TSTP Solution File: KLE056+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : KLE056+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n008.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 01:36:56 EDT 2022
% Result : Theorem 0.44s 1.08s
% Output : Refutation 0.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KLE056+1 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % Command : bliksem %s
% 0.14/0.34 % Computer : n008.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % DateTime : Thu Jun 16 14:03:07 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.44/1.08 *** allocated 10000 integers for termspace/termends
% 0.44/1.08 *** allocated 10000 integers for clauses
% 0.44/1.08 *** allocated 10000 integers for justifications
% 0.44/1.08 Bliksem 1.12
% 0.44/1.08
% 0.44/1.08
% 0.44/1.08 Automatic Strategy Selection
% 0.44/1.08
% 0.44/1.08
% 0.44/1.08 Clauses:
% 0.44/1.08
% 0.44/1.08 { addition( X, Y ) = addition( Y, X ) }.
% 0.44/1.08 { addition( Z, addition( Y, X ) ) = addition( addition( Z, Y ), X ) }.
% 0.44/1.08 { addition( X, zero ) = X }.
% 0.44/1.08 { addition( X, X ) = X }.
% 0.44/1.08 { multiplication( X, multiplication( Y, Z ) ) = multiplication(
% 0.44/1.08 multiplication( X, Y ), Z ) }.
% 0.44/1.08 { multiplication( X, one ) = X }.
% 0.44/1.08 { multiplication( one, X ) = X }.
% 0.44/1.08 { multiplication( X, addition( Y, Z ) ) = addition( multiplication( X, Y )
% 0.44/1.08 , multiplication( X, Z ) ) }.
% 0.44/1.08 { multiplication( addition( X, Y ), Z ) = addition( multiplication( X, Z )
% 0.44/1.08 , multiplication( Y, Z ) ) }.
% 0.44/1.08 { multiplication( X, zero ) = zero }.
% 0.44/1.08 { multiplication( zero, X ) = zero }.
% 0.44/1.08 { ! leq( X, Y ), addition( X, Y ) = Y }.
% 0.44/1.08 { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 0.44/1.08 { addition( X, multiplication( domain( X ), X ) ) = multiplication( domain
% 0.44/1.08 ( X ), X ) }.
% 0.44/1.08 { domain( multiplication( X, Y ) ) = domain( multiplication( X, domain( Y )
% 0.44/1.08 ) ) }.
% 0.44/1.08 { addition( domain( X ), one ) = one }.
% 0.44/1.08 { domain( zero ) = zero }.
% 0.44/1.08 { domain( addition( X, Y ) ) = addition( domain( X ), domain( Y ) ) }.
% 0.44/1.08 { domain( skol1 ) = zero }.
% 0.44/1.08 { ! skol1 = zero }.
% 0.44/1.08
% 0.44/1.08 percentage equality = 0.909091, percentage horn = 1.000000
% 0.44/1.08 This is a pure equality problem
% 0.44/1.08
% 0.44/1.08
% 0.44/1.08
% 0.44/1.08 Options Used:
% 0.44/1.08
% 0.44/1.08 useres = 1
% 0.44/1.08 useparamod = 1
% 0.44/1.08 useeqrefl = 1
% 0.44/1.08 useeqfact = 1
% 0.44/1.08 usefactor = 1
% 0.44/1.08 usesimpsplitting = 0
% 0.44/1.08 usesimpdemod = 5
% 0.44/1.08 usesimpres = 3
% 0.44/1.08
% 0.44/1.08 resimpinuse = 1000
% 0.44/1.08 resimpclauses = 20000
% 0.44/1.08 substype = eqrewr
% 0.44/1.08 backwardsubs = 1
% 0.44/1.08 selectoldest = 5
% 0.44/1.08
% 0.44/1.08 litorderings [0] = split
% 0.44/1.08 litorderings [1] = extend the termordering, first sorting on arguments
% 0.44/1.08
% 0.44/1.08 termordering = kbo
% 0.44/1.08
% 0.44/1.08 litapriori = 0
% 0.44/1.08 termapriori = 1
% 0.44/1.08 litaposteriori = 0
% 0.44/1.08 termaposteriori = 0
% 0.44/1.08 demodaposteriori = 0
% 0.44/1.08 ordereqreflfact = 0
% 0.44/1.08
% 0.44/1.08 litselect = negord
% 0.44/1.08
% 0.44/1.08 maxweight = 15
% 0.44/1.08 maxdepth = 30000
% 0.44/1.08 maxlength = 115
% 0.44/1.08 maxnrvars = 195
% 0.44/1.08 excuselevel = 1
% 0.44/1.08 increasemaxweight = 1
% 0.44/1.08
% 0.44/1.08 maxselected = 10000000
% 0.44/1.08 maxnrclauses = 10000000
% 0.44/1.08
% 0.44/1.08 showgenerated = 0
% 0.44/1.08 showkept = 0
% 0.44/1.08 showselected = 0
% 0.44/1.08 showdeleted = 0
% 0.44/1.08 showresimp = 1
% 0.44/1.08 showstatus = 2000
% 0.44/1.08
% 0.44/1.08 prologoutput = 0
% 0.44/1.08 nrgoals = 5000000
% 0.44/1.08 totalproof = 1
% 0.44/1.08
% 0.44/1.08 Symbols occurring in the translation:
% 0.44/1.08
% 0.44/1.08 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.44/1.08 . [1, 2] (w:1, o:20, a:1, s:1, b:0),
% 0.44/1.08 ! [4, 1] (w:0, o:14, a:1, s:1, b:0),
% 0.44/1.08 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.44/1.08 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.44/1.08 addition [37, 2] (w:1, o:44, a:1, s:1, b:0),
% 0.44/1.08 zero [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.44/1.08 multiplication [40, 2] (w:1, o:46, a:1, s:1, b:0),
% 0.44/1.08 one [41, 0] (w:1, o:10, a:1, s:1, b:0),
% 0.44/1.08 leq [42, 2] (w:1, o:45, a:1, s:1, b:0),
% 0.44/1.08 domain [44, 1] (w:1, o:19, a:1, s:1, b:0),
% 0.44/1.08 skol1 [46, 0] (w:1, o:13, a:1, s:1, b:1).
% 0.44/1.08
% 0.44/1.08
% 0.44/1.08 Starting Search:
% 0.44/1.08
% 0.44/1.08
% 0.44/1.08 Bliksems!, er is een bewijs:
% 0.44/1.08 % SZS status Theorem
% 0.44/1.08 % SZS output start Refutation
% 0.44/1.08
% 0.44/1.08 (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 0.44/1.08 (10) {G0,W5,D3,L1,V1,M1} I { multiplication( zero, X ) ==> zero }.
% 0.44/1.08 (13) {G0,W11,D5,L1,V1,M1} I { addition( X, multiplication( domain( X ), X )
% 0.44/1.08 ) ==> multiplication( domain( X ), X ) }.
% 0.44/1.08 (18) {G0,W4,D3,L1,V0,M1} I { domain( skol1 ) ==> zero }.
% 0.44/1.08 (19) {G0,W3,D2,L1,V0,M1} I { ! skol1 ==> zero }.
% 0.44/1.08 (98) {G1,W0,D0,L0,V0,M0} P(18,13);d(10);d(2);r(19) { }.
% 0.44/1.08
% 0.44/1.08
% 0.44/1.08 % SZS output end Refutation
% 0.44/1.08 found a proof!
% 0.44/1.08
% 0.44/1.08
% 0.44/1.08 Unprocessed initial clauses:
% 0.44/1.08
% 0.44/1.08 (100) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X ) }.
% 0.44/1.08 (101) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) = addition(
% 0.44/1.08 addition( Z, Y ), X ) }.
% 0.44/1.08 (102) {G0,W5,D3,L1,V1,M1} { addition( X, zero ) = X }.
% 0.44/1.08 (103) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 0.44/1.08 (104) {G0,W11,D4,L1,V3,M1} { multiplication( X, multiplication( Y, Z ) ) =
% 0.44/1.08 multiplication( multiplication( X, Y ), Z ) }.
% 0.44/1.08 (105) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 0.44/1.08 (106) {G0,W5,D3,L1,V1,M1} { multiplication( one, X ) = X }.
% 0.44/1.08 (107) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y, Z ) ) =
% 0.44/1.08 addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 0.44/1.08 (108) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Y ), Z ) =
% 0.44/1.08 addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 0.44/1.08 (109) {G0,W5,D3,L1,V1,M1} { multiplication( X, zero ) = zero }.
% 0.44/1.08 (110) {G0,W5,D3,L1,V1,M1} { multiplication( zero, X ) = zero }.
% 0.44/1.08 (111) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y }.
% 0.44/1.08 (112) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 0.44/1.08 (113) {G0,W11,D5,L1,V1,M1} { addition( X, multiplication( domain( X ), X )
% 0.44/1.08 ) = multiplication( domain( X ), X ) }.
% 0.44/1.08 (114) {G0,W10,D5,L1,V2,M1} { domain( multiplication( X, Y ) ) = domain(
% 0.44/1.08 multiplication( X, domain( Y ) ) ) }.
% 0.44/1.08 (115) {G0,W6,D4,L1,V1,M1} { addition( domain( X ), one ) = one }.
% 0.44/1.08 (116) {G0,W4,D3,L1,V0,M1} { domain( zero ) = zero }.
% 0.44/1.08 (117) {G0,W10,D4,L1,V2,M1} { domain( addition( X, Y ) ) = addition( domain
% 0.44/1.08 ( X ), domain( Y ) ) }.
% 0.44/1.08 (118) {G0,W4,D3,L1,V0,M1} { domain( skol1 ) = zero }.
% 0.44/1.08 (119) {G0,W3,D2,L1,V0,M1} { ! skol1 = zero }.
% 0.44/1.08
% 0.44/1.08
% 0.44/1.08 Total Proof:
% 0.44/1.08
% 0.44/1.08 subsumption: (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 0.44/1.08 parent0: (102) {G0,W5,D3,L1,V1,M1} { addition( X, zero ) = X }.
% 0.44/1.08 substitution0:
% 0.44/1.08 X := X
% 0.44/1.08 end
% 0.44/1.08 permutation0:
% 0.44/1.08 0 ==> 0
% 0.44/1.08 end
% 0.44/1.08
% 0.44/1.08 subsumption: (10) {G0,W5,D3,L1,V1,M1} I { multiplication( zero, X ) ==>
% 0.44/1.08 zero }.
% 0.44/1.08 parent0: (110) {G0,W5,D3,L1,V1,M1} { multiplication( zero, X ) = zero }.
% 0.44/1.08 substitution0:
% 0.44/1.08 X := X
% 0.44/1.08 end
% 0.44/1.08 permutation0:
% 0.44/1.08 0 ==> 0
% 0.44/1.08 end
% 0.44/1.08
% 0.44/1.08 subsumption: (13) {G0,W11,D5,L1,V1,M1} I { addition( X, multiplication(
% 0.44/1.08 domain( X ), X ) ) ==> multiplication( domain( X ), X ) }.
% 0.44/1.08 parent0: (113) {G0,W11,D5,L1,V1,M1} { addition( X, multiplication( domain
% 0.44/1.08 ( X ), X ) ) = multiplication( domain( X ), X ) }.
% 0.44/1.08 substitution0:
% 0.44/1.08 X := X
% 0.44/1.08 end
% 0.44/1.08 permutation0:
% 0.44/1.08 0 ==> 0
% 0.44/1.08 end
% 0.44/1.08
% 0.44/1.08 subsumption: (18) {G0,W4,D3,L1,V0,M1} I { domain( skol1 ) ==> zero }.
% 0.44/1.08 parent0: (118) {G0,W4,D3,L1,V0,M1} { domain( skol1 ) = zero }.
% 0.44/1.08 substitution0:
% 0.44/1.08 end
% 0.44/1.08 permutation0:
% 0.44/1.08 0 ==> 0
% 0.44/1.08 end
% 0.44/1.08
% 0.44/1.08 subsumption: (19) {G0,W3,D2,L1,V0,M1} I { ! skol1 ==> zero }.
% 0.44/1.08 parent0: (119) {G0,W3,D2,L1,V0,M1} { ! skol1 = zero }.
% 0.44/1.08 substitution0:
% 0.44/1.08 end
% 0.44/1.08 permutation0:
% 0.44/1.08 0 ==> 0
% 0.44/1.08 end
% 0.44/1.08
% 0.44/1.08 eqswap: (183) {G0,W11,D5,L1,V1,M1} { multiplication( domain( X ), X ) ==>
% 0.44/1.08 addition( X, multiplication( domain( X ), X ) ) }.
% 0.44/1.08 parent0[0]: (13) {G0,W11,D5,L1,V1,M1} I { addition( X, multiplication(
% 0.44/1.08 domain( X ), X ) ) ==> multiplication( domain( X ), X ) }.
% 0.44/1.08 substitution0:
% 0.44/1.08 X := X
% 0.44/1.08 end
% 0.44/1.08
% 0.44/1.08 eqswap: (186) {G0,W3,D2,L1,V0,M1} { ! zero ==> skol1 }.
% 0.44/1.08 parent0[0]: (19) {G0,W3,D2,L1,V0,M1} I { ! skol1 ==> zero }.
% 0.44/1.08 substitution0:
% 0.44/1.08 end
% 0.44/1.08
% 0.44/1.08 paramod: (188) {G1,W10,D4,L1,V0,M1} { multiplication( domain( skol1 ),
% 0.44/1.08 skol1 ) ==> addition( skol1, multiplication( zero, skol1 ) ) }.
% 0.44/1.08 parent0[0]: (18) {G0,W4,D3,L1,V0,M1} I { domain( skol1 ) ==> zero }.
% 0.44/1.08 parent1[0; 8]: (183) {G0,W11,D5,L1,V1,M1} { multiplication( domain( X ), X
% 0.44/1.08 ) ==> addition( X, multiplication( domain( X ), X ) ) }.
% 0.44/1.08 substitution0:
% 0.44/1.08 end
% 0.44/1.08 substitution1:
% 0.44/1.08 X := skol1
% 0.44/1.08 end
% 0.44/1.08
% 0.44/1.08 paramod: (189) {G1,W9,D4,L1,V0,M1} { multiplication( zero, skol1 ) ==>
% 0.44/1.08 addition( skol1, multiplication( zero, skol1 ) ) }.
% 0.44/1.08 parent0[0]: (18) {G0,W4,D3,L1,V0,M1} I { domain( skol1 ) ==> zero }.
% 0.44/1.08 parent1[0; 2]: (188) {G1,W10,D4,L1,V0,M1} { multiplication( domain( skol1
% 0.44/1.08 ), skol1 ) ==> addition( skol1, multiplication( zero, skol1 ) ) }.
% 0.44/1.08 substitution0:
% 0.44/1.08 end
% 0.44/1.08 substitution1:
% 0.44/1.08 end
% 0.44/1.08
% 0.44/1.08 paramod: (193) {G1,W7,D3,L1,V0,M1} { multiplication( zero, skol1 ) ==>
% 0.44/1.08 addition( skol1, zero ) }.
% 0.44/1.08 parent0[0]: (10) {G0,W5,D3,L1,V1,M1} I { multiplication( zero, X ) ==> zero
% 0.44/1.08 }.
% 0.44/1.08 parent1[0; 6]: (189) {G1,W9,D4,L1,V0,M1} { multiplication( zero, skol1 )
% 0.44/1.08 ==> addition( skol1, multiplication( zero, skol1 ) ) }.
% 0.44/1.08 substitution0:
% 0.44/1.08 X := skol1
% 0.44/1.08 end
% 0.44/1.08 substitution1:
% 0.44/1.08 end
% 0.44/1.08
% 0.44/1.08 paramod: (194) {G1,W5,D3,L1,V0,M1} { zero ==> addition( skol1, zero ) }.
% 0.44/1.08 parent0[0]: (10) {G0,W5,D3,L1,V1,M1} I { multiplication( zero, X ) ==> zero
% 0.44/1.08 }.
% 0.44/1.08 parent1[0; 1]: (193) {G1,W7,D3,L1,V0,M1} { multiplication( zero, skol1 )
% 0.44/1.08 ==> addition( skol1, zero ) }.
% 0.44/1.08 substitution0:
% 0.44/1.08 X := skol1
% 0.44/1.08 end
% 0.44/1.08 substitution1:
% 0.44/1.08 end
% 0.44/1.08
% 0.44/1.08 paramod: (196) {G1,W3,D2,L1,V0,M1} { zero ==> skol1 }.
% 0.44/1.08 parent0[0]: (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 0.44/1.08 parent1[0; 2]: (194) {G1,W5,D3,L1,V0,M1} { zero ==> addition( skol1, zero
% 0.44/1.08 ) }.
% 0.44/1.08 substitution0:
% 0.44/1.08 X := skol1
% 0.44/1.08 end
% 0.44/1.08 substitution1:
% 0.44/1.08 end
% 0.44/1.08
% 0.44/1.08 resolution: (197) {G1,W0,D0,L0,V0,M0} { }.
% 0.44/1.08 parent0[0]: (186) {G0,W3,D2,L1,V0,M1} { ! zero ==> skol1 }.
% 0.44/1.08 parent1[0]: (196) {G1,W3,D2,L1,V0,M1} { zero ==> skol1 }.
% 0.44/1.08 substitution0:
% 0.44/1.08 end
% 0.44/1.08 substitution1:
% 0.44/1.08 end
% 0.44/1.08
% 0.44/1.08 subsumption: (98) {G1,W0,D0,L0,V0,M0} P(18,13);d(10);d(2);r(19) { }.
% 0.44/1.08 parent0: (197) {G1,W0,D0,L0,V0,M0} { }.
% 0.44/1.08 substitution0:
% 0.44/1.08 end
% 0.44/1.08 permutation0:
% 0.44/1.08 end
% 0.44/1.08
% 0.44/1.08 Proof check complete!
% 0.44/1.08
% 0.44/1.08 Memory use:
% 0.44/1.08
% 0.44/1.08 space for terms: 1393
% 0.44/1.08 space for clauses: 7899
% 0.44/1.08
% 0.44/1.08
% 0.44/1.08 clauses generated: 408
% 0.44/1.08 clauses kept: 99
% 0.44/1.08 clauses selected: 29
% 0.44/1.08 clauses deleted: 2
% 0.44/1.08 clauses inuse deleted: 0
% 0.44/1.08
% 0.44/1.08 subsentry: 627
% 0.44/1.08 literals s-matched: 359
% 0.44/1.08 literals matched: 359
% 0.44/1.08 full subsumption: 20
% 0.44/1.08
% 0.44/1.08 checksum: -1678965263
% 0.44/1.08
% 0.44/1.08
% 0.44/1.08 Bliksem ended
%------------------------------------------------------------------------------