TSTP Solution File: SYN986+1.002 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SYN986+1.002 : TPTP v8.1.0. Released v4.0.0.
% 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 21 02:58:37 EDT 2022
% Result : Theorem 0.71s 1.07s
% Output : Refutation 0.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN986+1.002 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12 % 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 : Tue Jul 12 05:23:39 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.71/1.07 *** allocated 10000 integers for termspace/termends
% 0.71/1.07 *** allocated 10000 integers for clauses
% 0.71/1.07 *** allocated 10000 integers for justifications
% 0.71/1.07 Bliksem 1.12
% 0.71/1.07
% 0.71/1.07
% 0.71/1.07 Automatic Strategy Selection
% 0.71/1.07
% 0.71/1.07
% 0.71/1.07 Clauses:
% 0.71/1.07
% 0.71/1.07 { r( X, zero, succ( X ) ) }.
% 0.71/1.07 { ! r( X, Y, Z ), ! r( Z, Y, T ), r( X, succ( Y ), T ) }.
% 0.71/1.07 { ! r( zero, zero, X ), ! r( zero, X, Y ), ! r( zero, Y, Z ) }.
% 0.71/1.07
% 0.71/1.07 percentage equality = 0.000000, percentage horn = 1.000000
% 0.71/1.07 This is a near-Horn, non-equality problem
% 0.71/1.07
% 0.71/1.07
% 0.71/1.07 Options Used:
% 0.71/1.07
% 0.71/1.07 useres = 1
% 0.71/1.07 useparamod = 0
% 0.71/1.07 useeqrefl = 0
% 0.71/1.07 useeqfact = 0
% 0.71/1.07 usefactor = 1
% 0.71/1.07 usesimpsplitting = 0
% 0.71/1.07 usesimpdemod = 0
% 0.71/1.07 usesimpres = 4
% 0.71/1.07
% 0.71/1.07 resimpinuse = 1000
% 0.71/1.07 resimpclauses = 20000
% 0.71/1.07 substype = standard
% 0.71/1.07 backwardsubs = 1
% 0.71/1.07 selectoldest = 5
% 0.71/1.07
% 0.71/1.07 litorderings [0] = split
% 0.71/1.07 litorderings [1] = liftord
% 0.71/1.07
% 0.71/1.07 termordering = none
% 0.71/1.07
% 0.71/1.07 litapriori = 1
% 0.71/1.07 termapriori = 0
% 0.71/1.07 litaposteriori = 0
% 0.71/1.07 termaposteriori = 0
% 0.71/1.07 demodaposteriori = 0
% 0.71/1.07 ordereqreflfact = 0
% 0.71/1.07
% 0.71/1.07 litselect = negative
% 0.71/1.07
% 0.71/1.07 maxweight = 30000
% 0.71/1.07 maxdepth = 30000
% 0.71/1.07 maxlength = 115
% 0.71/1.07 maxnrvars = 195
% 0.71/1.07 excuselevel = 0
% 0.71/1.07 increasemaxweight = 0
% 0.71/1.07
% 0.71/1.07 maxselected = 10000000
% 0.71/1.07 maxnrclauses = 10000000
% 0.71/1.07
% 0.71/1.07 showgenerated = 0
% 0.71/1.07 showkept = 0
% 0.71/1.07 showselected = 0
% 0.71/1.07 showdeleted = 0
% 0.71/1.07 showresimp = 1
% 0.71/1.07 showstatus = 2000
% 0.71/1.07
% 0.71/1.07 prologoutput = 0
% 0.71/1.07 nrgoals = 5000000
% 0.71/1.07 totalproof = 1
% 0.71/1.07
% 0.71/1.07 Symbols occurring in the translation:
% 0.71/1.07
% 0.71/1.07 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.71/1.07 . [1, 2] (w:1, o:19, a:1, s:1, b:0),
% 0.71/1.07 ! [4, 1] (w:1, o:13, a:1, s:1, b:0),
% 0.71/1.07 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.71/1.07 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.71/1.07 zero [36, 0] (w:1, o:8, a:1, s:1, b:0),
% 0.71/1.07 succ [37, 1] (w:1, o:18, a:1, s:1, b:0),
% 0.71/1.07 r [38, 3] (w:1, o:43, a:1, s:1, b:0).
% 0.71/1.07
% 0.71/1.07
% 0.71/1.07 Starting Search:
% 0.71/1.07
% 0.71/1.07
% 0.71/1.07 Bliksems!, er is een bewijs:
% 0.71/1.07 % SZS status Theorem
% 0.71/1.07 % SZS output start Refutation
% 0.71/1.07
% 0.71/1.07 (0) {G0,W5,D3,L1,V1,M1} I { r( X, zero, succ( X ) ) }.
% 0.71/1.07 (1) {G0,W15,D3,L3,V4,M1} I { ! r( X, Y, Z ), r( X, succ( Y ), T ), ! r( Z,
% 0.71/1.07 Y, T ) }.
% 0.71/1.07 (2) {G0,W15,D2,L3,V3,M1} I { ! r( zero, X, Y ), ! r( zero, zero, X ), ! r(
% 0.71/1.07 zero, Y, Z ) }.
% 0.71/1.07 (8) {G1,W11,D3,L2,V2,M1} R(1,0) { r( X, succ( zero ), succ( Y ) ), ! r( X,
% 0.71/1.07 zero, Y ) }.
% 0.71/1.07 (9) {G2,W7,D4,L1,V1,M1} R(8,0) { r( X, succ( zero ), succ( succ( X ) ) )
% 0.71/1.07 }.
% 0.71/1.07 (10) {G3,W14,D4,L2,V2,M1} R(9,1) { r( X, succ( succ( zero ) ), succ( succ(
% 0.71/1.07 Y ) ) ), ! r( X, succ( zero ), Y ) }.
% 0.71/1.07 (11) {G4,W10,D6,L1,V1,M1} R(10,9) { r( X, succ( succ( zero ) ), succ( succ
% 0.71/1.07 ( succ( succ( X ) ) ) ) ) }.
% 0.71/1.07 (13) {G5,W12,D4,L2,V1,M1} R(11,2) { ! r( zero, zero, X ), ! r( zero, X,
% 0.71/1.07 succ( succ( zero ) ) ) }.
% 0.71/1.07 (15) {G6,W0,D0,L0,V0,M0} R(13,9);r(0) { }.
% 0.71/1.07
% 0.71/1.07
% 0.71/1.07 % SZS output end Refutation
% 0.71/1.07 found a proof!
% 0.71/1.07
% 0.71/1.07
% 0.71/1.07 Unprocessed initial clauses:
% 0.71/1.07
% 0.71/1.07 (17) {G0,W5,D3,L1,V1,M1} { r( X, zero, succ( X ) ) }.
% 0.71/1.07 (18) {G0,W15,D3,L3,V4,M3} { ! r( X, Y, Z ), ! r( Z, Y, T ), r( X, succ( Y
% 0.71/1.07 ), T ) }.
% 0.71/1.07 (19) {G0,W15,D2,L3,V3,M3} { ! r( zero, zero, X ), ! r( zero, X, Y ), ! r(
% 0.71/1.07 zero, Y, Z ) }.
% 0.71/1.07
% 0.71/1.07
% 0.71/1.07 Total Proof:
% 0.71/1.07
% 0.71/1.07 subsumption: (0) {G0,W5,D3,L1,V1,M1} I { r( X, zero, succ( X ) ) }.
% 0.71/1.07 parent0: (17) {G0,W5,D3,L1,V1,M1} { r( X, zero, succ( X ) ) }.
% 0.71/1.07 substitution0:
% 0.71/1.07 X := X
% 0.71/1.07 end
% 0.71/1.07 permutation0:
% 0.71/1.07 0 ==> 0
% 0.71/1.07 end
% 0.71/1.07
% 0.71/1.07 subsumption: (1) {G0,W15,D3,L3,V4,M1} I { ! r( X, Y, Z ), r( X, succ( Y ),
% 0.71/1.07 T ), ! r( Z, Y, T ) }.
% 0.71/1.07 parent0: (18) {G0,W15,D3,L3,V4,M3} { ! r( X, Y, Z ), ! r( Z, Y, T ), r( X
% 0.71/1.07 , succ( Y ), T ) }.
% 0.71/1.07 substitution0:
% 0.71/1.07 X := X
% 0.71/1.07 Y := Y
% 0.71/1.07 Z := Z
% 0.71/1.07 T := T
% 0.71/1.07 end
% 0.71/1.07 permutation0:
% 0.71/1.07 0 ==> 0
% 0.71/1.07 1 ==> 2
% 0.71/1.07 2 ==> 1
% 0.71/1.07 end
% 0.71/1.07
% 0.71/1.07 subsumption: (2) {G0,W15,D2,L3,V3,M1} I { ! r( zero, X, Y ), ! r( zero,
% 0.71/1.07 zero, X ), ! r( zero, Y, Z ) }.
% 0.71/1.07 parent0: (19) {G0,W15,D2,L3,V3,M3} { ! r( zero, zero, X ), ! r( zero, X, Y
% 0.71/1.07 ), ! r( zero, Y, Z ) }.
% 0.71/1.07 substitution0:
% 0.71/1.07 X := X
% 0.71/1.07 Y := Y
% 0.71/1.07 Z := Z
% 0.71/1.07 end
% 0.71/1.07 permutation0:
% 0.71/1.07 0 ==> 1
% 0.71/1.07 1 ==> 0
% 0.71/1.07 2 ==> 2
% 0.71/1.07 end
% 0.71/1.07
% 0.71/1.07 resolution: (27) {G1,W11,D3,L2,V2,M2} { ! r( X, zero, Y ), r( X, succ(
% 0.71/1.07 zero ), succ( Y ) ) }.
% 0.71/1.07 parent0[2]: (1) {G0,W15,D3,L3,V4,M1} I { ! r( X, Y, Z ), r( X, succ( Y ), T
% 0.71/1.07 ), ! r( Z, Y, T ) }.
% 0.71/1.07 parent1[0]: (0) {G0,W5,D3,L1,V1,M1} I { r( X, zero, succ( X ) ) }.
% 0.71/1.07 substitution0:
% 0.71/1.07 X := X
% 0.71/1.07 Y := zero
% 0.71/1.07 Z := Y
% 0.71/1.07 T := succ( Y )
% 0.71/1.07 end
% 0.71/1.07 substitution1:
% 0.71/1.07 X := Y
% 0.71/1.07 end
% 0.71/1.07
% 0.71/1.07 subsumption: (8) {G1,W11,D3,L2,V2,M1} R(1,0) { r( X, succ( zero ), succ( Y
% 0.71/1.07 ) ), ! r( X, zero, Y ) }.
% 0.71/1.07 parent0: (27) {G1,W11,D3,L2,V2,M2} { ! r( X, zero, Y ), r( X, succ( zero )
% 0.71/1.07 , succ( Y ) ) }.
% 0.71/1.07 substitution0:
% 0.71/1.07 X := X
% 0.71/1.07 Y := Y
% 0.71/1.07 end
% 0.71/1.07 permutation0:
% 0.71/1.07 0 ==> 1
% 0.71/1.07 1 ==> 0
% 0.71/1.07 end
% 0.71/1.07
% 0.71/1.07 resolution: (28) {G1,W7,D4,L1,V1,M1} { r( X, succ( zero ), succ( succ( X )
% 0.71/1.07 ) ) }.
% 0.71/1.07 parent0[1]: (8) {G1,W11,D3,L2,V2,M1} R(1,0) { r( X, succ( zero ), succ( Y )
% 0.71/1.07 ), ! r( X, zero, Y ) }.
% 0.71/1.07 parent1[0]: (0) {G0,W5,D3,L1,V1,M1} I { r( X, zero, succ( X ) ) }.
% 0.71/1.07 substitution0:
% 0.71/1.07 X := X
% 0.71/1.07 Y := succ( X )
% 0.71/1.07 end
% 0.71/1.07 substitution1:
% 0.71/1.07 X := X
% 0.71/1.07 end
% 0.71/1.07
% 0.71/1.07 subsumption: (9) {G2,W7,D4,L1,V1,M1} R(8,0) { r( X, succ( zero ), succ(
% 0.71/1.07 succ( X ) ) ) }.
% 0.71/1.07 parent0: (28) {G1,W7,D4,L1,V1,M1} { r( X, succ( zero ), succ( succ( X ) )
% 0.71/1.07 ) }.
% 0.71/1.07 substitution0:
% 0.71/1.07 X := X
% 0.71/1.07 end
% 0.71/1.07 permutation0:
% 0.71/1.07 0 ==> 0
% 0.71/1.07 end
% 0.71/1.07
% 0.71/1.07 resolution: (30) {G1,W14,D4,L2,V2,M2} { ! r( X, succ( zero ), Y ), r( X,
% 0.71/1.07 succ( succ( zero ) ), succ( succ( Y ) ) ) }.
% 0.71/1.07 parent0[2]: (1) {G0,W15,D3,L3,V4,M1} I { ! r( X, Y, Z ), r( X, succ( Y ), T
% 0.71/1.07 ), ! r( Z, Y, T ) }.
% 0.71/1.07 parent1[0]: (9) {G2,W7,D4,L1,V1,M1} R(8,0) { r( X, succ( zero ), succ( succ
% 0.71/1.07 ( X ) ) ) }.
% 0.71/1.07 substitution0:
% 0.71/1.07 X := X
% 0.71/1.07 Y := succ( zero )
% 0.71/1.07 Z := Y
% 0.71/1.07 T := succ( succ( Y ) )
% 0.71/1.07 end
% 0.71/1.07 substitution1:
% 0.71/1.07 X := Y
% 0.71/1.07 end
% 0.71/1.07
% 0.71/1.07 subsumption: (10) {G3,W14,D4,L2,V2,M1} R(9,1) { r( X, succ( succ( zero ) )
% 0.71/1.07 , succ( succ( Y ) ) ), ! r( X, succ( zero ), Y ) }.
% 0.71/1.07 parent0: (30) {G1,W14,D4,L2,V2,M2} { ! r( X, succ( zero ), Y ), r( X, succ
% 0.71/1.07 ( succ( zero ) ), succ( succ( Y ) ) ) }.
% 0.71/1.07 substitution0:
% 0.71/1.07 X := X
% 0.71/1.07 Y := Y
% 0.71/1.07 end
% 0.71/1.07 permutation0:
% 0.71/1.07 0 ==> 1
% 0.71/1.07 1 ==> 0
% 0.71/1.07 end
% 0.71/1.07
% 0.71/1.07 resolution: (31) {G3,W10,D6,L1,V1,M1} { r( X, succ( succ( zero ) ), succ(
% 0.71/1.07 succ( succ( succ( X ) ) ) ) ) }.
% 0.71/1.07 parent0[1]: (10) {G3,W14,D4,L2,V2,M1} R(9,1) { r( X, succ( succ( zero ) ),
% 0.71/1.07 succ( succ( Y ) ) ), ! r( X, succ( zero ), Y ) }.
% 0.71/1.07 parent1[0]: (9) {G2,W7,D4,L1,V1,M1} R(8,0) { r( X, succ( zero ), succ( succ
% 0.71/1.07 ( X ) ) ) }.
% 0.71/1.07 substitution0:
% 0.71/1.07 X := X
% 0.71/1.07 Y := succ( succ( X ) )
% 0.71/1.07 end
% 0.71/1.07 substitution1:
% 0.71/1.07 X := X
% 0.71/1.07 end
% 0.71/1.07
% 0.71/1.07 subsumption: (11) {G4,W10,D6,L1,V1,M1} R(10,9) { r( X, succ( succ( zero ) )
% 0.71/1.07 , succ( succ( succ( succ( X ) ) ) ) ) }.
% 0.71/1.07 parent0: (31) {G3,W10,D6,L1,V1,M1} { r( X, succ( succ( zero ) ), succ(
% 0.71/1.07 succ( succ( succ( X ) ) ) ) ) }.
% 0.71/1.07 substitution0:
% 0.71/1.07 X := X
% 0.71/1.07 end
% 0.71/1.07 permutation0:
% 0.71/1.07 0 ==> 0
% 0.71/1.07 end
% 0.71/1.07
% 0.71/1.07 resolution: (33) {G1,W12,D4,L2,V1,M2} { ! r( zero, X, succ( succ( zero ) )
% 0.71/1.07 ), ! r( zero, zero, X ) }.
% 0.71/1.07 parent0[2]: (2) {G0,W15,D2,L3,V3,M1} I { ! r( zero, X, Y ), ! r( zero, zero
% 0.71/1.07 , X ), ! r( zero, Y, Z ) }.
% 0.71/1.07 parent1[0]: (11) {G4,W10,D6,L1,V1,M1} R(10,9) { r( X, succ( succ( zero ) )
% 0.71/1.07 , succ( succ( succ( succ( X ) ) ) ) ) }.
% 0.71/1.07 substitution0:
% 0.71/1.07 X := X
% 0.71/1.07 Y := succ( succ( zero ) )
% 0.71/1.07 Z := succ( succ( succ( succ( zero ) ) ) )
% 0.71/1.07 end
% 0.71/1.07 substitution1:
% 0.71/1.07 X := zero
% 0.71/1.07 end
% 0.71/1.07
% 0.71/1.07 subsumption: (13) {G5,W12,D4,L2,V1,M1} R(11,2) { ! r( zero, zero, X ), ! r
% 0.71/1.07 ( zero, X, succ( succ( zero ) ) ) }.
% 0.71/1.07 parent0: (33) {G1,W12,D4,L2,V1,M2} { ! r( zero, X, succ( succ( zero ) ) )
% 0.71/1.07 , ! r( zero, zero, X ) }.
% 0.71/1.07 substitution0:
% 0.71/1.07 X := X
% 0.71/1.07 end
% 0.71/1.07 permutation0:
% 0.71/1.07 0 ==> 1
% 0.71/1.07 1 ==> 0
% 0.71/1.07 end
% 0.71/1.07
% 0.71/1.07 resolution: (34) {G3,W6,D3,L1,V0,M1} { ! r( zero, zero, succ( zero ) ) }.
% 0.71/1.07 parent0[1]: (13) {G5,W12,D4,L2,V1,M1} R(11,2) { ! r( zero, zero, X ), ! r(
% 0.71/1.07 zero, X, succ( succ( zero ) ) ) }.
% 0.71/1.07 parent1[0]: (9) {G2,W7,D4,L1,V1,M1} R(8,0) { r( X, succ( zero ), succ( succ
% 0.71/1.07 ( X ) ) ) }.
% 0.71/1.07 substitution0:
% 0.71/1.07 X := succ( zero )
% 0.71/1.07 end
% 0.71/1.07 substitution1:
% 0.71/1.07 X := zero
% 0.71/1.07 end
% 0.71/1.07
% 0.71/1.07 resolution: (35) {G1,W0,D0,L0,V0,M0} { }.
% 0.71/1.07 parent0[0]: (34) {G3,W6,D3,L1,V0,M1} { ! r( zero, zero, succ( zero ) ) }.
% 0.71/1.07 parent1[0]: (0) {G0,W5,D3,L1,V1,M1} I { r( X, zero, succ( X ) ) }.
% 0.71/1.07 substitution0:
% 0.71/1.07 end
% 0.71/1.07 substitution1:
% 0.71/1.07 X := zero
% 0.71/1.07 end
% 0.71/1.07
% 0.71/1.07 subsumption: (15) {G6,W0,D0,L0,V0,M0} R(13,9);r(0) { }.
% 0.71/1.07 parent0: (35) {G1,W0,D0,L0,V0,M0} { }.
% 0.71/1.07 substitution0:
% 0.71/1.07 end
% 0.71/1.07 permutation0:
% 0.71/1.07 end
% 0.71/1.07
% 0.71/1.07 Proof check complete!
% 0.71/1.07
% 0.71/1.07 Memory use:
% 0.71/1.07
% 0.71/1.07 space for terms: 260
% 0.71/1.07 space for clauses: 970
% 0.71/1.07
% 0.71/1.07
% 0.71/1.07 clauses generated: 20
% 0.71/1.07 clauses kept: 16
% 0.71/1.07 clauses selected: 13
% 0.71/1.07 clauses deleted: 1
% 0.71/1.07 clauses inuse deleted: 0
% 0.71/1.07
% 0.71/1.07 subsentry: 59
% 0.71/1.07 literals s-matched: 15
% 0.71/1.07 literals matched: 7
% 0.71/1.07 full subsumption: 0
% 0.71/1.07
% 0.71/1.07 checksum: 1072905968
% 0.71/1.07
% 0.71/1.07
% 0.71/1.07 Bliksem ended
%------------------------------------------------------------------------------