TSTP Solution File: KLE001+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : KLE001+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n014.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 01:36:30 EDT 2022
% Result : Theorem 0.43s 1.04s
% Output : Refutation 0.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KLE001+1 : TPTP v8.1.0. Released v4.0.0.
% 0.00/0.12 % Command : bliksem %s
% 0.13/0.33 % Computer : n014.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % DateTime : Thu Jun 16 14:45:20 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.43/1.04 *** allocated 10000 integers for termspace/termends
% 0.43/1.04 *** allocated 10000 integers for clauses
% 0.43/1.04 *** allocated 10000 integers for justifications
% 0.43/1.04 Bliksem 1.12
% 0.43/1.04
% 0.43/1.04
% 0.43/1.04 Automatic Strategy Selection
% 0.43/1.04
% 0.43/1.04
% 0.43/1.04 Clauses:
% 0.43/1.04
% 0.43/1.04 { addition( X, Y ) = addition( Y, X ) }.
% 0.43/1.04 { addition( Z, addition( Y, X ) ) = addition( addition( Z, Y ), X ) }.
% 0.43/1.04 { addition( X, zero ) = X }.
% 0.43/1.04 { addition( X, X ) = X }.
% 0.43/1.04 { multiplication( X, multiplication( Y, Z ) ) = multiplication(
% 0.43/1.04 multiplication( X, Y ), Z ) }.
% 0.43/1.04 { multiplication( X, one ) = X }.
% 0.43/1.04 { multiplication( one, X ) = X }.
% 0.43/1.04 { multiplication( X, addition( Y, Z ) ) = addition( multiplication( X, Y )
% 0.43/1.04 , multiplication( X, Z ) ) }.
% 0.43/1.04 { multiplication( addition( X, Y ), Z ) = addition( multiplication( X, Z )
% 0.43/1.04 , multiplication( Y, Z ) ) }.
% 0.43/1.04 { multiplication( X, zero ) = zero }.
% 0.43/1.04 { multiplication( zero, X ) = zero }.
% 0.43/1.04 { ! leq( X, Y ), addition( X, Y ) = Y }.
% 0.43/1.04 { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 0.43/1.04 { leq( skol1, skol2 ) }.
% 0.43/1.04 { ! leq( addition( skol1, skol3 ), addition( skol1, skol3 ) ) }.
% 0.43/1.04
% 0.43/1.04 percentage equality = 0.764706, percentage horn = 1.000000
% 0.43/1.04 This is a problem with some equality
% 0.43/1.04
% 0.43/1.04
% 0.43/1.04
% 0.43/1.04 Options Used:
% 0.43/1.04
% 0.43/1.04 useres = 1
% 0.43/1.04 useparamod = 1
% 0.43/1.04 useeqrefl = 1
% 0.43/1.04 useeqfact = 1
% 0.43/1.04 usefactor = 1
% 0.43/1.04 usesimpsplitting = 0
% 0.43/1.04 usesimpdemod = 5
% 0.43/1.04 usesimpres = 3
% 0.43/1.04
% 0.43/1.04 resimpinuse = 1000
% 0.43/1.04 resimpclauses = 20000
% 0.43/1.04 substype = eqrewr
% 0.43/1.04 backwardsubs = 1
% 0.43/1.04 selectoldest = 5
% 0.43/1.04
% 0.43/1.04 litorderings [0] = split
% 0.43/1.04 litorderings [1] = extend the termordering, first sorting on arguments
% 0.43/1.04
% 0.43/1.04 termordering = kbo
% 0.43/1.04
% 0.43/1.04 litapriori = 0
% 0.43/1.04 termapriori = 1
% 0.43/1.04 litaposteriori = 0
% 0.43/1.04 termaposteriori = 0
% 0.43/1.04 demodaposteriori = 0
% 0.43/1.04 ordereqreflfact = 0
% 0.43/1.04
% 0.43/1.04 litselect = negord
% 0.43/1.04
% 0.43/1.04 maxweight = 15
% 0.43/1.04 maxdepth = 30000
% 0.43/1.04 maxlength = 115
% 0.43/1.04 maxnrvars = 195
% 0.43/1.04 excuselevel = 1
% 0.43/1.04 increasemaxweight = 1
% 0.43/1.04
% 0.43/1.04 maxselected = 10000000
% 0.43/1.04 maxnrclauses = 10000000
% 0.43/1.04
% 0.43/1.04 showgenerated = 0
% 0.43/1.04 showkept = 0
% 0.43/1.04 showselected = 0
% 0.43/1.04 showdeleted = 0
% 0.43/1.04 showresimp = 1
% 0.43/1.04 showstatus = 2000
% 0.43/1.04
% 0.43/1.04 prologoutput = 0
% 0.43/1.04 nrgoals = 5000000
% 0.43/1.04 totalproof = 1
% 0.43/1.04
% 0.43/1.04 Symbols occurring in the translation:
% 0.43/1.04
% 0.43/1.04 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.43/1.04 . [1, 2] (w:1, o:22, a:1, s:1, b:0),
% 0.43/1.04 ! [4, 1] (w:0, o:17, a:1, s:1, b:0),
% 0.43/1.04 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.43/1.04 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.43/1.04 addition [37, 2] (w:1, o:46, a:1, s:1, b:0),
% 0.43/1.04 zero [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.43/1.04 multiplication [40, 2] (w:1, o:48, a:1, s:1, b:0),
% 0.43/1.04 one [41, 0] (w:1, o:10, a:1, s:1, b:0),
% 0.43/1.04 leq [42, 2] (w:1, o:47, a:1, s:1, b:0),
% 0.43/1.04 skol1 [46, 0] (w:1, o:14, a:1, s:1, b:1),
% 0.43/1.04 skol2 [47, 0] (w:1, o:15, a:1, s:1, b:1),
% 0.43/1.04 skol3 [48, 0] (w:1, o:16, a:1, s:1, b:1).
% 0.43/1.04
% 0.43/1.04
% 0.43/1.04 Starting Search:
% 0.43/1.04
% 0.43/1.04
% 0.43/1.04 Bliksems!, er is een bewijs:
% 0.43/1.04 % SZS status Theorem
% 0.43/1.04 % SZS output start Refutation
% 0.43/1.04
% 0.43/1.04 (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X ) }.
% 0.43/1.04 (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) ) ==> addition(
% 0.43/1.04 addition( Z, Y ), X ) }.
% 0.43/1.04 (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 0.43/1.04 (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X, Y ) }.
% 0.43/1.04 (14) {G0,W7,D3,L1,V0,M1} I { ! leq( addition( skol1, skol3 ), addition(
% 0.43/1.04 skol1, skol3 ) ) }.
% 0.43/1.04 (16) {G1,W7,D3,L1,V0,M1} P(0,14) { ! leq( addition( skol3, skol1 ),
% 0.43/1.04 addition( skol3, skol1 ) ) }.
% 0.43/1.04 (17) {G1,W11,D5,L1,V2,M1} P(1,3) { addition( addition( addition( X, Y ), X
% 0.43/1.04 ), Y ) ==> addition( X, Y ) }.
% 0.43/1.04 (21) {G2,W0,D0,L0,V0,M0} R(12,16);d(1);d(17);q { }.
% 0.43/1.04
% 0.43/1.04
% 0.43/1.04 % SZS output end Refutation
% 0.43/1.04 found a proof!
% 0.43/1.04
% 0.43/1.04
% 0.43/1.04 Unprocessed initial clauses:
% 0.43/1.04
% 0.43/1.04 (23) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X ) }.
% 0.43/1.04 (24) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) = addition(
% 0.43/1.04 addition( Z, Y ), X ) }.
% 0.43/1.04 (25) {G0,W5,D3,L1,V1,M1} { addition( X, zero ) = X }.
% 0.43/1.04 (26) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 0.43/1.04 (27) {G0,W11,D4,L1,V3,M1} { multiplication( X, multiplication( Y, Z ) ) =
% 0.43/1.04 multiplication( multiplication( X, Y ), Z ) }.
% 0.43/1.04 (28) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 0.43/1.04 (29) {G0,W5,D3,L1,V1,M1} { multiplication( one, X ) = X }.
% 0.43/1.04 (30) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y, Z ) ) =
% 0.43/1.04 addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 0.43/1.04 (31) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Y ), Z ) =
% 0.43/1.04 addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 0.43/1.04 (32) {G0,W5,D3,L1,V1,M1} { multiplication( X, zero ) = zero }.
% 0.43/1.04 (33) {G0,W5,D3,L1,V1,M1} { multiplication( zero, X ) = zero }.
% 0.43/1.04 (34) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y }.
% 0.43/1.04 (35) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 0.43/1.04 (36) {G0,W3,D2,L1,V0,M1} { leq( skol1, skol2 ) }.
% 0.43/1.04 (37) {G0,W7,D3,L1,V0,M1} { ! leq( addition( skol1, skol3 ), addition(
% 0.43/1.04 skol1, skol3 ) ) }.
% 0.43/1.04
% 0.43/1.04
% 0.43/1.04 Total Proof:
% 0.43/1.04
% 0.43/1.04 subsumption: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X
% 0.43/1.04 ) }.
% 0.43/1.04 parent0: (23) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X )
% 0.43/1.04 }.
% 0.43/1.04 substitution0:
% 0.43/1.04 X := X
% 0.43/1.04 Y := Y
% 0.43/1.04 end
% 0.43/1.04 permutation0:
% 0.43/1.04 0 ==> 0
% 0.43/1.04 end
% 0.43/1.04
% 0.43/1.04 subsumption: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 0.43/1.04 ==> addition( addition( Z, Y ), X ) }.
% 0.43/1.04 parent0: (24) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) =
% 0.43/1.04 addition( addition( Z, Y ), X ) }.
% 0.43/1.04 substitution0:
% 0.43/1.04 X := X
% 0.43/1.04 Y := Y
% 0.43/1.04 Z := Z
% 0.43/1.04 end
% 0.43/1.04 permutation0:
% 0.43/1.04 0 ==> 0
% 0.43/1.04 end
% 0.43/1.04
% 0.43/1.04 subsumption: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 0.43/1.04 parent0: (26) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 0.43/1.04 substitution0:
% 0.43/1.04 X := X
% 0.43/1.04 end
% 0.43/1.04 permutation0:
% 0.43/1.04 0 ==> 0
% 0.43/1.04 end
% 0.43/1.04
% 0.43/1.04 subsumption: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X
% 0.43/1.04 , Y ) }.
% 0.43/1.04 parent0: (35) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y )
% 0.43/1.04 }.
% 0.43/1.04 substitution0:
% 0.43/1.04 X := X
% 0.43/1.04 Y := Y
% 0.43/1.04 end
% 0.43/1.04 permutation0:
% 0.43/1.04 0 ==> 0
% 0.43/1.04 1 ==> 1
% 0.43/1.04 end
% 0.43/1.04
% 0.43/1.04 subsumption: (14) {G0,W7,D3,L1,V0,M1} I { ! leq( addition( skol1, skol3 ),
% 0.43/1.04 addition( skol1, skol3 ) ) }.
% 0.43/1.04 parent0: (37) {G0,W7,D3,L1,V0,M1} { ! leq( addition( skol1, skol3 ),
% 0.43/1.04 addition( skol1, skol3 ) ) }.
% 0.43/1.04 substitution0:
% 0.43/1.04 end
% 0.43/1.04 permutation0:
% 0.43/1.04 0 ==> 0
% 0.43/1.04 end
% 0.43/1.04
% 0.43/1.04 paramod: (67) {G1,W7,D3,L1,V0,M1} { ! leq( addition( skol1, skol3 ),
% 0.43/1.04 addition( skol3, skol1 ) ) }.
% 0.43/1.04 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 0.43/1.04 }.
% 0.43/1.04 parent1[0; 5]: (14) {G0,W7,D3,L1,V0,M1} I { ! leq( addition( skol1, skol3 )
% 0.43/1.04 , addition( skol1, skol3 ) ) }.
% 0.43/1.04 substitution0:
% 0.43/1.04 X := skol1
% 0.43/1.04 Y := skol3
% 0.43/1.04 end
% 0.43/1.04 substitution1:
% 0.43/1.04 end
% 0.43/1.04
% 0.43/1.04 paramod: (68) {G1,W7,D3,L1,V0,M1} { ! leq( addition( skol3, skol1 ),
% 0.43/1.04 addition( skol3, skol1 ) ) }.
% 0.43/1.04 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 0.43/1.04 }.
% 0.43/1.04 parent1[0; 2]: (67) {G1,W7,D3,L1,V0,M1} { ! leq( addition( skol1, skol3 )
% 0.43/1.04 , addition( skol3, skol1 ) ) }.
% 0.43/1.04 substitution0:
% 0.43/1.04 X := skol1
% 0.43/1.04 Y := skol3
% 0.43/1.04 end
% 0.43/1.04 substitution1:
% 0.43/1.04 end
% 0.43/1.04
% 0.43/1.04 subsumption: (16) {G1,W7,D3,L1,V0,M1} P(0,14) { ! leq( addition( skol3,
% 0.43/1.04 skol1 ), addition( skol3, skol1 ) ) }.
% 0.43/1.04 parent0: (68) {G1,W7,D3,L1,V0,M1} { ! leq( addition( skol3, skol1 ),
% 0.43/1.04 addition( skol3, skol1 ) ) }.
% 0.43/1.04 substitution0:
% 0.43/1.04 end
% 0.43/1.04 permutation0:
% 0.43/1.04 0 ==> 0
% 0.43/1.04 end
% 0.43/1.04
% 0.43/1.04 eqswap: (70) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z ) ==>
% 0.43/1.04 addition( X, addition( Y, Z ) ) }.
% 0.43/1.04 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 0.43/1.04 ==> addition( addition( Z, Y ), X ) }.
% 0.43/1.04 substitution0:
% 0.43/1.04 X := Z
% 0.43/1.04 Y := Y
% 0.43/1.04 Z := X
% 0.43/1.04 end
% 0.43/1.04
% 0.43/1.04 paramod: (74) {G1,W11,D5,L1,V2,M1} { addition( addition( addition( X, Y )
% 0.43/1.04 , X ), Y ) ==> addition( X, Y ) }.
% 0.43/1.04 parent0[0]: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 0.43/1.04 parent1[0; 8]: (70) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z )
% 0.43/1.04 ==> addition( X, addition( Y, Z ) ) }.
% 0.43/1.04 substitution0:
% 0.43/1.04 X := addition( X, Y )
% 0.43/1.04 end
% 0.43/1.04 substitution1:
% 0.43/1.04 X := addition( X, Y )
% 0.43/1.04 Y := X
% 0.43/1.04 Z := Y
% 0.43/1.04 end
% 0.43/1.04
% 0.43/1.04 subsumption: (17) {G1,W11,D5,L1,V2,M1} P(1,3) { addition( addition(
% 0.43/1.04 addition( X, Y ), X ), Y ) ==> addition( X, Y ) }.
% 0.43/1.04 parent0: (74) {G1,W11,D5,L1,V2,M1} { addition( addition( addition( X, Y )
% 0.43/1.04 , X ), Y ) ==> addition( X, Y ) }.
% 0.43/1.04 substitution0:
% 0.43/1.04 X := X
% 0.43/1.04 Y := Y
% 0.43/1.04 end
% 0.43/1.04 permutation0:
% 0.43/1.04 0 ==> 0
% 0.43/1.04 end
% 0.43/1.04
% 0.43/1.04 eqswap: (80) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y )
% 0.43/1.04 }.
% 0.43/1.04 parent0[0]: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 0.43/1.04 Y ) }.
% 0.43/1.04 substitution0:
% 0.43/1.04 X := X
% 0.43/1.04 Y := Y
% 0.43/1.04 end
% 0.43/1.04
% 0.43/1.04 resolution: (83) {G1,W11,D4,L1,V0,M1} { ! addition( skol3, skol1 ) ==>
% 0.43/1.04 addition( addition( skol3, skol1 ), addition( skol3, skol1 ) ) }.
% 0.43/1.04 parent0[0]: (16) {G1,W7,D3,L1,V0,M1} P(0,14) { ! leq( addition( skol3,
% 0.43/1.04 skol1 ), addition( skol3, skol1 ) ) }.
% 0.43/1.04 parent1[1]: (80) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y
% 0.43/1.04 ) }.
% 0.43/1.04 substitution0:
% 0.43/1.04 end
% 0.43/1.04 substitution1:
% 0.43/1.04 X := addition( skol3, skol1 )
% 0.43/1.04 Y := addition( skol3, skol1 )
% 0.43/1.04 end
% 0.43/1.04
% 0.43/1.04 paramod: (84) {G1,W11,D5,L1,V0,M1} { ! addition( skol3, skol1 ) ==>
% 0.43/1.04 addition( addition( addition( skol3, skol1 ), skol3 ), skol1 ) }.
% 0.43/1.04 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 0.43/1.04 ==> addition( addition( Z, Y ), X ) }.
% 0.43/1.04 parent1[0; 5]: (83) {G1,W11,D4,L1,V0,M1} { ! addition( skol3, skol1 ) ==>
% 0.43/1.04 addition( addition( skol3, skol1 ), addition( skol3, skol1 ) ) }.
% 0.43/1.04 substitution0:
% 0.43/1.04 X := skol1
% 0.43/1.04 Y := skol3
% 0.43/1.04 Z := addition( skol3, skol1 )
% 0.43/1.04 end
% 0.43/1.04 substitution1:
% 0.43/1.04 end
% 0.43/1.04
% 0.43/1.04 paramod: (85) {G2,W7,D3,L1,V0,M1} { ! addition( skol3, skol1 ) ==>
% 0.43/1.04 addition( skol3, skol1 ) }.
% 0.43/1.04 parent0[0]: (17) {G1,W11,D5,L1,V2,M1} P(1,3) { addition( addition( addition
% 0.43/1.04 ( X, Y ), X ), Y ) ==> addition( X, Y ) }.
% 0.43/1.04 parent1[0; 5]: (84) {G1,W11,D5,L1,V0,M1} { ! addition( skol3, skol1 ) ==>
% 0.43/1.04 addition( addition( addition( skol3, skol1 ), skol3 ), skol1 ) }.
% 0.43/1.04 substitution0:
% 0.43/1.04 X := skol3
% 0.43/1.04 Y := skol1
% 0.43/1.04 end
% 0.43/1.04 substitution1:
% 0.43/1.04 end
% 0.43/1.04
% 0.43/1.04 eqrefl: (86) {G0,W0,D0,L0,V0,M0} { }.
% 0.43/1.04 parent0[0]: (85) {G2,W7,D3,L1,V0,M1} { ! addition( skol3, skol1 ) ==>
% 0.43/1.04 addition( skol3, skol1 ) }.
% 0.43/1.04 substitution0:
% 0.43/1.04 end
% 0.43/1.04
% 0.43/1.04 subsumption: (21) {G2,W0,D0,L0,V0,M0} R(12,16);d(1);d(17);q { }.
% 0.43/1.04 parent0: (86) {G0,W0,D0,L0,V0,M0} { }.
% 0.43/1.04 substitution0:
% 0.43/1.04 end
% 0.43/1.04 permutation0:
% 0.43/1.04 end
% 0.43/1.04
% 0.43/1.04 Proof check complete!
% 0.43/1.04
% 0.43/1.04 Memory use:
% 0.43/1.04
% 0.43/1.04 space for terms: 472
% 0.43/1.04 space for clauses: 1941
% 0.43/1.04
% 0.43/1.04
% 0.43/1.04 clauses generated: 89
% 0.43/1.04 clauses kept: 22
% 0.43/1.04 clauses selected: 13
% 0.43/1.04 clauses deleted: 0
% 0.43/1.04 clauses inuse deleted: 0
% 0.43/1.04
% 0.43/1.04 subsentry: 287
% 0.43/1.04 literals s-matched: 129
% 0.43/1.04 literals matched: 127
% 0.43/1.04 full subsumption: 0
% 0.43/1.04
% 0.43/1.04 checksum: 1325554015
% 0.43/1.04
% 0.43/1.04
% 0.43/1.04 Bliksem ended
%------------------------------------------------------------------------------