TSTP Solution File: KLE144+2 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : KLE144+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Sun Jul 17 01:37:26 EDT 2022
% Result : Theorem 2.07s 2.50s
% Output : Refutation 2.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : KLE144+2 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.14 % Command : bliksem %s
% 0.14/0.36 % Computer : n027.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % DateTime : Thu Jun 16 08:32:05 EDT 2022
% 0.14/0.36 % CPUTime :
% 2.07/2.50 *** allocated 10000 integers for termspace/termends
% 2.07/2.50 *** allocated 10000 integers for clauses
% 2.07/2.50 *** allocated 10000 integers for justifications
% 2.07/2.50 Bliksem 1.12
% 2.07/2.50
% 2.07/2.50
% 2.07/2.50 Automatic Strategy Selection
% 2.07/2.50
% 2.07/2.50
% 2.07/2.50 Clauses:
% 2.07/2.50
% 2.07/2.50 { addition( X, Y ) = addition( Y, X ) }.
% 2.07/2.50 { addition( Z, addition( Y, X ) ) = addition( addition( Z, Y ), X ) }.
% 2.07/2.50 { addition( X, zero ) = X }.
% 2.07/2.50 { addition( X, X ) = X }.
% 2.07/2.50 { multiplication( X, multiplication( Y, Z ) ) = multiplication(
% 2.07/2.50 multiplication( X, Y ), Z ) }.
% 2.07/2.50 { multiplication( X, one ) = X }.
% 2.07/2.50 { multiplication( one, X ) = X }.
% 2.07/2.50 { multiplication( X, addition( Y, Z ) ) = addition( multiplication( X, Y )
% 2.07/2.50 , multiplication( X, Z ) ) }.
% 2.07/2.50 { multiplication( addition( X, Y ), Z ) = addition( multiplication( X, Z )
% 2.07/2.50 , multiplication( Y, Z ) ) }.
% 2.07/2.50 { multiplication( zero, X ) = zero }.
% 2.07/2.50 { addition( one, multiplication( X, star( X ) ) ) = star( X ) }.
% 2.07/2.50 { addition( one, multiplication( star( X ), X ) ) = star( X ) }.
% 2.07/2.50 { ! leq( addition( multiplication( X, Z ), Y ), Z ), leq( multiplication(
% 2.07/2.50 star( X ), Y ), Z ) }.
% 2.07/2.50 { ! leq( addition( multiplication( Z, X ), Y ), Z ), leq( multiplication( Y
% 2.07/2.50 , star( X ) ), Z ) }.
% 2.07/2.50 { strong_iteration( X ) = addition( multiplication( X, strong_iteration( X
% 2.07/2.50 ) ), one ) }.
% 2.07/2.50 { ! leq( Z, addition( multiplication( X, Z ), Y ) ), leq( Z, multiplication
% 2.07/2.50 ( strong_iteration( X ), Y ) ) }.
% 2.07/2.50 { strong_iteration( X ) = addition( star( X ), multiplication(
% 2.07/2.50 strong_iteration( X ), zero ) ) }.
% 2.07/2.50 { ! leq( X, Y ), addition( X, Y ) = Y }.
% 2.07/2.50 { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 2.07/2.50 { ! leq( strong_iteration( star( skol1 ) ), strong_iteration( one ) ), !
% 2.07/2.50 leq( strong_iteration( one ), strong_iteration( star( skol1 ) ) ) }.
% 2.07/2.50
% 2.07/2.50 percentage equality = 0.615385, percentage horn = 1.000000
% 2.07/2.50 This is a problem with some equality
% 2.07/2.50
% 2.07/2.50
% 2.07/2.50
% 2.07/2.50 Options Used:
% 2.07/2.50
% 2.07/2.50 useres = 1
% 2.07/2.50 useparamod = 1
% 2.07/2.50 useeqrefl = 1
% 2.07/2.50 useeqfact = 1
% 2.07/2.50 usefactor = 1
% 2.07/2.50 usesimpsplitting = 0
% 2.07/2.50 usesimpdemod = 5
% 2.07/2.50 usesimpres = 3
% 2.07/2.50
% 2.07/2.50 resimpinuse = 1000
% 2.07/2.50 resimpclauses = 20000
% 2.07/2.50 substype = eqrewr
% 2.07/2.50 backwardsubs = 1
% 2.07/2.50 selectoldest = 5
% 2.07/2.50
% 2.07/2.50 litorderings [0] = split
% 2.07/2.50 litorderings [1] = extend the termordering, first sorting on arguments
% 2.07/2.50
% 2.07/2.50 termordering = kbo
% 2.07/2.50
% 2.07/2.50 litapriori = 0
% 2.07/2.50 termapriori = 1
% 2.07/2.50 litaposteriori = 0
% 2.07/2.50 termaposteriori = 0
% 2.07/2.50 demodaposteriori = 0
% 2.07/2.50 ordereqreflfact = 0
% 2.07/2.50
% 2.07/2.50 litselect = negord
% 2.07/2.50
% 2.07/2.50 maxweight = 15
% 2.07/2.50 maxdepth = 30000
% 2.07/2.50 maxlength = 115
% 2.07/2.50 maxnrvars = 195
% 2.07/2.50 excuselevel = 1
% 2.07/2.50 increasemaxweight = 1
% 2.07/2.50
% 2.07/2.50 maxselected = 10000000
% 2.07/2.50 maxnrclauses = 10000000
% 2.07/2.50
% 2.07/2.50 showgenerated = 0
% 2.07/2.50 showkept = 0
% 2.07/2.50 showselected = 0
% 2.07/2.50 showdeleted = 0
% 2.07/2.50 showresimp = 1
% 2.07/2.50 showstatus = 2000
% 2.07/2.50
% 2.07/2.50 prologoutput = 0
% 2.07/2.50 nrgoals = 5000000
% 2.07/2.50 totalproof = 1
% 2.07/2.50
% 2.07/2.50 Symbols occurring in the translation:
% 2.07/2.50
% 2.07/2.50 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 2.07/2.50 . [1, 2] (w:1, o:20, a:1, s:1, b:0),
% 2.07/2.50 ! [4, 1] (w:0, o:13, a:1, s:1, b:0),
% 2.07/2.50 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 2.07/2.50 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 2.07/2.50 addition [37, 2] (w:1, o:44, a:1, s:1, b:0),
% 2.07/2.50 zero [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 2.07/2.50 multiplication [40, 2] (w:1, o:46, a:1, s:1, b:0),
% 2.07/2.50 one [41, 0] (w:1, o:10, a:1, s:1, b:0),
% 2.07/2.50 star [42, 1] (w:1, o:18, a:1, s:1, b:0),
% 2.07/2.50 leq [43, 2] (w:1, o:45, a:1, s:1, b:0),
% 2.07/2.50 strong_iteration [44, 1] (w:1, o:19, a:1, s:1, b:0),
% 2.07/2.50 skol1 [46, 0] (w:1, o:12, a:1, s:1, b:1).
% 2.07/2.50
% 2.07/2.50
% 2.07/2.50 Starting Search:
% 2.07/2.50
% 2.07/2.50 *** allocated 15000 integers for clauses
% 2.07/2.50 *** allocated 22500 integers for clauses
% 2.07/2.50 *** allocated 33750 integers for clauses
% 2.07/2.50 *** allocated 50625 integers for clauses
% 2.07/2.50 *** allocated 15000 integers for termspace/termends
% 2.07/2.50 *** allocated 75937 integers for clauses
% 2.07/2.50 Resimplifying inuse:
% 2.07/2.50 Done
% 2.07/2.50
% 2.07/2.50 *** allocated 22500 integers for termspace/termends
% 2.07/2.50 *** allocated 113905 integers for clauses
% 2.07/2.50 *** allocated 33750 integers for termspace/termends
% 2.07/2.50
% 2.07/2.50 Intermediate Status:
% 2.07/2.50 Generated: 21706
% 2.07/2.50 Kept: 2058
% 2.07/2.50 Inuse: 233
% 2.07/2.50 Deleted: 53
% 2.07/2.50 Deletedinuse: 30
% 2.07/2.50
% 2.07/2.50 Resimplifying inuse:
% 2.07/2.50 Done
% 2.07/2.50
% 2.07/2.50 *** allocated 170857 integers for clauses
% 2.07/2.50 *** allocated 50625 integers for termspace/termends
% 2.07/2.50 Resimplifying inuse:
% 2.07/2.50 Done
% 2.07/2.50
% 2.07/2.50 *** allocated 256285 integers for clauses
% 2.07/2.50 *** allocated 75937 integers for termspace/termends
% 2.07/2.50
% 2.07/2.50 Intermediate Status:
% 2.07/2.50 Generated: 47839
% 2.07/2.50 Kept: 4058
% 2.07/2.50 Inuse: 399
% 2.07/2.50 Deleted: 68
% 2.07/2.50 Deletedinuse: 31
% 2.07/2.50
% 2.07/2.50 Resimplifying inuse:
% 2.07/2.50 Done
% 2.07/2.50
% 2.07/2.50 *** allocated 384427 integers for clauses
% 2.07/2.50 Resimplifying inuse:
% 2.07/2.50 Done
% 2.07/2.50
% 2.07/2.50 *** allocated 113905 integers for termspace/termends
% 2.07/2.50
% 2.07/2.50 Intermediate Status:
% 2.07/2.50 Generated: 77700
% 2.07/2.50 Kept: 6134
% 2.07/2.50 Inuse: 588
% 2.07/2.50 Deleted: 122
% 2.07/2.50 Deletedinuse: 35
% 2.07/2.50
% 2.07/2.50 Resimplifying inuse:
% 2.07/2.50 Done
% 2.07/2.50
% 2.07/2.50 Resimplifying inuse:
% 2.07/2.50 Done
% 2.07/2.50
% 2.07/2.50 *** allocated 576640 integers for clauses
% 2.07/2.50
% 2.07/2.50 Intermediate Status:
% 2.07/2.50 Generated: 108831
% 2.07/2.50 Kept: 8223
% 2.07/2.50 Inuse: 729
% 2.07/2.50 Deleted: 136
% 2.07/2.50 Deletedinuse: 35
% 2.07/2.50
% 2.07/2.50 Resimplifying inuse:
% 2.07/2.50 Done
% 2.07/2.50
% 2.07/2.50 *** allocated 170857 integers for termspace/termends
% 2.07/2.50 Resimplifying inuse:
% 2.07/2.50 Done
% 2.07/2.50
% 2.07/2.50
% 2.07/2.50 Bliksems!, er is een bewijs:
% 2.07/2.50 % SZS status Theorem
% 2.07/2.50 % SZS output start Refutation
% 2.07/2.50
% 2.07/2.50 (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X ) }.
% 2.07/2.50 (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) ) ==> addition(
% 2.07/2.50 addition( Z, Y ), X ) }.
% 2.07/2.50 (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 2.07/2.50 (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 2.07/2.50 (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 2.07/2.50 (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 2.07/2.50 (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 2.07/2.50 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 2.07/2.50 (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ),
% 2.07/2.50 multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 2.07/2.50 (11) {G0,W9,D5,L1,V1,M1} I { addition( one, multiplication( star( X ), X )
% 2.07/2.50 ) ==> star( X ) }.
% 2.07/2.50 (15) {G0,W13,D4,L2,V3,M2} I { ! leq( Z, addition( multiplication( X, Z ), Y
% 2.07/2.50 ) ), leq( Z, multiplication( strong_iteration( X ), Y ) ) }.
% 2.07/2.50 (17) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y ) ==> Y }.
% 2.07/2.50 (18) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X, Y ) }.
% 2.07/2.50 (19) {G0,W12,D4,L2,V0,M2} I { ! leq( strong_iteration( star( skol1 ) ),
% 2.07/2.50 strong_iteration( one ) ), ! leq( strong_iteration( one ),
% 2.07/2.50 strong_iteration( star( skol1 ) ) ) }.
% 2.07/2.50 (20) {G1,W5,D3,L1,V1,M1} P(0,2) { addition( zero, X ) ==> X }.
% 2.07/2.50 (25) {G1,W14,D4,L2,V3,M2} P(1,18) { ! addition( addition( X, Y ), Z ) ==>
% 2.07/2.50 addition( Y, Z ), leq( X, addition( Y, Z ) ) }.
% 2.07/2.50 (26) {G1,W11,D4,L1,V3,M1} P(1,0) { addition( addition( X, Y ), Z ) =
% 2.07/2.50 addition( addition( Y, Z ), X ) }.
% 2.07/2.50 (35) {G1,W12,D4,L2,V3,M2} P(17,1) { addition( addition( Z, X ), Y ) ==>
% 2.07/2.50 addition( Z, Y ), ! leq( X, Y ) }.
% 2.07/2.50 (36) {G1,W8,D3,L2,V2,M2} P(17,0) { addition( Y, X ) ==> Y, ! leq( X, Y )
% 2.07/2.50 }.
% 2.07/2.50 (67) {G1,W16,D4,L2,V3,M2} P(7,18) { ! multiplication( X, addition( Y, Z ) )
% 2.07/2.50 ==> multiplication( X, Z ), leq( multiplication( X, Y ), multiplication
% 2.07/2.50 ( X, Z ) ) }.
% 2.07/2.50 (102) {G1,W11,D4,L1,V2,M1} P(6,8) { addition( multiplication( Y, X ), X ) =
% 2.07/2.50 multiplication( addition( Y, one ), X ) }.
% 2.07/2.50 (145) {G1,W9,D5,L1,V1,M1} P(11,0) { addition( multiplication( star( X ), X
% 2.07/2.50 ), one ) ==> star( X ) }.
% 2.07/2.50 (324) {G2,W5,D3,L1,V2,M1} P(3,25);q { leq( X, addition( X, Y ) ) }.
% 2.07/2.50 (363) {G3,W5,D3,L1,V2,M1} P(0,324) { leq( X, addition( Y, X ) ) }.
% 2.07/2.50 (366) {G4,W7,D4,L1,V3,M1} P(26,363) { leq( Z, addition( addition( Y, Z ), X
% 2.07/2.50 ) ) }.
% 2.07/2.50 (674) {G5,W8,D3,L2,V3,M2} P(35,366) { leq( Y, addition( X, Z ) ), ! leq( Y
% 2.07/2.50 , Z ) }.
% 2.07/2.50 (1634) {G2,W7,D3,L1,V2,M1} P(20,67);q { leq( multiplication( Y, zero ),
% 2.07/2.50 multiplication( Y, X ) ) }.
% 2.07/2.50 (1729) {G3,W5,D3,L1,V1,M1} P(5,1634) { leq( multiplication( X, zero ), X )
% 2.07/2.50 }.
% 2.07/2.50 (1733) {G4,W7,D4,L1,V1,M1} R(1729,36) { addition( X, multiplication( X,
% 2.07/2.50 zero ) ) ==> X }.
% 2.07/2.50 (1737) {G4,W7,D4,L1,V1,M1} R(1729,17) { addition( multiplication( X, zero )
% 2.07/2.50 , X ) ==> X }.
% 2.07/2.50 (2097) {G6,W8,D3,L2,V2,M2} P(1733,674) { leq( Y, X ), ! leq( Y,
% 2.07/2.50 multiplication( X, zero ) ) }.
% 2.07/2.50 (3493) {G5,W8,D5,L1,V3,M1} P(102,15);r(366) { leq( Y, multiplication(
% 2.07/2.50 strong_iteration( addition( X, one ) ), Z ) ) }.
% 2.07/2.50 (9565) {G7,W6,D4,L1,V2,M1} R(3493,2097) { leq( X, strong_iteration(
% 2.07/2.50 addition( Y, one ) ) ) }.
% 2.07/2.50 (9617) {G8,W5,D4,L1,V2,M1} P(145,9565) { leq( Y, strong_iteration( star( X
% 2.07/2.50 ) ) ) }.
% 2.07/2.50 (9619) {G8,W4,D3,L1,V1,M1} P(1737,9565) { leq( X, strong_iteration( one ) )
% 2.07/2.50 }.
% 2.07/2.50 (9669) {G9,W0,D0,L0,V0,M0} R(9619,19);r(9617) { }.
% 2.07/2.50
% 2.07/2.50
% 2.07/2.50 % SZS output end Refutation
% 2.07/2.50 found a proof!
% 2.07/2.50
% 2.07/2.50
% 2.07/2.50 Unprocessed initial clauses:
% 2.07/2.50
% 2.07/2.50 (9671) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X ) }.
% 2.07/2.50 (9672) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) = addition(
% 2.07/2.50 addition( Z, Y ), X ) }.
% 2.07/2.50 (9673) {G0,W5,D3,L1,V1,M1} { addition( X, zero ) = X }.
% 2.07/2.50 (9674) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 2.07/2.50 (9675) {G0,W11,D4,L1,V3,M1} { multiplication( X, multiplication( Y, Z ) )
% 2.07/2.50 = multiplication( multiplication( X, Y ), Z ) }.
% 2.07/2.50 (9676) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 2.07/2.50 (9677) {G0,W5,D3,L1,V1,M1} { multiplication( one, X ) = X }.
% 2.07/2.50 (9678) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y, Z ) ) =
% 2.07/2.50 addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 2.07/2.50 (9679) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Y ), Z ) =
% 2.07/2.50 addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 2.07/2.50 (9680) {G0,W5,D3,L1,V1,M1} { multiplication( zero, X ) = zero }.
% 2.07/2.50 (9681) {G0,W9,D5,L1,V1,M1} { addition( one, multiplication( X, star( X ) )
% 2.07/2.50 ) = star( X ) }.
% 2.07/2.50 (9682) {G0,W9,D5,L1,V1,M1} { addition( one, multiplication( star( X ), X )
% 2.07/2.50 ) = star( X ) }.
% 2.07/2.50 (9683) {G0,W13,D4,L2,V3,M2} { ! leq( addition( multiplication( X, Z ), Y )
% 2.07/2.50 , Z ), leq( multiplication( star( X ), Y ), Z ) }.
% 2.07/2.50 (9684) {G0,W13,D4,L2,V3,M2} { ! leq( addition( multiplication( Z, X ), Y )
% 2.07/2.50 , Z ), leq( multiplication( Y, star( X ) ), Z ) }.
% 2.07/2.50 (9685) {G0,W9,D5,L1,V1,M1} { strong_iteration( X ) = addition(
% 2.07/2.50 multiplication( X, strong_iteration( X ) ), one ) }.
% 2.07/2.50 (9686) {G0,W13,D4,L2,V3,M2} { ! leq( Z, addition( multiplication( X, Z ),
% 2.07/2.50 Y ) ), leq( Z, multiplication( strong_iteration( X ), Y ) ) }.
% 2.07/2.50 (9687) {G0,W10,D5,L1,V1,M1} { strong_iteration( X ) = addition( star( X )
% 2.07/2.50 , multiplication( strong_iteration( X ), zero ) ) }.
% 2.07/2.50 (9688) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y }.
% 2.07/2.50 (9689) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 2.07/2.50 (9690) {G0,W12,D4,L2,V0,M2} { ! leq( strong_iteration( star( skol1 ) ),
% 2.07/2.50 strong_iteration( one ) ), ! leq( strong_iteration( one ),
% 2.07/2.50 strong_iteration( star( skol1 ) ) ) }.
% 2.07/2.50
% 2.07/2.50
% 2.07/2.50 Total Proof:
% 2.07/2.50
% 2.07/2.50 subsumption: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X
% 2.07/2.50 ) }.
% 2.07/2.50 parent0: (9671) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X )
% 2.07/2.50 }.
% 2.07/2.50 substitution0:
% 2.07/2.50 X := X
% 2.07/2.50 Y := Y
% 2.07/2.50 end
% 2.07/2.50 permutation0:
% 2.07/2.50 0 ==> 0
% 2.07/2.50 end
% 2.07/2.50
% 2.07/2.50 subsumption: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 2.07/2.50 ==> addition( addition( Z, Y ), X ) }.
% 2.07/2.50 parent0: (9672) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) =
% 2.07/2.50 addition( addition( Z, Y ), X ) }.
% 2.07/2.50 substitution0:
% 2.07/2.50 X := X
% 2.07/2.50 Y := Y
% 2.07/2.50 Z := Z
% 2.07/2.50 end
% 2.07/2.50 permutation0:
% 2.07/2.50 0 ==> 0
% 2.07/2.50 end
% 2.07/2.50
% 2.07/2.50 subsumption: (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 2.07/2.50 parent0: (9673) {G0,W5,D3,L1,V1,M1} { addition( X, zero ) = X }.
% 2.07/2.50 substitution0:
% 2.07/2.50 X := X
% 2.07/2.50 end
% 2.07/2.50 permutation0:
% 2.07/2.50 0 ==> 0
% 2.07/2.50 end
% 2.07/2.50
% 2.07/2.50 subsumption: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 2.07/2.50 parent0: (9674) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 2.07/2.50 substitution0:
% 2.07/2.50 X := X
% 2.07/2.50 end
% 2.07/2.50 permutation0:
% 2.07/2.50 0 ==> 0
% 2.07/2.50 end
% 2.07/2.50
% 2.07/2.50 subsumption: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 2.07/2.50 parent0: (9676) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 2.07/2.50 substitution0:
% 2.07/2.50 X := X
% 2.07/2.50 end
% 2.07/2.50 permutation0:
% 2.07/2.50 0 ==> 0
% 2.07/2.50 end
% 2.07/2.50
% 2.07/2.50 subsumption: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 2.07/2.50 parent0: (9677) {G0,W5,D3,L1,V1,M1} { multiplication( one, X ) = X }.
% 2.07/2.50 substitution0:
% 2.07/2.50 X := X
% 2.07/2.50 end
% 2.07/2.50 permutation0:
% 2.07/2.50 0 ==> 0
% 2.07/2.50 end
% 2.07/2.50
% 2.07/2.50 eqswap: (9714) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Y ),
% 2.07/2.50 multiplication( X, Z ) ) = multiplication( X, addition( Y, Z ) ) }.
% 2.07/2.50 parent0[0]: (9678) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y,
% 2.07/2.50 Z ) ) = addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 2.07/2.50 substitution0:
% 2.07/2.50 X := X
% 2.07/2.50 Y := Y
% 2.07/2.50 Z := Z
% 2.07/2.50 end
% 2.07/2.50
% 2.07/2.50 subsumption: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y )
% 2.07/2.50 , multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 2.07/2.50 parent0: (9714) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Y ),
% 2.07/2.50 multiplication( X, Z ) ) = multiplication( X, addition( Y, Z ) ) }.
% 2.07/2.50 substitution0:
% 2.07/2.50 X := X
% 2.07/2.50 Y := Y
% 2.07/2.50 Z := Z
% 2.07/2.50 end
% 2.07/2.50 permutation0:
% 2.07/2.50 0 ==> 0
% 2.07/2.50 end
% 2.07/2.50
% 2.07/2.50 eqswap: (9722) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Z ),
% 2.07/2.50 multiplication( Y, Z ) ) = multiplication( addition( X, Y ), Z ) }.
% 2.07/2.50 parent0[0]: (9679) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Y )
% 2.07/2.50 , Z ) = addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 2.07/2.50 substitution0:
% 2.07/2.50 X := X
% 2.07/2.50 Y := Y
% 2.07/2.50 Z := Z
% 2.07/2.50 end
% 2.07/2.50
% 2.07/2.50 subsumption: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z )
% 2.07/2.50 , multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 2.07/2.50 parent0: (9722) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Z ),
% 2.07/2.50 multiplication( Y, Z ) ) = multiplication( addition( X, Y ), Z ) }.
% 2.07/2.50 substitution0:
% 2.07/2.50 X := X
% 2.07/2.50 Y := Y
% 2.07/2.50 Z := Z
% 2.07/2.50 end
% 2.07/2.50 permutation0:
% 2.07/2.50 0 ==> 0
% 2.07/2.50 end
% 2.07/2.50
% 2.07/2.50 subsumption: (11) {G0,W9,D5,L1,V1,M1} I { addition( one, multiplication(
% 2.07/2.50 star( X ), X ) ) ==> star( X ) }.
% 2.07/2.50 parent0: (9682) {G0,W9,D5,L1,V1,M1} { addition( one, multiplication( star
% 2.07/2.50 ( X ), X ) ) = star( X ) }.
% 2.07/2.50 substitution0:
% 2.07/2.50 X := X
% 2.07/2.50 end
% 2.07/2.50 permutation0:
% 2.07/2.50 0 ==> 0
% 2.07/2.50 end
% 2.07/2.50
% 2.07/2.50 subsumption: (15) {G0,W13,D4,L2,V3,M2} I { ! leq( Z, addition(
% 2.07/2.50 multiplication( X, Z ), Y ) ), leq( Z, multiplication( strong_iteration(
% 2.07/2.50 X ), Y ) ) }.
% 2.07/2.50 parent0: (9686) {G0,W13,D4,L2,V3,M2} { ! leq( Z, addition( multiplication
% 2.07/2.50 ( X, Z ), Y ) ), leq( Z, multiplication( strong_iteration( X ), Y ) ) }.
% 2.07/2.50 substitution0:
% 2.07/2.50 X := X
% 2.07/2.50 Y := Y
% 2.07/2.50 Z := Z
% 2.07/2.50 end
% 2.07/2.50 permutation0:
% 2.07/2.50 0 ==> 0
% 2.07/2.50 1 ==> 1
% 2.07/2.50 end
% 2.07/2.50
% 2.07/2.50 subsumption: (17) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 2.07/2.50 ==> Y }.
% 2.07/2.50 parent0: (9688) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y
% 2.07/2.50 }.
% 2.07/2.50 substitution0:
% 2.07/2.50 X := X
% 2.07/2.50 Y := Y
% 2.07/2.50 end
% 2.07/2.50 permutation0:
% 2.07/2.50 0 ==> 0
% 2.07/2.50 1 ==> 1
% 2.07/2.50 end
% 2.07/2.50
% 2.07/2.50 subsumption: (18) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X
% 2.07/2.50 , Y ) }.
% 2.07/2.50 parent0: (9689) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y )
% 2.07/2.50 }.
% 2.07/2.50 substitution0:
% 2.07/2.50 X := X
% 2.07/2.50 Y := Y
% 2.07/2.50 end
% 2.07/2.50 permutation0:
% 2.07/2.50 0 ==> 0
% 2.07/2.50 1 ==> 1
% 2.07/2.50 end
% 2.07/2.50
% 2.07/2.50 subsumption: (19) {G0,W12,D4,L2,V0,M2} I { ! leq( strong_iteration( star(
% 2.07/2.50 skol1 ) ), strong_iteration( one ) ), ! leq( strong_iteration( one ),
% 2.07/2.50 strong_iteration( star( skol1 ) ) ) }.
% 2.07/2.50 parent0: (9690) {G0,W12,D4,L2,V0,M2} { ! leq( strong_iteration( star(
% 2.07/2.50 skol1 ) ), strong_iteration( one ) ), ! leq( strong_iteration( one ),
% 2.07/2.50 strong_iteration( star( skol1 ) ) ) }.
% 2.07/2.50 substitution0:
% 2.07/2.50 end
% 2.07/2.50 permutation0:
% 2.07/2.50 0 ==> 0
% 2.07/2.50 1 ==> 1
% 2.07/2.50 end
% 2.07/2.50
% 2.07/2.50 eqswap: (9790) {G0,W5,D3,L1,V1,M1} { X ==> addition( X, zero ) }.
% 2.07/2.50 parent0[0]: (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 2.07/2.50 substitution0:
% 2.07/2.50 X := X
% 2.07/2.50 end
% 2.07/2.50
% 2.07/2.50 paramod: (9791) {G1,W5,D3,L1,V1,M1} { X ==> addition( zero, X ) }.
% 2.07/2.50 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 2.07/2.50 }.
% 2.07/2.50 parent1[0; 2]: (9790) {G0,W5,D3,L1,V1,M1} { X ==> addition( X, zero ) }.
% 2.07/2.50 substitution0:
% 2.07/2.50 X := X
% 2.07/2.50 Y := zero
% 2.07/2.50 end
% 2.07/2.50 substitution1:
% 2.07/2.50 X := X
% 2.07/2.50 end
% 2.07/2.50
% 2.07/2.50 eqswap: (9794) {G1,W5,D3,L1,V1,M1} { addition( zero, X ) ==> X }.
% 2.07/2.50 parent0[0]: (9791) {G1,W5,D3,L1,V1,M1} { X ==> addition( zero, X ) }.
% 2.07/2.50 substitution0:
% 2.07/2.50 X := X
% 2.07/2.50 end
% 2.07/2.50
% 2.07/2.50 subsumption: (20) {G1,W5,D3,L1,V1,M1} P(0,2) { addition( zero, X ) ==> X
% 2.07/2.50 }.
% 2.07/2.50 parent0: (9794) {G1,W5,D3,L1,V1,M1} { addition( zero, X ) ==> X }.
% 2.07/2.50 substitution0:
% 2.07/2.50 X := X
% 2.07/2.50 end
% 2.07/2.50 permutation0:
% 2.07/2.50 0 ==> 0
% 2.07/2.50 end
% 2.07/2.50
% 2.07/2.50 eqswap: (9796) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y )
% 2.07/2.50 }.
% 2.07/2.50 parent0[0]: (18) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 2.07/2.50 Y ) }.
% 2.07/2.50 substitution0:
% 2.07/2.50 X := X
% 2.07/2.50 Y := Y
% 2.07/2.50 end
% 2.07/2.50
% 2.07/2.50 paramod: (9797) {G1,W14,D4,L2,V3,M2} { ! addition( X, Y ) ==> addition(
% 2.07/2.50 addition( Z, X ), Y ), leq( Z, addition( X, Y ) ) }.
% 2.07/2.50 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 2.07/2.50 ==> addition( addition( Z, Y ), X ) }.
% 2.07/2.50 parent1[0; 5]: (9796) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq
% 2.07/2.50 ( X, Y ) }.
% 2.07/2.50 substitution0:
% 2.07/2.50 X := Y
% 2.07/2.50 Y := X
% 2.07/2.50 Z := Z
% 2.07/2.50 end
% 2.07/2.50 substitution1:
% 2.07/2.50 X := Z
% 2.07/2.50 Y := addition( X, Y )
% 2.07/2.50 end
% 2.07/2.50
% 2.07/2.50 eqswap: (9798) {G1,W14,D4,L2,V3,M2} { ! addition( addition( Z, X ), Y )
% 2.07/2.50 ==> addition( X, Y ), leq( Z, addition( X, Y ) ) }.
% 2.07/2.50 parent0[0]: (9797) {G1,W14,D4,L2,V3,M2} { ! addition( X, Y ) ==> addition
% 2.07/2.50 ( addition( Z, X ), Y ), leq( Z, addition( X, Y ) ) }.
% 2.07/2.50 substitution0:
% 2.07/2.50 X := X
% 2.07/2.50 Y := Y
% 2.07/2.50 Z := Z
% 2.07/2.50 end
% 2.07/2.50
% 2.07/2.50 subsumption: (25) {G1,W14,D4,L2,V3,M2} P(1,18) { ! addition( addition( X, Y
% 2.07/2.50 ), Z ) ==> addition( Y, Z ), leq( X, addition( Y, Z ) ) }.
% 2.07/2.50 parent0: (9798) {G1,W14,D4,L2,V3,M2} { ! addition( addition( Z, X ), Y )
% 2.07/2.50 ==> addition( X, Y ), leq( Z, addition( X, Y ) ) }.
% 2.07/2.50 substitution0:
% 2.07/2.50 X := Y
% 2.07/2.50 Y := Z
% 2.07/2.50 Z := X
% 2.07/2.50 end
% 2.07/2.50 permutation0:
% 2.07/2.50 0 ==> 0
% 2.07/2.50 1 ==> 1
% 2.07/2.50 end
% 2.07/2.50
% 2.07/2.50 eqswap: (9799) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z ) ==>
% 2.07/2.50 addition( X, addition( Y, Z ) ) }.
% 2.07/2.50 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 2.07/2.50 ==> addition( addition( Z, Y ), X ) }.
% 2.07/2.50 substitution0:
% 2.07/2.50 X := Z
% 2.07/2.50 Y := Y
% 2.07/2.50 Z := X
% 2.07/2.50 end
% 2.07/2.50
% 2.07/2.50 paramod: (9802) {G1,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z ) ==>
% 2.07/2.50 addition( addition( Y, Z ), X ) }.
% 2.07/2.50 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 2.07/2.50 }.
% 2.07/2.50 parent1[0; 6]: (9799) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z
% 2.07/2.50 ) ==> addition( X, addition( Y, Z ) ) }.
% 2.07/2.50 substitution0:
% 2.07/2.50 X := X
% 2.07/2.50 Y := addition( Y, Z )
% 2.07/2.50 end
% 2.07/2.50 substitution1:
% 2.07/2.50 X := X
% 2.07/2.50 Y := Y
% 2.07/2.50 Z := Z
% 2.07/2.50 end
% 2.07/2.50
% 2.07/2.50 subsumption: (26) {G1,W11,D4,L1,V3,M1} P(1,0) { addition( addition( X, Y )
% 2.07/2.50 , Z ) = addition( addition( Y, Z ), X ) }.
% 2.07/2.50 parent0: (9802) {G1,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z ) ==>
% 2.07/2.50 addition( addition( Y, Z ), X ) }.
% 2.07/2.50 substitution0:
% 2.07/2.50 X := X
% 2.07/2.50 Y := Y
% 2.07/2.50 Z := Z
% 2.07/2.50 end
% 2.07/2.50 permutation0:
% 2.07/2.50 0 ==> 0
% 2.07/2.50 end
% 2.07/2.50
% 2.07/2.50 eqswap: (9817) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z ) ==>
% 2.07/2.50 addition( X, addition( Y, Z ) ) }.
% 2.07/2.50 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 2.07/2.50 ==> addition( addition( Z, Y ), X ) }.
% 2.07/2.50 substitution0:
% 2.07/2.50 X := Z
% 2.07/2.50 Y := Y
% 2.07/2.50 Z := X
% 2.07/2.50 end
% 2.07/2.50
% 2.07/2.50 paramod: (9823) {G1,W12,D4,L2,V3,M2} { addition( addition( X, Y ), Z ) ==>
% 2.07/2.50 addition( X, Z ), ! leq( Y, Z ) }.
% 2.07/2.50 parent0[1]: (17) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 2.07/2.50 ==> Y }.
% 2.07/2.50 parent1[0; 8]: (9817) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z
% 2.07/2.50 ) ==> addition( X, addition( Y, Z ) ) }.
% 2.07/2.50 substitution0:
% 2.07/2.50 X := Y
% 2.07/2.50 Y := Z
% 2.07/2.50 end
% 2.07/2.50 substitution1:
% 2.07/2.50 X := X
% 2.07/2.50 Y := Y
% 2.07/2.50 Z := Z
% 2.07/2.50 end
% 2.07/2.50
% 2.07/2.50 subsumption: (35) {G1,W12,D4,L2,V3,M2} P(17,1) { addition( addition( Z, X )
% 2.07/2.50 , Y ) ==> addition( Z, Y ), ! leq( X, Y ) }.
% 2.07/2.50 parent0: (9823) {G1,W12,D4,L2,V3,M2} { addition( addition( X, Y ), Z ) ==>
% 2.07/2.50 addition( X, Z ), ! leq( Y, Z ) }.
% 2.07/2.50 substitution0:
% 2.07/2.50 X := Z
% 2.07/2.50 Y := X
% 2.07/2.50 Z := Y
% 2.07/2.50 end
% 2.07/2.50 permutation0:
% 2.07/2.50 0 ==> 0
% 2.07/2.50 1 ==> 1
% 2.07/2.50 end
% 2.07/2.50
% 2.07/2.50 eqswap: (9870) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X, Y )
% 2.07/2.50 }.
% 2.07/2.50 parent0[1]: (17) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 2.07/2.50 ==> Y }.
% 2.07/2.50 substitution0:
% 2.07/2.50 X := X
% 2.07/2.50 Y := Y
% 2.07/2.50 end
% 2.07/2.50
% 2.07/2.50 paramod: (9871) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y, X
% 2.07/2.50 ) }.
% 2.07/2.50 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 2.07/2.50 }.
% 2.07/2.50 parent1[0; 2]: (9870) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq
% 2.07/2.50 ( X, Y ) }.
% 2.07/2.50 substitution0:
% 2.07/2.50 X := Y
% 2.07/2.50 Y := X
% 2.07/2.50 end
% 2.07/2.50 substitution1:
% 2.07/2.50 X := Y
% 2.07/2.50 Y := X
% 2.07/2.50 end
% 2.07/2.50
% 2.07/2.50 eqswap: (9874) {G1,W8,D3,L2,V2,M2} { addition( X, Y ) ==> X, ! leq( Y, X )
% 2.07/2.50 }.
% 2.07/2.50 parent0[0]: (9871) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y
% 2.07/2.50 , X ) }.
% 2.07/2.50 substitution0:
% 2.07/2.50 X := X
% 2.07/2.50 Y := Y
% 2.07/2.50 end
% 2.07/2.50
% 2.07/2.50 subsumption: (36) {G1,W8,D3,L2,V2,M2} P(17,0) { addition( Y, X ) ==> Y, !
% 2.07/2.50 leq( X, Y ) }.
% 2.07/2.50 parent0: (9874) {G1,W8,D3,L2,V2,M2} { addition( X, Y ) ==> X, ! leq( Y, X
% 2.07/2.50 ) }.
% 2.07/2.50 substitution0:
% 2.07/2.50 X := Y
% 2.07/2.50 Y := X
% 2.07/2.50 end
% 2.07/2.50 permutation0:
% 2.07/2.50 0 ==> 0
% 2.07/2.50 1 ==> 1
% 2.07/2.50 end
% 2.07/2.50
% 2.07/2.50 eqswap: (9876) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y )
% 2.07/2.50 }.
% 2.07/2.50 parent0[0]: (18) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 2.07/2.50 Y ) }.
% 2.07/2.50 substitution0:
% 2.07/2.50 X := X
% 2.07/2.50 Y := Y
% 2.07/2.50 end
% 2.07/2.50
% 2.07/2.50 paramod: (9877) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Y ) ==>
% 2.07/2.50 multiplication( X, addition( Z, Y ) ), leq( multiplication( X, Z ),
% 2.07/2.50 multiplication( X, Y ) ) }.
% 2.07/2.50 parent0[0]: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 2.07/2.50 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 2.07/2.50 parent1[0; 5]: (9876) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq
% 2.07/2.50 ( X, Y ) }.
% 2.07/2.50 substitution0:
% 2.07/2.50 X := X
% 2.07/2.50 Y := Z
% 2.07/2.50 Z := Y
% 2.07/2.50 end
% 2.07/2.50 substitution1:
% 2.07/2.50 X := multiplication( X, Z )
% 2.07/2.50 Y := multiplication( X, Y )
% 2.07/2.50 end
% 2.07/2.50
% 2.07/2.50 eqswap: (9878) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, addition( Z, Y
% 2.07/2.50 ) ) ==> multiplication( X, Y ), leq( multiplication( X, Z ),
% 2.07/2.50 multiplication( X, Y ) ) }.
% 2.07/2.50 parent0[0]: (9877) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Y ) ==>
% 2.07/2.50 multiplication( X, addition( Z, Y ) ), leq( multiplication( X, Z ),
% 2.07/2.50 multiplication( X, Y ) ) }.
% 2.07/2.50 substitution0:
% 2.07/2.50 X := X
% 2.07/2.50 Y := Y
% 2.07/2.50 Z := Z
% 2.07/2.50 end
% 2.07/2.50
% 2.07/2.50 subsumption: (67) {G1,W16,D4,L2,V3,M2} P(7,18) { ! multiplication( X,
% 2.07/2.50 addition( Y, Z ) ) ==> multiplication( X, Z ), leq( multiplication( X, Y
% 2.07/2.50 ), multiplication( X, Z ) ) }.
% 2.07/2.50 parent0: (9878) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, addition( Z, Y
% 2.07/2.50 ) ) ==> multiplication( X, Y ), leq( multiplication( X, Z ),
% 2.07/2.50 multiplication( X, Y ) ) }.
% 2.07/2.50 substitution0:
% 2.07/2.50 X := X
% 2.07/2.50 Y := Z
% 2.07/2.50 Z := Y
% 2.07/2.50 end
% 2.07/2.50 permutation0:
% 2.07/2.50 0 ==> 0
% 2.07/2.50 1 ==> 1
% 2.07/2.50 end
% 2.07/2.50
% 2.07/2.50 eqswap: (9880) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Z ), Y
% 2.07/2.50 ) ==> addition( multiplication( X, Y ), multiplication( Z, Y ) ) }.
% 2.07/2.50 parent0[0]: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ),
% 2.07/2.50 multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 2.07/2.50 substitution0:
% 2.07/2.50 X := X
% 2.07/2.50 Y := Z
% 2.07/2.50 Z := Y
% 2.07/2.50 end
% 2.07/2.50
% 2.07/2.50 paramod: (9882) {G1,W11,D4,L1,V2,M1} { multiplication( addition( X, one )
% 2.07/2.50 , Y ) ==> addition( multiplication( X, Y ), Y ) }.
% 2.07/2.50 parent0[0]: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 2.07/2.50 parent1[0; 10]: (9880) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X
% 2.07/2.50 , Z ), Y ) ==> addition( multiplication( X, Y ), multiplication( Z, Y ) )
% 2.07/2.50 }.
% 2.07/2.50 substitution0:
% 2.07/2.50 X := Y
% 2.07/2.50 end
% 2.07/2.50 substitution1:
% 2.07/2.50 X := X
% 2.07/2.50 Y := Y
% 2.07/2.50 Z := one
% 2.07/2.50 end
% 2.07/2.50
% 2.07/2.50 eqswap: (9884) {G1,W11,D4,L1,V2,M1} { addition( multiplication( X, Y ), Y
% 2.07/2.50 ) ==> multiplication( addition( X, one ), Y ) }.
% 2.07/2.50 parent0[0]: (9882) {G1,W11,D4,L1,V2,M1} { multiplication( addition( X, one
% 2.07/2.50 ), Y ) ==> addition( multiplication( X, Y ), Y ) }.
% 2.07/2.50 substitution0:
% 2.07/2.50 X := X
% 2.07/2.50 Y := Y
% 2.07/2.50 end
% 2.07/2.50
% 2.07/2.50 subsumption: (102) {G1,W11,D4,L1,V2,M1} P(6,8) { addition( multiplication(
% 2.07/2.50 Y, X ), X ) = multiplication( addition( Y, one ), X ) }.
% 2.07/2.50 parent0: (9884) {G1,W11,D4,L1,V2,M1} { addition( multiplication( X, Y ), Y
% 2.07/2.50 ) ==> multiplication( addition( X, one ), Y ) }.
% 2.07/2.50 substitution0:
% 2.07/2.50 X := Y
% 2.07/2.50 Y := X
% 2.07/2.50 end
% 2.07/2.50 permutation0:
% 2.07/2.50 0 ==> 0
% 2.07/2.50 end
% 2.07/2.50
% 2.07/2.50 eqswap: (9885) {G0,W9,D5,L1,V1,M1} { star( X ) ==> addition( one,
% 2.07/2.50 multiplication( star( X ), X ) ) }.
% 2.07/2.50 parent0[0]: (11) {G0,W9,D5,L1,V1,M1} I { addition( one, multiplication(
% 2.07/2.50 star( X ), X ) ) ==> star( X ) }.
% 2.07/2.50 substitution0:
% 2.07/2.50 X := X
% 2.07/2.50 end
% 2.07/2.50
% 2.07/2.50 paramod: (9886) {G1,W9,D5,L1,V1,M1} { star( X ) ==> addition(
% 2.07/2.50 multiplication( star( X ), X ), one ) }.
% 2.07/2.50 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 2.07/2.50 }.
% 2.07/2.50 parent1[0; 3]: (9885) {G0,W9,D5,L1,V1,M1} { star( X ) ==> addition( one,
% 2.07/2.50 multiplication( star( X ), X ) ) }.
% 2.07/2.50 substitution0:
% 2.07/2.50 X := one
% 2.07/2.50 Y := multiplication( star( X ), X )
% 2.07/2.50 end
% 2.07/2.50 substitution1:
% 2.07/2.50 X := X
% 2.07/2.50 end
% 2.07/2.50
% 2.07/2.50 eqswap: (9889) {G1,W9,D5,L1,V1,M1} { addition( multiplication( star( X ),
% 2.07/2.50 X ), one ) ==> star( X ) }.
% 2.07/2.50 parent0[0]: (9886) {G1,W9,D5,L1,V1,M1} { star( X ) ==> addition(
% 2.07/2.50 multiplication( star( X ), X ), one ) }.
% 2.07/2.50 substitution0:
% 2.07/2.50 X := X
% 2.07/2.50 end
% 2.07/2.50
% 2.07/2.50 subsumption: (145) {G1,W9,D5,L1,V1,M1} P(11,0) { addition( multiplication(
% 2.07/2.50 star( X ), X ), one ) ==> star( X ) }.
% 2.07/2.50 parent0: (9889) {G1,W9,D5,L1,V1,M1} { addition( multiplication( star( X )
% 2.07/2.50 , X ), one ) ==> star( X ) }.
% 2.07/2.50 substitution0:
% 2.07/2.50 X := X
% 2.07/2.50 end
% 2.07/2.50 permutation0:
% 2.07/2.50 0 ==> 0
% 2.07/2.50 end
% 2.07/2.50
% 2.07/2.50 eqswap: (9891) {G1,W14,D4,L2,V3,M2} { ! addition( Y, Z ) ==> addition(
% 2.07/2.50 addition( X, Y ), Z ), leq( X, addition( Y, Z ) ) }.
% 2.07/2.50 parent0[0]: (25) {G1,W14,D4,L2,V3,M2} P(1,18) { ! addition( addition( X, Y
% 2.07/2.50 ), Z ) ==> addition( Y, Z ), leq( X, addition( Y, Z ) ) }.
% 2.07/2.50 substitution0:
% 2.07/2.50 X := X
% 2.07/2.50 Y := Y
% 2.07/2.50 Z := Z
% 2.07/2.50 end
% 2.07/2.50
% 2.07/2.50 paramod: (9894) {G1,W12,D3,L2,V2,M2} { ! addition( X, Y ) ==> addition( X
% 2.07/2.50 , Y ), leq( X, addition( X, Y ) ) }.
% 2.07/2.50 parent0[0]: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 2.07/2.50 parent1[0; 6]: (9891) {G1,W14,D4,L2,V3,M2} { ! addition( Y, Z ) ==>
% 2.07/2.50 addition( addition( X, Y ), Z ), leq( X, addition( Y, Z ) ) }.
% 2.07/2.50 substitution0:
% 2.07/2.50 X := X
% 2.07/2.50 end
% 2.07/2.50 substitution1:
% 2.07/2.50 X := X
% 2.07/2.50 Y := X
% 2.07/2.50 Z := Y
% 2.07/2.50 end
% 2.07/2.50
% 2.07/2.50 eqrefl: (9897) {G0,W5,D3,L1,V2,M1} { leq( X, addition( X, Y ) ) }.
% 2.07/2.50 parent0[0]: (9894) {G1,W12,D3,L2,V2,M2} { ! addition( X, Y ) ==> addition
% 2.07/2.50 ( X, Y ), leq( X, addition( X, Y ) ) }.
% 2.07/2.50 substitution0:
% 2.07/2.50 X := X
% 2.07/2.50 Y := Y
% 2.07/2.50 end
% 2.07/2.50
% 2.07/2.50 subsumption: (324) {G2,W5,D3,L1,V2,M1} P(3,25);q { leq( X, addition( X, Y )
% 2.07/2.50 ) }.
% 2.07/2.50 parent0: (9897) {G0,W5,D3,L1,V2,M1} { leq( X, addition( X, Y ) ) }.
% 2.07/2.50 substitution0:
% 2.07/2.50 X := X
% 2.07/2.50 Y := Y
% 2.07/2.50 end
% 2.07/2.50 permutation0:
% 2.07/2.50 0 ==> 0
% 2.07/2.50 end
% 2.07/2.50
% 2.07/2.50 paramod: (9898) {G1,W5,D3,L1,V2,M1} { leq( X, addition( Y, X ) ) }.
% 2.07/2.50 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 2.07/2.50 }.
% 2.07/2.50 parent1[0; 2]: (324) {G2,W5,D3,L1,V2,M1} P(3,25);q { leq( X, addition( X, Y
% 2.07/2.50 ) ) }.
% 2.07/2.50 substitution0:
% 2.07/2.50 X := X
% 2.07/2.50 Y := Y
% 2.07/2.50 end
% 2.07/2.50 substitution1:
% 2.07/2.50 X := X
% 2.07/2.50 Y := Y
% 2.07/2.50 end
% 2.07/2.50
% 2.07/2.50 subsumption: (363) {G3,W5,D3,L1,V2,M1} P(0,324) { leq( X, addition( Y, X )
% 2.07/2.50 ) }.
% 2.07/2.50 parent0: (9898) {G1,W5,D3,L1,V2,M1} { leq( X, addition( Y, X ) ) }.
% 2.07/2.50 substitution0:
% 2.07/2.50 X := X
% 2.07/2.50 Y := Y
% 2.07/2.50 end
% 2.07/2.50 permutation0:
% 2.07/2.50 0 ==> 0
% 2.07/2.50 end
% 2.07/2.50
% 2.07/2.50 eqswap: (9900) {G1,W11,D4,L1,V3,M1} { addition( addition( Y, Z ), X ) =
% 2.07/2.50 addition( addition( X, Y ), Z ) }.
% 2.07/2.50 parent0[0]: (26) {G1,W11,D4,L1,V3,M1} P(1,0) { addition( addition( X, Y ),
% 2.07/2.50 Z ) = addition( addition( Y, Z ), X ) }.
% 2.07/2.50 substitution0:
% 2.07/2.50 X := X
% 2.07/2.50 Y := Y
% 2.07/2.50 Z := Z
% 2.07/2.50 end
% 2.07/2.50
% 2.07/2.50 paramod: (9901) {G2,W7,D4,L1,V3,M1} { leq( X, addition( addition( X, Y ),
% 2.07/2.50 Z ) ) }.
% 2.07/2.50 parent0[0]: (9900) {G1,W11,D4,L1,V3,M1} { addition( addition( Y, Z ), X )
% 2.07/2.50 = addition( addition( X, Y ), Z ) }.
% 2.07/2.50 parent1[0; 2]: (363) {G3,W5,D3,L1,V2,M1} P(0,324) { leq( X, addition( Y, X
% 2.07/2.50 ) ) }.
% 2.07/2.50 substitution0:
% 2.07/2.50 X := X
% 2.07/2.50 Y := Y
% 2.07/2.50 Z := Z
% 2.07/2.50 end
% 2.07/2.50 substitution1:
% 2.07/2.50 X := X
% 2.07/2.50 Y := addition( Y, Z )
% 2.07/2.50 end
% 2.07/2.50
% 2.07/2.50 paramod: (9902) {G2,W7,D4,L1,V3,M1} { leq( X, addition( addition( Z, X ),
% 2.07/2.50 Y ) ) }.
% 2.07/2.50 parent0[0]: (9900) {G1,W11,D4,L1,V3,M1} { addition( addition( Y, Z ), X )
% 2.07/2.50 = addition( addition( X, Y ), Z ) }.
% 2.07/2.50 parent1[0; 2]: (9901) {G2,W7,D4,L1,V3,M1} { leq( X, addition( addition( X
% 2.07/2.50 , Y ), Z ) ) }.
% 2.07/2.50 substitution0:
% 2.07/2.50 X := Z
% 2.07/2.50 Y := X
% 2.07/2.50 Z := Y
% 2.07/2.50 end
% 2.07/2.50 substitution1:
% 2.07/2.50 X := X
% 2.07/2.50 Y := Y
% 2.07/2.50 Z := Z
% 2.07/2.50 end
% 2.07/2.50
% 2.07/2.50 subsumption: (366) {G4,W7,D4,L1,V3,M1} P(26,363) { leq( Z, addition(
% 2.07/2.50 addition( Y, Z ), X ) ) }.
% 2.07/2.50 parent0: (9902) {G2,W7,D4,L1,V3,M1} { leq( X, addition( addition( Z, X ),
% 2.07/2.50 Y ) ) }.
% 2.07/2.50 substitution0:
% 2.07/2.50 X := Z
% 2.07/2.50 Y := X
% 2.07/2.50 Z := Y
% 2.07/2.50 end
% 2.07/2.50 permutation0:
% 2.07/2.50 0 ==> 0
% 2.07/2.50 end
% 2.07/2.50
% 2.07/2.50 paramod: (9905) {G2,W8,D3,L2,V3,M2} { leq( X, addition( Y, Z ) ), ! leq( X
% 2.07/2.50 , Z ) }.
% 2.07/2.50 parent0[0]: (35) {G1,W12,D4,L2,V3,M2} P(17,1) { addition( addition( Z, X )
% 2.07/2.50 , Y ) ==> addition( Z, Y ), ! leq( X, Y ) }.
% 2.07/2.50 parent1[0; 2]: (366) {G4,W7,D4,L1,V3,M1} P(26,363) { leq( Z, addition(
% 2.07/2.50 addition( Y, Z ), X ) ) }.
% 2.07/2.50 substitution0:
% 2.07/2.50 X := X
% 2.07/2.50 Y := Z
% 2.07/2.50 Z := Y
% 2.07/2.50 end
% 2.07/2.50 substitution1:
% 2.07/2.50 X := Z
% 2.07/2.50 Y := Y
% 2.07/2.50 Z := X
% 2.07/2.50 end
% 2.07/2.50
% 2.07/2.50 subsumption: (674) {G5,W8,D3,L2,V3,M2} P(35,366) { leq( Y, addition( X, Z )
% 2.07/2.50 ), ! leq( Y, Z ) }.
% 2.07/2.50 parent0: (9905) {G2,W8,D3,L2,V3,M2} { leq( X, addition( Y, Z ) ), ! leq( X
% 2.07/2.50 , Z ) }.
% 2.07/2.50 substitution0:
% 2.07/2.50 X := Y
% 2.07/2.50 Y := X
% 2.07/2.50 Z := Z
% 2.07/2.50 end
% 2.07/2.50 permutation0:
% 2.07/2.50 0 ==> 0
% 2.07/2.50 1 ==> 1
% 2.07/2.50 end
% 2.07/2.50
% 2.07/2.50 eqswap: (9909) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Z ) ==>
% 2.07/2.50 multiplication( X, addition( Y, Z ) ), leq( multiplication( X, Y ),
% 2.07/2.50 multiplication( X, Z ) ) }.
% 2.07/2.50 parent0[0]: (67) {G1,W16,D4,L2,V3,M2} P(7,18) { ! multiplication( X,
% 2.07/2.50 addition( Y, Z ) ) ==> multiplication( X, Z ), leq( multiplication( X, Y
% 2.07/2.50 ), multiplication( X, Z ) ) }.
% 2.07/2.50 substitution0:
% 2.07/2.50 X := X
% 2.07/2.50 Y := Y
% 2.07/2.50 Z := Z
% 2.07/2.50 end
% 2.07/2.50
% 2.07/2.50 paramod: (9910) {G2,W14,D3,L2,V2,M2} { ! multiplication( X, Y ) ==>
% 2.07/2.50 multiplication( X, Y ), leq( multiplication( X, zero ), multiplication( X
% 2.07/2.50 , Y ) ) }.
% 2.07/2.50 parent0[0]: (20) {G1,W5,D3,L1,V1,M1} P(0,2) { addition( zero, X ) ==> X }.
% 2.07/2.50 parent1[0; 7]: (9909) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Z ) ==>
% 2.07/2.50 multiplication( X, addition( Y, Z ) ), leq( multiplication( X, Y ),
% 2.07/2.50 multiplication( X, Z ) ) }.
% 2.07/2.50 substitution0:
% 2.07/2.50 X := Y
% 2.07/2.50 end
% 2.07/2.50 substitution1:
% 2.07/2.50 X := X
% 2.07/2.50 Y := zero
% 2.07/2.50 Z := Y
% 2.07/2.50 end
% 2.07/2.50
% 2.07/2.50 eqrefl: (9911) {G0,W7,D3,L1,V2,M1} { leq( multiplication( X, zero ),
% 2.07/2.50 multiplication( X, Y ) ) }.
% 2.07/2.50 parent0[0]: (9910) {G2,W14,D3,L2,V2,M2} { ! multiplication( X, Y ) ==>
% 2.07/2.50 multiplication( X, Y ), leq( multiplication( X, zero ), multiplication( X
% 2.07/2.50 , Y ) ) }.
% 2.07/2.50 substitution0:
% 2.07/2.50 X := X
% 2.07/2.50 Y := Y
% 2.07/2.50 end
% 2.07/2.50
% 2.07/2.50 subsumption: (1634) {G2,W7,D3,L1,V2,M1} P(20,67);q { leq( multiplication( Y
% 2.07/2.50 , zero ), multiplication( Y, X ) ) }.
% 2.07/2.50 parent0: (9911) {G0,W7,D3,L1,V2,M1} { leq( multiplication( X, zero ),
% 2.07/2.50 multiplication( X, Y ) ) }.
% 2.07/2.50 substitution0:
% 2.07/2.50 X := Y
% 2.07/2.50 Y := X
% 2.07/2.50 end
% 2.07/2.50 permutation0:
% 2.07/2.50 0 ==> 0
% 2.07/2.50 end
% 2.07/2.50
% 2.07/2.50 paramod: (9913) {G1,W5,D3,L1,V1,M1} { leq( multiplication( X, zero ), X )
% 2.07/2.50 }.
% 2.07/2.50 parent0[0]: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 2.07/2.50 parent1[0; 4]: (1634) {G2,W7,D3,L1,V2,M1} P(20,67);q { leq( multiplication
% 2.07/2.50 ( Y, zero ), multiplication( Y, X ) ) }.
% 2.07/2.50 substitution0:
% 2.07/2.50 X := X
% 2.07/2.50 end
% 2.07/2.50 substitution1:
% 2.07/2.50 X := one
% 2.07/2.50 Y := X
% 2.07/2.50 end
% 2.07/2.50
% 2.07/2.50 subsumption: (1729) {G3,W5,D3,L1,V1,M1} P(5,1634) { leq( multiplication( X
% 2.07/2.50 , zero ), X ) }.
% 2.07/2.50 parent0: (9913) {G1,W5,D3,L1,V1,M1} { leq( multiplication( X, zero ), X )
% 2.07/2.50 }.
% 2.07/2.50 substitution0:
% 2.07/2.50 X := X
% 2.07/2.50 end
% 2.07/2.50 permutation0:
% 2.07/2.50 0 ==> 0
% 2.07/2.50 end
% 2.07/2.50
% 2.07/2.50 eqswap: (9914) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y, X )
% 2.07/2.50 }.
% 2.07/2.50 parent0[0]: (36) {G1,W8,D3,L2,V2,M2} P(17,0) { addition( Y, X ) ==> Y, !
% 2.07/2.50 leq( X, Y ) }.
% 2.07/2.50 substitution0:
% 2.07/2.50 X := Y
% 2.07/2.50 Y := X
% 2.07/2.50 end
% 2.07/2.50
% 2.07/2.50 resolution: (9915) {G2,W7,D4,L1,V1,M1} { X ==> addition( X, multiplication
% 2.07/2.50 ( X, zero ) ) }.
% 2.07/2.50 parent0[1]: (9914) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y
% 2.07/2.50 , X ) }.
% 2.07/2.50 parent1[0]: (1729) {G3,W5,D3,L1,V1,M1} P(5,1634) { leq( multiplication( X,
% 2.07/2.50 zero ), X ) }.
% 2.07/2.50 substitution0:
% 2.07/2.50 X := X
% 2.07/2.50 Y := multiplication( X, zero )
% 2.07/2.50 end
% 2.07/2.50 substitution1:
% 2.07/2.50 X := X
% 2.07/2.50 end
% 2.07/2.50
% 2.07/2.50 eqswap: (9916) {G2,W7,D4,L1,V1,M1} { addition( X, multiplication( X, zero
% 2.07/2.50 ) ) ==> X }.
% 2.07/2.50 parent0[0]: (9915) {G2,W7,D4,L1,V1,M1} { X ==> addition( X, multiplication
% 2.07/2.50 ( X, zero ) ) }.
% 2.07/2.50 substitution0:
% 2.07/2.50 X := X
% 2.07/2.50 end
% 2.07/2.50
% 2.07/2.50 subsumption: (1733) {G4,W7,D4,L1,V1,M1} R(1729,36) { addition( X,
% 2.07/2.50 multiplication( X, zero ) ) ==> X }.
% 2.07/2.50 parent0: (9916) {G2,W7,D4,L1,V1,M1} { addition( X, multiplication( X, zero
% 2.07/2.50 ) ) ==> X }.
% 2.07/2.50 substitution0:
% 2.07/2.50 X := X
% 2.07/2.50 end
% 2.07/2.50 permutation0:
% 2.07/2.50 0 ==> 0
% 2.07/2.50 end
% 2.07/2.50
% 2.07/2.50 eqswap: (9917) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X, Y )
% 2.07/2.50 }.
% 2.07/2.50 parent0[1]: (17) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 2.07/2.50 ==> Y }.
% 2.07/2.50 substitution0:
% 2.07/2.50 X := X
% 2.07/2.50 Y := Y
% 2.07/2.50 end
% 2.07/2.50
% 2.07/2.50 resolution: (9918) {G1,W7,D4,L1,V1,M1} { X ==> addition( multiplication( X
% 2.07/2.50 , zero ), X ) }.
% 2.07/2.50 parent0[1]: (9917) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X
% 2.07/2.50 , Y ) }.
% 2.07/2.50 parent1[0]: (1729) {G3,W5,D3,L1,V1,M1} P(5,1634) { leq( multiplication( X,
% 2.07/2.50 zero ), X ) }.
% 2.07/2.50 substitution0:
% 2.07/2.50 X := multiplication( X, zero )
% 2.07/2.50 Y := X
% 2.07/2.50 end
% 2.07/2.50 substitution1:
% 2.07/2.50 X := X
% 2.07/2.50 end
% 2.07/2.50
% 2.07/2.50 eqswap: (9919) {G1,W7,D4,L1,V1,M1} { addition( multiplication( X, zero ),
% 2.07/2.50 X ) ==> X }.
% 2.07/2.50 parent0[0]: (9918) {G1,W7,D4,L1,V1,M1} { X ==> addition( multiplication( X
% 2.07/2.50 , zero ), X ) }.
% 2.07/2.50 substitution0:
% 2.07/2.50 X := X
% 2.07/2.50 end
% 2.07/2.50
% 2.07/2.50 subsumption: (1737) {G4,W7,D4,L1,V1,M1} R(1729,17) { addition(
% 2.07/2.50 multiplication( X, zero ), X ) ==> X }.
% 2.07/2.50 parent0: (9919) {G1,W7,D4,L1,V1,M1} { addition( multiplication( X, zero )
% 2.07/2.50 , X ) ==> X }.
% 2.07/2.50 substitution0:
% 2.07/2.50 X := X
% 2.07/2.50 end
% 2.07/2.50 permutation0:
% 2.07/2.50 0 ==> 0
% 2.07/2.50 end
% 2.07/2.50
% 2.07/2.50 paramod: (9921) {G5,W8,D3,L2,V2,M2} { leq( X, Y ), ! leq( X,
% 2.07/2.50 multiplication( Y, zero ) ) }.
% 2.07/2.50 parent0[0]: (1733) {G4,W7,D4,L1,V1,M1} R(1729,36) { addition( X,
% 2.07/2.50 multiplication( X, zero ) ) ==> X }.
% 2.07/2.50 parent1[0; 2]: (674) {G5,W8,D3,L2,V3,M2} P(35,366) { leq( Y, addition( X, Z
% 2.07/2.50 ) ), ! leq( Y, Z ) }.
% 2.07/2.50 substitution0:
% 2.07/2.50 X := Y
% 2.07/2.50 end
% 2.07/2.50 substitution1:
% 2.07/2.50 X := Y
% 2.07/2.50 Y := X
% 2.07/2.50 Z := multiplication( Y, zero )
% 2.07/2.50 end
% 2.07/2.50
% 2.07/2.50 subsumption: (2097) {G6,W8,D3,L2,V2,M2} P(1733,674) { leq( Y, X ), ! leq( Y
% 2.07/2.50 , multiplication( X, zero ) ) }.
% 2.07/2.50 parent0: (9921) {G5,W8,D3,L2,V2,M2} { leq( X, Y ), ! leq( X,
% 2.07/2.50 multiplication( Y, zero ) ) }.
% 2.07/2.50 substitution0:
% 2.07/2.50 X := Y
% 2.07/2.50 Y := X
% 2.07/2.50 end
% 2.07/2.50 permutation0:
% 2.07/2.50 0 ==> 0
% 2.07/2.50 1 ==> 1
% 2.07/2.50 end
% 2.07/2.50
% 2.07/2.50 eqswap: (9922) {G1,W11,D4,L1,V2,M1} { multiplication( addition( X, one ),
% 2.07/2.50 Y ) = addition( multiplication( X, Y ), Y ) }.
% 2.07/2.50 parent0[0]: (102) {G1,W11,D4,L1,V2,M1} P(6,8) { addition( multiplication( Y
% 2.07/2.50 , X ), X ) = multiplication( addition( Y, one ), X ) }.
% 2.07/2.50 substitution0:
% 2.07/2.50 X := Y
% 2.07/2.50 Y := X
% 2.07/2.50 end
% 2.07/2.50
% 2.07/2.50 paramod: (9923) {G1,W17,D5,L2,V3,M2} { ! leq( X, addition( addition(
% 2.07/2.50 multiplication( Y, X ), X ), Z ) ), leq( X, multiplication(
% 2.07/2.50 strong_iteration( addition( Y, one ) ), Z ) ) }.
% 2.07/2.50 parent0[0]: (9922) {G1,W11,D4,L1,V2,M1} { multiplication( addition( X, one
% 2.07/2.50 ), Y ) = addition( multiplication( X, Y ), Y ) }.
% 2.07/2.50 parent1[0; 4]: (15) {G0,W13,D4,L2,V3,M2} I { ! leq( Z, addition(
% 2.07/2.50 multiplication( X, Z ), Y ) ), leq( Z, multiplication( strong_iteration(
% 2.07/2.50 X ), Y ) ) }.
% 2.07/2.50 substitution0:
% 2.07/2.50 X := Y
% 2.07/2.50 Y := X
% 2.07/2.50 end
% 2.07/2.50 substitution1:
% 2.07/2.50 X := addition( Y, one )
% 2.07/2.50 Y := Z
% 2.07/2.50 Z := X
% 2.07/2.50 end
% 2.07/2.50
% 2.07/2.50 resolution: (9924) {G2,W8,D5,L1,V3,M1} { leq( X, multiplication(
% 2.07/2.50 strong_iteration( addition( Y, one ) ), Z ) ) }.
% 2.07/2.50 parent0[0]: (9923) {G1,W17,D5,L2,V3,M2} { ! leq( X, addition( addition(
% 2.07/2.50 multiplication( Y, X ), X ), Z ) ), leq( X, multiplication(
% 2.07/2.50 strong_iteration( addition( Y, one ) ), Z ) ) }.
% 2.07/2.50 parent1[0]: (366) {G4,W7,D4,L1,V3,M1} P(26,363) { leq( Z, addition(
% 2.07/2.50 addition( Y, Z ), X ) ) }.
% 2.07/2.50 substitution0:
% 2.07/2.50 X := X
% 2.07/2.50 Y := Y
% 2.07/2.50 Z := Z
% 2.07/2.50 end
% 2.07/2.50 substitution1:
% 2.07/2.50 X := Z
% 2.07/2.50 Y := multiplication( Y, X )
% 2.07/2.50 Z := X
% 2.07/2.50 end
% 2.07/2.50
% 2.07/2.50 subsumption: (3493) {G5,W8,D5,L1,V3,M1} P(102,15);r(366) { leq( Y,
% 2.07/2.50 multiplication( strong_iteration( addition( X, one ) ), Z ) ) }.
% 2.07/2.50 parent0: (9924) {G2,W8,D5,L1,V3,M1} { leq( X, multiplication(
% 2.07/2.50 strong_iteration( addition( Y, one ) ), Z ) ) }.
% 2.07/2.50 substitution0:
% 2.07/2.50 X := Y
% 2.07/2.50 Y := X
% 2.07/2.50 Z := Z
% 2.07/2.50 end
% 2.07/2.50 permutation0:
% 2.07/2.50 0 ==> 0
% 2.07/2.50 end
% 2.07/2.50
% 2.07/2.50 resolution: (9925) {G6,W6,D4,L1,V2,M1} { leq( X, strong_iteration(
% 2.07/2.50 addition( Y, one ) ) ) }.
% 2.07/2.50 parent0[1]: (2097) {G6,W8,D3,L2,V2,M2} P(1733,674) { leq( Y, X ), ! leq( Y
% 2.07/2.50 , multiplication( X, zero ) ) }.
% 2.07/2.50 parent1[0]: (3493) {G5,W8,D5,L1,V3,M1} P(102,15);r(366) { leq( Y,
% 2.07/2.50 multiplication( strong_iteration( addition( X, one ) ), Z ) ) }.
% 2.07/2.50 substitution0:
% 2.07/2.50 X := strong_iteration( addition( Y, one ) )
% 2.07/2.51 Y := X
% 2.07/2.51 end
% 2.07/2.51 substitution1:
% 2.07/2.51 X := Y
% 2.07/2.51 Y := X
% 2.07/2.51 Z := zero
% 2.07/2.51 end
% 2.07/2.51
% 2.07/2.51 subsumption: (9565) {G7,W6,D4,L1,V2,M1} R(3493,2097) { leq( X,
% 2.07/2.51 strong_iteration( addition( Y, one ) ) ) }.
% 2.07/2.51 parent0: (9925) {G6,W6,D4,L1,V2,M1} { leq( X, strong_iteration( addition(
% 2.07/2.51 Y, one ) ) ) }.
% 2.07/2.51 substitution0:
% 2.07/2.51 X := X
% 2.07/2.51 Y := Y
% 2.07/2.51 end
% 2.07/2.51 permutation0:
% 2.07/2.51 0 ==> 0
% 2.07/2.51 end
% 2.07/2.51
% 2.07/2.51 paramod: (9927) {G2,W5,D4,L1,V2,M1} { leq( X, strong_iteration( star( Y )
% 2.07/2.51 ) ) }.
% 2.07/2.51 parent0[0]: (145) {G1,W9,D5,L1,V1,M1} P(11,0) { addition( multiplication(
% 2.07/2.51 star( X ), X ), one ) ==> star( X ) }.
% 2.07/2.51 parent1[0; 3]: (9565) {G7,W6,D4,L1,V2,M1} R(3493,2097) { leq( X,
% 2.07/2.51 strong_iteration( addition( Y, one ) ) ) }.
% 2.07/2.51 substitution0:
% 2.07/2.51 X := Y
% 2.07/2.51 end
% 2.07/2.51 substitution1:
% 2.07/2.51 X := X
% 2.07/2.51 Y := multiplication( star( Y ), Y )
% 2.07/2.51 end
% 2.07/2.51
% 2.07/2.51 subsumption: (9617) {G8,W5,D4,L1,V2,M1} P(145,9565) { leq( Y,
% 2.07/2.51 strong_iteration( star( X ) ) ) }.
% 2.07/2.51 parent0: (9927) {G2,W5,D4,L1,V2,M1} { leq( X, strong_iteration( star( Y )
% 2.07/2.51 ) ) }.
% 2.07/2.51 substitution0:
% 2.07/2.51 X := Y
% 2.07/2.51 Y := X
% 2.07/2.51 end
% 2.07/2.51 permutation0:
% 2.07/2.51 0 ==> 0
% 2.07/2.51 end
% 2.07/2.51
% 2.07/2.51 paramod: (9929) {G5,W4,D3,L1,V1,M1} { leq( X, strong_iteration( one ) )
% 2.07/2.51 }.
% 2.07/2.51 parent0[0]: (1737) {G4,W7,D4,L1,V1,M1} R(1729,17) { addition(
% 2.07/2.51 multiplication( X, zero ), X ) ==> X }.
% 2.07/2.51 parent1[0; 3]: (9565) {G7,W6,D4,L1,V2,M1} R(3493,2097) { leq( X,
% 2.07/2.51 strong_iteration( addition( Y, one ) ) ) }.
% 2.07/2.51 substitution0:
% 2.07/2.51 X := one
% 2.07/2.51 end
% 2.07/2.51 substitution1:
% 2.07/2.51 X := X
% 2.07/2.51 Y := multiplication( one, zero )
% 2.07/2.51 end
% 2.07/2.51
% 2.07/2.51 subsumption: (9619) {G8,W4,D3,L1,V1,M1} P(1737,9565) { leq( X,
% 2.07/2.51 strong_iteration( one ) ) }.
% 2.07/2.51 parent0: (9929) {G5,W4,D3,L1,V1,M1} { leq( X, strong_iteration( one ) )
% 2.07/2.51 }.
% 2.07/2.51 substitution0:
% 2.07/2.51 X := X
% 2.07/2.51 end
% 2.07/2.51 permutation0:
% 2.07/2.51 0 ==> 0
% 2.07/2.51 end
% 2.07/2.51
% 2.07/2.51 resolution: (9930) {G1,W6,D4,L1,V0,M1} { ! leq( strong_iteration( one ),
% 2.07/2.51 strong_iteration( star( skol1 ) ) ) }.
% 2.07/2.51 parent0[0]: (19) {G0,W12,D4,L2,V0,M2} I { ! leq( strong_iteration( star(
% 2.07/2.51 skol1 ) ), strong_iteration( one ) ), ! leq( strong_iteration( one ),
% 2.07/2.51 strong_iteration( star( skol1 ) ) ) }.
% 2.07/2.51 parent1[0]: (9619) {G8,W4,D3,L1,V1,M1} P(1737,9565) { leq( X,
% 2.07/2.51 strong_iteration( one ) ) }.
% 2.07/2.51 substitution0:
% 2.07/2.51 end
% 2.07/2.51 substitution1:
% 2.07/2.51 X := strong_iteration( star( skol1 ) )
% 2.07/2.51 end
% 2.07/2.51
% 2.07/2.51 resolution: (9931) {G2,W0,D0,L0,V0,M0} { }.
% 2.07/2.51 parent0[0]: (9930) {G1,W6,D4,L1,V0,M1} { ! leq( strong_iteration( one ),
% 2.07/2.51 strong_iteration( star( skol1 ) ) ) }.
% 2.07/2.51 parent1[0]: (9617) {G8,W5,D4,L1,V2,M1} P(145,9565) { leq( Y,
% 2.07/2.51 strong_iteration( star( X ) ) ) }.
% 2.07/2.51 substitution0:
% 2.07/2.51 end
% 2.07/2.51 substitution1:
% 2.07/2.51 X := skol1
% 2.07/2.51 Y := strong_iteration( one )
% 2.07/2.51 end
% 2.07/2.51
% 2.07/2.51 subsumption: (9669) {G9,W0,D0,L0,V0,M0} R(9619,19);r(9617) { }.
% 2.07/2.51 parent0: (9931) {G2,W0,D0,L0,V0,M0} { }.
% 2.07/2.51 substitution0:
% 2.07/2.51 end
% 2.07/2.51 permutation0:
% 2.07/2.51 end
% 2.07/2.51
% 2.07/2.51 Proof check complete!
% 2.07/2.51
% 2.07/2.51 Memory use:
% 2.07/2.51
% 2.07/2.51 space for terms: 119733
% 2.07/2.51 space for clauses: 519851
% 2.07/2.51
% 2.07/2.51
% 2.07/2.51 clauses generated: 121184
% 2.07/2.51 clauses kept: 9670
% 2.07/2.51 clauses selected: 751
% 2.07/2.51 clauses deleted: 138
% 2.07/2.51 clauses inuse deleted: 37
% 2.07/2.51
% 2.07/2.51 subsentry: 410599
% 2.07/2.51 literals s-matched: 268850
% 2.07/2.51 literals matched: 261458
% 2.07/2.51 full subsumption: 76321
% 2.07/2.51
% 2.07/2.51 checksum: 1243152607
% 2.07/2.51
% 2.07/2.51
% 2.07/2.51 Bliksem ended
%------------------------------------------------------------------------------