TSTP Solution File: KLE150+1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : KLE150+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n013.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 01:37:30 EDT 2022
% Result : Theorem 3.27s 3.67s
% Output : Refutation 3.27s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : KLE150+1 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n013.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 07:13:29 EDT 2022
% 0.12/0.33 % CPUTime :
% 3.27/3.67 *** allocated 10000 integers for termspace/termends
% 3.27/3.67 *** allocated 10000 integers for clauses
% 3.27/3.67 *** allocated 10000 integers for justifications
% 3.27/3.67 Bliksem 1.12
% 3.27/3.67
% 3.27/3.67
% 3.27/3.67 Automatic Strategy Selection
% 3.27/3.67
% 3.27/3.67
% 3.27/3.67 Clauses:
% 3.27/3.67
% 3.27/3.67 { addition( X, Y ) = addition( Y, X ) }.
% 3.27/3.67 { addition( Z, addition( Y, X ) ) = addition( addition( Z, Y ), X ) }.
% 3.27/3.67 { addition( X, zero ) = X }.
% 3.27/3.67 { addition( X, X ) = X }.
% 3.27/3.67 { multiplication( X, multiplication( Y, Z ) ) = multiplication(
% 3.27/3.67 multiplication( X, Y ), Z ) }.
% 3.27/3.67 { multiplication( X, one ) = X }.
% 3.27/3.67 { multiplication( one, X ) = X }.
% 3.27/3.67 { multiplication( X, addition( Y, Z ) ) = addition( multiplication( X, Y )
% 3.27/3.67 , multiplication( X, Z ) ) }.
% 3.27/3.67 { multiplication( addition( X, Y ), Z ) = addition( multiplication( X, Z )
% 3.27/3.67 , multiplication( Y, Z ) ) }.
% 3.27/3.67 { multiplication( zero, X ) = zero }.
% 3.27/3.67 { addition( one, multiplication( X, star( X ) ) ) = star( X ) }.
% 3.27/3.67 { addition( one, multiplication( star( X ), X ) ) = star( X ) }.
% 3.27/3.67 { ! leq( addition( multiplication( X, Z ), Y ), Z ), leq( multiplication(
% 3.27/3.67 star( X ), Y ), Z ) }.
% 3.27/3.67 { ! leq( addition( multiplication( Z, X ), Y ), Z ), leq( multiplication( Y
% 3.27/3.67 , star( X ) ), Z ) }.
% 3.27/3.67 { strong_iteration( X ) = addition( multiplication( X, strong_iteration( X
% 3.27/3.67 ) ), one ) }.
% 3.27/3.67 { ! leq( Z, addition( multiplication( X, Z ), Y ) ), leq( Z, multiplication
% 3.27/3.67 ( strong_iteration( X ), Y ) ) }.
% 3.27/3.67 { strong_iteration( X ) = addition( star( X ), multiplication(
% 3.27/3.67 strong_iteration( X ), zero ) ) }.
% 3.27/3.67 { ! leq( X, Y ), addition( X, Y ) = Y }.
% 3.27/3.67 { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 3.27/3.67 { ! strong_iteration( multiplication( skol1, zero ) ) = addition( one,
% 3.27/3.67 multiplication( skol1, zero ) ) }.
% 3.27/3.67
% 3.27/3.67 percentage equality = 0.680000, percentage horn = 1.000000
% 3.27/3.67 This is a problem with some equality
% 3.27/3.67
% 3.27/3.67
% 3.27/3.67
% 3.27/3.67 Options Used:
% 3.27/3.67
% 3.27/3.67 useres = 1
% 3.27/3.67 useparamod = 1
% 3.27/3.67 useeqrefl = 1
% 3.27/3.67 useeqfact = 1
% 3.27/3.67 usefactor = 1
% 3.27/3.67 usesimpsplitting = 0
% 3.27/3.67 usesimpdemod = 5
% 3.27/3.67 usesimpres = 3
% 3.27/3.67
% 3.27/3.67 resimpinuse = 1000
% 3.27/3.67 resimpclauses = 20000
% 3.27/3.67 substype = eqrewr
% 3.27/3.67 backwardsubs = 1
% 3.27/3.67 selectoldest = 5
% 3.27/3.67
% 3.27/3.67 litorderings [0] = split
% 3.27/3.67 litorderings [1] = extend the termordering, first sorting on arguments
% 3.27/3.67
% 3.27/3.67 termordering = kbo
% 3.27/3.67
% 3.27/3.67 litapriori = 0
% 3.27/3.67 termapriori = 1
% 3.27/3.67 litaposteriori = 0
% 3.27/3.67 termaposteriori = 0
% 3.27/3.67 demodaposteriori = 0
% 3.27/3.67 ordereqreflfact = 0
% 3.27/3.67
% 3.27/3.67 litselect = negord
% 3.27/3.67
% 3.27/3.67 maxweight = 15
% 3.27/3.67 maxdepth = 30000
% 3.27/3.67 maxlength = 115
% 3.27/3.67 maxnrvars = 195
% 3.27/3.67 excuselevel = 1
% 3.27/3.67 increasemaxweight = 1
% 3.27/3.67
% 3.27/3.67 maxselected = 10000000
% 3.27/3.67 maxnrclauses = 10000000
% 3.27/3.67
% 3.27/3.67 showgenerated = 0
% 3.27/3.67 showkept = 0
% 3.27/3.67 showselected = 0
% 3.27/3.67 showdeleted = 0
% 3.27/3.67 showresimp = 1
% 3.27/3.67 showstatus = 2000
% 3.27/3.67
% 3.27/3.67 prologoutput = 0
% 3.27/3.67 nrgoals = 5000000
% 3.27/3.67 totalproof = 1
% 3.27/3.67
% 3.27/3.67 Symbols occurring in the translation:
% 3.27/3.67
% 3.27/3.67 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 3.27/3.67 . [1, 2] (w:1, o:20, a:1, s:1, b:0),
% 3.27/3.67 ! [4, 1] (w:0, o:13, a:1, s:1, b:0),
% 3.27/3.67 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 3.27/3.67 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 3.27/3.67 addition [37, 2] (w:1, o:44, a:1, s:1, b:0),
% 3.27/3.67 zero [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 3.27/3.67 multiplication [40, 2] (w:1, o:46, a:1, s:1, b:0),
% 3.27/3.67 one [41, 0] (w:1, o:10, a:1, s:1, b:0),
% 3.27/3.67 star [42, 1] (w:1, o:18, a:1, s:1, b:0),
% 3.27/3.67 leq [43, 2] (w:1, o:45, a:1, s:1, b:0),
% 3.27/3.67 strong_iteration [44, 1] (w:1, o:19, a:1, s:1, b:0),
% 3.27/3.67 skol1 [46, 0] (w:1, o:12, a:1, s:1, b:1).
% 3.27/3.67
% 3.27/3.67
% 3.27/3.67 Starting Search:
% 3.27/3.67
% 3.27/3.67 *** allocated 15000 integers for clauses
% 3.27/3.67 *** allocated 22500 integers for clauses
% 3.27/3.67 *** allocated 33750 integers for clauses
% 3.27/3.67 *** allocated 50625 integers for clauses
% 3.27/3.67 *** allocated 15000 integers for termspace/termends
% 3.27/3.67 *** allocated 75937 integers for clauses
% 3.27/3.67 Resimplifying inuse:
% 3.27/3.67 Done
% 3.27/3.67
% 3.27/3.67 *** allocated 22500 integers for termspace/termends
% 3.27/3.67 *** allocated 113905 integers for clauses
% 3.27/3.67 *** allocated 33750 integers for termspace/termends
% 3.27/3.67 *** allocated 170857 integers for clauses
% 3.27/3.67
% 3.27/3.67 Intermediate Status:
% 3.27/3.67 Generated: 22564
% 3.27/3.67 Kept: 2001
% 3.27/3.67 Inuse: 260
% 3.27/3.67 Deleted: 68
% 3.27/3.67 Deletedinuse: 34
% 3.27/3.67
% 3.27/3.67 Resimplifying inuse:
% 3.27/3.67 Done
% 3.27/3.67
% 3.27/3.67 *** allocated 50625 integers for termspace/termends
% 3.27/3.67 *** allocated 256285 integers for clauses
% 3.27/3.67 Resimplifying inuse:
% 3.27/3.67 Done
% 3.27/3.67
% 3.27/3.67
% 3.27/3.67 Intermediate Status:
% 3.27/3.67 Generated: 49435
% 3.27/3.67 Kept: 4004
% 3.27/3.67 Inuse: 436
% 3.27/3.67 Deleted: 81
% 3.27/3.67 Deletedinuse: 36
% 3.27/3.67
% 3.27/3.67 *** allocated 75937 integers for termspace/termends
% 3.27/3.67 Resimplifying inuse:
% 3.27/3.67 Done
% 3.27/3.67
% 3.27/3.67 *** allocated 384427 integers for clauses
% 3.27/3.67 Resimplifying inuse:
% 3.27/3.67 Done
% 3.27/3.67
% 3.27/3.67
% 3.27/3.67 Intermediate Status:
% 3.27/3.67 Generated: 79246
% 3.27/3.67 Kept: 6049
% 3.27/3.67 Inuse: 600
% 3.27/3.67 Deleted: 128
% 3.27/3.67 Deletedinuse: 39
% 3.27/3.67
% 3.27/3.67 *** allocated 113905 integers for termspace/termends
% 3.27/3.67 Resimplifying inuse:
% 3.27/3.67 Done
% 3.27/3.67
% 3.27/3.67 Resimplifying inuse:
% 3.27/3.67 Done
% 3.27/3.67
% 3.27/3.67 *** allocated 576640 integers for clauses
% 3.27/3.67
% 3.27/3.67 Intermediate Status:
% 3.27/3.67 Generated: 105840
% 3.27/3.67 Kept: 8092
% 3.27/3.67 Inuse: 717
% 3.27/3.67 Deleted: 142
% 3.27/3.67 Deletedinuse: 40
% 3.27/3.67
% 3.27/3.67 Resimplifying inuse:
% 3.27/3.67 Done
% 3.27/3.67
% 3.27/3.67 *** allocated 170857 integers for termspace/termends
% 3.27/3.67 Resimplifying inuse:
% 3.27/3.67 Done
% 3.27/3.67
% 3.27/3.67
% 3.27/3.67 Intermediate Status:
% 3.27/3.67 Generated: 129543
% 3.27/3.67 Kept: 10098
% 3.27/3.67 Inuse: 792
% 3.27/3.67 Deleted: 161
% 3.27/3.67 Deletedinuse: 42
% 3.27/3.67
% 3.27/3.67 Resimplifying inuse:
% 3.27/3.67 Done
% 3.27/3.67
% 3.27/3.67 *** allocated 864960 integers for clauses
% 3.27/3.67 Resimplifying inuse:
% 3.27/3.67 Done
% 3.27/3.67
% 3.27/3.67
% 3.27/3.67 Intermediate Status:
% 3.27/3.67 Generated: 170260
% 3.27/3.67 Kept: 12137
% 3.27/3.67 Inuse: 921
% 3.27/3.67 Deleted: 312
% 3.27/3.67 Deletedinuse: 141
% 3.27/3.67
% 3.27/3.67 Resimplifying inuse:
% 3.27/3.67 Done
% 3.27/3.67
% 3.27/3.67 Resimplifying inuse:
% 3.27/3.67 Done
% 3.27/3.67
% 3.27/3.67
% 3.27/3.67 Bliksems!, er is een bewijs:
% 3.27/3.67 % SZS status Theorem
% 3.27/3.67 % SZS output start Refutation
% 3.27/3.67
% 3.27/3.67 (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X ) }.
% 3.27/3.67 (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 3.27/3.67 (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 3.27/3.67 (4) {G0,W11,D4,L1,V3,M1} I { multiplication( X, multiplication( Y, Z ) )
% 3.27/3.67 ==> multiplication( multiplication( X, Y ), Z ) }.
% 3.27/3.67 (9) {G0,W5,D3,L1,V1,M1} I { multiplication( zero, X ) ==> zero }.
% 3.27/3.67 (10) {G0,W9,D5,L1,V1,M1} I { addition( one, multiplication( X, star( X ) )
% 3.27/3.67 ) ==> star( X ) }.
% 3.27/3.67 (13) {G0,W13,D4,L2,V3,M2} I { ! leq( addition( multiplication( Z, X ), Y )
% 3.27/3.67 , Z ), leq( multiplication( Y, star( X ) ), Z ) }.
% 3.27/3.67 (14) {G0,W9,D5,L1,V1,M1} I { addition( multiplication( X, strong_iteration
% 3.27/3.67 ( X ) ), one ) ==> strong_iteration( X ) }.
% 3.27/3.67 (17) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y ) ==> Y }.
% 3.27/3.67 (18) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X, Y ) }.
% 3.27/3.67 (19) {G0,W10,D4,L1,V0,M1} I { ! addition( one, multiplication( skol1, zero
% 3.27/3.67 ) ) ==> strong_iteration( multiplication( skol1, zero ) ) }.
% 3.27/3.67 (22) {G1,W3,D2,L1,V1,M1} R(18,3) { leq( X, X ) }.
% 3.27/3.67 (37) {G1,W6,D2,L2,V1,M2} P(17,2) { zero = X, ! leq( X, zero ) }.
% 3.27/3.67 (86) {G2,W8,D3,L2,V2,M2} P(37,9) { multiplication( X, Y ) ==> X, ! leq( X,
% 3.27/3.67 zero ) }.
% 3.27/3.67 (109) {G3,W12,D4,L2,V3,M2} P(86,4) { multiplication( multiplication( Z, X )
% 3.27/3.67 , Y ) ==> multiplication( Z, X ), ! leq( X, zero ) }.
% 3.27/3.67 (120) {G1,W9,D5,L1,V1,M1} P(10,0) { addition( multiplication( X, star( X )
% 3.27/3.67 ), one ) ==> star( X ) }.
% 3.27/3.67 (198) {G1,W13,D4,L2,V2,M2} P(3,13) { ! leq( multiplication( X, Y ), X ),
% 3.27/3.67 leq( multiplication( multiplication( X, Y ), star( Y ) ), X ) }.
% 3.27/3.67 (305) {G2,W13,D4,L2,V1,M2} P(37,19) { ! addition( one, multiplication(
% 3.27/3.67 skol1, X ) ) ==> strong_iteration( multiplication( skol1, X ) ), ! leq( X
% 3.27/3.67 , zero ) }.
% 3.27/3.67 (3365) {G4,W13,D4,L2,V2,M2} P(109,14) { addition( multiplication( X, Y ),
% 3.27/3.67 one ) ==> strong_iteration( multiplication( X, Y ) ), ! leq( Y, zero )
% 3.27/3.67 }.
% 3.27/3.67 (3366) {G4,W13,D4,L2,V2,M2} P(109,10) { addition( one, multiplication( X, Y
% 3.27/3.67 ) ) ==> star( multiplication( X, Y ) ), ! leq( Y, zero ) }.
% 3.27/3.67 (3889) {G5,W12,D4,L2,V2,M2} P(109,120);d(3365) { ! leq( Y, zero ),
% 3.27/3.67 strong_iteration( multiplication( X, Y ) ) ==> star( multiplication( X, Y
% 3.27/3.67 ) ) }.
% 3.27/3.67 (13601) {G6,W3,D2,L1,V1,M1} S(305);d(3366);d(3889);q { ! leq( X, zero ) }.
% 3.27/3.67 (13602) {G7,W0,D0,L0,V0,M0} R(13601,198);d(9);r(22) { }.
% 3.27/3.67
% 3.27/3.67
% 3.27/3.67 % SZS output end Refutation
% 3.27/3.67 found a proof!
% 3.27/3.67
% 3.27/3.67
% 3.27/3.67 Unprocessed initial clauses:
% 3.27/3.67
% 3.27/3.67 (13604) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X ) }.
% 3.27/3.67 (13605) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) = addition
% 3.27/3.67 ( addition( Z, Y ), X ) }.
% 3.27/3.67 (13606) {G0,W5,D3,L1,V1,M1} { addition( X, zero ) = X }.
% 3.27/3.67 (13607) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 3.27/3.67 (13608) {G0,W11,D4,L1,V3,M1} { multiplication( X, multiplication( Y, Z ) )
% 3.27/3.67 = multiplication( multiplication( X, Y ), Z ) }.
% 3.27/3.67 (13609) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 3.27/3.67 (13610) {G0,W5,D3,L1,V1,M1} { multiplication( one, X ) = X }.
% 3.27/3.67 (13611) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y, Z ) ) =
% 3.27/3.67 addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 3.27/3.67 (13612) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Y ), Z ) =
% 3.27/3.67 addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 3.27/3.67 (13613) {G0,W5,D3,L1,V1,M1} { multiplication( zero, X ) = zero }.
% 3.27/3.67 (13614) {G0,W9,D5,L1,V1,M1} { addition( one, multiplication( X, star( X )
% 3.27/3.67 ) ) = star( X ) }.
% 3.27/3.67 (13615) {G0,W9,D5,L1,V1,M1} { addition( one, multiplication( star( X ), X
% 3.27/3.67 ) ) = star( X ) }.
% 3.27/3.67 (13616) {G0,W13,D4,L2,V3,M2} { ! leq( addition( multiplication( X, Z ), Y
% 3.27/3.67 ), Z ), leq( multiplication( star( X ), Y ), Z ) }.
% 3.27/3.67 (13617) {G0,W13,D4,L2,V3,M2} { ! leq( addition( multiplication( Z, X ), Y
% 3.27/3.67 ), Z ), leq( multiplication( Y, star( X ) ), Z ) }.
% 3.27/3.67 (13618) {G0,W9,D5,L1,V1,M1} { strong_iteration( X ) = addition(
% 3.27/3.67 multiplication( X, strong_iteration( X ) ), one ) }.
% 3.27/3.67 (13619) {G0,W13,D4,L2,V3,M2} { ! leq( Z, addition( multiplication( X, Z )
% 3.27/3.67 , Y ) ), leq( Z, multiplication( strong_iteration( X ), Y ) ) }.
% 3.27/3.67 (13620) {G0,W10,D5,L1,V1,M1} { strong_iteration( X ) = addition( star( X )
% 3.27/3.67 , multiplication( strong_iteration( X ), zero ) ) }.
% 3.27/3.67 (13621) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y }.
% 3.27/3.67 (13622) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 3.27/3.67 (13623) {G0,W10,D4,L1,V0,M1} { ! strong_iteration( multiplication( skol1,
% 3.27/3.67 zero ) ) = addition( one, multiplication( skol1, zero ) ) }.
% 3.27/3.67
% 3.27/3.67
% 3.27/3.67 Total Proof:
% 3.27/3.67
% 3.27/3.67 subsumption: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X
% 3.27/3.67 ) }.
% 3.27/3.67 parent0: (13604) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X )
% 3.27/3.67 }.
% 3.27/3.67 substitution0:
% 3.27/3.67 X := X
% 3.27/3.67 Y := Y
% 3.27/3.67 end
% 3.27/3.67 permutation0:
% 3.27/3.67 0 ==> 0
% 3.27/3.67 end
% 3.27/3.67
% 3.27/3.67 subsumption: (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 3.27/3.67 parent0: (13606) {G0,W5,D3,L1,V1,M1} { addition( X, zero ) = X }.
% 3.27/3.67 substitution0:
% 3.27/3.67 X := X
% 3.27/3.67 end
% 3.27/3.67 permutation0:
% 3.27/3.67 0 ==> 0
% 3.27/3.67 end
% 3.27/3.67
% 3.27/3.67 subsumption: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 3.27/3.67 parent0: (13607) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 3.27/3.67 substitution0:
% 3.27/3.67 X := X
% 3.27/3.67 end
% 3.27/3.67 permutation0:
% 3.27/3.67 0 ==> 0
% 3.27/3.67 end
% 3.27/3.67
% 3.27/3.67 subsumption: (4) {G0,W11,D4,L1,V3,M1} I { multiplication( X, multiplication
% 3.27/3.67 ( Y, Z ) ) ==> multiplication( multiplication( X, Y ), Z ) }.
% 3.27/3.67 parent0: (13608) {G0,W11,D4,L1,V3,M1} { multiplication( X, multiplication
% 3.27/3.67 ( Y, Z ) ) = multiplication( multiplication( X, Y ), Z ) }.
% 3.27/3.67 substitution0:
% 3.27/3.67 X := X
% 3.27/3.67 Y := Y
% 3.27/3.67 Z := Z
% 3.27/3.67 end
% 3.27/3.67 permutation0:
% 3.27/3.67 0 ==> 0
% 3.27/3.67 end
% 3.27/3.67
% 3.27/3.67 subsumption: (9) {G0,W5,D3,L1,V1,M1} I { multiplication( zero, X ) ==> zero
% 3.27/3.67 }.
% 3.27/3.67 parent0: (13613) {G0,W5,D3,L1,V1,M1} { multiplication( zero, X ) = zero
% 3.27/3.67 }.
% 3.27/3.67 substitution0:
% 3.27/3.67 X := X
% 3.27/3.67 end
% 3.27/3.67 permutation0:
% 3.27/3.67 0 ==> 0
% 3.27/3.67 end
% 3.27/3.67
% 3.27/3.67 subsumption: (10) {G0,W9,D5,L1,V1,M1} I { addition( one, multiplication( X
% 3.27/3.67 , star( X ) ) ) ==> star( X ) }.
% 3.27/3.67 parent0: (13614) {G0,W9,D5,L1,V1,M1} { addition( one, multiplication( X,
% 3.27/3.67 star( X ) ) ) = star( X ) }.
% 3.27/3.67 substitution0:
% 3.27/3.67 X := X
% 3.27/3.67 end
% 3.27/3.67 permutation0:
% 3.27/3.67 0 ==> 0
% 3.27/3.67 end
% 3.27/3.67
% 3.27/3.67 subsumption: (13) {G0,W13,D4,L2,V3,M2} I { ! leq( addition( multiplication
% 3.27/3.67 ( Z, X ), Y ), Z ), leq( multiplication( Y, star( X ) ), Z ) }.
% 3.27/3.67 parent0: (13617) {G0,W13,D4,L2,V3,M2} { ! leq( addition( multiplication( Z
% 3.27/3.67 , X ), Y ), Z ), leq( multiplication( Y, star( X ) ), Z ) }.
% 3.27/3.67 substitution0:
% 3.27/3.67 X := X
% 3.27/3.67 Y := Y
% 3.27/3.67 Z := Z
% 3.27/3.67 end
% 3.27/3.67 permutation0:
% 3.27/3.67 0 ==> 0
% 3.27/3.67 1 ==> 1
% 3.27/3.67 end
% 3.27/3.67
% 3.27/3.67 eqswap: (13674) {G0,W9,D5,L1,V1,M1} { addition( multiplication( X,
% 3.27/3.67 strong_iteration( X ) ), one ) = strong_iteration( X ) }.
% 3.27/3.67 parent0[0]: (13618) {G0,W9,D5,L1,V1,M1} { strong_iteration( X ) = addition
% 3.27/3.67 ( multiplication( X, strong_iteration( X ) ), one ) }.
% 3.27/3.67 substitution0:
% 3.27/3.67 X := X
% 3.27/3.67 end
% 3.27/3.67
% 3.27/3.67 subsumption: (14) {G0,W9,D5,L1,V1,M1} I { addition( multiplication( X,
% 3.27/3.67 strong_iteration( X ) ), one ) ==> strong_iteration( X ) }.
% 3.27/3.67 parent0: (13674) {G0,W9,D5,L1,V1,M1} { addition( multiplication( X,
% 3.27/3.67 strong_iteration( X ) ), one ) = strong_iteration( X ) }.
% 3.27/3.67 substitution0:
% 3.27/3.67 X := X
% 3.27/3.67 end
% 3.27/3.67 permutation0:
% 3.27/3.67 0 ==> 0
% 3.27/3.67 end
% 3.27/3.67
% 3.27/3.67 subsumption: (17) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 16.61/17.02 ==> Y }.
% 16.61/17.02 parent0: (13621) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y
% 16.61/17.02 }.
% 16.61/17.02 substitution0:
% 16.61/17.02 X := X
% 16.61/17.02 Y := Y
% 16.61/17.02 end
% 16.61/17.02 permutation0:
% 16.61/17.02 0 ==> 0
% 16.61/17.02 1 ==> 1
% 16.61/17.02 end
% 16.61/17.02
% 16.61/17.02 subsumption: (18) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X
% 16.61/17.02 , Y ) }.
% 16.61/17.02 parent0: (13622) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y )
% 16.61/17.02 }.
% 16.61/17.02 substitution0:
% 16.61/17.02 X := X
% 16.61/17.02 Y := Y
% 16.61/17.02 end
% 16.61/17.02 permutation0:
% 16.61/17.02 0 ==> 0
% 16.61/17.02 1 ==> 1
% 16.61/17.02 end
% 16.61/17.02
% 16.61/17.02 eqswap: (13719) {G0,W10,D4,L1,V0,M1} { ! addition( one, multiplication(
% 16.61/17.02 skol1, zero ) ) = strong_iteration( multiplication( skol1, zero ) ) }.
% 16.61/17.02 parent0[0]: (13623) {G0,W10,D4,L1,V0,M1} { ! strong_iteration(
% 16.61/17.02 multiplication( skol1, zero ) ) = addition( one, multiplication( skol1,
% 16.61/17.02 zero ) ) }.
% 16.61/17.02 substitution0:
% 16.61/17.02 end
% 16.61/17.02
% 16.61/17.02 subsumption: (19) {G0,W10,D4,L1,V0,M1} I { ! addition( one, multiplication
% 16.61/17.02 ( skol1, zero ) ) ==> strong_iteration( multiplication( skol1, zero ) )
% 16.61/17.02 }.
% 16.61/17.02 parent0: (13719) {G0,W10,D4,L1,V0,M1} { ! addition( one, multiplication(
% 16.61/17.02 skol1, zero ) ) = strong_iteration( multiplication( skol1, zero ) ) }.
% 16.61/17.02 substitution0:
% 16.61/17.02 end
% 16.61/17.02 permutation0:
% 16.61/17.02 0 ==> 0
% 16.61/17.02 end
% 16.61/17.02
% 16.61/17.02 eqswap: (13720) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y
% 16.61/17.02 ) }.
% 16.61/17.02 parent0[0]: (18) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 16.61/17.02 Y ) }.
% 16.61/17.02 substitution0:
% 16.61/17.02 X := X
% 16.61/17.02 Y := Y
% 16.61/17.02 end
% 16.61/17.02
% 16.61/17.02 eqswap: (13721) {G0,W5,D3,L1,V1,M1} { X ==> addition( X, X ) }.
% 16.61/17.02 parent0[0]: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 16.61/17.02 substitution0:
% 16.61/17.02 X := X
% 16.61/17.02 end
% 16.61/17.02
% 16.61/17.02 resolution: (13722) {G1,W3,D2,L1,V1,M1} { leq( X, X ) }.
% 16.61/17.02 parent0[0]: (13720) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X
% 16.61/17.02 , Y ) }.
% 16.61/17.02 parent1[0]: (13721) {G0,W5,D3,L1,V1,M1} { X ==> addition( X, X ) }.
% 16.61/17.02 substitution0:
% 16.61/17.02 X := X
% 16.61/17.02 Y := X
% 16.61/17.02 end
% 16.61/17.02 substitution1:
% 16.61/17.02 X := X
% 16.61/17.02 end
% 16.61/17.02
% 16.61/17.02 subsumption: (22) {G1,W3,D2,L1,V1,M1} R(18,3) { leq( X, X ) }.
% 16.61/17.02 parent0: (13722) {G1,W3,D2,L1,V1,M1} { leq( X, X ) }.
% 16.61/17.02 substitution0:
% 16.61/17.02 X := X
% 16.61/17.02 end
% 16.61/17.02 permutation0:
% 16.61/17.02 0 ==> 0
% 16.61/17.02 end
% 16.61/17.02
% 16.61/17.02 eqswap: (13723) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X, Y
% 16.61/17.02 ) }.
% 16.61/17.02 parent0[1]: (17) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 16.61/17.02 ==> Y }.
% 16.61/17.02 substitution0:
% 16.61/17.02 X := X
% 16.61/17.02 Y := Y
% 16.61/17.02 end
% 16.61/17.02
% 16.61/17.02 paramod: (13725) {G1,W6,D2,L2,V1,M2} { zero ==> X, ! leq( X, zero ) }.
% 16.61/17.02 parent0[0]: (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 16.61/17.02 parent1[0; 2]: (13723) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq
% 16.61/17.02 ( X, Y ) }.
% 16.61/17.02 substitution0:
% 16.61/17.02 X := X
% 16.61/17.02 end
% 16.61/17.02 substitution1:
% 16.61/17.02 X := X
% 16.61/17.02 Y := zero
% 16.61/17.02 end
% 16.61/17.02
% 16.61/17.02 subsumption: (37) {G1,W6,D2,L2,V1,M2} P(17,2) { zero = X, ! leq( X, zero )
% 16.61/17.02 }.
% 16.61/17.02 parent0: (13725) {G1,W6,D2,L2,V1,M2} { zero ==> X, ! leq( X, zero ) }.
% 16.61/17.02 substitution0:
% 16.61/17.02 X := X
% 16.61/17.02 end
% 16.61/17.02 permutation0:
% 16.61/17.02 0 ==> 0
% 16.61/17.02 1 ==> 1
% 16.61/17.02 end
% 16.61/17.02
% 16.61/17.02 *** allocated 256285 integers for termspace/termends
% 16.61/17.02 *** allocated 15000 integers for justifications
% 16.61/17.02 *** allocated 22500 integers for justifications
% 16.61/17.02 *** allocated 33750 integers for justifications
% 16.61/17.02 *** allocated 50625 integers for justifications
% 16.61/17.02 *** allocated 75937 integers for justifications
% 16.61/17.02 *** allocated 113905 integers for justifications
% 16.61/17.02 *** allocated 384427 integers for termspace/termends
% 16.61/17.02 *** allocated 170857 integers for justifications
% 16.61/17.02 *** allocated 256285 integers for justifications
% 16.61/17.02 *** allocated 1297440 integers for clauses
% 16.61/17.02 eqswap: (13728) {G0,W5,D3,L1,V1,M1} { zero ==> multiplication( zero, X )
% 16.61/17.02 }.
% 16.61/17.02 parent0[0]: (9) {G0,W5,D3,L1,V1,M1} I { multiplication( zero, X ) ==> zero
% 16.61/17.02 }.
% 16.61/17.02 substitution0:
% 16.61/17.02 X := X
% 16.61/17.02 end
% 16.61/17.02
% 16.61/17.02 paramod: (13776) {G1,W8,D3,L2,V2,M2} { zero ==> multiplication( Y, X ), !
% 16.61/17.02 leq( Y, zero ) }.
% 16.61/17.02 parent0[0]: (37) {G1,W6,D2,L2,V1,M2} P(17,2) { zero = X, ! leq( X, zero )
% 16.61/17.02 }.
% 16.61/17.02 parent1[0; 3]: (13728) {G0,W5,D3,L1,V1,M1} { zero ==> multiplication( zero
% 16.61/17.02 , X ) }.
% 16.61/17.02 substitution0:
% 16.61/17.02 X := Y
% 16.61/17.02 end
% 16.61/17.02 substitution1:
% 16.61/17.02 X := X
% 16.61/17.02 end
% 16.61/17.02
% 16.61/17.02 paramod: (13777) {G2,W11,D3,L3,V3,M3} { Z ==> multiplication( X, Y ), !
% 16.61/17.02 leq( Z, zero ), ! leq( X, zero ) }.
% 16.61/17.02 parent0[0]: (37) {G1,W6,D2,L2,V1,M2} P(17,2) { zero = X, ! leq( X, zero )
% 16.61/17.02 }.
% 16.61/17.02 parent1[0; 1]: (13776) {G1,W8,D3,L2,V2,M2} { zero ==> multiplication( Y, X
% 16.61/17.02 ), ! leq( Y, zero ) }.
% 16.61/17.02 substitution0:
% 16.61/17.02 X := Z
% 16.61/17.02 end
% 16.61/17.02 substitution1:
% 16.61/17.02 X := Y
% 16.61/17.02 Y := X
% 16.61/17.02 end
% 16.61/17.02
% 16.61/17.02 eqswap: (13798) {G2,W11,D3,L3,V3,M3} { multiplication( Y, Z ) ==> X, ! leq
% 30.00/30.36 ( X, zero ), ! leq( Y, zero ) }.
% 30.00/30.36 parent0[0]: (13777) {G2,W11,D3,L3,V3,M3} { Z ==> multiplication( X, Y ), !
% 30.00/30.36 leq( Z, zero ), ! leq( X, zero ) }.
% 30.00/30.36 substitution0:
% 30.00/30.36 X := Y
% 30.00/30.36 Y := Z
% 30.00/30.36 Z := X
% 30.00/30.36 end
% 30.00/30.36
% 30.00/30.36 factor: (18655) {G2,W8,D3,L2,V2,M2} { multiplication( X, Y ) ==> X, ! leq
% 30.00/30.36 ( X, zero ) }.
% 30.00/30.36 parent0[1, 2]: (13798) {G2,W11,D3,L3,V3,M3} { multiplication( Y, Z ) ==> X
% 30.00/30.36 , ! leq( X, zero ), ! leq( Y, zero ) }.
% 30.00/30.36 substitution0:
% 30.00/30.36 X := X
% 30.00/30.36 Y := X
% 30.00/30.36 Z := Y
% 30.00/30.36 end
% 30.00/30.36
% 30.00/30.36 subsumption: (86) {G2,W8,D3,L2,V2,M2} P(37,9) { multiplication( X, Y ) ==>
% 30.00/30.36 X, ! leq( X, zero ) }.
% 30.00/30.36 parent0: (18655) {G2,W8,D3,L2,V2,M2} { multiplication( X, Y ) ==> X, ! leq
% 30.00/30.36 ( X, zero ) }.
% 30.00/30.36 substitution0:
% 30.00/30.36 X := X
% 30.00/30.36 Y := Y
% 30.00/30.36 end
% 30.00/30.36 permutation0:
% 30.00/30.36 0 ==> 0
% 30.00/30.36 1 ==> 1
% 30.00/30.36 end
% 30.00/30.36
% 30.00/30.36 eqswap: (18658) {G0,W11,D4,L1,V3,M1} { multiplication( multiplication( X,
% 30.00/30.36 Y ), Z ) ==> multiplication( X, multiplication( Y, Z ) ) }.
% 30.00/30.36 parent0[0]: (4) {G0,W11,D4,L1,V3,M1} I { multiplication( X, multiplication
% 30.00/30.36 ( Y, Z ) ) ==> multiplication( multiplication( X, Y ), Z ) }.
% 30.00/30.36 substitution0:
% 30.00/30.36 X := X
% 30.00/30.36 Y := Y
% 30.00/30.36 Z := Z
% 30.00/30.36 end
% 30.00/30.36
% 30.00/30.36 paramod: (18664) {G1,W12,D4,L2,V3,M2} { multiplication( multiplication( X
% 30.00/30.36 , Y ), Z ) ==> multiplication( X, Y ), ! leq( Y, zero ) }.
% 30.00/30.36 parent0[0]: (86) {G2,W8,D3,L2,V2,M2} P(37,9) { multiplication( X, Y ) ==> X
% 30.00/30.36 , ! leq( X, zero ) }.
% 30.00/30.36 parent1[0; 8]: (18658) {G0,W11,D4,L1,V3,M1} { multiplication(
% 30.00/30.36 multiplication( X, Y ), Z ) ==> multiplication( X, multiplication( Y, Z )
% 30.00/30.36 ) }.
% 30.00/30.36 substitution0:
% 30.00/30.36 X := Y
% 30.00/30.36 Y := Z
% 30.00/30.36 end
% 30.00/30.36 substitution1:
% 30.00/30.36 X := X
% 30.00/30.36 Y := Y
% 30.00/30.36 Z := Z
% 30.00/30.36 end
% 30.00/30.36
% 30.00/30.36 subsumption: (109) {G3,W12,D4,L2,V3,M2} P(86,4) { multiplication(
% 30.00/30.36 multiplication( Z, X ), Y ) ==> multiplication( Z, X ), ! leq( X, zero )
% 30.00/30.36 }.
% 30.00/30.36 parent0: (18664) {G1,W12,D4,L2,V3,M2} { multiplication( multiplication( X
% 30.00/30.36 , Y ), Z ) ==> multiplication( X, Y ), ! leq( Y, zero ) }.
% 30.00/30.36 substitution0:
% 30.00/30.36 X := Z
% 30.00/30.36 Y := X
% 30.00/30.36 Z := Y
% 30.00/30.36 end
% 30.00/30.36 permutation0:
% 30.00/30.36 0 ==> 0
% 30.00/30.36 1 ==> 1
% 30.00/30.36 end
% 30.00/30.36
% 30.00/30.36 eqswap: (18692) {G0,W9,D5,L1,V1,M1} { star( X ) ==> addition( one,
% 30.00/30.36 multiplication( X, star( X ) ) ) }.
% 30.00/30.36 parent0[0]: (10) {G0,W9,D5,L1,V1,M1} I { addition( one, multiplication( X,
% 30.00/30.36 star( X ) ) ) ==> star( X ) }.
% 30.00/30.36 substitution0:
% 30.00/30.36 X := X
% 30.00/30.36 end
% 30.00/30.36
% 30.00/30.36 paramod: (18693) {G1,W9,D5,L1,V1,M1} { star( X ) ==> addition(
% 30.00/30.36 multiplication( X, star( X ) ), one ) }.
% 30.00/30.36 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 30.00/30.36 }.
% 30.00/30.36 parent1[0; 3]: (18692) {G0,W9,D5,L1,V1,M1} { star( X ) ==> addition( one,
% 30.00/30.36 multiplication( X, star( X ) ) ) }.
% 30.00/30.36 substitution0:
% 30.00/30.36 X := one
% 30.00/30.36 Y := multiplication( X, star( X ) )
% 30.00/30.36 end
% 30.00/30.36 substitution1:
% 30.00/30.36 X := X
% 30.00/30.36 end
% 30.00/30.36
% 30.00/30.36 eqswap: (18696) {G1,W9,D5,L1,V1,M1} { addition( multiplication( X, star( X
% 30.00/30.36 ) ), one ) ==> star( X ) }.
% 30.00/30.36 parent0[0]: (18693) {G1,W9,D5,L1,V1,M1} { star( X ) ==> addition(
% 30.00/30.36 multiplication( X, star( X ) ), one ) }.
% 30.00/30.36 substitution0:
% 30.00/30.36 X := X
% 30.00/30.36 end
% 30.00/30.36
% 30.00/30.36 subsumption: (120) {G1,W9,D5,L1,V1,M1} P(10,0) { addition( multiplication(
% 30.00/30.36 X, star( X ) ), one ) ==> star( X ) }.
% 30.00/30.36 parent0: (18696) {G1,W9,D5,L1,V1,M1} { addition( multiplication( X, star(
% 30.00/30.36 X ) ), one ) ==> star( X ) }.
% 30.00/30.36 substitution0:
% 30.00/30.36 X := X
% 30.00/30.36 end
% 30.00/30.36 permutation0:
% 30.00/30.36 0 ==> 0
% 30.00/30.36 end
% 30.00/30.36
% 30.00/30.36 paramod: (18698) {G1,W13,D4,L2,V2,M2} { ! leq( multiplication( X, Y ), X )
% 30.00/30.36 , leq( multiplication( multiplication( X, Y ), star( Y ) ), X ) }.
% 30.00/30.36 parent0[0]: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 30.00/30.36 parent1[0; 2]: (13) {G0,W13,D4,L2,V3,M2} I { ! leq( addition(
% 30.00/30.36 multiplication( Z, X ), Y ), Z ), leq( multiplication( Y, star( X ) ), Z
% 30.00/30.36 ) }.
% 30.00/30.36 substitution0:
% 30.00/30.36 X := multiplication( X, Y )
% 30.00/30.36 end
% 30.00/30.36 substitution1:
% 30.00/30.36 X := Y
% 30.00/30.36 Y := multiplication( X, Y )
% 30.00/30.36 Z := X
% 30.00/30.36 end
% 30.00/30.36
% 30.00/30.36 subsumption: (198) {G1,W13,D4,L2,V2,M2} P(3,13) { ! leq( multiplication( X
% 30.00/30.36 , Y ), X ), leq( multiplication( multiplication( X, Y ), star( Y ) ), X )
% 30.00/30.36 }.
% 30.00/30.36 parent0: (18698) {G1,W13,D4,L2,V2,M2} { ! leq( multiplication( X, Y ), X )
% 30.00/30.36 , leq( multiplication( multiplication( X, Y ), star( Y ) ), X ) }.
% 30.00/30.36 substitution0:
% 30.00/30.36 X := X
% 30.00/30.36 Y := Y
% 30.00/30.36 end
% 30.00/30.36 permutation0:
% 30.00/30.36 0 ==> 0
% 30.00/30.36 1 ==> 1
% 30.00/30.36 end
% 30.00/30.36
% 30.00/30.36 *** allocated 576640 integers for termspace/termends
% 30.00/30.36 eqswap: (18700) {G0,W10,D4,L1,V0,M1} { ! strong_iteration( multiplication
% 30.00/30.36 ( skol1, zero ) ) ==> addition( one, multiplication( skol1, zero ) ) }.
% 30.00/30.36 parent0[0]: (19) {G0,W10,D4,L1,V0,M1} I { ! addition( one, multiplication(
% 30.00/30.36 skol1, zero ) ) ==> strong_iteration( multiplication( skol1, zero ) ) }.
% 30.00/30.36 substitution0:
% 30.00/30.36 end
% 30.00/30.36
% 30.00/30.36 paramod: (18946) {G1,W13,D4,L2,V1,M2} { ! strong_iteration( multiplication
% 30.00/30.36 ( skol1, zero ) ) ==> addition( one, multiplication( skol1, X ) ), ! leq
% 30.00/30.36 ( X, zero ) }.
% 30.00/30.36 parent0[0]: (37) {G1,W6,D2,L2,V1,M2} P(17,2) { zero = X, ! leq( X, zero )
% 30.00/30.36 }.
% 30.00/30.36 parent1[0; 10]: (18700) {G0,W10,D4,L1,V0,M1} { ! strong_iteration(
% 30.00/30.36 multiplication( skol1, zero ) ) ==> addition( one, multiplication( skol1
% 30.00/30.36 , zero ) ) }.
% 30.00/30.36 substitution0:
% 30.00/30.36 X := X
% 30.00/30.36 end
% 30.00/30.36 substitution1:
% 30.00/30.36 end
% 30.00/30.36
% 30.00/30.36 paramod: (18947) {G2,W16,D4,L3,V2,M3} { ! strong_iteration( multiplication
% 30.00/30.36 ( skol1, Y ) ) ==> addition( one, multiplication( skol1, X ) ), ! leq( Y
% 30.00/30.36 , zero ), ! leq( X, zero ) }.
% 30.00/30.36 parent0[0]: (37) {G1,W6,D2,L2,V1,M2} P(17,2) { zero = X, ! leq( X, zero )
% 30.00/30.36 }.
% 30.00/30.36 parent1[0; 5]: (18946) {G1,W13,D4,L2,V1,M2} { ! strong_iteration(
% 30.00/30.36 multiplication( skol1, zero ) ) ==> addition( one, multiplication( skol1
% 30.00/30.36 , X ) ), ! leq( X, zero ) }.
% 30.00/30.36 substitution0:
% 30.00/30.36 X := Y
% 30.00/30.36 end
% 30.00/30.36 substitution1:
% 30.00/30.36 X := X
% 30.00/30.36 end
% 30.00/30.36
% 30.00/30.36 eqswap: (18968) {G2,W16,D4,L3,V2,M3} { ! addition( one, multiplication(
% 30.00/30.36 skol1, Y ) ) ==> strong_iteration( multiplication( skol1, X ) ), ! leq( X
% 30.00/30.36 , zero ), ! leq( Y, zero ) }.
% 30.00/30.36 parent0[0]: (18947) {G2,W16,D4,L3,V2,M3} { ! strong_iteration(
% 30.00/30.36 multiplication( skol1, Y ) ) ==> addition( one, multiplication( skol1, X
% 30.00/30.36 ) ), ! leq( Y, zero ), ! leq( X, zero ) }.
% 30.00/30.36 substitution0:
% 30.00/30.36 X := Y
% 30.00/30.36 Y := X
% 30.00/30.36 end
% 30.00/30.36
% 30.00/30.36 factor: (23825) {G2,W13,D4,L2,V1,M2} { ! addition( one, multiplication(
% 30.00/30.36 skol1, X ) ) ==> strong_iteration( multiplication( skol1, X ) ), ! leq( X
% 30.00/30.36 , zero ) }.
% 30.00/30.36 parent0[1, 2]: (18968) {G2,W16,D4,L3,V2,M3} { ! addition( one,
% 30.00/30.36 multiplication( skol1, Y ) ) ==> strong_iteration( multiplication( skol1
% 30.00/30.36 , X ) ), ! leq( X, zero ), ! leq( Y, zero ) }.
% 30.00/30.36 substitution0:
% 30.00/30.36 X := X
% 30.00/30.36 Y := X
% 30.00/30.36 end
% 30.00/30.36
% 30.00/30.36 subsumption: (305) {G2,W13,D4,L2,V1,M2} P(37,19) { ! addition( one,
% 30.00/30.36 multiplication( skol1, X ) ) ==> strong_iteration( multiplication( skol1
% 30.00/30.36 , X ) ), ! leq( X, zero ) }.
% 30.00/30.36 parent0: (23825) {G2,W13,D4,L2,V1,M2} { ! addition( one, multiplication(
% 30.00/30.36 skol1, X ) ) ==> strong_iteration( multiplication( skol1, X ) ), ! leq( X
% 30.00/30.36 , zero ) }.
% 30.00/30.36 substitution0:
% 30.00/30.36 X := X
% 30.00/30.36 end
% 30.00/30.36 permutation0:
% 30.00/30.36 0 ==> 0
% 30.00/30.36 1 ==> 1
% 30.00/30.36 end
% 30.00/30.36
% 30.00/30.36 eqswap: (23828) {G0,W9,D5,L1,V1,M1} { strong_iteration( X ) ==> addition(
% 30.00/30.36 multiplication( X, strong_iteration( X ) ), one ) }.
% 30.00/30.36 parent0[0]: (14) {G0,W9,D5,L1,V1,M1} I { addition( multiplication( X,
% 30.00/30.36 strong_iteration( X ) ), one ) ==> strong_iteration( X ) }.
% 30.00/30.36 substitution0:
% 30.00/30.36 X := X
% 30.00/30.36 end
% 30.00/30.36
% 30.00/30.36 paramod: (23829) {G1,W13,D4,L2,V2,M2} { strong_iteration( multiplication(
% 30.00/30.36 X, Y ) ) ==> addition( multiplication( X, Y ), one ), ! leq( Y, zero )
% 30.00/30.36 }.
% 30.00/30.36 parent0[0]: (109) {G3,W12,D4,L2,V3,M2} P(86,4) { multiplication(
% 30.00/30.36 multiplication( Z, X ), Y ) ==> multiplication( Z, X ), ! leq( X, zero )
% 30.00/30.36 }.
% 30.00/30.36 parent1[0; 6]: (23828) {G0,W9,D5,L1,V1,M1} { strong_iteration( X ) ==>
% 30.00/30.36 addition( multiplication( X, strong_iteration( X ) ), one ) }.
% 30.00/30.36 substitution0:
% 30.00/30.36 X := Y
% 30.00/30.36 Y := strong_iteration( multiplication( X, Y ) )
% 30.00/30.36 Z := X
% 30.00/30.36 end
% 30.00/30.36 substitution1:
% 30.00/30.36 X := multiplication( X, Y )
% 30.00/30.36 end
% 30.00/30.36
% 30.00/30.36 eqswap: (23830) {G1,W13,D4,L2,V2,M2} { addition( multiplication( X, Y ),
% 30.00/30.36 one ) ==> strong_iteration( multiplication( X, Y ) ), ! leq( Y, zero )
% 30.00/30.36 }.
% 30.00/30.36 parent0[0]: (23829) {G1,W13,D4,L2,V2,M2} { strong_iteration(
% 30.00/30.36 multiplication( X, Y ) ) ==> addition( multiplication( X, Y ), one ), !
% 30.00/30.36 leq( Y, zero ) }.
% 30.00/30.36 substitution0:
% 30.00/30.36 X := X
% 30.00/30.36 Y := Y
% 30.00/30.36 end
% 30.00/30.36
% 30.00/30.36 subsumption: (3365) {G4,W13,D4,L2,V2,M2} P(109,14) { addition(
% 30.00/30.36 multiplication( X, Y ), one ) ==> strong_iteration( multiplication( X, Y
% 30.00/30.36 ) ), ! leq( Y, zero ) }.
% 30.00/30.36 parent0: (23830) {G1,W13,D4,L2,V2,M2} { addition( multiplication( X, Y ),
% 30.00/30.36 one ) ==> strong_iteration( multiplication( X, Y ) ), ! leq( Y, zero )
% 30.00/30.36 }.
% 30.00/30.36 substitution0:
% 30.00/30.36 X := X
% 30.00/30.36 Y := Y
% 30.00/30.36 end
% 30.00/30.36 permutation0:
% 30.00/30.36 0 ==> 0
% 30.00/30.36 1 ==> 1
% 30.00/30.36 end
% 30.00/30.36
% 30.00/30.36 eqswap: (23832) {G0,W9,D5,L1,V1,M1} { star( X ) ==> addition( one,
% 30.00/30.36 multiplication( X, star( X ) ) ) }.
% 30.00/30.36 parent0[0]: (10) {G0,W9,D5,L1,V1,M1} I { addition( one, multiplication( X,
% 30.00/30.36 star( X ) ) ) ==> star( X ) }.
% 30.00/30.36 substitution0:
% 30.00/30.36 X := X
% 30.00/30.36 end
% 30.00/30.36
% 30.00/30.36 paramod: (23833) {G1,W13,D4,L2,V2,M2} { star( multiplication( X, Y ) ) ==>
% 30.00/30.36 addition( one, multiplication( X, Y ) ), ! leq( Y, zero ) }.
% 30.00/30.36 parent0[0]: (109) {G3,W12,D4,L2,V3,M2} P(86,4) { multiplication(
% 30.00/30.36 multiplication( Z, X ), Y ) ==> multiplication( Z, X ), ! leq( X, zero )
% 30.00/30.36 }.
% 30.00/30.36 parent1[0; 7]: (23832) {G0,W9,D5,L1,V1,M1} { star( X ) ==> addition( one,
% 30.00/30.36 multiplication( X, star( X ) ) ) }.
% 30.00/30.36 substitution0:
% 30.00/30.36 X := Y
% 30.00/30.36 Y := star( multiplication( X, Y ) )
% 30.00/30.36 Z := X
% 30.00/30.36 end
% 30.00/30.36 substitution1:
% 30.00/30.36 X := multiplication( X, Y )
% 30.00/30.36 end
% 30.00/30.36
% 30.00/30.36 eqswap: (23834) {G1,W13,D4,L2,V2,M2} { addition( one, multiplication( X, Y
% 30.00/30.36 ) ) ==> star( multiplication( X, Y ) ), ! leq( Y, zero ) }.
% 30.00/30.36 parent0[0]: (23833) {G1,W13,D4,L2,V2,M2} { star( multiplication( X, Y ) )
% 30.00/30.36 ==> addition( one, multiplication( X, Y ) ), ! leq( Y, zero ) }.
% 30.00/30.36 substitution0:
% 30.00/30.36 X := X
% 30.00/30.36 Y := Y
% 30.00/30.36 end
% 30.00/30.36
% 30.00/30.36 subsumption: (3366) {G4,W13,D4,L2,V2,M2} P(109,10) { addition( one,
% 30.00/30.36 multiplication( X, Y ) ) ==> star( multiplication( X, Y ) ), ! leq( Y,
% 30.00/30.36 zero ) }.
% 30.00/30.36 parent0: (23834) {G1,W13,D4,L2,V2,M2} { addition( one, multiplication( X,
% 30.00/30.36 Y ) ) ==> star( multiplication( X, Y ) ), ! leq( Y, zero ) }.
% 30.00/30.36 substitution0:
% 30.00/30.36 X := X
% 30.00/30.36 Y := Y
% 30.00/30.36 end
% 30.00/30.36 permutation0:
% 30.00/30.36 0 ==> 0
% 30.00/30.36 1 ==> 1
% 30.00/30.36 end
% 30.00/30.36
% 30.00/30.36 eqswap: (23836) {G1,W9,D5,L1,V1,M1} { star( X ) ==> addition(
% 30.00/30.36 multiplication( X, star( X ) ), one ) }.
% 30.00/30.36 parent0[0]: (120) {G1,W9,D5,L1,V1,M1} P(10,0) { addition( multiplication( X
% 30.00/30.36 , star( X ) ), one ) ==> star( X ) }.
% 30.00/30.36 substitution0:
% 30.00/30.36 X := X
% 30.00/30.36 end
% 30.00/30.36
% 30.00/30.36 paramod: (23838) {G2,W13,D4,L2,V2,M2} { star( multiplication( X, Y ) ) ==>
% 30.00/30.36 addition( multiplication( X, Y ), one ), ! leq( Y, zero ) }.
% 30.00/30.36 parent0[0]: (109) {G3,W12,D4,L2,V3,M2} P(86,4) { multiplication(
% 30.00/30.36 multiplication( Z, X ), Y ) ==> multiplication( Z, X ), ! leq( X, zero )
% 30.00/30.36 }.
% 30.00/30.36 parent1[0; 6]: (23836) {G1,W9,D5,L1,V1,M1} { star( X ) ==> addition(
% 30.00/30.36 multiplication( X, star( X ) ), one ) }.
% 30.00/30.36 substitution0:
% 30.00/30.36 X := Y
% 30.00/30.36 Y := star( multiplication( X, Y ) )
% 30.00/30.36 Z := X
% 30.00/30.36 end
% 30.00/30.36 substitution1:
% 30.00/30.36 X := multiplication( X, Y )
% 30.00/30.36 end
% 30.00/30.36
% 30.00/30.36 paramod: (23839) {G3,W15,D4,L3,V2,M3} { star( multiplication( X, Y ) ) ==>
% 30.00/30.36 strong_iteration( multiplication( X, Y ) ), ! leq( Y, zero ), ! leq( Y,
% 30.00/30.36 zero ) }.
% 30.00/30.36 parent0[0]: (3365) {G4,W13,D4,L2,V2,M2} P(109,14) { addition(
% 30.00/30.36 multiplication( X, Y ), one ) ==> strong_iteration( multiplication( X, Y
% 30.00/30.36 ) ), ! leq( Y, zero ) }.
% 30.00/30.36 parent1[0; 5]: (23838) {G2,W13,D4,L2,V2,M2} { star( multiplication( X, Y )
% 30.00/30.36 ) ==> addition( multiplication( X, Y ), one ), ! leq( Y, zero ) }.
% 30.00/30.36 substitution0:
% 30.00/30.36 X := X
% 30.00/30.36 Y := Y
% 30.00/30.36 end
% 30.00/30.36 substitution1:
% 30.00/30.36 X := X
% 30.00/30.36 Y := Y
% 30.00/30.36 end
% 30.00/30.36
% 30.00/30.36 eqswap: (23840) {G3,W15,D4,L3,V2,M3} { strong_iteration( multiplication( X
% 30.00/30.36 , Y ) ) ==> star( multiplication( X, Y ) ), ! leq( Y, zero ), ! leq( Y,
% 30.00/30.36 zero ) }.
% 30.00/30.36 parent0[0]: (23839) {G3,W15,D4,L3,V2,M3} { star( multiplication( X, Y ) )
% 30.00/30.36 ==> strong_iteration( multiplication( X, Y ) ), ! leq( Y, zero ), ! leq(
% 30.00/30.36 Y, zero ) }.
% 30.00/30.36 substitution0:
% 30.00/30.36 X := X
% 30.00/30.36 Y := Y
% 30.00/30.36 end
% 30.00/30.36
% 30.00/30.36 factor: (23841) {G3,W12,D4,L2,V2,M2} { strong_iteration( multiplication( X
% 30.00/30.36 , Y ) ) ==> star( multiplication( X, Y ) ), ! leq( Y, zero ) }.
% 30.00/30.36 parent0[1, 2]: (23840) {G3,W15,D4,L3,V2,M3} { strong_iteration(
% 30.00/30.36 multiplication( X, Y ) ) ==> star( multiplication( X, Y ) ), ! leq( Y,
% 30.00/30.36 zero ), ! leq( Y, zero ) }.
% 30.00/30.36 substitution0:
% 30.00/30.36 X := X
% 30.00/30.36 Y := Y
% 30.00/30.36 end
% 30.00/30.36
% 30.00/30.36 subsumption: (3889) {G5,W12,D4,L2,V2,M2} P(109,120);d(3365) { ! leq( Y,
% 30.00/30.36 zero ), strong_iteration( multiplication( X, Y ) ) ==> star(
% 30.00/30.36 multiplication( X, Y ) ) }.
% 30.00/30.36 parent0: (23841) {G3,W12,D4,L2,V2,M2} { strong_iteration( multiplication(
% 30.00/30.36 X, Y ) ) ==> star( multiplication( X, Y ) ), ! leq( Y, zero ) }.
% 30.00/30.36 substitution0:
% 30.00/30.36 X := X
% 30.00/30.36 Y := Y
% 30.00/30.36 end
% 30.00/30.36 permutation0:
% 30.00/30.36 0 ==> 1
% 30.00/30.36 1 ==> 0
% 30.00/30.36 end
% 30.00/30.36
% 30.00/30.36 paramod: (23846) {G3,W15,D4,L3,V1,M3} { ! star( multiplication( skol1, X )
% 30.00/30.36 ) ==> strong_iteration( multiplication( skol1, X ) ), ! leq( X, zero ),
% 30.00/30.36 ! leq( X, zero ) }.
% 30.00/30.36 parent0[0]: (3366) {G4,W13,D4,L2,V2,M2} P(109,10) { addition( one,
% 30.00/30.36 multiplication( X, Y ) ) ==> star( multiplication( X, Y ) ), ! leq( Y,
% 30.00/30.36 zero ) }.
% 30.00/30.36 parent1[0; 2]: (305) {G2,W13,D4,L2,V1,M2} P(37,19) { ! addition( one,
% 30.00/30.36 multiplication( skol1, X ) ) ==> strong_iteration( multiplication( skol1
% 30.00/30.36 , X ) ), ! leq( X, zero ) }.
% 30.00/30.36 substitution0:
% 30.00/30.36 X := skol1
% 30.00/30.36 Y := X
% 30.00/30.36 end
% 30.00/30.36 substitution1:
% 30.00/30.36 X := X
% 30.00/30.36 end
% 30.00/30.36
% 30.00/30.36 factor: (23847) {G3,W12,D4,L2,V1,M2} { ! star( multiplication( skol1, X )
% 30.00/30.36 ) ==> strong_iteration( multiplication( skol1, X ) ), ! leq( X, zero )
% 30.00/30.36 }.
% 30.00/30.36 parent0[1, 2]: (23846) {G3,W15,D4,L3,V1,M3} { ! star( multiplication(
% 30.00/30.36 skol1, X ) ) ==> strong_iteration( multiplication( skol1, X ) ), ! leq( X
% 30.00/30.36 , zero ), ! leq( X, zero ) }.
% 30.00/30.36 substitution0:
% 30.00/30.36 X := X
% 30.00/30.36 end
% 30.00/30.36
% 30.00/30.36 paramod: (23848) {G4,W15,D4,L3,V1,M3} { ! star( multiplication( skol1, X )
% 30.00/30.36 ) ==> star( multiplication( skol1, X ) ), ! leq( X, zero ), ! leq( X,
% 30.00/30.36 zero ) }.
% 30.00/30.36 parent0[1]: (3889) {G5,W12,D4,L2,V2,M2} P(109,120);d(3365) { ! leq( Y, zero
% 30.00/30.36 ), strong_iteration( multiplication( X, Y ) ) ==> star( multiplication(
% 30.00/30.36 X, Y ) ) }.
% 30.00/30.36 parent1[0; 6]: (23847) {G3,W12,D4,L2,V1,M2} { ! star( multiplication(
% 30.00/30.36 skol1, X ) ) ==> strong_iteration( multiplication( skol1, X ) ), ! leq( X
% 30.00/30.36 , zero ) }.
% 30.00/30.36 substitution0:
% 30.00/30.36 X := skol1
% 30.00/30.36 Y := X
% 30.00/30.36 end
% 30.00/30.36 substitution1:
% 30.00/30.36 X := X
% 30.00/30.36 end
% 30.00/30.36
% 30.00/30.36 factor: (23849) {G4,W12,D4,L2,V1,M2} { ! star( multiplication( skol1, X )
% 30.00/30.36 ) ==> star( multiplication( skol1, X ) ), ! leq( X, zero ) }.
% 30.00/30.36 parent0[1, 2]: (23848) {G4,W15,D4,L3,V1,M3} { ! star( multiplication(
% 30.00/30.36 skol1, X ) ) ==> star( multiplication( skol1, X ) ), ! leq( X, zero ), !
% 30.00/30.36 leq( X, zero ) }.
% 30.00/30.36 substitution0:
% 30.00/30.36 X := X
% 30.00/30.36 end
% 30.00/30.36
% 30.00/30.36 eqrefl: (23850) {G0,W3,D2,L1,V1,M1} { ! leq( X, zero ) }.
% 30.00/30.36 parent0[0]: (23849) {G4,W12,D4,L2,V1,M2} { ! star( multiplication( skol1,
% 30.00/30.36 X ) ) ==> star( multiplication( skol1, X ) ), ! leq( X, zero ) }.
% 30.00/30.36 substitution0:
% 30.00/30.36 X := X
% 30.00/30.36 end
% 30.00/30.36
% 30.00/30.36 subsumption: (13601) {G6,W3,D2,L1,V1,M1} S(305);d(3366);d(3889);q { ! leq(
% 30.00/30.36 X, zero ) }.
% 30.00/30.36 parent0: (23850) {G0,W3,D2,L1,V1,M1} { ! leq( X, zero ) }.
% 30.00/30.36 substitution0:
% 30.00/30.36 X := X
% 30.00/30.36 end
% 30.00/30.36 permutation0:
% 30.00/30.36 0 ==> 0
% 30.00/30.36 end
% 30.00/30.36
% 30.00/30.36 resolution: (23852) {G2,W5,D3,L1,V1,M1} { ! leq( multiplication( zero, X )
% 30.00/30.36 , zero ) }.
% 30.00/30.36 parent0[0]: (13601) {G6,W3,D2,L1,V1,M1} S(305);d(3366);d(3889);q { ! leq( X
% 30.00/30.36 , zero ) }.
% 30.00/30.36 parent1[1]: (198) {G1,W13,D4,L2,V2,M2} P(3,13) { ! leq( multiplication( X,
% 30.00/30.36 Y ), X ), leq( multiplication( multiplication( X, Y ), star( Y ) ), X )
% 30.00/30.36 }.
% 30.00/30.36 substitution0:
% 30.00/30.36 X := multiplication( multiplication( zero, X ), star( X ) )
% 30.00/30.36 end
% 30.00/30.36 substitution1:
% 30.00/30.36 X := zero
% 30.00/30.36 Y := X
% 30.00/30.36 end
% 30.00/30.36
% 30.00/30.36 paramod: (23853) {G1,W3,D2,L1,V0,M1} { ! leq( zero, zero ) }.
% 30.00/30.36 parent0[0]: (9) {G0,W5,D3,L1,V1,M1} I { multiplication( zero, X ) ==> zero
% 30.00/30.36 }.
% 30.00/30.36 parent1[0; 2]: (23852) {G2,W5,D3,L1,V1,M1} { ! leq( multiplication( zero,
% 30.00/30.36 X ), zero ) }.
% 30.00/30.36 substitution0:
% 30.00/30.36 X := X
% 30.00/30.36 end
% 30.00/30.36 substitution1:
% 30.00/30.36 X := X
% 30.00/30.36 end
% 30.00/30.36
% 30.00/30.36 resolution: (23854) {G2,W0,D0,L0,V0,M0} { }.
% 30.00/30.36 parent0[0]: (23853) {G1,W3,D2,L1,V0,M1} { ! leq( zero, zero ) }.
% 30.00/30.36 parent1[0]: (22) {G1,W3,D2,L1,V1,M1} R(18,3) { leq( X, X ) }.
% 30.00/30.36 substitution0:
% 30.00/30.36 end
% 30.00/30.36 substitution1:
% 30.00/30.36 X := zero
% 30.00/30.36 end
% 30.00/30.36
% 30.00/30.36 subsumption: (13602) {G7,W0,D0,L0,V0,M0} R(13601,198);d(9);r(22) { }.
% 30.00/30.36 parent0: (23854) {G2,W0,D0,L0,V0,M0} { }.
% 30.00/30.36 substitution0:
% 30.00/30.36 end
% 30.00/30.36 permutation0:
% 30.00/30.36 end
% 30.00/30.36
% 30.00/30.36 Proof check complete!
% 30.00/30.36
% 30.00/30.36 Memory use:
% 30.00/30.36
% 30.00/30.36 space for terms: 168692
% 30.00/30.36 space for clauses: 731771
% 30.00/30.36
% 30.00/30.36
% 30.00/30.36 clauses generated: 189903
% 30.00/30.36 clauses kept: 13603
% 30.00/30.36 clauses selected: 970
% 30.00/30.36 clauses deleted: 428
% 30.00/30.36 clauses inuse deleted: 216
% 30.00/30.36
% 30.00/30.36 subsentry: 21467820
% 30.00/30.36 literals s-matched: 8179946
% 30.00/30.36 literals matched: 6652214
% 30.00/30.36 full subsumption: 6362174
% 30.00/30.36
% 30.00/30.36 checksum: 1374095550
% 30.00/30.36
% 30.00/30.36
% 30.00/30.36 Bliksem ended
%------------------------------------------------------------------------------