TSTP Solution File: KLE138+1 by Bliksem---1.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : KLE138+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n018.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 : Sun Jul 17 01:37:23 EDT 2022
% Result : Theorem 0.41s 1.07s
% Output : Refutation 0.41s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : KLE138+1 : TPTP v8.1.0. Released v4.0.0.
% 0.00/0.12 % Command : bliksem %s
% 0.11/0.33 % Computer : n018.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % DateTime : Thu Jun 16 12:51:01 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.41/1.07 *** allocated 10000 integers for termspace/termends
% 0.41/1.07 *** allocated 10000 integers for clauses
% 0.41/1.07 *** allocated 10000 integers for justifications
% 0.41/1.07 Bliksem 1.12
% 0.41/1.07
% 0.41/1.07
% 0.41/1.07 Automatic Strategy Selection
% 0.41/1.07
% 0.41/1.07
% 0.41/1.07 Clauses:
% 0.41/1.07
% 0.41/1.07 { addition( X, Y ) = addition( Y, X ) }.
% 0.41/1.07 { addition( Z, addition( Y, X ) ) = addition( addition( Z, Y ), X ) }.
% 0.41/1.07 { addition( X, zero ) = X }.
% 0.41/1.07 { addition( X, X ) = X }.
% 0.41/1.07 { multiplication( X, multiplication( Y, Z ) ) = multiplication(
% 0.41/1.07 multiplication( X, Y ), Z ) }.
% 0.41/1.07 { multiplication( X, one ) = X }.
% 0.41/1.07 { multiplication( one, X ) = X }.
% 0.41/1.07 { multiplication( X, addition( Y, Z ) ) = addition( multiplication( X, Y )
% 0.41/1.07 , multiplication( X, Z ) ) }.
% 0.41/1.07 { multiplication( addition( X, Y ), Z ) = addition( multiplication( X, Z )
% 0.41/1.07 , multiplication( Y, Z ) ) }.
% 0.41/1.07 { multiplication( zero, X ) = zero }.
% 0.41/1.07 { addition( one, multiplication( X, star( X ) ) ) = star( X ) }.
% 0.41/1.07 { addition( one, multiplication( star( X ), X ) ) = star( X ) }.
% 0.41/1.07 { ! leq( addition( multiplication( X, Z ), Y ), Z ), leq( multiplication(
% 0.41/1.07 star( X ), Y ), Z ) }.
% 0.41/1.07 { ! leq( addition( multiplication( Z, X ), Y ), Z ), leq( multiplication( Y
% 0.41/1.07 , star( X ) ), Z ) }.
% 0.41/1.07 { strong_iteration( X ) = addition( multiplication( X, strong_iteration( X
% 0.41/1.07 ) ), one ) }.
% 0.41/1.07 { ! leq( Z, addition( multiplication( X, Z ), Y ) ), leq( Z, multiplication
% 0.41/1.07 ( strong_iteration( X ), Y ) ) }.
% 0.41/1.07 { strong_iteration( X ) = addition( star( X ), multiplication(
% 0.41/1.07 strong_iteration( X ), zero ) ) }.
% 0.41/1.07 { ! leq( X, Y ), addition( X, Y ) = Y }.
% 0.41/1.07 { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 0.41/1.07 { ! strong_iteration( zero ) = one }.
% 0.41/1.07
% 0.41/1.07 percentage equality = 0.680000, percentage horn = 1.000000
% 0.41/1.07 This is a problem with some equality
% 0.41/1.07
% 0.41/1.07
% 0.41/1.07
% 0.41/1.07 Options Used:
% 0.41/1.07
% 0.41/1.07 useres = 1
% 0.41/1.07 useparamod = 1
% 0.41/1.07 useeqrefl = 1
% 0.41/1.07 useeqfact = 1
% 0.41/1.07 usefactor = 1
% 0.41/1.07 usesimpsplitting = 0
% 0.41/1.07 usesimpdemod = 5
% 0.41/1.07 usesimpres = 3
% 0.41/1.07
% 0.41/1.07 resimpinuse = 1000
% 0.41/1.07 resimpclauses = 20000
% 0.41/1.07 substype = eqrewr
% 0.41/1.07 backwardsubs = 1
% 0.41/1.07 selectoldest = 5
% 0.41/1.07
% 0.41/1.07 litorderings [0] = split
% 0.41/1.07 litorderings [1] = extend the termordering, first sorting on arguments
% 0.41/1.07
% 0.41/1.07 termordering = kbo
% 0.41/1.07
% 0.41/1.07 litapriori = 0
% 0.41/1.07 termapriori = 1
% 0.41/1.07 litaposteriori = 0
% 0.41/1.07 termaposteriori = 0
% 0.41/1.07 demodaposteriori = 0
% 0.41/1.07 ordereqreflfact = 0
% 0.41/1.07
% 0.41/1.07 litselect = negord
% 0.41/1.07
% 0.41/1.07 maxweight = 15
% 0.41/1.07 maxdepth = 30000
% 0.41/1.07 maxlength = 115
% 0.41/1.07 maxnrvars = 195
% 0.41/1.07 excuselevel = 1
% 0.41/1.07 increasemaxweight = 1
% 0.41/1.07
% 0.41/1.07 maxselected = 10000000
% 0.41/1.07 maxnrclauses = 10000000
% 0.41/1.07
% 0.41/1.07 showgenerated = 0
% 0.41/1.07 showkept = 0
% 0.41/1.07 showselected = 0
% 0.41/1.07 showdeleted = 0
% 0.41/1.07 showresimp = 1
% 0.41/1.07 showstatus = 2000
% 0.41/1.07
% 0.41/1.07 prologoutput = 0
% 0.41/1.07 nrgoals = 5000000
% 0.41/1.07 totalproof = 1
% 0.41/1.07
% 0.41/1.07 Symbols occurring in the translation:
% 0.41/1.07
% 0.41/1.07 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.41/1.07 . [1, 2] (w:1, o:18, a:1, s:1, b:0),
% 0.41/1.07 ! [4, 1] (w:0, o:11, a:1, s:1, b:0),
% 0.41/1.07 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.41/1.07 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.41/1.07 addition [37, 2] (w:1, o:42, a:1, s:1, b:0),
% 0.41/1.07 zero [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.41/1.07 multiplication [40, 2] (w:1, o:44, a:1, s:1, b:0),
% 0.41/1.07 one [41, 0] (w:1, o:10, a:1, s:1, b:0),
% 0.41/1.07 star [42, 1] (w:1, o:16, a:1, s:1, b:0),
% 0.41/1.07 leq [43, 2] (w:1, o:43, a:1, s:1, b:0),
% 0.41/1.07 strong_iteration [44, 1] (w:1, o:17, a:1, s:1, b:0).
% 0.41/1.07
% 0.41/1.07
% 0.41/1.07 Starting Search:
% 0.41/1.07
% 0.41/1.07 *** allocated 15000 integers for clauses
% 0.41/1.07 *** allocated 22500 integers for clauses
% 0.41/1.07
% 0.41/1.07 Bliksems!, er is een bewijs:
% 0.41/1.07 % SZS status Theorem
% 0.41/1.07 % SZS output start Refutation
% 0.41/1.07
% 0.41/1.07 (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X ) }.
% 0.41/1.07 (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 0.41/1.07 (9) {G0,W5,D3,L1,V1,M1} I { multiplication( zero, X ) ==> zero }.
% 0.41/1.07 (14) {G0,W9,D5,L1,V1,M1} I { addition( multiplication( X, strong_iteration
% 0.41/1.07 ( X ) ), one ) ==> strong_iteration( X ) }.
% 0.41/1.07 (19) {G0,W4,D3,L1,V0,M1} I { ! strong_iteration( zero ) ==> one }.
% 0.41/1.07 (20) {G1,W5,D3,L1,V1,M1} P(2,0) { addition( zero, X ) ==> X }.
% 0.41/1.07 (220) {G2,W4,D3,L1,V0,M1} P(9,14);d(20) { strong_iteration( zero ) ==> one
% 0.41/1.07 }.
% 0.41/1.07 (221) {G3,W0,D0,L0,V0,M0} S(220);r(19) { }.
% 0.41/1.07
% 0.41/1.07
% 0.41/1.07 % SZS output end Refutation
% 0.41/1.07 found a proof!
% 0.41/1.07
% 0.41/1.07
% 0.41/1.07 Unprocessed initial clauses:
% 0.41/1.07
% 0.41/1.07 (223) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X ) }.
% 0.41/1.07 (224) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) = addition(
% 0.41/1.07 addition( Z, Y ), X ) }.
% 0.41/1.07 (225) {G0,W5,D3,L1,V1,M1} { addition( X, zero ) = X }.
% 0.41/1.07 (226) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 0.41/1.07 (227) {G0,W11,D4,L1,V3,M1} { multiplication( X, multiplication( Y, Z ) ) =
% 0.41/1.07 multiplication( multiplication( X, Y ), Z ) }.
% 0.41/1.07 (228) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 0.41/1.07 (229) {G0,W5,D3,L1,V1,M1} { multiplication( one, X ) = X }.
% 0.41/1.07 (230) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y, Z ) ) =
% 0.41/1.07 addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 0.41/1.07 (231) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Y ), Z ) =
% 0.41/1.07 addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 0.41/1.07 (232) {G0,W5,D3,L1,V1,M1} { multiplication( zero, X ) = zero }.
% 0.41/1.07 (233) {G0,W9,D5,L1,V1,M1} { addition( one, multiplication( X, star( X ) )
% 0.41/1.07 ) = star( X ) }.
% 0.41/1.07 (234) {G0,W9,D5,L1,V1,M1} { addition( one, multiplication( star( X ), X )
% 0.41/1.07 ) = star( X ) }.
% 0.41/1.07 (235) {G0,W13,D4,L2,V3,M2} { ! leq( addition( multiplication( X, Z ), Y )
% 0.41/1.07 , Z ), leq( multiplication( star( X ), Y ), Z ) }.
% 0.41/1.07 (236) {G0,W13,D4,L2,V3,M2} { ! leq( addition( multiplication( Z, X ), Y )
% 0.41/1.07 , Z ), leq( multiplication( Y, star( X ) ), Z ) }.
% 0.41/1.07 (237) {G0,W9,D5,L1,V1,M1} { strong_iteration( X ) = addition(
% 0.41/1.07 multiplication( X, strong_iteration( X ) ), one ) }.
% 0.41/1.07 (238) {G0,W13,D4,L2,V3,M2} { ! leq( Z, addition( multiplication( X, Z ), Y
% 0.41/1.07 ) ), leq( Z, multiplication( strong_iteration( X ), Y ) ) }.
% 0.41/1.07 (239) {G0,W10,D5,L1,V1,M1} { strong_iteration( X ) = addition( star( X ),
% 0.41/1.07 multiplication( strong_iteration( X ), zero ) ) }.
% 0.41/1.07 (240) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y }.
% 0.41/1.07 (241) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 0.41/1.07 (242) {G0,W4,D3,L1,V0,M1} { ! strong_iteration( zero ) = one }.
% 0.41/1.07
% 0.41/1.07
% 0.41/1.07 Total Proof:
% 0.41/1.07
% 0.41/1.07 subsumption: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X
% 0.41/1.07 ) }.
% 0.41/1.07 parent0: (223) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X )
% 0.41/1.07 }.
% 0.41/1.07 substitution0:
% 0.41/1.07 X := X
% 0.41/1.07 Y := Y
% 0.41/1.07 end
% 0.41/1.07 permutation0:
% 0.41/1.07 0 ==> 0
% 0.41/1.07 end
% 0.41/1.07
% 0.41/1.07 subsumption: (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 0.41/1.07 parent0: (225) {G0,W5,D3,L1,V1,M1} { addition( X, zero ) = X }.
% 0.41/1.07 substitution0:
% 0.41/1.07 X := X
% 0.41/1.07 end
% 0.41/1.07 permutation0:
% 0.41/1.07 0 ==> 0
% 0.41/1.07 end
% 0.41/1.07
% 0.41/1.07 subsumption: (9) {G0,W5,D3,L1,V1,M1} I { multiplication( zero, X ) ==> zero
% 0.41/1.07 }.
% 0.41/1.07 parent0: (232) {G0,W5,D3,L1,V1,M1} { multiplication( zero, X ) = zero }.
% 0.41/1.07 substitution0:
% 0.41/1.07 X := X
% 0.41/1.07 end
% 0.41/1.07 permutation0:
% 0.41/1.07 0 ==> 0
% 0.41/1.07 end
% 0.41/1.07
% 0.41/1.07 eqswap: (265) {G0,W9,D5,L1,V1,M1} { addition( multiplication( X,
% 0.41/1.07 strong_iteration( X ) ), one ) = strong_iteration( X ) }.
% 0.41/1.07 parent0[0]: (237) {G0,W9,D5,L1,V1,M1} { strong_iteration( X ) = addition(
% 0.41/1.07 multiplication( X, strong_iteration( X ) ), one ) }.
% 0.41/1.07 substitution0:
% 0.41/1.07 X := X
% 0.41/1.07 end
% 0.41/1.07
% 0.41/1.07 subsumption: (14) {G0,W9,D5,L1,V1,M1} I { addition( multiplication( X,
% 0.41/1.07 strong_iteration( X ) ), one ) ==> strong_iteration( X ) }.
% 0.41/1.07 parent0: (265) {G0,W9,D5,L1,V1,M1} { addition( multiplication( X,
% 0.41/1.07 strong_iteration( X ) ), one ) = strong_iteration( X ) }.
% 0.41/1.07 substitution0:
% 0.41/1.07 X := X
% 0.41/1.07 end
% 0.41/1.07 permutation0:
% 0.41/1.07 0 ==> 0
% 0.41/1.07 end
% 0.41/1.07
% 0.41/1.07 subsumption: (19) {G0,W4,D3,L1,V0,M1} I { ! strong_iteration( zero ) ==>
% 0.41/1.07 one }.
% 0.41/1.07 parent0: (242) {G0,W4,D3,L1,V0,M1} { ! strong_iteration( zero ) = one }.
% 0.41/1.07 substitution0:
% 0.41/1.07 end
% 0.41/1.07 permutation0:
% 0.41/1.07 0 ==> 0
% 0.41/1.07 end
% 0.41/1.07
% 0.41/1.07 eqswap: (282) {G0,W5,D3,L1,V1,M1} { X ==> addition( X, zero ) }.
% 0.41/1.07 parent0[0]: (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 0.41/1.07 substitution0:
% 0.41/1.07 X := X
% 0.41/1.07 end
% 0.41/1.07
% 0.41/1.07 paramod: (283) {G1,W5,D3,L1,V1,M1} { X ==> addition( zero, X ) }.
% 0.41/1.07 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 0.41/1.07 }.
% 0.41/1.07 parent1[0; 2]: (282) {G0,W5,D3,L1,V1,M1} { X ==> addition( X, zero ) }.
% 0.41/1.07 substitution0:
% 0.41/1.07 X := X
% 0.41/1.07 Y := zero
% 0.41/1.07 end
% 0.41/1.07 substitution1:
% 0.41/1.07 X := X
% 0.41/1.07 end
% 0.41/1.07
% 0.41/1.07 eqswap: (286) {G1,W5,D3,L1,V1,M1} { addition( zero, X ) ==> X }.
% 0.41/1.07 parent0[0]: (283) {G1,W5,D3,L1,V1,M1} { X ==> addition( zero, X ) }.
% 0.41/1.07 substitution0:
% 0.41/1.07 X := X
% 0.41/1.07 end
% 0.41/1.07
% 0.41/1.07 subsumption: (20) {G1,W5,D3,L1,V1,M1} P(2,0) { addition( zero, X ) ==> X
% 0.41/1.07 }.
% 0.41/1.07 parent0: (286) {G1,W5,D3,L1,V1,M1} { addition( zero, X ) ==> X }.
% 0.41/1.07 substitution0:
% 0.41/1.07 X := X
% 0.41/1.07 end
% 0.41/1.07 permutation0:
% 0.41/1.07 0 ==> 0
% 0.41/1.07 end
% 0.41/1.07
% 0.41/1.07 eqswap: (288) {G0,W9,D5,L1,V1,M1} { strong_iteration( X ) ==> addition(
% 0.41/1.07 multiplication( X, strong_iteration( X ) ), one ) }.
% 0.41/1.07 parent0[0]: (14) {G0,W9,D5,L1,V1,M1} I { addition( multiplication( X,
% 0.41/1.07 strong_iteration( X ) ), one ) ==> strong_iteration( X ) }.
% 0.41/1.07 substitution0:
% 0.41/1.07 X := X
% 0.41/1.07 end
% 0.41/1.07
% 0.41/1.07 paramod: (290) {G1,W6,D3,L1,V0,M1} { strong_iteration( zero ) ==> addition
% 0.41/1.07 ( zero, one ) }.
% 0.41/1.07 parent0[0]: (9) {G0,W5,D3,L1,V1,M1} I { multiplication( zero, X ) ==> zero
% 0.41/1.07 }.
% 0.41/1.07 parent1[0; 4]: (288) {G0,W9,D5,L1,V1,M1} { strong_iteration( X ) ==>
% 0.41/1.07 addition( multiplication( X, strong_iteration( X ) ), one ) }.
% 0.41/1.07 substitution0:
% 0.41/1.07 X := strong_iteration( zero )
% 0.41/1.07 end
% 0.41/1.07 substitution1:
% 0.41/1.07 X := zero
% 0.41/1.07 end
% 0.41/1.07
% 0.41/1.07 paramod: (291) {G2,W4,D3,L1,V0,M1} { strong_iteration( zero ) ==> one }.
% 0.41/1.07 parent0[0]: (20) {G1,W5,D3,L1,V1,M1} P(2,0) { addition( zero, X ) ==> X }.
% 0.41/1.07 parent1[0; 3]: (290) {G1,W6,D3,L1,V0,M1} { strong_iteration( zero ) ==>
% 0.41/1.07 addition( zero, one ) }.
% 0.41/1.07 substitution0:
% 0.41/1.07 X := one
% 0.41/1.07 end
% 0.41/1.07 substitution1:
% 0.41/1.07 end
% 0.41/1.07
% 0.41/1.07 subsumption: (220) {G2,W4,D3,L1,V0,M1} P(9,14);d(20) { strong_iteration(
% 0.41/1.07 zero ) ==> one }.
% 0.41/1.07 parent0: (291) {G2,W4,D3,L1,V0,M1} { strong_iteration( zero ) ==> one }.
% 0.41/1.07 substitution0:
% 0.41/1.07 end
% 0.41/1.07 permutation0:
% 0.41/1.07 0 ==> 0
% 0.41/1.07 end
% 0.41/1.07
% 0.41/1.07 resolution: (295) {G1,W0,D0,L0,V0,M0} { }.
% 0.41/1.07 parent0[0]: (19) {G0,W4,D3,L1,V0,M1} I { ! strong_iteration( zero ) ==> one
% 0.41/1.07 }.
% 0.41/1.07 parent1[0]: (220) {G2,W4,D3,L1,V0,M1} P(9,14);d(20) { strong_iteration(
% 0.41/1.07 zero ) ==> one }.
% 0.41/1.07 substitution0:
% 0.41/1.07 end
% 0.41/1.07 substitution1:
% 0.41/1.07 end
% 0.41/1.07
% 0.41/1.07 subsumption: (221) {G3,W0,D0,L0,V0,M0} S(220);r(19) { }.
% 0.41/1.07 parent0: (295) {G1,W0,D0,L0,V0,M0} { }.
% 0.41/1.07 substitution0:
% 0.41/1.07 end
% 0.41/1.07 permutation0:
% 0.41/1.07 end
% 0.41/1.07
% 0.41/1.07 Proof check complete!
% 0.41/1.07
% 0.41/1.07 Memory use:
% 0.41/1.07
% 0.41/1.07 space for terms: 3032
% 0.41/1.07 space for clauses: 15166
% 0.41/1.07
% 0.41/1.07
% 0.41/1.07 clauses generated: 953
% 0.41/1.07 clauses kept: 222
% 0.41/1.07 clauses selected: 47
% 0.41/1.07 clauses deleted: 5
% 0.41/1.07 clauses inuse deleted: 0
% 0.41/1.07
% 0.41/1.07 subsentry: 1128
% 0.41/1.07 literals s-matched: 831
% 0.41/1.07 literals matched: 831
% 0.41/1.07 full subsumption: 86
% 0.41/1.07
% 0.41/1.07 checksum: -1505149148
% 0.41/1.07
% 0.41/1.07
% 0.41/1.07 Bliksem ended
%------------------------------------------------------------------------------