TSTP Solution File: KLE039+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : KLE039+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n028.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 2.09s 2.49s
% Output : Refutation 2.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE039+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n028.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 12:52:11 EDT 2022
% 0.13/0.34 % CPUTime :
% 2.09/2.49 *** allocated 10000 integers for termspace/termends
% 2.09/2.49 *** allocated 10000 integers for clauses
% 2.09/2.49 *** allocated 10000 integers for justifications
% 2.09/2.49 Bliksem 1.12
% 2.09/2.49
% 2.09/2.49
% 2.09/2.49 Automatic Strategy Selection
% 2.09/2.49
% 2.09/2.49
% 2.09/2.49 Clauses:
% 2.09/2.49
% 2.09/2.49 { addition( X, Y ) = addition( Y, X ) }.
% 2.09/2.49 { addition( Z, addition( Y, X ) ) = addition( addition( Z, Y ), X ) }.
% 2.09/2.49 { addition( X, zero ) = X }.
% 2.09/2.49 { addition( X, X ) = X }.
% 2.09/2.49 { multiplication( X, multiplication( Y, Z ) ) = multiplication(
% 2.09/2.49 multiplication( X, Y ), Z ) }.
% 2.09/2.49 { multiplication( X, one ) = X }.
% 2.09/2.49 { multiplication( one, X ) = X }.
% 2.09/2.49 { multiplication( X, addition( Y, Z ) ) = addition( multiplication( X, Y )
% 2.09/2.49 , multiplication( X, Z ) ) }.
% 2.09/2.49 { multiplication( addition( X, Y ), Z ) = addition( multiplication( X, Z )
% 2.09/2.49 , multiplication( Y, Z ) ) }.
% 2.09/2.49 { multiplication( X, zero ) = zero }.
% 2.09/2.49 { multiplication( zero, X ) = zero }.
% 2.09/2.49 { ! leq( X, Y ), addition( X, Y ) = Y }.
% 2.09/2.49 { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 2.09/2.49 { leq( addition( one, multiplication( X, star( X ) ) ), star( X ) ) }.
% 2.09/2.49 { leq( addition( one, multiplication( star( X ), X ) ), star( X ) ) }.
% 2.09/2.49 { ! leq( addition( multiplication( X, Y ), Z ), Y ), leq( multiplication(
% 2.09/2.49 star( X ), Z ), Y ) }.
% 2.09/2.49 { ! leq( addition( multiplication( X, Y ), Z ), X ), leq( multiplication( Z
% 2.09/2.49 , star( Y ) ), X ) }.
% 2.09/2.49 { ! star( star( skol1 ) ) = star( skol1 ) }.
% 2.09/2.49
% 2.09/2.49 percentage equality = 0.636364, percentage horn = 1.000000
% 2.09/2.49 This is a problem with some equality
% 2.09/2.49
% 2.09/2.49
% 2.09/2.49
% 2.09/2.49 Options Used:
% 2.09/2.49
% 2.09/2.49 useres = 1
% 2.09/2.49 useparamod = 1
% 2.09/2.49 useeqrefl = 1
% 2.09/2.49 useeqfact = 1
% 2.09/2.49 usefactor = 1
% 2.09/2.49 usesimpsplitting = 0
% 2.09/2.49 usesimpdemod = 5
% 2.09/2.49 usesimpres = 3
% 2.09/2.49
% 2.09/2.49 resimpinuse = 1000
% 2.09/2.49 resimpclauses = 20000
% 2.09/2.49 substype = eqrewr
% 2.09/2.49 backwardsubs = 1
% 2.09/2.49 selectoldest = 5
% 2.09/2.49
% 2.09/2.49 litorderings [0] = split
% 2.09/2.49 litorderings [1] = extend the termordering, first sorting on arguments
% 2.09/2.49
% 2.09/2.49 termordering = kbo
% 2.09/2.49
% 2.09/2.49 litapriori = 0
% 2.09/2.49 termapriori = 1
% 2.09/2.49 litaposteriori = 0
% 2.09/2.49 termaposteriori = 0
% 2.09/2.49 demodaposteriori = 0
% 2.09/2.49 ordereqreflfact = 0
% 2.09/2.49
% 2.09/2.49 litselect = negord
% 2.09/2.49
% 2.09/2.49 maxweight = 15
% 2.09/2.49 maxdepth = 30000
% 2.09/2.49 maxlength = 115
% 2.09/2.49 maxnrvars = 195
% 2.09/2.49 excuselevel = 1
% 2.09/2.49 increasemaxweight = 1
% 2.09/2.49
% 2.09/2.49 maxselected = 10000000
% 2.09/2.49 maxnrclauses = 10000000
% 2.09/2.49
% 2.09/2.49 showgenerated = 0
% 2.09/2.49 showkept = 0
% 2.09/2.49 showselected = 0
% 2.09/2.49 showdeleted = 0
% 2.09/2.49 showresimp = 1
% 2.09/2.49 showstatus = 2000
% 2.09/2.49
% 2.09/2.49 prologoutput = 0
% 2.09/2.49 nrgoals = 5000000
% 2.09/2.49 totalproof = 1
% 2.09/2.49
% 2.09/2.49 Symbols occurring in the translation:
% 2.09/2.49
% 2.09/2.49 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 2.09/2.49 . [1, 2] (w:1, o:19, a:1, s:1, b:0),
% 2.09/2.49 ! [4, 1] (w:0, o:13, a:1, s:1, b:0),
% 2.09/2.49 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 2.09/2.49 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 2.09/2.49 addition [37, 2] (w:1, o:43, a:1, s:1, b:0),
% 2.09/2.49 zero [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 2.09/2.49 multiplication [40, 2] (w:1, o:45, a:1, s:1, b:0),
% 2.09/2.49 one [41, 0] (w:1, o:10, a:1, s:1, b:0),
% 2.09/2.49 leq [42, 2] (w:1, o:44, a:1, s:1, b:0),
% 2.09/2.49 star [43, 1] (w:1, o:18, a:1, s:1, b:0),
% 2.09/2.49 skol1 [45, 0] (w:1, o:12, a:1, s:1, b:1).
% 2.09/2.49
% 2.09/2.49
% 2.09/2.49 Starting Search:
% 2.09/2.49
% 2.09/2.49 *** allocated 15000 integers for clauses
% 2.09/2.49 *** allocated 22500 integers for clauses
% 2.09/2.49 *** allocated 33750 integers for clauses
% 2.09/2.49 *** allocated 50625 integers for clauses
% 2.09/2.49 *** allocated 15000 integers for termspace/termends
% 2.09/2.49 Resimplifying inuse:
% 2.09/2.49 Done
% 2.09/2.49
% 2.09/2.49 *** allocated 75937 integers for clauses
% 2.09/2.49 *** allocated 22500 integers for termspace/termends
% 2.09/2.49 *** allocated 33750 integers for termspace/termends
% 2.09/2.49 *** allocated 113905 integers for clauses
% 2.09/2.49
% 2.09/2.49 Intermediate Status:
% 2.09/2.49 Generated: 20955
% 2.09/2.49 Kept: 2002
% 2.09/2.49 Inuse: 175
% 2.09/2.49 Deleted: 54
% 2.09/2.49 Deletedinuse: 19
% 2.09/2.49
% 2.09/2.49 Resimplifying inuse:
% 2.09/2.49 Done
% 2.09/2.49
% 2.09/2.49 *** allocated 50625 integers for termspace/termends
% 2.09/2.49 *** allocated 170857 integers for clauses
% 2.09/2.49 Resimplifying inuse:
% 2.09/2.49 Done
% 2.09/2.49
% 2.09/2.49 *** allocated 75937 integers for termspace/termends
% 2.09/2.49 *** allocated 256285 integers for clauses
% 2.09/2.49
% 2.09/2.49 Intermediate Status:
% 2.09/2.49 Generated: 42530
% 2.09/2.49 Kept: 4010
% 2.09/2.49 Inuse: 270
% 2.09/2.49 Deleted: 60
% 2.09/2.49 Deletedinuse: 19
% 2.09/2.49
% 2.09/2.49 Resimplifying inuse:
% 2.09/2.49 Done
% 2.09/2.49
% 2.09/2.49 Resimplifying inuse:
% 2.09/2.49 Done
% 2.09/2.49
% 2.09/2.49 *** allocated 384427 integers for clauses
% 2.09/2.49 *** allocated 113905 integers for termspace/termends
% 2.09/2.49
% 2.09/2.49 Intermediate Status:
% 2.09/2.49 Generated: 56876
% 2.09/2.49 Kept: 6047
% 2.09/2.49 Inuse: 329
% 2.09/2.49 Deleted: 73
% 2.09/2.49 Deletedinuse: 21
% 2.09/2.49
% 2.09/2.49 Resimplifying inuse:
% 2.09/2.49 Done
% 2.09/2.49
% 2.09/2.49 Resimplifying inuse:
% 2.09/2.49 Done
% 2.09/2.49
% 2.09/2.49 *** allocated 576640 integers for clauses
% 2.09/2.49
% 2.09/2.49 Intermediate Status:
% 2.09/2.49 Generated: 77786
% 2.09/2.49 Kept: 8055
% 2.09/2.49 Inuse: 434
% 2.09/2.49 Deleted: 82
% 2.09/2.49 Deletedinuse: 27
% 2.09/2.49
% 2.09/2.49 Resimplifying inuse:
% 2.09/2.49 Done
% 2.09/2.49
% 2.09/2.49 *** allocated 170857 integers for termspace/termends
% 2.09/2.49 Resimplifying inuse:
% 2.09/2.49 Done
% 2.09/2.49
% 2.09/2.49
% 2.09/2.49 Intermediate Status:
% 2.09/2.49 Generated: 101847
% 2.09/2.49 Kept: 10057
% 2.09/2.49 Inuse: 546
% 2.09/2.49 Deleted: 121
% 2.09/2.49 Deletedinuse: 47
% 2.09/2.49
% 2.09/2.49 Resimplifying inuse:
% 2.09/2.49 Done
% 2.09/2.49
% 2.09/2.49 Resimplifying inuse:
% 2.09/2.49 Done
% 2.09/2.49
% 2.09/2.49
% 2.09/2.49 Bliksems!, er is een bewijs:
% 2.09/2.49 % SZS status Theorem
% 2.09/2.49 % SZS output start Refutation
% 2.09/2.49
% 2.09/2.49 (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X ) }.
% 2.09/2.49 (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) ) ==> addition(
% 2.09/2.49 addition( Z, Y ), X ) }.
% 2.09/2.49 (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 2.09/2.49 (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 2.09/2.49 (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 2.09/2.49 (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 2.09/2.49 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 2.09/2.49 (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ),
% 2.09/2.49 multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 2.09/2.49 (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y ) ==> Y }.
% 2.09/2.49 (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X, Y ) }.
% 2.09/2.49 (13) {G0,W9,D5,L1,V1,M1} I { leq( addition( one, multiplication( X, star( X
% 2.09/2.49 ) ) ), star( X ) ) }.
% 2.09/2.49 (14) {G0,W9,D5,L1,V1,M1} I { leq( addition( one, multiplication( star( X )
% 2.09/2.49 , X ) ), star( X ) ) }.
% 2.09/2.49 (15) {G0,W13,D4,L2,V3,M2} I { ! leq( addition( multiplication( X, Y ), Z )
% 2.09/2.49 , Y ), leq( multiplication( star( X ), Z ), Y ) }.
% 2.09/2.49 (16) {G0,W13,D4,L2,V3,M2} I { ! leq( addition( multiplication( X, Y ), Z )
% 2.09/2.49 , X ), leq( multiplication( Z, star( Y ) ), X ) }.
% 2.09/2.49 (17) {G0,W6,D4,L1,V0,M1} I { ! star( star( skol1 ) ) ==> star( skol1 ) }.
% 2.09/2.49 (20) {G1,W3,D2,L1,V1,M1} R(12,3) { leq( X, X ) }.
% 2.09/2.49 (23) {G1,W14,D4,L2,V3,M2} P(1,12) { ! addition( addition( X, Y ), Z ) ==>
% 2.09/2.49 addition( Y, Z ), leq( X, addition( Y, Z ) ) }.
% 2.09/2.49 (24) {G1,W11,D4,L1,V3,M1} P(1,0) { addition( addition( X, Y ), Z ) =
% 2.09/2.49 addition( addition( Y, Z ), X ) }.
% 2.09/2.49 (35) {G1,W8,D3,L2,V2,M2} P(11,0) { addition( Y, X ) ==> Y, ! leq( X, Y )
% 2.09/2.49 }.
% 2.09/2.49 (69) {G1,W16,D4,L2,V3,M2} P(7,12) { ! multiplication( X, addition( Y, Z ) )
% 2.09/2.49 ==> multiplication( X, Z ), leq( multiplication( X, Y ), multiplication
% 2.09/2.49 ( X, Z ) ) }.
% 2.09/2.49 (101) {G1,W16,D4,L2,V3,M2} P(8,12) { ! multiplication( addition( X, Z ), Y
% 2.09/2.49 ) ==> multiplication( Z, Y ), leq( multiplication( X, Y ),
% 2.09/2.49 multiplication( Z, Y ) ) }.
% 2.09/2.49 (156) {G1,W14,D4,L3,V3,M3} P(11,15) { ! leq( Z, Y ), leq( multiplication(
% 2.09/2.49 star( X ), Z ), Y ), ! leq( multiplication( X, Y ), Z ) }.
% 2.09/2.49 (190) {G1,W11,D4,L2,V2,M2} P(6,16) { ! leq( addition( multiplication( Y, X
% 2.09/2.49 ), one ), Y ), leq( star( X ), Y ) }.
% 2.09/2.49 (203) {G2,W5,D3,L1,V2,M1} P(3,23);q { leq( X, addition( X, Y ) ) }.
% 2.09/2.49 (212) {G3,W7,D4,L1,V3,M1} P(1,203) { leq( X, addition( addition( X, Y ), Z
% 2.09/2.49 ) ) }.
% 2.09/2.49 (213) {G3,W5,D3,L1,V2,M1} P(0,203) { leq( X, addition( Y, X ) ) }.
% 2.09/2.49 (234) {G4,W7,D4,L1,V3,M1} P(24,213) { leq( Z, addition( addition( Y, Z ), X
% 2.09/2.49 ) ) }.
% 2.09/2.49 (293) {G5,W8,D3,L2,V3,M2} P(11,234) { leq( Y, Z ), ! leq( addition( X, Y )
% 2.09/2.49 , Z ) }.
% 2.09/2.49 (303) {G4,W8,D3,L2,V3,M2} P(11,212) { leq( X, Z ), ! leq( addition( X, Y )
% 2.09/2.49 , Z ) }.
% 2.09/2.49 (435) {G5,W4,D3,L1,V1,M1} R(303,14) { leq( one, star( X ) ) }.
% 2.09/2.49 (444) {G5,W9,D2,L3,V3,M3} P(11,303) { leq( X, Z ), ! leq( Y, Z ), ! leq( X
% 2.09/2.49 , Y ) }.
% 2.09/2.49 (446) {G6,W7,D4,L1,V1,M1} R(435,11) { addition( one, star( X ) ) ==> star(
% 2.09/2.49 X ) }.
% 2.09/2.49 (473) {G7,W7,D3,L2,V2,M2} P(446,303) { leq( one, Y ), ! leq( star( X ), Y )
% 2.09/2.49 }.
% 2.09/2.49 (561) {G2,W9,D2,L3,V2,M3} P(35,11) { ! leq( X, Y ), X = Y, ! leq( Y, X )
% 2.09/2.49 }.
% 2.09/2.49 (612) {G6,W7,D4,L1,V1,M1} R(293,14) { leq( multiplication( star( X ), X ),
% 2.09/2.49 star( X ) ) }.
% 2.09/2.49 (613) {G6,W7,D4,L1,V1,M1} R(293,13) { leq( multiplication( X, star( X ) ),
% 2.09/2.49 star( X ) ) }.
% 2.09/2.49 (2122) {G7,W6,D4,L1,V2,M1} P(446,69);q;d(5) { leq( Y, multiplication( Y,
% 2.09/2.49 star( X ) ) ) }.
% 2.09/2.49 (2146) {G8,W7,D4,L1,V2,M1} R(2122,473) { leq( one, multiplication( star( X
% 2.09/2.49 ), star( Y ) ) ) }.
% 2.09/2.49 (2179) {G9,W13,D5,L1,V2,M1} R(2146,35) { addition( multiplication( star( X
% 2.09/2.49 ), star( Y ) ), one ) ==> multiplication( star( X ), star( Y ) ) }.
% 2.09/2.49 (3809) {G7,W6,D4,L1,V2,M1} P(446,101);q;d(6) { leq( Y, multiplication( star
% 2.09/2.49 ( X ), Y ) ) }.
% 2.09/2.49 (3821) {G8,W9,D4,L2,V3,M2} R(3809,444) { leq( X, Y ), ! leq( multiplication
% 2.09/2.49 ( star( Z ), X ), Y ) }.
% 2.09/2.49 (5868) {G9,W4,D3,L1,V1,M1} R(3821,612) { leq( X, star( X ) ) }.
% 2.09/2.49 (5883) {G10,W8,D3,L2,V1,M2} R(5868,561) { star( X ) ==> X, ! leq( star( X )
% 2.09/2.49 , X ) }.
% 2.09/2.49 (7635) {G7,W8,D4,L1,V1,M1} R(156,613);r(20) { leq( multiplication( star( X
% 2.09/2.49 ), star( X ) ), star( X ) ) }.
% 2.09/2.49 (11625) {G11,W6,D4,L1,V0,M1} R(5883,17) { ! leq( star( star( skol1 ) ),
% 2.09/2.49 star( skol1 ) ) }.
% 2.09/2.49 (11641) {G12,W0,D0,L0,V0,M0} R(11625,190);d(2179);r(7635) { }.
% 2.09/2.49
% 2.09/2.49
% 2.09/2.49 % SZS output end Refutation
% 2.09/2.49 found a proof!
% 2.09/2.49
% 2.09/2.49
% 2.09/2.49 Unprocessed initial clauses:
% 2.09/2.49
% 2.09/2.49 (11643) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X ) }.
% 2.09/2.49 (11644) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) = addition
% 2.09/2.49 ( addition( Z, Y ), X ) }.
% 2.09/2.49 (11645) {G0,W5,D3,L1,V1,M1} { addition( X, zero ) = X }.
% 2.09/2.49 (11646) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 2.09/2.49 (11647) {G0,W11,D4,L1,V3,M1} { multiplication( X, multiplication( Y, Z ) )
% 2.09/2.49 = multiplication( multiplication( X, Y ), Z ) }.
% 2.09/2.49 (11648) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 2.09/2.49 (11649) {G0,W5,D3,L1,V1,M1} { multiplication( one, X ) = X }.
% 2.09/2.49 (11650) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y, Z ) ) =
% 2.09/2.49 addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 2.09/2.49 (11651) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Y ), Z ) =
% 2.09/2.49 addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 2.09/2.49 (11652) {G0,W5,D3,L1,V1,M1} { multiplication( X, zero ) = zero }.
% 2.09/2.49 (11653) {G0,W5,D3,L1,V1,M1} { multiplication( zero, X ) = zero }.
% 2.09/2.49 (11654) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y }.
% 2.09/2.49 (11655) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 2.09/2.49 (11656) {G0,W9,D5,L1,V1,M1} { leq( addition( one, multiplication( X, star
% 2.09/2.49 ( X ) ) ), star( X ) ) }.
% 2.09/2.49 (11657) {G0,W9,D5,L1,V1,M1} { leq( addition( one, multiplication( star( X
% 2.09/2.49 ), X ) ), star( X ) ) }.
% 2.09/2.49 (11658) {G0,W13,D4,L2,V3,M2} { ! leq( addition( multiplication( X, Y ), Z
% 2.09/2.49 ), Y ), leq( multiplication( star( X ), Z ), Y ) }.
% 2.09/2.49 (11659) {G0,W13,D4,L2,V3,M2} { ! leq( addition( multiplication( X, Y ), Z
% 2.09/2.49 ), X ), leq( multiplication( Z, star( Y ) ), X ) }.
% 2.09/2.49 (11660) {G0,W6,D4,L1,V0,M1} { ! star( star( skol1 ) ) = star( skol1 ) }.
% 2.09/2.49
% 2.09/2.49
% 2.09/2.49 Total Proof:
% 2.09/2.49
% 2.09/2.49 subsumption: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X
% 2.09/2.49 ) }.
% 2.09/2.49 parent0: (11643) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X )
% 2.09/2.49 }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := X
% 2.09/2.49 Y := Y
% 2.09/2.49 end
% 2.09/2.49 permutation0:
% 2.09/2.49 0 ==> 0
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 subsumption: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 2.09/2.49 ==> addition( addition( Z, Y ), X ) }.
% 2.09/2.49 parent0: (11644) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) =
% 2.09/2.49 addition( addition( Z, Y ), X ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := X
% 2.09/2.49 Y := Y
% 2.09/2.49 Z := Z
% 2.09/2.49 end
% 2.09/2.49 permutation0:
% 2.09/2.49 0 ==> 0
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 subsumption: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 2.09/2.49 parent0: (11646) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := X
% 2.09/2.49 end
% 2.09/2.49 permutation0:
% 2.09/2.49 0 ==> 0
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 subsumption: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 2.09/2.49 parent0: (11648) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := X
% 2.09/2.49 end
% 2.09/2.49 permutation0:
% 2.09/2.49 0 ==> 0
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 subsumption: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 2.09/2.49 parent0: (11649) {G0,W5,D3,L1,V1,M1} { multiplication( one, X ) = X }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := X
% 2.09/2.49 end
% 2.09/2.49 permutation0:
% 2.09/2.49 0 ==> 0
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 eqswap: (11682) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Y ),
% 2.09/2.49 multiplication( X, Z ) ) = multiplication( X, addition( Y, Z ) ) }.
% 2.09/2.49 parent0[0]: (11650) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y
% 2.09/2.49 , Z ) ) = addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := X
% 2.09/2.49 Y := Y
% 2.09/2.49 Z := Z
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 subsumption: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y )
% 2.09/2.49 , multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 2.09/2.49 parent0: (11682) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Y ),
% 2.09/2.49 multiplication( X, Z ) ) = multiplication( X, addition( Y, Z ) ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := X
% 2.09/2.49 Y := Y
% 2.09/2.49 Z := Z
% 2.09/2.49 end
% 2.09/2.49 permutation0:
% 2.09/2.49 0 ==> 0
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 eqswap: (11690) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Z ),
% 2.09/2.49 multiplication( Y, Z ) ) = multiplication( addition( X, Y ), Z ) }.
% 2.09/2.49 parent0[0]: (11651) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Y
% 2.09/2.49 ), Z ) = addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := X
% 2.09/2.49 Y := Y
% 2.09/2.49 Z := Z
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 subsumption: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z )
% 2.09/2.49 , multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 2.09/2.49 parent0: (11690) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Z ),
% 2.09/2.49 multiplication( Y, Z ) ) = multiplication( addition( X, Y ), Z ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := X
% 2.09/2.49 Y := Y
% 2.09/2.49 Z := Z
% 2.09/2.49 end
% 2.09/2.49 permutation0:
% 2.09/2.49 0 ==> 0
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 subsumption: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 2.09/2.49 ==> Y }.
% 2.09/2.49 parent0: (11654) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y
% 2.09/2.49 }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := X
% 2.09/2.49 Y := Y
% 2.09/2.49 end
% 2.09/2.49 permutation0:
% 2.09/2.49 0 ==> 0
% 2.09/2.49 1 ==> 1
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 subsumption: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X
% 2.09/2.49 , Y ) }.
% 2.09/2.49 parent0: (11655) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y )
% 2.09/2.49 }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := X
% 2.09/2.49 Y := Y
% 2.09/2.49 end
% 2.09/2.49 permutation0:
% 2.09/2.49 0 ==> 0
% 2.09/2.49 1 ==> 1
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 subsumption: (13) {G0,W9,D5,L1,V1,M1} I { leq( addition( one,
% 2.09/2.49 multiplication( X, star( X ) ) ), star( X ) ) }.
% 2.09/2.49 parent0: (11656) {G0,W9,D5,L1,V1,M1} { leq( addition( one, multiplication
% 2.09/2.49 ( X, star( X ) ) ), star( X ) ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := X
% 2.09/2.49 end
% 2.09/2.49 permutation0:
% 2.09/2.49 0 ==> 0
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 subsumption: (14) {G0,W9,D5,L1,V1,M1} I { leq( addition( one,
% 2.09/2.49 multiplication( star( X ), X ) ), star( X ) ) }.
% 2.09/2.49 parent0: (11657) {G0,W9,D5,L1,V1,M1} { leq( addition( one, multiplication
% 2.09/2.49 ( star( X ), X ) ), star( X ) ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := X
% 2.09/2.49 end
% 2.09/2.49 permutation0:
% 2.09/2.49 0 ==> 0
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 subsumption: (15) {G0,W13,D4,L2,V3,M2} I { ! leq( addition( multiplication
% 2.09/2.49 ( X, Y ), Z ), Y ), leq( multiplication( star( X ), Z ), Y ) }.
% 2.09/2.49 parent0: (11658) {G0,W13,D4,L2,V3,M2} { ! leq( addition( multiplication( X
% 2.09/2.49 , Y ), Z ), Y ), leq( multiplication( star( X ), Z ), Y ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := X
% 2.09/2.49 Y := Y
% 2.09/2.49 Z := Z
% 2.09/2.49 end
% 2.09/2.49 permutation0:
% 2.09/2.49 0 ==> 0
% 2.09/2.49 1 ==> 1
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 subsumption: (16) {G0,W13,D4,L2,V3,M2} I { ! leq( addition( multiplication
% 2.09/2.49 ( X, Y ), Z ), X ), leq( multiplication( Z, star( Y ) ), X ) }.
% 2.09/2.49 parent0: (11659) {G0,W13,D4,L2,V3,M2} { ! leq( addition( multiplication( X
% 2.09/2.49 , Y ), Z ), X ), leq( multiplication( Z, star( Y ) ), X ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := X
% 2.09/2.49 Y := Y
% 2.09/2.49 Z := Z
% 2.09/2.49 end
% 2.09/2.49 permutation0:
% 2.09/2.49 0 ==> 0
% 2.09/2.49 1 ==> 1
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 subsumption: (17) {G0,W6,D4,L1,V0,M1} I { ! star( star( skol1 ) ) ==> star
% 2.09/2.49 ( skol1 ) }.
% 2.09/2.49 parent0: (11660) {G0,W6,D4,L1,V0,M1} { ! star( star( skol1 ) ) = star(
% 2.09/2.49 skol1 ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 end
% 2.09/2.49 permutation0:
% 2.09/2.49 0 ==> 0
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 eqswap: (11775) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y
% 2.09/2.49 ) }.
% 2.09/2.49 parent0[0]: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 2.09/2.49 Y ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := X
% 2.09/2.49 Y := Y
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 eqswap: (11776) {G0,W5,D3,L1,V1,M1} { X ==> addition( X, X ) }.
% 2.09/2.49 parent0[0]: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := X
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 resolution: (11777) {G1,W3,D2,L1,V1,M1} { leq( X, X ) }.
% 2.09/2.49 parent0[0]: (11775) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X
% 2.09/2.49 , Y ) }.
% 2.09/2.49 parent1[0]: (11776) {G0,W5,D3,L1,V1,M1} { X ==> addition( X, X ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := X
% 2.09/2.49 Y := X
% 2.09/2.49 end
% 2.09/2.49 substitution1:
% 2.09/2.49 X := X
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 subsumption: (20) {G1,W3,D2,L1,V1,M1} R(12,3) { leq( X, X ) }.
% 2.09/2.49 parent0: (11777) {G1,W3,D2,L1,V1,M1} { leq( X, X ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := X
% 2.09/2.49 end
% 2.09/2.49 permutation0:
% 2.09/2.49 0 ==> 0
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 eqswap: (11779) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y
% 2.09/2.49 ) }.
% 2.09/2.49 parent0[0]: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 2.09/2.49 Y ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := X
% 2.09/2.49 Y := Y
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 paramod: (11780) {G1,W14,D4,L2,V3,M2} { ! addition( X, Y ) ==> addition(
% 2.09/2.49 addition( Z, X ), Y ), leq( Z, addition( X, Y ) ) }.
% 2.09/2.49 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 2.09/2.49 ==> addition( addition( Z, Y ), X ) }.
% 2.09/2.49 parent1[0; 5]: (11779) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq
% 2.09/2.49 ( X, Y ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := Y
% 2.09/2.49 Y := X
% 2.09/2.49 Z := Z
% 2.09/2.49 end
% 2.09/2.49 substitution1:
% 2.09/2.49 X := Z
% 2.09/2.49 Y := addition( X, Y )
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 eqswap: (11781) {G1,W14,D4,L2,V3,M2} { ! addition( addition( Z, X ), Y )
% 2.09/2.49 ==> addition( X, Y ), leq( Z, addition( X, Y ) ) }.
% 2.09/2.49 parent0[0]: (11780) {G1,W14,D4,L2,V3,M2} { ! addition( X, Y ) ==> addition
% 2.09/2.49 ( addition( Z, X ), Y ), leq( Z, addition( X, Y ) ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := X
% 2.09/2.49 Y := Y
% 2.09/2.49 Z := Z
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 subsumption: (23) {G1,W14,D4,L2,V3,M2} P(1,12) { ! addition( addition( X, Y
% 2.09/2.49 ), Z ) ==> addition( Y, Z ), leq( X, addition( Y, Z ) ) }.
% 2.09/2.49 parent0: (11781) {G1,W14,D4,L2,V3,M2} { ! addition( addition( Z, X ), Y )
% 2.09/2.49 ==> addition( X, Y ), leq( Z, addition( X, Y ) ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := Y
% 2.09/2.49 Y := Z
% 2.09/2.49 Z := X
% 2.09/2.49 end
% 2.09/2.49 permutation0:
% 2.09/2.49 0 ==> 0
% 2.09/2.49 1 ==> 1
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 eqswap: (11782) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z ) ==>
% 2.09/2.49 addition( X, addition( Y, Z ) ) }.
% 2.09/2.49 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 2.09/2.49 ==> addition( addition( Z, Y ), X ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := Z
% 2.09/2.49 Y := Y
% 2.09/2.49 Z := X
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 paramod: (11785) {G1,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z )
% 2.09/2.49 ==> addition( addition( Y, Z ), X ) }.
% 2.09/2.49 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 2.09/2.49 }.
% 2.09/2.49 parent1[0; 6]: (11782) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y ),
% 2.09/2.49 Z ) ==> addition( X, addition( Y, Z ) ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := X
% 2.09/2.49 Y := addition( Y, Z )
% 2.09/2.49 end
% 2.09/2.49 substitution1:
% 2.09/2.49 X := X
% 2.09/2.49 Y := Y
% 2.09/2.49 Z := Z
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 subsumption: (24) {G1,W11,D4,L1,V3,M1} P(1,0) { addition( addition( X, Y )
% 2.09/2.49 , Z ) = addition( addition( Y, Z ), X ) }.
% 2.09/2.49 parent0: (11785) {G1,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z )
% 2.09/2.49 ==> addition( addition( Y, Z ), X ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := X
% 2.09/2.49 Y := Y
% 2.09/2.49 Z := Z
% 2.09/2.49 end
% 2.09/2.49 permutation0:
% 2.09/2.49 0 ==> 0
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 eqswap: (11799) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X, Y
% 2.09/2.49 ) }.
% 2.09/2.49 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 2.09/2.49 ==> Y }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := X
% 2.09/2.49 Y := Y
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 paramod: (11800) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y, X
% 2.09/2.49 ) }.
% 2.09/2.49 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 2.09/2.49 }.
% 2.09/2.49 parent1[0; 2]: (11799) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq
% 2.09/2.49 ( X, Y ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := Y
% 2.09/2.49 Y := X
% 2.09/2.49 end
% 2.09/2.49 substitution1:
% 2.09/2.49 X := Y
% 2.09/2.49 Y := X
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 eqswap: (11803) {G1,W8,D3,L2,V2,M2} { addition( X, Y ) ==> X, ! leq( Y, X
% 2.09/2.49 ) }.
% 2.09/2.49 parent0[0]: (11800) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y
% 2.09/2.49 , X ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := X
% 2.09/2.49 Y := Y
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 subsumption: (35) {G1,W8,D3,L2,V2,M2} P(11,0) { addition( Y, X ) ==> Y, !
% 2.09/2.49 leq( X, Y ) }.
% 2.09/2.49 parent0: (11803) {G1,W8,D3,L2,V2,M2} { addition( X, Y ) ==> X, ! leq( Y, X
% 2.09/2.49 ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := Y
% 2.09/2.49 Y := X
% 2.09/2.49 end
% 2.09/2.49 permutation0:
% 2.09/2.49 0 ==> 0
% 2.09/2.49 1 ==> 1
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 eqswap: (11805) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y
% 2.09/2.49 ) }.
% 2.09/2.49 parent0[0]: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 2.09/2.49 Y ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := X
% 2.09/2.49 Y := Y
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 paramod: (11806) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Y ) ==>
% 2.09/2.49 multiplication( X, addition( Z, Y ) ), leq( multiplication( X, Z ),
% 2.09/2.49 multiplication( X, Y ) ) }.
% 2.09/2.49 parent0[0]: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 2.09/2.49 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 2.09/2.49 parent1[0; 5]: (11805) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq
% 2.09/2.49 ( X, Y ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := X
% 2.09/2.49 Y := Z
% 2.09/2.49 Z := Y
% 2.09/2.49 end
% 2.09/2.49 substitution1:
% 2.09/2.49 X := multiplication( X, Z )
% 2.09/2.49 Y := multiplication( X, Y )
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 eqswap: (11807) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, addition( Z, Y
% 2.09/2.49 ) ) ==> multiplication( X, Y ), leq( multiplication( X, Z ),
% 2.09/2.49 multiplication( X, Y ) ) }.
% 2.09/2.49 parent0[0]: (11806) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Y ) ==>
% 2.09/2.49 multiplication( X, addition( Z, Y ) ), leq( multiplication( X, Z ),
% 2.09/2.49 multiplication( X, Y ) ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := X
% 2.09/2.49 Y := Y
% 2.09/2.49 Z := Z
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 subsumption: (69) {G1,W16,D4,L2,V3,M2} P(7,12) { ! multiplication( X,
% 2.09/2.49 addition( Y, Z ) ) ==> multiplication( X, Z ), leq( multiplication( X, Y
% 2.09/2.49 ), multiplication( X, Z ) ) }.
% 2.09/2.49 parent0: (11807) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, addition( Z,
% 2.09/2.49 Y ) ) ==> multiplication( X, Y ), leq( multiplication( X, Z ),
% 2.09/2.49 multiplication( X, Y ) ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := X
% 2.09/2.49 Y := Z
% 2.09/2.49 Z := Y
% 2.09/2.49 end
% 2.09/2.49 permutation0:
% 2.09/2.49 0 ==> 0
% 2.09/2.49 1 ==> 1
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 eqswap: (11809) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y
% 2.09/2.49 ) }.
% 2.09/2.49 parent0[0]: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 2.09/2.49 Y ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := X
% 2.09/2.49 Y := Y
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 paramod: (11810) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Y ) ==>
% 2.09/2.49 multiplication( addition( Z, X ), Y ), leq( multiplication( Z, Y ),
% 2.09/2.49 multiplication( X, Y ) ) }.
% 2.09/2.49 parent0[0]: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ),
% 2.09/2.49 multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 2.09/2.49 parent1[0; 5]: (11809) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq
% 2.09/2.49 ( X, Y ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := Z
% 2.09/2.49 Y := X
% 2.09/2.49 Z := Y
% 2.09/2.49 end
% 2.09/2.49 substitution1:
% 2.09/2.49 X := multiplication( Z, Y )
% 2.09/2.49 Y := multiplication( X, Y )
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 eqswap: (11811) {G1,W16,D4,L2,V3,M2} { ! multiplication( addition( Z, X )
% 2.09/2.49 , Y ) ==> multiplication( X, Y ), leq( multiplication( Z, Y ),
% 2.09/2.49 multiplication( X, Y ) ) }.
% 2.09/2.49 parent0[0]: (11810) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Y ) ==>
% 2.09/2.49 multiplication( addition( Z, X ), Y ), leq( multiplication( Z, Y ),
% 2.09/2.49 multiplication( X, Y ) ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := X
% 2.09/2.49 Y := Y
% 2.09/2.49 Z := Z
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 subsumption: (101) {G1,W16,D4,L2,V3,M2} P(8,12) { ! multiplication(
% 2.09/2.49 addition( X, Z ), Y ) ==> multiplication( Z, Y ), leq( multiplication( X
% 2.09/2.49 , Y ), multiplication( Z, Y ) ) }.
% 2.09/2.49 parent0: (11811) {G1,W16,D4,L2,V3,M2} { ! multiplication( addition( Z, X )
% 2.09/2.49 , Y ) ==> multiplication( X, Y ), leq( multiplication( Z, Y ),
% 2.09/2.49 multiplication( X, Y ) ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := Z
% 2.09/2.49 Y := Y
% 2.09/2.49 Z := X
% 2.09/2.49 end
% 2.09/2.49 permutation0:
% 2.09/2.49 0 ==> 0
% 2.09/2.49 1 ==> 1
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 paramod: (11813) {G1,W14,D4,L3,V3,M3} { ! leq( Z, Y ), ! leq(
% 2.09/2.49 multiplication( X, Y ), Z ), leq( multiplication( star( X ), Z ), Y ) }.
% 2.09/2.49 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 2.09/2.49 ==> Y }.
% 2.09/2.49 parent1[0; 2]: (15) {G0,W13,D4,L2,V3,M2} I { ! leq( addition(
% 2.09/2.49 multiplication( X, Y ), Z ), Y ), leq( multiplication( star( X ), Z ), Y
% 2.09/2.49 ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := multiplication( X, Y )
% 2.09/2.49 Y := Z
% 2.09/2.49 end
% 2.09/2.49 substitution1:
% 2.09/2.49 X := X
% 2.09/2.49 Y := Y
% 2.09/2.49 Z := Z
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 subsumption: (156) {G1,W14,D4,L3,V3,M3} P(11,15) { ! leq( Z, Y ), leq(
% 2.09/2.49 multiplication( star( X ), Z ), Y ), ! leq( multiplication( X, Y ), Z )
% 2.09/2.49 }.
% 2.09/2.49 parent0: (11813) {G1,W14,D4,L3,V3,M3} { ! leq( Z, Y ), ! leq(
% 2.09/2.49 multiplication( X, Y ), Z ), leq( multiplication( star( X ), Z ), Y ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := X
% 2.09/2.49 Y := Y
% 2.09/2.49 Z := Z
% 2.09/2.49 end
% 2.09/2.49 permutation0:
% 2.09/2.49 0 ==> 0
% 2.09/2.49 1 ==> 2
% 2.09/2.49 2 ==> 1
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 paramod: (11816) {G1,W11,D4,L2,V2,M2} { leq( star( X ), Y ), ! leq(
% 2.09/2.49 addition( multiplication( Y, X ), one ), Y ) }.
% 2.09/2.49 parent0[0]: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 2.09/2.49 parent1[1; 1]: (16) {G0,W13,D4,L2,V3,M2} I { ! leq( addition(
% 2.09/2.49 multiplication( X, Y ), Z ), X ), leq( multiplication( Z, star( Y ) ), X
% 2.09/2.49 ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := star( X )
% 2.09/2.49 end
% 2.09/2.49 substitution1:
% 2.09/2.49 X := Y
% 2.09/2.49 Y := X
% 2.09/2.49 Z := one
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 subsumption: (190) {G1,W11,D4,L2,V2,M2} P(6,16) { ! leq( addition(
% 2.09/2.49 multiplication( Y, X ), one ), Y ), leq( star( X ), Y ) }.
% 2.09/2.49 parent0: (11816) {G1,W11,D4,L2,V2,M2} { leq( star( X ), Y ), ! leq(
% 2.09/2.49 addition( multiplication( Y, X ), one ), Y ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := X
% 2.09/2.49 Y := Y
% 2.09/2.49 end
% 2.09/2.49 permutation0:
% 2.09/2.49 0 ==> 1
% 2.09/2.49 1 ==> 0
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 eqswap: (11818) {G1,W14,D4,L2,V3,M2} { ! addition( Y, Z ) ==> addition(
% 2.09/2.49 addition( X, Y ), Z ), leq( X, addition( Y, Z ) ) }.
% 2.09/2.49 parent0[0]: (23) {G1,W14,D4,L2,V3,M2} P(1,12) { ! addition( addition( X, Y
% 2.09/2.49 ), Z ) ==> addition( Y, Z ), leq( X, addition( Y, Z ) ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := X
% 2.09/2.49 Y := Y
% 2.09/2.49 Z := Z
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 paramod: (11821) {G1,W12,D3,L2,V2,M2} { ! addition( X, Y ) ==> addition( X
% 2.09/2.49 , Y ), leq( X, addition( X, Y ) ) }.
% 2.09/2.49 parent0[0]: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 2.09/2.49 parent1[0; 6]: (11818) {G1,W14,D4,L2,V3,M2} { ! addition( Y, Z ) ==>
% 2.09/2.49 addition( addition( X, Y ), Z ), leq( X, addition( Y, Z ) ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := X
% 2.09/2.49 end
% 2.09/2.49 substitution1:
% 2.09/2.49 X := X
% 2.09/2.49 Y := X
% 2.09/2.49 Z := Y
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 eqrefl: (11824) {G0,W5,D3,L1,V2,M1} { leq( X, addition( X, Y ) ) }.
% 2.09/2.49 parent0[0]: (11821) {G1,W12,D3,L2,V2,M2} { ! addition( X, Y ) ==> addition
% 2.09/2.49 ( X, Y ), leq( X, addition( X, Y ) ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := X
% 2.09/2.49 Y := Y
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 subsumption: (203) {G2,W5,D3,L1,V2,M1} P(3,23);q { leq( X, addition( X, Y )
% 2.09/2.49 ) }.
% 2.09/2.49 parent0: (11824) {G0,W5,D3,L1,V2,M1} { leq( X, addition( X, Y ) ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := X
% 2.09/2.49 Y := Y
% 2.09/2.49 end
% 2.09/2.49 permutation0:
% 2.09/2.49 0 ==> 0
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 paramod: (11826) {G1,W7,D4,L1,V3,M1} { leq( X, addition( addition( X, Y )
% 2.09/2.49 , Z ) ) }.
% 2.09/2.49 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 2.09/2.49 ==> addition( addition( Z, Y ), X ) }.
% 2.09/2.49 parent1[0; 2]: (203) {G2,W5,D3,L1,V2,M1} P(3,23);q { leq( X, addition( X, Y
% 2.09/2.49 ) ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := Z
% 2.09/2.49 Y := Y
% 2.09/2.49 Z := X
% 2.09/2.49 end
% 2.09/2.49 substitution1:
% 2.09/2.49 X := X
% 2.09/2.49 Y := addition( Y, Z )
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 subsumption: (212) {G3,W7,D4,L1,V3,M1} P(1,203) { leq( X, addition(
% 2.09/2.49 addition( X, Y ), Z ) ) }.
% 2.09/2.49 parent0: (11826) {G1,W7,D4,L1,V3,M1} { leq( X, addition( addition( X, Y )
% 2.09/2.49 , Z ) ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := X
% 2.09/2.49 Y := Y
% 2.09/2.49 Z := Z
% 2.09/2.49 end
% 2.09/2.49 permutation0:
% 2.09/2.49 0 ==> 0
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 paramod: (11827) {G1,W5,D3,L1,V2,M1} { leq( X, addition( Y, X ) ) }.
% 2.09/2.49 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 2.09/2.49 }.
% 2.09/2.49 parent1[0; 2]: (203) {G2,W5,D3,L1,V2,M1} P(3,23);q { leq( X, addition( X, Y
% 2.09/2.49 ) ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := X
% 2.09/2.49 Y := Y
% 2.09/2.49 end
% 2.09/2.49 substitution1:
% 2.09/2.49 X := X
% 2.09/2.49 Y := Y
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 subsumption: (213) {G3,W5,D3,L1,V2,M1} P(0,203) { leq( X, addition( Y, X )
% 2.09/2.49 ) }.
% 2.09/2.49 parent0: (11827) {G1,W5,D3,L1,V2,M1} { leq( X, addition( Y, X ) ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := X
% 2.09/2.49 Y := Y
% 2.09/2.49 end
% 2.09/2.49 permutation0:
% 2.09/2.49 0 ==> 0
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 eqswap: (11829) {G1,W11,D4,L1,V3,M1} { addition( addition( Y, Z ), X ) =
% 2.09/2.49 addition( addition( X, Y ), Z ) }.
% 2.09/2.49 parent0[0]: (24) {G1,W11,D4,L1,V3,M1} P(1,0) { addition( addition( X, Y ),
% 2.09/2.49 Z ) = addition( addition( Y, Z ), X ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := X
% 2.09/2.49 Y := Y
% 2.09/2.49 Z := Z
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 paramod: (11830) {G2,W7,D4,L1,V3,M1} { leq( X, addition( addition( X, Y )
% 2.09/2.49 , Z ) ) }.
% 2.09/2.49 parent0[0]: (11829) {G1,W11,D4,L1,V3,M1} { addition( addition( Y, Z ), X )
% 2.09/2.49 = addition( addition( X, Y ), Z ) }.
% 2.09/2.49 parent1[0; 2]: (213) {G3,W5,D3,L1,V2,M1} P(0,203) { leq( X, addition( Y, X
% 2.09/2.49 ) ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := X
% 2.09/2.49 Y := Y
% 2.09/2.49 Z := Z
% 2.09/2.49 end
% 2.09/2.49 substitution1:
% 2.09/2.49 X := X
% 2.09/2.49 Y := addition( Y, Z )
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 paramod: (11831) {G2,W7,D4,L1,V3,M1} { leq( X, addition( addition( Z, X )
% 2.09/2.49 , Y ) ) }.
% 2.09/2.49 parent0[0]: (11829) {G1,W11,D4,L1,V3,M1} { addition( addition( Y, Z ), X )
% 2.09/2.49 = addition( addition( X, Y ), Z ) }.
% 2.09/2.49 parent1[0; 2]: (11830) {G2,W7,D4,L1,V3,M1} { leq( X, addition( addition( X
% 2.09/2.49 , Y ), Z ) ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := Z
% 2.09/2.49 Y := X
% 2.09/2.49 Z := Y
% 2.09/2.49 end
% 2.09/2.49 substitution1:
% 2.09/2.49 X := X
% 2.09/2.49 Y := Y
% 2.09/2.49 Z := Z
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 subsumption: (234) {G4,W7,D4,L1,V3,M1} P(24,213) { leq( Z, addition(
% 2.09/2.49 addition( Y, Z ), X ) ) }.
% 2.09/2.49 parent0: (11831) {G2,W7,D4,L1,V3,M1} { leq( X, addition( addition( Z, X )
% 2.09/2.49 , Y ) ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := Z
% 2.09/2.49 Y := X
% 2.09/2.49 Z := Y
% 2.09/2.49 end
% 2.09/2.49 permutation0:
% 2.09/2.49 0 ==> 0
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 paramod: (11834) {G1,W8,D3,L2,V3,M2} { leq( X, Z ), ! leq( addition( Y, X
% 2.09/2.49 ), Z ) }.
% 2.09/2.49 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 2.09/2.49 ==> Y }.
% 2.09/2.49 parent1[0; 2]: (234) {G4,W7,D4,L1,V3,M1} P(24,213) { leq( Z, addition(
% 2.09/2.49 addition( Y, Z ), X ) ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := addition( Y, X )
% 2.09/2.49 Y := Z
% 2.09/2.49 end
% 2.09/2.49 substitution1:
% 2.09/2.49 X := Z
% 2.09/2.49 Y := Y
% 2.09/2.49 Z := X
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 subsumption: (293) {G5,W8,D3,L2,V3,M2} P(11,234) { leq( Y, Z ), ! leq(
% 2.09/2.49 addition( X, Y ), Z ) }.
% 2.09/2.49 parent0: (11834) {G1,W8,D3,L2,V3,M2} { leq( X, Z ), ! leq( addition( Y, X
% 2.09/2.49 ), Z ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := Y
% 2.09/2.49 Y := X
% 2.09/2.49 Z := Z
% 2.09/2.49 end
% 2.09/2.49 permutation0:
% 2.09/2.49 0 ==> 0
% 2.09/2.49 1 ==> 1
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 paramod: (11839) {G1,W8,D3,L2,V3,M2} { leq( X, Z ), ! leq( addition( X, Y
% 2.09/2.49 ), Z ) }.
% 2.09/2.49 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 2.09/2.49 ==> Y }.
% 2.09/2.49 parent1[0; 2]: (212) {G3,W7,D4,L1,V3,M1} P(1,203) { leq( X, addition(
% 2.09/2.49 addition( X, Y ), Z ) ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := addition( X, Y )
% 2.09/2.49 Y := Z
% 2.09/2.49 end
% 2.09/2.49 substitution1:
% 2.09/2.49 X := X
% 2.09/2.49 Y := Y
% 2.09/2.49 Z := Z
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 subsumption: (303) {G4,W8,D3,L2,V3,M2} P(11,212) { leq( X, Z ), ! leq(
% 2.09/2.49 addition( X, Y ), Z ) }.
% 2.09/2.49 parent0: (11839) {G1,W8,D3,L2,V3,M2} { leq( X, Z ), ! leq( addition( X, Y
% 2.09/2.49 ), Z ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := X
% 2.09/2.49 Y := Y
% 2.09/2.49 Z := Z
% 2.09/2.49 end
% 2.09/2.49 permutation0:
% 2.09/2.49 0 ==> 0
% 2.09/2.49 1 ==> 1
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 resolution: (11843) {G1,W4,D3,L1,V1,M1} { leq( one, star( X ) ) }.
% 2.09/2.49 parent0[1]: (303) {G4,W8,D3,L2,V3,M2} P(11,212) { leq( X, Z ), ! leq(
% 2.09/2.49 addition( X, Y ), Z ) }.
% 2.09/2.49 parent1[0]: (14) {G0,W9,D5,L1,V1,M1} I { leq( addition( one, multiplication
% 2.09/2.49 ( star( X ), X ) ), star( X ) ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := one
% 2.09/2.49 Y := multiplication( star( X ), X )
% 2.09/2.49 Z := star( X )
% 2.09/2.49 end
% 2.09/2.49 substitution1:
% 2.09/2.49 X := X
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 subsumption: (435) {G5,W4,D3,L1,V1,M1} R(303,14) { leq( one, star( X ) )
% 2.09/2.49 }.
% 2.09/2.49 parent0: (11843) {G1,W4,D3,L1,V1,M1} { leq( one, star( X ) ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := X
% 2.09/2.49 end
% 2.09/2.49 permutation0:
% 2.09/2.49 0 ==> 0
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 paramod: (11845) {G1,W9,D2,L3,V3,M3} { ! leq( Y, Z ), ! leq( X, Y ), leq(
% 2.09/2.49 X, Z ) }.
% 2.09/2.49 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 2.09/2.49 ==> Y }.
% 2.09/2.49 parent1[1; 2]: (303) {G4,W8,D3,L2,V3,M2} P(11,212) { leq( X, Z ), ! leq(
% 2.09/2.49 addition( X, Y ), Z ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := X
% 2.09/2.49 Y := Y
% 2.09/2.49 end
% 2.09/2.49 substitution1:
% 2.09/2.49 X := X
% 2.09/2.49 Y := Y
% 2.09/2.49 Z := Z
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 subsumption: (444) {G5,W9,D2,L3,V3,M3} P(11,303) { leq( X, Z ), ! leq( Y, Z
% 2.09/2.49 ), ! leq( X, Y ) }.
% 2.09/2.49 parent0: (11845) {G1,W9,D2,L3,V3,M3} { ! leq( Y, Z ), ! leq( X, Y ), leq(
% 2.09/2.49 X, Z ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := X
% 2.09/2.49 Y := Y
% 2.09/2.49 Z := Z
% 2.09/2.49 end
% 2.09/2.49 permutation0:
% 2.09/2.49 0 ==> 1
% 2.09/2.49 1 ==> 2
% 2.09/2.49 2 ==> 0
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 eqswap: (11847) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X, Y
% 2.09/2.49 ) }.
% 2.09/2.49 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 2.09/2.49 ==> Y }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := X
% 2.09/2.49 Y := Y
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 resolution: (11848) {G1,W7,D4,L1,V1,M1} { star( X ) ==> addition( one,
% 2.09/2.49 star( X ) ) }.
% 2.09/2.49 parent0[1]: (11847) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X
% 2.09/2.49 , Y ) }.
% 2.09/2.49 parent1[0]: (435) {G5,W4,D3,L1,V1,M1} R(303,14) { leq( one, star( X ) ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := one
% 2.09/2.49 Y := star( X )
% 2.09/2.49 end
% 2.09/2.49 substitution1:
% 2.09/2.49 X := X
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 eqswap: (11849) {G1,W7,D4,L1,V1,M1} { addition( one, star( X ) ) ==> star
% 2.09/2.49 ( X ) }.
% 2.09/2.49 parent0[0]: (11848) {G1,W7,D4,L1,V1,M1} { star( X ) ==> addition( one,
% 2.09/2.49 star( X ) ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := X
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 subsumption: (446) {G6,W7,D4,L1,V1,M1} R(435,11) { addition( one, star( X )
% 2.09/2.49 ) ==> star( X ) }.
% 2.09/2.49 parent0: (11849) {G1,W7,D4,L1,V1,M1} { addition( one, star( X ) ) ==> star
% 2.09/2.49 ( X ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := X
% 2.09/2.49 end
% 2.09/2.49 permutation0:
% 2.09/2.49 0 ==> 0
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 paramod: (11851) {G5,W7,D3,L2,V2,M2} { ! leq( star( X ), Y ), leq( one, Y
% 2.09/2.49 ) }.
% 2.09/2.49 parent0[0]: (446) {G6,W7,D4,L1,V1,M1} R(435,11) { addition( one, star( X )
% 2.09/2.49 ) ==> star( X ) }.
% 2.09/2.49 parent1[1; 2]: (303) {G4,W8,D3,L2,V3,M2} P(11,212) { leq( X, Z ), ! leq(
% 2.09/2.49 addition( X, Y ), Z ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := X
% 2.09/2.49 end
% 2.09/2.49 substitution1:
% 2.09/2.49 X := one
% 2.09/2.49 Y := star( X )
% 2.09/2.49 Z := Y
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 subsumption: (473) {G7,W7,D3,L2,V2,M2} P(446,303) { leq( one, Y ), ! leq(
% 2.09/2.49 star( X ), Y ) }.
% 2.09/2.49 parent0: (11851) {G5,W7,D3,L2,V2,M2} { ! leq( star( X ), Y ), leq( one, Y
% 2.09/2.49 ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := X
% 2.09/2.49 Y := Y
% 2.09/2.49 end
% 2.09/2.49 permutation0:
% 2.09/2.49 0 ==> 1
% 2.09/2.49 1 ==> 0
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 eqswap: (11852) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y, X
% 2.09/2.49 ) }.
% 2.09/2.49 parent0[0]: (35) {G1,W8,D3,L2,V2,M2} P(11,0) { addition( Y, X ) ==> Y, !
% 2.09/2.49 leq( X, Y ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := Y
% 2.09/2.49 Y := X
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 paramod: (11854) {G1,W9,D2,L3,V2,M3} { X ==> Y, ! leq( X, Y ), ! leq( Y, X
% 2.09/2.49 ) }.
% 2.09/2.49 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 2.09/2.49 ==> Y }.
% 2.09/2.49 parent1[0; 2]: (11852) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq
% 2.09/2.49 ( Y, X ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := X
% 2.09/2.49 Y := Y
% 2.09/2.49 end
% 2.09/2.49 substitution1:
% 2.09/2.49 X := X
% 2.09/2.49 Y := Y
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 subsumption: (561) {G2,W9,D2,L3,V2,M3} P(35,11) { ! leq( X, Y ), X = Y, !
% 2.09/2.49 leq( Y, X ) }.
% 2.09/2.49 parent0: (11854) {G1,W9,D2,L3,V2,M3} { X ==> Y, ! leq( X, Y ), ! leq( Y, X
% 2.09/2.49 ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := X
% 2.09/2.49 Y := Y
% 2.09/2.49 end
% 2.09/2.49 permutation0:
% 2.09/2.49 0 ==> 1
% 2.09/2.49 1 ==> 0
% 2.09/2.49 2 ==> 2
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 resolution: (11856) {G1,W7,D4,L1,V1,M1} { leq( multiplication( star( X ),
% 2.09/2.49 X ), star( X ) ) }.
% 2.09/2.49 parent0[1]: (293) {G5,W8,D3,L2,V3,M2} P(11,234) { leq( Y, Z ), ! leq(
% 2.09/2.49 addition( X, Y ), Z ) }.
% 2.09/2.49 parent1[0]: (14) {G0,W9,D5,L1,V1,M1} I { leq( addition( one, multiplication
% 2.09/2.49 ( star( X ), X ) ), star( X ) ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := one
% 2.09/2.49 Y := multiplication( star( X ), X )
% 2.09/2.49 Z := star( X )
% 2.09/2.49 end
% 2.09/2.49 substitution1:
% 2.09/2.49 X := X
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 subsumption: (612) {G6,W7,D4,L1,V1,M1} R(293,14) { leq( multiplication(
% 2.09/2.49 star( X ), X ), star( X ) ) }.
% 2.09/2.49 parent0: (11856) {G1,W7,D4,L1,V1,M1} { leq( multiplication( star( X ), X )
% 2.09/2.49 , star( X ) ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := X
% 2.09/2.49 end
% 2.09/2.49 permutation0:
% 2.09/2.49 0 ==> 0
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 resolution: (11857) {G1,W7,D4,L1,V1,M1} { leq( multiplication( X, star( X
% 2.09/2.49 ) ), star( X ) ) }.
% 2.09/2.49 parent0[1]: (293) {G5,W8,D3,L2,V3,M2} P(11,234) { leq( Y, Z ), ! leq(
% 2.09/2.49 addition( X, Y ), Z ) }.
% 2.09/2.49 parent1[0]: (13) {G0,W9,D5,L1,V1,M1} I { leq( addition( one, multiplication
% 2.09/2.49 ( X, star( X ) ) ), star( X ) ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := one
% 2.09/2.49 Y := multiplication( X, star( X ) )
% 2.09/2.49 Z := star( X )
% 2.09/2.49 end
% 2.09/2.49 substitution1:
% 2.09/2.49 X := X
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 subsumption: (613) {G6,W7,D4,L1,V1,M1} R(293,13) { leq( multiplication( X,
% 2.09/2.49 star( X ) ), star( X ) ) }.
% 2.09/2.49 parent0: (11857) {G1,W7,D4,L1,V1,M1} { leq( multiplication( X, star( X ) )
% 2.09/2.49 , star( X ) ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := X
% 2.09/2.49 end
% 2.09/2.49 permutation0:
% 2.09/2.49 0 ==> 0
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 eqswap: (11859) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Z ) ==>
% 2.09/2.49 multiplication( X, addition( Y, Z ) ), leq( multiplication( X, Y ),
% 2.09/2.49 multiplication( X, Z ) ) }.
% 2.09/2.49 parent0[0]: (69) {G1,W16,D4,L2,V3,M2} P(7,12) { ! multiplication( X,
% 2.09/2.49 addition( Y, Z ) ) ==> multiplication( X, Z ), leq( multiplication( X, Y
% 2.09/2.49 ), multiplication( X, Z ) ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := X
% 2.09/2.49 Y := Y
% 2.09/2.49 Z := Z
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 paramod: (11861) {G2,W17,D4,L2,V2,M2} { ! multiplication( X, star( Y ) )
% 2.09/2.49 ==> multiplication( X, star( Y ) ), leq( multiplication( X, one ),
% 2.09/2.49 multiplication( X, star( Y ) ) ) }.
% 2.09/2.49 parent0[0]: (446) {G6,W7,D4,L1,V1,M1} R(435,11) { addition( one, star( X )
% 2.09/2.49 ) ==> star( X ) }.
% 2.09/2.49 parent1[0; 8]: (11859) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Z ) ==>
% 2.09/2.49 multiplication( X, addition( Y, Z ) ), leq( multiplication( X, Y ),
% 2.09/2.49 multiplication( X, Z ) ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := Y
% 2.09/2.49 end
% 2.09/2.49 substitution1:
% 2.09/2.49 X := X
% 2.09/2.49 Y := one
% 2.09/2.49 Z := star( Y )
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 eqrefl: (11862) {G0,W8,D4,L1,V2,M1} { leq( multiplication( X, one ),
% 2.09/2.49 multiplication( X, star( Y ) ) ) }.
% 2.09/2.49 parent0[0]: (11861) {G2,W17,D4,L2,V2,M2} { ! multiplication( X, star( Y )
% 2.09/2.49 ) ==> multiplication( X, star( Y ) ), leq( multiplication( X, one ),
% 2.09/2.49 multiplication( X, star( Y ) ) ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := X
% 2.09/2.49 Y := Y
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 paramod: (11863) {G1,W6,D4,L1,V2,M1} { leq( X, multiplication( X, star( Y
% 2.09/2.49 ) ) ) }.
% 2.09/2.49 parent0[0]: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 2.09/2.49 parent1[0; 1]: (11862) {G0,W8,D4,L1,V2,M1} { leq( multiplication( X, one )
% 2.09/2.49 , multiplication( X, star( Y ) ) ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := X
% 2.09/2.49 end
% 2.09/2.49 substitution1:
% 2.09/2.49 X := X
% 2.09/2.49 Y := Y
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 subsumption: (2122) {G7,W6,D4,L1,V2,M1} P(446,69);q;d(5) { leq( Y,
% 2.09/2.49 multiplication( Y, star( X ) ) ) }.
% 2.09/2.49 parent0: (11863) {G1,W6,D4,L1,V2,M1} { leq( X, multiplication( X, star( Y
% 2.09/2.49 ) ) ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := Y
% 2.09/2.49 Y := X
% 2.09/2.49 end
% 2.09/2.49 permutation0:
% 2.09/2.49 0 ==> 0
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 resolution: (11864) {G8,W7,D4,L1,V2,M1} { leq( one, multiplication( star(
% 2.09/2.49 X ), star( Y ) ) ) }.
% 2.09/2.49 parent0[1]: (473) {G7,W7,D3,L2,V2,M2} P(446,303) { leq( one, Y ), ! leq(
% 2.09/2.49 star( X ), Y ) }.
% 2.09/2.49 parent1[0]: (2122) {G7,W6,D4,L1,V2,M1} P(446,69);q;d(5) { leq( Y,
% 2.09/2.49 multiplication( Y, star( X ) ) ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := X
% 2.09/2.49 Y := multiplication( star( X ), star( Y ) )
% 2.09/2.49 end
% 2.09/2.49 substitution1:
% 2.09/2.49 X := Y
% 2.09/2.49 Y := star( X )
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 subsumption: (2146) {G8,W7,D4,L1,V2,M1} R(2122,473) { leq( one,
% 2.09/2.49 multiplication( star( X ), star( Y ) ) ) }.
% 2.09/2.49 parent0: (11864) {G8,W7,D4,L1,V2,M1} { leq( one, multiplication( star( X )
% 2.09/2.49 , star( Y ) ) ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := X
% 2.09/2.49 Y := Y
% 2.09/2.49 end
% 2.09/2.49 permutation0:
% 2.09/2.49 0 ==> 0
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 eqswap: (11865) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y, X
% 2.09/2.49 ) }.
% 2.09/2.49 parent0[0]: (35) {G1,W8,D3,L2,V2,M2} P(11,0) { addition( Y, X ) ==> Y, !
% 2.09/2.49 leq( X, Y ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := Y
% 2.09/2.49 Y := X
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 resolution: (11866) {G2,W13,D5,L1,V2,M1} { multiplication( star( X ), star
% 2.09/2.49 ( Y ) ) ==> addition( multiplication( star( X ), star( Y ) ), one ) }.
% 2.09/2.49 parent0[1]: (11865) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y
% 2.09/2.49 , X ) }.
% 2.09/2.49 parent1[0]: (2146) {G8,W7,D4,L1,V2,M1} R(2122,473) { leq( one,
% 2.09/2.49 multiplication( star( X ), star( Y ) ) ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := multiplication( star( X ), star( Y ) )
% 2.09/2.49 Y := one
% 2.09/2.49 end
% 2.09/2.49 substitution1:
% 2.09/2.49 X := X
% 2.09/2.49 Y := Y
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 eqswap: (11867) {G2,W13,D5,L1,V2,M1} { addition( multiplication( star( X )
% 2.09/2.49 , star( Y ) ), one ) ==> multiplication( star( X ), star( Y ) ) }.
% 2.09/2.49 parent0[0]: (11866) {G2,W13,D5,L1,V2,M1} { multiplication( star( X ), star
% 2.09/2.49 ( Y ) ) ==> addition( multiplication( star( X ), star( Y ) ), one ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := X
% 2.09/2.49 Y := Y
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 subsumption: (2179) {G9,W13,D5,L1,V2,M1} R(2146,35) { addition(
% 2.09/2.49 multiplication( star( X ), star( Y ) ), one ) ==> multiplication( star( X
% 2.09/2.49 ), star( Y ) ) }.
% 2.09/2.49 parent0: (11867) {G2,W13,D5,L1,V2,M1} { addition( multiplication( star( X
% 2.09/2.49 ), star( Y ) ), one ) ==> multiplication( star( X ), star( Y ) ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := X
% 2.09/2.49 Y := Y
% 2.09/2.49 end
% 2.09/2.49 permutation0:
% 2.09/2.49 0 ==> 0
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 eqswap: (11869) {G1,W16,D4,L2,V3,M2} { ! multiplication( Y, Z ) ==>
% 2.09/2.49 multiplication( addition( X, Y ), Z ), leq( multiplication( X, Z ),
% 2.09/2.49 multiplication( Y, Z ) ) }.
% 2.09/2.49 parent0[0]: (101) {G1,W16,D4,L2,V3,M2} P(8,12) { ! multiplication( addition
% 2.09/2.49 ( X, Z ), Y ) ==> multiplication( Z, Y ), leq( multiplication( X, Y ),
% 2.09/2.49 multiplication( Z, Y ) ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := X
% 2.09/2.49 Y := Z
% 2.09/2.49 Z := Y
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 paramod: (11871) {G2,W17,D4,L2,V2,M2} { ! multiplication( star( X ), Y )
% 2.09/2.49 ==> multiplication( star( X ), Y ), leq( multiplication( one, Y ),
% 2.09/2.49 multiplication( star( X ), Y ) ) }.
% 2.09/2.49 parent0[0]: (446) {G6,W7,D4,L1,V1,M1} R(435,11) { addition( one, star( X )
% 2.09/2.49 ) ==> star( X ) }.
% 2.09/2.49 parent1[0; 7]: (11869) {G1,W16,D4,L2,V3,M2} { ! multiplication( Y, Z ) ==>
% 2.09/2.49 multiplication( addition( X, Y ), Z ), leq( multiplication( X, Z ),
% 2.09/2.49 multiplication( Y, Z ) ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := X
% 2.09/2.49 end
% 2.09/2.49 substitution1:
% 2.09/2.49 X := one
% 2.09/2.49 Y := star( X )
% 2.09/2.49 Z := Y
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 eqrefl: (11872) {G0,W8,D4,L1,V2,M1} { leq( multiplication( one, Y ),
% 2.09/2.49 multiplication( star( X ), Y ) ) }.
% 2.09/2.49 parent0[0]: (11871) {G2,W17,D4,L2,V2,M2} { ! multiplication( star( X ), Y
% 2.09/2.49 ) ==> multiplication( star( X ), Y ), leq( multiplication( one, Y ),
% 2.09/2.49 multiplication( star( X ), Y ) ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := X
% 2.09/2.49 Y := Y
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 paramod: (11873) {G1,W6,D4,L1,V2,M1} { leq( X, multiplication( star( Y ),
% 2.09/2.49 X ) ) }.
% 2.09/2.49 parent0[0]: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 2.09/2.49 parent1[0; 1]: (11872) {G0,W8,D4,L1,V2,M1} { leq( multiplication( one, Y )
% 2.09/2.49 , multiplication( star( X ), Y ) ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := X
% 2.09/2.49 end
% 2.09/2.49 substitution1:
% 2.09/2.49 X := Y
% 2.09/2.49 Y := X
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 subsumption: (3809) {G7,W6,D4,L1,V2,M1} P(446,101);q;d(6) { leq( Y,
% 2.09/2.49 multiplication( star( X ), Y ) ) }.
% 2.09/2.49 parent0: (11873) {G1,W6,D4,L1,V2,M1} { leq( X, multiplication( star( Y ),
% 2.09/2.49 X ) ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := Y
% 2.09/2.49 Y := X
% 2.09/2.49 end
% 2.09/2.49 permutation0:
% 2.09/2.49 0 ==> 0
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 resolution: (11875) {G6,W9,D4,L2,V3,M2} { leq( X, Y ), ! leq(
% 2.09/2.49 multiplication( star( Z ), X ), Y ) }.
% 2.09/2.49 parent0[2]: (444) {G5,W9,D2,L3,V3,M3} P(11,303) { leq( X, Z ), ! leq( Y, Z
% 2.09/2.49 ), ! leq( X, Y ) }.
% 2.09/2.49 parent1[0]: (3809) {G7,W6,D4,L1,V2,M1} P(446,101);q;d(6) { leq( Y,
% 2.09/2.49 multiplication( star( X ), Y ) ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := X
% 2.09/2.49 Y := multiplication( star( Z ), X )
% 2.09/2.49 Z := Y
% 2.09/2.49 end
% 2.09/2.49 substitution1:
% 2.09/2.49 X := Z
% 2.09/2.49 Y := X
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 subsumption: (3821) {G8,W9,D4,L2,V3,M2} R(3809,444) { leq( X, Y ), ! leq(
% 2.09/2.49 multiplication( star( Z ), X ), Y ) }.
% 2.09/2.49 parent0: (11875) {G6,W9,D4,L2,V3,M2} { leq( X, Y ), ! leq( multiplication
% 2.09/2.49 ( star( Z ), X ), Y ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := X
% 2.09/2.49 Y := Y
% 2.09/2.49 Z := Z
% 2.09/2.49 end
% 2.09/2.49 permutation0:
% 2.09/2.49 0 ==> 0
% 2.09/2.49 1 ==> 1
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 resolution: (11876) {G7,W4,D3,L1,V1,M1} { leq( X, star( X ) ) }.
% 2.09/2.49 parent0[1]: (3821) {G8,W9,D4,L2,V3,M2} R(3809,444) { leq( X, Y ), ! leq(
% 2.09/2.49 multiplication( star( Z ), X ), Y ) }.
% 2.09/2.49 parent1[0]: (612) {G6,W7,D4,L1,V1,M1} R(293,14) { leq( multiplication( star
% 2.09/2.49 ( X ), X ), star( X ) ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := X
% 2.09/2.49 Y := star( X )
% 2.09/2.49 Z := X
% 2.09/2.49 end
% 2.09/2.49 substitution1:
% 2.09/2.49 X := X
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 subsumption: (5868) {G9,W4,D3,L1,V1,M1} R(3821,612) { leq( X, star( X ) )
% 2.09/2.49 }.
% 2.09/2.49 parent0: (11876) {G7,W4,D3,L1,V1,M1} { leq( X, star( X ) ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := X
% 2.09/2.49 end
% 2.09/2.49 permutation0:
% 2.09/2.49 0 ==> 0
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 resolution: (11878) {G3,W8,D3,L2,V1,M2} { ! leq( star( X ), X ), star( X )
% 2.09/2.49 = X }.
% 2.09/2.49 parent0[2]: (561) {G2,W9,D2,L3,V2,M3} P(35,11) { ! leq( X, Y ), X = Y, !
% 2.09/2.49 leq( Y, X ) }.
% 2.09/2.49 parent1[0]: (5868) {G9,W4,D3,L1,V1,M1} R(3821,612) { leq( X, star( X ) )
% 2.09/2.49 }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := star( X )
% 2.09/2.49 Y := X
% 2.09/2.49 end
% 2.09/2.49 substitution1:
% 2.09/2.49 X := X
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 subsumption: (5883) {G10,W8,D3,L2,V1,M2} R(5868,561) { star( X ) ==> X, !
% 2.09/2.49 leq( star( X ), X ) }.
% 2.09/2.49 parent0: (11878) {G3,W8,D3,L2,V1,M2} { ! leq( star( X ), X ), star( X ) =
% 2.09/2.49 X }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := X
% 2.09/2.49 end
% 2.09/2.49 permutation0:
% 2.09/2.49 0 ==> 1
% 2.09/2.49 1 ==> 0
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 resolution: (11880) {G2,W13,D4,L2,V1,M2} { ! leq( star( X ), star( X ) ),
% 2.09/2.49 leq( multiplication( star( X ), star( X ) ), star( X ) ) }.
% 2.09/2.49 parent0[2]: (156) {G1,W14,D4,L3,V3,M3} P(11,15) { ! leq( Z, Y ), leq(
% 2.09/2.49 multiplication( star( X ), Z ), Y ), ! leq( multiplication( X, Y ), Z )
% 2.09/2.49 }.
% 2.09/2.49 parent1[0]: (613) {G6,W7,D4,L1,V1,M1} R(293,13) { leq( multiplication( X,
% 2.09/2.49 star( X ) ), star( X ) ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := X
% 2.09/2.49 Y := star( X )
% 2.09/2.49 Z := star( X )
% 2.09/2.49 end
% 2.09/2.49 substitution1:
% 2.09/2.49 X := X
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 resolution: (11881) {G2,W8,D4,L1,V1,M1} { leq( multiplication( star( X ),
% 2.09/2.49 star( X ) ), star( X ) ) }.
% 2.09/2.49 parent0[0]: (11880) {G2,W13,D4,L2,V1,M2} { ! leq( star( X ), star( X ) ),
% 2.09/2.49 leq( multiplication( star( X ), star( X ) ), star( X ) ) }.
% 2.09/2.49 parent1[0]: (20) {G1,W3,D2,L1,V1,M1} R(12,3) { leq( X, X ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := X
% 2.09/2.49 end
% 2.09/2.49 substitution1:
% 2.09/2.49 X := star( X )
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 subsumption: (7635) {G7,W8,D4,L1,V1,M1} R(156,613);r(20) { leq(
% 2.09/2.49 multiplication( star( X ), star( X ) ), star( X ) ) }.
% 2.09/2.49 parent0: (11881) {G2,W8,D4,L1,V1,M1} { leq( multiplication( star( X ),
% 2.09/2.49 star( X ) ), star( X ) ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := X
% 2.09/2.49 end
% 2.09/2.49 permutation0:
% 2.09/2.49 0 ==> 0
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 eqswap: (11882) {G10,W8,D3,L2,V1,M2} { X ==> star( X ), ! leq( star( X ),
% 2.09/2.49 X ) }.
% 2.09/2.49 parent0[0]: (5883) {G10,W8,D3,L2,V1,M2} R(5868,561) { star( X ) ==> X, !
% 2.09/2.49 leq( star( X ), X ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := X
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 eqswap: (11883) {G0,W6,D4,L1,V0,M1} { ! star( skol1 ) ==> star( star(
% 2.09/2.49 skol1 ) ) }.
% 2.09/2.49 parent0[0]: (17) {G0,W6,D4,L1,V0,M1} I { ! star( star( skol1 ) ) ==> star(
% 2.09/2.49 skol1 ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 resolution: (11884) {G1,W6,D4,L1,V0,M1} { ! leq( star( star( skol1 ) ),
% 2.09/2.49 star( skol1 ) ) }.
% 2.09/2.49 parent0[0]: (11883) {G0,W6,D4,L1,V0,M1} { ! star( skol1 ) ==> star( star(
% 2.09/2.49 skol1 ) ) }.
% 2.09/2.49 parent1[0]: (11882) {G10,W8,D3,L2,V1,M2} { X ==> star( X ), ! leq( star( X
% 2.09/2.49 ), X ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 end
% 2.09/2.49 substitution1:
% 2.09/2.49 X := star( skol1 )
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 subsumption: (11625) {G11,W6,D4,L1,V0,M1} R(5883,17) { ! leq( star( star(
% 2.09/2.49 skol1 ) ), star( skol1 ) ) }.
% 2.09/2.49 parent0: (11884) {G1,W6,D4,L1,V0,M1} { ! leq( star( star( skol1 ) ), star
% 2.09/2.49 ( skol1 ) ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 end
% 2.09/2.49 permutation0:
% 2.09/2.49 0 ==> 0
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 resolution: (11886) {G2,W10,D5,L1,V0,M1} { ! leq( addition( multiplication
% 2.09/2.49 ( star( skol1 ), star( skol1 ) ), one ), star( skol1 ) ) }.
% 2.09/2.49 parent0[0]: (11625) {G11,W6,D4,L1,V0,M1} R(5883,17) { ! leq( star( star(
% 2.09/2.49 skol1 ) ), star( skol1 ) ) }.
% 2.09/2.49 parent1[1]: (190) {G1,W11,D4,L2,V2,M2} P(6,16) { ! leq( addition(
% 2.09/2.49 multiplication( Y, X ), one ), Y ), leq( star( X ), Y ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 end
% 2.09/2.49 substitution1:
% 2.09/2.49 X := star( skol1 )
% 2.09/2.49 Y := star( skol1 )
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 paramod: (11887) {G3,W8,D4,L1,V0,M1} { ! leq( multiplication( star( skol1
% 2.09/2.49 ), star( skol1 ) ), star( skol1 ) ) }.
% 2.09/2.49 parent0[0]: (2179) {G9,W13,D5,L1,V2,M1} R(2146,35) { addition(
% 2.09/2.49 multiplication( star( X ), star( Y ) ), one ) ==> multiplication( star( X
% 2.09/2.49 ), star( Y ) ) }.
% 2.09/2.49 parent1[0; 2]: (11886) {G2,W10,D5,L1,V0,M1} { ! leq( addition(
% 2.09/2.49 multiplication( star( skol1 ), star( skol1 ) ), one ), star( skol1 ) )
% 2.09/2.49 }.
% 2.09/2.49 substitution0:
% 2.09/2.49 X := skol1
% 2.09/2.49 Y := skol1
% 2.09/2.49 end
% 2.09/2.49 substitution1:
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 resolution: (11888) {G4,W0,D0,L0,V0,M0} { }.
% 2.09/2.49 parent0[0]: (11887) {G3,W8,D4,L1,V0,M1} { ! leq( multiplication( star(
% 2.09/2.49 skol1 ), star( skol1 ) ), star( skol1 ) ) }.
% 2.09/2.49 parent1[0]: (7635) {G7,W8,D4,L1,V1,M1} R(156,613);r(20) { leq(
% 2.09/2.49 multiplication( star( X ), star( X ) ), star( X ) ) }.
% 2.09/2.49 substitution0:
% 2.09/2.49 end
% 2.09/2.49 substitution1:
% 2.09/2.49 X := skol1
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 subsumption: (11641) {G12,W0,D0,L0,V0,M0} R(11625,190);d(2179);r(7635) {
% 2.09/2.49 }.
% 2.09/2.49 parent0: (11888) {G4,W0,D0,L0,V0,M0} { }.
% 2.09/2.49 substitution0:
% 2.09/2.49 end
% 2.09/2.49 permutation0:
% 2.09/2.49 end
% 2.09/2.49
% 2.09/2.49 Proof check complete!
% 2.09/2.49
% 2.09/2.49 Memory use:
% 2.09/2.49
% 2.09/2.49 space for terms: 159359
% 2.09/2.49 space for clauses: 567965
% 2.09/2.49
% 2.09/2.49
% 2.09/2.49 clauses generated: 116231
% 2.09/2.49 clauses kept: 11642
% 2.09/2.49 clauses selected: 595
% 2.09/2.49 clauses deleted: 137
% 2.09/2.49 clauses inuse deleted: 47
% 2.09/2.49
% 2.09/2.49 subsentry: 570683
% 2.09/2.49 literals s-matched: 283606
% 2.09/2.49 literals matched: 275345
% 2.09/2.49 full subsumption: 102454
% 2.09/2.49
% 2.09/2.49 checksum: 1421651191
% 2.09/2.49
% 2.09/2.49
% 2.09/2.49 Bliksem ended
%------------------------------------------------------------------------------