TSTP Solution File: KLE002+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : KLE002+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n021.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 0.72s 1.10s
% Output : Refutation 0.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KLE002+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : bliksem %s
% 0.13/0.35 % Computer : n021.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % DateTime : Thu Jun 16 13:04:29 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.72/1.10 *** allocated 10000 integers for termspace/termends
% 0.72/1.10 *** allocated 10000 integers for clauses
% 0.72/1.10 *** allocated 10000 integers for justifications
% 0.72/1.10 Bliksem 1.12
% 0.72/1.10
% 0.72/1.10
% 0.72/1.10 Automatic Strategy Selection
% 0.72/1.10
% 0.72/1.10
% 0.72/1.10 Clauses:
% 0.72/1.10
% 0.72/1.10 { addition( X, Y ) = addition( Y, X ) }.
% 0.72/1.10 { addition( Z, addition( Y, X ) ) = addition( addition( Z, Y ), X ) }.
% 0.72/1.10 { addition( X, zero ) = X }.
% 0.72/1.10 { addition( X, X ) = X }.
% 0.72/1.10 { multiplication( X, multiplication( Y, Z ) ) = multiplication(
% 0.72/1.10 multiplication( X, Y ), Z ) }.
% 0.72/1.10 { multiplication( X, one ) = X }.
% 0.72/1.10 { multiplication( one, X ) = X }.
% 0.72/1.10 { multiplication( X, addition( Y, Z ) ) = addition( multiplication( X, Y )
% 0.72/1.10 , multiplication( X, Z ) ) }.
% 0.72/1.10 { multiplication( addition( X, Y ), Z ) = addition( multiplication( X, Z )
% 0.72/1.10 , multiplication( Y, Z ) ) }.
% 0.72/1.10 { multiplication( X, zero ) = zero }.
% 0.72/1.10 { multiplication( zero, X ) = zero }.
% 0.72/1.10 { ! leq( X, Y ), addition( X, Y ) = Y }.
% 0.72/1.10 { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 0.72/1.10 { leq( skol1, skol2 ) }.
% 0.72/1.10 { ! leq( multiplication( skol1, skol3 ), multiplication( skol2, skol3 ) ) }
% 0.72/1.10 .
% 0.72/1.10
% 0.72/1.10 percentage equality = 0.764706, percentage horn = 1.000000
% 0.72/1.10 This is a problem with some equality
% 0.72/1.10
% 0.72/1.10
% 0.72/1.10
% 0.72/1.10 Options Used:
% 0.72/1.10
% 0.72/1.10 useres = 1
% 0.72/1.10 useparamod = 1
% 0.72/1.10 useeqrefl = 1
% 0.72/1.10 useeqfact = 1
% 0.72/1.10 usefactor = 1
% 0.72/1.10 usesimpsplitting = 0
% 0.72/1.10 usesimpdemod = 5
% 0.72/1.10 usesimpres = 3
% 0.72/1.10
% 0.72/1.10 resimpinuse = 1000
% 0.72/1.10 resimpclauses = 20000
% 0.72/1.10 substype = eqrewr
% 0.72/1.10 backwardsubs = 1
% 0.72/1.10 selectoldest = 5
% 0.72/1.10
% 0.72/1.10 litorderings [0] = split
% 0.72/1.10 litorderings [1] = extend the termordering, first sorting on arguments
% 0.72/1.10
% 0.72/1.10 termordering = kbo
% 0.72/1.10
% 0.72/1.10 litapriori = 0
% 0.72/1.10 termapriori = 1
% 0.72/1.10 litaposteriori = 0
% 0.72/1.10 termaposteriori = 0
% 0.72/1.10 demodaposteriori = 0
% 0.72/1.10 ordereqreflfact = 0
% 0.72/1.10
% 0.72/1.10 litselect = negord
% 0.72/1.10
% 0.72/1.10 maxweight = 15
% 0.72/1.10 maxdepth = 30000
% 0.72/1.10 maxlength = 115
% 0.72/1.10 maxnrvars = 195
% 0.72/1.10 excuselevel = 1
% 0.72/1.10 increasemaxweight = 1
% 0.72/1.10
% 0.72/1.10 maxselected = 10000000
% 0.72/1.10 maxnrclauses = 10000000
% 0.72/1.10
% 0.72/1.10 showgenerated = 0
% 0.72/1.10 showkept = 0
% 0.72/1.10 showselected = 0
% 0.72/1.10 showdeleted = 0
% 0.72/1.10 showresimp = 1
% 0.72/1.10 showstatus = 2000
% 0.72/1.10
% 0.72/1.10 prologoutput = 0
% 0.72/1.10 nrgoals = 5000000
% 0.72/1.10 totalproof = 1
% 0.72/1.10
% 0.72/1.10 Symbols occurring in the translation:
% 0.72/1.10
% 0.72/1.10 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.72/1.10 . [1, 2] (w:1, o:22, a:1, s:1, b:0),
% 0.72/1.10 ! [4, 1] (w:0, o:17, a:1, s:1, b:0),
% 0.72/1.10 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.72/1.10 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.72/1.10 addition [37, 2] (w:1, o:46, a:1, s:1, b:0),
% 0.72/1.10 zero [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.72/1.10 multiplication [40, 2] (w:1, o:48, a:1, s:1, b:0),
% 0.72/1.10 one [41, 0] (w:1, o:10, a:1, s:1, b:0),
% 0.72/1.10 leq [42, 2] (w:1, o:47, a:1, s:1, b:0),
% 0.72/1.10 skol1 [46, 0] (w:1, o:14, a:1, s:1, b:1),
% 0.72/1.10 skol2 [47, 0] (w:1, o:15, a:1, s:1, b:1),
% 0.72/1.10 skol3 [48, 0] (w:1, o:16, a:1, s:1, b:1).
% 0.72/1.10
% 0.72/1.10
% 0.72/1.10 Starting Search:
% 0.72/1.10
% 0.72/1.10 *** allocated 15000 integers for clauses
% 0.72/1.10
% 0.72/1.10 Bliksems!, er is een bewijs:
% 0.72/1.10 % SZS status Theorem
% 0.72/1.10 % SZS output start Refutation
% 0.72/1.10
% 0.72/1.10 (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ),
% 0.72/1.10 multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 0.72/1.10 (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y ) ==> Y }.
% 0.72/1.10 (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X, Y ) }.
% 0.72/1.10 (13) {G0,W3,D2,L1,V0,M1} I { leq( skol1, skol2 ) }.
% 0.72/1.10 (14) {G0,W7,D3,L1,V0,M1} I { ! leq( multiplication( skol1, skol3 ),
% 0.72/1.10 multiplication( skol2, skol3 ) ) }.
% 0.72/1.10 (20) {G1,W9,D4,L1,V0,M1} R(12,14);d(8) { ! multiplication( addition( skol1
% 0.72/1.10 , skol2 ), skol3 ) ==> multiplication( skol2, skol3 ) }.
% 0.72/1.10 (30) {G1,W5,D3,L1,V0,M1} R(11,13) { addition( skol1, skol2 ) ==> skol2 }.
% 0.72/1.10 (193) {G2,W0,D0,L0,V0,M0} S(20);d(30);q { }.
% 0.72/1.10
% 0.72/1.10
% 0.72/1.10 % SZS output end Refutation
% 0.72/1.10 found a proof!
% 0.72/1.10
% 0.72/1.10
% 0.72/1.10 Unprocessed initial clauses:
% 0.72/1.10
% 0.72/1.10 (195) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X ) }.
% 0.72/1.10 (196) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) = addition(
% 0.72/1.10 addition( Z, Y ), X ) }.
% 0.72/1.10 (197) {G0,W5,D3,L1,V1,M1} { addition( X, zero ) = X }.
% 0.72/1.10 (198) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 0.72/1.10 (199) {G0,W11,D4,L1,V3,M1} { multiplication( X, multiplication( Y, Z ) ) =
% 0.72/1.10 multiplication( multiplication( X, Y ), Z ) }.
% 0.72/1.10 (200) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 0.72/1.10 (201) {G0,W5,D3,L1,V1,M1} { multiplication( one, X ) = X }.
% 0.72/1.10 (202) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y, Z ) ) =
% 0.72/1.10 addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 0.72/1.10 (203) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Y ), Z ) =
% 0.72/1.10 addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 0.72/1.10 (204) {G0,W5,D3,L1,V1,M1} { multiplication( X, zero ) = zero }.
% 0.72/1.10 (205) {G0,W5,D3,L1,V1,M1} { multiplication( zero, X ) = zero }.
% 0.72/1.10 (206) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y }.
% 0.72/1.10 (207) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 0.72/1.10 (208) {G0,W3,D2,L1,V0,M1} { leq( skol1, skol2 ) }.
% 0.72/1.10 (209) {G0,W7,D3,L1,V0,M1} { ! leq( multiplication( skol1, skol3 ),
% 0.72/1.10 multiplication( skol2, skol3 ) ) }.
% 0.72/1.10
% 0.72/1.10
% 0.72/1.10 Total Proof:
% 0.72/1.10
% 0.72/1.10 eqswap: (217) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Z ),
% 0.72/1.10 multiplication( Y, Z ) ) = multiplication( addition( X, Y ), Z ) }.
% 0.72/1.10 parent0[0]: (203) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Y )
% 0.72/1.10 , Z ) = addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 0.72/1.10 substitution0:
% 0.72/1.10 X := X
% 0.72/1.10 Y := Y
% 0.72/1.10 Z := Z
% 0.72/1.10 end
% 0.72/1.10
% 0.72/1.10 subsumption: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z )
% 0.72/1.10 , multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 0.72/1.10 parent0: (217) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Z ),
% 0.72/1.10 multiplication( Y, Z ) ) = multiplication( addition( X, Y ), Z ) }.
% 0.72/1.10 substitution0:
% 0.72/1.10 X := X
% 0.72/1.10 Y := Y
% 0.72/1.10 Z := Z
% 0.72/1.10 end
% 0.72/1.10 permutation0:
% 0.72/1.10 0 ==> 0
% 0.72/1.10 end
% 0.72/1.10
% 0.72/1.10 subsumption: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 0.72/1.10 ==> Y }.
% 0.72/1.10 parent0: (206) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y
% 0.72/1.10 }.
% 0.72/1.10 substitution0:
% 0.72/1.10 X := X
% 0.72/1.10 Y := Y
% 0.72/1.10 end
% 0.72/1.10 permutation0:
% 0.72/1.10 0 ==> 0
% 0.72/1.10 1 ==> 1
% 0.72/1.10 end
% 0.72/1.10
% 0.72/1.10 subsumption: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X
% 0.72/1.10 , Y ) }.
% 0.72/1.10 parent0: (207) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y )
% 0.72/1.10 }.
% 0.72/1.10 substitution0:
% 0.72/1.10 X := X
% 0.72/1.10 Y := Y
% 0.72/1.10 end
% 0.72/1.10 permutation0:
% 0.72/1.10 0 ==> 0
% 0.72/1.10 1 ==> 1
% 0.72/1.10 end
% 0.72/1.10
% 0.72/1.10 subsumption: (13) {G0,W3,D2,L1,V0,M1} I { leq( skol1, skol2 ) }.
% 0.72/1.10 parent0: (208) {G0,W3,D2,L1,V0,M1} { leq( skol1, skol2 ) }.
% 0.72/1.10 substitution0:
% 0.72/1.10 end
% 0.72/1.10 permutation0:
% 0.72/1.10 0 ==> 0
% 0.72/1.10 end
% 0.72/1.10
% 0.72/1.10 subsumption: (14) {G0,W7,D3,L1,V0,M1} I { ! leq( multiplication( skol1,
% 0.72/1.10 skol3 ), multiplication( skol2, skol3 ) ) }.
% 0.72/1.10 parent0: (209) {G0,W7,D3,L1,V0,M1} { ! leq( multiplication( skol1, skol3 )
% 0.72/1.10 , multiplication( skol2, skol3 ) ) }.
% 0.72/1.10 substitution0:
% 0.72/1.10 end
% 0.72/1.10 permutation0:
% 0.72/1.10 0 ==> 0
% 0.72/1.10 end
% 0.72/1.10
% 0.72/1.10 eqswap: (265) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y )
% 0.72/1.10 }.
% 0.72/1.10 parent0[0]: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 0.72/1.10 Y ) }.
% 0.72/1.10 substitution0:
% 0.72/1.10 X := X
% 0.72/1.10 Y := Y
% 0.72/1.10 end
% 0.72/1.10
% 0.72/1.10 resolution: (267) {G1,W11,D4,L1,V0,M1} { ! multiplication( skol2, skol3 )
% 0.72/1.10 ==> addition( multiplication( skol1, skol3 ), multiplication( skol2,
% 0.72/1.10 skol3 ) ) }.
% 0.72/1.10 parent0[0]: (14) {G0,W7,D3,L1,V0,M1} I { ! leq( multiplication( skol1,
% 0.72/1.10 skol3 ), multiplication( skol2, skol3 ) ) }.
% 0.72/1.10 parent1[1]: (265) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X,
% 0.72/1.10 Y ) }.
% 0.72/1.10 substitution0:
% 0.72/1.10 end
% 0.72/1.10 substitution1:
% 0.72/1.10 X := multiplication( skol1, skol3 )
% 0.72/1.10 Y := multiplication( skol2, skol3 )
% 0.72/1.10 end
% 0.72/1.10
% 0.72/1.10 paramod: (268) {G1,W9,D4,L1,V0,M1} { ! multiplication( skol2, skol3 ) ==>
% 0.72/1.10 multiplication( addition( skol1, skol2 ), skol3 ) }.
% 0.72/1.10 parent0[0]: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ),
% 0.72/1.10 multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 0.72/1.10 parent1[0; 5]: (267) {G1,W11,D4,L1,V0,M1} { ! multiplication( skol2, skol3
% 0.72/1.10 ) ==> addition( multiplication( skol1, skol3 ), multiplication( skol2,
% 0.72/1.10 skol3 ) ) }.
% 0.72/1.10 substitution0:
% 0.72/1.10 X := skol1
% 0.72/1.10 Y := skol2
% 0.72/1.10 Z := skol3
% 0.72/1.10 end
% 0.72/1.10 substitution1:
% 0.72/1.10 end
% 0.72/1.10
% 0.72/1.10 eqswap: (269) {G1,W9,D4,L1,V0,M1} { ! multiplication( addition( skol1,
% 0.72/1.10 skol2 ), skol3 ) ==> multiplication( skol2, skol3 ) }.
% 0.72/1.10 parent0[0]: (268) {G1,W9,D4,L1,V0,M1} { ! multiplication( skol2, skol3 )
% 0.72/1.10 ==> multiplication( addition( skol1, skol2 ), skol3 ) }.
% 0.72/1.10 substitution0:
% 0.72/1.10 end
% 0.72/1.10
% 0.72/1.10 subsumption: (20) {G1,W9,D4,L1,V0,M1} R(12,14);d(8) { ! multiplication(
% 0.72/1.10 addition( skol1, skol2 ), skol3 ) ==> multiplication( skol2, skol3 ) }.
% 0.72/1.10 parent0: (269) {G1,W9,D4,L1,V0,M1} { ! multiplication( addition( skol1,
% 0.72/1.10 skol2 ), skol3 ) ==> multiplication( skol2, skol3 ) }.
% 0.72/1.10 substitution0:
% 0.72/1.10 end
% 0.72/1.10 permutation0:
% 0.72/1.10 0 ==> 0
% 0.72/1.10 end
% 0.72/1.10
% 0.72/1.10 eqswap: (270) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X, Y )
% 0.72/1.10 }.
% 0.72/1.10 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 0.72/1.10 ==> Y }.
% 0.72/1.10 substitution0:
% 0.72/1.10 X := X
% 0.72/1.10 Y := Y
% 0.72/1.10 end
% 0.72/1.10
% 0.72/1.10 resolution: (271) {G1,W5,D3,L1,V0,M1} { skol2 ==> addition( skol1, skol2 )
% 0.72/1.10 }.
% 0.72/1.10 parent0[1]: (270) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X,
% 0.72/1.10 Y ) }.
% 0.72/1.10 parent1[0]: (13) {G0,W3,D2,L1,V0,M1} I { leq( skol1, skol2 ) }.
% 0.72/1.10 substitution0:
% 0.72/1.10 X := skol1
% 0.72/1.10 Y := skol2
% 0.72/1.10 end
% 0.72/1.10 substitution1:
% 0.72/1.10 end
% 0.72/1.10
% 0.72/1.10 eqswap: (272) {G1,W5,D3,L1,V0,M1} { addition( skol1, skol2 ) ==> skol2 }.
% 0.72/1.10 parent0[0]: (271) {G1,W5,D3,L1,V0,M1} { skol2 ==> addition( skol1, skol2 )
% 0.72/1.10 }.
% 0.72/1.10 substitution0:
% 0.72/1.10 end
% 0.72/1.10
% 0.72/1.10 subsumption: (30) {G1,W5,D3,L1,V0,M1} R(11,13) { addition( skol1, skol2 )
% 0.72/1.10 ==> skol2 }.
% 0.72/1.10 parent0: (272) {G1,W5,D3,L1,V0,M1} { addition( skol1, skol2 ) ==> skol2
% 0.72/1.10 }.
% 0.72/1.10 substitution0:
% 0.72/1.10 end
% 0.72/1.10 permutation0:
% 0.72/1.10 0 ==> 0
% 0.72/1.10 end
% 0.72/1.10
% 0.72/1.10 paramod: (275) {G2,W7,D3,L1,V0,M1} { ! multiplication( skol2, skol3 ) ==>
% 0.72/1.10 multiplication( skol2, skol3 ) }.
% 0.72/1.10 parent0[0]: (30) {G1,W5,D3,L1,V0,M1} R(11,13) { addition( skol1, skol2 )
% 0.72/1.10 ==> skol2 }.
% 0.72/1.10 parent1[0; 3]: (20) {G1,W9,D4,L1,V0,M1} R(12,14);d(8) { ! multiplication(
% 0.72/1.10 addition( skol1, skol2 ), skol3 ) ==> multiplication( skol2, skol3 ) }.
% 0.72/1.10 substitution0:
% 0.72/1.10 end
% 0.72/1.10 substitution1:
% 0.72/1.10 end
% 0.72/1.10
% 0.72/1.10 eqrefl: (276) {G0,W0,D0,L0,V0,M0} { }.
% 0.72/1.10 parent0[0]: (275) {G2,W7,D3,L1,V0,M1} { ! multiplication( skol2, skol3 )
% 0.72/1.10 ==> multiplication( skol2, skol3 ) }.
% 0.72/1.10 substitution0:
% 0.72/1.10 end
% 0.72/1.10
% 0.72/1.10 subsumption: (193) {G2,W0,D0,L0,V0,M0} S(20);d(30);q { }.
% 0.72/1.10 parent0: (276) {G0,W0,D0,L0,V0,M0} { }.
% 0.72/1.10 substitution0:
% 0.72/1.10 end
% 0.72/1.10 permutation0:
% 0.72/1.10 end
% 0.72/1.10
% 0.72/1.10 Proof check complete!
% 0.72/1.10
% 0.72/1.10 Memory use:
% 0.72/1.10
% 0.72/1.10 space for terms: 2298
% 0.72/1.10 space for clauses: 12875
% 0.72/1.10
% 0.72/1.10
% 0.72/1.10 clauses generated: 1079
% 0.72/1.10 clauses kept: 194
% 0.72/1.10 clauses selected: 50
% 0.72/1.10 clauses deleted: 1
% 0.72/1.10 clauses inuse deleted: 0
% 0.72/1.10
% 0.72/1.10 subsentry: 1201
% 0.72/1.10 literals s-matched: 881
% 0.72/1.10 literals matched: 874
% 0.72/1.10 full subsumption: 38
% 0.72/1.10
% 0.72/1.10 checksum: -1724411161
% 0.72/1.10
% 0.72/1.10
% 0.72/1.10 Bliksem ended
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