TSTP Solution File: KLE141+1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : KLE141+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Sun Jul 17 01:37:24 EDT 2022
% Result : Theorem 0.70s 1.52s
% Output : Refutation 0.70s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : KLE141+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12 % Command : bliksem %s
% 0.10/0.32 % Computer : n017.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % DateTime : Thu Jun 16 12:19:40 EDT 2022
% 0.10/0.32 % CPUTime :
% 0.70/1.52 *** allocated 10000 integers for termspace/termends
% 0.70/1.52 *** allocated 10000 integers for clauses
% 0.70/1.52 *** allocated 10000 integers for justifications
% 0.70/1.52 Bliksem 1.12
% 0.70/1.52
% 0.70/1.52
% 0.70/1.52 Automatic Strategy Selection
% 0.70/1.52
% 0.70/1.52
% 0.70/1.52 Clauses:
% 0.70/1.52
% 0.70/1.52 { addition( X, Y ) = addition( Y, X ) }.
% 0.70/1.52 { addition( Z, addition( Y, X ) ) = addition( addition( Z, Y ), X ) }.
% 0.70/1.52 { addition( X, zero ) = X }.
% 0.70/1.52 { addition( X, X ) = X }.
% 0.70/1.52 { multiplication( X, multiplication( Y, Z ) ) = multiplication(
% 0.70/1.52 multiplication( X, Y ), Z ) }.
% 0.70/1.52 { multiplication( X, one ) = X }.
% 0.70/1.52 { multiplication( one, X ) = X }.
% 0.70/1.52 { multiplication( X, addition( Y, Z ) ) = addition( multiplication( X, Y )
% 0.70/1.52 , multiplication( X, Z ) ) }.
% 0.70/1.52 { multiplication( addition( X, Y ), Z ) = addition( multiplication( X, Z )
% 0.70/1.52 , multiplication( Y, Z ) ) }.
% 0.70/1.52 { multiplication( zero, X ) = zero }.
% 0.70/1.52 { addition( one, multiplication( X, star( X ) ) ) = star( X ) }.
% 0.70/1.52 { addition( one, multiplication( star( X ), X ) ) = star( X ) }.
% 0.70/1.52 { ! leq( addition( multiplication( X, Z ), Y ), Z ), leq( multiplication(
% 0.70/1.52 star( X ), Y ), Z ) }.
% 0.70/1.52 { ! leq( addition( multiplication( Z, X ), Y ), Z ), leq( multiplication( Y
% 0.70/1.52 , star( X ) ), Z ) }.
% 0.70/1.52 { strong_iteration( X ) = addition( multiplication( X, strong_iteration( X
% 0.70/1.52 ) ), one ) }.
% 0.70/1.52 { ! leq( Z, addition( multiplication( X, Z ), Y ) ), leq( Z, multiplication
% 0.70/1.52 ( strong_iteration( X ), Y ) ) }.
% 0.70/1.52 { strong_iteration( X ) = addition( star( X ), multiplication(
% 0.70/1.52 strong_iteration( X ), zero ) ) }.
% 0.70/1.52 { ! leq( X, Y ), addition( X, Y ) = Y }.
% 0.70/1.52 { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 0.70/1.52 { ! multiplication( strong_iteration( one ), skol1 ) = strong_iteration(
% 0.70/1.52 one ) }.
% 0.70/1.52
% 0.70/1.52 percentage equality = 0.680000, percentage horn = 1.000000
% 0.70/1.52 This is a problem with some equality
% 0.70/1.52
% 0.70/1.52
% 0.70/1.52
% 0.70/1.52 Options Used:
% 0.70/1.52
% 0.70/1.52 useres = 1
% 0.70/1.52 useparamod = 1
% 0.70/1.52 useeqrefl = 1
% 0.70/1.52 useeqfact = 1
% 0.70/1.52 usefactor = 1
% 0.70/1.52 usesimpsplitting = 0
% 0.70/1.52 usesimpdemod = 5
% 0.70/1.52 usesimpres = 3
% 0.70/1.52
% 0.70/1.52 resimpinuse = 1000
% 0.70/1.52 resimpclauses = 20000
% 0.70/1.52 substype = eqrewr
% 0.70/1.52 backwardsubs = 1
% 0.70/1.52 selectoldest = 5
% 0.70/1.52
% 0.70/1.52 litorderings [0] = split
% 0.70/1.52 litorderings [1] = extend the termordering, first sorting on arguments
% 0.70/1.52
% 0.70/1.52 termordering = kbo
% 0.70/1.52
% 0.70/1.52 litapriori = 0
% 0.70/1.52 termapriori = 1
% 0.70/1.52 litaposteriori = 0
% 0.70/1.52 termaposteriori = 0
% 0.70/1.52 demodaposteriori = 0
% 0.70/1.52 ordereqreflfact = 0
% 0.70/1.52
% 0.70/1.52 litselect = negord
% 0.70/1.52
% 0.70/1.52 maxweight = 15
% 0.70/1.52 maxdepth = 30000
% 0.70/1.52 maxlength = 115
% 0.70/1.52 maxnrvars = 195
% 0.70/1.52 excuselevel = 1
% 0.70/1.52 increasemaxweight = 1
% 0.70/1.52
% 0.70/1.52 maxselected = 10000000
% 0.70/1.52 maxnrclauses = 10000000
% 0.70/1.52
% 0.70/1.52 showgenerated = 0
% 0.70/1.52 showkept = 0
% 0.70/1.52 showselected = 0
% 0.70/1.52 showdeleted = 0
% 0.70/1.52 showresimp = 1
% 0.70/1.52 showstatus = 2000
% 0.70/1.52
% 0.70/1.52 prologoutput = 0
% 0.70/1.52 nrgoals = 5000000
% 0.70/1.52 totalproof = 1
% 0.70/1.52
% 0.70/1.52 Symbols occurring in the translation:
% 0.70/1.52
% 0.70/1.52 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.70/1.52 . [1, 2] (w:1, o:20, a:1, s:1, b:0),
% 0.70/1.52 ! [4, 1] (w:0, o:13, a:1, s:1, b:0),
% 0.70/1.52 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.70/1.52 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.70/1.52 addition [37, 2] (w:1, o:44, a:1, s:1, b:0),
% 0.70/1.52 zero [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.70/1.52 multiplication [40, 2] (w:1, o:46, a:1, s:1, b:0),
% 0.70/1.52 one [41, 0] (w:1, o:10, a:1, s:1, b:0),
% 0.70/1.52 star [42, 1] (w:1, o:18, a:1, s:1, b:0),
% 0.70/1.52 leq [43, 2] (w:1, o:45, a:1, s:1, b:0),
% 0.70/1.52 strong_iteration [44, 1] (w:1, o:19, a:1, s:1, b:0),
% 0.70/1.52 skol1 [46, 0] (w:1, o:12, a:1, s:1, b:1).
% 0.70/1.52
% 0.70/1.52
% 0.70/1.52 Starting Search:
% 0.70/1.52
% 0.70/1.52 *** allocated 15000 integers for clauses
% 0.70/1.52 *** allocated 22500 integers for clauses
% 0.70/1.52 *** allocated 33750 integers for clauses
% 0.70/1.52 *** allocated 50625 integers for clauses
% 0.70/1.52 *** allocated 75937 integers for clauses
% 0.70/1.52 *** allocated 15000 integers for termspace/termends
% 0.70/1.52 Resimplifying inuse:
% 0.70/1.52 Done
% 0.70/1.52
% 0.70/1.52 *** allocated 22500 integers for termspace/termends
% 0.70/1.52 *** allocated 113905 integers for clauses
% 0.70/1.52 *** allocated 33750 integers for termspace/termends
% 0.70/1.52
% 0.70/1.52 Intermediate Status:
% 0.70/1.52 Generated: 13749
% 0.70/1.52 Kept: 2003
% 0.70/1.52 Inuse: 218
% 0.70/1.52 Deleted: 41
% 0.70/1.52 Deletedinuse: 15
% 0.70/1.52
% 0.70/1.52 Resimplifying inuse:
% 0.70/1.52 Done
% 0.70/1.52
% 0.70/1.52 *** allocated 170857 integers for clauses
% 0.70/1.52 *** allocated 50625 integers for termspace/termends
% 0.70/1.52 Resimplifying inuse:
% 0.70/1.52 Done
% 0.70/1.52
% 0.70/1.52 *** allocated 256285 integers for clauses
% 0.70/1.52
% 0.70/1.52 Intermediate Status:
% 0.70/1.52 Generated: 29007
% 0.70/1.52 Kept: 4021
% 0.70/1.52 Inuse: 323
% 0.70/1.52 Deleted: 44
% 0.70/1.52 Deletedinuse: 16
% 0.70/1.52
% 0.70/1.52 *** allocated 75937 integers for termspace/termends
% 0.70/1.52 Resimplifying inuse:
% 0.70/1.52 Done
% 0.70/1.52
% 0.70/1.52 *** allocated 384427 integers for clauses
% 0.70/1.52 Resimplifying inuse:
% 0.70/1.52 Done
% 0.70/1.52
% 0.70/1.52
% 0.70/1.52 Bliksems!, er is een bewijs:
% 0.70/1.52 % SZS status Theorem
% 0.70/1.52 % SZS output start Refutation
% 0.70/1.52
% 0.70/1.52 (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X ) }.
% 0.70/1.52 (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) ) ==> addition(
% 0.70/1.52 addition( Z, Y ), X ) }.
% 0.70/1.52 (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 0.70/1.52 (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 0.70/1.52 (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 0.70/1.52 (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 0.70/1.52 (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 0.70/1.52 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 0.70/1.52 (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ),
% 0.70/1.52 multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 0.70/1.52 (15) {G0,W13,D4,L2,V3,M2} I { ! leq( Z, addition( multiplication( X, Z ), Y
% 0.70/1.52 ) ), leq( Z, multiplication( strong_iteration( X ), Y ) ) }.
% 0.70/1.52 (17) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y ) ==> Y }.
% 0.70/1.52 (18) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X, Y ) }.
% 0.70/1.52 (19) {G0,W7,D4,L1,V0,M1} I { ! multiplication( strong_iteration( one ),
% 0.70/1.52 skol1 ) ==> strong_iteration( one ) }.
% 0.70/1.52 (20) {G1,W5,D3,L1,V1,M1} P(0,2) { addition( zero, X ) ==> X }.
% 0.70/1.52 (25) {G1,W14,D4,L2,V3,M2} P(1,18) { ! addition( addition( X, Y ), Z ) ==>
% 0.70/1.52 addition( Y, Z ), leq( X, addition( Y, Z ) ) }.
% 0.70/1.52 (26) {G1,W11,D4,L1,V3,M1} P(1,0) { addition( addition( X, Y ), Z ) =
% 0.70/1.52 addition( addition( Y, Z ), X ) }.
% 0.70/1.52 (35) {G1,W12,D4,L2,V3,M2} P(17,1) { addition( addition( Z, X ), Y ) ==>
% 0.70/1.52 addition( Z, Y ), ! leq( X, Y ) }.
% 0.70/1.52 (36) {G1,W8,D3,L2,V2,M2} P(17,0) { addition( Y, X ) ==> Y, ! leq( X, Y )
% 0.70/1.52 }.
% 0.70/1.52 (65) {G1,W16,D4,L2,V3,M2} P(7,17) { ! leq( multiplication( X, Y ),
% 0.70/1.52 multiplication( X, Z ) ), multiplication( X, addition( Y, Z ) ) ==>
% 0.70/1.52 multiplication( X, Z ) }.
% 0.70/1.52 (67) {G1,W16,D4,L2,V3,M2} P(7,18) { ! multiplication( X, addition( Y, Z ) )
% 0.70/1.52 ==> multiplication( X, Z ), leq( multiplication( X, Y ), multiplication
% 0.70/1.52 ( X, Z ) ) }.
% 0.70/1.52 (69) {G1,W11,D4,L1,V2,M1} P(5,7) { addition( X, multiplication( X, Y ) ) =
% 0.70/1.52 multiplication( X, addition( one, Y ) ) }.
% 0.70/1.52 (101) {G1,W11,D4,L1,V2,M1} P(6,8) { addition( multiplication( Y, X ), X ) =
% 0.70/1.52 multiplication( addition( Y, one ), X ) }.
% 0.70/1.52 (298) {G2,W5,D3,L1,V2,M1} P(3,25);q { leq( X, addition( X, Y ) ) }.
% 0.70/1.52 (312) {G3,W5,D3,L1,V2,M1} P(0,298) { leq( X, addition( Y, X ) ) }.
% 0.70/1.52 (335) {G4,W7,D4,L1,V3,M1} P(26,312) { leq( Z, addition( addition( Y, Z ), X
% 0.70/1.52 ) ) }.
% 0.70/1.52 (572) {G5,W8,D3,L2,V3,M2} P(35,335) { leq( Y, addition( X, Z ) ), ! leq( Y
% 0.70/1.52 , Z ) }.
% 0.70/1.52 (1855) {G2,W7,D3,L1,V2,M1} P(20,67);q { leq( multiplication( Y, zero ),
% 0.70/1.52 multiplication( Y, X ) ) }.
% 0.70/1.52 (1918) {G3,W5,D3,L1,V1,M1} P(5,1855) { leq( multiplication( X, zero ), X )
% 0.70/1.52 }.
% 0.70/1.52 (1922) {G4,W7,D4,L1,V1,M1} R(1918,36) { addition( X, multiplication( X,
% 0.70/1.52 zero ) ) ==> X }.
% 0.70/1.52 (1926) {G4,W7,D4,L1,V1,M1} R(1918,17) { addition( multiplication( X, zero )
% 0.70/1.52 , X ) ==> X }.
% 0.70/1.52 (2182) {G6,W8,D3,L2,V2,M2} P(1922,572) { leq( Y, X ), ! leq( Y,
% 0.70/1.52 multiplication( X, zero ) ) }.
% 0.70/1.52 (4197) {G5,W8,D5,L1,V3,M1} P(101,15);r(335) { leq( Y, multiplication(
% 0.70/1.52 strong_iteration( addition( X, one ) ), Z ) ) }.
% 0.70/1.52 (5101) {G7,W6,D4,L1,V2,M1} R(4197,2182) { leq( X, strong_iteration(
% 0.70/1.52 addition( Y, one ) ) ) }.
% 0.70/1.52 (5117) {G6,W6,D4,L1,V2,M1} P(1926,4197) { leq( X, multiplication(
% 0.70/1.52 strong_iteration( one ), Y ) ) }.
% 0.70/1.52 (5137) {G8,W4,D3,L1,V1,M1} P(1926,5101) { leq( X, strong_iteration( one ) )
% 0.70/1.52 }.
% 0.70/1.52 (5147) {G9,W7,D4,L1,V1,M1} R(5137,36) { addition( strong_iteration( one ),
% 0.70/1.52 X ) ==> strong_iteration( one ) }.
% 0.70/1.52 (5212) {G7,W11,D4,L1,V2,M1} R(5117,65) { multiplication( strong_iteration(
% 0.70/1.52 one ), addition( X, Y ) ) ==> multiplication( strong_iteration( one ), Y
% 0.70/1.52 ) }.
% 0.70/1.52 (5467) {G10,W7,D4,L1,V1,M1} P(5147,69);d(5212) { multiplication(
% 0.70/1.52 strong_iteration( one ), X ) ==> strong_iteration( one ) }.
% 0.70/1.52 (5543) {G11,W0,D0,L0,V0,M0} R(5467,19) { }.
% 0.70/1.52
% 0.70/1.52
% 0.70/1.52 % SZS output end Refutation
% 0.70/1.52 found a proof!
% 0.70/1.52
% 0.70/1.52
% 0.70/1.52 Unprocessed initial clauses:
% 0.70/1.52
% 0.70/1.52 (5545) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X ) }.
% 0.70/1.52 (5546) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) = addition(
% 0.70/1.52 addition( Z, Y ), X ) }.
% 0.70/1.52 (5547) {G0,W5,D3,L1,V1,M1} { addition( X, zero ) = X }.
% 0.70/1.52 (5548) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 0.70/1.52 (5549) {G0,W11,D4,L1,V3,M1} { multiplication( X, multiplication( Y, Z ) )
% 0.70/1.52 = multiplication( multiplication( X, Y ), Z ) }.
% 0.70/1.52 (5550) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 0.70/1.52 (5551) {G0,W5,D3,L1,V1,M1} { multiplication( one, X ) = X }.
% 0.70/1.52 (5552) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y, Z ) ) =
% 0.70/1.52 addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 0.70/1.52 (5553) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Y ), Z ) =
% 0.70/1.52 addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 0.70/1.52 (5554) {G0,W5,D3,L1,V1,M1} { multiplication( zero, X ) = zero }.
% 0.70/1.52 (5555) {G0,W9,D5,L1,V1,M1} { addition( one, multiplication( X, star( X ) )
% 0.70/1.52 ) = star( X ) }.
% 0.70/1.52 (5556) {G0,W9,D5,L1,V1,M1} { addition( one, multiplication( star( X ), X )
% 0.70/1.52 ) = star( X ) }.
% 0.70/1.52 (5557) {G0,W13,D4,L2,V3,M2} { ! leq( addition( multiplication( X, Z ), Y )
% 0.70/1.52 , Z ), leq( multiplication( star( X ), Y ), Z ) }.
% 0.70/1.52 (5558) {G0,W13,D4,L2,V3,M2} { ! leq( addition( multiplication( Z, X ), Y )
% 0.70/1.52 , Z ), leq( multiplication( Y, star( X ) ), Z ) }.
% 0.70/1.52 (5559) {G0,W9,D5,L1,V1,M1} { strong_iteration( X ) = addition(
% 0.70/1.52 multiplication( X, strong_iteration( X ) ), one ) }.
% 0.70/1.52 (5560) {G0,W13,D4,L2,V3,M2} { ! leq( Z, addition( multiplication( X, Z ),
% 0.70/1.52 Y ) ), leq( Z, multiplication( strong_iteration( X ), Y ) ) }.
% 0.70/1.52 (5561) {G0,W10,D5,L1,V1,M1} { strong_iteration( X ) = addition( star( X )
% 0.70/1.52 , multiplication( strong_iteration( X ), zero ) ) }.
% 0.70/1.52 (5562) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y }.
% 0.70/1.52 (5563) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 0.70/1.52 (5564) {G0,W7,D4,L1,V0,M1} { ! multiplication( strong_iteration( one ),
% 0.70/1.52 skol1 ) = strong_iteration( one ) }.
% 0.70/1.52
% 0.70/1.52
% 0.70/1.52 Total Proof:
% 0.70/1.52
% 0.70/1.52 subsumption: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X
% 0.70/1.52 ) }.
% 0.70/1.52 parent0: (5545) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X )
% 0.70/1.52 }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := X
% 0.70/1.52 Y := Y
% 0.70/1.52 end
% 0.70/1.52 permutation0:
% 0.70/1.52 0 ==> 0
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 subsumption: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 0.70/1.52 ==> addition( addition( Z, Y ), X ) }.
% 0.70/1.52 parent0: (5546) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) =
% 0.70/1.52 addition( addition( Z, Y ), X ) }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := X
% 0.70/1.52 Y := Y
% 0.70/1.52 Z := Z
% 0.70/1.52 end
% 0.70/1.52 permutation0:
% 0.70/1.52 0 ==> 0
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 subsumption: (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 0.70/1.52 parent0: (5547) {G0,W5,D3,L1,V1,M1} { addition( X, zero ) = X }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := X
% 0.70/1.52 end
% 0.70/1.52 permutation0:
% 0.70/1.52 0 ==> 0
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 subsumption: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 0.70/1.52 parent0: (5548) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := X
% 0.70/1.52 end
% 0.70/1.52 permutation0:
% 0.70/1.52 0 ==> 0
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 subsumption: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 0.70/1.52 parent0: (5550) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := X
% 0.70/1.52 end
% 0.70/1.52 permutation0:
% 0.70/1.52 0 ==> 0
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 subsumption: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 0.70/1.52 parent0: (5551) {G0,W5,D3,L1,V1,M1} { multiplication( one, X ) = X }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := X
% 0.70/1.52 end
% 0.70/1.52 permutation0:
% 0.70/1.52 0 ==> 0
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 eqswap: (5588) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Y ),
% 0.70/1.52 multiplication( X, Z ) ) = multiplication( X, addition( Y, Z ) ) }.
% 0.70/1.52 parent0[0]: (5552) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y,
% 0.70/1.52 Z ) ) = addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := X
% 0.70/1.52 Y := Y
% 0.70/1.52 Z := Z
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 subsumption: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y )
% 0.70/1.52 , multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 0.70/1.52 parent0: (5588) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Y ),
% 0.70/1.52 multiplication( X, Z ) ) = multiplication( X, addition( Y, Z ) ) }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := X
% 0.70/1.52 Y := Y
% 0.70/1.52 Z := Z
% 0.70/1.52 end
% 0.70/1.52 permutation0:
% 0.70/1.52 0 ==> 0
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 eqswap: (5596) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Z ),
% 0.70/1.52 multiplication( Y, Z ) ) = multiplication( addition( X, Y ), Z ) }.
% 0.70/1.52 parent0[0]: (5553) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Y )
% 0.70/1.52 , Z ) = addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := X
% 0.70/1.52 Y := Y
% 0.70/1.52 Z := Z
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 subsumption: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z )
% 0.70/1.52 , multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 0.70/1.52 parent0: (5596) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Z ),
% 0.70/1.52 multiplication( Y, Z ) ) = multiplication( addition( X, Y ), Z ) }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := X
% 0.70/1.52 Y := Y
% 0.70/1.52 Z := Z
% 0.70/1.52 end
% 0.70/1.52 permutation0:
% 0.70/1.52 0 ==> 0
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 subsumption: (15) {G0,W13,D4,L2,V3,M2} I { ! leq( Z, addition(
% 0.70/1.52 multiplication( X, Z ), Y ) ), leq( Z, multiplication( strong_iteration(
% 0.70/1.52 X ), Y ) ) }.
% 0.70/1.52 parent0: (5560) {G0,W13,D4,L2,V3,M2} { ! leq( Z, addition( multiplication
% 0.70/1.52 ( X, Z ), Y ) ), leq( Z, multiplication( strong_iteration( X ), Y ) ) }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := X
% 0.70/1.52 Y := Y
% 0.70/1.52 Z := Z
% 0.70/1.52 end
% 0.70/1.52 permutation0:
% 0.70/1.52 0 ==> 0
% 0.70/1.52 1 ==> 1
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 subsumption: (17) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 0.70/1.52 ==> Y }.
% 0.70/1.52 parent0: (5562) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y
% 0.70/1.52 }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := X
% 0.70/1.52 Y := Y
% 0.70/1.52 end
% 0.70/1.52 permutation0:
% 0.70/1.52 0 ==> 0
% 0.70/1.52 1 ==> 1
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 subsumption: (18) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X
% 0.70/1.52 , Y ) }.
% 0.70/1.52 parent0: (5563) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y )
% 0.70/1.52 }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := X
% 0.70/1.52 Y := Y
% 0.70/1.52 end
% 0.70/1.52 permutation0:
% 0.70/1.52 0 ==> 0
% 0.70/1.52 1 ==> 1
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 subsumption: (19) {G0,W7,D4,L1,V0,M1} I { ! multiplication(
% 0.70/1.52 strong_iteration( one ), skol1 ) ==> strong_iteration( one ) }.
% 0.70/1.52 parent0: (5564) {G0,W7,D4,L1,V0,M1} { ! multiplication( strong_iteration(
% 0.70/1.52 one ), skol1 ) = strong_iteration( one ) }.
% 0.70/1.52 substitution0:
% 0.70/1.52 end
% 0.70/1.52 permutation0:
% 0.70/1.52 0 ==> 0
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 eqswap: (5654) {G0,W5,D3,L1,V1,M1} { X ==> addition( X, zero ) }.
% 0.70/1.52 parent0[0]: (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := X
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 paramod: (5655) {G1,W5,D3,L1,V1,M1} { X ==> addition( zero, X ) }.
% 0.70/1.52 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 0.70/1.52 }.
% 0.70/1.52 parent1[0; 2]: (5654) {G0,W5,D3,L1,V1,M1} { X ==> addition( X, zero ) }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := X
% 0.70/1.52 Y := zero
% 0.70/1.52 end
% 0.70/1.52 substitution1:
% 0.70/1.52 X := X
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 eqswap: (5658) {G1,W5,D3,L1,V1,M1} { addition( zero, X ) ==> X }.
% 0.70/1.52 parent0[0]: (5655) {G1,W5,D3,L1,V1,M1} { X ==> addition( zero, X ) }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := X
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 subsumption: (20) {G1,W5,D3,L1,V1,M1} P(0,2) { addition( zero, X ) ==> X
% 0.70/1.52 }.
% 0.70/1.52 parent0: (5658) {G1,W5,D3,L1,V1,M1} { addition( zero, X ) ==> X }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := X
% 0.70/1.52 end
% 0.70/1.52 permutation0:
% 0.70/1.52 0 ==> 0
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 eqswap: (5660) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y )
% 0.70/1.52 }.
% 0.70/1.52 parent0[0]: (18) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 0.70/1.52 Y ) }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := X
% 0.70/1.52 Y := Y
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 paramod: (5661) {G1,W14,D4,L2,V3,M2} { ! addition( X, Y ) ==> addition(
% 0.70/1.52 addition( Z, X ), Y ), leq( Z, addition( X, Y ) ) }.
% 0.70/1.52 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 0.70/1.52 ==> addition( addition( Z, Y ), X ) }.
% 0.70/1.52 parent1[0; 5]: (5660) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq
% 0.70/1.52 ( X, Y ) }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := Y
% 0.70/1.52 Y := X
% 0.70/1.52 Z := Z
% 0.70/1.52 end
% 0.70/1.52 substitution1:
% 0.70/1.52 X := Z
% 0.70/1.52 Y := addition( X, Y )
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 eqswap: (5662) {G1,W14,D4,L2,V3,M2} { ! addition( addition( Z, X ), Y )
% 0.70/1.52 ==> addition( X, Y ), leq( Z, addition( X, Y ) ) }.
% 0.70/1.52 parent0[0]: (5661) {G1,W14,D4,L2,V3,M2} { ! addition( X, Y ) ==> addition
% 0.70/1.52 ( addition( Z, X ), Y ), leq( Z, addition( X, Y ) ) }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := X
% 0.70/1.52 Y := Y
% 0.70/1.52 Z := Z
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 subsumption: (25) {G1,W14,D4,L2,V3,M2} P(1,18) { ! addition( addition( X, Y
% 0.70/1.52 ), Z ) ==> addition( Y, Z ), leq( X, addition( Y, Z ) ) }.
% 0.70/1.52 parent0: (5662) {G1,W14,D4,L2,V3,M2} { ! addition( addition( Z, X ), Y )
% 0.70/1.52 ==> addition( X, Y ), leq( Z, addition( X, Y ) ) }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := Y
% 0.70/1.52 Y := Z
% 0.70/1.52 Z := X
% 0.70/1.52 end
% 0.70/1.52 permutation0:
% 0.70/1.52 0 ==> 0
% 0.70/1.52 1 ==> 1
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 eqswap: (5663) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z ) ==>
% 0.70/1.52 addition( X, addition( Y, Z ) ) }.
% 0.70/1.52 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 0.70/1.52 ==> addition( addition( Z, Y ), X ) }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := Z
% 0.70/1.52 Y := Y
% 0.70/1.52 Z := X
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 paramod: (5666) {G1,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z ) ==>
% 0.70/1.52 addition( addition( Y, Z ), X ) }.
% 0.70/1.52 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 0.70/1.52 }.
% 0.70/1.52 parent1[0; 6]: (5663) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z
% 0.70/1.52 ) ==> addition( X, addition( Y, Z ) ) }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := X
% 0.70/1.52 Y := addition( Y, Z )
% 0.70/1.52 end
% 0.70/1.52 substitution1:
% 0.70/1.52 X := X
% 0.70/1.52 Y := Y
% 0.70/1.52 Z := Z
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 subsumption: (26) {G1,W11,D4,L1,V3,M1} P(1,0) { addition( addition( X, Y )
% 0.70/1.52 , Z ) = addition( addition( Y, Z ), X ) }.
% 0.70/1.52 parent0: (5666) {G1,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z ) ==>
% 0.70/1.52 addition( addition( Y, Z ), X ) }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := X
% 0.70/1.52 Y := Y
% 0.70/1.52 Z := Z
% 0.70/1.52 end
% 0.70/1.52 permutation0:
% 0.70/1.52 0 ==> 0
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 eqswap: (5681) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z ) ==>
% 0.70/1.52 addition( X, addition( Y, Z ) ) }.
% 0.70/1.52 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 0.70/1.52 ==> addition( addition( Z, Y ), X ) }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := Z
% 0.70/1.52 Y := Y
% 0.70/1.52 Z := X
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 paramod: (5687) {G1,W12,D4,L2,V3,M2} { addition( addition( X, Y ), Z ) ==>
% 0.70/1.52 addition( X, Z ), ! leq( Y, Z ) }.
% 0.70/1.52 parent0[1]: (17) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 0.70/1.52 ==> Y }.
% 0.70/1.52 parent1[0; 8]: (5681) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z
% 0.70/1.52 ) ==> addition( X, addition( Y, Z ) ) }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := Y
% 0.70/1.52 Y := Z
% 0.70/1.52 end
% 0.70/1.52 substitution1:
% 0.70/1.52 X := X
% 0.70/1.52 Y := Y
% 0.70/1.52 Z := Z
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 subsumption: (35) {G1,W12,D4,L2,V3,M2} P(17,1) { addition( addition( Z, X )
% 0.70/1.52 , Y ) ==> addition( Z, Y ), ! leq( X, Y ) }.
% 0.70/1.52 parent0: (5687) {G1,W12,D4,L2,V3,M2} { addition( addition( X, Y ), Z ) ==>
% 0.70/1.52 addition( X, Z ), ! leq( Y, Z ) }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := Z
% 0.70/1.52 Y := X
% 0.70/1.52 Z := Y
% 0.70/1.52 end
% 0.70/1.52 permutation0:
% 0.70/1.52 0 ==> 0
% 0.70/1.52 1 ==> 1
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 eqswap: (5734) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X, Y )
% 0.70/1.52 }.
% 0.70/1.52 parent0[1]: (17) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 0.70/1.52 ==> Y }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := X
% 0.70/1.52 Y := Y
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 paramod: (5735) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y, X
% 0.70/1.52 ) }.
% 0.70/1.52 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 0.70/1.52 }.
% 0.70/1.52 parent1[0; 2]: (5734) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq
% 0.70/1.52 ( X, Y ) }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := Y
% 0.70/1.52 Y := X
% 0.70/1.52 end
% 0.70/1.52 substitution1:
% 0.70/1.52 X := Y
% 0.70/1.52 Y := X
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 eqswap: (5738) {G1,W8,D3,L2,V2,M2} { addition( X, Y ) ==> X, ! leq( Y, X )
% 0.70/1.52 }.
% 0.70/1.52 parent0[0]: (5735) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y
% 0.70/1.52 , X ) }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := X
% 0.70/1.52 Y := Y
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 subsumption: (36) {G1,W8,D3,L2,V2,M2} P(17,0) { addition( Y, X ) ==> Y, !
% 0.70/1.52 leq( X, Y ) }.
% 0.70/1.52 parent0: (5738) {G1,W8,D3,L2,V2,M2} { addition( X, Y ) ==> X, ! leq( Y, X
% 0.70/1.52 ) }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := Y
% 0.70/1.52 Y := X
% 0.70/1.52 end
% 0.70/1.52 permutation0:
% 0.70/1.52 0 ==> 0
% 0.70/1.52 1 ==> 1
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 eqswap: (5739) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y, Z )
% 0.70/1.52 ) ==> addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 0.70/1.52 parent0[0]: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 0.70/1.52 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := X
% 0.70/1.52 Y := Y
% 0.70/1.52 Z := Z
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 paramod: (5742) {G1,W16,D4,L2,V3,M2} { multiplication( X, addition( Y, Z )
% 0.70/1.52 ) ==> multiplication( X, Z ), ! leq( multiplication( X, Y ),
% 0.70/1.52 multiplication( X, Z ) ) }.
% 0.70/1.52 parent0[1]: (17) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 0.70/1.52 ==> Y }.
% 0.70/1.52 parent1[0; 6]: (5739) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition(
% 0.70/1.52 Y, Z ) ) ==> addition( multiplication( X, Y ), multiplication( X, Z ) )
% 0.70/1.52 }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := multiplication( X, Y )
% 0.70/1.52 Y := multiplication( X, Z )
% 0.70/1.52 end
% 0.70/1.52 substitution1:
% 0.70/1.52 X := X
% 0.70/1.52 Y := Y
% 0.70/1.52 Z := Z
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 subsumption: (65) {G1,W16,D4,L2,V3,M2} P(7,17) { ! leq( multiplication( X,
% 0.70/1.52 Y ), multiplication( X, Z ) ), multiplication( X, addition( Y, Z ) ) ==>
% 0.70/1.52 multiplication( X, Z ) }.
% 0.70/1.52 parent0: (5742) {G1,W16,D4,L2,V3,M2} { multiplication( X, addition( Y, Z )
% 0.70/1.52 ) ==> multiplication( X, Z ), ! leq( multiplication( X, Y ),
% 0.70/1.52 multiplication( X, Z ) ) }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := X
% 0.70/1.52 Y := Y
% 0.70/1.52 Z := Z
% 0.70/1.52 end
% 0.70/1.52 permutation0:
% 0.70/1.52 0 ==> 1
% 0.70/1.52 1 ==> 0
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 eqswap: (5747) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y )
% 0.70/1.52 }.
% 0.70/1.52 parent0[0]: (18) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 0.70/1.52 Y ) }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := X
% 0.70/1.52 Y := Y
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 paramod: (5748) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Y ) ==>
% 0.70/1.52 multiplication( X, addition( Z, Y ) ), leq( multiplication( X, Z ),
% 0.70/1.52 multiplication( X, Y ) ) }.
% 0.70/1.52 parent0[0]: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 0.70/1.52 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 0.70/1.52 parent1[0; 5]: (5747) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq
% 0.70/1.52 ( X, Y ) }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := X
% 0.70/1.52 Y := Z
% 0.70/1.52 Z := Y
% 0.70/1.52 end
% 0.70/1.52 substitution1:
% 0.70/1.52 X := multiplication( X, Z )
% 0.70/1.52 Y := multiplication( X, Y )
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 eqswap: (5749) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, addition( Z, Y
% 0.70/1.52 ) ) ==> multiplication( X, Y ), leq( multiplication( X, Z ),
% 0.70/1.52 multiplication( X, Y ) ) }.
% 0.70/1.52 parent0[0]: (5748) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Y ) ==>
% 0.70/1.52 multiplication( X, addition( Z, Y ) ), leq( multiplication( X, Z ),
% 0.70/1.52 multiplication( X, Y ) ) }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := X
% 0.70/1.52 Y := Y
% 0.70/1.52 Z := Z
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 subsumption: (67) {G1,W16,D4,L2,V3,M2} P(7,18) { ! multiplication( X,
% 0.70/1.52 addition( Y, Z ) ) ==> multiplication( X, Z ), leq( multiplication( X, Y
% 0.70/1.52 ), multiplication( X, Z ) ) }.
% 0.70/1.52 parent0: (5749) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, addition( Z, Y
% 0.70/1.52 ) ) ==> multiplication( X, Y ), leq( multiplication( X, Z ),
% 0.70/1.52 multiplication( X, Y ) ) }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := X
% 0.70/1.52 Y := Z
% 0.70/1.52 Z := Y
% 0.70/1.52 end
% 0.70/1.52 permutation0:
% 0.70/1.52 0 ==> 0
% 0.70/1.52 1 ==> 1
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 eqswap: (5751) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y, Z )
% 0.70/1.52 ) ==> addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 0.70/1.52 parent0[0]: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 0.70/1.52 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := X
% 0.70/1.52 Y := Y
% 0.70/1.52 Z := Z
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 paramod: (5752) {G1,W11,D4,L1,V2,M1} { multiplication( X, addition( one, Y
% 0.70/1.52 ) ) ==> addition( X, multiplication( X, Y ) ) }.
% 0.70/1.52 parent0[0]: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 0.70/1.52 parent1[0; 7]: (5751) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition(
% 0.70/1.52 Y, Z ) ) ==> addition( multiplication( X, Y ), multiplication( X, Z ) )
% 0.70/1.52 }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := X
% 0.70/1.52 end
% 0.70/1.52 substitution1:
% 0.70/1.52 X := X
% 0.70/1.52 Y := one
% 0.70/1.52 Z := Y
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 eqswap: (5754) {G1,W11,D4,L1,V2,M1} { addition( X, multiplication( X, Y )
% 0.70/1.52 ) ==> multiplication( X, addition( one, Y ) ) }.
% 0.70/1.52 parent0[0]: (5752) {G1,W11,D4,L1,V2,M1} { multiplication( X, addition( one
% 0.70/1.52 , Y ) ) ==> addition( X, multiplication( X, Y ) ) }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := X
% 0.70/1.52 Y := Y
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 subsumption: (69) {G1,W11,D4,L1,V2,M1} P(5,7) { addition( X, multiplication
% 0.70/1.52 ( X, Y ) ) = multiplication( X, addition( one, Y ) ) }.
% 0.70/1.52 parent0: (5754) {G1,W11,D4,L1,V2,M1} { addition( X, multiplication( X, Y )
% 0.70/1.52 ) ==> multiplication( X, addition( one, Y ) ) }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := X
% 0.70/1.52 Y := Y
% 0.70/1.52 end
% 0.70/1.52 permutation0:
% 0.70/1.52 0 ==> 0
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 eqswap: (5757) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Z ), Y
% 0.70/1.52 ) ==> addition( multiplication( X, Y ), multiplication( Z, Y ) ) }.
% 0.70/1.52 parent0[0]: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ),
% 0.70/1.52 multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := X
% 0.70/1.52 Y := Z
% 0.70/1.52 Z := Y
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 paramod: (5759) {G1,W11,D4,L1,V2,M1} { multiplication( addition( X, one )
% 0.70/1.52 , Y ) ==> addition( multiplication( X, Y ), Y ) }.
% 0.70/1.52 parent0[0]: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 0.70/1.52 parent1[0; 10]: (5757) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X
% 0.70/1.52 , Z ), Y ) ==> addition( multiplication( X, Y ), multiplication( Z, Y ) )
% 0.70/1.52 }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := Y
% 0.70/1.52 end
% 0.70/1.52 substitution1:
% 0.70/1.52 X := X
% 0.70/1.52 Y := Y
% 0.70/1.52 Z := one
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 eqswap: (5761) {G1,W11,D4,L1,V2,M1} { addition( multiplication( X, Y ), Y
% 0.70/1.52 ) ==> multiplication( addition( X, one ), Y ) }.
% 0.70/1.52 parent0[0]: (5759) {G1,W11,D4,L1,V2,M1} { multiplication( addition( X, one
% 0.70/1.52 ), Y ) ==> addition( multiplication( X, Y ), Y ) }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := X
% 0.70/1.52 Y := Y
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 subsumption: (101) {G1,W11,D4,L1,V2,M1} P(6,8) { addition( multiplication(
% 0.70/1.52 Y, X ), X ) = multiplication( addition( Y, one ), X ) }.
% 0.70/1.52 parent0: (5761) {G1,W11,D4,L1,V2,M1} { addition( multiplication( X, Y ), Y
% 0.70/1.52 ) ==> multiplication( addition( X, one ), Y ) }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := Y
% 0.70/1.52 Y := X
% 0.70/1.52 end
% 0.70/1.52 permutation0:
% 0.70/1.52 0 ==> 0
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 eqswap: (5763) {G1,W14,D4,L2,V3,M2} { ! addition( Y, Z ) ==> addition(
% 0.70/1.52 addition( X, Y ), Z ), leq( X, addition( Y, Z ) ) }.
% 0.70/1.52 parent0[0]: (25) {G1,W14,D4,L2,V3,M2} P(1,18) { ! addition( addition( X, Y
% 0.70/1.52 ), Z ) ==> addition( Y, Z ), leq( X, addition( Y, Z ) ) }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := X
% 0.70/1.52 Y := Y
% 0.70/1.52 Z := Z
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 paramod: (5766) {G1,W12,D3,L2,V2,M2} { ! addition( X, Y ) ==> addition( X
% 0.70/1.52 , Y ), leq( X, addition( X, Y ) ) }.
% 0.70/1.52 parent0[0]: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 0.70/1.52 parent1[0; 6]: (5763) {G1,W14,D4,L2,V3,M2} { ! addition( Y, Z ) ==>
% 0.70/1.52 addition( addition( X, Y ), Z ), leq( X, addition( Y, Z ) ) }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := X
% 0.70/1.52 end
% 0.70/1.52 substitution1:
% 0.70/1.52 X := X
% 0.70/1.52 Y := X
% 0.70/1.52 Z := Y
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 eqrefl: (5769) {G0,W5,D3,L1,V2,M1} { leq( X, addition( X, Y ) ) }.
% 0.70/1.52 parent0[0]: (5766) {G1,W12,D3,L2,V2,M2} { ! addition( X, Y ) ==> addition
% 0.70/1.52 ( X, Y ), leq( X, addition( X, Y ) ) }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := X
% 0.70/1.52 Y := Y
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 subsumption: (298) {G2,W5,D3,L1,V2,M1} P(3,25);q { leq( X, addition( X, Y )
% 0.70/1.52 ) }.
% 0.70/1.52 parent0: (5769) {G0,W5,D3,L1,V2,M1} { leq( X, addition( X, Y ) ) }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := X
% 0.70/1.52 Y := Y
% 0.70/1.52 end
% 0.70/1.52 permutation0:
% 0.70/1.52 0 ==> 0
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 paramod: (5770) {G1,W5,D3,L1,V2,M1} { leq( X, addition( Y, X ) ) }.
% 0.70/1.52 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 0.70/1.52 }.
% 0.70/1.52 parent1[0; 2]: (298) {G2,W5,D3,L1,V2,M1} P(3,25);q { leq( X, addition( X, Y
% 0.70/1.52 ) ) }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := X
% 0.70/1.52 Y := Y
% 0.70/1.52 end
% 0.70/1.52 substitution1:
% 0.70/1.52 X := X
% 0.70/1.52 Y := Y
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 subsumption: (312) {G3,W5,D3,L1,V2,M1} P(0,298) { leq( X, addition( Y, X )
% 0.70/1.52 ) }.
% 0.70/1.52 parent0: (5770) {G1,W5,D3,L1,V2,M1} { leq( X, addition( Y, X ) ) }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := X
% 0.70/1.52 Y := Y
% 0.70/1.52 end
% 0.70/1.52 permutation0:
% 0.70/1.52 0 ==> 0
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 eqswap: (5772) {G1,W11,D4,L1,V3,M1} { addition( addition( Y, Z ), X ) =
% 0.70/1.52 addition( addition( X, Y ), Z ) }.
% 0.70/1.52 parent0[0]: (26) {G1,W11,D4,L1,V3,M1} P(1,0) { addition( addition( X, Y ),
% 0.70/1.52 Z ) = addition( addition( Y, Z ), X ) }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := X
% 0.70/1.52 Y := Y
% 0.70/1.52 Z := Z
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 paramod: (5773) {G2,W7,D4,L1,V3,M1} { leq( X, addition( addition( X, Y ),
% 0.70/1.52 Z ) ) }.
% 0.70/1.52 parent0[0]: (5772) {G1,W11,D4,L1,V3,M1} { addition( addition( Y, Z ), X )
% 0.70/1.52 = addition( addition( X, Y ), Z ) }.
% 0.70/1.52 parent1[0; 2]: (312) {G3,W5,D3,L1,V2,M1} P(0,298) { leq( X, addition( Y, X
% 0.70/1.52 ) ) }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := X
% 0.70/1.52 Y := Y
% 0.70/1.52 Z := Z
% 0.70/1.52 end
% 0.70/1.52 substitution1:
% 0.70/1.52 X := X
% 0.70/1.52 Y := addition( Y, Z )
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 paramod: (5774) {G2,W7,D4,L1,V3,M1} { leq( X, addition( addition( Z, X ),
% 0.70/1.52 Y ) ) }.
% 0.70/1.52 parent0[0]: (5772) {G1,W11,D4,L1,V3,M1} { addition( addition( Y, Z ), X )
% 0.70/1.52 = addition( addition( X, Y ), Z ) }.
% 0.70/1.52 parent1[0; 2]: (5773) {G2,W7,D4,L1,V3,M1} { leq( X, addition( addition( X
% 0.70/1.52 , Y ), Z ) ) }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := Z
% 0.70/1.52 Y := X
% 0.70/1.52 Z := Y
% 0.70/1.52 end
% 0.70/1.52 substitution1:
% 0.70/1.52 X := X
% 0.70/1.52 Y := Y
% 0.70/1.52 Z := Z
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 subsumption: (335) {G4,W7,D4,L1,V3,M1} P(26,312) { leq( Z, addition(
% 0.70/1.52 addition( Y, Z ), X ) ) }.
% 0.70/1.52 parent0: (5774) {G2,W7,D4,L1,V3,M1} { leq( X, addition( addition( Z, X ),
% 0.70/1.52 Y ) ) }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := Z
% 0.70/1.52 Y := X
% 0.70/1.52 Z := Y
% 0.70/1.52 end
% 0.70/1.52 permutation0:
% 0.70/1.52 0 ==> 0
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 paramod: (5777) {G2,W8,D3,L2,V3,M2} { leq( X, addition( Y, Z ) ), ! leq( X
% 0.70/1.52 , Z ) }.
% 0.70/1.52 parent0[0]: (35) {G1,W12,D4,L2,V3,M2} P(17,1) { addition( addition( Z, X )
% 0.70/1.52 , Y ) ==> addition( Z, Y ), ! leq( X, Y ) }.
% 0.70/1.52 parent1[0; 2]: (335) {G4,W7,D4,L1,V3,M1} P(26,312) { leq( Z, addition(
% 0.70/1.52 addition( Y, Z ), X ) ) }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := X
% 0.70/1.52 Y := Z
% 0.70/1.52 Z := Y
% 0.70/1.52 end
% 0.70/1.52 substitution1:
% 0.70/1.52 X := Z
% 0.70/1.52 Y := Y
% 0.70/1.52 Z := X
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 subsumption: (572) {G5,W8,D3,L2,V3,M2} P(35,335) { leq( Y, addition( X, Z )
% 0.70/1.52 ), ! leq( Y, Z ) }.
% 0.70/1.52 parent0: (5777) {G2,W8,D3,L2,V3,M2} { leq( X, addition( Y, Z ) ), ! leq( X
% 0.70/1.52 , Z ) }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := Y
% 0.70/1.52 Y := X
% 0.70/1.52 Z := Z
% 0.70/1.52 end
% 0.70/1.52 permutation0:
% 0.70/1.52 0 ==> 0
% 0.70/1.52 1 ==> 1
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 eqswap: (5781) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Z ) ==>
% 0.70/1.52 multiplication( X, addition( Y, Z ) ), leq( multiplication( X, Y ),
% 0.70/1.52 multiplication( X, Z ) ) }.
% 0.70/1.52 parent0[0]: (67) {G1,W16,D4,L2,V3,M2} P(7,18) { ! multiplication( X,
% 0.70/1.52 addition( Y, Z ) ) ==> multiplication( X, Z ), leq( multiplication( X, Y
% 0.70/1.52 ), multiplication( X, Z ) ) }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := X
% 0.70/1.52 Y := Y
% 0.70/1.52 Z := Z
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 paramod: (5782) {G2,W14,D3,L2,V2,M2} { ! multiplication( X, Y ) ==>
% 0.70/1.52 multiplication( X, Y ), leq( multiplication( X, zero ), multiplication( X
% 0.70/1.52 , Y ) ) }.
% 0.70/1.52 parent0[0]: (20) {G1,W5,D3,L1,V1,M1} P(0,2) { addition( zero, X ) ==> X }.
% 0.70/1.52 parent1[0; 7]: (5781) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Z ) ==>
% 0.70/1.52 multiplication( X, addition( Y, Z ) ), leq( multiplication( X, Y ),
% 0.70/1.52 multiplication( X, Z ) ) }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := Y
% 0.70/1.52 end
% 0.70/1.52 substitution1:
% 0.70/1.52 X := X
% 0.70/1.52 Y := zero
% 0.70/1.52 Z := Y
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 eqrefl: (5783) {G0,W7,D3,L1,V2,M1} { leq( multiplication( X, zero ),
% 0.70/1.52 multiplication( X, Y ) ) }.
% 0.70/1.52 parent0[0]: (5782) {G2,W14,D3,L2,V2,M2} { ! multiplication( X, Y ) ==>
% 0.70/1.52 multiplication( X, Y ), leq( multiplication( X, zero ), multiplication( X
% 0.70/1.52 , Y ) ) }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := X
% 0.70/1.52 Y := Y
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 subsumption: (1855) {G2,W7,D3,L1,V2,M1} P(20,67);q { leq( multiplication( Y
% 0.70/1.52 , zero ), multiplication( Y, X ) ) }.
% 0.70/1.52 parent0: (5783) {G0,W7,D3,L1,V2,M1} { leq( multiplication( X, zero ),
% 0.70/1.52 multiplication( X, Y ) ) }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := Y
% 0.70/1.52 Y := X
% 0.70/1.52 end
% 0.70/1.52 permutation0:
% 0.70/1.52 0 ==> 0
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 paramod: (5785) {G1,W5,D3,L1,V1,M1} { leq( multiplication( X, zero ), X )
% 0.70/1.52 }.
% 0.70/1.52 parent0[0]: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 0.70/1.52 parent1[0; 4]: (1855) {G2,W7,D3,L1,V2,M1} P(20,67);q { leq( multiplication
% 0.70/1.52 ( Y, zero ), multiplication( Y, X ) ) }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := X
% 0.70/1.52 end
% 0.70/1.52 substitution1:
% 0.70/1.52 X := one
% 0.70/1.52 Y := X
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 subsumption: (1918) {G3,W5,D3,L1,V1,M1} P(5,1855) { leq( multiplication( X
% 0.70/1.52 , zero ), X ) }.
% 0.70/1.52 parent0: (5785) {G1,W5,D3,L1,V1,M1} { leq( multiplication( X, zero ), X )
% 0.70/1.52 }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := X
% 0.70/1.52 end
% 0.70/1.52 permutation0:
% 0.70/1.52 0 ==> 0
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 eqswap: (5786) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y, X )
% 0.70/1.52 }.
% 0.70/1.52 parent0[0]: (36) {G1,W8,D3,L2,V2,M2} P(17,0) { addition( Y, X ) ==> Y, !
% 0.70/1.52 leq( X, Y ) }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := Y
% 0.70/1.52 Y := X
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 resolution: (5787) {G2,W7,D4,L1,V1,M1} { X ==> addition( X, multiplication
% 0.70/1.52 ( X, zero ) ) }.
% 0.70/1.52 parent0[1]: (5786) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y
% 0.70/1.52 , X ) }.
% 0.70/1.52 parent1[0]: (1918) {G3,W5,D3,L1,V1,M1} P(5,1855) { leq( multiplication( X,
% 0.70/1.52 zero ), X ) }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := X
% 0.70/1.52 Y := multiplication( X, zero )
% 0.70/1.52 end
% 0.70/1.52 substitution1:
% 0.70/1.52 X := X
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 eqswap: (5788) {G2,W7,D4,L1,V1,M1} { addition( X, multiplication( X, zero
% 0.70/1.52 ) ) ==> X }.
% 0.70/1.52 parent0[0]: (5787) {G2,W7,D4,L1,V1,M1} { X ==> addition( X, multiplication
% 0.70/1.52 ( X, zero ) ) }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := X
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 subsumption: (1922) {G4,W7,D4,L1,V1,M1} R(1918,36) { addition( X,
% 0.70/1.52 multiplication( X, zero ) ) ==> X }.
% 0.70/1.52 parent0: (5788) {G2,W7,D4,L1,V1,M1} { addition( X, multiplication( X, zero
% 0.70/1.52 ) ) ==> X }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := X
% 0.70/1.52 end
% 0.70/1.52 permutation0:
% 0.70/1.52 0 ==> 0
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 eqswap: (5789) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X, Y )
% 0.70/1.52 }.
% 0.70/1.52 parent0[1]: (17) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 0.70/1.52 ==> Y }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := X
% 0.70/1.52 Y := Y
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 resolution: (5790) {G1,W7,D4,L1,V1,M1} { X ==> addition( multiplication( X
% 0.70/1.52 , zero ), X ) }.
% 0.70/1.52 parent0[1]: (5789) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X
% 0.70/1.52 , Y ) }.
% 0.70/1.52 parent1[0]: (1918) {G3,W5,D3,L1,V1,M1} P(5,1855) { leq( multiplication( X,
% 0.70/1.52 zero ), X ) }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := multiplication( X, zero )
% 0.70/1.52 Y := X
% 0.70/1.52 end
% 0.70/1.52 substitution1:
% 0.70/1.52 X := X
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 eqswap: (5791) {G1,W7,D4,L1,V1,M1} { addition( multiplication( X, zero ),
% 0.70/1.52 X ) ==> X }.
% 0.70/1.52 parent0[0]: (5790) {G1,W7,D4,L1,V1,M1} { X ==> addition( multiplication( X
% 0.70/1.52 , zero ), X ) }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := X
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 subsumption: (1926) {G4,W7,D4,L1,V1,M1} R(1918,17) { addition(
% 0.70/1.52 multiplication( X, zero ), X ) ==> X }.
% 0.70/1.52 parent0: (5791) {G1,W7,D4,L1,V1,M1} { addition( multiplication( X, zero )
% 0.70/1.52 , X ) ==> X }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := X
% 0.70/1.52 end
% 0.70/1.52 permutation0:
% 0.70/1.52 0 ==> 0
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 paramod: (5793) {G5,W8,D3,L2,V2,M2} { leq( X, Y ), ! leq( X,
% 0.70/1.52 multiplication( Y, zero ) ) }.
% 0.70/1.52 parent0[0]: (1922) {G4,W7,D4,L1,V1,M1} R(1918,36) { addition( X,
% 0.70/1.52 multiplication( X, zero ) ) ==> X }.
% 0.70/1.52 parent1[0; 2]: (572) {G5,W8,D3,L2,V3,M2} P(35,335) { leq( Y, addition( X, Z
% 0.70/1.52 ) ), ! leq( Y, Z ) }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := Y
% 0.70/1.52 end
% 0.70/1.52 substitution1:
% 0.70/1.52 X := Y
% 0.70/1.52 Y := X
% 0.70/1.52 Z := multiplication( Y, zero )
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 subsumption: (2182) {G6,W8,D3,L2,V2,M2} P(1922,572) { leq( Y, X ), ! leq( Y
% 0.70/1.52 , multiplication( X, zero ) ) }.
% 0.70/1.52 parent0: (5793) {G5,W8,D3,L2,V2,M2} { leq( X, Y ), ! leq( X,
% 0.70/1.52 multiplication( Y, zero ) ) }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := Y
% 0.70/1.52 Y := X
% 0.70/1.52 end
% 0.70/1.52 permutation0:
% 0.70/1.52 0 ==> 0
% 0.70/1.52 1 ==> 1
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 eqswap: (5794) {G1,W11,D4,L1,V2,M1} { multiplication( addition( X, one ),
% 0.70/1.52 Y ) = addition( multiplication( X, Y ), Y ) }.
% 0.70/1.52 parent0[0]: (101) {G1,W11,D4,L1,V2,M1} P(6,8) { addition( multiplication( Y
% 0.70/1.52 , X ), X ) = multiplication( addition( Y, one ), X ) }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := Y
% 0.70/1.52 Y := X
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 paramod: (5795) {G1,W17,D5,L2,V3,M2} { ! leq( X, addition( addition(
% 0.70/1.52 multiplication( Y, X ), X ), Z ) ), leq( X, multiplication(
% 0.70/1.52 strong_iteration( addition( Y, one ) ), Z ) ) }.
% 0.70/1.52 parent0[0]: (5794) {G1,W11,D4,L1,V2,M1} { multiplication( addition( X, one
% 0.70/1.52 ), Y ) = addition( multiplication( X, Y ), Y ) }.
% 0.70/1.52 parent1[0; 4]: (15) {G0,W13,D4,L2,V3,M2} I { ! leq( Z, addition(
% 0.70/1.52 multiplication( X, Z ), Y ) ), leq( Z, multiplication( strong_iteration(
% 0.70/1.52 X ), Y ) ) }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := Y
% 0.70/1.52 Y := X
% 0.70/1.52 end
% 0.70/1.52 substitution1:
% 0.70/1.52 X := addition( Y, one )
% 0.70/1.52 Y := Z
% 0.70/1.52 Z := X
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 resolution: (5796) {G2,W8,D5,L1,V3,M1} { leq( X, multiplication(
% 0.70/1.52 strong_iteration( addition( Y, one ) ), Z ) ) }.
% 0.70/1.52 parent0[0]: (5795) {G1,W17,D5,L2,V3,M2} { ! leq( X, addition( addition(
% 0.70/1.52 multiplication( Y, X ), X ), Z ) ), leq( X, multiplication(
% 0.70/1.52 strong_iteration( addition( Y, one ) ), Z ) ) }.
% 0.70/1.52 parent1[0]: (335) {G4,W7,D4,L1,V3,M1} P(26,312) { leq( Z, addition(
% 0.70/1.52 addition( Y, Z ), X ) ) }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := X
% 0.70/1.52 Y := Y
% 0.70/1.52 Z := Z
% 0.70/1.52 end
% 0.70/1.52 substitution1:
% 0.70/1.52 X := Z
% 0.70/1.52 Y := multiplication( Y, X )
% 0.70/1.52 Z := X
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 subsumption: (4197) {G5,W8,D5,L1,V3,M1} P(101,15);r(335) { leq( Y,
% 0.70/1.52 multiplication( strong_iteration( addition( X, one ) ), Z ) ) }.
% 0.70/1.52 parent0: (5796) {G2,W8,D5,L1,V3,M1} { leq( X, multiplication(
% 0.70/1.52 strong_iteration( addition( Y, one ) ), Z ) ) }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := Y
% 0.70/1.52 Y := X
% 0.70/1.52 Z := Z
% 0.70/1.52 end
% 0.70/1.52 permutation0:
% 0.70/1.52 0 ==> 0
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 resolution: (5797) {G6,W6,D4,L1,V2,M1} { leq( X, strong_iteration(
% 0.70/1.52 addition( Y, one ) ) ) }.
% 0.70/1.52 parent0[1]: (2182) {G6,W8,D3,L2,V2,M2} P(1922,572) { leq( Y, X ), ! leq( Y
% 0.70/1.52 , multiplication( X, zero ) ) }.
% 0.70/1.52 parent1[0]: (4197) {G5,W8,D5,L1,V3,M1} P(101,15);r(335) { leq( Y,
% 0.70/1.52 multiplication( strong_iteration( addition( X, one ) ), Z ) ) }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := strong_iteration( addition( Y, one ) )
% 0.70/1.52 Y := X
% 0.70/1.52 end
% 0.70/1.52 substitution1:
% 0.70/1.52 X := Y
% 0.70/1.52 Y := X
% 0.70/1.52 Z := zero
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 subsumption: (5101) {G7,W6,D4,L1,V2,M1} R(4197,2182) { leq( X,
% 0.70/1.52 strong_iteration( addition( Y, one ) ) ) }.
% 0.70/1.52 parent0: (5797) {G6,W6,D4,L1,V2,M1} { leq( X, strong_iteration( addition(
% 0.70/1.52 Y, one ) ) ) }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := X
% 0.70/1.52 Y := Y
% 0.70/1.52 end
% 0.70/1.52 permutation0:
% 0.70/1.52 0 ==> 0
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 paramod: (5799) {G5,W6,D4,L1,V2,M1} { leq( X, multiplication(
% 0.70/1.52 strong_iteration( one ), Y ) ) }.
% 0.70/1.52 parent0[0]: (1926) {G4,W7,D4,L1,V1,M1} R(1918,17) { addition(
% 0.70/1.52 multiplication( X, zero ), X ) ==> X }.
% 0.70/1.52 parent1[0; 4]: (4197) {G5,W8,D5,L1,V3,M1} P(101,15);r(335) { leq( Y,
% 0.70/1.52 multiplication( strong_iteration( addition( X, one ) ), Z ) ) }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := one
% 0.70/1.52 end
% 0.70/1.52 substitution1:
% 0.70/1.52 X := multiplication( one, zero )
% 0.70/1.52 Y := X
% 0.70/1.52 Z := Y
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 subsumption: (5117) {G6,W6,D4,L1,V2,M1} P(1926,4197) { leq( X,
% 0.70/1.52 multiplication( strong_iteration( one ), Y ) ) }.
% 0.70/1.52 parent0: (5799) {G5,W6,D4,L1,V2,M1} { leq( X, multiplication(
% 0.70/1.52 strong_iteration( one ), Y ) ) }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := X
% 0.70/1.52 Y := Y
% 0.70/1.52 end
% 0.70/1.52 permutation0:
% 0.70/1.52 0 ==> 0
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 paramod: (5801) {G5,W4,D3,L1,V1,M1} { leq( X, strong_iteration( one ) )
% 0.70/1.52 }.
% 0.70/1.52 parent0[0]: (1926) {G4,W7,D4,L1,V1,M1} R(1918,17) { addition(
% 0.70/1.52 multiplication( X, zero ), X ) ==> X }.
% 0.70/1.52 parent1[0; 3]: (5101) {G7,W6,D4,L1,V2,M1} R(4197,2182) { leq( X,
% 0.70/1.52 strong_iteration( addition( Y, one ) ) ) }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := one
% 0.70/1.52 end
% 0.70/1.52 substitution1:
% 0.70/1.52 X := X
% 0.70/1.52 Y := multiplication( one, zero )
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 subsumption: (5137) {G8,W4,D3,L1,V1,M1} P(1926,5101) { leq( X,
% 0.70/1.52 strong_iteration( one ) ) }.
% 0.70/1.52 parent0: (5801) {G5,W4,D3,L1,V1,M1} { leq( X, strong_iteration( one ) )
% 0.70/1.52 }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := X
% 0.70/1.52 end
% 0.70/1.52 permutation0:
% 0.70/1.52 0 ==> 0
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 eqswap: (5802) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y, X )
% 0.70/1.52 }.
% 0.70/1.52 parent0[0]: (36) {G1,W8,D3,L2,V2,M2} P(17,0) { addition( Y, X ) ==> Y, !
% 0.70/1.52 leq( X, Y ) }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := Y
% 0.70/1.52 Y := X
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 resolution: (5803) {G2,W7,D4,L1,V1,M1} { strong_iteration( one ) ==>
% 0.70/1.52 addition( strong_iteration( one ), X ) }.
% 0.70/1.52 parent0[1]: (5802) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y
% 0.70/1.52 , X ) }.
% 0.70/1.52 parent1[0]: (5137) {G8,W4,D3,L1,V1,M1} P(1926,5101) { leq( X,
% 0.70/1.52 strong_iteration( one ) ) }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := strong_iteration( one )
% 0.70/1.52 Y := X
% 0.70/1.52 end
% 0.70/1.52 substitution1:
% 0.70/1.52 X := X
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 eqswap: (5804) {G2,W7,D4,L1,V1,M1} { addition( strong_iteration( one ), X
% 0.70/1.52 ) ==> strong_iteration( one ) }.
% 0.70/1.52 parent0[0]: (5803) {G2,W7,D4,L1,V1,M1} { strong_iteration( one ) ==>
% 0.70/1.52 addition( strong_iteration( one ), X ) }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := X
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 subsumption: (5147) {G9,W7,D4,L1,V1,M1} R(5137,36) { addition(
% 0.70/1.52 strong_iteration( one ), X ) ==> strong_iteration( one ) }.
% 0.70/1.52 parent0: (5804) {G2,W7,D4,L1,V1,M1} { addition( strong_iteration( one ), X
% 0.70/1.52 ) ==> strong_iteration( one ) }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := X
% 0.70/1.52 end
% 0.70/1.52 permutation0:
% 0.70/1.52 0 ==> 0
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 eqswap: (5805) {G1,W16,D4,L2,V3,M2} { multiplication( X, Z ) ==>
% 0.70/1.52 multiplication( X, addition( Y, Z ) ), ! leq( multiplication( X, Y ),
% 0.70/1.52 multiplication( X, Z ) ) }.
% 0.70/1.52 parent0[1]: (65) {G1,W16,D4,L2,V3,M2} P(7,17) { ! leq( multiplication( X, Y
% 0.70/1.52 ), multiplication( X, Z ) ), multiplication( X, addition( Y, Z ) ) ==>
% 0.70/1.52 multiplication( X, Z ) }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := X
% 0.70/1.52 Y := Y
% 0.70/1.52 Z := Z
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 resolution: (5806) {G2,W11,D4,L1,V2,M1} { multiplication( strong_iteration
% 0.70/1.52 ( one ), X ) ==> multiplication( strong_iteration( one ), addition( Y, X
% 0.70/1.52 ) ) }.
% 0.70/1.52 parent0[1]: (5805) {G1,W16,D4,L2,V3,M2} { multiplication( X, Z ) ==>
% 0.70/1.52 multiplication( X, addition( Y, Z ) ), ! leq( multiplication( X, Y ),
% 0.70/1.52 multiplication( X, Z ) ) }.
% 0.70/1.52 parent1[0]: (5117) {G6,W6,D4,L1,V2,M1} P(1926,4197) { leq( X,
% 0.70/1.52 multiplication( strong_iteration( one ), Y ) ) }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := strong_iteration( one )
% 0.70/1.52 Y := Y
% 0.70/1.52 Z := X
% 0.70/1.52 end
% 0.70/1.52 substitution1:
% 0.70/1.52 X := multiplication( strong_iteration( one ), Y )
% 0.70/1.52 Y := X
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 eqswap: (5807) {G2,W11,D4,L1,V2,M1} { multiplication( strong_iteration(
% 0.70/1.52 one ), addition( Y, X ) ) ==> multiplication( strong_iteration( one ), X
% 0.70/1.52 ) }.
% 0.70/1.52 parent0[0]: (5806) {G2,W11,D4,L1,V2,M1} { multiplication( strong_iteration
% 0.70/1.52 ( one ), X ) ==> multiplication( strong_iteration( one ), addition( Y, X
% 0.70/1.52 ) ) }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := X
% 0.70/1.52 Y := Y
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 subsumption: (5212) {G7,W11,D4,L1,V2,M1} R(5117,65) { multiplication(
% 0.70/1.52 strong_iteration( one ), addition( X, Y ) ) ==> multiplication(
% 0.70/1.52 strong_iteration( one ), Y ) }.
% 0.70/1.52 parent0: (5807) {G2,W11,D4,L1,V2,M1} { multiplication( strong_iteration(
% 0.70/1.52 one ), addition( Y, X ) ) ==> multiplication( strong_iteration( one ), X
% 0.70/1.52 ) }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := Y
% 0.70/1.52 Y := X
% 0.70/1.52 end
% 0.70/1.52 permutation0:
% 0.70/1.52 0 ==> 0
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 eqswap: (5808) {G9,W7,D4,L1,V1,M1} { strong_iteration( one ) ==> addition
% 0.70/1.52 ( strong_iteration( one ), X ) }.
% 0.70/1.52 parent0[0]: (5147) {G9,W7,D4,L1,V1,M1} R(5137,36) { addition(
% 0.70/1.52 strong_iteration( one ), X ) ==> strong_iteration( one ) }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := X
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 paramod: (5811) {G2,W9,D4,L1,V1,M1} { strong_iteration( one ) ==>
% 0.70/1.52 multiplication( strong_iteration( one ), addition( one, X ) ) }.
% 0.70/1.52 parent0[0]: (69) {G1,W11,D4,L1,V2,M1} P(5,7) { addition( X, multiplication
% 0.70/1.52 ( X, Y ) ) = multiplication( X, addition( one, Y ) ) }.
% 0.70/1.52 parent1[0; 3]: (5808) {G9,W7,D4,L1,V1,M1} { strong_iteration( one ) ==>
% 0.70/1.52 addition( strong_iteration( one ), X ) }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := strong_iteration( one )
% 0.70/1.52 Y := X
% 0.70/1.52 end
% 0.70/1.52 substitution1:
% 0.70/1.52 X := multiplication( strong_iteration( one ), X )
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 paramod: (5812) {G3,W7,D4,L1,V1,M1} { strong_iteration( one ) ==>
% 0.70/1.52 multiplication( strong_iteration( one ), X ) }.
% 0.70/1.52 parent0[0]: (5212) {G7,W11,D4,L1,V2,M1} R(5117,65) { multiplication(
% 0.70/1.52 strong_iteration( one ), addition( X, Y ) ) ==> multiplication(
% 0.70/1.52 strong_iteration( one ), Y ) }.
% 0.70/1.52 parent1[0; 3]: (5811) {G2,W9,D4,L1,V1,M1} { strong_iteration( one ) ==>
% 0.70/1.52 multiplication( strong_iteration( one ), addition( one, X ) ) }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := one
% 0.70/1.52 Y := X
% 0.70/1.52 end
% 0.70/1.52 substitution1:
% 0.70/1.52 X := X
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 eqswap: (5813) {G3,W7,D4,L1,V1,M1} { multiplication( strong_iteration( one
% 0.70/1.52 ), X ) ==> strong_iteration( one ) }.
% 0.70/1.52 parent0[0]: (5812) {G3,W7,D4,L1,V1,M1} { strong_iteration( one ) ==>
% 0.70/1.52 multiplication( strong_iteration( one ), X ) }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := X
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 subsumption: (5467) {G10,W7,D4,L1,V1,M1} P(5147,69);d(5212) {
% 0.70/1.52 multiplication( strong_iteration( one ), X ) ==> strong_iteration( one )
% 0.70/1.52 }.
% 0.70/1.52 parent0: (5813) {G3,W7,D4,L1,V1,M1} { multiplication( strong_iteration(
% 0.70/1.52 one ), X ) ==> strong_iteration( one ) }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := X
% 0.70/1.52 end
% 0.70/1.52 permutation0:
% 0.70/1.52 0 ==> 0
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 eqswap: (5814) {G10,W7,D4,L1,V1,M1} { strong_iteration( one ) ==>
% 0.70/1.52 multiplication( strong_iteration( one ), X ) }.
% 0.70/1.52 parent0[0]: (5467) {G10,W7,D4,L1,V1,M1} P(5147,69);d(5212) { multiplication
% 0.70/1.52 ( strong_iteration( one ), X ) ==> strong_iteration( one ) }.
% 0.70/1.52 substitution0:
% 0.70/1.52 X := X
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 eqswap: (5815) {G0,W7,D4,L1,V0,M1} { ! strong_iteration( one ) ==>
% 0.70/1.52 multiplication( strong_iteration( one ), skol1 ) }.
% 0.70/1.52 parent0[0]: (19) {G0,W7,D4,L1,V0,M1} I { ! multiplication( strong_iteration
% 0.70/1.52 ( one ), skol1 ) ==> strong_iteration( one ) }.
% 0.70/1.52 substitution0:
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 resolution: (5816) {G1,W0,D0,L0,V0,M0} { }.
% 0.70/1.52 parent0[0]: (5815) {G0,W7,D4,L1,V0,M1} { ! strong_iteration( one ) ==>
% 0.70/1.52 multiplication( strong_iteration( one ), skol1 ) }.
% 0.70/1.52 parent1[0]: (5814) {G10,W7,D4,L1,V1,M1} { strong_iteration( one ) ==>
% 0.70/1.52 multiplication( strong_iteration( one ), X ) }.
% 0.70/1.52 substitution0:
% 0.70/1.52 end
% 0.70/1.52 substitution1:
% 0.70/1.52 X := skol1
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 subsumption: (5543) {G11,W0,D0,L0,V0,M0} R(5467,19) { }.
% 0.70/1.52 parent0: (5816) {G1,W0,D0,L0,V0,M0} { }.
% 0.70/1.52 substitution0:
% 0.70/1.52 end
% 0.70/1.52 permutation0:
% 0.70/1.52 end
% 0.70/1.52
% 0.70/1.52 Proof check complete!
% 0.70/1.52
% 0.70/1.52 Memory use:
% 0.70/1.52
% 0.70/1.52 space for terms: 68652
% 0.70/1.52 space for clauses: 310173
% 0.70/1.52
% 0.70/1.52
% 0.70/1.52 clauses generated: 40032
% 0.70/1.52 clauses kept: 5544
% 0.70/1.52 clauses selected: 400
% 0.70/1.52 clauses deleted: 78
% 0.70/1.52 clauses inuse deleted: 36
% 0.70/1.52
% 0.70/1.52 subsentry: 122796
% 0.70/1.52 literals s-matched: 76851
% 0.70/1.52 literals matched: 72790
% 0.70/1.52 full subsumption: 16192
% 0.70/1.52
% 0.70/1.52 checksum: 389043111
% 0.70/1.52
% 0.70/1.52
% 0.70/1.52 Bliksem ended
%------------------------------------------------------------------------------