%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : ALG030+1 : TPTP v8.1.0. Released v2.7.0.
% 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 : Thu Jul 14 12:09:10 EDT 2022
% Result : Theorem 6.61s 6.99s
% Output : Refutation 6.61s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ALG030+1 : TPTP v8.1.0. Released v2.7.0.
% 0.03/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n027.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % DateTime : Thu Jun 9 00:43:12 EDT 2022
% 0.13/0.34 % CPUTime :
% 6.61/6.99 *** allocated 10000 integers for termspace/termends
% 6.61/6.99 *** allocated 10000 integers for clauses
% 6.61/6.99 *** allocated 10000 integers for justifications
% 6.61/6.99 Bliksem 1.12
% 6.61/6.99
% 6.61/6.99
% 6.61/6.99 Automatic Strategy Selection
% 6.61/6.99
% 6.61/6.99
% 6.61/6.99 Clauses:
% 6.61/6.99
% 6.61/6.99 { ! sorti1( X ), ! sorti1( Y ), sorti1( op1( X, Y ) ) }.
% 6.61/6.99 { ! sorti2( X ), ! sorti2( Y ), sorti2( op2( X, Y ) ) }.
% 6.61/6.99 { sorti1( skol1 ) }.
% 6.61/6.99 { sorti1( skol2 ) }.
% 6.61/6.99 { ! op1( skol1, skol2 ) = op1( skol2, skol1 ) }.
% 6.61/6.99 { ! sorti2( X ), ! sorti2( Y ), op2( X, Y ) = op2( Y, X ) }.
% 6.61/6.99 { ! sorti1( X ), sorti2( h( X ) ) }.
% 6.61/6.99 { ! sorti2( X ), sorti1( j( X ) ) }.
% 6.61/6.99 { ! sorti1( X ), ! sorti1( Y ), h( op1( X, Y ) ) = op2( h( X ), h( Y ) ) }
% 6.61/6.99 .
% 6.61/6.99 { ! sorti2( X ), ! sorti2( Y ), j( op2( X, Y ) ) = op1( j( X ), j( Y ) ) }
% 6.61/6.99 .
% 6.61/6.99 { ! sorti2( X ), h( j( X ) ) = X }.
% 6.61/6.99 { ! sorti1( X ), j( h( X ) ) = X }.
% 6.61/6.99
% 6.61/6.99 percentage equality = 0.230769, percentage horn = 1.000000
% 6.61/6.99 This is a problem with some equality
% 6.61/6.99
% 6.61/6.99
% 6.61/6.99
% 6.61/6.99 Options Used:
% 6.61/6.99
% 6.61/6.99 useres = 1
% 6.61/6.99 useparamod = 1
% 6.61/6.99 useeqrefl = 1
% 6.61/6.99 useeqfact = 1
% 6.61/6.99 usefactor = 1
% 6.61/6.99 usesimpsplitting = 0
% 6.61/6.99 usesimpdemod = 5
% 6.61/6.99 usesimpres = 3
% 6.61/6.99
% 6.61/6.99 resimpinuse = 1000
% 6.61/6.99 resimpclauses = 20000
% 6.61/6.99 substype = eqrewr
% 6.61/6.99 backwardsubs = 1
% 6.61/6.99 selectoldest = 5
% 6.61/6.99
% 6.61/6.99 litorderings [0] = split
% 6.61/6.99 litorderings [1] = extend the termordering, first sorting on arguments
% 6.61/6.99
% 6.61/6.99 termordering = kbo
% 6.61/6.99
% 6.61/6.99 litapriori = 0
% 6.61/6.99 termapriori = 1
% 6.61/6.99 litaposteriori = 0
% 6.61/6.99 termaposteriori = 0
% 6.61/6.99 demodaposteriori = 0
% 6.61/6.99 ordereqreflfact = 0
% 6.61/6.99
% 6.61/6.99 litselect = negord
% 6.61/6.99
% 6.61/6.99 maxweight = 15
% 6.61/6.99 maxdepth = 30000
% 6.61/6.99 maxlength = 115
% 6.61/6.99 maxnrvars = 195
% 6.61/6.99 excuselevel = 1
% 6.61/6.99 increasemaxweight = 1
% 6.61/6.99
% 6.61/6.99 maxselected = 10000000
% 6.61/6.99 maxnrclauses = 10000000
% 6.61/6.99
% 6.61/6.99 showgenerated = 0
% 6.61/6.99 showkept = 0
% 6.61/6.99 showselected = 0
% 6.61/6.99 showdeleted = 0
% 6.61/6.99 showresimp = 1
% 6.61/6.99 showstatus = 2000
% 6.61/6.99
% 6.61/6.99 prologoutput = 0
% 6.61/6.99 nrgoals = 5000000
% 6.61/6.99 totalproof = 1
% 6.61/6.99
% 6.61/6.99 Symbols occurring in the translation:
% 6.61/6.99
% 6.61/6.99 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 6.61/6.99 . [1, 2] (w:1, o:25, a:1, s:1, b:0),
% 6.61/6.99 ! [4, 1] (w:0, o:16, a:1, s:1, b:0),
% 6.61/6.99 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 6.61/6.99 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 6.61/6.99 sorti1 [36, 1] (w:1, o:21, a:1, s:1, b:0),
% 6.61/6.99 op1 [38, 2] (w:1, o:49, a:1, s:1, b:0),
% 6.61/6.99 sorti2 [39, 1] (w:1, o:22, a:1, s:1, b:0),
% 6.61/6.99 op2 [40, 2] (w:1, o:50, a:1, s:1, b:0),
% 6.61/6.99 h [41, 1] (w:1, o:23, a:1, s:1, b:0),
% 6.61/6.99 j [42, 1] (w:1, o:24, a:1, s:1, b:0),
% 6.61/6.99 skol1 [49, 0] (w:1, o:14, a:1, s:1, b:1),
% 6.61/6.99 skol2 [50, 0] (w:1, o:15, a:1, s:1, b:1).
% 6.61/6.99
% 6.61/6.99
% 6.61/6.99 Starting Search:
% 6.61/6.99
% 6.61/6.99 *** allocated 15000 integers for clauses
% 6.61/6.99 *** allocated 22500 integers for clauses
% 6.61/6.99 *** allocated 33750 integers for clauses
% 6.61/6.99 *** allocated 50625 integers for clauses
% 6.61/6.99 *** allocated 15000 integers for termspace/termends
% 6.61/6.99 *** allocated 75937 integers for clauses
% 6.61/6.99 Resimplifying inuse:
% 6.61/6.99 Done
% 6.61/6.99
% 6.61/6.99 *** allocated 22500 integers for termspace/termends
% 6.61/6.99 *** allocated 113905 integers for clauses
% 6.61/6.99 *** allocated 33750 integers for termspace/termends
% 6.61/6.99 *** allocated 170857 integers for clauses
% 6.61/6.99
% 6.61/6.99 Intermediate Status:
% 6.61/6.99 Generated: 4120
% 6.61/6.99 Kept: 2029
% 6.61/6.99 Inuse: 106
% 6.61/6.99 Deleted: 24
% 6.61/6.99 Deletedinuse: 6
% 6.61/6.99
% 6.61/6.99 Resimplifying inuse:
% 6.61/6.99 Done
% 6.61/6.99
% 6.61/6.99 *** allocated 50625 integers for termspace/termends
% 6.61/6.99 *** allocated 256285 integers for clauses
% 6.61/6.99 Resimplifying inuse:
% 6.61/6.99 Done
% 6.61/6.99
% 6.61/6.99 *** allocated 75937 integers for termspace/termends
% 6.61/6.99
% 6.61/6.99 Intermediate Status:
% 6.61/6.99 Generated: 7239
% 6.61/6.99 Kept: 4126
% 6.61/6.99 Inuse: 130
% 6.61/6.99 Deleted: 28
% 6.61/6.99 Deletedinuse: 6
% 6.61/6.99
% 6.61/6.99 Resimplifying inuse:
% 6.61/6.99 Done
% 6.61/6.99
% 6.61/6.99 *** allocated 384427 integers for clauses
% 6.61/6.99 Resimplifying inuse:
% 6.61/6.99 Done
% 6.61/6.99
% 6.61/6.99 *** allocated 113905 integers for termspace/termends
% 6.61/6.99
% 6.61/6.99 Intermediate Status:
% 6.61/6.99 Generated: 10689
% 6.61/6.99 Kept: 6208
% 6.61/6.99 Inuse: 154
% 6.61/6.99 Deleted: 30
% 6.61/6.99 Deletedinuse: 6
% 6.61/6.99
% 6.61/6.99 Resimplifying inuse:
% 6.61/6.99 Done
% 6.61/6.99
% 6.61/6.99 *** allocated 576640 integers for clauses
% 6.61/6.99 Resimplifying inuse:
% 6.61/6.99 Done
% 6.61/6.99
% 6.61/6.99
% 6.61/6.99 Intermediate Status:
% 6.61/6.99 Generated: 15028
% 6.61/6.99 Kept: 8354
% 6.61/6.99 Inuse: 197
% 6.61/6.99 Deleted: 35
% 6.61/6.99 Deletedinuse: 6
% 6.61/6.99
% 6.61/6.99 Resimplifying inuse:
% 6.61/6.99 Done
% 6.61/6.99
% 6.61/6.99 *** allocated 170857 integers for termspace/termends
% 6.61/6.99 Resimplifying inuse:
% 6.61/6.99 Done
% 6.61/6.99
% 6.61/6.99
% 6.61/6.99 Intermediate Status:
% 6.61/6.99 Generated: 18530
% 6.61/6.99 Kept: 10495
% 6.61/6.99 Inuse: 227
% 6.61/6.99 Deleted: 35
% 6.61/6.99 Deletedinuse: 6
% 6.61/6.99
% 6.61/6.99 Resimplifying inuse:
% 6.61/6.99 Done
% 6.61/6.99
% 6.61/6.99 *** allocated 864960 integers for clauses
% 6.61/6.99 Resimplifying inuse:
% 6.61/6.99 Done
% 6.61/6.99
% 6.61/6.99
% 6.61/6.99 Intermediate Status:
% 6.61/6.99 Generated: 22454
% 6.61/6.99 Kept: 12518
% 6.61/6.99 Inuse: 257
% 6.61/6.99 Deleted: 43
% 6.61/6.99 Deletedinuse: 6
% 6.61/6.99
% 6.61/6.99 Resimplifying inuse:
% 6.61/6.99 Done
% 6.61/6.99
% 6.61/6.99 *** allocated 256285 integers for termspace/termends
% 6.61/6.99 Resimplifying inuse:
% 6.61/6.99 Done
% 6.61/6.99
% 6.61/6.99
% 6.61/6.99 Intermediate Status:
% 6.61/6.99 Generated: 28437
% 6.61/6.99 Kept: 14615
% 6.61/6.99 Inuse: 303
% 6.61/6.99 Deleted: 60
% 6.61/6.99 Deletedinuse: 17
% 6.61/6.99
% 6.61/6.99 Resimplifying inuse:
% 6.61/6.99 Done
% 6.61/6.99
% 6.61/6.99 Resimplifying inuse:
% 6.61/6.99 Done
% 6.61/6.99
% 6.61/6.99 *** allocated 1297440 integers for clauses
% 6.61/6.99
% 6.61/6.99 Intermediate Status:
% 6.61/6.99 Generated: 32775
% 6.61/6.99 Kept: 16695
% 6.61/6.99 Inuse: 319
% 6.61/6.99 Deleted: 63
% 6.61/6.99 Deletedinuse: 17
% 6.61/6.99
% 6.61/6.99 Resimplifying inuse:
% 6.61/6.99 Done
% 6.61/6.99
% 6.61/6.99 Resimplifying inuse:
% 6.61/6.99 Done
% 6.61/6.99
% 6.61/6.99 *** allocated 384427 integers for termspace/termends
% 6.61/6.99
% 6.61/6.99 Intermediate Status:
% 6.61/6.99 Generated: 38022
% 6.61/6.99 Kept: 18724
% 6.61/6.99 Inuse: 337
% 6.61/6.99 Deleted: 63
% 6.61/6.99 Deletedinuse: 17
% 6.61/6.99
% 6.61/6.99 Resimplifying inuse:
% 6.61/6.99 Done
% 6.61/6.99
% 6.61/6.99 Resimplifying inuse:
% 6.61/6.99 Done
% 6.61/6.99
% 6.61/6.99 Resimplifying clauses:
% 6.61/6.99 Done
% 6.61/6.99
% 6.61/6.99
% 6.61/6.99 Bliksems!, er is een bewijs:
% 6.61/6.99 % SZS status Theorem
% 6.61/6.99 % SZS output start Refutation
% 6.61/6.99
% 6.61/6.99 (0) {G0,W8,D3,L3,V2,M3} I { ! sorti1( X ), ! sorti1( Y ), sorti1( op1( X, Y
% 6.61/6.99 ) ) }.
% 6.61/6.99 (2) {G0,W2,D2,L1,V0,M1} I { sorti1( skol1 ) }.
% 6.61/6.99 (3) {G0,W2,D2,L1,V0,M1} I { sorti1( skol2 ) }.
% 6.61/6.99 (4) {G0,W7,D3,L1,V0,M1} I { ! op1( skol1, skol2 ) ==> op1( skol2, skol1 )
% 6.61/6.99 }.
% 6.61/6.99 (5) {G0,W11,D3,L3,V2,M3} I { ! sorti2( X ), ! sorti2( Y ), op2( X, Y ) =
% 6.61/6.99 op2( Y, X ) }.
% 6.61/6.99 (6) {G0,W5,D3,L2,V1,M2} I { ! sorti1( X ), sorti2( h( X ) ) }.
% 6.61/6.99 (8) {G0,W14,D4,L3,V2,M3} I { ! sorti1( X ), ! sorti1( Y ), op2( h( X ), h(
% 6.61/6.99 Y ) ) ==> h( op1( X, Y ) ) }.
% 6.61/6.99 (11) {G0,W7,D4,L2,V1,M2} I { ! sorti1( X ), j( h( X ) ) ==> X }.
% 6.61/6.99 (16) {G1,W3,D3,L1,V0,M1} R(6,2) { sorti2( h( skol1 ) ) }.
% 6.61/6.99 (17) {G1,W3,D3,L1,V0,M1} R(6,3) { sorti2( h( skol2 ) ) }.
% 6.61/6.99 (24) {G1,W6,D3,L2,V1,M2} R(0,2) { ! sorti1( X ), sorti1( op1( skol1, X ) )
% 6.61/6.99 }.
% 6.61/6.99 (25) {G1,W6,D3,L2,V1,M2} R(0,2) { ! sorti1( X ), sorti1( op1( X, skol1 ) )
% 6.61/6.99 }.
% 6.61/6.99 (77) {G2,W4,D3,L1,V0,M1} R(24,3) { sorti1( op1( skol1, skol2 ) ) }.
% 6.61/6.99 (107) {G2,W4,D3,L1,V0,M1} R(25,3) { sorti1( op1( skol2, skol1 ) ) }.
% 6.61/6.99 (121) {G2,W11,D4,L2,V1,M2} R(5,17) { ! sorti2( X ), op2( h( skol2 ), X ) =
% 6.61/6.99 op2( X, h( skol2 ) ) }.
% 6.61/6.99 (165) {G1,W12,D4,L2,V1,M2} R(8,2) { ! sorti1( X ), op2( h( skol1 ), h( X )
% 6.61/6.99 ) ==> h( op1( skol1, X ) ) }.
% 6.61/6.99 (166) {G1,W12,D4,L2,V1,M2} R(8,2) { ! sorti1( X ), op2( h( X ), h( skol1 )
% 6.61/6.99 ) ==> h( op1( X, skol1 ) ) }.
% 6.61/6.99 (308) {G3,W9,D5,L1,V0,M1} R(11,107) { j( h( op1( skol2, skol1 ) ) ) ==> op1
% 6.61/6.99 ( skol2, skol1 ) }.
% 6.61/6.99 (310) {G3,W9,D5,L1,V0,M1} R(11,77) { j( h( op1( skol1, skol2 ) ) ) ==> op1
% 6.61/6.99 ( skol1, skol2 ) }.
% 6.61/6.99 (12571) {G3,W11,D4,L1,V0,M1} R(121,16) { op2( h( skol1 ), h( skol2 ) ) ==>
% 6.61/6.99 op2( h( skol2 ), h( skol1 ) ) }.
% 6.61/6.99 (20068) {G4,W10,D4,L1,V0,M1} R(165,3);d(12571) { op2( h( skol2 ), h( skol1
% 6.61/6.99 ) ) ==> h( op1( skol1, skol2 ) ) }.
% 6.61/6.99 (20529) {G5,W9,D4,L1,V0,M1} R(166,3);d(20068) { h( op1( skol1, skol2 ) )
% 6.61/6.99 ==> h( op1( skol2, skol1 ) ) }.
% 6.61/6.99 (20531) {G6,W7,D3,L1,V0,M1} P(20529,310);d(308) { op1( skol1, skol2 ) ==>
% 6.61/6.99 op1( skol2, skol1 ) }.
% 6.61/6.99 (20532) {G7,W0,D0,L0,V0,M0} S(20531);r(4) { }.
% 6.61/6.99
% 6.61/6.99
% 6.61/6.99 % SZS output end Refutation
% 6.61/6.99 found a proof!
% 6.61/6.99
% 6.61/6.99
% 6.61/6.99 Unprocessed initial clauses:
% 6.61/6.99
% 6.61/6.99 (20534) {G0,W8,D3,L3,V2,M3} { ! sorti1( X ), ! sorti1( Y ), sorti1( op1( X
% 6.61/6.99 , Y ) ) }.
% 6.61/6.99 (20535) {G0,W8,D3,L3,V2,M3} { ! sorti2( X ), ! sorti2( Y ), sorti2( op2( X
% 6.61/6.99 , Y ) ) }.
% 6.61/6.99 (20536) {G0,W2,D2,L1,V0,M1} { sorti1( skol1 ) }.
% 6.61/6.99 (20537) {G0,W2,D2,L1,V0,M1} { sorti1( skol2 ) }.
% 6.61/6.99 (20538) {G0,W7,D3,L1,V0,M1} { ! op1( skol1, skol2 ) = op1( skol2, skol1 )
% 6.61/6.99 }.
% 6.61/6.99 (20539) {G0,W11,D3,L3,V2,M3} { ! sorti2( X ), ! sorti2( Y ), op2( X, Y ) =
% 6.61/6.99 op2( Y, X ) }.
% 6.61/6.99 (20540) {G0,W5,D3,L2,V1,M2} { ! sorti1( X ), sorti2( h( X ) ) }.
% 6.61/6.99 (20541) {G0,W5,D3,L2,V1,M2} { ! sorti2( X ), sorti1( j( X ) ) }.
% 6.61/6.99 (20542) {G0,W14,D4,L3,V2,M3} { ! sorti1( X ), ! sorti1( Y ), h( op1( X, Y
% 6.61/6.99 ) ) = op2( h( X ), h( Y ) ) }.
% 6.61/6.99 (20543) {G0,W14,D4,L3,V2,M3} { ! sorti2( X ), ! sorti2( Y ), j( op2( X, Y
% 6.61/6.99 ) ) = op1( j( X ), j( Y ) ) }.
% 6.61/6.99 (20544) {G0,W7,D4,L2,V1,M2} { ! sorti2( X ), h( j( X ) ) = X }.
% 6.61/6.99 (20545) {G0,W7,D4,L2,V1,M2} { ! sorti1( X ), j( h( X ) ) = X }.
% 6.61/6.99
% 6.61/6.99
% 6.61/6.99 Total Proof:
% 6.61/6.99
% 6.61/6.99 subsumption: (0) {G0,W8,D3,L3,V2,M3} I { ! sorti1( X ), ! sorti1( Y ),
% 6.61/6.99 sorti1( op1( X, Y ) ) }.
% 6.61/6.99 parent0: (20534) {G0,W8,D3,L3,V2,M3} { ! sorti1( X ), ! sorti1( Y ),
% 6.61/6.99 sorti1( op1( X, Y ) ) }.
% 6.61/6.99 substitution0:
% 6.61/6.99 X := X
% 6.61/6.99 Y := Y
% 6.61/6.99 end
% 6.61/6.99 permutation0:
% 6.61/6.99 0 ==> 0
% 6.61/6.99 1 ==> 1
% 6.61/6.99 2 ==> 2
% 6.61/6.99 end
% 6.61/6.99
% 6.61/6.99 subsumption: (2) {G0,W2,D2,L1,V0,M1} I { sorti1( skol1 ) }.
% 6.61/6.99 parent0: (20536) {G0,W2,D2,L1,V0,M1} { sorti1( skol1 ) }.
% 6.61/6.99 substitution0:
% 6.61/6.99 end
% 6.61/6.99 permutation0:
% 6.61/6.99 0 ==> 0
% 6.61/6.99 end
% 6.61/6.99
% 6.61/6.99 subsumption: (3) {G0,W2,D2,L1,V0,M1} I { sorti1( skol2 ) }.
% 6.61/6.99 parent0: (20537) {G0,W2,D2,L1,V0,M1} { sorti1( skol2 ) }.
% 6.61/6.99 substitution0:
% 6.61/6.99 end
% 6.61/6.99 permutation0:
% 6.61/6.99 0 ==> 0
% 6.61/6.99 end
% 6.61/6.99
% 6.61/6.99 subsumption: (4) {G0,W7,D3,L1,V0,M1} I { ! op1( skol1, skol2 ) ==> op1(
% 6.61/6.99 skol2, skol1 ) }.
% 6.61/6.99 parent0: (20538) {G0,W7,D3,L1,V0,M1} { ! op1( skol1, skol2 ) = op1( skol2
% 6.61/6.99 , skol1 ) }.
% 6.61/6.99 substitution0:
% 6.61/6.99 end
% 6.61/6.99 permutation0:
% 6.61/6.99 0 ==> 0
% 6.61/6.99 end
% 6.61/6.99
% 6.61/6.99 subsumption: (5) {G0,W11,D3,L3,V2,M3} I { ! sorti2( X ), ! sorti2( Y ), op2
% 6.61/6.99 ( X, Y ) = op2( Y, X ) }.
% 6.61/6.99 parent0: (20539) {G0,W11,D3,L3,V2,M3} { ! sorti2( X ), ! sorti2( Y ), op2
% 6.61/6.99 ( X, Y ) = op2( Y, X ) }.
% 6.61/6.99 substitution0:
% 6.61/6.99 X := X
% 6.61/6.99 Y := Y
% 6.61/6.99 end
% 6.61/6.99 permutation0:
% 6.61/6.99 0 ==> 0
% 6.61/6.99 1 ==> 1
% 6.61/6.99 2 ==> 2
% 6.61/6.99 end
% 6.61/6.99
% 6.61/6.99 subsumption: (6) {G0,W5,D3,L2,V1,M2} I { ! sorti1( X ), sorti2( h( X ) )
% 6.61/6.99 }.
% 6.61/6.99 parent0: (20540) {G0,W5,D3,L2,V1,M2} { ! sorti1( X ), sorti2( h( X ) ) }.
% 6.61/6.99 substitution0:
% 6.61/6.99 X := X
% 6.61/6.99 end
% 6.61/6.99 permutation0:
% 6.61/6.99 0 ==> 0
% 6.61/6.99 1 ==> 1
% 6.61/6.99 end
% 6.61/6.99
% 6.61/6.99 eqswap: (20566) {G0,W14,D4,L3,V2,M3} { op2( h( X ), h( Y ) ) = h( op1( X,
% 6.61/6.99 Y ) ), ! sorti1( X ), ! sorti1( Y ) }.
% 6.61/6.99 parent0[2]: (20542) {G0,W14,D4,L3,V2,M3} { ! sorti1( X ), ! sorti1( Y ), h
% 6.61/6.99 ( op1( X, Y ) ) = op2( h( X ), h( Y ) ) }.
% 6.61/6.99 substitution0:
% 6.61/6.99 X := X
% 6.61/6.99 Y := Y
% 6.61/6.99 end
% 6.61/6.99
% 6.61/6.99 subsumption: (8) {G0,W14,D4,L3,V2,M3} I { ! sorti1( X ), ! sorti1( Y ), op2
% 6.61/6.99 ( h( X ), h( Y ) ) ==> h( op1( X, Y ) ) }.
% 6.61/6.99 parent0: (20566) {G0,W14,D4,L3,V2,M3} { op2( h( X ), h( Y ) ) = h( op1( X
% 6.61/6.99 , Y ) ), ! sorti1( X ), ! sorti1( Y ) }.
% 6.61/6.99 substitution0:
% 6.61/6.99 X := X
% 6.61/6.99 Y := Y
% 6.61/6.99 end
% 6.61/6.99 permutation0:
% 6.61/6.99 0 ==> 2
% 6.61/6.99 1 ==> 0
% 6.61/6.99 2 ==> 1
% 6.61/6.99 end
% 6.61/6.99
% 6.61/6.99 subsumption: (11) {G0,W7,D4,L2,V1,M2} I { ! sorti1( X ), j( h( X ) ) ==> X
% 6.61/6.99 }.
% 6.61/6.99 parent0: (20545) {G0,W7,D4,L2,V1,M2} { ! sorti1( X ), j( h( X ) ) = X }.
% 6.61/6.99 substitution0:
% 6.61/6.99 X := X
% 6.61/6.99 end
% 6.61/6.99 permutation0:
% 6.61/6.99 0 ==> 0
% 6.61/6.99 1 ==> 1
% 6.61/6.99 end
% 6.61/6.99
% 6.61/6.99 resolution: (20581) {G1,W3,D3,L1,V0,M1} { sorti2( h( skol1 ) ) }.
% 6.61/6.99 parent0[0]: (6) {G0,W5,D3,L2,V1,M2} I { ! sorti1( X ), sorti2( h( X ) ) }.
% 6.61/6.99 parent1[0]: (2) {G0,W2,D2,L1,V0,M1} I { sorti1( skol1 ) }.
% 6.61/6.99 substitution0:
% 6.61/6.99 X := skol1
% 6.61/6.99 end
% 6.61/6.99 substitution1:
% 6.61/6.99 end
% 6.61/6.99
% 6.61/6.99 subsumption: (16) {G1,W3,D3,L1,V0,M1} R(6,2) { sorti2( h( skol1 ) ) }.
% 6.61/6.99 parent0: (20581) {G1,W3,D3,L1,V0,M1} { sorti2( h( skol1 ) ) }.
% 6.61/6.99 substitution0:
% 6.61/6.99 end
% 6.61/6.99 permutation0:
% 6.61/6.99 0 ==> 0
% 6.61/6.99 end
% 6.61/6.99
% 6.61/6.99 resolution: (20582) {G1,W3,D3,L1,V0,M1} { sorti2( h( skol2 ) ) }.
% 6.61/6.99 parent0[0]: (6) {G0,W5,D3,L2,V1,M2} I { ! sorti1( X ), sorti2( h( X ) ) }.
% 6.61/6.99 parent1[0]: (3) {G0,W2,D2,L1,V0,M1} I { sorti1( skol2 ) }.
% 6.61/6.99 substitution0:
% 6.61/6.99 X := skol2
% 6.61/6.99 end
% 6.61/6.99 substitution1:
% 6.61/6.99 end
% 6.61/6.99
% 6.61/6.99 subsumption: (17) {G1,W3,D3,L1,V0,M1} R(6,3) { sorti2( h( skol2 ) ) }.
% 6.61/6.99 parent0: (20582) {G1,W3,D3,L1,V0,M1} { sorti2( h( skol2 ) ) }.
% 6.61/6.99 substitution0:
% 6.61/6.99 end
% 6.61/6.99 permutation0:
% 6.61/6.99 0 ==> 0
% 6.61/6.99 end
% 6.61/6.99
% 6.61/6.99 resolution: (20583) {G1,W6,D3,L2,V1,M2} { ! sorti1( X ), sorti1( op1(
% 6.61/6.99 skol1, X ) ) }.
% 6.61/6.99 parent0[0]: (0) {G0,W8,D3,L3,V2,M3} I { ! sorti1( X ), ! sorti1( Y ),
% 6.61/6.99 sorti1( op1( X, Y ) ) }.
% 6.61/6.99 parent1[0]: (2) {G0,W2,D2,L1,V0,M1} I { sorti1( skol1 ) }.
% 6.61/6.99 substitution0:
% 6.61/6.99 X := skol1
% 6.61/6.99 Y := X
% 6.61/6.99 end
% 6.61/6.99 substitution1:
% 6.61/6.99 end
% 6.61/6.99
% 6.61/6.99 subsumption: (24) {G1,W6,D3,L2,V1,M2} R(0,2) { ! sorti1( X ), sorti1( op1(
% 6.61/6.99 skol1, X ) ) }.
% 6.61/6.99 parent0: (20583) {G1,W6,D3,L2,V1,M2} { ! sorti1( X ), sorti1( op1( skol1,
% 6.61/6.99 X ) ) }.
% 6.61/6.99 substitution0:
% 6.61/6.99 X := X
% 6.61/6.99 end
% 6.61/6.99 permutation0:
% 6.61/6.99 0 ==> 0
% 6.61/6.99 1 ==> 1
% 6.61/6.99 end
% 6.61/6.99
% 6.61/6.99 resolution: (20586) {G1,W6,D3,L2,V1,M2} { ! sorti1( X ), sorti1( op1( X,
% 6.61/6.99 skol1 ) ) }.
% 6.61/6.99 parent0[1]: (0) {G0,W8,D3,L3,V2,M3} I { ! sorti1( X ), ! sorti1( Y ),
% 6.61/6.99 sorti1( op1( X, Y ) ) }.
% 6.61/6.99 parent1[0]: (2) {G0,W2,D2,L1,V0,M1} I { sorti1( skol1 ) }.
% 6.61/6.99 substitution0:
% 6.61/6.99 X := X
% 6.61/6.99 Y := skol1
% 6.61/6.99 end
% 6.61/6.99 substitution1:
% 6.61/6.99 end
% 6.61/6.99
% 6.61/6.99 subsumption: (25) {G1,W6,D3,L2,V1,M2} R(0,2) { ! sorti1( X ), sorti1( op1(
% 6.61/6.99 X, skol1 ) ) }.
% 6.61/6.99 parent0: (20586) {G1,W6,D3,L2,V1,M2} { ! sorti1( X ), sorti1( op1( X,
% 6.61/6.99 skol1 ) ) }.
% 6.61/6.99 substitution0:
% 6.61/6.99 X := X
% 6.61/6.99 end
% 6.61/6.99 permutation0:
% 6.61/6.99 0 ==> 0
% 6.61/6.99 1 ==> 1
% 6.61/6.99 end
% 6.61/6.99
% 6.61/6.99 resolution: (20587) {G1,W4,D3,L1,V0,M1} { sorti1( op1( skol1, skol2 ) )
% 6.61/6.99 }.
% 6.61/6.99 parent0[0]: (24) {G1,W6,D3,L2,V1,M2} R(0,2) { ! sorti1( X ), sorti1( op1(
% 6.61/6.99 skol1, X ) ) }.
% 6.61/6.99 parent1[0]: (3) {G0,W2,D2,L1,V0,M1} I { sorti1( skol2 ) }.
% 6.61/6.99 substitution0:
% 6.61/6.99 X := skol2
% 6.61/6.99 end
% 6.61/6.99 substitution1:
% 6.61/6.99 end
% 6.61/6.99
% 6.61/6.99 subsumption: (77) {G2,W4,D3,L1,V0,M1} R(24,3) { sorti1( op1( skol1, skol2 )
% 6.61/6.99 ) }.
% 6.61/6.99 parent0: (20587) {G1,W4,D3,L1,V0,M1} { sorti1( op1( skol1, skol2 ) ) }.
% 6.61/6.99 substitution0:
% 6.61/6.99 end
% 6.61/6.99 permutation0:
% 6.61/6.99 0 ==> 0
% 6.61/6.99 end
% 6.61/6.99
% 6.61/6.99 resolution: (20588) {G1,W4,D3,L1,V0,M1} { sorti1( op1( skol2, skol1 ) )
% 6.61/6.99 }.
% 6.61/6.99 parent0[0]: (25) {G1,W6,D3,L2,V1,M2} R(0,2) { ! sorti1( X ), sorti1( op1( X
% 6.61/6.99 , skol1 ) ) }.
% 6.61/6.99 parent1[0]: (3) {G0,W2,D2,L1,V0,M1} I { sorti1( skol2 ) }.
% 6.61/6.99 substitution0:
% 6.61/6.99 X := skol2
% 6.61/6.99 end
% 6.61/6.99 substitution1:
% 6.61/6.99 end
% 6.61/6.99
% 6.61/6.99 subsumption: (107) {G2,W4,D3,L1,V0,M1} R(25,3) { sorti1( op1( skol2, skol1
% 6.61/6.99 ) ) }.
% 6.61/6.99 parent0: (20588) {G1,W4,D3,L1,V0,M1} { sorti1( op1( skol2, skol1 ) ) }.
% 6.61/6.99 substitution0:
% 6.61/6.99 end
% 6.61/6.99 permutation0:
% 6.61/6.99 0 ==> 0
% 6.61/6.99 end
% 6.61/6.99
% 6.61/6.99 resolution: (20589) {G1,W11,D4,L2,V1,M2} { ! sorti2( X ), op2( h( skol2 )
% 6.61/6.99 , X ) = op2( X, h( skol2 ) ) }.
% 6.61/6.99 parent0[0]: (5) {G0,W11,D3,L3,V2,M3} I { ! sorti2( X ), ! sorti2( Y ), op2
% 6.61/6.99 ( X, Y ) = op2( Y, X ) }.
% 6.61/6.99 parent1[0]: (17) {G1,W3,D3,L1,V0,M1} R(6,3) { sorti2( h( skol2 ) ) }.
% 6.61/6.99 substitution0:
% 6.61/6.99 X := h( skol2 )
% 6.61/6.99 Y := X
% 6.61/6.99 end
% 6.61/6.99 substitution1:
% 6.61/6.99 end
% 6.61/6.99
% 6.61/6.99 subsumption: (121) {G2,W11,D4,L2,V1,M2} R(5,17) { ! sorti2( X ), op2( h(
% 6.61/6.99 skol2 ), X ) = op2( X, h( skol2 ) ) }.
% 6.61/6.99 parent0: (20589) {G1,W11,D4,L2,V1,M2} { ! sorti2( X ), op2( h( skol2 ), X
% 6.61/6.99 ) = op2( X, h( skol2 ) ) }.
% 6.61/6.99 substitution0:
% 6.61/6.99 X := X
% 6.61/6.99 end
% 6.61/6.99 permutation0:
% 6.61/6.99 0 ==> 0
% 6.61/6.99 1 ==> 1
% 6.61/6.99 end
% 6.61/6.99
% 6.61/6.99 eqswap: (20591) {G0,W14,D4,L3,V2,M3} { h( op1( X, Y ) ) ==> op2( h( X ), h
% 6.61/6.99 ( Y ) ), ! sorti1( X ), ! sorti1( Y ) }.
% 6.61/6.99 parent0[2]: (8) {G0,W14,D4,L3,V2,M3} I { ! sorti1( X ), ! sorti1( Y ), op2
% 6.61/6.99 ( h( X ), h( Y ) ) ==> h( op1( X, Y ) ) }.
% 6.61/6.99 substitution0:
% 6.61/6.99 X := X
% 6.61/6.99 Y := Y
% 6.61/6.99 end
% 6.61/6.99
% 6.61/6.99 resolution: (20592) {G1,W12,D4,L2,V1,M2} { h( op1( skol1, X ) ) ==> op2( h
% 6.61/6.99 ( skol1 ), h( X ) ), ! sorti1( X ) }.
% 6.61/6.99 parent0[1]: (20591) {G0,W14,D4,L3,V2,M3} { h( op1( X, Y ) ) ==> op2( h( X
% 6.61/6.99 ), h( Y ) ), ! sorti1( X ), ! sorti1( Y ) }.
% 6.61/6.99 parent1[0]: (2) {G0,W2,D2,L1,V0,M1} I { sorti1( skol1 ) }.
% 6.61/6.99 substitution0:
% 6.61/6.99 X := skol1
% 6.61/6.99 Y := X
% 6.61/6.99 end
% 6.61/6.99 substitution1:
% 6.61/6.99 end
% 6.61/6.99
% 6.61/6.99 eqswap: (20595) {G1,W12,D4,L2,V1,M2} { op2( h( skol1 ), h( X ) ) ==> h(
% 6.61/6.99 op1( skol1, X ) ), ! sorti1( X ) }.
% 6.61/6.99 parent0[0]: (20592) {G1,W12,D4,L2,V1,M2} { h( op1( skol1, X ) ) ==> op2( h
% 6.61/6.99 ( skol1 ), h( X ) ), ! sorti1( X ) }.
% 6.61/6.99 substitution0:
% 6.61/6.99 X := X
% 6.61/6.99 end
% 6.61/6.99
% 6.61/6.99 subsumption: (165) {G1,W12,D4,L2,V1,M2} R(8,2) { ! sorti1( X ), op2( h(
% 6.61/6.99 skol1 ), h( X ) ) ==> h( op1( skol1, X ) ) }.
% 6.61/6.99 parent0: (20595) {G1,W12,D4,L2,V1,M2} { op2( h( skol1 ), h( X ) ) ==> h(
% 6.61/6.99 op1( skol1, X ) ), ! sorti1( X ) }.
% 6.61/6.99 substitution0:
% 6.61/6.99 X := X
% 6.61/6.99 end
% 6.61/6.99 permutation0:
% 6.61/6.99 0 ==> 1
% 6.61/6.99 1 ==> 0
% 6.61/6.99 end
% 6.61/6.99
% 6.61/6.99 eqswap: (20596) {G0,W14,D4,L3,V2,M3} { h( op1( X, Y ) ) ==> op2( h( X ), h
% 6.61/6.99 ( Y ) ), ! sorti1( X ), ! sorti1( Y ) }.
% 6.61/6.99 parent0[2]: (8) {G0,W14,D4,L3,V2,M3} I { ! sorti1( X ), ! sorti1( Y ), op2
% 6.61/6.99 ( h( X ), h( Y ) ) ==> h( op1( X, Y ) ) }.
% 6.61/6.99 substitution0:
% 6.61/6.99 X := X
% 6.61/6.99 Y := Y
% 6.61/6.99 end
% 6.61/6.99
% 6.61/6.99 resolution: (20598) {G1,W12,D4,L2,V1,M2} { h( op1( X, skol1 ) ) ==> op2( h
% 6.61/6.99 ( X ), h( skol1 ) ), ! sorti1( X ) }.
% 6.61/6.99 parent0[2]: (20596) {G0,W14,D4,L3,V2,M3} { h( op1( X, Y ) ) ==> op2( h( X
% 6.61/6.99 ), h( Y ) ), ! sorti1( X ), ! sorti1( Y ) }.
% 6.61/6.99 parent1[0]: (2) {G0,W2,D2,L1,V0,M1} I { sorti1( skol1 ) }.
% 6.61/6.99 substitution0:
% 6.61/6.99 X := X
% 6.61/6.99 Y := skol1
% 6.61/6.99 end
% 6.61/6.99 substitution1:
% 6.61/6.99 end
% 6.61/6.99
% 6.61/6.99 eqswap: (20599) {G1,W12,D4,L2,V1,M2} { op2( h( X ), h( skol1 ) ) ==> h(
% 6.61/6.99 op1( X, skol1 ) ), ! sorti1( X ) }.
% 6.61/6.99 parent0[0]: (20598) {G1,W12,D4,L2,V1,M2} { h( op1( X, skol1 ) ) ==> op2( h
% 6.61/6.99 ( X ), h( skol1 ) ), ! sorti1( X ) }.
% 6.61/6.99 substitution0:
% 6.61/6.99 X := X
% 6.61/6.99 end
% 6.61/6.99
% 6.61/6.99 subsumption: (166) {G1,W12,D4,L2,V1,M2} R(8,2) { ! sorti1( X ), op2( h( X )
% 6.61/6.99 , h( skol1 ) ) ==> h( op1( X, skol1 ) ) }.
% 6.61/6.99 parent0: (20599) {G1,W12,D4,L2,V1,M2} { op2( h( X ), h( skol1 ) ) ==> h(
% 6.61/6.99 op1( X, skol1 ) ), ! sorti1( X ) }.
% 6.61/6.99 substitution0:
% 6.61/6.99 X := X
% 6.61/6.99 end
% 6.61/6.99 permutation0:
% 6.61/6.99 0 ==> 1
% 6.61/6.99 1 ==> 0
% 6.61/6.99 end
% 6.61/6.99
% 6.61/6.99 eqswap: (20601) {G0,W7,D4,L2,V1,M2} { X ==> j( h( X ) ), ! sorti1( X ) }.
% 6.61/6.99 parent0[1]: (11) {G0,W7,D4,L2,V1,M2} I { ! sorti1( X ), j( h( X ) ) ==> X
% 6.61/6.99 }.
% 6.61/6.99 substitution0:
% 6.61/6.99 X := X
% 6.61/6.99 end
% 6.61/6.99
% 6.61/6.99 resolution: (20602) {G1,W9,D5,L1,V0,M1} { op1( skol2, skol1 ) ==> j( h(
% 6.61/6.99 op1( skol2, skol1 ) ) ) }.
% 6.61/6.99 parent0[1]: (20601) {G0,W7,D4,L2,V1,M2} { X ==> j( h( X ) ), ! sorti1( X )
% 6.61/6.99 }.
% 6.61/6.99 parent1[0]: (107) {G2,W4,D3,L1,V0,M1} R(25,3) { sorti1( op1( skol2, skol1 )
% 6.61/6.99 ) }.
% 6.61/6.99 substitution0:
% 6.61/6.99 X := op1( skol2, skol1 )
% 6.61/6.99 end
% 6.61/6.99 substitution1:
% 6.61/6.99 end
% 6.61/6.99
% 6.61/6.99 eqswap: (20603) {G1,W9,D5,L1,V0,M1} { j( h( op1( skol2, skol1 ) ) ) ==>
% 6.61/6.99 op1( skol2, skol1 ) }.
% 6.61/6.99 parent0[0]: (20602) {G1,W9,D5,L1,V0,M1} { op1( skol2, skol1 ) ==> j( h(
% 6.61/6.99 op1( skol2, skol1 ) ) ) }.
% 6.61/6.99 substitution0:
% 6.61/6.99 end
% 6.61/6.99
% 6.61/6.99 subsumption: (308) {G3,W9,D5,L1,V0,M1} R(11,107) { j( h( op1( skol2, skol1
% 6.61/6.99 ) ) ) ==> op1( skol2, skol1 ) }.
% 6.61/6.99 parent0: (20603) {G1,W9,D5,L1,V0,M1} { j( h( op1( skol2, skol1 ) ) ) ==>
% 6.61/6.99 op1( skol2, skol1 ) }.
% 6.61/6.99 substitution0:
% 6.61/6.99 end
% 6.61/6.99 permutation0:
% 6.61/6.99 0 ==> 0
% 6.61/6.99 end
% 6.61/6.99
% 6.61/6.99 eqswap: (20604) {G0,W7,D4,L2,V1,M2} { X ==> j( h( X ) ), ! sorti1( X ) }.
% 6.61/6.99 parent0[1]: (11) {G0,W7,D4,L2,V1,M2} I { ! sorti1( X ), j( h( X ) ) ==> X
% 6.61/6.99 }.
% 6.61/6.99 substitution0:
% 6.61/6.99 X := X
% 6.61/6.99 end
% 6.61/6.99
% 6.61/6.99 resolution: (20605) {G1,W9,D5,L1,V0,M1} { op1( skol1, skol2 ) ==> j( h(
% 6.61/6.99 op1( skol1, skol2 ) ) ) }.
% 6.61/6.99 parent0[1]: (20604) {G0,W7,D4,L2,V1,M2} { X ==> j( h( X ) ), ! sorti1( X )
% 6.61/6.99 }.
% 6.61/6.99 parent1[0]: (77) {G2,W4,D3,L1,V0,M1} R(24,3) { sorti1( op1( skol1, skol2 )
% 6.61/6.99 ) }.
% 6.61/6.99 substitution0:
% 6.61/6.99 X := op1( skol1, skol2 )
% 6.61/6.99 end
% 6.61/6.99 substitution1:
% 6.61/6.99 end
% 6.61/6.99
% 6.61/6.99 eqswap: (20606) {G1,W9,D5,L1,V0,M1} { j( h( op1( skol1, skol2 ) ) ) ==>
% 6.61/6.99 op1( skol1, skol2 ) }.
% 6.61/6.99 parent0[0]: (20605) {G1,W9,D5,L1,V0,M1} { op1( skol1, skol2 ) ==> j( h(
% 6.61/6.99 op1( skol1, skol2 ) ) ) }.
% 6.61/6.99 substitution0:
% 6.61/6.99 end
% 6.61/6.99
% 6.61/6.99 subsumption: (310) {G3,W9,D5,L1,V0,M1} R(11,77) { j( h( op1( skol1, skol2 )
% 6.61/6.99 ) ) ==> op1( skol1, skol2 ) }.
% 6.61/6.99 parent0: (20606) {G1,W9,D5,L1,V0,M1} { j( h( op1( skol1, skol2 ) ) ) ==>
% 6.61/6.99 op1( skol1, skol2 ) }.
% 6.61/6.99 substitution0:
% 6.61/6.99 end
% 6.61/6.99 permutation0:
% 6.61/6.99 0 ==> 0
% 6.61/6.99 end
% 6.61/6.99
% 6.61/6.99 eqswap: (20607) {G2,W11,D4,L2,V1,M2} { op2( X, h( skol2 ) ) = op2( h(
% 6.61/6.99 skol2 ), X ), ! sorti2( X ) }.
% 6.61/6.99 parent0[1]: (121) {G2,W11,D4,L2,V1,M2} R(5,17) { ! sorti2( X ), op2( h(
% 6.61/6.99 skol2 ), X ) = op2( X, h( skol2 ) ) }.
% 6.61/6.99 substitution0:
% 6.61/6.99 X := X
% 6.61/6.99 end
% 6.61/6.99
% 6.61/6.99 resolution: (20608) {G2,W11,D4,L1,V0,M1} { op2( h( skol1 ), h( skol2 ) ) =
% 6.61/6.99 op2( h( skol2 ), h( skol1 ) ) }.
% 6.61/6.99 parent0[1]: (20607) {G2,W11,D4,L2,V1,M2} { op2( X, h( skol2 ) ) = op2( h(
% 6.61/6.99 skol2 ), X ), ! sorti2( X ) }.
% 6.61/6.99 parent1[0]: (16) {G1,W3,D3,L1,V0,M1} R(6,2) { sorti2( h( skol1 ) ) }.
% 6.61/6.99 substitution0:
% 6.61/6.99 X := h( skol1 )
% 6.61/6.99 end
% 6.61/6.99 substitution1:
% 6.61/6.99 end
% 6.61/6.99
% 6.61/6.99 subsumption: (12571) {G3,W11,D4,L1,V0,M1} R(121,16) { op2( h( skol1 ), h(
% 6.61/6.99 skol2 ) ) ==> op2( h( skol2 ), h( skol1 ) ) }.
% 6.61/6.99 parent0: (20608) {G2,W11,D4,L1,V0,M1} { op2( h( skol1 ), h( skol2 ) ) =
% 6.61/6.99 op2( h( skol2 ), h( skol1 ) ) }.
% 6.61/6.99 substitution0:
% 6.61/6.99 end
% 6.61/6.99 permutation0:
% 6.61/6.99 0 ==> 0
% 6.61/6.99 end
% 6.61/6.99
% 6.61/6.99 eqswap: (20610) {G1,W12,D4,L2,V1,M2} { h( op1( skol1, X ) ) ==> op2( h(
% 6.61/6.99 skol1 ), h( X ) ), ! sorti1( X ) }.
% 6.61/6.99 parent0[1]: (165) {G1,W12,D4,L2,V1,M2} R(8,2) { ! sorti1( X ), op2( h(
% 6.61/6.99 skol1 ), h( X ) ) ==> h( op1( skol1, X ) ) }.
% 6.61/6.99 substitution0:
% 6.61/6.99 X := X
% 6.61/6.99 end
% 6.61/6.99
% 6.61/6.99 resolution: (20612) {G1,W10,D4,L1,V0,M1} { h( op1( skol1, skol2 ) ) ==>
% 6.61/6.99 op2( h( skol1 ), h( skol2 ) ) }.
% 6.61/6.99 parent0[1]: (20610) {G1,W12,D4,L2,V1,M2} { h( op1( skol1, X ) ) ==> op2( h
% 6.61/6.99 ( skol1 ), h( X ) ), ! sorti1( X ) }.
% 6.61/6.99 parent1[0]: (3) {G0,W2,D2,L1,V0,M1} I { sorti1( skol2 ) }.
% 6.61/6.99 substitution0:
% 6.61/6.99 X := skol2
% 6.61/6.99 end
% 6.61/6.99 substitution1:
% 6.61/6.99 end
% 6.61/6.99
% 6.61/6.99 paramod: (20613) {G2,W10,D4,L1,V0,M1} { h( op1( skol1, skol2 ) ) ==> op2(
% 6.61/6.99 h( skol2 ), h( skol1 ) ) }.
% 6.61/6.99 parent0[0]: (12571) {G3,W11,D4,L1,V0,M1} R(121,16) { op2( h( skol1 ), h(
% 6.61/6.99 skol2 ) ) ==> op2( h( skol2 ), h( skol1 ) ) }.
% 6.61/6.99 parent1[0; 5]: (20612) {G1,W10,D4,L1,V0,M1} { h( op1( skol1, skol2 ) ) ==>
% 6.61/6.99 op2( h( skol1 ), h( skol2 ) ) }.
% 6.61/6.99 substitution0:
% 6.61/6.99 end
% 6.61/6.99 substitution1:
% 6.61/6.99 end
% 6.61/6.99
% 6.61/6.99 eqswap: (20614) {G2,W10,D4,L1,V0,M1} { op2( h( skol2 ), h( skol1 ) ) ==> h
% 6.61/6.99 ( op1( skol1, skol2 ) ) }.
% 6.61/6.99 parent0[0]: (20613) {G2,W10,D4,L1,V0,M1} { h( op1( skol1, skol2 ) ) ==>
% 6.61/6.99 op2( h( skol2 ), h( skol1 ) ) }.
% 6.61/6.99 substitution0:
% 6.61/6.99 end
% 6.61/6.99
% 6.61/6.99 subsumption: (20068) {G4,W10,D4,L1,V0,M1} R(165,3);d(12571) { op2( h( skol2
% 6.61/6.99 ), h( skol1 ) ) ==> h( op1( skol1, skol2 ) ) }.
% 6.61/6.99 parent0: (20614) {G2,W10,D4,L1,V0,M1} { op2( h( skol2 ), h( skol1 ) ) ==>
% 6.61/6.99 h( op1( skol1, skol2 ) ) }.
% 6.61/6.99 substitution0:
% 6.61/6.99 end
% 6.61/6.99 permutation0:
% 6.61/6.99 0 ==> 0
% 6.61/6.99 end
% 6.61/6.99
% 6.61/6.99 eqswap: (20615) {G1,W12,D4,L2,V1,M2} { h( op1( X, skol1 ) ) ==> op2( h( X
% 6.61/6.99 ), h( skol1 ) ), ! sorti1( X ) }.
% 6.61/6.99 parent0[1]: (166) {G1,W12,D4,L2,V1,M2} R(8,2) { ! sorti1( X ), op2( h( X )
% 6.61/6.99 , h( skol1 ) ) ==> h( op1( X, skol1 ) ) }.
% 6.61/6.99 substitution0:
% 6.61/6.99 X := X
% 6.61/6.99 end
% 6.61/6.99
% 6.61/6.99 resolution: (20617) {G1,W10,D4,L1,V0,M1} { h( op1( skol2, skol1 ) ) ==>
% 6.61/6.99 op2( h( skol2 ), h( skol1 ) ) }.
% 6.61/6.99 parent0[1]: (20615) {G1,W12,D4,L2,V1,M2} { h( op1( X, skol1 ) ) ==> op2( h
% 6.61/6.99 ( X ), h( skol1 ) ), ! sorti1( X ) }.
% 6.61/6.99 parent1[0]: (3) {G0,W2,D2,L1,V0,M1} I { sorti1( skol2 ) }.
% 6.61/6.99 substitution0:
% 6.61/6.99 X := skol2
% 6.61/6.99 end
% 6.61/6.99 substitution1:
% 6.61/6.99 end
% 6.61/6.99
% 6.61/6.99 paramod: (20618) {G2,W9,D4,L1,V0,M1} { h( op1( skol2, skol1 ) ) ==> h( op1
% 6.61/6.99 ( skol1, skol2 ) ) }.
% 6.61/6.99 parent0[0]: (20068) {G4,W10,D4,L1,V0,M1} R(165,3);d(12571) { op2( h( skol2
% 6.61/6.99 ), h( skol1 ) ) ==> h( op1( skol1, skol2 ) ) }.
% 6.61/6.99 parent1[0; 5]: (20617) {G1,W10,D4,L1,V0,M1} { h( op1( skol2, skol1 ) ) ==>
% 6.61/6.99 op2( h( skol2 ), h( skol1 ) ) }.
% 6.61/6.99 substitution0:
% 6.61/6.99 end
% 6.61/6.99 substitution1:
% 6.61/6.99 end
% 6.61/6.99
% 6.61/6.99 eqswap: (20619) {G2,W9,D4,L1,V0,M1} { h( op1( skol1, skol2 ) ) ==> h( op1
% 6.61/6.99 ( skol2, skol1 ) ) }.
% 6.61/6.99 parent0[0]: (20618) {G2,W9,D4,L1,V0,M1} { h( op1( skol2, skol1 ) ) ==> h(
% 6.61/6.99 op1( skol1, skol2 ) ) }.
% 6.61/6.99 substitution0:
% 6.61/6.99 end
% 6.61/6.99
% 6.61/6.99 subsumption: (20529) {G5,W9,D4,L1,V0,M1} R(166,3);d(20068) { h( op1( skol1
% 6.61/6.99 , skol2 ) ) ==> h( op1( skol2, skol1 ) ) }.
% 6.61/6.99 parent0: (20619) {G2,W9,D4,L1,V0,M1} { h( op1( skol1, skol2 ) ) ==> h( op1
% 6.61/6.99 ( skol2, skol1 ) ) }.
% 6.61/6.99 substitution0:
% 6.61/6.99 end
% 6.61/6.99 permutation0:
% 6.61/6.99 0 ==> 0
% 6.61/6.99 end
% 6.61/6.99
% 6.61/6.99 eqswap: (20621) {G3,W9,D5,L1,V0,M1} { op1( skol1, skol2 ) ==> j( h( op1(
% 6.61/6.99 skol1, skol2 ) ) ) }.
% 6.61/6.99 parent0[0]: (310) {G3,W9,D5,L1,V0,M1} R(11,77) { j( h( op1( skol1, skol2 )
% 6.61/6.99 ) ) ==> op1( skol1, skol2 ) }.
% 6.61/6.99 substitution0:
% 6.61/6.99 end
% 6.61/6.99
% 6.61/6.99 paramod: (20623) {G4,W9,D5,L1,V0,M1} { op1( skol1, skol2 ) ==> j( h( op1(
% 6.61/6.99 skol2, skol1 ) ) ) }.
% 6.61/6.99 parent0[0]: (20529) {G5,W9,D4,L1,V0,M1} R(166,3);d(20068) { h( op1( skol1,
% 6.61/6.99 skol2 ) ) ==> h( op1( skol2, skol1 ) ) }.
% 6.61/6.99 parent1[0; 5]: (20621) {G3,W9,D5,L1,V0,M1} { op1( skol1, skol2 ) ==> j( h
% 6.61/6.99 ( op1( skol1, skol2 ) ) ) }.
% 6.61/6.99 substitution0:
% 6.61/6.99 end
% 6.61/6.99 substitution1:
% 6.61/6.99 end
% 6.61/6.99
% 6.61/6.99 paramod: (20624) {G4,W7,D3,L1,V0,M1} { op1( skol1, skol2 ) ==> op1( skol2
% 6.61/6.99 , skol1 ) }.
% 6.61/6.99 parent0[0]: (308) {G3,W9,D5,L1,V0,M1} R(11,107) { j( h( op1( skol2, skol1 )
% 6.61/6.99 ) ) ==> op1( skol2, skol1 ) }.
% 6.61/6.99 parent1[0; 4]: (20623) {G4,W9,D5,L1,V0,M1} { op1( skol1, skol2 ) ==> j( h
% 6.61/6.99 ( op1( skol2, skol1 ) ) ) }.
% 6.61/6.99 substitution0:
% 6.61/6.99 end
% 6.61/6.99 substitution1:
% 6.61/6.99 end
% 6.61/6.99
% 6.61/6.99 subsumption: (20531) {G6,W7,D3,L1,V0,M1} P(20529,310);d(308) { op1( skol1,
% 6.61/6.99 skol2 ) ==> op1( skol2, skol1 ) }.
% 6.61/6.99 parent0: (20624) {G4,W7,D3,L1,V0,M1} { op1( skol1, skol2 ) ==> op1( skol2
% 6.61/6.99 , skol1 ) }.
% 6.61/6.99 substitution0:
% 6.61/6.99 end
% 6.61/6.99 permutation0:
% 6.61/6.99 0 ==> 0
% 6.61/6.99 end
% 6.61/6.99
% 6.61/6.99 resolution: (20628) {G1,W0,D0,L0,V0,M0} { }.
% 6.61/6.99 parent0[0]: (4) {G0,W7,D3,L1,V0,M1} I { ! op1( skol1, skol2 ) ==> op1(
% 6.61/6.99 skol2, skol1 ) }.
% 6.61/6.99 parent1[0]: (20531) {G6,W7,D3,L1,V0,M1} P(20529,310);d(308) { op1( skol1,
% 6.61/6.99 skol2 ) ==> op1( skol2, skol1 ) }.
% 6.61/6.99 substitution0:
% 6.61/6.99 end
% 6.61/6.99 substitution1:
% 6.61/6.99 end
% 6.61/6.99
% 6.61/6.99 subsumption: (20532) {G7,W0,D0,L0,V0,M0} S(20531);r(4) { }.
% 6.61/6.99 parent0: (20628) {G1,W0,D0,L0,V0,M0} { }.
% 6.61/6.99 substitution0:
% 6.61/6.99 end
% 6.61/6.99 permutation0:
% 6.61/6.99 end
% 6.61/6.99
% 6.61/6.99 Proof check complete!
% 6.61/6.99
% 6.61/6.99 Memory use:
% 6.61/6.99
% 6.61/6.99 space for terms: 283651
% 6.61/6.99 space for clauses: 1096841
% 6.61/6.99
% 6.61/6.99
% 6.61/6.99 clauses generated: 43466
% 6.61/6.99 clauses kept: 20533
% 6.61/6.99 clauses selected: 356
% 6.61/6.99 clauses deleted: 441
% 6.61/6.99 clauses inuse deleted: 17
% 6.61/6.99
% 6.61/6.99 subsentry: 258535
% 6.61/6.99 literals s-matched: 69062
% 6.61/6.99 literals matched: 69062
% 6.61/6.99 full subsumption: 27349
% 6.61/6.99
% 6.61/6.99 checksum: -1845456491
% 6.61/6.99
% 6.61/6.99
% 6.61/6.99 Bliksem ended
%------------------------------------------------------------------------------