TSTP Solution File: ALG019+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : ALG019+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n023.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 12:09:06 EDT 2022
% Result : Theorem 0.71s 1.08s
% Output : Refutation 0.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : ALG019+1 : TPTP v8.1.0. Released v2.7.0.
% 0.10/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n023.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 20:46:23 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.71/1.08 *** allocated 10000 integers for termspace/termends
% 0.71/1.08 *** allocated 10000 integers for clauses
% 0.71/1.08 *** allocated 10000 integers for justifications
% 0.71/1.08 Bliksem 1.12
% 0.71/1.08
% 0.71/1.08
% 0.71/1.08 Automatic Strategy Selection
% 0.71/1.08
% 0.71/1.08
% 0.71/1.08 Clauses:
% 0.71/1.08
% 0.71/1.08 { ! sorti1( X ), ! sorti1( Y ), sorti1( op1( X, Y ) ) }.
% 0.71/1.08 { ! sorti2( X ), ! sorti2( Y ), sorti2( op2( X, Y ) ) }.
% 0.71/1.08 { ! sorti1( X ), sorti1( skol1( Y ) ) }.
% 0.71/1.08 { ! sorti1( X ), ! op1( skol1( X ), skol1( X ) ) = X }.
% 0.71/1.08 { sorti2( skol2 ) }.
% 0.71/1.08 { ! sorti2( X ), op2( X, X ) = skol2 }.
% 0.71/1.08 { ! sorti1( X ), sorti2( h( X ) ) }.
% 0.71/1.08 { ! sorti2( X ), sorti1( j( X ) ) }.
% 0.71/1.08 { ! sorti1( X ), ! sorti1( Y ), h( op1( X, Y ) ) = op2( h( X ), h( Y ) ) }
% 0.71/1.08 .
% 0.71/1.08 { ! sorti2( X ), ! sorti2( Y ), j( op2( X, Y ) ) = op1( j( X ), j( Y ) ) }
% 0.71/1.08 .
% 0.71/1.08 { ! sorti2( X ), h( j( X ) ) = X }.
% 0.71/1.08 { ! sorti1( X ), j( h( X ) ) = X }.
% 0.71/1.08
% 0.71/1.08 percentage equality = 0.222222, percentage horn = 1.000000
% 0.71/1.08 This is a problem with some equality
% 0.71/1.08
% 0.71/1.08
% 0.71/1.08
% 0.71/1.08 Options Used:
% 0.71/1.08
% 0.71/1.08 useres = 1
% 0.71/1.08 useparamod = 1
% 0.71/1.08 useeqrefl = 1
% 0.71/1.08 useeqfact = 1
% 0.71/1.08 usefactor = 1
% 0.71/1.08 usesimpsplitting = 0
% 0.71/1.08 usesimpdemod = 5
% 0.71/1.08 usesimpres = 3
% 0.71/1.08
% 0.71/1.08 resimpinuse = 1000
% 0.71/1.08 resimpclauses = 20000
% 0.71/1.08 substype = eqrewr
% 0.71/1.08 backwardsubs = 1
% 0.71/1.08 selectoldest = 5
% 0.71/1.08
% 0.71/1.08 litorderings [0] = split
% 0.71/1.08 litorderings [1] = extend the termordering, first sorting on arguments
% 0.71/1.08
% 0.71/1.08 termordering = kbo
% 0.71/1.08
% 0.71/1.08 litapriori = 0
% 0.71/1.08 termapriori = 1
% 0.71/1.08 litaposteriori = 0
% 0.71/1.08 termaposteriori = 0
% 0.71/1.08 demodaposteriori = 0
% 0.71/1.08 ordereqreflfact = 0
% 0.71/1.08
% 0.71/1.08 litselect = negord
% 0.71/1.08
% 0.71/1.08 maxweight = 15
% 0.71/1.08 maxdepth = 30000
% 0.71/1.08 maxlength = 115
% 0.71/1.08 maxnrvars = 195
% 0.71/1.08 excuselevel = 1
% 0.71/1.08 increasemaxweight = 1
% 0.71/1.08
% 0.71/1.08 maxselected = 10000000
% 0.71/1.08 maxnrclauses = 10000000
% 0.71/1.08
% 0.71/1.08 showgenerated = 0
% 0.71/1.08 showkept = 0
% 0.71/1.08 showselected = 0
% 0.71/1.08 showdeleted = 0
% 0.71/1.08 showresimp = 1
% 0.71/1.08 showstatus = 2000
% 0.71/1.08
% 0.71/1.08 prologoutput = 0
% 0.71/1.08 nrgoals = 5000000
% 0.71/1.08 totalproof = 1
% 0.71/1.08
% 0.71/1.08 Symbols occurring in the translation:
% 0.71/1.08
% 0.71/1.08 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.71/1.08 . [1, 2] (w:1, o:25, a:1, s:1, b:0),
% 0.71/1.08 ! [4, 1] (w:0, o:15, a:1, s:1, b:0),
% 0.71/1.08 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.71/1.08 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.71/1.08 sorti1 [36, 1] (w:1, o:20, a:1, s:1, b:0),
% 0.71/1.08 op1 [38, 2] (w:1, o:49, a:1, s:1, b:0),
% 0.71/1.08 sorti2 [39, 1] (w:1, o:21, a:1, s:1, b:0),
% 0.71/1.08 op2 [40, 2] (w:1, o:50, a:1, s:1, b:0),
% 0.71/1.08 h [41, 1] (w:1, o:22, a:1, s:1, b:0),
% 0.71/1.08 j [42, 1] (w:1, o:23, a:1, s:1, b:0),
% 0.71/1.08 skol1 [49, 1] (w:1, o:24, a:1, s:1, b:1),
% 0.71/1.08 skol2 [50, 0] (w:1, o:14, a:1, s:1, b:1).
% 0.71/1.08
% 0.71/1.08
% 0.71/1.08 Starting Search:
% 0.71/1.08
% 0.71/1.08 *** allocated 15000 integers for clauses
% 0.71/1.08 *** allocated 22500 integers for clauses
% 0.71/1.08 *** allocated 33750 integers for clauses
% 0.71/1.08 *** allocated 50625 integers for clauses
% 0.71/1.08
% 0.71/1.08 Bliksems!, er is een bewijs:
% 0.71/1.08 % SZS status Theorem
% 0.71/1.08 % SZS output start Refutation
% 0.71/1.08
% 0.71/1.08 (0) {G0,W8,D3,L3,V2,M3} I { ! sorti1( X ), ! sorti1( Y ), sorti1( op1( X, Y
% 0.71/1.08 ) ) }.
% 0.71/1.08 (1) {G0,W8,D3,L3,V2,M3} I { ! sorti2( X ), ! sorti2( Y ), sorti2( op2( X, Y
% 0.71/1.08 ) ) }.
% 0.71/1.08 (2) {G0,W5,D3,L2,V2,M2} I { ! sorti1( X ), sorti1( skol1( Y ) ) }.
% 0.71/1.08 (3) {G0,W9,D4,L2,V1,M2} I { ! sorti1( X ), ! op1( skol1( X ), skol1( X ) )
% 0.71/1.08 ==> X }.
% 0.71/1.08 (4) {G0,W2,D2,L1,V0,M1} I { sorti2( skol2 ) }.
% 0.71/1.08 (5) {G0,W7,D3,L2,V1,M2} I { ! sorti2( X ), op2( X, X ) ==> skol2 }.
% 0.71/1.08 (6) {G0,W5,D3,L2,V1,M2} I { ! sorti1( X ), sorti2( h( X ) ) }.
% 0.71/1.08 (7) {G0,W5,D3,L2,V1,M2} I { ! sorti2( X ), sorti1( j( X ) ) }.
% 0.71/1.08 (8) {G0,W14,D4,L3,V2,M3} I { ! sorti1( X ), ! sorti1( Y ), op2( h( X ), h(
% 0.71/1.08 Y ) ) ==> h( op1( X, Y ) ) }.
% 0.71/1.08 (11) {G0,W7,D4,L2,V1,M2} I { ! sorti1( X ), j( h( X ) ) ==> X }.
% 0.71/1.08 (12) {G1,W6,D3,L2,V1,M2} F(0) { ! sorti1( X ), sorti1( op1( X, X ) ) }.
% 0.71/1.08 (13) {G1,W12,D4,L2,V1,M2} F(8) { ! sorti1( X ), op2( h( X ), h( X ) ) ==> h
% 0.71/1.08 ( op1( X, X ) ) }.
% 0.71/1.08 (16) {G1,W3,D3,L1,V0,M1} R(7,4) { sorti1( j( skol2 ) ) }.
% 0.71/1.08 (17) {G2,W3,D3,L1,V1,M1} R(16,2) { sorti1( skol1( X ) ) }.
% 0.71/1.08 (35) {G3,W4,D4,L1,V1,M1} R(6,17) { sorti2( h( skol1( X ) ) ) }.
% 0.71/1.08 (50) {G1,W6,D3,L2,V1,M2} R(1,4) { ! sorti2( X ), sorti2( op2( X, skol2 ) )
% 0.71/1.08 }.
% 0.71/1.08 (92) {G4,W6,D5,L1,V1,M1} R(50,35) { sorti2( op2( h( skol1( X ) ), skol2 ) )
% 0.71/1.08 }.
% 0.71/1.08 (114) {G2,W8,D4,L2,V1,M2} R(5,6);d(13) { ! sorti1( X ), h( op1( X, X ) )
% 0.71/1.08 ==> skol2 }.
% 0.71/1.08 (137) {G5,W7,D6,L1,V1,M1} R(92,7) { sorti1( j( op2( h( skol1( X ) ), skol2
% 0.71/1.08 ) ) ) }.
% 0.71/1.08 (235) {G3,W8,D3,L2,V1,M2} R(11,12);d(114) { ! sorti1( X ), op1( X, X ) ==>
% 0.71/1.08 j( skol2 ) }.
% 0.71/1.08 (640) {G4,W3,D3,L1,V0,M1} R(235,3);r(17) { ! sorti1( j( skol2 ) ) }.
% 0.71/1.08 (643) {G5,W2,D2,L1,V1,M1} P(235,12);f;r(640) { ! sorti1( X ) }.
% 0.71/1.08 (644) {G6,W0,D0,L0,V0,M0} R(643,137) { }.
% 0.71/1.08
% 0.71/1.08
% 0.71/1.08 % SZS output end Refutation
% 0.71/1.08 found a proof!
% 0.71/1.08
% 0.71/1.08
% 0.71/1.08 Unprocessed initial clauses:
% 0.71/1.08
% 0.71/1.08 (646) {G0,W8,D3,L3,V2,M3} { ! sorti1( X ), ! sorti1( Y ), sorti1( op1( X,
% 0.71/1.08 Y ) ) }.
% 0.71/1.08 (647) {G0,W8,D3,L3,V2,M3} { ! sorti2( X ), ! sorti2( Y ), sorti2( op2( X,
% 0.71/1.08 Y ) ) }.
% 0.71/1.08 (648) {G0,W5,D3,L2,V2,M2} { ! sorti1( X ), sorti1( skol1( Y ) ) }.
% 0.71/1.08 (649) {G0,W9,D4,L2,V1,M2} { ! sorti1( X ), ! op1( skol1( X ), skol1( X ) )
% 0.71/1.08 = X }.
% 0.71/1.08 (650) {G0,W2,D2,L1,V0,M1} { sorti2( skol2 ) }.
% 0.71/1.08 (651) {G0,W7,D3,L2,V1,M2} { ! sorti2( X ), op2( X, X ) = skol2 }.
% 0.71/1.08 (652) {G0,W5,D3,L2,V1,M2} { ! sorti1( X ), sorti2( h( X ) ) }.
% 0.71/1.08 (653) {G0,W5,D3,L2,V1,M2} { ! sorti2( X ), sorti1( j( X ) ) }.
% 0.71/1.08 (654) {G0,W14,D4,L3,V2,M3} { ! sorti1( X ), ! sorti1( Y ), h( op1( X, Y )
% 0.71/1.08 ) = op2( h( X ), h( Y ) ) }.
% 0.71/1.08 (655) {G0,W14,D4,L3,V2,M3} { ! sorti2( X ), ! sorti2( Y ), j( op2( X, Y )
% 0.71/1.08 ) = op1( j( X ), j( Y ) ) }.
% 0.71/1.08 (656) {G0,W7,D4,L2,V1,M2} { ! sorti2( X ), h( j( X ) ) = X }.
% 0.71/1.08 (657) {G0,W7,D4,L2,V1,M2} { ! sorti1( X ), j( h( X ) ) = X }.
% 0.71/1.08
% 0.71/1.08
% 0.71/1.08 Total Proof:
% 0.71/1.08
% 0.71/1.08 subsumption: (0) {G0,W8,D3,L3,V2,M3} I { ! sorti1( X ), ! sorti1( Y ),
% 0.71/1.08 sorti1( op1( X, Y ) ) }.
% 0.71/1.08 parent0: (646) {G0,W8,D3,L3,V2,M3} { ! sorti1( X ), ! sorti1( Y ), sorti1
% 0.71/1.08 ( op1( X, Y ) ) }.
% 0.71/1.08 substitution0:
% 0.71/1.08 X := X
% 0.71/1.08 Y := Y
% 0.71/1.08 end
% 0.71/1.08 permutation0:
% 0.71/1.08 0 ==> 0
% 0.71/1.08 1 ==> 1
% 0.71/1.08 2 ==> 2
% 0.71/1.08 end
% 0.71/1.08
% 0.71/1.08 subsumption: (1) {G0,W8,D3,L3,V2,M3} I { ! sorti2( X ), ! sorti2( Y ),
% 0.71/1.08 sorti2( op2( X, Y ) ) }.
% 0.71/1.08 parent0: (647) {G0,W8,D3,L3,V2,M3} { ! sorti2( X ), ! sorti2( Y ), sorti2
% 0.71/1.08 ( op2( X, Y ) ) }.
% 0.71/1.08 substitution0:
% 0.71/1.08 X := X
% 0.71/1.08 Y := Y
% 0.71/1.08 end
% 0.71/1.08 permutation0:
% 0.71/1.08 0 ==> 0
% 0.71/1.08 1 ==> 1
% 0.71/1.08 2 ==> 2
% 0.71/1.08 end
% 0.71/1.08
% 0.71/1.08 subsumption: (2) {G0,W5,D3,L2,V2,M2} I { ! sorti1( X ), sorti1( skol1( Y )
% 0.71/1.08 ) }.
% 0.71/1.08 parent0: (648) {G0,W5,D3,L2,V2,M2} { ! sorti1( X ), sorti1( skol1( Y ) )
% 0.71/1.08 }.
% 0.71/1.08 substitution0:
% 0.71/1.08 X := X
% 0.71/1.08 Y := Y
% 0.71/1.08 end
% 0.71/1.08 permutation0:
% 0.71/1.08 0 ==> 0
% 0.71/1.08 1 ==> 1
% 0.71/1.08 end
% 0.71/1.08
% 0.71/1.08 subsumption: (3) {G0,W9,D4,L2,V1,M2} I { ! sorti1( X ), ! op1( skol1( X ),
% 0.71/1.08 skol1( X ) ) ==> X }.
% 0.71/1.08 parent0: (649) {G0,W9,D4,L2,V1,M2} { ! sorti1( X ), ! op1( skol1( X ),
% 0.71/1.08 skol1( X ) ) = X }.
% 0.71/1.08 substitution0:
% 0.71/1.08 X := X
% 0.71/1.08 end
% 0.71/1.08 permutation0:
% 0.71/1.08 0 ==> 0
% 0.71/1.08 1 ==> 1
% 0.71/1.08 end
% 0.71/1.08
% 0.71/1.08 subsumption: (4) {G0,W2,D2,L1,V0,M1} I { sorti2( skol2 ) }.
% 0.71/1.08 parent0: (650) {G0,W2,D2,L1,V0,M1} { sorti2( skol2 ) }.
% 0.71/1.08 substitution0:
% 0.71/1.08 end
% 0.71/1.08 permutation0:
% 0.71/1.08 0 ==> 0
% 0.71/1.08 end
% 0.71/1.08
% 0.71/1.08 subsumption: (5) {G0,W7,D3,L2,V1,M2} I { ! sorti2( X ), op2( X, X ) ==>
% 0.71/1.08 skol2 }.
% 0.71/1.08 parent0: (651) {G0,W7,D3,L2,V1,M2} { ! sorti2( X ), op2( X, X ) = skol2
% 0.71/1.08 }.
% 0.71/1.08 substitution0:
% 0.71/1.08 X := X
% 0.71/1.08 end
% 0.71/1.08 permutation0:
% 0.71/1.08 0 ==> 0
% 0.71/1.08 1 ==> 1
% 0.71/1.08 end
% 0.71/1.08
% 0.71/1.08 subsumption: (6) {G0,W5,D3,L2,V1,M2} I { ! sorti1( X ), sorti2( h( X ) )
% 0.71/1.08 }.
% 0.71/1.08 parent0: (652) {G0,W5,D3,L2,V1,M2} { ! sorti1( X ), sorti2( h( X ) ) }.
% 0.71/1.08 substitution0:
% 0.71/1.08 X := X
% 0.71/1.08 end
% 0.71/1.08 permutation0:
% 0.71/1.08 0 ==> 0
% 0.71/1.08 1 ==> 1
% 0.71/1.08 end
% 0.71/1.08
% 0.71/1.08 subsumption: (7) {G0,W5,D3,L2,V1,M2} I { ! sorti2( X ), sorti1( j( X ) )
% 0.71/1.08 }.
% 0.71/1.08 parent0: (653) {G0,W5,D3,L2,V1,M2} { ! sorti2( X ), sorti1( j( X ) ) }.
% 0.71/1.08 substitution0:
% 0.71/1.08 X := X
% 0.71/1.08 end
% 0.71/1.08 permutation0:
% 0.71/1.08 0 ==> 0
% 0.71/1.08 1 ==> 1
% 0.71/1.08 end
% 0.71/1.08
% 0.71/1.08 eqswap: (685) {G0,W14,D4,L3,V2,M3} { op2( h( X ), h( Y ) ) = h( op1( X, Y
% 0.71/1.08 ) ), ! sorti1( X ), ! sorti1( Y ) }.
% 0.71/1.08 parent0[2]: (654) {G0,W14,D4,L3,V2,M3} { ! sorti1( X ), ! sorti1( Y ), h(
% 0.71/1.08 op1( X, Y ) ) = op2( h( X ), h( Y ) ) }.
% 0.71/1.08 substitution0:
% 0.71/1.08 X := X
% 0.71/1.08 Y := Y
% 0.71/1.08 end
% 0.71/1.08
% 0.71/1.08 subsumption: (8) {G0,W14,D4,L3,V2,M3} I { ! sorti1( X ), ! sorti1( Y ), op2
% 0.71/1.08 ( h( X ), h( Y ) ) ==> h( op1( X, Y ) ) }.
% 0.71/1.08 parent0: (685) {G0,W14,D4,L3,V2,M3} { op2( h( X ), h( Y ) ) = h( op1( X, Y
% 0.71/1.08 ) ), ! sorti1( X ), ! sorti1( Y ) }.
% 0.71/1.08 substitution0:
% 0.71/1.08 X := X
% 0.71/1.08 Y := Y
% 0.71/1.08 end
% 0.71/1.08 permutation0:
% 0.71/1.08 0 ==> 2
% 0.71/1.08 1 ==> 0
% 0.71/1.08 2 ==> 1
% 0.71/1.08 end
% 0.71/1.08
% 0.71/1.08 subsumption: (11) {G0,W7,D4,L2,V1,M2} I { ! sorti1( X ), j( h( X ) ) ==> X
% 0.71/1.08 }.
% 0.71/1.08 parent0: (657) {G0,W7,D4,L2,V1,M2} { ! sorti1( X ), j( h( X ) ) = X }.
% 0.71/1.08 substitution0:
% 0.71/1.08 X := X
% 0.71/1.08 end
% 0.71/1.08 permutation0:
% 0.71/1.08 0 ==> 0
% 0.71/1.08 1 ==> 1
% 0.71/1.08 end
% 0.71/1.08
% 0.71/1.08 factor: (700) {G0,W6,D3,L2,V1,M2} { ! sorti1( X ), sorti1( op1( X, X ) )
% 0.71/1.08 }.
% 0.71/1.08 parent0[0, 1]: (0) {G0,W8,D3,L3,V2,M3} I { ! sorti1( X ), ! sorti1( Y ),
% 0.71/1.08 sorti1( op1( X, Y ) ) }.
% 0.71/1.08 substitution0:
% 0.71/1.08 X := X
% 0.71/1.08 Y := X
% 0.71/1.08 end
% 0.71/1.08
% 0.71/1.08 subsumption: (12) {G1,W6,D3,L2,V1,M2} F(0) { ! sorti1( X ), sorti1( op1( X
% 0.71/1.08 , X ) ) }.
% 0.71/1.08 parent0: (700) {G0,W6,D3,L2,V1,M2} { ! sorti1( X ), sorti1( op1( X, X ) )
% 0.71/1.08 }.
% 0.71/1.08 substitution0:
% 0.71/1.08 X := X
% 0.71/1.08 end
% 0.71/1.08 permutation0:
% 0.71/1.08 0 ==> 0
% 0.71/1.08 1 ==> 1
% 0.71/1.08 end
% 0.71/1.08
% 0.71/1.08 factor: (702) {G0,W12,D4,L2,V1,M2} { ! sorti1( X ), op2( h( X ), h( X ) )
% 0.71/1.08 ==> h( op1( X, X ) ) }.
% 0.71/1.08 parent0[0, 1]: (8) {G0,W14,D4,L3,V2,M3} I { ! sorti1( X ), ! sorti1( Y ),
% 0.71/1.08 op2( h( X ), h( Y ) ) ==> h( op1( X, Y ) ) }.
% 0.71/1.08 substitution0:
% 0.71/1.08 X := X
% 0.71/1.08 Y := X
% 0.71/1.08 end
% 0.71/1.08
% 0.71/1.08 subsumption: (13) {G1,W12,D4,L2,V1,M2} F(8) { ! sorti1( X ), op2( h( X ), h
% 0.71/1.08 ( X ) ) ==> h( op1( X, X ) ) }.
% 0.71/1.08 parent0: (702) {G0,W12,D4,L2,V1,M2} { ! sorti1( X ), op2( h( X ), h( X ) )
% 0.71/1.08 ==> h( op1( X, X ) ) }.
% 0.71/1.08 substitution0:
% 0.71/1.08 X := X
% 0.71/1.08 end
% 0.71/1.08 permutation0:
% 0.71/1.08 0 ==> 0
% 0.71/1.08 1 ==> 1
% 0.71/1.08 end
% 0.71/1.08
% 0.71/1.08 resolution: (704) {G1,W3,D3,L1,V0,M1} { sorti1( j( skol2 ) ) }.
% 0.71/1.08 parent0[0]: (7) {G0,W5,D3,L2,V1,M2} I { ! sorti2( X ), sorti1( j( X ) ) }.
% 0.71/1.08 parent1[0]: (4) {G0,W2,D2,L1,V0,M1} I { sorti2( skol2 ) }.
% 0.71/1.08 substitution0:
% 0.71/1.08 X := skol2
% 0.71/1.08 end
% 0.71/1.08 substitution1:
% 0.71/1.08 end
% 0.71/1.08
% 0.71/1.08 subsumption: (16) {G1,W3,D3,L1,V0,M1} R(7,4) { sorti1( j( skol2 ) ) }.
% 0.71/1.08 parent0: (704) {G1,W3,D3,L1,V0,M1} { sorti1( j( skol2 ) ) }.
% 0.71/1.08 substitution0:
% 0.71/1.08 end
% 0.71/1.08 permutation0:
% 0.71/1.08 0 ==> 0
% 0.71/1.08 end
% 0.71/1.08
% 0.71/1.08 resolution: (705) {G1,W3,D3,L1,V1,M1} { sorti1( skol1( X ) ) }.
% 0.71/1.08 parent0[0]: (2) {G0,W5,D3,L2,V2,M2} I { ! sorti1( X ), sorti1( skol1( Y ) )
% 0.71/1.08 }.
% 0.71/1.08 parent1[0]: (16) {G1,W3,D3,L1,V0,M1} R(7,4) { sorti1( j( skol2 ) ) }.
% 0.71/1.08 substitution0:
% 0.71/1.08 X := j( skol2 )
% 0.71/1.08 Y := X
% 0.71/1.08 end
% 0.71/1.08 substitution1:
% 0.71/1.08 end
% 0.71/1.08
% 0.71/1.08 subsumption: (17) {G2,W3,D3,L1,V1,M1} R(16,2) { sorti1( skol1( X ) ) }.
% 0.71/1.08 parent0: (705) {G1,W3,D3,L1,V1,M1} { sorti1( skol1( X ) ) }.
% 0.71/1.08 substitution0:
% 0.71/1.08 X := X
% 0.71/1.08 end
% 0.71/1.08 permutation0:
% 0.71/1.08 0 ==> 0
% 0.71/1.08 end
% 0.71/1.08
% 0.71/1.08 resolution: (706) {G1,W4,D4,L1,V1,M1} { sorti2( h( skol1( X ) ) ) }.
% 0.71/1.08 parent0[0]: (6) {G0,W5,D3,L2,V1,M2} I { ! sorti1( X ), sorti2( h( X ) ) }.
% 0.71/1.08 parent1[0]: (17) {G2,W3,D3,L1,V1,M1} R(16,2) { sorti1( skol1( X ) ) }.
% 0.71/1.08 substitution0:
% 0.71/1.08 X := skol1( X )
% 0.71/1.08 end
% 0.71/1.08 substitution1:
% 0.71/1.08 X := X
% 0.71/1.08 end
% 0.71/1.08
% 0.71/1.08 subsumption: (35) {G3,W4,D4,L1,V1,M1} R(6,17) { sorti2( h( skol1( X ) ) )
% 0.71/1.08 }.
% 0.71/1.08 parent0: (706) {G1,W4,D4,L1,V1,M1} { sorti2( h( skol1( X ) ) ) }.
% 0.71/1.08 substitution0:
% 0.71/1.08 X := X
% 0.71/1.08 end
% 0.71/1.08 permutation0:
% 0.71/1.08 0 ==> 0
% 0.71/1.08 end
% 0.71/1.08
% 0.71/1.08 resolution: (708) {G1,W6,D3,L2,V1,M2} { ! sorti2( X ), sorti2( op2( X,
% 0.71/1.08 skol2 ) ) }.
% 0.71/1.08 parent0[1]: (1) {G0,W8,D3,L3,V2,M3} I { ! sorti2( X ), ! sorti2( Y ),
% 0.71/1.08 sorti2( op2( X, Y ) ) }.
% 0.71/1.08 parent1[0]: (4) {G0,W2,D2,L1,V0,M1} I { sorti2( skol2 ) }.
% 0.71/1.08 substitution0:
% 0.71/1.08 X := X
% 0.71/1.08 Y := skol2
% 0.71/1.08 end
% 0.71/1.08 substitution1:
% 0.71/1.08 end
% 0.71/1.08
% 0.71/1.08 subsumption: (50) {G1,W6,D3,L2,V1,M2} R(1,4) { ! sorti2( X ), sorti2( op2(
% 0.71/1.08 X, skol2 ) ) }.
% 0.71/1.08 parent0: (708) {G1,W6,D3,L2,V1,M2} { ! sorti2( X ), sorti2( op2( X, skol2
% 0.71/1.08 ) ) }.
% 0.71/1.08 substitution0:
% 0.71/1.08 X := X
% 0.71/1.08 end
% 0.71/1.08 permutation0:
% 0.71/1.08 0 ==> 0
% 0.71/1.08 1 ==> 1
% 0.71/1.08 end
% 0.71/1.08
% 0.71/1.08 resolution: (709) {G2,W6,D5,L1,V1,M1} { sorti2( op2( h( skol1( X ) ),
% 0.71/1.08 skol2 ) ) }.
% 0.71/1.08 parent0[0]: (50) {G1,W6,D3,L2,V1,M2} R(1,4) { ! sorti2( X ), sorti2( op2( X
% 0.71/1.08 , skol2 ) ) }.
% 0.71/1.08 parent1[0]: (35) {G3,W4,D4,L1,V1,M1} R(6,17) { sorti2( h( skol1( X ) ) )
% 0.71/1.08 }.
% 0.71/1.08 substitution0:
% 0.71/1.08 X := h( skol1( X ) )
% 0.71/1.08 end
% 0.71/1.08 substitution1:
% 0.71/1.08 X := X
% 0.71/1.08 end
% 0.71/1.08
% 0.71/1.08 subsumption: (92) {G4,W6,D5,L1,V1,M1} R(50,35) { sorti2( op2( h( skol1( X )
% 0.71/1.08 ), skol2 ) ) }.
% 0.71/1.08 parent0: (709) {G2,W6,D5,L1,V1,M1} { sorti2( op2( h( skol1( X ) ), skol2 )
% 0.71/1.08 ) }.
% 0.71/1.08 substitution0:
% 0.71/1.08 X := X
% 0.71/1.08 end
% 0.71/1.08 permutation0:
% 0.71/1.08 0 ==> 0
% 0.71/1.08 end
% 0.71/1.08
% 0.71/1.08 eqswap: (710) {G0,W7,D3,L2,V1,M2} { skol2 ==> op2( X, X ), ! sorti2( X )
% 0.71/1.08 }.
% 0.71/1.08 parent0[1]: (5) {G0,W7,D3,L2,V1,M2} I { ! sorti2( X ), op2( X, X ) ==>
% 0.71/1.08 skol2 }.
% 0.71/1.08 substitution0:
% 0.71/1.08 X := X
% 0.71/1.08 end
% 0.71/1.08
% 0.71/1.08 resolution: (712) {G1,W9,D4,L2,V1,M2} { skol2 ==> op2( h( X ), h( X ) ), !
% 0.71/1.08 sorti1( X ) }.
% 0.71/1.08 parent0[1]: (710) {G0,W7,D3,L2,V1,M2} { skol2 ==> op2( X, X ), ! sorti2( X
% 0.71/1.08 ) }.
% 0.71/1.08 parent1[1]: (6) {G0,W5,D3,L2,V1,M2} I { ! sorti1( X ), sorti2( h( X ) ) }.
% 0.71/1.08 substitution0:
% 0.71/1.08 X := h( X )
% 0.71/1.08 end
% 0.71/1.08 substitution1:
% 0.71/1.08 X := X
% 0.71/1.08 end
% 0.71/1.08
% 0.71/1.08 paramod: (713) {G2,W10,D4,L3,V1,M3} { skol2 ==> h( op1( X, X ) ), ! sorti1
% 0.71/1.08 ( X ), ! sorti1( X ) }.
% 0.71/1.08 parent0[1]: (13) {G1,W12,D4,L2,V1,M2} F(8) { ! sorti1( X ), op2( h( X ), h
% 0.71/1.08 ( X ) ) ==> h( op1( X, X ) ) }.
% 0.71/1.08 parent1[0; 2]: (712) {G1,W9,D4,L2,V1,M2} { skol2 ==> op2( h( X ), h( X ) )
% 0.71/1.08 , ! sorti1( X ) }.
% 0.71/1.08 substitution0:
% 0.71/1.08 X := X
% 0.71/1.08 end
% 0.71/1.08 substitution1:
% 0.71/1.08 X := X
% 0.71/1.08 end
% 0.71/1.08
% 0.71/1.08 eqswap: (714) {G2,W10,D4,L3,V1,M3} { h( op1( X, X ) ) ==> skol2, ! sorti1
% 0.71/1.08 ( X ), ! sorti1( X ) }.
% 0.71/1.08 parent0[0]: (713) {G2,W10,D4,L3,V1,M3} { skol2 ==> h( op1( X, X ) ), !
% 0.71/1.08 sorti1( X ), ! sorti1( X ) }.
% 0.71/1.08 substitution0:
% 0.71/1.08 X := X
% 0.71/1.08 end
% 0.71/1.08
% 0.71/1.08 factor: (715) {G2,W8,D4,L2,V1,M2} { h( op1( X, X ) ) ==> skol2, ! sorti1(
% 0.71/1.08 X ) }.
% 0.71/1.08 parent0[1, 2]: (714) {G2,W10,D4,L3,V1,M3} { h( op1( X, X ) ) ==> skol2, !
% 0.71/1.08 sorti1( X ), ! sorti1( X ) }.
% 0.71/1.08 substitution0:
% 0.71/1.08 X := X
% 0.71/1.08 end
% 0.71/1.08
% 0.71/1.08 subsumption: (114) {G2,W8,D4,L2,V1,M2} R(5,6);d(13) { ! sorti1( X ), h( op1
% 0.71/1.08 ( X, X ) ) ==> skol2 }.
% 0.71/1.08 parent0: (715) {G2,W8,D4,L2,V1,M2} { h( op1( X, X ) ) ==> skol2, ! sorti1
% 0.71/1.08 ( X ) }.
% 0.71/1.08 substitution0:
% 0.71/1.08 X := X
% 0.71/1.08 end
% 0.71/1.08 permutation0:
% 0.71/1.08 0 ==> 1
% 0.71/1.08 1 ==> 0
% 0.71/1.08 end
% 0.71/1.08
% 0.71/1.08 resolution: (717) {G1,W7,D6,L1,V1,M1} { sorti1( j( op2( h( skol1( X ) ),
% 0.71/1.08 skol2 ) ) ) }.
% 0.71/1.08 parent0[0]: (7) {G0,W5,D3,L2,V1,M2} I { ! sorti2( X ), sorti1( j( X ) ) }.
% 0.71/1.08 parent1[0]: (92) {G4,W6,D5,L1,V1,M1} R(50,35) { sorti2( op2( h( skol1( X )
% 0.71/1.08 ), skol2 ) ) }.
% 0.71/1.08 substitution0:
% 0.71/1.08 X := op2( h( skol1( X ) ), skol2 )
% 0.71/1.08 end
% 0.71/1.08 substitution1:
% 0.71/1.08 X := X
% 0.71/1.08 end
% 0.71/1.08
% 0.71/1.08 subsumption: (137) {G5,W7,D6,L1,V1,M1} R(92,7) { sorti1( j( op2( h( skol1(
% 0.71/1.08 X ) ), skol2 ) ) ) }.
% 0.71/1.08 parent0: (717) {G1,W7,D6,L1,V1,M1} { sorti1( j( op2( h( skol1( X ) ),
% 0.71/1.08 skol2 ) ) ) }.
% 0.71/1.08 substitution0:
% 0.71/1.08 X := X
% 0.71/1.08 end
% 0.71/1.08 permutation0:
% 0.71/1.08 0 ==> 0
% 0.71/1.08 end
% 0.71/1.08
% 0.71/1.08 eqswap: (718) {G0,W7,D4,L2,V1,M2} { X ==> j( h( X ) ), ! sorti1( X ) }.
% 0.71/1.08 parent0[1]: (11) {G0,W7,D4,L2,V1,M2} I { ! sorti1( X ), j( h( X ) ) ==> X
% 0.71/1.08 }.
% 0.71/1.08 substitution0:
% 0.71/1.08 X := X
% 0.71/1.08 end
% 0.71/1.08
% 0.71/1.08 resolution: (720) {G1,W11,D5,L2,V1,M2} { op1( X, X ) ==> j( h( op1( X, X )
% 0.71/1.08 ) ), ! sorti1( X ) }.
% 0.71/1.08 parent0[1]: (718) {G0,W7,D4,L2,V1,M2} { X ==> j( h( X ) ), ! sorti1( X )
% 0.71/1.08 }.
% 0.71/1.08 parent1[1]: (12) {G1,W6,D3,L2,V1,M2} F(0) { ! sorti1( X ), sorti1( op1( X,
% 0.71/1.08 X ) ) }.
% 0.71/1.08 substitution0:
% 0.71/1.08 X := op1( X, X )
% 0.71/1.08 end
% 0.71/1.08 substitution1:
% 0.71/1.08 X := X
% 0.71/1.08 end
% 0.71/1.08
% 0.71/1.08 paramod: (721) {G2,W10,D3,L3,V1,M3} { op1( X, X ) ==> j( skol2 ), ! sorti1
% 0.71/1.08 ( X ), ! sorti1( X ) }.
% 0.71/1.08 parent0[1]: (114) {G2,W8,D4,L2,V1,M2} R(5,6);d(13) { ! sorti1( X ), h( op1
% 0.71/1.08 ( X, X ) ) ==> skol2 }.
% 0.71/1.08 parent1[0; 5]: (720) {G1,W11,D5,L2,V1,M2} { op1( X, X ) ==> j( h( op1( X,
% 0.71/1.08 X ) ) ), ! sorti1( X ) }.
% 0.71/1.08 substitution0:
% 0.71/1.08 X := X
% 0.71/1.08 end
% 0.71/1.08 substitution1:
% 0.71/1.08 X := X
% 0.71/1.08 end
% 0.71/1.08
% 0.71/1.08 factor: (724) {G2,W8,D3,L2,V1,M2} { op1( X, X ) ==> j( skol2 ), ! sorti1(
% 0.71/1.08 X ) }.
% 0.71/1.08 parent0[1, 2]: (721) {G2,W10,D3,L3,V1,M3} { op1( X, X ) ==> j( skol2 ), !
% 0.71/1.08 sorti1( X ), ! sorti1( X ) }.
% 0.71/1.08 substitution0:
% 0.71/1.08 X := X
% 0.71/1.08 end
% 0.71/1.08
% 0.71/1.08 subsumption: (235) {G3,W8,D3,L2,V1,M2} R(11,12);d(114) { ! sorti1( X ), op1
% 0.71/1.08 ( X, X ) ==> j( skol2 ) }.
% 0.71/1.08 parent0: (724) {G2,W8,D3,L2,V1,M2} { op1( X, X ) ==> j( skol2 ), ! sorti1
% 0.71/1.08 ( X ) }.
% 0.71/1.08 substitution0:
% 0.71/1.08 X := X
% 0.71/1.08 end
% 0.71/1.08 permutation0:
% 0.71/1.08 0 ==> 1
% 0.71/1.08 1 ==> 0
% 0.71/1.08 end
% 0.71/1.08
% 0.71/1.08 eqswap: (725) {G3,W8,D3,L2,V1,M2} { j( skol2 ) ==> op1( X, X ), ! sorti1(
% 0.71/1.08 X ) }.
% 0.71/1.08 parent0[1]: (235) {G3,W8,D3,L2,V1,M2} R(11,12);d(114) { ! sorti1( X ), op1
% 0.71/1.08 ( X, X ) ==> j( skol2 ) }.
% 0.71/1.08 substitution0:
% 0.71/1.08 X := X
% 0.71/1.08 end
% 0.71/1.08
% 0.71/1.08 eqswap: (726) {G0,W9,D4,L2,V1,M2} { ! X ==> op1( skol1( X ), skol1( X ) )
% 0.71/1.08 , ! sorti1( X ) }.
% 0.71/1.08 parent0[1]: (3) {G0,W9,D4,L2,V1,M2} I { ! sorti1( X ), ! op1( skol1( X ),
% 0.71/1.08 skol1( X ) ) ==> X }.
% 0.71/1.08 substitution0:
% 0.71/1.08 X := X
% 0.71/1.08 end
% 0.71/1.08
% 0.71/1.08 resolution: (727) {G1,W7,D4,L2,V0,M2} { ! sorti1( j( skol2 ) ), ! sorti1(
% 0.71/1.08 skol1( j( skol2 ) ) ) }.
% 0.71/1.08 parent0[0]: (726) {G0,W9,D4,L2,V1,M2} { ! X ==> op1( skol1( X ), skol1( X
% 0.71/1.08 ) ), ! sorti1( X ) }.
% 0.71/1.08 parent1[0]: (725) {G3,W8,D3,L2,V1,M2} { j( skol2 ) ==> op1( X, X ), !
% 0.71/1.08 sorti1( X ) }.
% 0.71/1.08 substitution0:
% 0.71/1.08 X := j( skol2 )
% 0.71/1.08 end
% 0.71/1.08 substitution1:
% 0.71/1.08 X := skol1( j( skol2 ) )
% 0.71/1.08 end
% 0.71/1.08
% 0.71/1.08 resolution: (728) {G2,W3,D3,L1,V0,M1} { ! sorti1( j( skol2 ) ) }.
% 0.71/1.08 parent0[1]: (727) {G1,W7,D4,L2,V0,M2} { ! sorti1( j( skol2 ) ), ! sorti1(
% 0.71/1.08 skol1( j( skol2 ) ) ) }.
% 0.71/1.08 parent1[0]: (17) {G2,W3,D3,L1,V1,M1} R(16,2) { sorti1( skol1( X ) ) }.
% 0.71/1.08 substitution0:
% 0.71/1.08 end
% 0.71/1.08 substitution1:
% 0.71/1.08 X := j( skol2 )
% 0.71/1.08 end
% 0.71/1.08
% 0.71/1.08 subsumption: (640) {G4,W3,D3,L1,V0,M1} R(235,3);r(17) { ! sorti1( j( skol2
% 0.71/1.08 ) ) }.
% 0.71/1.08 parent0: (728) {G2,W3,D3,L1,V0,M1} { ! sorti1( j( skol2 ) ) }.
% 0.71/1.08 substitution0:
% 0.71/1.08 end
% 0.71/1.08 permutation0:
% 0.71/1.08 0 ==> 0
% 0.71/1.08 end
% 0.71/1.08
% 0.71/1.08 paramod: (730) {G2,W7,D3,L3,V1,M3} { sorti1( j( skol2 ) ), ! sorti1( X ),
% 0.71/1.08 ! sorti1( X ) }.
% 0.71/1.08 parent0[1]: (235) {G3,W8,D3,L2,V1,M2} R(11,12);d(114) { ! sorti1( X ), op1
% 0.71/1.08 ( X, X ) ==> j( skol2 ) }.
% 0.71/1.08 parent1[1; 1]: (12) {G1,W6,D3,L2,V1,M2} F(0) { ! sorti1( X ), sorti1( op1(
% 0.71/1.08 X, X ) ) }.
% 0.71/1.08 substitution0:
% 0.71/1.08 X := X
% 0.71/1.08 end
% 0.71/1.08 substitution1:
% 0.71/1.08 X := X
% 0.71/1.08 end
% 0.71/1.08
% 0.71/1.08 resolution: (732) {G3,W4,D2,L2,V1,M2} { ! sorti1( X ), ! sorti1( X ) }.
% 0.71/1.08 parent0[0]: (640) {G4,W3,D3,L1,V0,M1} R(235,3);r(17) { ! sorti1( j( skol2 )
% 0.71/1.08 ) }.
% 0.71/1.08 parent1[0]: (730) {G2,W7,D3,L3,V1,M3} { sorti1( j( skol2 ) ), ! sorti1( X
% 0.71/1.08 ), ! sorti1( X ) }.
% 0.71/1.08 substitution0:
% 0.71/1.08 end
% 0.71/1.08 substitution1:
% 0.71/1.08 X := X
% 0.71/1.08 end
% 0.71/1.08
% 0.71/1.08 factor: (733) {G3,W2,D2,L1,V1,M1} { ! sorti1( X ) }.
% 0.71/1.08 parent0[0, 1]: (732) {G3,W4,D2,L2,V1,M2} { ! sorti1( X ), ! sorti1( X )
% 0.71/1.08 }.
% 0.71/1.08 substitution0:
% 0.71/1.08 X := X
% 0.71/1.08 end
% 0.71/1.08
% 0.71/1.08 subsumption: (643) {G5,W2,D2,L1,V1,M1} P(235,12);f;r(640) { ! sorti1( X )
% 0.71/1.08 }.
% 0.71/1.08 parent0: (733) {G3,W2,D2,L1,V1,M1} { ! sorti1( X ) }.
% 0.71/1.08 substitution0:
% 0.71/1.08 X := X
% 0.71/1.08 end
% 0.71/1.08 permutation0:
% 0.71/1.08 0 ==> 0
% 0.71/1.08 end
% 0.71/1.08
% 0.71/1.08 resolution: (734) {G6,W0,D0,L0,V0,M0} { }.
% 0.71/1.08 parent0[0]: (643) {G5,W2,D2,L1,V1,M1} P(235,12);f;r(640) { ! sorti1( X )
% 0.71/1.08 }.
% 0.71/1.08 parent1[0]: (137) {G5,W7,D6,L1,V1,M1} R(92,7) { sorti1( j( op2( h( skol1( X
% 0.71/1.08 ) ), skol2 ) ) ) }.
% 0.71/1.08 substitution0:
% 0.71/1.08 X := j( op2( h( skol1( X ) ), skol2 ) )
% 0.71/1.08 end
% 0.71/1.08 substitution1:
% 0.71/1.08 X := X
% 0.71/1.08 end
% 0.71/1.08
% 0.71/1.08 subsumption: (644) {G6,W0,D0,L0,V0,M0} R(643,137) { }.
% 0.71/1.08 parent0: (734) {G6,W0,D0,L0,V0,M0} { }.
% 0.71/1.08 substitution0:
% 0.71/1.08 end
% 0.71/1.08 permutation0:
% 0.71/1.08 end
% 0.71/1.08
% 0.71/1.08 Proof check complete!
% 0.71/1.08
% 0.71/1.08 Memory use:
% 0.71/1.08
% 0.71/1.08 space for terms: 8365
% 0.71/1.08 space for clauses: 41206
% 0.71/1.08
% 0.71/1.08
% 0.71/1.08 clauses generated: 1332
% 0.71/1.08 clauses kept: 645
% 0.71/1.08 clauses selected: 56
% 0.71/1.08 clauses deleted: 12
% 0.71/1.08 clauses inuse deleted: 0
% 0.71/1.08
% 0.71/1.08 subsentry: 2926
% 0.71/1.08 literals s-matched: 1423
% 0.71/1.08 literals matched: 1423
% 0.71/1.08 full subsumption: 717
% 0.71/1.08
% 0.71/1.08 checksum: 514615357
% 0.71/1.08
% 0.71/1.08
% 0.71/1.08 Bliksem ended
%------------------------------------------------------------------------------