TSTP Solution File: KLE146+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : KLE146+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n017.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 01:37:27 EDT 2022
% Result : Theorem 0.42s 1.08s
% Output : Refutation 0.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE146+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : bliksem %s
% 0.12/0.33 % Computer : n017.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 : Thu Jun 16 15:53:41 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.42/1.08 *** allocated 10000 integers for termspace/termends
% 0.42/1.08 *** allocated 10000 integers for clauses
% 0.42/1.08 *** allocated 10000 integers for justifications
% 0.42/1.08 Bliksem 1.12
% 0.42/1.08
% 0.42/1.08
% 0.42/1.08 Automatic Strategy Selection
% 0.42/1.08
% 0.42/1.08
% 0.42/1.08 Clauses:
% 0.42/1.08
% 0.42/1.08 { addition( X, Y ) = addition( Y, X ) }.
% 0.42/1.08 { addition( Z, addition( Y, X ) ) = addition( addition( Z, Y ), X ) }.
% 0.42/1.08 { addition( X, zero ) = X }.
% 0.42/1.08 { addition( X, X ) = X }.
% 0.42/1.08 { multiplication( X, multiplication( Y, Z ) ) = multiplication(
% 0.42/1.08 multiplication( X, Y ), Z ) }.
% 0.42/1.08 { multiplication( X, one ) = X }.
% 0.42/1.08 { multiplication( one, X ) = X }.
% 0.42/1.08 { multiplication( X, addition( Y, Z ) ) = addition( multiplication( X, Y )
% 0.42/1.08 , multiplication( X, Z ) ) }.
% 0.42/1.08 { multiplication( addition( X, Y ), Z ) = addition( multiplication( X, Z )
% 0.42/1.08 , multiplication( Y, Z ) ) }.
% 0.42/1.08 { multiplication( zero, X ) = zero }.
% 0.42/1.08 { addition( one, multiplication( X, star( X ) ) ) = star( X ) }.
% 0.42/1.08 { addition( one, multiplication( star( X ), X ) ) = star( X ) }.
% 0.42/1.08 { ! leq( addition( multiplication( X, Z ), Y ), Z ), leq( multiplication(
% 0.42/1.08 star( X ), Y ), Z ) }.
% 0.42/1.08 { ! leq( addition( multiplication( Z, X ), Y ), Z ), leq( multiplication( Y
% 0.42/1.08 , star( X ) ), Z ) }.
% 0.42/1.08 { strong_iteration( X ) = addition( multiplication( X, strong_iteration( X
% 0.42/1.08 ) ), one ) }.
% 0.42/1.08 { ! leq( Z, addition( multiplication( X, Z ), Y ) ), leq( Z, multiplication
% 0.42/1.08 ( strong_iteration( X ), Y ) ) }.
% 0.42/1.08 { strong_iteration( X ) = addition( star( X ), multiplication(
% 0.42/1.08 strong_iteration( X ), zero ) ) }.
% 0.42/1.08 { ! leq( X, Y ), addition( X, Y ) = Y }.
% 0.42/1.08 { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 0.42/1.08 { ! leq( one, strong_iteration( skol1 ) ) }.
% 0.42/1.08
% 0.42/1.08 percentage equality = 0.640000, percentage horn = 1.000000
% 0.42/1.08 This is a problem with some equality
% 0.42/1.08
% 0.42/1.08
% 0.42/1.08
% 0.42/1.08 Options Used:
% 0.42/1.08
% 0.42/1.08 useres = 1
% 0.42/1.08 useparamod = 1
% 0.42/1.08 useeqrefl = 1
% 0.42/1.08 useeqfact = 1
% 0.42/1.08 usefactor = 1
% 0.42/1.08 usesimpsplitting = 0
% 0.42/1.08 usesimpdemod = 5
% 0.42/1.08 usesimpres = 3
% 0.42/1.08
% 0.42/1.08 resimpinuse = 1000
% 0.42/1.08 resimpclauses = 20000
% 0.42/1.08 substype = eqrewr
% 0.42/1.08 backwardsubs = 1
% 0.42/1.08 selectoldest = 5
% 0.42/1.08
% 0.42/1.08 litorderings [0] = split
% 0.42/1.08 litorderings [1] = extend the termordering, first sorting on arguments
% 0.42/1.08
% 0.42/1.08 termordering = kbo
% 0.42/1.08
% 0.42/1.08 litapriori = 0
% 0.42/1.08 termapriori = 1
% 0.42/1.08 litaposteriori = 0
% 0.42/1.08 termaposteriori = 0
% 0.42/1.08 demodaposteriori = 0
% 0.42/1.08 ordereqreflfact = 0
% 0.42/1.08
% 0.42/1.08 litselect = negord
% 0.42/1.08
% 0.42/1.08 maxweight = 15
% 0.42/1.08 maxdepth = 30000
% 0.42/1.08 maxlength = 115
% 0.42/1.08 maxnrvars = 195
% 0.42/1.08 excuselevel = 1
% 0.42/1.08 increasemaxweight = 1
% 0.42/1.08
% 0.42/1.08 maxselected = 10000000
% 0.42/1.08 maxnrclauses = 10000000
% 0.42/1.08
% 0.42/1.08 showgenerated = 0
% 0.42/1.08 showkept = 0
% 0.42/1.08 showselected = 0
% 0.42/1.08 showdeleted = 0
% 0.42/1.08 showresimp = 1
% 0.42/1.08 showstatus = 2000
% 0.42/1.08
% 0.42/1.08 prologoutput = 0
% 0.42/1.08 nrgoals = 5000000
% 0.42/1.08 totalproof = 1
% 0.42/1.08
% 0.42/1.08 Symbols occurring in the translation:
% 0.42/1.08
% 0.42/1.08 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.42/1.08 . [1, 2] (w:1, o:20, a:1, s:1, b:0),
% 0.42/1.08 ! [4, 1] (w:0, o:13, a:1, s:1, b:0),
% 0.42/1.08 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.42/1.08 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.42/1.08 addition [37, 2] (w:1, o:44, a:1, s:1, b:0),
% 0.42/1.08 zero [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.42/1.08 multiplication [40, 2] (w:1, o:46, a:1, s:1, b:0),
% 0.42/1.08 one [41, 0] (w:1, o:10, a:1, s:1, b:0),
% 0.42/1.08 star [42, 1] (w:1, o:18, a:1, s:1, b:0),
% 0.42/1.08 leq [43, 2] (w:1, o:45, a:1, s:1, b:0),
% 0.42/1.08 strong_iteration [44, 1] (w:1, o:19, a:1, s:1, b:0),
% 0.42/1.08 skol1 [46, 0] (w:1, o:12, a:1, s:1, b:1).
% 0.42/1.08
% 0.42/1.08
% 0.42/1.08 Starting Search:
% 0.42/1.08
% 0.42/1.08 *** allocated 15000 integers for clauses
% 0.42/1.08 *** allocated 22500 integers for clauses
% 0.42/1.08 *** allocated 33750 integers for clauses
% 0.42/1.08
% 0.42/1.08 Bliksems!, er is een bewijs:
% 0.42/1.08 % SZS status Theorem
% 0.42/1.08 % SZS output start Refutation
% 0.42/1.08
% 0.42/1.08 (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X ) }.
% 0.42/1.08 (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) ) ==> addition(
% 0.42/1.08 addition( Z, Y ), X ) }.
% 0.42/1.08 (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 0.42/1.08 (14) {G0,W9,D5,L1,V1,M1} I { addition( multiplication( X, strong_iteration
% 0.42/1.08 ( X ) ), one ) ==> strong_iteration( X ) }.
% 0.42/1.08 (18) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X, Y ) }.
% 0.42/1.08 (19) {G0,W4,D3,L1,V0,M1} I { ! leq( one, strong_iteration( skol1 ) ) }.
% 0.42/1.08 (26) {G1,W14,D4,L2,V3,M2} P(1,18) { ! addition( addition( X, Y ), Z ) ==>
% 0.71/1.08 addition( Y, Z ), leq( X, addition( Y, Z ) ) }.
% 0.71/1.08 (292) {G2,W5,D3,L1,V2,M1} P(3,26);q { leq( X, addition( X, Y ) ) }.
% 0.71/1.08 (307) {G3,W5,D3,L1,V2,M1} P(0,292) { leq( X, addition( Y, X ) ) }.
% 0.71/1.08 (319) {G4,W4,D3,L1,V1,M1} P(14,307) { leq( one, strong_iteration( X ) ) }.
% 0.71/1.08 (328) {G5,W0,D0,L0,V0,M0} R(319,19) { }.
% 0.71/1.08
% 0.71/1.08
% 0.71/1.08 % SZS output end Refutation
% 0.71/1.08 found a proof!
% 0.71/1.08
% 0.71/1.08
% 0.71/1.08 Unprocessed initial clauses:
% 0.71/1.08
% 0.71/1.08 (330) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X ) }.
% 0.71/1.08 (331) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) = addition(
% 0.71/1.08 addition( Z, Y ), X ) }.
% 0.71/1.08 (332) {G0,W5,D3,L1,V1,M1} { addition( X, zero ) = X }.
% 0.71/1.08 (333) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 0.71/1.08 (334) {G0,W11,D4,L1,V3,M1} { multiplication( X, multiplication( Y, Z ) ) =
% 0.71/1.08 multiplication( multiplication( X, Y ), Z ) }.
% 0.71/1.08 (335) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 0.71/1.08 (336) {G0,W5,D3,L1,V1,M1} { multiplication( one, X ) = X }.
% 0.71/1.08 (337) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y, Z ) ) =
% 0.71/1.08 addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 0.71/1.08 (338) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Y ), Z ) =
% 0.71/1.08 addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 0.71/1.08 (339) {G0,W5,D3,L1,V1,M1} { multiplication( zero, X ) = zero }.
% 0.71/1.08 (340) {G0,W9,D5,L1,V1,M1} { addition( one, multiplication( X, star( X ) )
% 0.71/1.08 ) = star( X ) }.
% 0.71/1.08 (341) {G0,W9,D5,L1,V1,M1} { addition( one, multiplication( star( X ), X )
% 0.71/1.08 ) = star( X ) }.
% 0.71/1.08 (342) {G0,W13,D4,L2,V3,M2} { ! leq( addition( multiplication( X, Z ), Y )
% 0.71/1.08 , Z ), leq( multiplication( star( X ), Y ), Z ) }.
% 0.71/1.08 (343) {G0,W13,D4,L2,V3,M2} { ! leq( addition( multiplication( Z, X ), Y )
% 0.71/1.08 , Z ), leq( multiplication( Y, star( X ) ), Z ) }.
% 0.71/1.08 (344) {G0,W9,D5,L1,V1,M1} { strong_iteration( X ) = addition(
% 0.71/1.08 multiplication( X, strong_iteration( X ) ), one ) }.
% 0.71/1.08 (345) {G0,W13,D4,L2,V3,M2} { ! leq( Z, addition( multiplication( X, Z ), Y
% 0.71/1.08 ) ), leq( Z, multiplication( strong_iteration( X ), Y ) ) }.
% 0.71/1.08 (346) {G0,W10,D5,L1,V1,M1} { strong_iteration( X ) = addition( star( X ),
% 0.71/1.08 multiplication( strong_iteration( X ), zero ) ) }.
% 0.71/1.08 (347) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y }.
% 0.71/1.08 (348) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 0.71/1.08 (349) {G0,W4,D3,L1,V0,M1} { ! leq( one, strong_iteration( skol1 ) ) }.
% 0.71/1.08
% 0.71/1.08
% 0.71/1.08 Total Proof:
% 0.71/1.08
% 0.71/1.08 subsumption: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X
% 0.71/1.08 ) }.
% 0.71/1.08 parent0: (330) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X )
% 0.71/1.08 }.
% 0.71/1.08 substitution0:
% 0.71/1.08 X := X
% 0.71/1.08 Y := Y
% 0.71/1.08 end
% 0.71/1.08 permutation0:
% 0.71/1.08 0 ==> 0
% 0.71/1.08 end
% 0.71/1.08
% 0.71/1.08 subsumption: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 0.71/1.08 ==> addition( addition( Z, Y ), X ) }.
% 0.71/1.08 parent0: (331) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) =
% 0.71/1.08 addition( addition( Z, Y ), X ) }.
% 0.71/1.08 substitution0:
% 0.71/1.08 X := X
% 0.71/1.08 Y := Y
% 0.71/1.08 Z := Z
% 0.71/1.08 end
% 0.71/1.08 permutation0:
% 0.71/1.08 0 ==> 0
% 0.71/1.08 end
% 0.71/1.08
% 0.71/1.08 subsumption: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 0.71/1.08 parent0: (333) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 0.71/1.08 substitution0:
% 0.71/1.08 X := X
% 0.71/1.08 end
% 0.71/1.08 permutation0:
% 0.71/1.08 0 ==> 0
% 0.71/1.08 end
% 0.71/1.08
% 0.71/1.08 eqswap: (365) {G0,W9,D5,L1,V1,M1} { addition( multiplication( X,
% 0.71/1.08 strong_iteration( X ) ), one ) = strong_iteration( X ) }.
% 0.71/1.08 parent0[0]: (344) {G0,W9,D5,L1,V1,M1} { strong_iteration( X ) = addition(
% 0.71/1.08 multiplication( X, strong_iteration( X ) ), one ) }.
% 0.71/1.08 substitution0:
% 0.71/1.08 X := X
% 0.71/1.08 end
% 0.71/1.08
% 0.71/1.08 subsumption: (14) {G0,W9,D5,L1,V1,M1} I { addition( multiplication( X,
% 0.71/1.08 strong_iteration( X ) ), one ) ==> strong_iteration( X ) }.
% 0.71/1.08 parent0: (365) {G0,W9,D5,L1,V1,M1} { addition( multiplication( X,
% 0.71/1.08 strong_iteration( X ) ), one ) = strong_iteration( X ) }.
% 0.71/1.08 substitution0:
% 0.71/1.08 X := X
% 0.71/1.08 end
% 0.71/1.08 permutation0:
% 0.71/1.08 0 ==> 0
% 0.71/1.08 end
% 0.71/1.08
% 0.71/1.08 subsumption: (18) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X
% 0.71/1.08 , Y ) }.
% 0.71/1.08 parent0: (348) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y )
% 0.71/1.08 }.
% 0.71/1.08 substitution0:
% 0.71/1.08 X := X
% 0.71/1.08 Y := Y
% 0.71/1.08 end
% 0.71/1.08 permutation0:
% 0.71/1.08 0 ==> 0
% 0.71/1.08 1 ==> 1
% 0.71/1.08 end
% 0.71/1.08
% 0.71/1.08 subsumption: (19) {G0,W4,D3,L1,V0,M1} I { ! leq( one, strong_iteration(
% 0.71/1.08 skol1 ) ) }.
% 0.71/1.08 parent0: (349) {G0,W4,D3,L1,V0,M1} { ! leq( one, strong_iteration( skol1 )
% 0.71/1.08 ) }.
% 0.71/1.08 substitution0:
% 0.71/1.08 end
% 0.71/1.08 permutation0:
% 0.71/1.08 0 ==> 0
% 0.71/1.08 end
% 0.71/1.08
% 0.71/1.08 eqswap: (397) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y )
% 0.71/1.08 }.
% 0.71/1.08 parent0[0]: (18) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 0.71/1.08 Y ) }.
% 0.71/1.08 substitution0:
% 0.71/1.08 X := X
% 0.71/1.08 Y := Y
% 0.71/1.08 end
% 0.71/1.08
% 0.71/1.08 paramod: (398) {G1,W14,D4,L2,V3,M2} { ! addition( X, Y ) ==> addition(
% 0.71/1.08 addition( Z, X ), Y ), leq( Z, addition( X, Y ) ) }.
% 0.71/1.08 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 0.71/1.08 ==> addition( addition( Z, Y ), X ) }.
% 0.71/1.08 parent1[0; 5]: (397) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq(
% 0.71/1.08 X, Y ) }.
% 0.71/1.08 substitution0:
% 0.71/1.08 X := Y
% 0.71/1.08 Y := X
% 0.71/1.08 Z := Z
% 0.71/1.08 end
% 0.71/1.08 substitution1:
% 0.71/1.08 X := Z
% 0.71/1.08 Y := addition( X, Y )
% 0.71/1.08 end
% 0.71/1.08
% 0.71/1.08 eqswap: (399) {G1,W14,D4,L2,V3,M2} { ! addition( addition( Z, X ), Y ) ==>
% 0.71/1.08 addition( X, Y ), leq( Z, addition( X, Y ) ) }.
% 0.71/1.08 parent0[0]: (398) {G1,W14,D4,L2,V3,M2} { ! addition( X, Y ) ==> addition(
% 0.71/1.08 addition( Z, X ), Y ), leq( Z, addition( X, Y ) ) }.
% 0.71/1.08 substitution0:
% 0.71/1.08 X := X
% 0.71/1.08 Y := Y
% 0.71/1.08 Z := Z
% 0.71/1.08 end
% 0.71/1.08
% 0.71/1.08 subsumption: (26) {G1,W14,D4,L2,V3,M2} P(1,18) { ! addition( addition( X, Y
% 0.71/1.08 ), Z ) ==> addition( Y, Z ), leq( X, addition( Y, Z ) ) }.
% 0.71/1.08 parent0: (399) {G1,W14,D4,L2,V3,M2} { ! addition( addition( Z, X ), Y )
% 0.71/1.08 ==> addition( X, Y ), leq( Z, addition( X, Y ) ) }.
% 0.71/1.08 substitution0:
% 0.71/1.08 X := Y
% 0.71/1.08 Y := Z
% 0.71/1.08 Z := X
% 0.71/1.08 end
% 0.71/1.08 permutation0:
% 0.71/1.08 0 ==> 0
% 0.71/1.08 1 ==> 1
% 0.71/1.08 end
% 0.71/1.08
% 0.71/1.08 eqswap: (401) {G1,W14,D4,L2,V3,M2} { ! addition( Y, Z ) ==> addition(
% 0.71/1.08 addition( X, Y ), Z ), leq( X, addition( Y, Z ) ) }.
% 0.71/1.08 parent0[0]: (26) {G1,W14,D4,L2,V3,M2} P(1,18) { ! addition( addition( X, Y
% 0.71/1.08 ), Z ) ==> addition( Y, Z ), leq( X, addition( Y, Z ) ) }.
% 0.71/1.08 substitution0:
% 0.71/1.08 X := X
% 0.71/1.08 Y := Y
% 0.71/1.08 Z := Z
% 0.71/1.08 end
% 0.71/1.08
% 0.71/1.08 paramod: (404) {G1,W12,D3,L2,V2,M2} { ! addition( X, Y ) ==> addition( X,
% 0.71/1.08 Y ), leq( X, addition( X, Y ) ) }.
% 0.71/1.08 parent0[0]: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 0.71/1.08 parent1[0; 6]: (401) {G1,W14,D4,L2,V3,M2} { ! addition( Y, Z ) ==>
% 0.71/1.08 addition( addition( X, Y ), Z ), leq( X, addition( Y, Z ) ) }.
% 0.71/1.08 substitution0:
% 0.71/1.08 X := X
% 0.71/1.08 end
% 0.71/1.08 substitution1:
% 0.71/1.08 X := X
% 0.71/1.08 Y := X
% 0.71/1.08 Z := Y
% 0.71/1.08 end
% 0.71/1.08
% 0.71/1.08 eqrefl: (407) {G0,W5,D3,L1,V2,M1} { leq( X, addition( X, Y ) ) }.
% 0.71/1.08 parent0[0]: (404) {G1,W12,D3,L2,V2,M2} { ! addition( X, Y ) ==> addition(
% 0.71/1.08 X, Y ), leq( X, addition( X, Y ) ) }.
% 0.71/1.08 substitution0:
% 0.71/1.08 X := X
% 0.71/1.08 Y := Y
% 0.71/1.08 end
% 0.71/1.08
% 0.71/1.08 subsumption: (292) {G2,W5,D3,L1,V2,M1} P(3,26);q { leq( X, addition( X, Y )
% 0.71/1.08 ) }.
% 0.71/1.08 parent0: (407) {G0,W5,D3,L1,V2,M1} { leq( X, addition( X, Y ) ) }.
% 0.71/1.08 substitution0:
% 0.71/1.08 X := X
% 0.71/1.08 Y := Y
% 0.71/1.08 end
% 0.71/1.08 permutation0:
% 0.71/1.08 0 ==> 0
% 0.71/1.08 end
% 0.71/1.08
% 0.71/1.08 paramod: (408) {G1,W5,D3,L1,V2,M1} { leq( X, addition( Y, X ) ) }.
% 0.71/1.08 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 0.71/1.08 }.
% 0.71/1.08 parent1[0; 2]: (292) {G2,W5,D3,L1,V2,M1} P(3,26);q { leq( X, addition( X, Y
% 0.71/1.08 ) ) }.
% 0.71/1.08 substitution0:
% 0.71/1.08 X := X
% 0.71/1.08 Y := Y
% 0.71/1.08 end
% 0.71/1.08 substitution1:
% 0.71/1.08 X := X
% 0.71/1.08 Y := Y
% 0.71/1.08 end
% 0.71/1.08
% 0.71/1.08 subsumption: (307) {G3,W5,D3,L1,V2,M1} P(0,292) { leq( X, addition( Y, X )
% 0.71/1.08 ) }.
% 0.71/1.08 parent0: (408) {G1,W5,D3,L1,V2,M1} { leq( X, addition( Y, X ) ) }.
% 0.71/1.08 substitution0:
% 0.71/1.08 X := X
% 0.71/1.08 Y := Y
% 0.71/1.08 end
% 0.71/1.08 permutation0:
% 0.71/1.08 0 ==> 0
% 0.71/1.08 end
% 0.71/1.08
% 0.71/1.08 paramod: (411) {G1,W4,D3,L1,V1,M1} { leq( one, strong_iteration( X ) ) }.
% 0.71/1.08 parent0[0]: (14) {G0,W9,D5,L1,V1,M1} I { addition( multiplication( X,
% 0.71/1.08 strong_iteration( X ) ), one ) ==> strong_iteration( X ) }.
% 0.71/1.08 parent1[0; 2]: (307) {G3,W5,D3,L1,V2,M1} P(0,292) { leq( X, addition( Y, X
% 0.71/1.08 ) ) }.
% 0.71/1.08 substitution0:
% 0.71/1.08 X := X
% 0.71/1.08 end
% 0.71/1.08 substitution1:
% 0.71/1.08 X := one
% 0.71/1.08 Y := multiplication( X, strong_iteration( X ) )
% 0.71/1.08 end
% 0.71/1.08
% 0.71/1.08 subsumption: (319) {G4,W4,D3,L1,V1,M1} P(14,307) { leq( one,
% 0.71/1.08 strong_iteration( X ) ) }.
% 0.71/1.08 parent0: (411) {G1,W4,D3,L1,V1,M1} { leq( one, strong_iteration( X ) ) }.
% 0.71/1.08 substitution0:
% 0.71/1.08 X := X
% 0.71/1.08 end
% 0.71/1.08 permutation0:
% 0.71/1.08 0 ==> 0
% 0.71/1.08 end
% 0.71/1.08
% 0.71/1.08 resolution: (412) {G1,W0,D0,L0,V0,M0} { }.
% 0.71/1.08 parent0[0]: (19) {G0,W4,D3,L1,V0,M1} I { ! leq( one, strong_iteration(
% 0.71/1.08 skol1 ) ) }.
% 0.71/1.08 parent1[0]: (319) {G4,W4,D3,L1,V1,M1} P(14,307) { leq( one,
% 0.71/1.08 strong_iteration( X ) ) }.
% 0.71/1.08 substitution0:
% 0.71/1.08 end
% 0.71/1.08 substitution1:
% 0.71/1.08 X := skol1
% 0.71/1.08 end
% 0.71/1.08
% 0.71/1.08 subsumption: (328) {G5,W0,D0,L0,V0,M0} R(319,19) { }.
% 0.71/1.08 parent0: (412) {G1,W0,D0,L0,V0,M0} { }.
% 0.71/1.08 substitution0:
% 0.71/1.08 end
% 0.71/1.08 permutation0:
% 0.71/1.08 end
% 0.71/1.08
% 0.71/1.08 Proof check complete!
% 0.71/1.08
% 0.71/1.08 Memory use:
% 0.71/1.08
% 0.71/1.08 space for terms: 4275
% 0.71/1.08 space for clauses: 22567
% 0.71/1.08
% 0.71/1.08
% 0.71/1.08 clauses generated: 1243
% 0.71/1.08 clauses kept: 329
% 0.71/1.08 clauses selected: 68
% 0.71/1.08 clauses deleted: 2
% 0.71/1.08 clauses inuse deleted: 0
% 0.71/1.08
% 0.71/1.08 subsentry: 1280
% 0.71/1.08 literals s-matched: 1006
% 0.71/1.08 literals matched: 1004
% 0.71/1.08 full subsumption: 75
% 0.71/1.08
% 0.71/1.08 checksum: -442814493
% 0.71/1.08
% 0.71/1.08
% 0.71/1.08 Bliksem ended
%------------------------------------------------------------------------------