TSTP Solution File: KLE039+2 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : KLE039+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n015.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 01:36:49 EDT 2022
% Result : Theorem 3.44s 3.79s
% Output : Refutation 3.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KLE039+2 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n015.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % DateTime : Thu Jun 16 09:36:56 EDT 2022
% 0.13/0.34 % CPUTime :
% 3.44/3.79 *** allocated 10000 integers for termspace/termends
% 3.44/3.79 *** allocated 10000 integers for clauses
% 3.44/3.79 *** allocated 10000 integers for justifications
% 3.44/3.79 Bliksem 1.12
% 3.44/3.79
% 3.44/3.79
% 3.44/3.79 Automatic Strategy Selection
% 3.44/3.79
% 3.44/3.79
% 3.44/3.79 Clauses:
% 3.44/3.79
% 3.44/3.79 { addition( X, Y ) = addition( Y, X ) }.
% 3.44/3.79 { addition( Z, addition( Y, X ) ) = addition( addition( Z, Y ), X ) }.
% 3.44/3.79 { addition( X, zero ) = X }.
% 3.44/3.79 { addition( X, X ) = X }.
% 3.44/3.79 { multiplication( X, multiplication( Y, Z ) ) = multiplication(
% 3.44/3.79 multiplication( X, Y ), Z ) }.
% 3.44/3.79 { multiplication( X, one ) = X }.
% 3.44/3.79 { multiplication( one, X ) = X }.
% 3.44/3.79 { multiplication( X, addition( Y, Z ) ) = addition( multiplication( X, Y )
% 3.44/3.79 , multiplication( X, Z ) ) }.
% 3.44/3.79 { multiplication( addition( X, Y ), Z ) = addition( multiplication( X, Z )
% 3.44/3.79 , multiplication( Y, Z ) ) }.
% 3.44/3.79 { multiplication( X, zero ) = zero }.
% 3.44/3.79 { multiplication( zero, X ) = zero }.
% 3.44/3.79 { ! leq( X, Y ), addition( X, Y ) = Y }.
% 3.44/3.79 { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 3.44/3.79 { leq( addition( one, multiplication( X, star( X ) ) ), star( X ) ) }.
% 3.44/3.79 { leq( addition( one, multiplication( star( X ), X ) ), star( X ) ) }.
% 3.44/3.79 { ! leq( addition( multiplication( X, Y ), Z ), Y ), leq( multiplication(
% 3.44/3.79 star( X ), Z ), Y ) }.
% 3.44/3.79 { ! leq( addition( multiplication( X, Y ), Z ), X ), leq( multiplication( Z
% 3.44/3.79 , star( Y ) ), X ) }.
% 3.44/3.79 { ! leq( star( star( skol1 ) ), star( skol1 ) ), ! leq( star( skol1 ), star
% 3.44/3.79 ( star( skol1 ) ) ) }.
% 3.44/3.79
% 3.44/3.79 percentage equality = 0.565217, percentage horn = 1.000000
% 3.44/3.79 This is a problem with some equality
% 3.44/3.79
% 3.44/3.79
% 3.44/3.79
% 3.44/3.79 Options Used:
% 3.44/3.79
% 3.44/3.79 useres = 1
% 3.44/3.79 useparamod = 1
% 3.44/3.79 useeqrefl = 1
% 3.44/3.79 useeqfact = 1
% 3.44/3.79 usefactor = 1
% 3.44/3.79 usesimpsplitting = 0
% 3.44/3.79 usesimpdemod = 5
% 3.44/3.79 usesimpres = 3
% 3.44/3.79
% 3.44/3.79 resimpinuse = 1000
% 3.44/3.79 resimpclauses = 20000
% 3.44/3.79 substype = eqrewr
% 3.44/3.79 backwardsubs = 1
% 3.44/3.79 selectoldest = 5
% 3.44/3.79
% 3.44/3.79 litorderings [0] = split
% 3.44/3.79 litorderings [1] = extend the termordering, first sorting on arguments
% 3.44/3.79
% 3.44/3.79 termordering = kbo
% 3.44/3.79
% 3.44/3.79 litapriori = 0
% 3.44/3.79 termapriori = 1
% 3.44/3.79 litaposteriori = 0
% 3.44/3.79 termaposteriori = 0
% 3.44/3.79 demodaposteriori = 0
% 3.44/3.79 ordereqreflfact = 0
% 3.44/3.79
% 3.44/3.79 litselect = negord
% 3.44/3.79
% 3.44/3.79 maxweight = 15
% 3.44/3.79 maxdepth = 30000
% 3.44/3.79 maxlength = 115
% 3.44/3.79 maxnrvars = 195
% 3.44/3.79 excuselevel = 1
% 3.44/3.79 increasemaxweight = 1
% 3.44/3.79
% 3.44/3.79 maxselected = 10000000
% 3.44/3.79 maxnrclauses = 10000000
% 3.44/3.79
% 3.44/3.79 showgenerated = 0
% 3.44/3.79 showkept = 0
% 3.44/3.79 showselected = 0
% 3.44/3.79 showdeleted = 0
% 3.44/3.79 showresimp = 1
% 3.44/3.79 showstatus = 2000
% 3.44/3.79
% 3.44/3.79 prologoutput = 0
% 3.44/3.79 nrgoals = 5000000
% 3.44/3.79 totalproof = 1
% 3.44/3.79
% 3.44/3.79 Symbols occurring in the translation:
% 3.44/3.79
% 3.44/3.79 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 3.44/3.79 . [1, 2] (w:1, o:19, a:1, s:1, b:0),
% 3.44/3.79 ! [4, 1] (w:0, o:13, a:1, s:1, b:0),
% 3.44/3.79 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 3.44/3.79 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 3.44/3.79 addition [37, 2] (w:1, o:43, a:1, s:1, b:0),
% 3.44/3.79 zero [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 3.44/3.79 multiplication [40, 2] (w:1, o:45, a:1, s:1, b:0),
% 3.44/3.79 one [41, 0] (w:1, o:10, a:1, s:1, b:0),
% 3.44/3.79 leq [42, 2] (w:1, o:44, a:1, s:1, b:0),
% 3.44/3.79 star [43, 1] (w:1, o:18, a:1, s:1, b:0),
% 3.44/3.79 skol1 [45, 0] (w:1, o:12, a:1, s:1, b:1).
% 3.44/3.79
% 3.44/3.79
% 3.44/3.79 Starting Search:
% 3.44/3.79
% 3.44/3.79 *** allocated 15000 integers for clauses
% 3.44/3.79 *** allocated 22500 integers for clauses
% 3.44/3.79 *** allocated 33750 integers for clauses
% 3.44/3.79 *** allocated 50625 integers for clauses
% 3.44/3.79 *** allocated 15000 integers for termspace/termends
% 3.44/3.79 *** allocated 75937 integers for clauses
% 3.44/3.79 Resimplifying inuse:
% 3.44/3.79 Done
% 3.44/3.79
% 3.44/3.79 *** allocated 22500 integers for termspace/termends
% 3.44/3.79 *** allocated 113905 integers for clauses
% 3.44/3.79 *** allocated 33750 integers for termspace/termends
% 3.44/3.79
% 3.44/3.79 Intermediate Status:
% 3.44/3.79 Generated: 18573
% 3.44/3.79 Kept: 2002
% 3.44/3.79 Inuse: 208
% 3.44/3.79 Deleted: 66
% 3.44/3.79 Deletedinuse: 34
% 3.44/3.79
% 3.44/3.79 Resimplifying inuse:
% 3.44/3.79 Done
% 3.44/3.79
% 3.44/3.79 *** allocated 170857 integers for clauses
% 3.44/3.79 *** allocated 50625 integers for termspace/termends
% 3.44/3.79 Resimplifying inuse:
% 3.44/3.79 Done
% 3.44/3.79
% 3.44/3.79 *** allocated 256285 integers for clauses
% 3.44/3.79 *** allocated 75937 integers for termspace/termends
% 3.44/3.79
% 3.44/3.79 Intermediate Status:
% 3.44/3.79 Generated: 39814
% 3.44/3.79 Kept: 4005
% 3.44/3.79 Inuse: 348
% 3.44/3.79 Deleted: 105
% 3.44/3.79 Deletedinuse: 49
% 3.44/3.79
% 3.44/3.79 Resimplifying inuse:
% 3.44/3.79 Done
% 3.44/3.79
% 3.44/3.79 *** allocated 384427 integers for clauses
% 3.44/3.79 Resimplifying inuse:
% 3.44/3.79 Done
% 3.44/3.79
% 3.44/3.79 *** allocated 113905 integers for termspace/termends
% 3.44/3.79
% 3.44/3.79 Intermediate Status:
% 3.44/3.79 Generated: 69117
% 3.44/3.79 Kept: 6007
% 3.44/3.79 Inuse: 539
% 3.44/3.79 Deleted: 205
% 3.44/3.79 Deletedinuse: 75
% 3.44/3.79
% 3.44/3.79 Resimplifying inuse:
% 3.44/3.79 Done
% 3.44/3.79
% 3.44/3.79 Resimplifying inuse:
% 3.44/3.79 Done
% 3.44/3.79
% 3.44/3.79 *** allocated 576640 integers for clauses
% 3.44/3.79 *** allocated 170857 integers for termspace/termends
% 3.44/3.79
% 3.44/3.79 Intermediate Status:
% 3.44/3.79 Generated: 104597
% 3.44/3.79 Kept: 8940
% 3.44/3.79 Inuse: 603
% 3.44/3.79 Deleted: 235
% 3.44/3.79 Deletedinuse: 81
% 3.44/3.79
% 3.44/3.79 Resimplifying inuse:
% 3.44/3.79 Done
% 3.44/3.79
% 3.44/3.79 Resimplifying inuse:
% 3.44/3.79 Done
% 3.44/3.79
% 3.44/3.79
% 3.44/3.79 Intermediate Status:
% 3.44/3.79 Generated: 137573
% 3.44/3.79 Kept: 10971
% 3.44/3.79 Inuse: 680
% 3.44/3.79 Deleted: 272
% 3.44/3.79 Deletedinuse: 81
% 3.44/3.79
% 3.44/3.79 Resimplifying inuse:
% 3.44/3.79 Done
% 3.44/3.79
% 3.44/3.79 Resimplifying inuse:
% 3.44/3.79 Done
% 3.44/3.79
% 3.44/3.79 *** allocated 256285 integers for termspace/termends
% 3.44/3.79 *** allocated 864960 integers for clauses
% 3.44/3.79
% 3.44/3.79 Intermediate Status:
% 3.44/3.79 Generated: 166502
% 3.44/3.79 Kept: 13037
% 3.44/3.79 Inuse: 746
% 3.44/3.79 Deleted: 319
% 3.44/3.79 Deletedinuse: 81
% 3.44/3.79
% 3.44/3.79 Resimplifying inuse:
% 3.44/3.79 Done
% 3.44/3.79
% 3.44/3.79 Resimplifying inuse:
% 3.44/3.79 Done
% 3.44/3.79
% 3.44/3.79
% 3.44/3.79 Intermediate Status:
% 3.44/3.79 Generated: 197723
% 3.44/3.79 Kept: 15038
% 3.44/3.79 Inuse: 813
% 3.44/3.79 Deleted: 320
% 3.44/3.79 Deletedinuse: 81
% 3.44/3.79
% 3.44/3.79 Resimplifying inuse:
% 3.44/3.79 Done
% 3.44/3.79
% 3.44/3.79
% 3.44/3.79 Bliksems!, er is een bewijs:
% 3.44/3.79 % SZS status Theorem
% 3.44/3.79 % SZS output start Refutation
% 3.44/3.79
% 3.44/3.79 (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X ) }.
% 3.44/3.79 (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) ) ==> addition(
% 3.44/3.79 addition( Z, Y ), X ) }.
% 3.44/3.79 (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 3.44/3.79 (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 3.44/3.79 (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 3.44/3.79 (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 3.44/3.79 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 3.44/3.79 (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ),
% 3.44/3.79 multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 3.44/3.79 (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y ) ==> Y }.
% 3.44/3.79 (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X, Y ) }.
% 3.44/3.79 (13) {G0,W9,D5,L1,V1,M1} I { leq( addition( one, multiplication( X, star( X
% 3.44/3.79 ) ) ), star( X ) ) }.
% 3.44/3.79 (14) {G0,W9,D5,L1,V1,M1} I { leq( addition( one, multiplication( star( X )
% 3.44/3.79 , X ) ), star( X ) ) }.
% 3.44/3.79 (15) {G0,W13,D4,L2,V3,M2} I { ! leq( addition( multiplication( X, Y ), Z )
% 3.44/3.79 , Y ), leq( multiplication( star( X ), Z ), Y ) }.
% 3.44/3.79 (17) {G0,W12,D4,L2,V0,M2} I { ! leq( star( star( skol1 ) ), star( skol1 ) )
% 3.44/3.79 , ! leq( star( skol1 ), star( star( skol1 ) ) ) }.
% 3.44/3.79 (20) {G1,W3,D2,L1,V1,M1} R(12,3) { leq( X, X ) }.
% 3.44/3.79 (23) {G1,W14,D4,L2,V3,M2} P(1,12) { ! addition( addition( X, Y ), Z ) ==>
% 3.44/3.79 addition( Y, Z ), leq( X, addition( Y, Z ) ) }.
% 3.44/3.79 (24) {G1,W11,D4,L1,V3,M1} P(1,0) { addition( addition( X, Y ), Z ) =
% 3.44/3.79 addition( addition( Y, Z ), X ) }.
% 3.44/3.79 (35) {G1,W8,D3,L2,V2,M2} P(11,0) { addition( Y, X ) ==> Y, ! leq( X, Y )
% 3.44/3.79 }.
% 3.44/3.79 (63) {G1,W16,D4,L2,V3,M2} P(7,12) { ! multiplication( X, addition( Y, Z ) )
% 3.44/3.79 ==> multiplication( X, Z ), leq( multiplication( X, Y ), multiplication
% 3.44/3.79 ( X, Z ) ) }.
% 3.44/3.79 (94) {G1,W16,D4,L2,V3,M2} P(8,12) { ! multiplication( addition( X, Z ), Y )
% 3.44/3.79 ==> multiplication( Z, Y ), leq( multiplication( X, Y ), multiplication
% 3.44/3.79 ( Z, Y ) ) }.
% 3.44/3.79 (162) {G1,W14,D4,L3,V3,M3} P(11,15) { ! leq( Z, Y ), leq( multiplication(
% 3.44/3.79 star( X ), Z ), Y ), ! leq( multiplication( X, Y ), Z ) }.
% 3.44/3.79 (167) {G1,W11,D4,L2,V2,M2} P(5,15) { ! leq( addition( multiplication( X, Y
% 3.44/3.79 ), one ), Y ), leq( star( X ), Y ) }.
% 3.44/3.79 (233) {G2,W8,D3,L2,V3,M2} P(11,23);q { leq( X, addition( Y, Z ) ), ! leq( X
% 3.44/3.79 , Y ) }.
% 3.44/3.79 (237) {G2,W5,D3,L1,V2,M1} P(3,23);q { leq( X, addition( X, Y ) ) }.
% 3.44/3.79 (242) {G3,W7,D4,L1,V3,M1} P(1,237) { leq( X, addition( addition( X, Y ), Z
% 3.44/3.79 ) ) }.
% 3.44/3.79 (243) {G3,W5,D3,L1,V2,M1} P(0,237) { leq( X, addition( Y, X ) ) }.
% 3.44/3.79 (260) {G4,W7,D4,L1,V3,M1} P(24,243) { leq( Z, addition( addition( Y, Z ), X
% 3.44/3.79 ) ) }.
% 3.44/3.79 (451) {G5,W8,D3,L2,V3,M2} P(11,260) { leq( Y, Z ), ! leq( addition( X, Y )
% 3.44/3.79 , Z ) }.
% 3.44/3.79 (484) {G4,W8,D3,L2,V3,M2} P(11,242) { leq( X, Z ), ! leq( addition( X, Y )
% 3.44/3.79 , Z ) }.
% 3.44/3.79 (580) {G5,W4,D3,L1,V1,M1} R(484,14) { leq( one, star( X ) ) }.
% 3.44/3.79 (593) {G6,W7,D4,L1,V1,M1} R(580,35) { addition( star( X ), one ) ==> star(
% 3.44/3.79 X ) }.
% 3.44/3.79 (596) {G6,W7,D4,L1,V1,M1} R(580,11) { addition( one, star( X ) ) ==> star(
% 3.44/3.79 X ) }.
% 3.44/3.79 (602) {G7,W6,D4,L1,V2,M1} P(593,260) { leq( one, addition( star( X ), Y ) )
% 3.44/3.79 }.
% 3.44/3.79 (613) {G8,W7,D3,L2,V2,M2} P(11,602) { leq( one, Y ), ! leq( star( X ), Y )
% 3.44/3.79 }.
% 3.44/3.79 (720) {G6,W7,D4,L1,V1,M1} R(451,14) { leq( multiplication( star( X ), X ),
% 3.44/3.79 star( X ) ) }.
% 3.44/3.79 (721) {G6,W7,D4,L1,V1,M1} R(451,13) { leq( multiplication( X, star( X ) ),
% 3.44/3.79 star( X ) ) }.
% 3.44/3.79 (1638) {G7,W6,D4,L1,V2,M1} P(596,63);q;d(5) { leq( Y, multiplication( Y,
% 3.44/3.79 star( X ) ) ) }.
% 3.44/3.79 (1653) {G9,W7,D4,L1,V2,M1} R(1638,613) { leq( one, multiplication( star( X
% 3.44/3.79 ), star( Y ) ) ) }.
% 3.44/3.79 (1677) {G10,W13,D5,L1,V2,M1} R(1653,35) { addition( multiplication( star( X
% 3.44/3.79 ), star( Y ) ), one ) ==> multiplication( star( X ), star( Y ) ) }.
% 3.44/3.79 (2997) {G7,W6,D4,L1,V2,M1} P(596,94);q;d(6) { leq( Y, multiplication( star
% 3.44/3.79 ( X ), Y ) ) }.
% 3.44/3.79 (3009) {G8,W8,D5,L1,V3,M1} R(2997,233) { leq( X, addition( multiplication(
% 3.44/3.79 star( Y ), X ), Z ) ) }.
% 3.44/3.79 (5121) {G9,W9,D4,L2,V3,M2} P(11,3009) { leq( Y, Z ), ! leq( multiplication
% 3.44/3.79 ( star( X ), Y ), Z ) }.
% 3.44/3.79 (5635) {G7,W8,D4,L1,V1,M1} R(162,721);r(20) { leq( multiplication( star( X
% 3.44/3.79 ), star( X ) ), star( X ) ) }.
% 3.44/3.79 (5816) {G11,W6,D4,L1,V0,M1} R(167,17);d(1677);r(5635) { ! leq( star( skol1
% 3.44/3.79 ), star( star( skol1 ) ) ) }.
% 3.44/3.79 (15403) {G10,W4,D3,L1,V1,M1} R(5121,720) { leq( X, star( X ) ) }.
% 3.44/3.79 (15431) {G12,W0,D0,L0,V0,M0} R(15403,5816) { }.
% 3.44/3.79
% 3.44/3.79
% 3.44/3.79 % SZS output end Refutation
% 3.44/3.79 found a proof!
% 3.44/3.79
% 3.44/3.79
% 3.44/3.79 Unprocessed initial clauses:
% 3.44/3.79
% 3.44/3.79 (15433) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X ) }.
% 3.44/3.79 (15434) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) = addition
% 3.44/3.79 ( addition( Z, Y ), X ) }.
% 3.44/3.79 (15435) {G0,W5,D3,L1,V1,M1} { addition( X, zero ) = X }.
% 3.44/3.79 (15436) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 3.44/3.79 (15437) {G0,W11,D4,L1,V3,M1} { multiplication( X, multiplication( Y, Z ) )
% 3.44/3.79 = multiplication( multiplication( X, Y ), Z ) }.
% 3.44/3.79 (15438) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 3.44/3.79 (15439) {G0,W5,D3,L1,V1,M1} { multiplication( one, X ) = X }.
% 3.44/3.79 (15440) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y, Z ) ) =
% 3.44/3.79 addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 3.44/3.79 (15441) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Y ), Z ) =
% 3.44/3.79 addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 3.44/3.79 (15442) {G0,W5,D3,L1,V1,M1} { multiplication( X, zero ) = zero }.
% 3.44/3.79 (15443) {G0,W5,D3,L1,V1,M1} { multiplication( zero, X ) = zero }.
% 3.44/3.79 (15444) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y }.
% 3.44/3.79 (15445) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 3.44/3.79 (15446) {G0,W9,D5,L1,V1,M1} { leq( addition( one, multiplication( X, star
% 3.44/3.79 ( X ) ) ), star( X ) ) }.
% 3.44/3.79 (15447) {G0,W9,D5,L1,V1,M1} { leq( addition( one, multiplication( star( X
% 3.44/3.79 ), X ) ), star( X ) ) }.
% 3.44/3.79 (15448) {G0,W13,D4,L2,V3,M2} { ! leq( addition( multiplication( X, Y ), Z
% 3.44/3.79 ), Y ), leq( multiplication( star( X ), Z ), Y ) }.
% 3.44/3.79 (15449) {G0,W13,D4,L2,V3,M2} { ! leq( addition( multiplication( X, Y ), Z
% 3.44/3.79 ), X ), leq( multiplication( Z, star( Y ) ), X ) }.
% 3.44/3.79 (15450) {G0,W12,D4,L2,V0,M2} { ! leq( star( star( skol1 ) ), star( skol1 )
% 3.44/3.79 ), ! leq( star( skol1 ), star( star( skol1 ) ) ) }.
% 3.44/3.79
% 3.44/3.79
% 3.44/3.79 Total Proof:
% 3.44/3.79
% 3.44/3.79 subsumption: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X
% 3.44/3.79 ) }.
% 3.44/3.79 parent0: (15433) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X )
% 3.44/3.79 }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := X
% 3.44/3.79 Y := Y
% 3.44/3.79 end
% 3.44/3.79 permutation0:
% 3.44/3.79 0 ==> 0
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 subsumption: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 3.44/3.79 ==> addition( addition( Z, Y ), X ) }.
% 3.44/3.79 parent0: (15434) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) =
% 3.44/3.79 addition( addition( Z, Y ), X ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := X
% 3.44/3.79 Y := Y
% 3.44/3.79 Z := Z
% 3.44/3.79 end
% 3.44/3.79 permutation0:
% 3.44/3.79 0 ==> 0
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 subsumption: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 3.44/3.79 parent0: (15436) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := X
% 3.44/3.79 end
% 3.44/3.79 permutation0:
% 3.44/3.79 0 ==> 0
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 subsumption: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 3.44/3.79 parent0: (15438) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := X
% 3.44/3.79 end
% 3.44/3.79 permutation0:
% 3.44/3.79 0 ==> 0
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 subsumption: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 3.44/3.79 parent0: (15439) {G0,W5,D3,L1,V1,M1} { multiplication( one, X ) = X }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := X
% 3.44/3.79 end
% 3.44/3.79 permutation0:
% 3.44/3.79 0 ==> 0
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 eqswap: (15472) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Y ),
% 3.44/3.79 multiplication( X, Z ) ) = multiplication( X, addition( Y, Z ) ) }.
% 3.44/3.79 parent0[0]: (15440) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y
% 3.44/3.79 , Z ) ) = addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := X
% 3.44/3.79 Y := Y
% 3.44/3.79 Z := Z
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 subsumption: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y )
% 3.44/3.79 , multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 3.44/3.79 parent0: (15472) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Y ),
% 3.44/3.79 multiplication( X, Z ) ) = multiplication( X, addition( Y, Z ) ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := X
% 3.44/3.79 Y := Y
% 3.44/3.79 Z := Z
% 3.44/3.79 end
% 3.44/3.79 permutation0:
% 3.44/3.79 0 ==> 0
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 eqswap: (15480) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Z ),
% 3.44/3.79 multiplication( Y, Z ) ) = multiplication( addition( X, Y ), Z ) }.
% 3.44/3.79 parent0[0]: (15441) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Y
% 3.44/3.79 ), Z ) = addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := X
% 3.44/3.79 Y := Y
% 3.44/3.79 Z := Z
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 subsumption: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z )
% 3.44/3.79 , multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 3.44/3.79 parent0: (15480) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Z ),
% 3.44/3.79 multiplication( Y, Z ) ) = multiplication( addition( X, Y ), Z ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := X
% 3.44/3.79 Y := Y
% 3.44/3.79 Z := Z
% 3.44/3.79 end
% 3.44/3.79 permutation0:
% 3.44/3.79 0 ==> 0
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 subsumption: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 3.44/3.79 ==> Y }.
% 3.44/3.79 parent0: (15444) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y
% 3.44/3.79 }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := X
% 3.44/3.79 Y := Y
% 3.44/3.79 end
% 3.44/3.79 permutation0:
% 3.44/3.79 0 ==> 0
% 3.44/3.79 1 ==> 1
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 subsumption: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X
% 3.44/3.79 , Y ) }.
% 3.44/3.79 parent0: (15445) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y )
% 3.44/3.79 }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := X
% 3.44/3.79 Y := Y
% 3.44/3.79 end
% 3.44/3.79 permutation0:
% 3.44/3.79 0 ==> 0
% 3.44/3.79 1 ==> 1
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 subsumption: (13) {G0,W9,D5,L1,V1,M1} I { leq( addition( one,
% 3.44/3.79 multiplication( X, star( X ) ) ), star( X ) ) }.
% 3.44/3.79 parent0: (15446) {G0,W9,D5,L1,V1,M1} { leq( addition( one, multiplication
% 3.44/3.79 ( X, star( X ) ) ), star( X ) ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := X
% 3.44/3.79 end
% 3.44/3.79 permutation0:
% 3.44/3.79 0 ==> 0
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 subsumption: (14) {G0,W9,D5,L1,V1,M1} I { leq( addition( one,
% 3.44/3.79 multiplication( star( X ), X ) ), star( X ) ) }.
% 3.44/3.79 parent0: (15447) {G0,W9,D5,L1,V1,M1} { leq( addition( one, multiplication
% 3.44/3.79 ( star( X ), X ) ), star( X ) ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := X
% 3.44/3.79 end
% 3.44/3.79 permutation0:
% 3.44/3.79 0 ==> 0
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 subsumption: (15) {G0,W13,D4,L2,V3,M2} I { ! leq( addition( multiplication
% 3.44/3.79 ( X, Y ), Z ), Y ), leq( multiplication( star( X ), Z ), Y ) }.
% 3.44/3.79 parent0: (15448) {G0,W13,D4,L2,V3,M2} { ! leq( addition( multiplication( X
% 3.44/3.79 , Y ), Z ), Y ), leq( multiplication( star( X ), Z ), Y ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := X
% 3.44/3.79 Y := Y
% 3.44/3.79 Z := Z
% 3.44/3.79 end
% 3.44/3.79 permutation0:
% 3.44/3.79 0 ==> 0
% 3.44/3.79 1 ==> 1
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 subsumption: (17) {G0,W12,D4,L2,V0,M2} I { ! leq( star( star( skol1 ) ),
% 3.44/3.79 star( skol1 ) ), ! leq( star( skol1 ), star( star( skol1 ) ) ) }.
% 3.44/3.79 parent0: (15450) {G0,W12,D4,L2,V0,M2} { ! leq( star( star( skol1 ) ), star
% 3.44/3.79 ( skol1 ) ), ! leq( star( skol1 ), star( star( skol1 ) ) ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 end
% 3.44/3.79 permutation0:
% 3.44/3.79 0 ==> 0
% 3.44/3.79 1 ==> 1
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 eqswap: (15552) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y
% 3.44/3.79 ) }.
% 3.44/3.79 parent0[0]: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 3.44/3.79 Y ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := X
% 3.44/3.79 Y := Y
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 eqswap: (15553) {G0,W5,D3,L1,V1,M1} { X ==> addition( X, X ) }.
% 3.44/3.79 parent0[0]: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := X
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 resolution: (15554) {G1,W3,D2,L1,V1,M1} { leq( X, X ) }.
% 3.44/3.79 parent0[0]: (15552) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X
% 3.44/3.79 , Y ) }.
% 3.44/3.79 parent1[0]: (15553) {G0,W5,D3,L1,V1,M1} { X ==> addition( X, X ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := X
% 3.44/3.79 Y := X
% 3.44/3.79 end
% 3.44/3.79 substitution1:
% 3.44/3.79 X := X
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 subsumption: (20) {G1,W3,D2,L1,V1,M1} R(12,3) { leq( X, X ) }.
% 3.44/3.79 parent0: (15554) {G1,W3,D2,L1,V1,M1} { leq( X, X ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := X
% 3.44/3.79 end
% 3.44/3.79 permutation0:
% 3.44/3.79 0 ==> 0
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 eqswap: (15556) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y
% 3.44/3.79 ) }.
% 3.44/3.79 parent0[0]: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 3.44/3.79 Y ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := X
% 3.44/3.79 Y := Y
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 paramod: (15557) {G1,W14,D4,L2,V3,M2} { ! addition( X, Y ) ==> addition(
% 3.44/3.79 addition( Z, X ), Y ), leq( Z, addition( X, Y ) ) }.
% 3.44/3.79 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 3.44/3.79 ==> addition( addition( Z, Y ), X ) }.
% 3.44/3.79 parent1[0; 5]: (15556) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq
% 3.44/3.79 ( X, Y ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := Y
% 3.44/3.79 Y := X
% 3.44/3.79 Z := Z
% 3.44/3.79 end
% 3.44/3.79 substitution1:
% 3.44/3.79 X := Z
% 3.44/3.79 Y := addition( X, Y )
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 eqswap: (15558) {G1,W14,D4,L2,V3,M2} { ! addition( addition( Z, X ), Y )
% 3.44/3.79 ==> addition( X, Y ), leq( Z, addition( X, Y ) ) }.
% 3.44/3.79 parent0[0]: (15557) {G1,W14,D4,L2,V3,M2} { ! addition( X, Y ) ==> addition
% 3.44/3.79 ( addition( Z, X ), Y ), leq( Z, addition( X, Y ) ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := X
% 3.44/3.79 Y := Y
% 3.44/3.79 Z := Z
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 subsumption: (23) {G1,W14,D4,L2,V3,M2} P(1,12) { ! addition( addition( X, Y
% 3.44/3.79 ), Z ) ==> addition( Y, Z ), leq( X, addition( Y, Z ) ) }.
% 3.44/3.79 parent0: (15558) {G1,W14,D4,L2,V3,M2} { ! addition( addition( Z, X ), Y )
% 3.44/3.79 ==> addition( X, Y ), leq( Z, addition( X, Y ) ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := Y
% 3.44/3.79 Y := Z
% 3.44/3.79 Z := X
% 3.44/3.79 end
% 3.44/3.79 permutation0:
% 3.44/3.79 0 ==> 0
% 3.44/3.79 1 ==> 1
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 eqswap: (15559) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z ) ==>
% 3.44/3.79 addition( X, addition( Y, Z ) ) }.
% 3.44/3.79 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 3.44/3.79 ==> addition( addition( Z, Y ), X ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := Z
% 3.44/3.79 Y := Y
% 3.44/3.79 Z := X
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 paramod: (15562) {G1,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z )
% 3.44/3.79 ==> addition( addition( Y, Z ), X ) }.
% 3.44/3.79 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 3.44/3.79 }.
% 3.44/3.79 parent1[0; 6]: (15559) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y ),
% 3.44/3.79 Z ) ==> addition( X, addition( Y, Z ) ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := X
% 3.44/3.79 Y := addition( Y, Z )
% 3.44/3.79 end
% 3.44/3.79 substitution1:
% 3.44/3.79 X := X
% 3.44/3.79 Y := Y
% 3.44/3.79 Z := Z
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 subsumption: (24) {G1,W11,D4,L1,V3,M1} P(1,0) { addition( addition( X, Y )
% 3.44/3.79 , Z ) = addition( addition( Y, Z ), X ) }.
% 3.44/3.79 parent0: (15562) {G1,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z )
% 3.44/3.79 ==> addition( addition( Y, Z ), X ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := X
% 3.44/3.79 Y := Y
% 3.44/3.79 Z := Z
% 3.44/3.79 end
% 3.44/3.79 permutation0:
% 3.44/3.79 0 ==> 0
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 eqswap: (15576) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X, Y
% 3.44/3.79 ) }.
% 3.44/3.79 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 3.44/3.79 ==> Y }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := X
% 3.44/3.79 Y := Y
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 paramod: (15577) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y, X
% 3.44/3.79 ) }.
% 3.44/3.79 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 3.44/3.79 }.
% 3.44/3.79 parent1[0; 2]: (15576) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq
% 3.44/3.79 ( X, Y ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := Y
% 3.44/3.79 Y := X
% 3.44/3.79 end
% 3.44/3.79 substitution1:
% 3.44/3.79 X := Y
% 3.44/3.79 Y := X
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 eqswap: (15580) {G1,W8,D3,L2,V2,M2} { addition( X, Y ) ==> X, ! leq( Y, X
% 3.44/3.79 ) }.
% 3.44/3.79 parent0[0]: (15577) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y
% 3.44/3.79 , X ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := X
% 3.44/3.79 Y := Y
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 subsumption: (35) {G1,W8,D3,L2,V2,M2} P(11,0) { addition( Y, X ) ==> Y, !
% 3.44/3.79 leq( X, Y ) }.
% 3.44/3.79 parent0: (15580) {G1,W8,D3,L2,V2,M2} { addition( X, Y ) ==> X, ! leq( Y, X
% 3.44/3.79 ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := Y
% 3.44/3.79 Y := X
% 3.44/3.79 end
% 3.44/3.79 permutation0:
% 3.44/3.79 0 ==> 0
% 3.44/3.79 1 ==> 1
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 eqswap: (15582) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y
% 3.44/3.79 ) }.
% 3.44/3.79 parent0[0]: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 3.44/3.79 Y ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := X
% 3.44/3.79 Y := Y
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 paramod: (15583) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Y ) ==>
% 3.44/3.79 multiplication( X, addition( Z, Y ) ), leq( multiplication( X, Z ),
% 3.44/3.79 multiplication( X, Y ) ) }.
% 3.44/3.79 parent0[0]: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 3.44/3.79 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 3.44/3.79 parent1[0; 5]: (15582) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq
% 3.44/3.79 ( X, Y ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := X
% 3.44/3.79 Y := Z
% 3.44/3.79 Z := Y
% 3.44/3.79 end
% 3.44/3.79 substitution1:
% 3.44/3.79 X := multiplication( X, Z )
% 3.44/3.79 Y := multiplication( X, Y )
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 eqswap: (15584) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, addition( Z, Y
% 3.44/3.79 ) ) ==> multiplication( X, Y ), leq( multiplication( X, Z ),
% 3.44/3.79 multiplication( X, Y ) ) }.
% 3.44/3.79 parent0[0]: (15583) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Y ) ==>
% 3.44/3.79 multiplication( X, addition( Z, Y ) ), leq( multiplication( X, Z ),
% 3.44/3.79 multiplication( X, Y ) ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := X
% 3.44/3.79 Y := Y
% 3.44/3.79 Z := Z
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 subsumption: (63) {G1,W16,D4,L2,V3,M2} P(7,12) { ! multiplication( X,
% 3.44/3.79 addition( Y, Z ) ) ==> multiplication( X, Z ), leq( multiplication( X, Y
% 3.44/3.79 ), multiplication( X, Z ) ) }.
% 3.44/3.79 parent0: (15584) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, addition( Z,
% 3.44/3.79 Y ) ) ==> multiplication( X, Y ), leq( multiplication( X, Z ),
% 3.44/3.79 multiplication( X, Y ) ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := X
% 3.44/3.79 Y := Z
% 3.44/3.79 Z := Y
% 3.44/3.79 end
% 3.44/3.79 permutation0:
% 3.44/3.79 0 ==> 0
% 3.44/3.79 1 ==> 1
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 eqswap: (15586) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y
% 3.44/3.79 ) }.
% 3.44/3.79 parent0[0]: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 3.44/3.79 Y ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := X
% 3.44/3.79 Y := Y
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 paramod: (15587) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Y ) ==>
% 3.44/3.79 multiplication( addition( Z, X ), Y ), leq( multiplication( Z, Y ),
% 3.44/3.79 multiplication( X, Y ) ) }.
% 3.44/3.79 parent0[0]: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ),
% 3.44/3.79 multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 3.44/3.79 parent1[0; 5]: (15586) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq
% 3.44/3.79 ( X, Y ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := Z
% 3.44/3.79 Y := X
% 3.44/3.79 Z := Y
% 3.44/3.79 end
% 3.44/3.79 substitution1:
% 3.44/3.79 X := multiplication( Z, Y )
% 3.44/3.79 Y := multiplication( X, Y )
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 eqswap: (15588) {G1,W16,D4,L2,V3,M2} { ! multiplication( addition( Z, X )
% 3.44/3.79 , Y ) ==> multiplication( X, Y ), leq( multiplication( Z, Y ),
% 3.44/3.79 multiplication( X, Y ) ) }.
% 3.44/3.79 parent0[0]: (15587) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Y ) ==>
% 3.44/3.79 multiplication( addition( Z, X ), Y ), leq( multiplication( Z, Y ),
% 3.44/3.79 multiplication( X, Y ) ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := X
% 3.44/3.79 Y := Y
% 3.44/3.79 Z := Z
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 subsumption: (94) {G1,W16,D4,L2,V3,M2} P(8,12) { ! multiplication( addition
% 3.44/3.79 ( X, Z ), Y ) ==> multiplication( Z, Y ), leq( multiplication( X, Y ),
% 3.44/3.79 multiplication( Z, Y ) ) }.
% 3.44/3.79 parent0: (15588) {G1,W16,D4,L2,V3,M2} { ! multiplication( addition( Z, X )
% 3.44/3.79 , Y ) ==> multiplication( X, Y ), leq( multiplication( Z, Y ),
% 3.44/3.79 multiplication( X, Y ) ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := Z
% 3.44/3.79 Y := Y
% 3.44/3.79 Z := X
% 3.44/3.79 end
% 3.44/3.79 permutation0:
% 3.44/3.79 0 ==> 0
% 3.44/3.79 1 ==> 1
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 paramod: (15590) {G1,W14,D4,L3,V3,M3} { ! leq( Z, Y ), ! leq(
% 3.44/3.79 multiplication( X, Y ), Z ), leq( multiplication( star( X ), Z ), Y ) }.
% 3.44/3.79 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 3.44/3.79 ==> Y }.
% 3.44/3.79 parent1[0; 2]: (15) {G0,W13,D4,L2,V3,M2} I { ! leq( addition(
% 3.44/3.79 multiplication( X, Y ), Z ), Y ), leq( multiplication( star( X ), Z ), Y
% 3.44/3.79 ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := multiplication( X, Y )
% 3.44/3.79 Y := Z
% 3.44/3.79 end
% 3.44/3.79 substitution1:
% 3.44/3.79 X := X
% 3.44/3.79 Y := Y
% 3.44/3.79 Z := Z
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 subsumption: (162) {G1,W14,D4,L3,V3,M3} P(11,15) { ! leq( Z, Y ), leq(
% 3.44/3.79 multiplication( star( X ), Z ), Y ), ! leq( multiplication( X, Y ), Z )
% 3.44/3.79 }.
% 3.44/3.79 parent0: (15590) {G1,W14,D4,L3,V3,M3} { ! leq( Z, Y ), ! leq(
% 3.44/3.79 multiplication( X, Y ), Z ), leq( multiplication( star( X ), Z ), Y ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := X
% 3.44/3.79 Y := Y
% 3.44/3.79 Z := Z
% 3.44/3.79 end
% 3.44/3.79 permutation0:
% 3.44/3.79 0 ==> 0
% 3.44/3.79 1 ==> 2
% 3.44/3.79 2 ==> 1
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 paramod: (15593) {G1,W11,D4,L2,V2,M2} { leq( star( X ), Y ), ! leq(
% 3.44/3.79 addition( multiplication( X, Y ), one ), Y ) }.
% 3.44/3.79 parent0[0]: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 3.44/3.79 parent1[1; 1]: (15) {G0,W13,D4,L2,V3,M2} I { ! leq( addition(
% 3.44/3.79 multiplication( X, Y ), Z ), Y ), leq( multiplication( star( X ), Z ), Y
% 3.44/3.79 ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := star( X )
% 3.44/3.79 end
% 3.44/3.79 substitution1:
% 3.44/3.79 X := X
% 3.44/3.79 Y := Y
% 3.44/3.79 Z := one
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 subsumption: (167) {G1,W11,D4,L2,V2,M2} P(5,15) { ! leq( addition(
% 3.44/3.79 multiplication( X, Y ), one ), Y ), leq( star( X ), Y ) }.
% 3.44/3.79 parent0: (15593) {G1,W11,D4,L2,V2,M2} { leq( star( X ), Y ), ! leq(
% 3.44/3.79 addition( multiplication( X, Y ), one ), Y ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := X
% 3.44/3.79 Y := Y
% 3.44/3.79 end
% 3.44/3.79 permutation0:
% 3.44/3.79 0 ==> 1
% 3.44/3.79 1 ==> 0
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 eqswap: (15595) {G1,W14,D4,L2,V3,M2} { ! addition( Y, Z ) ==> addition(
% 3.44/3.79 addition( X, Y ), Z ), leq( X, addition( Y, Z ) ) }.
% 3.44/3.79 parent0[0]: (23) {G1,W14,D4,L2,V3,M2} P(1,12) { ! addition( addition( X, Y
% 3.44/3.79 ), Z ) ==> addition( Y, Z ), leq( X, addition( Y, Z ) ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := X
% 3.44/3.79 Y := Y
% 3.44/3.79 Z := Z
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 paramod: (15598) {G1,W15,D3,L3,V3,M3} { ! addition( X, Y ) ==> addition( X
% 3.44/3.79 , Y ), ! leq( Z, X ), leq( Z, addition( X, Y ) ) }.
% 3.44/3.79 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 3.44/3.79 ==> Y }.
% 3.44/3.79 parent1[0; 6]: (15595) {G1,W14,D4,L2,V3,M2} { ! addition( Y, Z ) ==>
% 3.44/3.79 addition( addition( X, Y ), Z ), leq( X, addition( Y, Z ) ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := Z
% 3.44/3.79 Y := X
% 3.44/3.79 end
% 3.44/3.79 substitution1:
% 3.44/3.79 X := Z
% 3.44/3.79 Y := X
% 3.44/3.79 Z := Y
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 eqrefl: (15647) {G0,W8,D3,L2,V3,M2} { ! leq( Z, X ), leq( Z, addition( X,
% 3.44/3.79 Y ) ) }.
% 3.44/3.79 parent0[0]: (15598) {G1,W15,D3,L3,V3,M3} { ! addition( X, Y ) ==> addition
% 3.44/3.79 ( X, Y ), ! leq( Z, X ), leq( Z, addition( X, Y ) ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := X
% 3.44/3.79 Y := Y
% 3.44/3.79 Z := Z
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 subsumption: (233) {G2,W8,D3,L2,V3,M2} P(11,23);q { leq( X, addition( Y, Z
% 3.44/3.79 ) ), ! leq( X, Y ) }.
% 3.44/3.79 parent0: (15647) {G0,W8,D3,L2,V3,M2} { ! leq( Z, X ), leq( Z, addition( X
% 3.44/3.79 , Y ) ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := Y
% 3.44/3.79 Y := Z
% 3.44/3.79 Z := X
% 3.44/3.79 end
% 3.44/3.79 permutation0:
% 3.44/3.79 0 ==> 1
% 3.44/3.79 1 ==> 0
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 eqswap: (15649) {G1,W14,D4,L2,V3,M2} { ! addition( Y, Z ) ==> addition(
% 3.44/3.79 addition( X, Y ), Z ), leq( X, addition( Y, Z ) ) }.
% 3.44/3.79 parent0[0]: (23) {G1,W14,D4,L2,V3,M2} P(1,12) { ! addition( addition( X, Y
% 3.44/3.79 ), Z ) ==> addition( Y, Z ), leq( X, addition( Y, Z ) ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := X
% 3.44/3.79 Y := Y
% 3.44/3.79 Z := Z
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 paramod: (15652) {G1,W12,D3,L2,V2,M2} { ! addition( X, Y ) ==> addition( X
% 3.44/3.79 , Y ), leq( X, addition( X, Y ) ) }.
% 3.44/3.79 parent0[0]: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 3.44/3.79 parent1[0; 6]: (15649) {G1,W14,D4,L2,V3,M2} { ! addition( Y, Z ) ==>
% 3.44/3.79 addition( addition( X, Y ), Z ), leq( X, addition( Y, Z ) ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := X
% 3.44/3.79 end
% 3.44/3.79 substitution1:
% 3.44/3.79 X := X
% 3.44/3.79 Y := X
% 3.44/3.79 Z := Y
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 eqrefl: (15655) {G0,W5,D3,L1,V2,M1} { leq( X, addition( X, Y ) ) }.
% 3.44/3.79 parent0[0]: (15652) {G1,W12,D3,L2,V2,M2} { ! addition( X, Y ) ==> addition
% 3.44/3.79 ( X, Y ), leq( X, addition( X, Y ) ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := X
% 3.44/3.79 Y := Y
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 subsumption: (237) {G2,W5,D3,L1,V2,M1} P(3,23);q { leq( X, addition( X, Y )
% 3.44/3.79 ) }.
% 3.44/3.79 parent0: (15655) {G0,W5,D3,L1,V2,M1} { leq( X, addition( X, Y ) ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := X
% 3.44/3.79 Y := Y
% 3.44/3.79 end
% 3.44/3.79 permutation0:
% 3.44/3.79 0 ==> 0
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 paramod: (15657) {G1,W7,D4,L1,V3,M1} { leq( X, addition( addition( X, Y )
% 3.44/3.79 , Z ) ) }.
% 3.44/3.79 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 3.44/3.79 ==> addition( addition( Z, Y ), X ) }.
% 3.44/3.79 parent1[0; 2]: (237) {G2,W5,D3,L1,V2,M1} P(3,23);q { leq( X, addition( X, Y
% 3.44/3.79 ) ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := Z
% 3.44/3.79 Y := Y
% 3.44/3.79 Z := X
% 3.44/3.79 end
% 3.44/3.79 substitution1:
% 3.44/3.79 X := X
% 3.44/3.79 Y := addition( Y, Z )
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 subsumption: (242) {G3,W7,D4,L1,V3,M1} P(1,237) { leq( X, addition(
% 3.44/3.79 addition( X, Y ), Z ) ) }.
% 3.44/3.79 parent0: (15657) {G1,W7,D4,L1,V3,M1} { leq( X, addition( addition( X, Y )
% 3.44/3.79 , Z ) ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := X
% 3.44/3.79 Y := Y
% 3.44/3.79 Z := Z
% 3.44/3.79 end
% 3.44/3.79 permutation0:
% 3.44/3.79 0 ==> 0
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 paramod: (15658) {G1,W5,D3,L1,V2,M1} { leq( X, addition( Y, X ) ) }.
% 3.44/3.79 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 3.44/3.79 }.
% 3.44/3.79 parent1[0; 2]: (237) {G2,W5,D3,L1,V2,M1} P(3,23);q { leq( X, addition( X, Y
% 3.44/3.79 ) ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := X
% 3.44/3.79 Y := Y
% 3.44/3.79 end
% 3.44/3.79 substitution1:
% 3.44/3.79 X := X
% 3.44/3.79 Y := Y
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 subsumption: (243) {G3,W5,D3,L1,V2,M1} P(0,237) { leq( X, addition( Y, X )
% 3.44/3.79 ) }.
% 3.44/3.79 parent0: (15658) {G1,W5,D3,L1,V2,M1} { leq( X, addition( Y, X ) ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := X
% 3.44/3.79 Y := Y
% 3.44/3.79 end
% 3.44/3.79 permutation0:
% 3.44/3.79 0 ==> 0
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 eqswap: (15660) {G1,W11,D4,L1,V3,M1} { addition( addition( Y, Z ), X ) =
% 3.44/3.79 addition( addition( X, Y ), Z ) }.
% 3.44/3.79 parent0[0]: (24) {G1,W11,D4,L1,V3,M1} P(1,0) { addition( addition( X, Y ),
% 3.44/3.79 Z ) = addition( addition( Y, Z ), X ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := X
% 3.44/3.79 Y := Y
% 3.44/3.79 Z := Z
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 paramod: (15661) {G2,W7,D4,L1,V3,M1} { leq( X, addition( addition( X, Y )
% 3.44/3.79 , Z ) ) }.
% 3.44/3.79 parent0[0]: (15660) {G1,W11,D4,L1,V3,M1} { addition( addition( Y, Z ), X )
% 3.44/3.79 = addition( addition( X, Y ), Z ) }.
% 3.44/3.79 parent1[0; 2]: (243) {G3,W5,D3,L1,V2,M1} P(0,237) { leq( X, addition( Y, X
% 3.44/3.79 ) ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := X
% 3.44/3.79 Y := Y
% 3.44/3.79 Z := Z
% 3.44/3.79 end
% 3.44/3.79 substitution1:
% 3.44/3.79 X := X
% 3.44/3.79 Y := addition( Y, Z )
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 paramod: (15662) {G2,W7,D4,L1,V3,M1} { leq( X, addition( addition( Z, X )
% 3.44/3.79 , Y ) ) }.
% 3.44/3.79 parent0[0]: (15660) {G1,W11,D4,L1,V3,M1} { addition( addition( Y, Z ), X )
% 3.44/3.79 = addition( addition( X, Y ), Z ) }.
% 3.44/3.79 parent1[0; 2]: (15661) {G2,W7,D4,L1,V3,M1} { leq( X, addition( addition( X
% 3.44/3.79 , Y ), Z ) ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := Z
% 3.44/3.79 Y := X
% 3.44/3.79 Z := Y
% 3.44/3.79 end
% 3.44/3.79 substitution1:
% 3.44/3.79 X := X
% 3.44/3.79 Y := Y
% 3.44/3.79 Z := Z
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 subsumption: (260) {G4,W7,D4,L1,V3,M1} P(24,243) { leq( Z, addition(
% 3.44/3.79 addition( Y, Z ), X ) ) }.
% 3.44/3.79 parent0: (15662) {G2,W7,D4,L1,V3,M1} { leq( X, addition( addition( Z, X )
% 3.44/3.79 , Y ) ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := Z
% 3.44/3.79 Y := X
% 3.44/3.79 Z := Y
% 3.44/3.79 end
% 3.44/3.79 permutation0:
% 3.44/3.79 0 ==> 0
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 paramod: (15665) {G1,W8,D3,L2,V3,M2} { leq( X, Z ), ! leq( addition( Y, X
% 3.44/3.79 ), Z ) }.
% 3.44/3.79 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 3.44/3.79 ==> Y }.
% 3.44/3.79 parent1[0; 2]: (260) {G4,W7,D4,L1,V3,M1} P(24,243) { leq( Z, addition(
% 3.44/3.79 addition( Y, Z ), X ) ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := addition( Y, X )
% 3.44/3.79 Y := Z
% 3.44/3.79 end
% 3.44/3.79 substitution1:
% 3.44/3.79 X := Z
% 3.44/3.79 Y := Y
% 3.44/3.79 Z := X
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 subsumption: (451) {G5,W8,D3,L2,V3,M2} P(11,260) { leq( Y, Z ), ! leq(
% 3.44/3.79 addition( X, Y ), Z ) }.
% 3.44/3.79 parent0: (15665) {G1,W8,D3,L2,V3,M2} { leq( X, Z ), ! leq( addition( Y, X
% 3.44/3.79 ), Z ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := Y
% 3.44/3.79 Y := X
% 3.44/3.79 Z := Z
% 3.44/3.79 end
% 3.44/3.79 permutation0:
% 3.44/3.79 0 ==> 0
% 3.44/3.79 1 ==> 1
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 paramod: (15670) {G1,W8,D3,L2,V3,M2} { leq( X, Z ), ! leq( addition( X, Y
% 3.44/3.79 ), Z ) }.
% 3.44/3.79 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 3.44/3.79 ==> Y }.
% 3.44/3.79 parent1[0; 2]: (242) {G3,W7,D4,L1,V3,M1} P(1,237) { leq( X, addition(
% 3.44/3.79 addition( X, Y ), Z ) ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := addition( X, Y )
% 3.44/3.79 Y := Z
% 3.44/3.79 end
% 3.44/3.79 substitution1:
% 3.44/3.79 X := X
% 3.44/3.79 Y := Y
% 3.44/3.79 Z := Z
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 subsumption: (484) {G4,W8,D3,L2,V3,M2} P(11,242) { leq( X, Z ), ! leq(
% 3.44/3.79 addition( X, Y ), Z ) }.
% 3.44/3.79 parent0: (15670) {G1,W8,D3,L2,V3,M2} { leq( X, Z ), ! leq( addition( X, Y
% 3.44/3.79 ), Z ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := X
% 3.44/3.79 Y := Y
% 3.44/3.79 Z := Z
% 3.44/3.79 end
% 3.44/3.79 permutation0:
% 3.44/3.79 0 ==> 0
% 3.44/3.79 1 ==> 1
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 resolution: (15674) {G1,W4,D3,L1,V1,M1} { leq( one, star( X ) ) }.
% 3.44/3.79 parent0[1]: (484) {G4,W8,D3,L2,V3,M2} P(11,242) { leq( X, Z ), ! leq(
% 3.44/3.79 addition( X, Y ), Z ) }.
% 3.44/3.79 parent1[0]: (14) {G0,W9,D5,L1,V1,M1} I { leq( addition( one, multiplication
% 3.44/3.79 ( star( X ), X ) ), star( X ) ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := one
% 3.44/3.79 Y := multiplication( star( X ), X )
% 3.44/3.79 Z := star( X )
% 3.44/3.79 end
% 3.44/3.79 substitution1:
% 3.44/3.79 X := X
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 subsumption: (580) {G5,W4,D3,L1,V1,M1} R(484,14) { leq( one, star( X ) )
% 3.44/3.79 }.
% 3.44/3.79 parent0: (15674) {G1,W4,D3,L1,V1,M1} { leq( one, star( X ) ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := X
% 3.44/3.79 end
% 3.44/3.79 permutation0:
% 3.44/3.79 0 ==> 0
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 eqswap: (15675) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y, X
% 3.44/3.79 ) }.
% 3.44/3.79 parent0[0]: (35) {G1,W8,D3,L2,V2,M2} P(11,0) { addition( Y, X ) ==> Y, !
% 3.44/3.79 leq( X, Y ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := Y
% 3.44/3.79 Y := X
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 resolution: (15676) {G2,W7,D4,L1,V1,M1} { star( X ) ==> addition( star( X
% 3.44/3.79 ), one ) }.
% 3.44/3.79 parent0[1]: (15675) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y
% 3.44/3.79 , X ) }.
% 3.44/3.79 parent1[0]: (580) {G5,W4,D3,L1,V1,M1} R(484,14) { leq( one, star( X ) ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := star( X )
% 3.44/3.79 Y := one
% 3.44/3.79 end
% 3.44/3.79 substitution1:
% 3.44/3.79 X := X
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 eqswap: (15677) {G2,W7,D4,L1,V1,M1} { addition( star( X ), one ) ==> star
% 3.44/3.79 ( X ) }.
% 3.44/3.79 parent0[0]: (15676) {G2,W7,D4,L1,V1,M1} { star( X ) ==> addition( star( X
% 3.44/3.79 ), one ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := X
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 subsumption: (593) {G6,W7,D4,L1,V1,M1} R(580,35) { addition( star( X ), one
% 3.44/3.79 ) ==> star( X ) }.
% 3.44/3.79 parent0: (15677) {G2,W7,D4,L1,V1,M1} { addition( star( X ), one ) ==> star
% 3.44/3.79 ( X ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := X
% 3.44/3.79 end
% 3.44/3.79 permutation0:
% 3.44/3.79 0 ==> 0
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 eqswap: (15678) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X, Y
% 3.44/3.79 ) }.
% 3.44/3.79 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 3.44/3.79 ==> Y }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := X
% 3.44/3.79 Y := Y
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 resolution: (15679) {G1,W7,D4,L1,V1,M1} { star( X ) ==> addition( one,
% 3.44/3.79 star( X ) ) }.
% 3.44/3.79 parent0[1]: (15678) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X
% 3.44/3.79 , Y ) }.
% 3.44/3.79 parent1[0]: (580) {G5,W4,D3,L1,V1,M1} R(484,14) { leq( one, star( X ) ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := one
% 3.44/3.79 Y := star( X )
% 3.44/3.79 end
% 3.44/3.79 substitution1:
% 3.44/3.79 X := X
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 eqswap: (15680) {G1,W7,D4,L1,V1,M1} { addition( one, star( X ) ) ==> star
% 3.44/3.79 ( X ) }.
% 3.44/3.79 parent0[0]: (15679) {G1,W7,D4,L1,V1,M1} { star( X ) ==> addition( one,
% 3.44/3.79 star( X ) ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := X
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 subsumption: (596) {G6,W7,D4,L1,V1,M1} R(580,11) { addition( one, star( X )
% 3.44/3.79 ) ==> star( X ) }.
% 3.44/3.79 parent0: (15680) {G1,W7,D4,L1,V1,M1} { addition( one, star( X ) ) ==> star
% 3.44/3.79 ( X ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := X
% 3.44/3.79 end
% 3.44/3.79 permutation0:
% 3.44/3.79 0 ==> 0
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 paramod: (15682) {G5,W6,D4,L1,V2,M1} { leq( one, addition( star( X ), Y )
% 3.44/3.79 ) }.
% 3.44/3.79 parent0[0]: (593) {G6,W7,D4,L1,V1,M1} R(580,35) { addition( star( X ), one
% 3.44/3.79 ) ==> star( X ) }.
% 3.44/3.79 parent1[0; 3]: (260) {G4,W7,D4,L1,V3,M1} P(24,243) { leq( Z, addition(
% 3.44/3.79 addition( Y, Z ), X ) ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := X
% 3.44/3.79 end
% 3.44/3.79 substitution1:
% 3.44/3.79 X := Y
% 3.44/3.79 Y := star( X )
% 3.44/3.79 Z := one
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 subsumption: (602) {G7,W6,D4,L1,V2,M1} P(593,260) { leq( one, addition(
% 3.44/3.79 star( X ), Y ) ) }.
% 3.44/3.79 parent0: (15682) {G5,W6,D4,L1,V2,M1} { leq( one, addition( star( X ), Y )
% 3.44/3.79 ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := X
% 3.44/3.79 Y := Y
% 3.44/3.79 end
% 3.44/3.79 permutation0:
% 3.44/3.79 0 ==> 0
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 paramod: (15684) {G1,W7,D3,L2,V2,M2} { leq( one, Y ), ! leq( star( X ), Y
% 3.44/3.79 ) }.
% 3.44/3.79 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 3.44/3.79 ==> Y }.
% 3.44/3.79 parent1[0; 2]: (602) {G7,W6,D4,L1,V2,M1} P(593,260) { leq( one, addition(
% 3.44/3.79 star( X ), Y ) ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := star( X )
% 3.44/3.79 Y := Y
% 3.44/3.79 end
% 3.44/3.79 substitution1:
% 3.44/3.79 X := X
% 3.44/3.79 Y := Y
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 subsumption: (613) {G8,W7,D3,L2,V2,M2} P(11,602) { leq( one, Y ), ! leq(
% 3.44/3.79 star( X ), Y ) }.
% 3.44/3.79 parent0: (15684) {G1,W7,D3,L2,V2,M2} { leq( one, Y ), ! leq( star( X ), Y
% 3.44/3.79 ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := X
% 3.44/3.79 Y := Y
% 3.44/3.79 end
% 3.44/3.79 permutation0:
% 3.44/3.79 0 ==> 0
% 3.44/3.79 1 ==> 1
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 resolution: (15685) {G1,W7,D4,L1,V1,M1} { leq( multiplication( star( X ),
% 3.44/3.79 X ), star( X ) ) }.
% 3.44/3.79 parent0[1]: (451) {G5,W8,D3,L2,V3,M2} P(11,260) { leq( Y, Z ), ! leq(
% 3.44/3.79 addition( X, Y ), Z ) }.
% 3.44/3.79 parent1[0]: (14) {G0,W9,D5,L1,V1,M1} I { leq( addition( one, multiplication
% 3.44/3.79 ( star( X ), X ) ), star( X ) ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := one
% 3.44/3.79 Y := multiplication( star( X ), X )
% 3.44/3.79 Z := star( X )
% 3.44/3.79 end
% 3.44/3.79 substitution1:
% 3.44/3.79 X := X
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 subsumption: (720) {G6,W7,D4,L1,V1,M1} R(451,14) { leq( multiplication(
% 3.44/3.79 star( X ), X ), star( X ) ) }.
% 3.44/3.79 parent0: (15685) {G1,W7,D4,L1,V1,M1} { leq( multiplication( star( X ), X )
% 3.44/3.79 , star( X ) ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := X
% 3.44/3.79 end
% 3.44/3.79 permutation0:
% 3.44/3.79 0 ==> 0
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 resolution: (15686) {G1,W7,D4,L1,V1,M1} { leq( multiplication( X, star( X
% 3.44/3.79 ) ), star( X ) ) }.
% 3.44/3.79 parent0[1]: (451) {G5,W8,D3,L2,V3,M2} P(11,260) { leq( Y, Z ), ! leq(
% 3.44/3.79 addition( X, Y ), Z ) }.
% 3.44/3.79 parent1[0]: (13) {G0,W9,D5,L1,V1,M1} I { leq( addition( one, multiplication
% 3.44/3.79 ( X, star( X ) ) ), star( X ) ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := one
% 3.44/3.79 Y := multiplication( X, star( X ) )
% 3.44/3.79 Z := star( X )
% 3.44/3.79 end
% 3.44/3.79 substitution1:
% 3.44/3.79 X := X
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 subsumption: (721) {G6,W7,D4,L1,V1,M1} R(451,13) { leq( multiplication( X,
% 3.44/3.79 star( X ) ), star( X ) ) }.
% 3.44/3.79 parent0: (15686) {G1,W7,D4,L1,V1,M1} { leq( multiplication( X, star( X ) )
% 3.44/3.79 , star( X ) ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := X
% 3.44/3.79 end
% 3.44/3.79 permutation0:
% 3.44/3.79 0 ==> 0
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 eqswap: (15688) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Z ) ==>
% 3.44/3.79 multiplication( X, addition( Y, Z ) ), leq( multiplication( X, Y ),
% 3.44/3.79 multiplication( X, Z ) ) }.
% 3.44/3.79 parent0[0]: (63) {G1,W16,D4,L2,V3,M2} P(7,12) { ! multiplication( X,
% 3.44/3.79 addition( Y, Z ) ) ==> multiplication( X, Z ), leq( multiplication( X, Y
% 3.44/3.79 ), multiplication( X, Z ) ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := X
% 3.44/3.79 Y := Y
% 3.44/3.79 Z := Z
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 paramod: (15690) {G2,W17,D4,L2,V2,M2} { ! multiplication( X, star( Y ) )
% 3.44/3.79 ==> multiplication( X, star( Y ) ), leq( multiplication( X, one ),
% 3.44/3.79 multiplication( X, star( Y ) ) ) }.
% 3.44/3.79 parent0[0]: (596) {G6,W7,D4,L1,V1,M1} R(580,11) { addition( one, star( X )
% 3.44/3.79 ) ==> star( X ) }.
% 3.44/3.79 parent1[0; 8]: (15688) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Z ) ==>
% 3.44/3.79 multiplication( X, addition( Y, Z ) ), leq( multiplication( X, Y ),
% 3.44/3.79 multiplication( X, Z ) ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := Y
% 3.44/3.79 end
% 3.44/3.79 substitution1:
% 3.44/3.79 X := X
% 3.44/3.79 Y := one
% 3.44/3.79 Z := star( Y )
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 eqrefl: (15691) {G0,W8,D4,L1,V2,M1} { leq( multiplication( X, one ),
% 3.44/3.79 multiplication( X, star( Y ) ) ) }.
% 3.44/3.79 parent0[0]: (15690) {G2,W17,D4,L2,V2,M2} { ! multiplication( X, star( Y )
% 3.44/3.79 ) ==> multiplication( X, star( Y ) ), leq( multiplication( X, one ),
% 3.44/3.79 multiplication( X, star( Y ) ) ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := X
% 3.44/3.79 Y := Y
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 paramod: (15692) {G1,W6,D4,L1,V2,M1} { leq( X, multiplication( X, star( Y
% 3.44/3.79 ) ) ) }.
% 3.44/3.79 parent0[0]: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 3.44/3.79 parent1[0; 1]: (15691) {G0,W8,D4,L1,V2,M1} { leq( multiplication( X, one )
% 3.44/3.79 , multiplication( X, star( Y ) ) ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := X
% 3.44/3.79 end
% 3.44/3.79 substitution1:
% 3.44/3.79 X := X
% 3.44/3.79 Y := Y
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 subsumption: (1638) {G7,W6,D4,L1,V2,M1} P(596,63);q;d(5) { leq( Y,
% 3.44/3.79 multiplication( Y, star( X ) ) ) }.
% 3.44/3.79 parent0: (15692) {G1,W6,D4,L1,V2,M1} { leq( X, multiplication( X, star( Y
% 3.44/3.79 ) ) ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := Y
% 3.44/3.79 Y := X
% 3.44/3.79 end
% 3.44/3.79 permutation0:
% 3.44/3.79 0 ==> 0
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 resolution: (15693) {G8,W7,D4,L1,V2,M1} { leq( one, multiplication( star(
% 3.44/3.79 X ), star( Y ) ) ) }.
% 3.44/3.79 parent0[1]: (613) {G8,W7,D3,L2,V2,M2} P(11,602) { leq( one, Y ), ! leq(
% 3.44/3.79 star( X ), Y ) }.
% 3.44/3.79 parent1[0]: (1638) {G7,W6,D4,L1,V2,M1} P(596,63);q;d(5) { leq( Y,
% 3.44/3.79 multiplication( Y, star( X ) ) ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := X
% 3.44/3.79 Y := multiplication( star( X ), star( Y ) )
% 3.44/3.79 end
% 3.44/3.79 substitution1:
% 3.44/3.79 X := Y
% 3.44/3.79 Y := star( X )
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 subsumption: (1653) {G9,W7,D4,L1,V2,M1} R(1638,613) { leq( one,
% 3.44/3.79 multiplication( star( X ), star( Y ) ) ) }.
% 3.44/3.79 parent0: (15693) {G8,W7,D4,L1,V2,M1} { leq( one, multiplication( star( X )
% 3.44/3.79 , star( Y ) ) ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := X
% 3.44/3.79 Y := Y
% 3.44/3.79 end
% 3.44/3.79 permutation0:
% 3.44/3.79 0 ==> 0
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 eqswap: (15694) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y, X
% 3.44/3.79 ) }.
% 3.44/3.79 parent0[0]: (35) {G1,W8,D3,L2,V2,M2} P(11,0) { addition( Y, X ) ==> Y, !
% 3.44/3.79 leq( X, Y ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := Y
% 3.44/3.79 Y := X
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 resolution: (15695) {G2,W13,D5,L1,V2,M1} { multiplication( star( X ), star
% 3.44/3.79 ( Y ) ) ==> addition( multiplication( star( X ), star( Y ) ), one ) }.
% 3.44/3.79 parent0[1]: (15694) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y
% 3.44/3.79 , X ) }.
% 3.44/3.79 parent1[0]: (1653) {G9,W7,D4,L1,V2,M1} R(1638,613) { leq( one,
% 3.44/3.79 multiplication( star( X ), star( Y ) ) ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := multiplication( star( X ), star( Y ) )
% 3.44/3.79 Y := one
% 3.44/3.79 end
% 3.44/3.79 substitution1:
% 3.44/3.79 X := X
% 3.44/3.79 Y := Y
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 eqswap: (15696) {G2,W13,D5,L1,V2,M1} { addition( multiplication( star( X )
% 3.44/3.79 , star( Y ) ), one ) ==> multiplication( star( X ), star( Y ) ) }.
% 3.44/3.79 parent0[0]: (15695) {G2,W13,D5,L1,V2,M1} { multiplication( star( X ), star
% 3.44/3.79 ( Y ) ) ==> addition( multiplication( star( X ), star( Y ) ), one ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := X
% 3.44/3.79 Y := Y
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 subsumption: (1677) {G10,W13,D5,L1,V2,M1} R(1653,35) { addition(
% 3.44/3.79 multiplication( star( X ), star( Y ) ), one ) ==> multiplication( star( X
% 3.44/3.79 ), star( Y ) ) }.
% 3.44/3.79 parent0: (15696) {G2,W13,D5,L1,V2,M1} { addition( multiplication( star( X
% 3.44/3.79 ), star( Y ) ), one ) ==> multiplication( star( X ), star( Y ) ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := X
% 3.44/3.79 Y := Y
% 3.44/3.79 end
% 3.44/3.79 permutation0:
% 3.44/3.79 0 ==> 0
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 eqswap: (15698) {G1,W16,D4,L2,V3,M2} { ! multiplication( Y, Z ) ==>
% 3.44/3.79 multiplication( addition( X, Y ), Z ), leq( multiplication( X, Z ),
% 3.44/3.79 multiplication( Y, Z ) ) }.
% 3.44/3.79 parent0[0]: (94) {G1,W16,D4,L2,V3,M2} P(8,12) { ! multiplication( addition
% 3.44/3.79 ( X, Z ), Y ) ==> multiplication( Z, Y ), leq( multiplication( X, Y ),
% 3.44/3.79 multiplication( Z, Y ) ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := X
% 3.44/3.79 Y := Z
% 3.44/3.79 Z := Y
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 paramod: (15700) {G2,W17,D4,L2,V2,M2} { ! multiplication( star( X ), Y )
% 3.44/3.79 ==> multiplication( star( X ), Y ), leq( multiplication( one, Y ),
% 3.44/3.79 multiplication( star( X ), Y ) ) }.
% 3.44/3.79 parent0[0]: (596) {G6,W7,D4,L1,V1,M1} R(580,11) { addition( one, star( X )
% 3.44/3.79 ) ==> star( X ) }.
% 3.44/3.79 parent1[0; 7]: (15698) {G1,W16,D4,L2,V3,M2} { ! multiplication( Y, Z ) ==>
% 3.44/3.79 multiplication( addition( X, Y ), Z ), leq( multiplication( X, Z ),
% 3.44/3.79 multiplication( Y, Z ) ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := X
% 3.44/3.79 end
% 3.44/3.79 substitution1:
% 3.44/3.79 X := one
% 3.44/3.79 Y := star( X )
% 3.44/3.79 Z := Y
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 eqrefl: (15701) {G0,W8,D4,L1,V2,M1} { leq( multiplication( one, Y ),
% 3.44/3.79 multiplication( star( X ), Y ) ) }.
% 3.44/3.79 parent0[0]: (15700) {G2,W17,D4,L2,V2,M2} { ! multiplication( star( X ), Y
% 3.44/3.79 ) ==> multiplication( star( X ), Y ), leq( multiplication( one, Y ),
% 3.44/3.79 multiplication( star( X ), Y ) ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := X
% 3.44/3.79 Y := Y
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 paramod: (15702) {G1,W6,D4,L1,V2,M1} { leq( X, multiplication( star( Y ),
% 3.44/3.79 X ) ) }.
% 3.44/3.79 parent0[0]: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 3.44/3.79 parent1[0; 1]: (15701) {G0,W8,D4,L1,V2,M1} { leq( multiplication( one, Y )
% 3.44/3.79 , multiplication( star( X ), Y ) ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := X
% 3.44/3.79 end
% 3.44/3.79 substitution1:
% 3.44/3.79 X := Y
% 3.44/3.79 Y := X
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 subsumption: (2997) {G7,W6,D4,L1,V2,M1} P(596,94);q;d(6) { leq( Y,
% 3.44/3.79 multiplication( star( X ), Y ) ) }.
% 3.44/3.79 parent0: (15702) {G1,W6,D4,L1,V2,M1} { leq( X, multiplication( star( Y ),
% 3.44/3.79 X ) ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := Y
% 3.44/3.79 Y := X
% 3.44/3.79 end
% 3.44/3.79 permutation0:
% 3.44/3.79 0 ==> 0
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 resolution: (15703) {G3,W8,D5,L1,V3,M1} { leq( X, addition( multiplication
% 3.44/3.79 ( star( Y ), X ), Z ) ) }.
% 3.44/3.79 parent0[1]: (233) {G2,W8,D3,L2,V3,M2} P(11,23);q { leq( X, addition( Y, Z )
% 3.44/3.79 ), ! leq( X, Y ) }.
% 3.44/3.79 parent1[0]: (2997) {G7,W6,D4,L1,V2,M1} P(596,94);q;d(6) { leq( Y,
% 3.44/3.79 multiplication( star( X ), Y ) ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := X
% 3.44/3.79 Y := multiplication( star( Y ), X )
% 3.44/3.79 Z := Z
% 3.44/3.79 end
% 3.44/3.79 substitution1:
% 3.44/3.79 X := Y
% 3.44/3.79 Y := X
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 subsumption: (3009) {G8,W8,D5,L1,V3,M1} R(2997,233) { leq( X, addition(
% 3.44/3.79 multiplication( star( Y ), X ), Z ) ) }.
% 3.44/3.79 parent0: (15703) {G3,W8,D5,L1,V3,M1} { leq( X, addition( multiplication(
% 3.44/3.79 star( Y ), X ), Z ) ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := X
% 3.44/3.79 Y := Y
% 3.44/3.79 Z := Z
% 3.44/3.79 end
% 3.44/3.79 permutation0:
% 3.44/3.79 0 ==> 0
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 paramod: (15705) {G1,W9,D4,L2,V3,M2} { leq( X, Z ), ! leq( multiplication
% 3.44/3.79 ( star( Y ), X ), Z ) }.
% 3.44/3.79 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 3.44/3.79 ==> Y }.
% 3.44/3.79 parent1[0; 2]: (3009) {G8,W8,D5,L1,V3,M1} R(2997,233) { leq( X, addition(
% 3.44/3.79 multiplication( star( Y ), X ), Z ) ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := multiplication( star( Y ), X )
% 3.44/3.79 Y := Z
% 3.44/3.79 end
% 3.44/3.79 substitution1:
% 3.44/3.79 X := X
% 3.44/3.79 Y := Y
% 3.44/3.79 Z := Z
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 subsumption: (5121) {G9,W9,D4,L2,V3,M2} P(11,3009) { leq( Y, Z ), ! leq(
% 3.44/3.79 multiplication( star( X ), Y ), Z ) }.
% 3.44/3.79 parent0: (15705) {G1,W9,D4,L2,V3,M2} { leq( X, Z ), ! leq( multiplication
% 3.44/3.79 ( star( Y ), X ), Z ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := Y
% 3.44/3.79 Y := X
% 3.44/3.79 Z := Z
% 3.44/3.79 end
% 3.44/3.79 permutation0:
% 3.44/3.79 0 ==> 0
% 3.44/3.79 1 ==> 1
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 resolution: (15707) {G2,W13,D4,L2,V1,M2} { ! leq( star( X ), star( X ) ),
% 3.44/3.79 leq( multiplication( star( X ), star( X ) ), star( X ) ) }.
% 3.44/3.79 parent0[2]: (162) {G1,W14,D4,L3,V3,M3} P(11,15) { ! leq( Z, Y ), leq(
% 3.44/3.79 multiplication( star( X ), Z ), Y ), ! leq( multiplication( X, Y ), Z )
% 3.44/3.79 }.
% 3.44/3.79 parent1[0]: (721) {G6,W7,D4,L1,V1,M1} R(451,13) { leq( multiplication( X,
% 3.44/3.79 star( X ) ), star( X ) ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := X
% 3.44/3.79 Y := star( X )
% 3.44/3.79 Z := star( X )
% 3.44/3.79 end
% 3.44/3.79 substitution1:
% 3.44/3.79 X := X
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 resolution: (15708) {G2,W8,D4,L1,V1,M1} { leq( multiplication( star( X ),
% 3.44/3.79 star( X ) ), star( X ) ) }.
% 3.44/3.79 parent0[0]: (15707) {G2,W13,D4,L2,V1,M2} { ! leq( star( X ), star( X ) ),
% 3.44/3.79 leq( multiplication( star( X ), star( X ) ), star( X ) ) }.
% 3.44/3.79 parent1[0]: (20) {G1,W3,D2,L1,V1,M1} R(12,3) { leq( X, X ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := X
% 3.44/3.79 end
% 3.44/3.79 substitution1:
% 3.44/3.79 X := star( X )
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 subsumption: (5635) {G7,W8,D4,L1,V1,M1} R(162,721);r(20) { leq(
% 3.44/3.79 multiplication( star( X ), star( X ) ), star( X ) ) }.
% 3.44/3.79 parent0: (15708) {G2,W8,D4,L1,V1,M1} { leq( multiplication( star( X ),
% 3.44/3.79 star( X ) ), star( X ) ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := X
% 3.44/3.79 end
% 3.44/3.79 permutation0:
% 3.44/3.79 0 ==> 0
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 resolution: (15710) {G1,W16,D5,L2,V0,M2} { ! leq( star( skol1 ), star(
% 3.44/3.79 star( skol1 ) ) ), ! leq( addition( multiplication( star( skol1 ), star(
% 3.44/3.79 skol1 ) ), one ), star( skol1 ) ) }.
% 3.44/3.79 parent0[0]: (17) {G0,W12,D4,L2,V0,M2} I { ! leq( star( star( skol1 ) ),
% 3.44/3.79 star( skol1 ) ), ! leq( star( skol1 ), star( star( skol1 ) ) ) }.
% 3.44/3.79 parent1[1]: (167) {G1,W11,D4,L2,V2,M2} P(5,15) { ! leq( addition(
% 3.44/3.79 multiplication( X, Y ), one ), Y ), leq( star( X ), Y ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 end
% 3.44/3.79 substitution1:
% 3.44/3.79 X := star( skol1 )
% 3.44/3.79 Y := star( skol1 )
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 paramod: (15712) {G2,W14,D4,L2,V0,M2} { ! leq( multiplication( star( skol1
% 3.44/3.79 ), star( skol1 ) ), star( skol1 ) ), ! leq( star( skol1 ), star( star(
% 3.44/3.79 skol1 ) ) ) }.
% 3.44/3.79 parent0[0]: (1677) {G10,W13,D5,L1,V2,M1} R(1653,35) { addition(
% 3.44/3.79 multiplication( star( X ), star( Y ) ), one ) ==> multiplication( star( X
% 3.44/3.79 ), star( Y ) ) }.
% 3.44/3.79 parent1[1; 2]: (15710) {G1,W16,D5,L2,V0,M2} { ! leq( star( skol1 ), star(
% 3.44/3.79 star( skol1 ) ) ), ! leq( addition( multiplication( star( skol1 ), star(
% 3.44/3.79 skol1 ) ), one ), star( skol1 ) ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := skol1
% 3.44/3.79 Y := skol1
% 3.44/3.79 end
% 3.44/3.79 substitution1:
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 resolution: (15713) {G3,W6,D4,L1,V0,M1} { ! leq( star( skol1 ), star( star
% 3.44/3.79 ( skol1 ) ) ) }.
% 3.44/3.79 parent0[0]: (15712) {G2,W14,D4,L2,V0,M2} { ! leq( multiplication( star(
% 3.44/3.79 skol1 ), star( skol1 ) ), star( skol1 ) ), ! leq( star( skol1 ), star(
% 3.44/3.79 star( skol1 ) ) ) }.
% 3.44/3.79 parent1[0]: (5635) {G7,W8,D4,L1,V1,M1} R(162,721);r(20) { leq(
% 3.44/3.79 multiplication( star( X ), star( X ) ), star( X ) ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 end
% 3.44/3.79 substitution1:
% 3.44/3.79 X := skol1
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 subsumption: (5816) {G11,W6,D4,L1,V0,M1} R(167,17);d(1677);r(5635) { ! leq
% 3.44/3.79 ( star( skol1 ), star( star( skol1 ) ) ) }.
% 3.44/3.79 parent0: (15713) {G3,W6,D4,L1,V0,M1} { ! leq( star( skol1 ), star( star(
% 3.44/3.79 skol1 ) ) ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 end
% 3.44/3.79 permutation0:
% 3.44/3.79 0 ==> 0
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 resolution: (15714) {G7,W4,D3,L1,V1,M1} { leq( X, star( X ) ) }.
% 3.44/3.79 parent0[1]: (5121) {G9,W9,D4,L2,V3,M2} P(11,3009) { leq( Y, Z ), ! leq(
% 3.44/3.79 multiplication( star( X ), Y ), Z ) }.
% 3.44/3.79 parent1[0]: (720) {G6,W7,D4,L1,V1,M1} R(451,14) { leq( multiplication( star
% 3.44/3.79 ( X ), X ), star( X ) ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := X
% 3.44/3.79 Y := X
% 3.44/3.79 Z := star( X )
% 3.44/3.79 end
% 3.44/3.79 substitution1:
% 3.44/3.79 X := X
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 subsumption: (15403) {G10,W4,D3,L1,V1,M1} R(5121,720) { leq( X, star( X ) )
% 3.44/3.79 }.
% 3.44/3.79 parent0: (15714) {G7,W4,D3,L1,V1,M1} { leq( X, star( X ) ) }.
% 3.44/3.79 substitution0:
% 3.44/3.79 X := X
% 3.44/3.79 end
% 3.44/3.79 permutation0:
% 3.44/3.79 0 ==> 0
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 resolution: (15715) {G11,W0,D0,L0,V0,M0} { }.
% 3.44/3.79 parent0[0]: (5816) {G11,W6,D4,L1,V0,M1} R(167,17);d(1677);r(5635) { ! leq(
% 3.44/3.79 star( skol1 ), star( star( skol1 ) ) ) }.
% 3.44/3.79 parent1[0]: (15403) {G10,W4,D3,L1,V1,M1} R(5121,720) { leq( X, star( X ) )
% 3.44/3.79 }.
% 3.44/3.79 substitution0:
% 3.44/3.79 end
% 3.44/3.79 substitution1:
% 3.44/3.79 X := star( skol1 )
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 subsumption: (15431) {G12,W0,D0,L0,V0,M0} R(15403,5816) { }.
% 3.44/3.79 parent0: (15715) {G11,W0,D0,L0,V0,M0} { }.
% 3.44/3.79 substitution0:
% 3.44/3.79 end
% 3.44/3.79 permutation0:
% 3.44/3.79 end
% 3.44/3.79
% 3.44/3.79 Proof check complete!
% 3.44/3.79
% 3.44/3.79 Memory use:
% 3.44/3.79
% 3.44/3.79 space for terms: 216739
% 3.44/3.79 space for clauses: 727519
% 3.44/3.79
% 3.44/3.79
% 3.44/3.79 clauses generated: 199436
% 3.44/3.79 clauses kept: 15432
% 3.44/3.79 clauses selected: 817
% 3.44/3.79 clauses deleted: 322
% 3.44/3.79 clauses inuse deleted: 81
% 3.44/3.79
% 3.44/3.79 subsentry: 1086937
% 3.44/3.79 literals s-matched: 574453
% 3.44/3.79 literals matched: 553245
% 3.44/3.79 full subsumption: 206540
% 3.44/3.79
% 3.44/3.79 checksum: -1124646097
% 3.44/3.79
% 3.44/3.79
% 3.44/3.79 Bliksem ended
%------------------------------------------------------------------------------