TSTP Solution File: ALG176+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : ALG176+1 : TPTP v8.1.0. Released v2.7.0.
% 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 : Thu Jul 14 12:09:48 EDT 2022
% Result : Theorem 11.81s 12.22s
% Output : Refutation 11.81s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : ALG176+1 : TPTP v8.1.0. Released v2.7.0.
% 0.10/0.12 % Command : bliksem %s
% 0.13/0.33 % Computer : n028.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % DateTime : Wed Jun 8 08:18:01 EDT 2022
% 0.13/0.33 % CPUTime :
% 11.81/12.22 *** allocated 10000 integers for termspace/termends
% 11.81/12.22 *** allocated 10000 integers for clauses
% 11.81/12.22 *** allocated 10000 integers for justifications
% 11.81/12.22 Bliksem 1.12
% 11.81/12.22
% 11.81/12.22
% 11.81/12.22 Automatic Strategy Selection
% 11.81/12.22
% 11.81/12.22
% 11.81/12.22 Clauses:
% 11.81/12.22
% 11.81/12.22 { ! sorti1( X ), ! sorti1( Y ), sorti1( op1( X, Y ) ) }.
% 11.81/12.22 { ! sorti2( X ), ! sorti2( Y ), sorti2( op2( X, Y ) ) }.
% 11.81/12.22 { sorti1( skol1 ) }.
% 11.81/12.22 { ! sorti1( X ), ! op1( X, skol1 ) = X }.
% 11.81/12.22 { ! sorti2( X ), sorti2( skol2( Y ) ) }.
% 11.81/12.22 { ! sorti2( X ), op2( skol2( X ), X ) = skol2( X ) }.
% 11.81/12.22 { ! sorti1( X ), sorti2( h( X ) ) }.
% 11.81/12.22 { ! sorti2( X ), sorti1( j( X ) ) }.
% 11.81/12.22 { ! sorti1( X ), ! sorti1( Y ), h( op1( X, Y ) ) = op2( h( X ), h( Y ) ) }
% 11.81/12.22 .
% 11.81/12.22 { ! sorti2( X ), ! sorti2( Y ), j( op2( X, Y ) ) = op1( j( X ), j( Y ) ) }
% 11.81/12.22 .
% 11.81/12.22 { ! sorti2( X ), h( j( X ) ) = X }.
% 11.81/12.22 { ! sorti1( X ), j( h( X ) ) = X }.
% 11.81/12.22
% 11.81/12.22 percentage equality = 0.222222, percentage horn = 1.000000
% 11.81/12.22 This is a problem with some equality
% 11.81/12.22
% 11.81/12.22
% 11.81/12.22
% 11.81/12.22 Options Used:
% 11.81/12.22
% 11.81/12.22 useres = 1
% 11.81/12.22 useparamod = 1
% 11.81/12.22 useeqrefl = 1
% 11.81/12.22 useeqfact = 1
% 11.81/12.22 usefactor = 1
% 11.81/12.22 usesimpsplitting = 0
% 11.81/12.22 usesimpdemod = 5
% 11.81/12.22 usesimpres = 3
% 11.81/12.22
% 11.81/12.22 resimpinuse = 1000
% 11.81/12.22 resimpclauses = 20000
% 11.81/12.22 substype = eqrewr
% 11.81/12.22 backwardsubs = 1
% 11.81/12.22 selectoldest = 5
% 11.81/12.22
% 11.81/12.22 litorderings [0] = split
% 11.81/12.22 litorderings [1] = extend the termordering, first sorting on arguments
% 11.81/12.22
% 11.81/12.22 termordering = kbo
% 11.81/12.22
% 11.81/12.22 litapriori = 0
% 11.81/12.22 termapriori = 1
% 11.81/12.22 litaposteriori = 0
% 11.81/12.22 termaposteriori = 0
% 11.81/12.22 demodaposteriori = 0
% 11.81/12.22 ordereqreflfact = 0
% 11.81/12.22
% 11.81/12.22 litselect = negord
% 11.81/12.22
% 11.81/12.22 maxweight = 15
% 11.81/12.22 maxdepth = 30000
% 11.81/12.22 maxlength = 115
% 11.81/12.22 maxnrvars = 195
% 11.81/12.22 excuselevel = 1
% 11.81/12.22 increasemaxweight = 1
% 11.81/12.22
% 11.81/12.22 maxselected = 10000000
% 11.81/12.22 maxnrclauses = 10000000
% 11.81/12.22
% 11.81/12.22 showgenerated = 0
% 11.81/12.22 showkept = 0
% 11.81/12.22 showselected = 0
% 11.81/12.22 showdeleted = 0
% 11.81/12.22 showresimp = 1
% 11.81/12.22 showstatus = 2000
% 11.81/12.22
% 11.81/12.22 prologoutput = 0
% 11.81/12.22 nrgoals = 5000000
% 11.81/12.22 totalproof = 1
% 11.81/12.22
% 11.81/12.22 Symbols occurring in the translation:
% 11.81/12.22
% 11.81/12.22 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 11.81/12.22 . [1, 2] (w:1, o:25, a:1, s:1, b:0),
% 11.81/12.22 ! [4, 1] (w:0, o:15, a:1, s:1, b:0),
% 11.81/12.22 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 11.81/12.22 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 11.81/12.22 sorti1 [36, 1] (w:1, o:20, a:1, s:1, b:0),
% 11.81/12.22 op1 [38, 2] (w:1, o:49, a:1, s:1, b:0),
% 11.81/12.22 sorti2 [39, 1] (w:1, o:21, a:1, s:1, b:0),
% 11.81/12.22 op2 [40, 2] (w:1, o:50, a:1, s:1, b:0),
% 11.81/12.22 h [41, 1] (w:1, o:22, a:1, s:1, b:0),
% 11.81/12.22 j [42, 1] (w:1, o:23, a:1, s:1, b:0),
% 11.81/12.22 skol1 [49, 0] (w:1, o:14, a:1, s:1, b:1),
% 11.81/12.22 skol2 [50, 1] (w:1, o:24, a:1, s:1, b:1).
% 11.81/12.22
% 11.81/12.22
% 11.81/12.22 Starting Search:
% 11.81/12.22
% 11.81/12.22 *** allocated 15000 integers for clauses
% 11.81/12.22 *** allocated 22500 integers for clauses
% 11.81/12.22 *** allocated 33750 integers for clauses
% 11.81/12.22 *** allocated 50625 integers for clauses
% 11.81/12.22 *** allocated 15000 integers for termspace/termends
% 11.81/12.22 *** allocated 75937 integers for clauses
% 11.81/12.22 Resimplifying inuse:
% 11.81/12.22 Done
% 11.81/12.22
% 11.81/12.22 *** allocated 22500 integers for termspace/termends
% 11.81/12.22 *** allocated 113905 integers for clauses
% 11.81/12.22 *** allocated 33750 integers for termspace/termends
% 11.81/12.22 *** allocated 170857 integers for clauses
% 11.81/12.22
% 11.81/12.22 Intermediate Status:
% 11.81/12.22 Generated: 4384
% 11.81/12.22 Kept: 2042
% 11.81/12.22 Inuse: 100
% 11.81/12.22 Deleted: 22
% 11.81/12.22 Deletedinuse: 10
% 11.81/12.22
% 11.81/12.22 Resimplifying inuse:
% 11.81/12.22 Done
% 11.81/12.22
% 11.81/12.22 *** allocated 50625 integers for termspace/termends
% 11.81/12.22 *** allocated 256285 integers for clauses
% 11.81/12.22 Resimplifying inuse:
% 11.81/12.22 Done
% 11.81/12.22
% 11.81/12.22 *** allocated 75937 integers for termspace/termends
% 11.81/12.22
% 11.81/12.22 Intermediate Status:
% 11.81/12.22 Generated: 9242
% 11.81/12.22 Kept: 4091
% 11.81/12.22 Inuse: 150
% 11.81/12.22 Deleted: 42
% 11.81/12.22 Deletedinuse: 10
% 11.81/12.22
% 11.81/12.22 Resimplifying inuse:
% 11.81/12.22 Done
% 11.81/12.22
% 11.81/12.22 *** allocated 384427 integers for clauses
% 11.81/12.22 Resimplifying inuse:
% 11.81/12.22 Done
% 11.81/12.22
% 11.81/12.22 *** allocated 113905 integers for termspace/termends
% 11.81/12.22
% 11.81/12.22 Intermediate Status:
% 11.81/12.22 Generated: 14571
% 11.81/12.22 Kept: 6125
% 11.81/12.22 Inuse: 190
% 11.81/12.22 Deleted: 44
% 11.81/12.22 Deletedinuse: 10
% 11.81/12.22
% 11.81/12.22 Resimplifying inuse:
% 11.81/12.22 Done
% 11.81/12.22
% 11.81/12.22 *** allocated 576640 integers for clauses
% 11.81/12.22 Resimplifying inuse:
% 11.81/12.22 Done
% 11.81/12.22
% 11.81/12.22 *** allocated 170857 integers for termspace/termends
% 11.81/12.22
% 11.81/12.22 Intermediate Status:
% 11.81/12.22 Generated: 21430
% 11.81/12.22 Kept: 8190
% 11.81/12.22 Inuse: 239
% 11.81/12.22 Deleted: 46
% 11.81/12.22 Deletedinuse: 10
% 11.81/12.22
% 11.81/12.22 Resimplifying inuse:
% 11.81/12.22 Done
% 11.81/12.22
% 11.81/12.22 Resimplifying inuse:
% 11.81/12.22 Done
% 11.81/12.22
% 11.81/12.22 *** allocated 864960 integers for clauses
% 11.81/12.22
% 11.81/12.22 Intermediate Status:
% 11.81/12.22 Generated: 27622
% 11.81/12.22 Kept: 10191
% 11.81/12.22 Inuse: 268
% 11.81/12.22 Deleted: 50
% 11.81/12.22 Deletedinuse: 10
% 11.81/12.22
% 11.81/12.22 Resimplifying inuse:
% 11.81/12.22 Done
% 11.81/12.22
% 11.81/12.22 Resimplifying inuse:
% 11.81/12.22 Done
% 11.81/12.22
% 11.81/12.22 *** allocated 256285 integers for termspace/termends
% 11.81/12.22
% 11.81/12.22 Intermediate Status:
% 11.81/12.22 Generated: 41434
% 11.81/12.22 Kept: 12213
% 11.81/12.22 Inuse: 321
% 11.81/12.22 Deleted: 52
% 11.81/12.22 Deletedinuse: 10
% 11.81/12.22
% 11.81/12.22 Resimplifying inuse:
% 11.81/12.22 Done
% 11.81/12.22
% 11.81/12.22 Resimplifying inuse:
% 11.81/12.22 Done
% 11.81/12.22
% 11.81/12.22
% 11.81/12.22 Intermediate Status:
% 11.81/12.22 Generated: 58824
% 11.81/12.22 Kept: 14257
% 11.81/12.22 Inuse: 377
% 11.81/12.22 Deleted: 59
% 11.81/12.22 Deletedinuse: 17
% 11.81/12.22
% 11.81/12.22 *** allocated 1297440 integers for clauses
% 11.81/12.22 Resimplifying inuse:
% 11.81/12.22 Done
% 11.81/12.22
% 11.81/12.22 Resimplifying inuse:
% 11.81/12.22 Done
% 11.81/12.22
% 11.81/12.22
% 11.81/12.22 Intermediate Status:
% 11.81/12.22 Generated: 77943
% 11.81/12.22 Kept: 16270
% 11.81/12.22 Inuse: 448
% 11.81/12.22 Deleted: 83
% 11.81/12.22 Deletedinuse: 28
% 11.81/12.22
% 11.81/12.22 Resimplifying inuse:
% 11.81/12.22 Done
% 11.81/12.22
% 11.81/12.22 *** allocated 384427 integers for termspace/termends
% 11.81/12.22 Resimplifying inuse:
% 11.81/12.22 Done
% 11.81/12.22
% 11.81/12.22
% 11.81/12.22 Intermediate Status:
% 11.81/12.22 Generated: 138857
% 11.81/12.22 Kept: 18285
% 11.81/12.22 Inuse: 601
% 11.81/12.22 Deleted: 121
% 11.81/12.22 Deletedinuse: 29
% 11.81/12.22
% 11.81/12.22 Resimplifying inuse:
% 11.81/12.22 Done
% 11.81/12.22
% 11.81/12.22 Resimplifying inuse:
% 11.81/12.22 Done
% 11.81/12.22
% 11.81/12.22
% 11.81/12.22 Bliksems!, er is een bewijs:
% 11.81/12.22 % SZS status Theorem
% 11.81/12.22 % SZS output start Refutation
% 11.81/12.22
% 11.81/12.22 (2) {G0,W2,D2,L1,V0,M1} I { sorti1( skol1 ) }.
% 11.81/12.22 (3) {G0,W7,D3,L2,V1,M2} I { ! sorti1( X ), ! op1( X, skol1 ) ==> X }.
% 11.81/12.22 (4) {G0,W5,D3,L2,V2,M2} I { ! sorti2( X ), sorti2( skol2( Y ) ) }.
% 11.81/12.22 (5) {G0,W9,D4,L2,V1,M2} I { ! sorti2( X ), op2( skol2( X ), X ) ==> skol2(
% 11.81/12.22 X ) }.
% 11.81/12.22 (6) {G0,W5,D3,L2,V1,M2} I { ! sorti1( X ), sorti2( h( X ) ) }.
% 11.81/12.22 (7) {G0,W5,D3,L2,V1,M2} I { ! sorti2( X ), sorti1( j( X ) ) }.
% 11.81/12.22 (9) {G0,W14,D4,L3,V2,M3} I { ! sorti2( X ), ! sorti2( Y ), op1( j( X ), j(
% 11.81/12.22 Y ) ) ==> j( op2( X, Y ) ) }.
% 11.81/12.22 (11) {G0,W7,D4,L2,V1,M2} I { ! sorti1( X ), j( h( X ) ) ==> X }.
% 11.81/12.22 (18) {G1,W3,D3,L1,V0,M1} R(6,2) { sorti2( h( skol1 ) ) }.
% 11.81/12.22 (20) {G2,W3,D3,L1,V1,M1} R(18,4) { sorti2( skol2( X ) ) }.
% 11.81/12.22 (37) {G3,W4,D4,L1,V1,M1} R(20,7) { sorti1( j( skol2( X ) ) ) }.
% 11.81/12.22 (87) {G4,W9,D5,L1,V1,M1} R(3,37) { ! op1( j( skol2( X ) ), skol1 ) ==> j(
% 11.81/12.22 skol2( X ) ) }.
% 11.81/12.22 (120) {G2,W10,D5,L1,V0,M1} R(5,18) { op2( skol2( h( skol1 ) ), h( skol1 ) )
% 11.81/12.22 ==> skol2( h( skol1 ) ) }.
% 11.81/12.22 (255) {G1,W5,D4,L1,V0,M1} R(11,2) { j( h( skol1 ) ) ==> skol1 }.
% 11.81/12.22 (257) {G2,W12,D5,L2,V1,M2} P(255,9);r(18) { ! sorti2( X ), j( op2( X, h(
% 11.81/12.22 skol1 ) ) ) ==> op1( j( X ), skol1 ) }.
% 11.81/12.22 (18015) {G3,W11,D6,L1,V0,M1} P(120,257);r(20) { op1( j( skol2( h( skol1 ) )
% 11.81/12.22 ), skol1 ) ==> j( skol2( h( skol1 ) ) ) }.
% 11.81/12.22 (19952) {G5,W0,D0,L0,V0,M0} S(18015);r(87) { }.
% 11.81/12.22
% 11.81/12.22
% 11.81/12.22 % SZS output end Refutation
% 11.81/12.22 found a proof!
% 11.81/12.22
% 11.81/12.22
% 11.81/12.22 Unprocessed initial clauses:
% 11.81/12.22
% 11.81/12.22 (19954) {G0,W8,D3,L3,V2,M3} { ! sorti1( X ), ! sorti1( Y ), sorti1( op1( X
% 11.81/12.22 , Y ) ) }.
% 11.81/12.22 (19955) {G0,W8,D3,L3,V2,M3} { ! sorti2( X ), ! sorti2( Y ), sorti2( op2( X
% 11.81/12.22 , Y ) ) }.
% 11.81/12.22 (19956) {G0,W2,D2,L1,V0,M1} { sorti1( skol1 ) }.
% 11.81/12.22 (19957) {G0,W7,D3,L2,V1,M2} { ! sorti1( X ), ! op1( X, skol1 ) = X }.
% 11.81/12.22 (19958) {G0,W5,D3,L2,V2,M2} { ! sorti2( X ), sorti2( skol2( Y ) ) }.
% 11.81/12.22 (19959) {G0,W9,D4,L2,V1,M2} { ! sorti2( X ), op2( skol2( X ), X ) = skol2
% 11.81/12.22 ( X ) }.
% 11.81/12.22 (19960) {G0,W5,D3,L2,V1,M2} { ! sorti1( X ), sorti2( h( X ) ) }.
% 11.81/12.22 (19961) {G0,W5,D3,L2,V1,M2} { ! sorti2( X ), sorti1( j( X ) ) }.
% 11.81/12.22 (19962) {G0,W14,D4,L3,V2,M3} { ! sorti1( X ), ! sorti1( Y ), h( op1( X, Y
% 11.81/12.22 ) ) = op2( h( X ), h( Y ) ) }.
% 11.81/12.22 (19963) {G0,W14,D4,L3,V2,M3} { ! sorti2( X ), ! sorti2( Y ), j( op2( X, Y
% 11.81/12.22 ) ) = op1( j( X ), j( Y ) ) }.
% 11.81/12.22 (19964) {G0,W7,D4,L2,V1,M2} { ! sorti2( X ), h( j( X ) ) = X }.
% 11.81/12.22 (19965) {G0,W7,D4,L2,V1,M2} { ! sorti1( X ), j( h( X ) ) = X }.
% 11.81/12.22
% 11.81/12.22
% 11.81/12.22 Total Proof:
% 11.81/12.22
% 11.81/12.22 subsumption: (2) {G0,W2,D2,L1,V0,M1} I { sorti1( skol1 ) }.
% 11.81/12.22 parent0: (19956) {G0,W2,D2,L1,V0,M1} { sorti1( skol1 ) }.
% 11.81/12.22 substitution0:
% 11.81/12.22 end
% 11.81/12.22 permutation0:
% 11.81/12.22 0 ==> 0
% 11.81/12.22 end
% 11.81/12.22
% 11.81/12.22 subsumption: (3) {G0,W7,D3,L2,V1,M2} I { ! sorti1( X ), ! op1( X, skol1 )
% 11.81/12.22 ==> X }.
% 11.81/12.22 parent0: (19957) {G0,W7,D3,L2,V1,M2} { ! sorti1( X ), ! op1( X, skol1 ) =
% 11.81/12.22 X }.
% 11.81/12.22 substitution0:
% 11.81/12.22 X := X
% 11.81/12.22 end
% 11.81/12.22 permutation0:
% 11.81/12.22 0 ==> 0
% 11.81/12.22 1 ==> 1
% 11.81/12.22 end
% 11.81/12.22
% 11.81/12.22 subsumption: (4) {G0,W5,D3,L2,V2,M2} I { ! sorti2( X ), sorti2( skol2( Y )
% 11.81/12.22 ) }.
% 11.81/12.22 parent0: (19958) {G0,W5,D3,L2,V2,M2} { ! sorti2( X ), sorti2( skol2( Y ) )
% 11.81/12.22 }.
% 11.81/12.22 substitution0:
% 11.81/12.22 X := X
% 11.81/12.22 Y := Y
% 11.81/12.22 end
% 11.81/12.22 permutation0:
% 11.81/12.22 0 ==> 0
% 11.81/12.22 1 ==> 1
% 11.81/12.22 end
% 11.81/12.22
% 11.81/12.22 subsumption: (5) {G0,W9,D4,L2,V1,M2} I { ! sorti2( X ), op2( skol2( X ), X
% 11.81/12.22 ) ==> skol2( X ) }.
% 11.81/12.22 parent0: (19959) {G0,W9,D4,L2,V1,M2} { ! sorti2( X ), op2( skol2( X ), X )
% 11.81/12.22 = skol2( X ) }.
% 11.81/12.22 substitution0:
% 11.81/12.22 X := X
% 11.81/12.22 end
% 11.81/12.22 permutation0:
% 11.81/12.22 0 ==> 0
% 11.81/12.22 1 ==> 1
% 11.81/12.22 end
% 11.81/12.22
% 11.81/12.22 subsumption: (6) {G0,W5,D3,L2,V1,M2} I { ! sorti1( X ), sorti2( h( X ) )
% 11.81/12.22 }.
% 11.81/12.22 parent0: (19960) {G0,W5,D3,L2,V1,M2} { ! sorti1( X ), sorti2( h( X ) ) }.
% 11.81/12.22 substitution0:
% 11.81/12.22 X := X
% 11.81/12.22 end
% 11.81/12.22 permutation0:
% 11.81/12.22 0 ==> 0
% 11.81/12.22 1 ==> 1
% 11.81/12.22 end
% 11.81/12.22
% 11.81/12.22 subsumption: (7) {G0,W5,D3,L2,V1,M2} I { ! sorti2( X ), sorti1( j( X ) )
% 11.81/12.22 }.
% 11.81/12.22 parent0: (19961) {G0,W5,D3,L2,V1,M2} { ! sorti2( X ), sorti1( j( X ) ) }.
% 11.81/12.22 substitution0:
% 11.81/12.22 X := X
% 11.81/12.22 end
% 11.81/12.22 permutation0:
% 11.81/12.22 0 ==> 0
% 11.81/12.22 1 ==> 1
% 11.81/12.22 end
% 11.81/12.22
% 11.81/12.22 eqswap: (19993) {G0,W14,D4,L3,V2,M3} { op1( j( X ), j( Y ) ) = j( op2( X,
% 11.81/12.22 Y ) ), ! sorti2( X ), ! sorti2( Y ) }.
% 11.81/12.22 parent0[2]: (19963) {G0,W14,D4,L3,V2,M3} { ! sorti2( X ), ! sorti2( Y ), j
% 11.81/12.22 ( op2( X, Y ) ) = op1( j( X ), j( Y ) ) }.
% 11.81/12.22 substitution0:
% 11.81/12.22 X := X
% 11.81/12.22 Y := Y
% 11.81/12.22 end
% 11.81/12.22
% 11.81/12.22 subsumption: (9) {G0,W14,D4,L3,V2,M3} I { ! sorti2( X ), ! sorti2( Y ), op1
% 11.81/12.22 ( j( X ), j( Y ) ) ==> j( op2( X, Y ) ) }.
% 11.81/12.22 parent0: (19993) {G0,W14,D4,L3,V2,M3} { op1( j( X ), j( Y ) ) = j( op2( X
% 11.81/12.22 , Y ) ), ! sorti2( X ), ! sorti2( Y ) }.
% 11.81/12.22 substitution0:
% 11.81/12.22 X := X
% 11.81/12.22 Y := Y
% 11.81/12.22 end
% 11.81/12.22 permutation0:
% 11.81/12.22 0 ==> 2
% 11.81/12.22 1 ==> 0
% 11.81/12.22 2 ==> 1
% 11.81/12.22 end
% 11.81/12.22
% 11.81/12.22 subsumption: (11) {G0,W7,D4,L2,V1,M2} I { ! sorti1( X ), j( h( X ) ) ==> X
% 11.81/12.22 }.
% 11.81/12.22 parent0: (19965) {G0,W7,D4,L2,V1,M2} { ! sorti1( X ), j( h( X ) ) = X }.
% 11.81/12.22 substitution0:
% 11.81/12.22 X := X
% 11.81/12.22 end
% 11.81/12.22 permutation0:
% 11.81/12.22 0 ==> 0
% 11.81/12.22 1 ==> 1
% 11.81/12.22 end
% 11.81/12.22
% 11.81/12.22 resolution: (20008) {G1,W3,D3,L1,V0,M1} { sorti2( h( skol1 ) ) }.
% 11.81/12.22 parent0[0]: (6) {G0,W5,D3,L2,V1,M2} I { ! sorti1( X ), sorti2( h( X ) ) }.
% 11.81/12.22 parent1[0]: (2) {G0,W2,D2,L1,V0,M1} I { sorti1( skol1 ) }.
% 11.81/12.22 substitution0:
% 11.81/12.22 X := skol1
% 11.81/12.22 end
% 11.81/12.22 substitution1:
% 11.81/12.22 end
% 11.81/12.22
% 11.81/12.22 subsumption: (18) {G1,W3,D3,L1,V0,M1} R(6,2) { sorti2( h( skol1 ) ) }.
% 11.81/12.22 parent0: (20008) {G1,W3,D3,L1,V0,M1} { sorti2( h( skol1 ) ) }.
% 11.81/12.22 substitution0:
% 11.81/12.22 end
% 11.81/12.22 permutation0:
% 11.81/12.22 0 ==> 0
% 11.81/12.22 end
% 11.81/12.22
% 11.81/12.22 resolution: (20009) {G1,W3,D3,L1,V1,M1} { sorti2( skol2( X ) ) }.
% 11.81/12.22 parent0[0]: (4) {G0,W5,D3,L2,V2,M2} I { ! sorti2( X ), sorti2( skol2( Y ) )
% 11.81/12.22 }.
% 11.81/12.22 parent1[0]: (18) {G1,W3,D3,L1,V0,M1} R(6,2) { sorti2( h( skol1 ) ) }.
% 11.81/12.22 substitution0:
% 11.81/12.22 X := h( skol1 )
% 11.81/12.22 Y := X
% 11.81/12.22 end
% 11.81/12.22 substitution1:
% 11.81/12.22 end
% 11.81/12.22
% 11.81/12.22 subsumption: (20) {G2,W3,D3,L1,V1,M1} R(18,4) { sorti2( skol2( X ) ) }.
% 11.81/12.22 parent0: (20009) {G1,W3,D3,L1,V1,M1} { sorti2( skol2( X ) ) }.
% 11.81/12.22 substitution0:
% 11.81/12.22 X := X
% 11.81/12.22 end
% 11.81/12.22 permutation0:
% 11.81/12.22 0 ==> 0
% 11.81/12.22 end
% 11.81/12.22
% 11.81/12.22 resolution: (20010) {G1,W4,D4,L1,V1,M1} { sorti1( j( skol2( X ) ) ) }.
% 11.81/12.22 parent0[0]: (7) {G0,W5,D3,L2,V1,M2} I { ! sorti2( X ), sorti1( j( X ) ) }.
% 11.81/12.22 parent1[0]: (20) {G2,W3,D3,L1,V1,M1} R(18,4) { sorti2( skol2( X ) ) }.
% 11.81/12.22 substitution0:
% 11.81/12.22 X := skol2( X )
% 11.81/12.22 end
% 11.81/12.22 substitution1:
% 11.81/12.22 X := X
% 11.81/12.22 end
% 11.81/12.22
% 11.81/12.22 subsumption: (37) {G3,W4,D4,L1,V1,M1} R(20,7) { sorti1( j( skol2( X ) ) )
% 11.81/12.22 }.
% 11.81/12.22 parent0: (20010) {G1,W4,D4,L1,V1,M1} { sorti1( j( skol2( X ) ) ) }.
% 11.81/12.22 substitution0:
% 11.81/12.22 X := X
% 11.81/12.22 end
% 11.81/12.22 permutation0:
% 11.81/12.22 0 ==> 0
% 11.81/12.22 end
% 11.81/12.22
% 11.81/12.22 eqswap: (20011) {G0,W7,D3,L2,V1,M2} { ! X ==> op1( X, skol1 ), ! sorti1( X
% 11.81/12.22 ) }.
% 11.81/12.22 parent0[1]: (3) {G0,W7,D3,L2,V1,M2} I { ! sorti1( X ), ! op1( X, skol1 )
% 11.81/12.22 ==> X }.
% 11.81/12.22 substitution0:
% 11.81/12.22 X := X
% 11.81/12.22 end
% 11.81/12.22
% 11.81/12.22 resolution: (20012) {G1,W9,D5,L1,V1,M1} { ! j( skol2( X ) ) ==> op1( j(
% 11.81/12.22 skol2( X ) ), skol1 ) }.
% 11.81/12.22 parent0[1]: (20011) {G0,W7,D3,L2,V1,M2} { ! X ==> op1( X, skol1 ), !
% 11.81/12.22 sorti1( X ) }.
% 11.81/12.22 parent1[0]: (37) {G3,W4,D4,L1,V1,M1} R(20,7) { sorti1( j( skol2( X ) ) )
% 11.81/12.22 }.
% 11.81/12.22 substitution0:
% 11.81/12.22 X := j( skol2( X ) )
% 11.81/12.22 end
% 11.81/12.22 substitution1:
% 11.81/12.22 X := X
% 11.81/12.22 end
% 11.81/12.22
% 11.81/12.22 eqswap: (20013) {G1,W9,D5,L1,V1,M1} { ! op1( j( skol2( X ) ), skol1 ) ==>
% 11.81/12.22 j( skol2( X ) ) }.
% 11.81/12.22 parent0[0]: (20012) {G1,W9,D5,L1,V1,M1} { ! j( skol2( X ) ) ==> op1( j(
% 11.81/12.22 skol2( X ) ), skol1 ) }.
% 11.81/12.22 substitution0:
% 11.81/12.22 X := X
% 11.81/12.22 end
% 11.81/12.22
% 11.81/12.22 subsumption: (87) {G4,W9,D5,L1,V1,M1} R(3,37) { ! op1( j( skol2( X ) ),
% 11.81/12.22 skol1 ) ==> j( skol2( X ) ) }.
% 11.81/12.22 parent0: (20013) {G1,W9,D5,L1,V1,M1} { ! op1( j( skol2( X ) ), skol1 ) ==>
% 11.81/12.22 j( skol2( X ) ) }.
% 11.81/12.22 substitution0:
% 11.81/12.22 X := X
% 11.81/12.22 end
% 11.81/12.22 permutation0:
% 11.81/12.22 0 ==> 0
% 11.81/12.22 end
% 11.81/12.22
% 11.81/12.22 eqswap: (20014) {G0,W9,D4,L2,V1,M2} { skol2( X ) ==> op2( skol2( X ), X )
% 11.81/12.22 , ! sorti2( X ) }.
% 11.81/12.22 parent0[1]: (5) {G0,W9,D4,L2,V1,M2} I { ! sorti2( X ), op2( skol2( X ), X )
% 11.81/12.22 ==> skol2( X ) }.
% 11.81/12.22 substitution0:
% 11.81/12.22 X := X
% 11.81/12.22 end
% 11.81/12.22
% 11.81/12.22 resolution: (20015) {G1,W10,D5,L1,V0,M1} { skol2( h( skol1 ) ) ==> op2(
% 11.81/12.22 skol2( h( skol1 ) ), h( skol1 ) ) }.
% 11.81/12.22 parent0[1]: (20014) {G0,W9,D4,L2,V1,M2} { skol2( X ) ==> op2( skol2( X ),
% 11.81/12.22 X ), ! sorti2( X ) }.
% 11.81/12.22 parent1[0]: (18) {G1,W3,D3,L1,V0,M1} R(6,2) { sorti2( h( skol1 ) ) }.
% 11.81/12.22 substitution0:
% 11.81/12.22 X := h( skol1 )
% 11.81/12.22 end
% 11.81/12.22 substitution1:
% 11.81/12.22 end
% 11.81/12.22
% 11.81/12.22 eqswap: (20016) {G1,W10,D5,L1,V0,M1} { op2( skol2( h( skol1 ) ), h( skol1
% 11.81/12.22 ) ) ==> skol2( h( skol1 ) ) }.
% 11.81/12.22 parent0[0]: (20015) {G1,W10,D5,L1,V0,M1} { skol2( h( skol1 ) ) ==> op2(
% 11.81/12.22 skol2( h( skol1 ) ), h( skol1 ) ) }.
% 11.81/12.22 substitution0:
% 11.81/12.22 end
% 11.81/12.22
% 11.81/12.22 subsumption: (120) {G2,W10,D5,L1,V0,M1} R(5,18) { op2( skol2( h( skol1 ) )
% 11.81/12.22 , h( skol1 ) ) ==> skol2( h( skol1 ) ) }.
% 11.81/12.22 parent0: (20016) {G1,W10,D5,L1,V0,M1} { op2( skol2( h( skol1 ) ), h( skol1
% 11.81/12.22 ) ) ==> skol2( h( skol1 ) ) }.
% 11.81/12.22 substitution0:
% 11.81/12.22 end
% 11.81/12.22 permutation0:
% 11.81/12.22 0 ==> 0
% 11.81/12.22 end
% 11.81/12.22
% 11.81/12.22 eqswap: (20017) {G0,W7,D4,L2,V1,M2} { X ==> j( h( X ) ), ! sorti1( X ) }.
% 11.81/12.22 parent0[1]: (11) {G0,W7,D4,L2,V1,M2} I { ! sorti1( X ), j( h( X ) ) ==> X
% 11.81/12.22 }.
% 11.81/12.22 substitution0:
% 11.81/12.22 X := X
% 11.81/12.22 end
% 11.81/12.22
% 11.81/12.22 resolution: (20018) {G1,W5,D4,L1,V0,M1} { skol1 ==> j( h( skol1 ) ) }.
% 11.81/12.22 parent0[1]: (20017) {G0,W7,D4,L2,V1,M2} { X ==> j( h( X ) ), ! sorti1( X )
% 11.81/12.22 }.
% 11.81/12.22 parent1[0]: (2) {G0,W2,D2,L1,V0,M1} I { sorti1( skol1 ) }.
% 11.81/12.22 substitution0:
% 11.81/12.22 X := skol1
% 11.81/12.22 end
% 11.81/12.22 substitution1:
% 11.81/12.22 end
% 11.81/12.22
% 11.81/12.22 eqswap: (20019) {G1,W5,D4,L1,V0,M1} { j( h( skol1 ) ) ==> skol1 }.
% 11.81/12.22 parent0[0]: (20018) {G1,W5,D4,L1,V0,M1} { skol1 ==> j( h( skol1 ) ) }.
% 11.81/12.22 substitution0:
% 11.81/12.22 end
% 11.81/12.22
% 11.81/12.22 subsumption: (255) {G1,W5,D4,L1,V0,M1} R(11,2) { j( h( skol1 ) ) ==> skol1
% 11.81/12.22 }.
% 11.81/12.22 parent0: (20019) {G1,W5,D4,L1,V0,M1} { j( h( skol1 ) ) ==> skol1 }.
% 11.81/12.22 substitution0:
% 11.81/12.22 end
% 11.81/12.22 permutation0:
% 11.81/12.22 0 ==> 0
% 11.81/12.22 end
% 11.81/12.22
% 11.81/12.22 eqswap: (20021) {G0,W14,D4,L3,V2,M3} { j( op2( X, Y ) ) ==> op1( j( X ), j
% 11.81/12.22 ( Y ) ), ! sorti2( X ), ! sorti2( Y ) }.
% 11.81/12.22 parent0[2]: (9) {G0,W14,D4,L3,V2,M3} I { ! sorti2( X ), ! sorti2( Y ), op1
% 11.81/12.22 ( j( X ), j( Y ) ) ==> j( op2( X, Y ) ) }.
% 11.81/12.22 substitution0:
% 11.81/12.22 X := X
% 11.81/12.22 Y := Y
% 11.81/12.22 end
% 11.81/12.22
% 11.81/12.22 paramod: (20023) {G1,W15,D5,L3,V1,M3} { j( op2( X, h( skol1 ) ) ) ==> op1
% 11.81/12.22 ( j( X ), skol1 ), ! sorti2( X ), ! sorti2( h( skol1 ) ) }.
% 11.81/12.22 parent0[0]: (255) {G1,W5,D4,L1,V0,M1} R(11,2) { j( h( skol1 ) ) ==> skol1
% 11.81/12.22 }.
% 11.81/12.22 parent1[0; 9]: (20021) {G0,W14,D4,L3,V2,M3} { j( op2( X, Y ) ) ==> op1( j
% 11.81/12.22 ( X ), j( Y ) ), ! sorti2( X ), ! sorti2( Y ) }.
% 11.81/12.22 substitution0:
% 11.81/12.22 end
% 11.81/12.22 substitution1:
% 11.81/12.22 X := X
% 11.81/12.22 Y := h( skol1 )
% 11.81/12.22 end
% 11.81/12.22
% 11.81/12.22 resolution: (20028) {G2,W12,D5,L2,V1,M2} { j( op2( X, h( skol1 ) ) ) ==>
% 11.81/12.22 op1( j( X ), skol1 ), ! sorti2( X ) }.
% 11.81/12.22 parent0[2]: (20023) {G1,W15,D5,L3,V1,M3} { j( op2( X, h( skol1 ) ) ) ==>
% 11.81/12.22 op1( j( X ), skol1 ), ! sorti2( X ), ! sorti2( h( skol1 ) ) }.
% 11.81/12.22 parent1[0]: (18) {G1,W3,D3,L1,V0,M1} R(6,2) { sorti2( h( skol1 ) ) }.
% 11.81/12.22 substitution0:
% 11.81/12.22 X := X
% 11.81/12.22 end
% 11.81/12.22 substitution1:
% 11.81/12.22 end
% 11.81/12.22
% 11.81/12.22 subsumption: (257) {G2,W12,D5,L2,V1,M2} P(255,9);r(18) { ! sorti2( X ), j(
% 11.81/12.22 op2( X, h( skol1 ) ) ) ==> op1( j( X ), skol1 ) }.
% 11.81/12.22 parent0: (20028) {G2,W12,D5,L2,V1,M2} { j( op2( X, h( skol1 ) ) ) ==> op1
% 11.81/12.22 ( j( X ), skol1 ), ! sorti2( X ) }.
% 11.81/12.22 substitution0:
% 11.81/12.22 X := X
% 11.81/12.22 end
% 11.81/12.22 permutation0:
% 11.81/12.22 0 ==> 1
% 11.81/12.22 1 ==> 0
% 11.81/12.22 end
% 11.81/12.22
% 11.81/12.22 eqswap: (20031) {G2,W12,D5,L2,V1,M2} { op1( j( X ), skol1 ) ==> j( op2( X
% 11.81/12.22 , h( skol1 ) ) ), ! sorti2( X ) }.
% 11.81/12.22 parent0[1]: (257) {G2,W12,D5,L2,V1,M2} P(255,9);r(18) { ! sorti2( X ), j(
% 11.81/12.22 op2( X, h( skol1 ) ) ) ==> op1( j( X ), skol1 ) }.
% 11.81/12.22 substitution0:
% 11.81/12.22 X := X
% 11.81/12.22 end
% 11.81/12.22
% 11.81/12.22 paramod: (20032) {G3,W15,D6,L2,V0,M2} { op1( j( skol2( h( skol1 ) ) ),
% 11.81/12.22 skol1 ) ==> j( skol2( h( skol1 ) ) ), ! sorti2( skol2( h( skol1 ) ) ) }.
% 11.81/12.22 parent0[0]: (120) {G2,W10,D5,L1,V0,M1} R(5,18) { op2( skol2( h( skol1 ) ),
% 11.81/12.22 h( skol1 ) ) ==> skol2( h( skol1 ) ) }.
% 11.81/12.22 parent1[0; 8]: (20031) {G2,W12,D5,L2,V1,M2} { op1( j( X ), skol1 ) ==> j(
% 11.81/12.22 op2( X, h( skol1 ) ) ), ! sorti2( X ) }.
% 11.81/12.22 substitution0:
% 11.81/12.22 end
% 11.81/12.22 substitution1:
% 11.81/12.22 X := skol2( h( skol1 ) )
% 11.81/12.22 end
% 11.81/12.22
% 11.81/12.22 resolution: (20033) {G3,W11,D6,L1,V0,M1} { op1( j( skol2( h( skol1 ) ) ),
% 11.81/12.22 skol1 ) ==> j( skol2( h( skol1 ) ) ) }.
% 11.81/12.22 parent0[1]: (20032) {G3,W15,D6,L2,V0,M2} { op1( j( skol2( h( skol1 ) ) ),
% 11.81/12.22 skol1 ) ==> j( skol2( h( skol1 ) ) ), ! sorti2( skol2( h( skol1 ) ) ) }.
% 11.81/12.22 parent1[0]: (20) {G2,W3,D3,L1,V1,M1} R(18,4) { sorti2( skol2( X ) ) }.
% 11.81/12.22 substitution0:
% 11.81/12.22 end
% 11.81/12.22 substitution1:
% 11.81/12.22 X := h( skol1 )
% 11.81/12.22 end
% 11.81/12.22
% 11.81/12.22 subsumption: (18015) {G3,W11,D6,L1,V0,M1} P(120,257);r(20) { op1( j( skol2
% 11.81/12.22 ( h( skol1 ) ) ), skol1 ) ==> j( skol2( h( skol1 ) ) ) }.
% 11.81/12.22 parent0: (20033) {G3,W11,D6,L1,V0,M1} { op1( j( skol2( h( skol1 ) ) ),
% 11.81/12.22 skol1 ) ==> j( skol2( h( skol1 ) ) ) }.
% 11.81/12.22 substitution0:
% 11.81/12.22 end
% 11.81/12.22 permutation0:
% 11.81/12.22 0 ==> 0
% 11.81/12.22 end
% 11.81/12.22
% 11.81/12.22 resolution: (20037) {G4,W0,D0,L0,V0,M0} { }.
% 11.81/12.22 parent0[0]: (87) {G4,W9,D5,L1,V1,M1} R(3,37) { ! op1( j( skol2( X ) ),
% 11.81/12.22 skol1 ) ==> j( skol2( X ) ) }.
% 11.81/12.22 parent1[0]: (18015) {G3,W11,D6,L1,V0,M1} P(120,257);r(20) { op1( j( skol2(
% 11.81/12.22 h( skol1 ) ) ), skol1 ) ==> j( skol2( h( skol1 ) ) ) }.
% 11.81/12.22 substitution0:
% 11.81/12.22 X := h( skol1 )
% 11.81/12.22 end
% 11.81/12.22 substitution1:
% 11.81/12.22 end
% 11.81/12.22
% 11.81/12.22 subsumption: (19952) {G5,W0,D0,L0,V0,M0} S(18015);r(87) { }.
% 11.81/12.22 parent0: (20037) {G4,W0,D0,L0,V0,M0} { }.
% 11.81/12.22 substitution0:
% 11.81/12.22 end
% 11.81/12.22 permutation0:
% 11.81/12.22 end
% 11.81/12.22
% 11.81/12.22 Proof check complete!
% 11.81/12.22
% 11.81/12.22 Memory use:
% 11.81/12.22
% 11.81/12.22 space for terms: 299619
% 11.81/12.22 space for clauses: 1197615
% 11.81/12.22
% 11.81/12.22
% 11.81/12.22 clauses generated: 185080
% 11.81/12.22 clauses kept: 19953
% 11.81/12.22 clauses selected: 671
% 11.81/12.22 clauses deleted: 142
% 11.81/12.22 clauses inuse deleted: 30
% 11.81/12.22
% 11.81/12.22 subsentry: 205784
% 11.81/12.22 literals s-matched: 68502
% 11.81/12.22 literals matched: 68502
% 11.81/12.22 full subsumption: 18936
% 11.81/12.22
% 11.81/12.22 checksum: 1562825946
% 11.81/12.22
% 11.81/12.22
% 11.81/12.22 Bliksem ended
%------------------------------------------------------------------------------