2.58 (14907) {G0,W5,D3,L1,V2,M1} { r2( Y, skol16( Z, Y ) ) }.
% 2.16/2.58 (14908) {G0,W8,D3,L1,V2,M1} { r3( X, skol16( X, Y ), skol11( X, Y ) ) }.
% 2.16/2.58 (14909) {G0,W7,D3,L1,V2,M1} { skol11( X, Y ) = skol5( X, Y ) }.
% 2.16/2.58 (14910) {G0,W7,D3,L1,V2,M1} { r2( skol19( X, Y ), skol5( X, Y ) ) }.
% 2.16/2.58 (14911) {G0,W6,D3,L1,V2,M1} { r3( X, Y, skol19( X, Y ) ) }.
% 2.16/2.58 (14912) {G0,W5,D3,L1,V2,M1} { r2( Y, skol17( Z, Y ) ) }.
% 2.16/2.58 (14913) {G0,W8,D3,L1,V2,M1} { r4( X, skol17( X, Y ), skol12( X, Y ) ) }.
% 2.16/2.58 (14914) {G0,W7,D3,L1,V2,M1} { skol12( X, Y ) = skol6( X, Y ) }.
% 2.16/2.58 (14915) {G0,W8,D3,L1,V2,M1} { r3( skol20( X, Y ), X, skol6( X, Y ) ) }.
% 2.16/2.58 (14916) {G0,W6,D3,L1,V2,M1} { r4( X, Y, skol20( X, Y ) ) }.
% 2.16/2.58 (14917) {G0,W12,D2,L4,V4,M4} { ! r2( X, T ), ! T = Z, ! r2( Y, Z ), X = Y
% 2.16/2.58 }.
% 2.16/2.58 (14918) {G0,W3,D3,L1,V1,M1} { r1( skol13( Y ) ) }.
% 2.16/2.58 (14919) {G0,W6,D3,L1,V1,M1} { r3( X, skol13( X ), skol7( X ) ) }.
% 2.16/2.58 (14920) {G0,W4,D3,L1,V1,M1} { skol7( X ) = X }.
% 2.16/2.58 (14921) {G0,W3,D3,L1,V1,M1} { r1( skol14( Z ) ) }.
% 2.16/2.58 (14922) {G0,W5,D3,L1,V1,M1} { skol8( Y ) = skol14( Y ) }.
% 2.16/2.58 (14923) {G0,W3,D3,L1,V1,M1} { r1( skol18( Y ) ) }.
% 2.16/2.58 (14924) {G0,W6,D3,L1,V1,M1} { r4( X, skol18( X ), skol8( X ) ) }.
% 2.16/2.58 (14925) {G0,W7,D3,L2,V2,M2} { alpha5( X ), r2( skol15( Y ), skol9( Y ) )
% 2.16/2.58 }.
% 2.16/2.58 (14926) {G0,W6,D3,L2,V1,M2} { alpha5( X ), X = skol9( X ) }.
% 2.16/2.58 (14927) {G0,W5,D3,L2,V2,M2} { ! alpha5( X ), r1( skol10( Y ) ) }.
% 2.16/2.58 (14928) {G0,W6,D3,L2,V1,M2} { ! alpha5( X ), X = skol10( X ) }.
% 2.16/2.58 (14929) {G0,W7,D2,L3,V2,M3} { ! r1( Y ), ! X = Y, alpha5( X ) }.
% 2.16/2.58 (14930) {G0,W8,D2,L3,V3,M3} { ! r1( Y ), ! Y = X, ! r2( Z, X ) }.
% 2.16/2.58 (14931) {G0,W15,D2,L5,V6,M5} { ! X = Y, ! r3( T, Z, X ), ! r2( U, Z ), !
% 2.16/2.58 r1( W ), ! r2( W, U ) }.
% 2.16/2.58
% 2.16/2.58
% 2.16/2.58 Total Proof:
% 2.16/2.58
% 2.16/2.58 subsumption: (0) {G0,W5,D2,L2,V1,M2} I { alpha1( skol1, X ), r1( X ) }.
% 2.16/2.58 parent0: (14887) {G0,W5,D2,L2,V1,M2} { alpha1( skol1, X ), r1( X ) }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := X
% 2.16/2.58 end
% 2.16/2.58 permutation0:
% 2.16/2.58 0 ==> 0
% 2.16/2.58 1 ==> 1
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 subsumption: (1) {G0,W6,D2,L2,V1,M2} I { alpha1( skol1, X ), X = skol1 }.
% 2.16/2.58 parent0: (14888) {G0,W6,D2,L2,V1,M2} { alpha1( skol1, X ), X = skol1 }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := X
% 2.16/2.58 end
% 2.16/2.58 permutation0:
% 2.16/2.58 0 ==> 0
% 2.16/2.58 1 ==> 1
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 subsumption: (2) {G0,W5,D2,L2,V2,M2} I { ! alpha1( X, Y ), ! r1( Y ) }.
% 2.16/2.58 parent0: (14889) {G0,W5,D2,L2,V2,M2} { ! alpha1( X, Y ), ! r1( Y ) }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := X
% 2.16/2.58 Y := Y
% 2.16/2.58 end
% 2.16/2.58 permutation0:
% 2.16/2.58 0 ==> 0
% 2.16/2.58 1 ==> 1
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 subsumption: (3) {G0,W6,D2,L2,V2,M2} I { ! alpha1( X, Y ), ! Y = X }.
% 2.16/2.58 parent0: (14890) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), ! Y = X }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := X
% 2.16/2.58 Y := Y
% 2.16/2.58 end
% 2.16/2.58 permutation0:
% 2.16/2.58 0 ==> 0
% 2.16/2.58 1 ==> 1
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 subsumption: (5) {G0,W8,D3,L2,V2,M2} I { alpha2( X, skol2( X ), Y ), r2( X
% 2.16/2.58 , Y ) }.
% 2.16/2.58 parent0: (14892) {G0,W8,D3,L2,V2,M2} { alpha2( X, skol2( X ), Y ), r2( X,
% 2.16/2.58 Y ) }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := X
% 2.16/2.58 Y := Y
% 2.16/2.58 end
% 2.16/2.58 permutation0:
% 2.16/2.58 0 ==> 0
% 2.16/2.58 1 ==> 1
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 subsumption: (8) {G0,W7,D2,L2,V3,M2} I { ! alpha2( X, Y, Z ), ! Z = Y }.
% 2.16/2.58 parent0: (14895) {G0,W7,D2,L2,V3,M2} { ! alpha2( X, Y, Z ), ! Z = Y }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := X
% 2.16/2.58 Y := Y
% 2.16/2.58 Z := Z
% 2.16/2.58 end
% 2.16/2.58 permutation0:
% 2.16/2.58 0 ==> 0
% 2.16/2.58 1 ==> 1
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 subsumption: (23) {G0,W7,D3,L1,V2,M1} I { r2( skol19( X, Y ), skol5( X, Y )
% 2.16/2.58 ) }.
% 2.16/2.58 parent0: (14910) {G0,W7,D3,L1,V2,M1} { r2( skol19( X, Y ), skol5( X, Y ) )
% 2.16/2.58 }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := X
% 2.16/2.58 Y := Y
% 2.16/2.58 end
% 2.16/2.58 permutation0:
% 2.16/2.58 0 ==> 0
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 subsumption: (28) {G0,W8,D3,L1,V2,M1} I { r3( skol20( X, Y ), X, skol6( X,
% 2.16/2.58 Y ) ) }.
% 2.16/2.58 parent0: (14915) {G0,W8,D3,L1,V2,M1} { r3( skol20( X, Y ), X, skol6( X, Y
% 2.16/2.58 ) ) }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := X
% 2.16/2.58 Y := Y
% 2.16/2.58 end
% 2.16/2.58 permutation0:
% 2.16/2.58 0 ==> 0
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 subsumption: (30) {G0,W12,D2,L4,V4,M4} I { ! r2( X, T ), ! T = Z, ! r2( Y,
% 2.16/2.58 Z ), X = Y }.
% 2.16/2.58 parent0: (14917) {G0,W12,D2,L4,V4,M4} { ! r2( X, T ), ! T = Z, ! r2( Y, Z
% 2.16/2.58 ), X = Y }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := X
% 2.16/2.58 Y := Y
% 2.16/2.58 Z := Z
% 2.16/2.58 T := T
% 2.16/2.58 end
% 2.16/2.58 permutation0:
% 2.16/2.58 0 ==> 0
% 2.16/2.58 1 ==> 1
% 2.16/2.58 2 ==> 2
% 2.16/2.58 3 ==> 3
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 subsumption: (36) {G0,W3,D3,L1,V1,M1} I { r1( skol18( Y ) ) }.
% 2.16/2.58 parent0: (14923) {G0,W3,D3,L1,V1,M1} { r1( skol18( Y ) ) }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := Z
% 2.16/2.58 Y := Y
% 2.16/2.58 end
% 2.16/2.58 permutation0:
% 2.16/2.58 0 ==> 0
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 subsumption: (38) {G0,W7,D3,L2,V2,M2} I { alpha5( X ), r2( skol15( Y ),
% 2.16/2.58 skol9( Y ) ) }.
% 2.16/2.58 parent0: (14925) {G0,W7,D3,L2,V2,M2} { alpha5( X ), r2( skol15( Y ), skol9
% 2.16/2.58 ( Y ) ) }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := X
% 2.16/2.58 Y := Y
% 2.16/2.58 end
% 2.16/2.58 permutation0:
% 2.16/2.58 0 ==> 0
% 2.16/2.58 1 ==> 1
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 eqswap: (15041) {G0,W6,D3,L2,V1,M2} { skol9( X ) = X, alpha5( X ) }.
% 2.16/2.58 parent0[1]: (14926) {G0,W6,D3,L2,V1,M2} { alpha5( X ), X = skol9( X ) }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := X
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 subsumption: (39) {G0,W6,D3,L2,V1,M2} I { alpha5( X ), skol9( X ) ==> X }.
% 2.16/2.58 parent0: (15041) {G0,W6,D3,L2,V1,M2} { skol9( X ) = X, alpha5( X ) }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := X
% 2.16/2.58 end
% 2.16/2.58 permutation0:
% 2.16/2.58 0 ==> 1
% 2.16/2.58 1 ==> 0
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 subsumption: (40) {G0,W5,D3,L2,V2,M2} I { ! alpha5( X ), r1( skol10( Y ) )
% 2.16/2.58 }.
% 2.16/2.58 parent0: (14927) {G0,W5,D3,L2,V2,M2} { ! alpha5( X ), r1( skol10( Y ) )
% 2.16/2.58 }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := X
% 2.16/2.58 Y := Y
% 2.16/2.58 end
% 2.16/2.58 permutation0:
% 2.16/2.58 0 ==> 0
% 2.16/2.58 1 ==> 1
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 eqswap: (15080) {G0,W6,D3,L2,V1,M2} { skol10( X ) = X, ! alpha5( X ) }.
% 2.16/2.58 parent0[1]: (14928) {G0,W6,D3,L2,V1,M2} { ! alpha5( X ), X = skol10( X )
% 2.16/2.58 }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := X
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 subsumption: (41) {G0,W6,D3,L2,V1,M2} I { ! alpha5( X ), skol10( X ) ==> X
% 2.16/2.58 }.
% 2.16/2.58 parent0: (15080) {G0,W6,D3,L2,V1,M2} { skol10( X ) = X, ! alpha5( X ) }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := X
% 2.16/2.58 end
% 2.16/2.58 permutation0:
% 2.16/2.58 0 ==> 1
% 2.16/2.58 1 ==> 0
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 subsumption: (42) {G0,W7,D2,L3,V2,M3} I { ! r1( Y ), ! X = Y, alpha5( X )
% 2.16/2.58 }.
% 2.16/2.58 parent0: (14929) {G0,W7,D2,L3,V2,M3} { ! r1( Y ), ! X = Y, alpha5( X ) }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := X
% 2.16/2.58 Y := Y
% 2.16/2.58 end
% 2.16/2.58 permutation0:
% 2.16/2.58 0 ==> 0
% 2.16/2.58 1 ==> 1
% 2.16/2.58 2 ==> 2
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 subsumption: (43) {G0,W8,D2,L3,V3,M3} I { ! r1( Y ), ! Y = X, ! r2( Z, X )
% 2.16/2.58 }.
% 2.16/2.58 parent0: (14930) {G0,W8,D2,L3,V3,M3} { ! r1( Y ), ! Y = X, ! r2( Z, X )
% 2.16/2.58 }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := X
% 2.16/2.58 Y := Y
% 2.16/2.58 Z := Z
% 2.16/2.58 end
% 2.16/2.58 permutation0:
% 2.16/2.58 0 ==> 0
% 2.16/2.58 1 ==> 1
% 2.16/2.58 2 ==> 2
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 subsumption: (44) {G0,W15,D2,L5,V6,M5} I { ! X = Y, ! r3( T, Z, X ), ! r2(
% 2.16/2.58 U, Z ), ! r1( W ), ! r2( W, U ) }.
% 2.16/2.58 parent0: (14931) {G0,W15,D2,L5,V6,M5} { ! X = Y, ! r3( T, Z, X ), ! r2( U
% 2.16/2.58 , Z ), ! r1( W ), ! r2( W, U ) }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := X
% 2.16/2.58 Y := Y
% 2.16/2.58 Z := Z
% 2.16/2.58 T := T
% 2.16/2.58 U := U
% 2.16/2.58 W := W
% 2.16/2.58 end
% 2.16/2.58 permutation0:
% 2.16/2.58 0 ==> 0
% 2.16/2.58 1 ==> 1
% 2.16/2.58 2 ==> 2
% 2.16/2.58 3 ==> 3
% 2.16/2.58 4 ==> 4
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 eqswap: (15149) {G0,W6,D2,L2,V2,M2} { ! Y = X, ! alpha1( Y, X ) }.
% 2.16/2.58 parent0[1]: (3) {G0,W6,D2,L2,V2,M2} I { ! alpha1( X, Y ), ! Y = X }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := Y
% 2.16/2.58 Y := X
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 eqrefl: (15150) {G0,W3,D2,L1,V1,M1} { ! alpha1( X, X ) }.
% 2.16/2.58 parent0[0]: (15149) {G0,W6,D2,L2,V2,M2} { ! Y = X, ! alpha1( Y, X ) }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := X
% 2.16/2.58 Y := X
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 subsumption: (45) {G1,W3,D2,L1,V1,M1} Q(3) { ! alpha1( X, X ) }.
% 2.16/2.58 parent0: (15150) {G0,W3,D2,L1,V1,M1} { ! alpha1( X, X ) }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := X
% 2.16/2.58 end
% 2.16/2.58 permutation0:
% 2.16/2.58 0 ==> 0
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 eqswap: (15151) {G0,W7,D2,L2,V3,M2} { ! Y = X, ! alpha2( Z, Y, X ) }.
% 2.16/2.58 parent0[1]: (8) {G0,W7,D2,L2,V3,M2} I { ! alpha2( X, Y, Z ), ! Z = Y }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := Z
% 2.16/2.58 Y := Y
% 2.16/2.58 Z := X
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 eqrefl: (15152) {G0,W4,D2,L1,V2,M1} { ! alpha2( Y, X, X ) }.
% 2.16/2.58 parent0[0]: (15151) {G0,W7,D2,L2,V3,M2} { ! Y = X, ! alpha2( Z, Y, X ) }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := X
% 2.16/2.58 Y := X
% 2.16/2.58 Z := Y
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 subsumption: (46) {G1,W4,D2,L1,V2,M1} Q(8) { ! alpha2( X, Y, Y ) }.
% 2.16/2.58 parent0: (15152) {G0,W4,D2,L1,V2,M1} { ! alpha2( Y, X, X ) }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := Y
% 2.16/2.58 Y := X
% 2.16/2.58 end
% 2.16/2.58 permutation0:
% 2.16/2.58 0 ==> 0
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 eqswap: (15153) {G0,W7,D2,L3,V2,M3} { ! Y = X, ! r1( Y ), alpha5( X ) }.
% 2.16/2.58 parent0[1]: (42) {G0,W7,D2,L3,V2,M3} I { ! r1( Y ), ! X = Y, alpha5( X )
% 2.16/2.58 }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := X
% 2.16/2.58 Y := Y
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 eqrefl: (15154) {G0,W4,D2,L2,V1,M2} { ! r1( X ), alpha5( X ) }.
% 2.16/2.58 parent0[0]: (15153) {G0,W7,D2,L3,V2,M3} { ! Y = X, ! r1( Y ), alpha5( X )
% 2.16/2.58 }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := X
% 2.16/2.58 Y := X
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 subsumption: (50) {G1,W4,D2,L2,V1,M2} Q(42) { ! r1( X ), alpha5( X ) }.
% 2.16/2.58 parent0: (15154) {G0,W4,D2,L2,V1,M2} { ! r1( X ), alpha5( X ) }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := X
% 2.16/2.58 end
% 2.16/2.58 permutation0:
% 2.16/2.58 0 ==> 0
% 2.16/2.58 1 ==> 1
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 eqswap: (15155) {G0,W8,D2,L3,V3,M3} { ! Y = X, ! r1( X ), ! r2( Z, Y ) }.
% 2.16/2.58 parent0[1]: (43) {G0,W8,D2,L3,V3,M3} I { ! r1( Y ), ! Y = X, ! r2( Z, X )
% 2.16/2.58 }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := Y
% 2.16/2.58 Y := X
% 2.16/2.58 Z := Z
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 eqrefl: (15156) {G0,W5,D2,L2,V2,M2} { ! r1( X ), ! r2( Y, X ) }.
% 2.16/2.58 parent0[0]: (15155) {G0,W8,D2,L3,V3,M3} { ! Y = X, ! r1( X ), ! r2( Z, Y )
% 2.16/2.58 }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := X
% 2.16/2.58 Y := X
% 2.16/2.58 Z := Y
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 subsumption: (51) {G1,W5,D2,L2,V2,M2} Q(43) { ! r1( X ), ! r2( Y, X ) }.
% 2.16/2.58 parent0: (15156) {G0,W5,D2,L2,V2,M2} { ! r1( X ), ! r2( Y, X ) }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := X
% 2.16/2.58 Y := Y
% 2.16/2.58 end
% 2.16/2.58 permutation0:
% 2.16/2.58 0 ==> 0
% 2.16/2.58 1 ==> 1
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 eqswap: (15157) {G0,W15,D2,L5,V6,M5} { ! Y = X, ! r3( Z, T, X ), ! r2( U,
% 2.16/2.58 T ), ! r1( W ), ! r2( W, U ) }.
% 2.16/2.58 parent0[0]: (44) {G0,W15,D2,L5,V6,M5} I { ! X = Y, ! r3( T, Z, X ), ! r2( U
% 2.16/2.58 , Z ), ! r1( W ), ! r2( W, U ) }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := X
% 2.16/2.58 Y := Y
% 2.16/2.58 Z := T
% 2.16/2.58 T := Z
% 2.16/2.58 U := U
% 2.16/2.58 W := W
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 eqrefl: (15158) {G0,W12,D2,L4,V5,M4} { ! r3( Y, Z, X ), ! r2( T, Z ), ! r1
% 2.16/2.58 ( U ), ! r2( U, T ) }.
% 2.16/2.58 parent0[0]: (15157) {G0,W15,D2,L5,V6,M5} { ! Y = X, ! r3( Z, T, X ), ! r2
% 2.16/2.58 ( U, T ), ! r1( W ), ! r2( W, U ) }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := X
% 2.16/2.58 Y := X
% 2.16/2.58 Z := Y
% 2.16/2.58 T := Z
% 2.16/2.58 U := T
% 2.16/2.58 W := U
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 subsumption: (52) {G1,W12,D2,L4,V5,M4} Q(44) { ! r3( X, Y, Z ), ! r2( T, Y
% 2.16/2.58 ), ! r1( U ), ! r2( U, T ) }.
% 2.16/2.58 parent0: (15158) {G0,W12,D2,L4,V5,M4} { ! r3( Y, Z, X ), ! r2( T, Z ), !
% 2.16/2.58 r1( U ), ! r2( U, T ) }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := Z
% 2.16/2.58 Y := X
% 2.16/2.58 Z := Y
% 2.16/2.58 T := T
% 2.16/2.58 U := U
% 2.16/2.58 end
% 2.16/2.58 permutation0:
% 2.16/2.58 0 ==> 0
% 2.16/2.58 1 ==> 1
% 2.16/2.58 2 ==> 2
% 2.16/2.58 3 ==> 3
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 resolution: (15160) {G1,W2,D2,L1,V0,M1} { r1( skol1 ) }.
% 2.16/2.58 parent0[0]: (45) {G1,W3,D2,L1,V1,M1} Q(3) { ! alpha1( X, X ) }.
% 2.16/2.58 parent1[0]: (0) {G0,W5,D2,L2,V1,M2} I { alpha1( skol1, X ), r1( X ) }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := skol1
% 2.16/2.58 end
% 2.16/2.58 substitution1:
% 2.16/2.58 X := skol1
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 subsumption: (53) {G2,W2,D2,L1,V0,M1} R(0,45) { r1( skol1 ) }.
% 2.16/2.58 parent0: (15160) {G1,W2,D2,L1,V0,M1} { r1( skol1 ) }.
% 2.16/2.58 substitution0:
% 2.16/2.58 end
% 2.16/2.58 permutation0:
% 2.16/2.58 0 ==> 0
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 resolution: (15161) {G1,W3,D3,L1,V1,M1} { alpha5( skol18( X ) ) }.
% 2.16/2.58 parent0[0]: (50) {G1,W4,D2,L2,V1,M2} Q(42) { ! r1( X ), alpha5( X ) }.
% 2.16/2.58 parent1[0]: (36) {G0,W3,D3,L1,V1,M1} I { r1( skol18( Y ) ) }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := skol18( X )
% 2.16/2.58 end
% 2.16/2.58 substitution1:
% 2.16/2.58 X := Y
% 2.16/2.58 Y := X
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 subsumption: (58) {G2,W3,D3,L1,V1,M1} R(50,36) { alpha5( skol18( X ) ) }.
% 2.16/2.58 parent0: (15161) {G1,W3,D3,L1,V1,M1} { alpha5( skol18( X ) ) }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := X
% 2.16/2.58 end
% 2.16/2.58 permutation0:
% 2.16/2.58 0 ==> 0
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 eqswap: (15162) {G0,W6,D2,L2,V1,M2} { skol1 = X, alpha1( skol1, X ) }.
% 2.16/2.58 parent0[1]: (1) {G0,W6,D2,L2,V1,M2} I { alpha1( skol1, X ), X = skol1 }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := X
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 resolution: (15163) {G1,W5,D2,L2,V1,M2} { ! r1( X ), skol1 = X }.
% 2.16/2.58 parent0[0]: (2) {G0,W5,D2,L2,V2,M2} I { ! alpha1( X, Y ), ! r1( Y ) }.
% 2.16/2.58 parent1[1]: (15162) {G0,W6,D2,L2,V1,M2} { skol1 = X, alpha1( skol1, X )
% 2.16/2.58 }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := skol1
% 2.16/2.58 Y := X
% 2.16/2.58 end
% 2.16/2.58 substitution1:
% 2.16/2.58 X := X
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 eqswap: (15164) {G1,W5,D2,L2,V1,M2} { X = skol1, ! r1( X ) }.
% 2.16/2.58 parent0[1]: (15163) {G1,W5,D2,L2,V1,M2} { ! r1( X ), skol1 = X }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := X
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 subsumption: (60) {G1,W5,D2,L2,V1,M2} R(2,1) { ! r1( X ), X = skol1 }.
% 2.16/2.58 parent0: (15164) {G1,W5,D2,L2,V1,M2} { X = skol1, ! r1( X ) }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := X
% 2.16/2.58 end
% 2.16/2.58 permutation0:
% 2.16/2.58 0 ==> 1
% 2.16/2.58 1 ==> 0
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 eqswap: (15165) {G0,W6,D2,L2,V2,M2} { ! Y = X, ! alpha1( Y, X ) }.
% 2.16/2.58 parent0[1]: (3) {G0,W6,D2,L2,V2,M2} I { ! alpha1( X, Y ), ! Y = X }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := Y
% 2.16/2.58 Y := X
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 resolution: (15166) {G1,W5,D2,L2,V1,M2} { ! skol1 = X, r1( X ) }.
% 2.16/2.58 parent0[1]: (15165) {G0,W6,D2,L2,V2,M2} { ! Y = X, ! alpha1( Y, X ) }.
% 2.16/2.58 parent1[0]: (0) {G0,W5,D2,L2,V1,M2} I { alpha1( skol1, X ), r1( X ) }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := X
% 2.16/2.58 Y := skol1
% 2.16/2.58 end
% 2.16/2.58 substitution1:
% 2.16/2.58 X := X
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 eqswap: (15167) {G1,W5,D2,L2,V1,M2} { ! X = skol1, r1( X ) }.
% 2.16/2.58 parent0[0]: (15166) {G1,W5,D2,L2,V1,M2} { ! skol1 = X, r1( X ) }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := X
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 subsumption: (69) {G1,W5,D2,L2,V1,M2} R(3,0) { ! X = skol1, r1( X ) }.
% 2.16/2.58 parent0: (15167) {G1,W5,D2,L2,V1,M2} { ! X = skol1, r1( X ) }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := X
% 2.16/2.58 end
% 2.16/2.58 permutation0:
% 2.16/2.58 0 ==> 0
% 2.16/2.58 1 ==> 1
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 resolution: (15168) {G2,W3,D2,L1,V1,M1} { ! r2( X, skol1 ) }.
% 2.16/2.58 parent0[0]: (51) {G1,W5,D2,L2,V2,M2} Q(43) { ! r1( X ), ! r2( Y, X ) }.
% 2.16/2.58 parent1[0]: (53) {G2,W2,D2,L1,V0,M1} R(0,45) { r1( skol1 ) }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := skol1
% 2.16/2.58 Y := X
% 2.16/2.58 end
% 2.16/2.58 substitution1:
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 subsumption: (73) {G3,W3,D2,L1,V1,M1} R(51,53) { ! r2( X, skol1 ) }.
% 2.16/2.58 parent0: (15168) {G2,W3,D2,L1,V1,M1} { ! r2( X, skol1 ) }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := X
% 2.16/2.58 end
% 2.16/2.58 permutation0:
% 2.16/2.58 0 ==> 0
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 resolution: (15169) {G1,W4,D3,L1,V1,M1} { r2( X, skol2( X ) ) }.
% 2.16/2.58 parent0[0]: (46) {G1,W4,D2,L1,V2,M1} Q(8) { ! alpha2( X, Y, Y ) }.
% 2.16/2.58 parent1[0]: (5) {G0,W8,D3,L2,V2,M2} I { alpha2( X, skol2( X ), Y ), r2( X,
% 2.16/2.58 Y ) }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := X
% 2.16/2.58 Y := skol2( X )
% 2.16/2.58 end
% 2.16/2.58 substitution1:
% 2.16/2.58 X := X
% 2.16/2.58 Y := skol2( X )
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 subsumption: (82) {G2,W4,D3,L1,V1,M1} R(5,46) { r2( X, skol2( X ) ) }.
% 2.16/2.58 parent0: (15169) {G1,W4,D3,L1,V1,M1} { r2( X, skol2( X ) ) }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := X
% 2.16/2.58 end
% 2.16/2.58 permutation0:
% 2.16/2.58 0 ==> 0
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 resolution: (15170) {G1,W3,D3,L1,V1,M1} { r1( skol10( Y ) ) }.
% 2.16/2.58 parent0[0]: (40) {G0,W5,D3,L2,V2,M2} I { ! alpha5( X ), r1( skol10( Y ) )
% 2.16/2.58 }.
% 2.16/2.58 parent1[0]: (58) {G2,W3,D3,L1,V1,M1} R(50,36) { alpha5( skol18( X ) ) }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := skol18( X )
% 2.16/2.58 Y := Y
% 2.16/2.58 end
% 2.16/2.58 substitution1:
% 2.16/2.58 X := X
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 subsumption: (186) {G3,W3,D3,L1,V1,M1} R(40,58) { r1( skol10( X ) ) }.
% 2.16/2.58 parent0: (15170) {G1,W3,D3,L1,V1,M1} { r1( skol10( Y ) ) }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := Y
% 2.16/2.58 Y := X
% 2.16/2.58 end
% 2.16/2.58 permutation0:
% 2.16/2.58 0 ==> 0
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 eqswap: (15171) {G1,W5,D2,L2,V1,M2} { skol1 = X, ! r1( X ) }.
% 2.16/2.58 parent0[1]: (60) {G1,W5,D2,L2,V1,M2} R(2,1) { ! r1( X ), X = skol1 }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := X
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 resolution: (15172) {G2,W4,D3,L1,V1,M1} { skol1 = skol10( X ) }.
% 2.16/2.58 parent0[1]: (15171) {G1,W5,D2,L2,V1,M2} { skol1 = X, ! r1( X ) }.
% 2.16/2.58 parent1[0]: (186) {G3,W3,D3,L1,V1,M1} R(40,58) { r1( skol10( X ) ) }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := skol10( X )
% 2.16/2.58 end
% 2.16/2.58 substitution1:
% 2.16/2.58 X := X
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 eqswap: (15173) {G2,W4,D3,L1,V1,M1} { skol10( X ) = skol1 }.
% 2.16/2.58 parent0[0]: (15172) {G2,W4,D3,L1,V1,M1} { skol1 = skol10( X ) }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := X
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 subsumption: (193) {G4,W4,D3,L1,V1,M1} R(186,60) { skol10( X ) ==> skol1
% 2.16/2.58 }.
% 2.16/2.58 parent0: (15173) {G2,W4,D3,L1,V1,M1} { skol10( X ) = skol1 }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := X
% 2.16/2.58 end
% 2.16/2.58 permutation0:
% 2.16/2.58 0 ==> 0
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 paramod: (15176) {G1,W5,D2,L2,V1,M2} { skol1 ==> X, ! alpha5( X ) }.
% 2.16/2.58 parent0[0]: (193) {G4,W4,D3,L1,V1,M1} R(186,60) { skol10( X ) ==> skol1 }.
% 2.16/2.58 parent1[1; 1]: (41) {G0,W6,D3,L2,V1,M2} I { ! alpha5( X ), skol10( X ) ==>
% 2.16/2.58 X }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := X
% 2.16/2.58 end
% 2.16/2.58 substitution1:
% 2.16/2.58 X := X
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 subsumption: (474) {G5,W5,D2,L2,V1,M2} S(41);d(193) { ! alpha5( X ), skol1
% 2.16/2.58 = X }.
% 2.16/2.58 parent0: (15176) {G1,W5,D2,L2,V1,M2} { skol1 ==> X, ! alpha5( X ) }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := X
% 2.16/2.58 end
% 2.16/2.58 permutation0:
% 2.16/2.58 0 ==> 1
% 2.16/2.58 1 ==> 0
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 paramod: (15190) {G4,W5,D2,L2,V2,M2} { ! r2( X, Y ), ! alpha5( Y ) }.
% 2.16/2.58 parent0[1]: (474) {G5,W5,D2,L2,V1,M2} S(41);d(193) { ! alpha5( X ), skol1 =
% 2.16/2.58 X }.
% 2.16/2.58 parent1[0; 3]: (73) {G3,W3,D2,L1,V1,M1} R(51,53) { ! r2( X, skol1 ) }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := Y
% 2.16/2.58 end
% 2.16/2.58 substitution1:
% 2.16/2.58 X := X
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 subsumption: (503) {G6,W5,D2,L2,V2,M2} P(474,73) { ! r2( Y, X ), ! alpha5(
% 2.16/2.58 X ) }.
% 2.16/2.58 parent0: (15190) {G4,W5,D2,L2,V2,M2} { ! r2( X, Y ), ! alpha5( Y ) }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := Y
% 2.16/2.58 Y := X
% 2.16/2.58 end
% 2.16/2.58 permutation0:
% 2.16/2.58 0 ==> 0
% 2.16/2.58 1 ==> 1
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 paramod: (15203) {G3,W4,D2,L2,V1,M2} { r1( X ), ! alpha5( X ) }.
% 2.16/2.58 parent0[1]: (474) {G5,W5,D2,L2,V1,M2} S(41);d(193) { ! alpha5( X ), skol1 =
% 2.16/2.58 X }.
% 2.16/2.58 parent1[0; 1]: (53) {G2,W2,D2,L1,V0,M1} R(0,45) { r1( skol1 ) }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := X
% 2.16/2.58 end
% 2.16/2.58 substitution1:
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 subsumption: (506) {G6,W4,D2,L2,V1,M2} P(474,53) { r1( X ), ! alpha5( X )
% 2.16/2.58 }.
% 2.16/2.58 parent0: (15203) {G3,W4,D2,L2,V1,M2} { r1( X ), ! alpha5( X ) }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := X
% 2.16/2.58 end
% 2.16/2.58 permutation0:
% 2.16/2.58 0 ==> 0
% 2.16/2.58 1 ==> 1
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 resolution: (15204) {G1,W4,D3,L1,V2,M1} { ! alpha5( skol5( X, Y ) ) }.
% 2.16/2.58 parent0[0]: (503) {G6,W5,D2,L2,V2,M2} P(474,73) { ! r2( Y, X ), ! alpha5( X
% 2.16/2.58 ) }.
% 2.16/2.58 parent1[0]: (23) {G0,W7,D3,L1,V2,M1} I { r2( skol19( X, Y ), skol5( X, Y )
% 2.16/2.58 ) }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := skol5( X, Y )
% 2.16/2.58 Y := skol19( X, Y )
% 2.16/2.58 end
% 2.16/2.58 substitution1:
% 2.16/2.58 X := X
% 2.16/2.58 Y := Y
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 subsumption: (520) {G7,W4,D3,L1,V2,M1} R(23,503) { ! alpha5( skol5( X, Y )
% 2.16/2.58 ) }.
% 2.16/2.58 parent0: (15204) {G1,W4,D3,L1,V2,M1} { ! alpha5( skol5( X, Y ) ) }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := X
% 2.16/2.58 Y := Y
% 2.16/2.58 end
% 2.16/2.58 permutation0:
% 2.16/2.58 0 ==> 0
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 eqswap: (15205) {G0,W6,D3,L2,V1,M2} { X ==> skol9( X ), alpha5( X ) }.
% 2.16/2.58 parent0[1]: (39) {G0,W6,D3,L2,V1,M2} I { alpha5( X ), skol9( X ) ==> X }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := X
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 resolution: (15206) {G1,W6,D3,L2,V1,M2} { r1( X ), X ==> skol9( X ) }.
% 2.16/2.58 parent0[1]: (506) {G6,W4,D2,L2,V1,M2} P(474,53) { r1( X ), ! alpha5( X )
% 2.16/2.58 }.
% 2.16/2.58 parent1[1]: (15205) {G0,W6,D3,L2,V1,M2} { X ==> skol9( X ), alpha5( X )
% 2.16/2.58 }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := X
% 2.16/2.58 end
% 2.16/2.58 substitution1:
% 2.16/2.58 X := X
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 eqswap: (15207) {G1,W6,D3,L2,V1,M2} { skol9( X ) ==> X, r1( X ) }.
% 2.16/2.58 parent0[1]: (15206) {G1,W6,D3,L2,V1,M2} { r1( X ), X ==> skol9( X ) }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := X
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 subsumption: (619) {G7,W6,D3,L2,V1,M2} R(39,506) { skol9( X ) ==> X, r1( X
% 2.16/2.58 ) }.
% 2.16/2.58 parent0: (15207) {G1,W6,D3,L2,V1,M2} { skol9( X ) ==> X, r1( X ) }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := X
% 2.16/2.58 end
% 2.16/2.58 permutation0:
% 2.16/2.58 0 ==> 0
% 2.16/2.58 1 ==> 1
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 resolution: (15208) {G1,W5,D3,L1,V1,M1} { r2( skol15( Z ), skol9( Z ) )
% 2.16/2.58 }.
% 2.16/2.58 parent0[0]: (520) {G7,W4,D3,L1,V2,M1} R(23,503) { ! alpha5( skol5( X, Y ) )
% 2.16/2.58 }.
% 2.16/2.58 parent1[0]: (38) {G0,W7,D3,L2,V2,M2} I { alpha5( X ), r2( skol15( Y ),
% 2.16/2.58 skol9( Y ) ) }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := X
% 2.16/2.58 Y := Y
% 2.16/2.58 end
% 2.16/2.58 substitution1:
% 2.16/2.58 X := skol5( X, Y )
% 2.16/2.58 Y := Z
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 subsumption: (833) {G8,W5,D3,L1,V1,M1} R(38,520) { r2( skol15( X ), skol9(
% 2.16/2.58 X ) ) }.
% 2.16/2.58 parent0: (15208) {G1,W5,D3,L1,V1,M1} { r2( skol15( Z ), skol9( Z ) ) }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := Y
% 2.16/2.58 Y := Z
% 2.16/2.58 Z := X
% 2.16/2.58 end
% 2.16/2.58 permutation0:
% 2.16/2.58 0 ==> 0
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 paramod: (15210) {G8,W6,D3,L2,V1,M2} { r2( skol15( X ), X ), r1( X ) }.
% 2.16/2.58 parent0[0]: (619) {G7,W6,D3,L2,V1,M2} R(39,506) { skol9( X ) ==> X, r1( X )
% 2.16/2.58 }.
% 2.16/2.58 parent1[0; 3]: (833) {G8,W5,D3,L1,V1,M1} R(38,520) { r2( skol15( X ), skol9
% 2.16/2.58 ( X ) ) }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := X
% 2.16/2.58 end
% 2.16/2.58 substitution1:
% 2.16/2.58 X := X
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 subsumption: (885) {G9,W6,D3,L2,V1,M2} P(619,833) { r2( skol15( X ), X ),
% 2.16/2.58 r1( X ) }.
% 2.16/2.58 parent0: (15210) {G8,W6,D3,L2,V1,M2} { r2( skol15( X ), X ), r1( X ) }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := X
% 2.16/2.58 end
% 2.16/2.58 permutation0:
% 2.16/2.58 0 ==> 0
% 2.16/2.58 1 ==> 1
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 resolution: (15211) {G2,W7,D3,L2,V2,M2} { ! r2( Y, X ), r2( skol15( X ), X
% 2.16/2.58 ) }.
% 2.16/2.58 parent0[0]: (51) {G1,W5,D2,L2,V2,M2} Q(43) { ! r1( X ), ! r2( Y, X ) }.
% 2.16/2.58 parent1[1]: (885) {G9,W6,D3,L2,V1,M2} P(619,833) { r2( skol15( X ), X ), r1
% 2.16/2.58 ( X ) }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := X
% 2.16/2.58 Y := Y
% 2.16/2.58 end
% 2.16/2.58 substitution1:
% 2.16/2.58 X := X
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 subsumption: (1041) {G10,W7,D3,L2,V2,M2} R(885,51) { r2( skol15( X ), X ),
% 2.16/2.58 ! r2( Y, X ) }.
% 2.16/2.58 parent0: (15211) {G2,W7,D3,L2,V2,M2} { ! r2( Y, X ), r2( skol15( X ), X )
% 2.16/2.58 }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := X
% 2.16/2.58 Y := Y
% 2.16/2.58 end
% 2.16/2.58 permutation0:
% 2.16/2.58 0 ==> 1
% 2.16/2.58 1 ==> 0
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 resolution: (15213) {G1,W8,D2,L3,V3,M3} { ! r2( Z, X ), ! r1( T ), ! r2( T
% 2.16/2.58 , Z ) }.
% 2.16/2.58 parent0[0]: (52) {G1,W12,D2,L4,V5,M4} Q(44) { ! r3( X, Y, Z ), ! r2( T, Y )
% 2.16/2.58 , ! r1( U ), ! r2( U, T ) }.
% 2.16/2.58 parent1[0]: (28) {G0,W8,D3,L1,V2,M1} I { r3( skol20( X, Y ), X, skol6( X, Y
% 2.16/2.58 ) ) }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := skol20( X, Y )
% 2.16/2.58 Y := X
% 2.16/2.58 Z := skol6( X, Y )
% 2.16/2.58 T := Z
% 2.16/2.58 U := T
% 2.16/2.58 end
% 2.16/2.58 substitution1:
% 2.16/2.58 X := X
% 2.16/2.58 Y := Y
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 subsumption: (1119) {G2,W8,D2,L3,V3,M3} R(52,28) { ! r2( X, Y ), ! r1( Z )
% 2.16/2.58 , ! r2( Z, X ) }.
% 2.16/2.58 parent0: (15213) {G1,W8,D2,L3,V3,M3} { ! r2( Z, X ), ! r1( T ), ! r2( T, Z
% 2.16/2.58 ) }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := Y
% 2.16/2.58 Y := T
% 2.16/2.58 Z := X
% 2.16/2.58 T := Z
% 2.16/2.58 end
% 2.16/2.58 permutation0:
% 2.16/2.58 0 ==> 0
% 2.16/2.58 1 ==> 1
% 2.16/2.58 2 ==> 2
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 eqswap: (15215) {G0,W12,D2,L4,V4,M4} { ! Y = X, ! r2( Z, X ), ! r2( T, Y )
% 2.16/2.58 , Z = T }.
% 2.16/2.58 parent0[1]: (30) {G0,W12,D2,L4,V4,M4} I { ! r2( X, T ), ! T = Z, ! r2( Y, Z
% 2.16/2.58 ), X = Y }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := Z
% 2.16/2.58 Y := T
% 2.16/2.58 Z := Y
% 2.16/2.58 T := X
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 resolution: (15217) {G1,W13,D3,L4,V4,M4} { ! X = Y, ! r2( Z, Y ), Z =
% 2.16/2.58 skol15( X ), ! r2( T, X ) }.
% 2.16/2.58 parent0[2]: (15215) {G0,W12,D2,L4,V4,M4} { ! Y = X, ! r2( Z, X ), ! r2( T
% 2.16/2.58 , Y ), Z = T }.
% 2.16/2.58 parent1[0]: (1041) {G10,W7,D3,L2,V2,M2} R(885,51) { r2( skol15( X ), X ), !
% 2.16/2.58 r2( Y, X ) }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := Y
% 2.16/2.58 Y := X
% 2.16/2.58 Z := Z
% 2.16/2.58 T := skol15( X )
% 2.16/2.58 end
% 2.16/2.58 substitution1:
% 2.16/2.58 X := X
% 2.16/2.58 Y := T
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 eqswap: (15219) {G1,W13,D3,L4,V4,M4} { skol15( Y ) = X, ! Y = Z, ! r2( X,
% 2.16/2.58 Z ), ! r2( T, Y ) }.
% 2.16/2.58 parent0[2]: (15217) {G1,W13,D3,L4,V4,M4} { ! X = Y, ! r2( Z, Y ), Z =
% 2.16/2.58 skol15( X ), ! r2( T, X ) }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := Y
% 2.16/2.58 Y := Z
% 2.16/2.58 Z := X
% 2.16/2.58 T := T
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 subsumption: (2326) {G11,W13,D3,L4,V4,M4} R(1041,30) { ! r2( X, Y ), ! Y =
% 2.16/2.58 Z, ! r2( T, Z ), skol15( Y ) = T }.
% 2.16/2.58 parent0: (15219) {G1,W13,D3,L4,V4,M4} { skol15( Y ) = X, ! Y = Z, ! r2( X
% 2.16/2.58 , Z ), ! r2( T, Y ) }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := T
% 2.16/2.58 Y := Y
% 2.16/2.58 Z := Z
% 2.16/2.58 T := X
% 2.16/2.58 end
% 2.16/2.58 permutation0:
% 2.16/2.58 0 ==> 3
% 2.16/2.58 1 ==> 1
% 2.16/2.58 2 ==> 2
% 2.16/2.58 3 ==> 0
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 eqswap: (15223) {G11,W13,D3,L4,V4,M4} { Y = skol15( X ), ! r2( Z, X ), ! X
% 2.16/2.58 = T, ! r2( Y, T ) }.
% 2.16/2.58 parent0[3]: (2326) {G11,W13,D3,L4,V4,M4} R(1041,30) { ! r2( X, Y ), ! Y = Z
% 2.16/2.58 , ! r2( T, Z ), skol15( Y ) = T }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := Z
% 2.16/2.58 Y := X
% 2.16/2.58 Z := T
% 2.16/2.58 T := Y
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 eqswap: (15224) {G11,W13,D3,L4,V4,M4} { ! Y = X, Z = skol15( X ), ! r2( T
% 2.16/2.58 , X ), ! r2( Z, Y ) }.
% 2.16/2.58 parent0[2]: (15223) {G11,W13,D3,L4,V4,M4} { Y = skol15( X ), ! r2( Z, X )
% 2.16/2.58 , ! X = T, ! r2( Y, T ) }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := X
% 2.16/2.58 Y := Z
% 2.16/2.58 Z := T
% 2.16/2.58 T := Y
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 factor: (15226) {G11,W10,D3,L3,V2,M3} { ! X = X, Y = skol15( X ), ! r2( Y
% 2.16/2.58 , X ) }.
% 2.16/2.58 parent0[2, 3]: (15224) {G11,W13,D3,L4,V4,M4} { ! Y = X, Z = skol15( X ), !
% 2.16/2.58 r2( T, X ), ! r2( Z, Y ) }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := X
% 2.16/2.58 Y := X
% 2.16/2.58 Z := Y
% 2.16/2.58 T := Y
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 eqrefl: (15227) {G0,W7,D3,L2,V2,M2} { Y = skol15( X ), ! r2( Y, X ) }.
% 2.16/2.58 parent0[0]: (15226) {G11,W10,D3,L3,V2,M3} { ! X = X, Y = skol15( X ), ! r2
% 2.16/2.58 ( Y, X ) }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := X
% 2.16/2.58 Y := Y
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 eqswap: (15228) {G0,W7,D3,L2,V2,M2} { skol15( Y ) = X, ! r2( X, Y ) }.
% 2.16/2.58 parent0[0]: (15227) {G0,W7,D3,L2,V2,M2} { Y = skol15( X ), ! r2( Y, X )
% 2.16/2.58 }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := Y
% 2.16/2.58 Y := X
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 subsumption: (2355) {G12,W7,D3,L2,V2,M2} F(2326);q { ! r2( X, Y ), skol15(
% 2.16/2.58 Y ) = X }.
% 2.16/2.58 parent0: (15228) {G0,W7,D3,L2,V2,M2} { skol15( Y ) = X, ! r2( X, Y ) }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := X
% 2.16/2.58 Y := Y
% 2.16/2.58 end
% 2.16/2.58 permutation0:
% 2.16/2.58 0 ==> 1
% 2.16/2.58 1 ==> 0
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 eqswap: (15229) {G12,W7,D3,L2,V2,M2} { Y = skol15( X ), ! r2( Y, X ) }.
% 2.16/2.58 parent0[1]: (2355) {G12,W7,D3,L2,V2,M2} F(2326);q { ! r2( X, Y ), skol15( Y
% 2.16/2.58 ) = X }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := Y
% 2.16/2.58 Y := X
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 resolution: (15230) {G3,W5,D4,L1,V1,M1} { X = skol15( skol2( X ) ) }.
% 2.16/2.58 parent0[1]: (15229) {G12,W7,D3,L2,V2,M2} { Y = skol15( X ), ! r2( Y, X )
% 2.16/2.58 }.
% 2.16/2.58 parent1[0]: (82) {G2,W4,D3,L1,V1,M1} R(5,46) { r2( X, skol2( X ) ) }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := skol2( X )
% 2.16/2.58 Y := X
% 2.16/2.58 end
% 2.16/2.58 substitution1:
% 2.16/2.58 X := X
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 eqswap: (15231) {G3,W5,D4,L1,V1,M1} { skol15( skol2( X ) ) = X }.
% 2.16/2.58 parent0[0]: (15230) {G3,W5,D4,L1,V1,M1} { X = skol15( skol2( X ) ) }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := X
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 subsumption: (2494) {G13,W5,D4,L1,V1,M1} R(2355,82) { skol15( skol2( X ) )
% 2.16/2.58 ==> X }.
% 2.16/2.58 parent0: (15231) {G3,W5,D4,L1,V1,M1} { skol15( skol2( X ) ) = X }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := X
% 2.16/2.58 end
% 2.16/2.58 permutation0:
% 2.16/2.58 0 ==> 0
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 eqswap: (15232) {G12,W7,D3,L2,V2,M2} { Y = skol15( X ), ! r2( Y, X ) }.
% 2.16/2.58 parent0[1]: (2355) {G12,W7,D3,L2,V2,M2} F(2326);q { ! r2( X, Y ), skol15( Y
% 2.16/2.58 ) = X }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := Y
% 2.16/2.58 Y := X
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 eqswap: (15233) {G1,W5,D2,L2,V1,M2} { ! skol1 = X, r1( X ) }.
% 2.16/2.58 parent0[0]: (69) {G1,W5,D2,L2,V1,M2} R(3,0) { ! X = skol1, r1( X ) }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := X
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 resolution: (15234) {G2,W6,D3,L2,V1,M2} { r1( skol15( X ) ), ! r2( skol1,
% 2.16/2.58 X ) }.
% 2.16/2.58 parent0[0]: (15233) {G1,W5,D2,L2,V1,M2} { ! skol1 = X, r1( X ) }.
% 2.16/2.58 parent1[0]: (15232) {G12,W7,D3,L2,V2,M2} { Y = skol15( X ), ! r2( Y, X )
% 2.16/2.58 }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := skol15( X )
% 2.16/2.58 end
% 2.16/2.58 substitution1:
% 2.16/2.58 X := X
% 2.16/2.58 Y := skol1
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 subsumption: (2497) {G13,W6,D3,L2,V1,M2} R(2355,69) { ! r2( skol1, X ), r1
% 2.16/2.58 ( skol15( X ) ) }.
% 2.16/2.58 parent0: (15234) {G2,W6,D3,L2,V1,M2} { r1( skol15( X ) ), ! r2( skol1, X )
% 2.16/2.58 }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := X
% 2.16/2.58 end
% 2.16/2.58 permutation0:
% 2.16/2.58 0 ==> 1
% 2.16/2.58 1 ==> 0
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 paramod: (15236) {G14,W6,D3,L2,V1,M2} { r1( X ), ! r2( skol1, skol2( X ) )
% 2.16/2.58 }.
% 2.16/2.58 parent0[0]: (2494) {G13,W5,D4,L1,V1,M1} R(2355,82) { skol15( skol2( X ) )
% 2.16/2.58 ==> X }.
% 2.16/2.58 parent1[1; 1]: (2497) {G13,W6,D3,L2,V1,M2} R(2355,69) { ! r2( skol1, X ),
% 2.16/2.58 r1( skol15( X ) ) }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := X
% 2.16/2.58 end
% 2.16/2.58 substitution1:
% 2.16/2.58 X := skol2( X )
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 subsumption: (2727) {G14,W6,D3,L2,V1,M2} P(2494,2497) { ! r2( skol1, skol2
% 2.16/2.58 ( X ) ), r1( X ) }.
% 2.16/2.58 parent0: (15236) {G14,W6,D3,L2,V1,M2} { r1( X ), ! r2( skol1, skol2( X ) )
% 2.16/2.58 }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := X
% 2.16/2.58 end
% 2.16/2.58 permutation0:
% 2.16/2.58 0 ==> 1
% 2.16/2.58 1 ==> 0
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 resolution: (15237) {G3,W10,D3,L3,V3,M3} { ! r2( X, Y ), ! r2( Z, X ), !
% 2.16/2.58 r2( skol1, skol2( Z ) ) }.
% 2.16/2.58 parent0[1]: (1119) {G2,W8,D2,L3,V3,M3} R(52,28) { ! r2( X, Y ), ! r1( Z ),
% 2.16/2.58 ! r2( Z, X ) }.
% 2.16/2.58 parent1[1]: (2727) {G14,W6,D3,L2,V1,M2} P(2494,2497) { ! r2( skol1, skol2(
% 2.16/2.58 X ) ), r1( X ) }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := X
% 2.16/2.58 Y := Y
% 2.16/2.58 Z := Z
% 2.16/2.58 end
% 2.16/2.58 substitution1:
% 2.16/2.58 X := Z
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 subsumption: (14808) {G15,W10,D3,L3,V3,M3} R(1119,2727) { ! r2( X, Y ), !
% 2.16/2.58 r2( Z, X ), ! r2( skol1, skol2( Z ) ) }.
% 2.16/2.58 parent0: (15237) {G3,W10,D3,L3,V3,M3} { ! r2( X, Y ), ! r2( Z, X ), ! r2(
% 2.16/2.58 skol1, skol2( Z ) ) }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := X
% 2.16/2.58 Y := Y
% 2.16/2.58 Z := Z
% 2.16/2.58 end
% 2.16/2.58 permutation0:
% 2.16/2.58 0 ==> 0
% 2.16/2.58 1 ==> 1
% 2.16/2.58 2 ==> 2
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 factor: (15243) {G15,W8,D3,L2,V1,M2} { ! r2( skol2( skol1 ), X ), ! r2(
% 2.16/2.58 skol1, skol2( skol1 ) ) }.
% 2.16/2.58 parent0[1, 2]: (14808) {G15,W10,D3,L3,V3,M3} R(1119,2727) { ! r2( X, Y ), !
% 2.16/2.58 r2( Z, X ), ! r2( skol1, skol2( Z ) ) }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := skol2( skol1 )
% 2.16/2.58 Y := X
% 2.16/2.58 Z := skol1
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 resolution: (15244) {G3,W4,D3,L1,V1,M1} { ! r2( skol2( skol1 ), X ) }.
% 2.16/2.58 parent0[1]: (15243) {G15,W8,D3,L2,V1,M2} { ! r2( skol2( skol1 ), X ), ! r2
% 2.16/2.58 ( skol1, skol2( skol1 ) ) }.
% 2.16/2.58 parent1[0]: (82) {G2,W4,D3,L1,V1,M1} R(5,46) { r2( X, skol2( X ) ) }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := X
% 2.16/2.58 end
% 2.16/2.58 substitution1:
% 2.16/2.58 X := skol1
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 subsumption: (14844) {G16,W4,D3,L1,V1,M1} F(14808);r(82) { ! r2( skol2(
% 2.16/2.58 skol1 ), X ) }.
% 2.16/2.58 parent0: (15244) {G3,W4,D3,L1,V1,M1} { ! r2( skol2( skol1 ), X ) }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := X
% 2.16/2.58 end
% 2.16/2.58 permutation0:
% 2.16/2.58 0 ==> 0
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 resolution: (15245) {G3,W0,D0,L0,V0,M0} { }.
% 2.16/2.58 parent0[0]: (14844) {G16,W4,D3,L1,V1,M1} F(14808);r(82) { ! r2( skol2(
% 2.16/2.58 skol1 ), X ) }.
% 2.16/2.58 parent1[0]: (82) {G2,W4,D3,L1,V1,M1} R(5,46) { r2( X, skol2( X ) ) }.
% 2.16/2.58 substitution0:
% 2.16/2.58 X := skol2( skol2( skol1 ) )
% 2.16/2.58 end
% 2.16/2.58 substitution1:
% 2.16/2.58 X := skol2( skol1 )
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 subsumption: (14885) {G17,W0,D0,L0,V0,M0} R(14844,82) { }.
% 2.16/2.58 parent0: (15245) {G3,W0,D0,L0,V0,M0} { }.
% 2.16/2.58 substitution0:
% 2.16/2.58 end
% 2.16/2.58 permutation0:
% 2.16/2.58 end
% 2.16/2.58
% 2.16/2.58 Proof check complete!
% 2.16/2.58
% 2.16/2.58 Memory use:
% 2.16/2.58
% 2.16/2.58 space for terms: 193073
% 2.16/2.58 space for clauses: 588832
% 2.16/2.58
% 2.16/2.58
% 2.16/2.58 clauses generated: 75926
% 2.16/2.58 clauses kept: 14886
% 2.16/2.58 clauses selected: 598
% 2.16/2.58 clauses deleted: 137
% 2.16/2.58 clauses inuse deleted: 53
% 2.16/2.58
% 2.16/2.58 subsentry: 214253
% 2.16/2.58 literals s-matched: 156244
% 2.16/2.58 literals matched: 144631
% 2.16/2.58 full subsumption: 55519
% 2.16/2.58
% 2.16/2.58 checksum: 1413746993
% 2.16/2.58
% 2.16/2.58
% 2.16/2.58 Bliksem ended
%------------------------------------------------------------------------------