TSTP Solution File: ALG202+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : ALG202+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 12:09:55 EDT 2022
% Result : Theorem 0.66s 1.06s
% Output : Refutation 0.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : ALG202+1 : TPTP v8.1.0. Released v2.7.0.
% 0.11/0.12 % 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 : Wed Jun 8 10:58:16 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.66/1.06 *** allocated 10000 integers for termspace/termends
% 0.66/1.06 *** allocated 10000 integers for clauses
% 0.66/1.06 *** allocated 10000 integers for justifications
% 0.66/1.06 Bliksem 1.12
% 0.66/1.06
% 0.66/1.06
% 0.66/1.06 Automatic Strategy Selection
% 0.66/1.06
% 0.66/1.06
% 0.66/1.06 Clauses:
% 0.66/1.06
% 0.66/1.06 { ! sorti1( X ), ! sorti1( Y ), sorti1( op1( X, Y ) ) }.
% 0.66/1.06 { ! sorti2( X ), ! sorti2( Y ), sorti2( op2( X, Y ) ) }.
% 0.66/1.06 { ! sorti1( X ), op1( X, X ) = X }.
% 0.66/1.06 { sorti2( skol1 ) }.
% 0.66/1.06 { ! op2( skol1, skol1 ) = skol1 }.
% 0.66/1.06 { ! sorti1( X ), sorti2( h( X ) ) }.
% 0.66/1.06 { ! sorti2( X ), sorti1( j( X ) ) }.
% 0.66/1.06 { ! sorti1( X ), ! sorti1( Y ), h( op1( X, Y ) ) = op2( h( X ), h( Y ) ) }
% 0.66/1.06 .
% 0.66/1.06 { ! sorti2( X ), ! sorti2( Y ), j( op2( X, Y ) ) = op1( j( X ), j( Y ) ) }
% 0.66/1.06 .
% 0.66/1.06 { ! sorti2( X ), h( j( X ) ) = X }.
% 0.66/1.06 { ! sorti1( X ), j( h( X ) ) = X }.
% 0.66/1.06
% 0.66/1.06 percentage equality = 0.250000, percentage horn = 1.000000
% 0.66/1.06 This is a problem with some equality
% 0.66/1.06
% 0.66/1.06
% 0.66/1.06
% 0.66/1.06 Options Used:
% 0.66/1.06
% 0.66/1.06 useres = 1
% 0.66/1.06 useparamod = 1
% 0.66/1.06 useeqrefl = 1
% 0.66/1.06 useeqfact = 1
% 0.66/1.06 usefactor = 1
% 0.66/1.06 usesimpsplitting = 0
% 0.66/1.06 usesimpdemod = 5
% 0.66/1.06 usesimpres = 3
% 0.66/1.06
% 0.66/1.06 resimpinuse = 1000
% 0.66/1.06 resimpclauses = 20000
% 0.66/1.06 substype = eqrewr
% 0.66/1.06 backwardsubs = 1
% 0.66/1.06 selectoldest = 5
% 0.66/1.06
% 0.66/1.06 litorderings [0] = split
% 0.66/1.06 litorderings [1] = extend the termordering, first sorting on arguments
% 0.66/1.06
% 0.66/1.06 termordering = kbo
% 0.66/1.06
% 0.66/1.06 litapriori = 0
% 0.66/1.06 termapriori = 1
% 0.66/1.06 litaposteriori = 0
% 0.66/1.06 termaposteriori = 0
% 0.66/1.06 demodaposteriori = 0
% 0.66/1.06 ordereqreflfact = 0
% 0.66/1.06
% 0.66/1.06 litselect = negord
% 0.66/1.06
% 0.66/1.06 maxweight = 15
% 0.66/1.06 maxdepth = 30000
% 0.66/1.06 maxlength = 115
% 0.66/1.06 maxnrvars = 195
% 0.66/1.06 excuselevel = 1
% 0.66/1.06 increasemaxweight = 1
% 0.66/1.06
% 0.66/1.06 maxselected = 10000000
% 0.66/1.06 maxnrclauses = 10000000
% 0.66/1.06
% 0.66/1.06 showgenerated = 0
% 0.66/1.06 showkept = 0
% 0.66/1.06 showselected = 0
% 0.66/1.06 showdeleted = 0
% 0.66/1.06 showresimp = 1
% 0.66/1.06 showstatus = 2000
% 0.66/1.06
% 0.66/1.06 prologoutput = 0
% 0.66/1.06 nrgoals = 5000000
% 0.66/1.06 totalproof = 1
% 0.66/1.06
% 0.66/1.06 Symbols occurring in the translation:
% 0.66/1.06
% 0.66/1.06 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.66/1.06 . [1, 2] (w:1, o:24, a:1, s:1, b:0),
% 0.66/1.06 ! [4, 1] (w:0, o:15, a:1, s:1, b:0),
% 0.66/1.06 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.66/1.06 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.66/1.06 sorti1 [36, 1] (w:1, o:20, a:1, s:1, b:0),
% 0.66/1.06 op1 [38, 2] (w:1, o:48, a:1, s:1, b:0),
% 0.66/1.06 sorti2 [39, 1] (w:1, o:21, a:1, s:1, b:0),
% 0.66/1.06 op2 [40, 2] (w:1, o:49, a:1, s:1, b:0),
% 0.66/1.06 h [41, 1] (w:1, o:22, a:1, s:1, b:0),
% 0.66/1.06 j [42, 1] (w:1, o:23, a:1, s:1, b:0),
% 0.66/1.06 skol1 [49, 0] (w:1, o:14, a:1, s:1, b:1).
% 0.66/1.06
% 0.66/1.06
% 0.66/1.06 Starting Search:
% 0.66/1.06
% 0.66/1.06 *** allocated 15000 integers for clauses
% 0.66/1.06 *** allocated 22500 integers for clauses
% 0.66/1.06
% 0.66/1.06 Bliksems!, er is een bewijs:
% 0.66/1.06 % SZS status Theorem
% 0.66/1.06 % SZS output start Refutation
% 0.66/1.06
% 0.66/1.06 (1) {G0,W8,D3,L3,V2,M3} I { ! sorti2( X ), ! sorti2( Y ), sorti2( op2( X, Y
% 0.66/1.06 ) ) }.
% 0.66/1.06 (2) {G0,W7,D3,L2,V1,M2} I { ! sorti1( X ), op1( X, X ) ==> X }.
% 0.66/1.06 (3) {G0,W2,D2,L1,V0,M1} I { sorti2( skol1 ) }.
% 0.66/1.06 (4) {G0,W5,D3,L1,V0,M1} I { ! op2( skol1, skol1 ) ==> skol1 }.
% 0.66/1.06 (5) {G0,W5,D3,L2,V1,M2} I { ! sorti1( X ), sorti2( h( X ) ) }.
% 0.66/1.06 (6) {G0,W5,D3,L2,V1,M2} I { ! sorti2( X ), sorti1( j( X ) ) }.
% 0.66/1.06 (8) {G0,W14,D4,L3,V2,M3} I { ! sorti2( X ), ! sorti2( Y ), op1( j( X ), j(
% 0.66/1.06 Y ) ) ==> j( op2( X, Y ) ) }.
% 0.66/1.06 (9) {G0,W7,D4,L2,V1,M2} I { ! sorti2( X ), h( j( X ) ) ==> X }.
% 0.66/1.06 (11) {G1,W6,D3,L2,V1,M2} F(1) { ! sorti2( X ), sorti2( op2( X, X ) ) }.
% 0.66/1.06 (13) {G1,W12,D4,L2,V1,M2} F(8) { ! sorti2( X ), op1( j( X ), j( X ) ) ==> j
% 0.66/1.06 ( op2( X, X ) ) }.
% 0.66/1.06 (14) {G1,W3,D3,L1,V0,M1} R(6,3) { sorti1( j( skol1 ) ) }.
% 0.66/1.06 (15) {G2,W4,D4,L1,V0,M1} R(5,14) { sorti2( h( j( skol1 ) ) ) }.
% 0.66/1.06 (27) {G3,W5,D5,L1,V0,M1} R(15,6) { sorti1( j( h( j( skol1 ) ) ) ) }.
% 0.66/1.06 (30) {G4,W6,D6,L1,V0,M1} R(27,5) { sorti2( h( j( h( j( skol1 ) ) ) ) ) }.
% 0.66/1.06 (96) {G2,W9,D4,L2,V1,M2} R(2,6);d(13) { ! sorti2( X ), j( op2( X, X ) ) ==>
% 0.66/1.06 j( X ) }.
% 0.66/1.06 (231) {G3,W7,D3,L2,V1,M2} R(9,11);d(96);d(9) { ! sorti2( X ), op2( X, X )
% 0.66/1.06 ==> X }.
% 0.66/1.06 (232) {G3,W9,D6,L1,V0,M1} R(9,15) { h( j( h( j( skol1 ) ) ) ) ==> h( j(
% 0.66/1.06 skol1 ) ) }.
% 0.66/1.06 (233) {G1,W5,D4,L1,V0,M1} R(9,3) { h( j( skol1 ) ) ==> skol1 }.
% 0.66/1.06 (236) {G5,W0,D0,L0,V0,M0} R(231,30);d(232);d(233);r(4) { }.
% 0.66/1.06
% 0.66/1.06
% 0.66/1.06 % SZS output end Refutation
% 0.66/1.06 found a proof!
% 0.66/1.06
% 0.66/1.06
% 0.66/1.06 Unprocessed initial clauses:
% 0.66/1.06
% 0.66/1.06 (238) {G0,W8,D3,L3,V2,M3} { ! sorti1( X ), ! sorti1( Y ), sorti1( op1( X,
% 0.66/1.06 Y ) ) }.
% 0.66/1.06 (239) {G0,W8,D3,L3,V2,M3} { ! sorti2( X ), ! sorti2( Y ), sorti2( op2( X,
% 0.66/1.06 Y ) ) }.
% 0.66/1.06 (240) {G0,W7,D3,L2,V1,M2} { ! sorti1( X ), op1( X, X ) = X }.
% 0.66/1.06 (241) {G0,W2,D2,L1,V0,M1} { sorti2( skol1 ) }.
% 0.66/1.06 (242) {G0,W5,D3,L1,V0,M1} { ! op2( skol1, skol1 ) = skol1 }.
% 0.66/1.06 (243) {G0,W5,D3,L2,V1,M2} { ! sorti1( X ), sorti2( h( X ) ) }.
% 0.66/1.06 (244) {G0,W5,D3,L2,V1,M2} { ! sorti2( X ), sorti1( j( X ) ) }.
% 0.66/1.06 (245) {G0,W14,D4,L3,V2,M3} { ! sorti1( X ), ! sorti1( Y ), h( op1( X, Y )
% 0.66/1.06 ) = op2( h( X ), h( Y ) ) }.
% 0.66/1.06 (246) {G0,W14,D4,L3,V2,M3} { ! sorti2( X ), ! sorti2( Y ), j( op2( X, Y )
% 0.66/1.06 ) = op1( j( X ), j( Y ) ) }.
% 0.66/1.06 (247) {G0,W7,D4,L2,V1,M2} { ! sorti2( X ), h( j( X ) ) = X }.
% 0.66/1.06 (248) {G0,W7,D4,L2,V1,M2} { ! sorti1( X ), j( h( X ) ) = X }.
% 0.66/1.06
% 0.66/1.06
% 0.66/1.06 Total Proof:
% 0.66/1.06
% 0.66/1.06 subsumption: (1) {G0,W8,D3,L3,V2,M3} I { ! sorti2( X ), ! sorti2( Y ),
% 0.66/1.06 sorti2( op2( X, Y ) ) }.
% 0.66/1.06 parent0: (239) {G0,W8,D3,L3,V2,M3} { ! sorti2( X ), ! sorti2( Y ), sorti2
% 0.66/1.06 ( op2( X, Y ) ) }.
% 0.66/1.06 substitution0:
% 0.66/1.06 X := X
% 0.66/1.06 Y := Y
% 0.66/1.06 end
% 0.66/1.06 permutation0:
% 0.66/1.06 0 ==> 0
% 0.66/1.06 1 ==> 1
% 0.66/1.06 2 ==> 2
% 0.66/1.06 end
% 0.66/1.06
% 0.66/1.06 subsumption: (2) {G0,W7,D3,L2,V1,M2} I { ! sorti1( X ), op1( X, X ) ==> X
% 0.66/1.06 }.
% 0.66/1.06 parent0: (240) {G0,W7,D3,L2,V1,M2} { ! sorti1( X ), op1( X, X ) = X }.
% 0.66/1.06 substitution0:
% 0.66/1.06 X := X
% 0.66/1.06 end
% 0.66/1.06 permutation0:
% 0.66/1.06 0 ==> 0
% 0.66/1.06 1 ==> 1
% 0.66/1.06 end
% 0.66/1.06
% 0.66/1.06 subsumption: (3) {G0,W2,D2,L1,V0,M1} I { sorti2( skol1 ) }.
% 0.66/1.06 parent0: (241) {G0,W2,D2,L1,V0,M1} { sorti2( skol1 ) }.
% 0.66/1.06 substitution0:
% 0.66/1.06 end
% 0.66/1.06 permutation0:
% 0.66/1.06 0 ==> 0
% 0.66/1.06 end
% 0.66/1.06
% 0.66/1.06 subsumption: (4) {G0,W5,D3,L1,V0,M1} I { ! op2( skol1, skol1 ) ==> skol1
% 0.66/1.06 }.
% 0.66/1.06 parent0: (242) {G0,W5,D3,L1,V0,M1} { ! op2( skol1, skol1 ) = skol1 }.
% 0.66/1.06 substitution0:
% 0.66/1.06 end
% 0.66/1.06 permutation0:
% 0.66/1.06 0 ==> 0
% 0.66/1.06 end
% 0.66/1.06
% 0.66/1.06 subsumption: (5) {G0,W5,D3,L2,V1,M2} I { ! sorti1( X ), sorti2( h( X ) )
% 0.66/1.06 }.
% 0.66/1.06 parent0: (243) {G0,W5,D3,L2,V1,M2} { ! sorti1( X ), sorti2( h( X ) ) }.
% 0.66/1.06 substitution0:
% 0.66/1.06 X := X
% 0.66/1.06 end
% 0.66/1.06 permutation0:
% 0.66/1.06 0 ==> 0
% 0.66/1.06 1 ==> 1
% 0.66/1.06 end
% 0.66/1.06
% 0.66/1.06 subsumption: (6) {G0,W5,D3,L2,V1,M2} I { ! sorti2( X ), sorti1( j( X ) )
% 0.66/1.06 }.
% 0.66/1.06 parent0: (244) {G0,W5,D3,L2,V1,M2} { ! sorti2( X ), sorti1( j( X ) ) }.
% 0.66/1.06 substitution0:
% 0.66/1.06 X := X
% 0.66/1.06 end
% 0.66/1.06 permutation0:
% 0.66/1.06 0 ==> 0
% 0.66/1.06 1 ==> 1
% 0.66/1.06 end
% 0.66/1.06
% 0.66/1.06 eqswap: (276) {G0,W14,D4,L3,V2,M3} { op1( j( X ), j( Y ) ) = j( op2( X, Y
% 0.66/1.06 ) ), ! sorti2( X ), ! sorti2( Y ) }.
% 0.66/1.06 parent0[2]: (246) {G0,W14,D4,L3,V2,M3} { ! sorti2( X ), ! sorti2( Y ), j(
% 0.66/1.06 op2( X, Y ) ) = op1( j( X ), j( Y ) ) }.
% 0.66/1.06 substitution0:
% 0.66/1.06 X := X
% 0.66/1.06 Y := Y
% 0.66/1.06 end
% 0.66/1.06
% 0.66/1.06 subsumption: (8) {G0,W14,D4,L3,V2,M3} I { ! sorti2( X ), ! sorti2( Y ), op1
% 0.66/1.06 ( j( X ), j( Y ) ) ==> j( op2( X, Y ) ) }.
% 0.66/1.06 parent0: (276) {G0,W14,D4,L3,V2,M3} { op1( j( X ), j( Y ) ) = j( op2( X, Y
% 0.66/1.06 ) ), ! sorti2( X ), ! sorti2( Y ) }.
% 0.66/1.06 substitution0:
% 0.66/1.06 X := X
% 0.66/1.06 Y := Y
% 0.66/1.06 end
% 0.66/1.06 permutation0:
% 0.66/1.06 0 ==> 2
% 0.66/1.06 1 ==> 0
% 0.66/1.06 2 ==> 1
% 0.66/1.06 end
% 0.66/1.06
% 0.66/1.06 subsumption: (9) {G0,W7,D4,L2,V1,M2} I { ! sorti2( X ), h( j( X ) ) ==> X
% 0.66/1.06 }.
% 0.66/1.06 parent0: (247) {G0,W7,D4,L2,V1,M2} { ! sorti2( X ), h( j( X ) ) = X }.
% 0.66/1.06 substitution0:
% 0.66/1.06 X := X
% 0.66/1.06 end
% 0.66/1.06 permutation0:
% 0.66/1.06 0 ==> 0
% 0.66/1.06 1 ==> 1
% 0.66/1.06 end
% 0.66/1.06
% 0.66/1.06 factor: (290) {G0,W6,D3,L2,V1,M2} { ! sorti2( X ), sorti2( op2( X, X ) )
% 0.66/1.06 }.
% 0.66/1.06 parent0[0, 1]: (1) {G0,W8,D3,L3,V2,M3} I { ! sorti2( X ), ! sorti2( Y ),
% 0.66/1.06 sorti2( op2( X, Y ) ) }.
% 0.66/1.06 substitution0:
% 0.66/1.06 X := X
% 0.66/1.06 Y := X
% 0.66/1.06 end
% 0.66/1.06
% 0.66/1.06 subsumption: (11) {G1,W6,D3,L2,V1,M2} F(1) { ! sorti2( X ), sorti2( op2( X
% 0.66/1.06 , X ) ) }.
% 0.66/1.06 parent0: (290) {G0,W6,D3,L2,V1,M2} { ! sorti2( X ), sorti2( op2( X, X ) )
% 0.66/1.06 }.
% 0.66/1.06 substitution0:
% 0.66/1.06 X := X
% 0.66/1.06 end
% 0.66/1.06 permutation0:
% 0.66/1.06 0 ==> 0
% 0.66/1.06 1 ==> 1
% 0.66/1.06 end
% 0.66/1.06
% 0.66/1.06 factor: (292) {G0,W12,D4,L2,V1,M2} { ! sorti2( X ), op1( j( X ), j( X ) )
% 0.66/1.06 ==> j( op2( X, X ) ) }.
% 0.66/1.06 parent0[0, 1]: (8) {G0,W14,D4,L3,V2,M3} I { ! sorti2( X ), ! sorti2( Y ),
% 0.66/1.06 op1( j( X ), j( Y ) ) ==> j( op2( X, Y ) ) }.
% 0.66/1.06 substitution0:
% 0.66/1.06 X := X
% 0.66/1.06 Y := X
% 0.66/1.06 end
% 0.66/1.06
% 0.66/1.06 subsumption: (13) {G1,W12,D4,L2,V1,M2} F(8) { ! sorti2( X ), op1( j( X ), j
% 0.66/1.06 ( X ) ) ==> j( op2( X, X ) ) }.
% 0.66/1.06 parent0: (292) {G0,W12,D4,L2,V1,M2} { ! sorti2( X ), op1( j( X ), j( X ) )
% 0.66/1.06 ==> j( op2( X, X ) ) }.
% 0.66/1.06 substitution0:
% 0.66/1.06 X := X
% 0.66/1.06 end
% 0.66/1.06 permutation0:
% 0.66/1.06 0 ==> 0
% 0.66/1.06 1 ==> 1
% 0.66/1.06 end
% 0.66/1.06
% 0.66/1.06 resolution: (294) {G1,W3,D3,L1,V0,M1} { sorti1( j( skol1 ) ) }.
% 0.66/1.06 parent0[0]: (6) {G0,W5,D3,L2,V1,M2} I { ! sorti2( X ), sorti1( j( X ) ) }.
% 0.66/1.06 parent1[0]: (3) {G0,W2,D2,L1,V0,M1} I { sorti2( skol1 ) }.
% 0.66/1.06 substitution0:
% 0.66/1.06 X := skol1
% 0.66/1.06 end
% 0.66/1.06 substitution1:
% 0.66/1.06 end
% 0.66/1.06
% 0.66/1.06 subsumption: (14) {G1,W3,D3,L1,V0,M1} R(6,3) { sorti1( j( skol1 ) ) }.
% 0.66/1.06 parent0: (294) {G1,W3,D3,L1,V0,M1} { sorti1( j( skol1 ) ) }.
% 0.66/1.06 substitution0:
% 0.66/1.06 end
% 0.66/1.06 permutation0:
% 0.66/1.06 0 ==> 0
% 0.66/1.06 end
% 0.66/1.06
% 0.66/1.06 resolution: (295) {G1,W4,D4,L1,V0,M1} { sorti2( h( j( skol1 ) ) ) }.
% 0.66/1.06 parent0[0]: (5) {G0,W5,D3,L2,V1,M2} I { ! sorti1( X ), sorti2( h( X ) ) }.
% 0.66/1.06 parent1[0]: (14) {G1,W3,D3,L1,V0,M1} R(6,3) { sorti1( j( skol1 ) ) }.
% 0.66/1.06 substitution0:
% 0.66/1.06 X := j( skol1 )
% 0.66/1.06 end
% 0.66/1.06 substitution1:
% 0.66/1.06 end
% 0.66/1.06
% 0.66/1.06 subsumption: (15) {G2,W4,D4,L1,V0,M1} R(5,14) { sorti2( h( j( skol1 ) ) )
% 0.66/1.06 }.
% 0.66/1.06 parent0: (295) {G1,W4,D4,L1,V0,M1} { sorti2( h( j( skol1 ) ) ) }.
% 0.66/1.06 substitution0:
% 0.66/1.06 end
% 0.66/1.06 permutation0:
% 0.66/1.06 0 ==> 0
% 0.66/1.06 end
% 0.66/1.06
% 0.66/1.06 resolution: (296) {G1,W5,D5,L1,V0,M1} { sorti1( j( h( j( skol1 ) ) ) ) }.
% 0.66/1.06 parent0[0]: (6) {G0,W5,D3,L2,V1,M2} I { ! sorti2( X ), sorti1( j( X ) ) }.
% 0.66/1.06 parent1[0]: (15) {G2,W4,D4,L1,V0,M1} R(5,14) { sorti2( h( j( skol1 ) ) )
% 0.66/1.06 }.
% 0.66/1.06 substitution0:
% 0.66/1.06 X := h( j( skol1 ) )
% 0.66/1.06 end
% 0.66/1.06 substitution1:
% 0.66/1.06 end
% 0.66/1.06
% 0.66/1.06 subsumption: (27) {G3,W5,D5,L1,V0,M1} R(15,6) { sorti1( j( h( j( skol1 ) )
% 0.66/1.06 ) ) }.
% 0.66/1.06 parent0: (296) {G1,W5,D5,L1,V0,M1} { sorti1( j( h( j( skol1 ) ) ) ) }.
% 0.66/1.06 substitution0:
% 0.66/1.06 end
% 0.66/1.06 permutation0:
% 0.66/1.06 0 ==> 0
% 0.66/1.06 end
% 0.66/1.06
% 0.66/1.06 resolution: (297) {G1,W6,D6,L1,V0,M1} { sorti2( h( j( h( j( skol1 ) ) ) )
% 0.66/1.06 ) }.
% 0.66/1.06 parent0[0]: (5) {G0,W5,D3,L2,V1,M2} I { ! sorti1( X ), sorti2( h( X ) ) }.
% 0.66/1.06 parent1[0]: (27) {G3,W5,D5,L1,V0,M1} R(15,6) { sorti1( j( h( j( skol1 ) ) )
% 0.66/1.06 ) }.
% 0.66/1.06 substitution0:
% 0.66/1.06 X := j( h( j( skol1 ) ) )
% 0.66/1.06 end
% 0.66/1.06 substitution1:
% 0.66/1.06 end
% 0.66/1.06
% 0.66/1.06 subsumption: (30) {G4,W6,D6,L1,V0,M1} R(27,5) { sorti2( h( j( h( j( skol1 )
% 0.66/1.06 ) ) ) ) }.
% 0.66/1.06 parent0: (297) {G1,W6,D6,L1,V0,M1} { sorti2( h( j( h( j( skol1 ) ) ) ) )
% 0.66/1.06 }.
% 0.66/1.06 substitution0:
% 0.66/1.06 end
% 0.66/1.06 permutation0:
% 0.66/1.06 0 ==> 0
% 0.66/1.06 end
% 0.66/1.06
% 0.66/1.06 eqswap: (298) {G0,W7,D3,L2,V1,M2} { X ==> op1( X, X ), ! sorti1( X ) }.
% 0.66/1.06 parent0[1]: (2) {G0,W7,D3,L2,V1,M2} I { ! sorti1( X ), op1( X, X ) ==> X
% 0.66/1.06 }.
% 0.66/1.06 substitution0:
% 0.66/1.06 X := X
% 0.66/1.06 end
% 0.66/1.06
% 0.66/1.06 resolution: (300) {G1,W10,D4,L2,V1,M2} { j( X ) ==> op1( j( X ), j( X ) )
% 0.66/1.06 , ! sorti2( X ) }.
% 0.66/1.06 parent0[1]: (298) {G0,W7,D3,L2,V1,M2} { X ==> op1( X, X ), ! sorti1( X )
% 0.66/1.06 }.
% 0.66/1.06 parent1[1]: (6) {G0,W5,D3,L2,V1,M2} I { ! sorti2( X ), sorti1( j( X ) ) }.
% 0.66/1.06 substitution0:
% 0.66/1.06 X := j( X )
% 0.66/1.06 end
% 0.66/1.06 substitution1:
% 0.66/1.06 X := X
% 0.66/1.06 end
% 0.66/1.06
% 0.66/1.06 paramod: (301) {G2,W11,D4,L3,V1,M3} { j( X ) ==> j( op2( X, X ) ), !
% 0.66/1.06 sorti2( X ), ! sorti2( X ) }.
% 0.66/1.06 parent0[1]: (13) {G1,W12,D4,L2,V1,M2} F(8) { ! sorti2( X ), op1( j( X ), j
% 0.66/1.06 ( X ) ) ==> j( op2( X, X ) ) }.
% 0.66/1.06 parent1[0; 3]: (300) {G1,W10,D4,L2,V1,M2} { j( X ) ==> op1( j( X ), j( X )
% 0.66/1.06 ), ! sorti2( X ) }.
% 0.66/1.06 substitution0:
% 0.66/1.06 X := X
% 0.66/1.06 end
% 0.66/1.06 substitution1:
% 0.66/1.06 X := X
% 0.66/1.06 end
% 0.66/1.06
% 0.66/1.06 eqswap: (302) {G2,W11,D4,L3,V1,M3} { j( op2( X, X ) ) ==> j( X ), ! sorti2
% 0.66/1.06 ( X ), ! sorti2( X ) }.
% 0.66/1.06 parent0[0]: (301) {G2,W11,D4,L3,V1,M3} { j( X ) ==> j( op2( X, X ) ), !
% 0.66/1.06 sorti2( X ), ! sorti2( X ) }.
% 0.66/1.06 substitution0:
% 0.66/1.06 X := X
% 0.66/1.06 end
% 0.66/1.06
% 0.66/1.06 factor: (303) {G2,W9,D4,L2,V1,M2} { j( op2( X, X ) ) ==> j( X ), ! sorti2
% 0.66/1.06 ( X ) }.
% 0.66/1.06 parent0[1, 2]: (302) {G2,W11,D4,L3,V1,M3} { j( op2( X, X ) ) ==> j( X ), !
% 0.66/1.06 sorti2( X ), ! sorti2( X ) }.
% 0.66/1.06 substitution0:
% 0.66/1.06 X := X
% 0.66/1.06 end
% 0.66/1.06
% 0.66/1.06 subsumption: (96) {G2,W9,D4,L2,V1,M2} R(2,6);d(13) { ! sorti2( X ), j( op2
% 0.66/1.06 ( X, X ) ) ==> j( X ) }.
% 0.66/1.06 parent0: (303) {G2,W9,D4,L2,V1,M2} { j( op2( X, X ) ) ==> j( X ), ! sorti2
% 0.66/1.06 ( X ) }.
% 0.66/1.06 substitution0:
% 0.66/1.06 X := X
% 0.66/1.06 end
% 0.66/1.06 permutation0:
% 0.66/1.06 0 ==> 1
% 0.66/1.06 1 ==> 0
% 0.66/1.06 end
% 0.66/1.06
% 0.66/1.06 eqswap: (305) {G0,W7,D4,L2,V1,M2} { X ==> h( j( X ) ), ! sorti2( X ) }.
% 0.66/1.06 parent0[1]: (9) {G0,W7,D4,L2,V1,M2} I { ! sorti2( X ), h( j( X ) ) ==> X
% 0.66/1.06 }.
% 0.66/1.06 substitution0:
% 0.66/1.06 X := X
% 0.66/1.06 end
% 0.66/1.06
% 0.66/1.06 resolution: (308) {G1,W11,D5,L2,V1,M2} { op2( X, X ) ==> h( j( op2( X, X )
% 0.66/1.06 ) ), ! sorti2( X ) }.
% 0.66/1.06 parent0[1]: (305) {G0,W7,D4,L2,V1,M2} { X ==> h( j( X ) ), ! sorti2( X )
% 0.66/1.06 }.
% 0.66/1.06 parent1[1]: (11) {G1,W6,D3,L2,V1,M2} F(1) { ! sorti2( X ), sorti2( op2( X,
% 0.66/1.06 X ) ) }.
% 0.66/1.06 substitution0:
% 0.66/1.06 X := op2( X, X )
% 0.66/1.06 end
% 0.66/1.06 substitution1:
% 0.66/1.06 X := X
% 0.66/1.06 end
% 0.66/1.06
% 0.66/1.06 paramod: (309) {G2,W11,D4,L3,V1,M3} { op2( X, X ) ==> h( j( X ) ), !
% 0.66/1.06 sorti2( X ), ! sorti2( X ) }.
% 0.66/1.06 parent0[1]: (96) {G2,W9,D4,L2,V1,M2} R(2,6);d(13) { ! sorti2( X ), j( op2(
% 0.66/1.06 X, X ) ) ==> j( X ) }.
% 0.66/1.06 parent1[0; 5]: (308) {G1,W11,D5,L2,V1,M2} { op2( X, X ) ==> h( j( op2( X,
% 0.66/1.06 X ) ) ), ! sorti2( X ) }.
% 0.66/1.06 substitution0:
% 0.66/1.06 X := X
% 0.66/1.06 end
% 0.66/1.06 substitution1:
% 0.66/1.06 X := X
% 0.66/1.06 end
% 0.66/1.06
% 0.66/1.06 factor: (310) {G2,W9,D4,L2,V1,M2} { op2( X, X ) ==> h( j( X ) ), ! sorti2
% 0.66/1.06 ( X ) }.
% 0.66/1.06 parent0[1, 2]: (309) {G2,W11,D4,L3,V1,M3} { op2( X, X ) ==> h( j( X ) ), !
% 0.66/1.06 sorti2( X ), ! sorti2( X ) }.
% 0.66/1.06 substitution0:
% 0.66/1.06 X := X
% 0.66/1.06 end
% 0.66/1.06
% 0.66/1.06 paramod: (311) {G1,W9,D3,L3,V1,M3} { op2( X, X ) ==> X, ! sorti2( X ), !
% 0.66/1.06 sorti2( X ) }.
% 0.66/1.06 parent0[1]: (9) {G0,W7,D4,L2,V1,M2} I { ! sorti2( X ), h( j( X ) ) ==> X
% 0.66/1.06 }.
% 0.66/1.06 parent1[0; 4]: (310) {G2,W9,D4,L2,V1,M2} { op2( X, X ) ==> h( j( X ) ), !
% 0.66/1.06 sorti2( X ) }.
% 0.66/1.06 substitution0:
% 0.66/1.06 X := X
% 0.66/1.06 end
% 0.66/1.06 substitution1:
% 0.66/1.06 X := X
% 0.66/1.06 end
% 0.66/1.06
% 0.66/1.06 factor: (314) {G1,W7,D3,L2,V1,M2} { op2( X, X ) ==> X, ! sorti2( X ) }.
% 0.66/1.06 parent0[1, 2]: (311) {G1,W9,D3,L3,V1,M3} { op2( X, X ) ==> X, ! sorti2( X
% 0.66/1.06 ), ! sorti2( X ) }.
% 0.66/1.06 substitution0:
% 0.66/1.06 X := X
% 0.66/1.06 end
% 0.66/1.06
% 0.66/1.06 subsumption: (231) {G3,W7,D3,L2,V1,M2} R(9,11);d(96);d(9) { ! sorti2( X ),
% 0.66/1.06 op2( X, X ) ==> X }.
% 0.66/1.06 parent0: (314) {G1,W7,D3,L2,V1,M2} { op2( X, X ) ==> X, ! sorti2( X ) }.
% 0.66/1.06 substitution0:
% 0.66/1.06 X := X
% 0.66/1.06 end
% 0.66/1.06 permutation0:
% 0.66/1.06 0 ==> 1
% 0.66/1.06 1 ==> 0
% 0.66/1.06 end
% 0.66/1.06
% 0.66/1.06 eqswap: (315) {G0,W7,D4,L2,V1,M2} { X ==> h( j( X ) ), ! sorti2( X ) }.
% 0.66/1.06 parent0[1]: (9) {G0,W7,D4,L2,V1,M2} I { ! sorti2( X ), h( j( X ) ) ==> X
% 0.66/1.06 }.
% 0.66/1.06 substitution0:
% 0.66/1.06 X := X
% 0.66/1.06 end
% 0.66/1.06
% 0.66/1.06 resolution: (316) {G1,W9,D6,L1,V0,M1} { h( j( skol1 ) ) ==> h( j( h( j(
% 0.66/1.06 skol1 ) ) ) ) }.
% 0.66/1.06 parent0[1]: (315) {G0,W7,D4,L2,V1,M2} { X ==> h( j( X ) ), ! sorti2( X )
% 0.66/1.06 }.
% 0.66/1.06 parent1[0]: (15) {G2,W4,D4,L1,V0,M1} R(5,14) { sorti2( h( j( skol1 ) ) )
% 0.66/1.06 }.
% 0.66/1.06 substitution0:
% 0.66/1.06 X := h( j( skol1 ) )
% 0.66/1.06 end
% 0.66/1.06 substitution1:
% 0.66/1.06 end
% 0.66/1.06
% 0.66/1.06 eqswap: (317) {G1,W9,D6,L1,V0,M1} { h( j( h( j( skol1 ) ) ) ) ==> h( j(
% 0.66/1.06 skol1 ) ) }.
% 0.66/1.06 parent0[0]: (316) {G1,W9,D6,L1,V0,M1} { h( j( skol1 ) ) ==> h( j( h( j(
% 0.66/1.06 skol1 ) ) ) ) }.
% 0.66/1.06 substitution0:
% 0.66/1.06 end
% 0.66/1.06
% 0.66/1.06 subsumption: (232) {G3,W9,D6,L1,V0,M1} R(9,15) { h( j( h( j( skol1 ) ) ) )
% 0.66/1.06 ==> h( j( skol1 ) ) }.
% 0.66/1.06 parent0: (317) {G1,W9,D6,L1,V0,M1} { h( j( h( j( skol1 ) ) ) ) ==> h( j(
% 0.66/1.06 skol1 ) ) }.
% 0.66/1.06 substitution0:
% 0.66/1.06 end
% 0.66/1.06 permutation0:
% 0.66/1.06 0 ==> 0
% 0.66/1.06 end
% 0.66/1.06
% 0.66/1.06 eqswap: (318) {G0,W7,D4,L2,V1,M2} { X ==> h( j( X ) ), ! sorti2( X ) }.
% 0.66/1.06 parent0[1]: (9) {G0,W7,D4,L2,V1,M2} I { ! sorti2( X ), h( j( X ) ) ==> X
% 0.66/1.06 }.
% 0.66/1.06 substitution0:
% 0.66/1.06 X := X
% 0.66/1.06 end
% 0.66/1.06
% 0.66/1.06 resolution: (319) {G1,W5,D4,L1,V0,M1} { skol1 ==> h( j( skol1 ) ) }.
% 0.66/1.06 parent0[1]: (318) {G0,W7,D4,L2,V1,M2} { X ==> h( j( X ) ), ! sorti2( X )
% 0.66/1.06 }.
% 0.66/1.06 parent1[0]: (3) {G0,W2,D2,L1,V0,M1} I { sorti2( skol1 ) }.
% 0.66/1.06 substitution0:
% 0.66/1.06 X := skol1
% 0.66/1.06 end
% 0.66/1.06 substitution1:
% 0.66/1.06 end
% 0.66/1.06
% 0.66/1.06 eqswap: (320) {G1,W5,D4,L1,V0,M1} { h( j( skol1 ) ) ==> skol1 }.
% 0.66/1.06 parent0[0]: (319) {G1,W5,D4,L1,V0,M1} { skol1 ==> h( j( skol1 ) ) }.
% 0.66/1.06 substitution0:
% 0.66/1.06 end
% 0.66/1.06
% 0.66/1.06 subsumption: (233) {G1,W5,D4,L1,V0,M1} R(9,3) { h( j( skol1 ) ) ==> skol1
% 0.66/1.06 }.
% 0.66/1.06 parent0: (320) {G1,W5,D4,L1,V0,M1} { h( j( skol1 ) ) ==> skol1 }.
% 0.66/1.06 substitution0:
% 0.66/1.06 end
% 0.66/1.06 permutation0:
% 0.66/1.06 0 ==> 0
% 0.66/1.06 end
% 0.66/1.06
% 0.66/1.06 eqswap: (321) {G3,W7,D3,L2,V1,M2} { X ==> op2( X, X ), ! sorti2( X ) }.
% 0.66/1.06 parent0[1]: (231) {G3,W7,D3,L2,V1,M2} R(9,11);d(96);d(9) { ! sorti2( X ),
% 0.66/1.06 op2( X, X ) ==> X }.
% 0.66/1.06 substitution0:
% 0.66/1.06 X := X
% 0.66/1.06 end
% 0.66/1.06
% 0.66/1.06 eqswap: (324) {G0,W5,D3,L1,V0,M1} { ! skol1 ==> op2( skol1, skol1 ) }.
% 0.66/1.06 parent0[0]: (4) {G0,W5,D3,L1,V0,M1} I { ! op2( skol1, skol1 ) ==> skol1 }.
% 0.66/1.06 substitution0:
% 0.66/1.06 end
% 0.66/1.06
% 0.66/1.06 resolution: (325) {G4,W17,D7,L1,V0,M1} { h( j( h( j( skol1 ) ) ) ) ==> op2
% 0.66/1.06 ( h( j( h( j( skol1 ) ) ) ), h( j( h( j( skol1 ) ) ) ) ) }.
% 0.66/1.06 parent0[1]: (321) {G3,W7,D3,L2,V1,M2} { X ==> op2( X, X ), ! sorti2( X )
% 0.66/1.06 }.
% 0.66/1.06 parent1[0]: (30) {G4,W6,D6,L1,V0,M1} R(27,5) { sorti2( h( j( h( j( skol1 )
% 0.66/1.06 ) ) ) ) }.
% 0.66/1.06 substitution0:
% 0.66/1.06 X := h( j( h( j( skol1 ) ) ) )
% 0.66/1.06 end
% 0.66/1.06 substitution1:
% 0.66/1.06 end
% 0.66/1.06
% 0.66/1.06 paramod: (328) {G4,W15,D7,L1,V0,M1} { h( j( h( j( skol1 ) ) ) ) ==> op2( h
% 0.66/1.06 ( j( h( j( skol1 ) ) ) ), h( j( skol1 ) ) ) }.
% 0.66/1.06 parent0[0]: (232) {G3,W9,D6,L1,V0,M1} R(9,15) { h( j( h( j( skol1 ) ) ) )
% 0.66/1.06 ==> h( j( skol1 ) ) }.
% 0.66/1.06 parent1[0; 12]: (325) {G4,W17,D7,L1,V0,M1} { h( j( h( j( skol1 ) ) ) ) ==>
% 0.66/1.06 op2( h( j( h( j( skol1 ) ) ) ), h( j( h( j( skol1 ) ) ) ) ) }.
% 0.66/1.06 substitution0:
% 0.66/1.06 end
% 0.66/1.06 substitution1:
% 0.66/1.06 end
% 0.66/1.06
% 0.66/1.06 paramod: (335) {G2,W13,D7,L1,V0,M1} { h( j( h( j( skol1 ) ) ) ) ==> op2( h
% 0.66/1.06 ( j( h( j( skol1 ) ) ) ), skol1 ) }.
% 0.66/1.06 parent0[0]: (233) {G1,W5,D4,L1,V0,M1} R(9,3) { h( j( skol1 ) ) ==> skol1
% 0.66/1.06 }.
% 0.66/1.06 parent1[0; 12]: (328) {G4,W15,D7,L1,V0,M1} { h( j( h( j( skol1 ) ) ) ) ==>
% 0.66/1.06 op2( h( j( h( j( skol1 ) ) ) ), h( j( skol1 ) ) ) }.
% 0.66/1.06 substitution0:
% 0.66/1.06 end
% 0.66/1.06 substitution1:
% 0.66/1.06 end
% 0.66/1.06
% 0.66/1.06 paramod: (337) {G2,W11,D6,L1,V0,M1} { h( j( h( j( skol1 ) ) ) ) ==> op2( h
% 0.66/1.06 ( j( skol1 ) ), skol1 ) }.
% 0.66/1.06 parent0[0]: (233) {G1,W5,D4,L1,V0,M1} R(9,3) { h( j( skol1 ) ) ==> skol1
% 0.66/1.06 }.
% 0.66/1.06 parent1[0; 9]: (335) {G2,W13,D7,L1,V0,M1} { h( j( h( j( skol1 ) ) ) ) ==>
% 0.66/1.06 op2( h( j( h( j( skol1 ) ) ) ), skol1 ) }.
% 0.66/1.06 substitution0:
% 0.66/1.06 end
% 0.66/1.06 substitution1:
% 0.66/1.06 end
% 0.66/1.06
% 0.66/1.06 paramod: (339) {G2,W9,D6,L1,V0,M1} { h( j( h( j( skol1 ) ) ) ) ==> op2(
% 0.66/1.06 skol1, skol1 ) }.
% 0.66/1.06 parent0[0]: (233) {G1,W5,D4,L1,V0,M1} R(9,3) { h( j( skol1 ) ) ==> skol1
% 0.66/1.06 }.
% 0.66/1.06 parent1[0; 7]: (337) {G2,W11,D6,L1,V0,M1} { h( j( h( j( skol1 ) ) ) ) ==>
% 0.66/1.06 op2( h( j( skol1 ) ), skol1 ) }.
% 0.66/1.06 substitution0:
% 0.66/1.06 end
% 0.66/1.06 substitution1:
% 0.66/1.06 end
% 0.66/1.06
% 0.66/1.06 paramod: (340) {G2,W7,D4,L1,V0,M1} { h( j( skol1 ) ) ==> op2( skol1, skol1
% 0.66/1.06 ) }.
% 0.66/1.06 parent0[0]: (233) {G1,W5,D4,L1,V0,M1} R(9,3) { h( j( skol1 ) ) ==> skol1
% 0.66/1.06 }.
% 0.66/1.06 parent1[0; 3]: (339) {G2,W9,D6,L1,V0,M1} { h( j( h( j( skol1 ) ) ) ) ==>
% 0.66/1.06 op2( skol1, skol1 ) }.
% 0.66/1.06 substitution0:
% 0.66/1.06 end
% 0.66/1.06 substitution1:
% 0.66/1.06 end
% 0.66/1.06
% 0.66/1.06 paramod: (341) {G2,W5,D3,L1,V0,M1} { skol1 ==> op2( skol1, skol1 ) }.
% 0.66/1.06 parent0[0]: (233) {G1,W5,D4,L1,V0,M1} R(9,3) { h( j( skol1 ) ) ==> skol1
% 0.66/1.06 }.
% 0.66/1.06 parent1[0; 1]: (340) {G2,W7,D4,L1,V0,M1} { h( j( skol1 ) ) ==> op2( skol1
% 0.66/1.06 , skol1 ) }.
% 0.66/1.06 substitution0:
% 0.66/1.06 end
% 0.66/1.06 substitution1:
% 0.66/1.06 end
% 0.66/1.06
% 0.66/1.06 resolution: (346) {G1,W0,D0,L0,V0,M0} { }.
% 0.66/1.06 parent0[0]: (324) {G0,W5,D3,L1,V0,M1} { ! skol1 ==> op2( skol1, skol1 )
% 0.66/1.06 }.
% 0.66/1.06 parent1[0]: (341) {G2,W5,D3,L1,V0,M1} { skol1 ==> op2( skol1, skol1 ) }.
% 0.66/1.06 substitution0:
% 0.66/1.06 end
% 0.66/1.06 substitution1:
% 0.66/1.06 end
% 0.66/1.06
% 0.66/1.06 subsumption: (236) {G5,W0,D0,L0,V0,M0} R(231,30);d(232);d(233);r(4) { }.
% 0.66/1.06 parent0: (346) {G1,W0,D0,L0,V0,M0} { }.
% 0.66/1.06 substitution0:
% 0.66/1.06 end
% 0.66/1.06 permutation0:
% 0.66/1.06 end
% 0.66/1.06
% 0.66/1.06 Proof check complete!
% 0.66/1.06
% 0.66/1.06 Memory use:
% 0.66/1.06
% 0.66/1.06 space for terms: 2774
% 0.66/1.06 space for clauses: 15841
% 0.66/1.06
% 0.66/1.06
% 0.66/1.06 clauses generated: 395
% 0.66/1.06 clauses kept: 237
% 0.66/1.06 clauses selected: 32
% 0.66/1.06 clauses deleted: 1
% 0.66/1.06 clauses inuse deleted: 0
% 0.66/1.06
% 0.66/1.06 subsentry: 879
% 0.66/1.06 literals s-matched: 312
% 0.66/1.06 literals matched: 312
% 0.66/1.06 full subsumption: 85
% 0.66/1.06
% 0.66/1.06 checksum: -318382706
% 0.66/1.06
% 0.66/1.06
% 0.66/1.06 Bliksem ended
%------------------------------------------------------------------------------