TSTP Solution File: KLE144+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : KLE144+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Sun Jul 17 01:37:25 EDT 2022
% Result : Theorem 2.33s 2.78s
% Output : Refutation 2.33s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : KLE144+1 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.14 % Command : bliksem %s
% 0.14/0.36 % Computer : n013.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 16:30:14 EDT 2022
% 0.14/0.36 % CPUTime :
% 2.33/2.77 *** allocated 10000 integers for termspace/termends
% 2.33/2.77 *** allocated 10000 integers for clauses
% 2.33/2.77 *** allocated 10000 integers for justifications
% 2.33/2.77 Bliksem 1.12
% 2.33/2.77
% 2.33/2.77
% 2.33/2.77 Automatic Strategy Selection
% 2.33/2.77
% 2.33/2.77
% 2.33/2.77 Clauses:
% 2.33/2.77
% 2.33/2.77 { addition( X, Y ) = addition( Y, X ) }.
% 2.33/2.77 { addition( Z, addition( Y, X ) ) = addition( addition( Z, Y ), X ) }.
% 2.33/2.77 { addition( X, zero ) = X }.
% 2.33/2.77 { addition( X, X ) = X }.
% 2.33/2.77 { multiplication( X, multiplication( Y, Z ) ) = multiplication(
% 2.33/2.77 multiplication( X, Y ), Z ) }.
% 2.33/2.77 { multiplication( X, one ) = X }.
% 2.33/2.77 { multiplication( one, X ) = X }.
% 2.33/2.77 { multiplication( X, addition( Y, Z ) ) = addition( multiplication( X, Y )
% 2.33/2.77 , multiplication( X, Z ) ) }.
% 2.33/2.77 { multiplication( addition( X, Y ), Z ) = addition( multiplication( X, Z )
% 2.33/2.77 , multiplication( Y, Z ) ) }.
% 2.33/2.77 { multiplication( zero, X ) = zero }.
% 2.33/2.77 { addition( one, multiplication( X, star( X ) ) ) = star( X ) }.
% 2.33/2.77 { addition( one, multiplication( star( X ), X ) ) = star( X ) }.
% 2.33/2.77 { ! leq( addition( multiplication( X, Z ), Y ), Z ), leq( multiplication(
% 2.33/2.77 star( X ), Y ), Z ) }.
% 2.33/2.77 { ! leq( addition( multiplication( Z, X ), Y ), Z ), leq( multiplication( Y
% 2.33/2.77 , star( X ) ), Z ) }.
% 2.33/2.77 { strong_iteration( X ) = addition( multiplication( X, strong_iteration( X
% 2.33/2.77 ) ), one ) }.
% 2.33/2.77 { ! leq( Z, addition( multiplication( X, Z ), Y ) ), leq( Z, multiplication
% 2.33/2.77 ( strong_iteration( X ), Y ) ) }.
% 2.33/2.77 { strong_iteration( X ) = addition( star( X ), multiplication(
% 2.33/2.77 strong_iteration( X ), zero ) ) }.
% 2.33/2.77 { ! leq( X, Y ), addition( X, Y ) = Y }.
% 2.33/2.77 { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 2.33/2.77 { ! strong_iteration( star( skol1 ) ) = strong_iteration( one ) }.
% 2.33/2.77
% 2.33/2.77 percentage equality = 0.680000, percentage horn = 1.000000
% 2.33/2.77 This is a problem with some equality
% 2.33/2.77
% 2.33/2.77
% 2.33/2.77
% 2.33/2.77 Options Used:
% 2.33/2.77
% 2.33/2.77 useres = 1
% 2.33/2.77 useparamod = 1
% 2.33/2.77 useeqrefl = 1
% 2.33/2.77 useeqfact = 1
% 2.33/2.77 usefactor = 1
% 2.33/2.77 usesimpsplitting = 0
% 2.33/2.77 usesimpdemod = 5
% 2.33/2.77 usesimpres = 3
% 2.33/2.77
% 2.33/2.77 resimpinuse = 1000
% 2.33/2.77 resimpclauses = 20000
% 2.33/2.77 substype = eqrewr
% 2.33/2.77 backwardsubs = 1
% 2.33/2.77 selectoldest = 5
% 2.33/2.77
% 2.33/2.77 litorderings [0] = split
% 2.33/2.77 litorderings [1] = extend the termordering, first sorting on arguments
% 2.33/2.77
% 2.33/2.77 termordering = kbo
% 2.33/2.77
% 2.33/2.77 litapriori = 0
% 2.33/2.77 termapriori = 1
% 2.33/2.77 litaposteriori = 0
% 2.33/2.77 termaposteriori = 0
% 2.33/2.77 demodaposteriori = 0
% 2.33/2.77 ordereqreflfact = 0
% 2.33/2.77
% 2.33/2.77 litselect = negord
% 2.33/2.77
% 2.33/2.77 maxweight = 15
% 2.33/2.77 maxdepth = 30000
% 2.33/2.77 maxlength = 115
% 2.33/2.77 maxnrvars = 195
% 2.33/2.77 excuselevel = 1
% 2.33/2.77 increasemaxweight = 1
% 2.33/2.77
% 2.33/2.77 maxselected = 10000000
% 2.33/2.77 maxnrclauses = 10000000
% 2.33/2.77
% 2.33/2.77 showgenerated = 0
% 2.33/2.77 showkept = 0
% 2.33/2.77 showselected = 0
% 2.33/2.77 showdeleted = 0
% 2.33/2.77 showresimp = 1
% 2.33/2.77 showstatus = 2000
% 2.33/2.77
% 2.33/2.77 prologoutput = 0
% 2.33/2.77 nrgoals = 5000000
% 2.33/2.77 totalproof = 1
% 2.33/2.77
% 2.33/2.77 Symbols occurring in the translation:
% 2.33/2.77
% 2.33/2.77 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 2.33/2.77 . [1, 2] (w:1, o:20, a:1, s:1, b:0),
% 2.33/2.77 ! [4, 1] (w:0, o:13, a:1, s:1, b:0),
% 2.33/2.77 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 2.33/2.77 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 2.33/2.77 addition [37, 2] (w:1, o:44, a:1, s:1, b:0),
% 2.33/2.77 zero [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 2.33/2.77 multiplication [40, 2] (w:1, o:46, a:1, s:1, b:0),
% 2.33/2.77 one [41, 0] (w:1, o:10, a:1, s:1, b:0),
% 2.33/2.77 star [42, 1] (w:1, o:18, a:1, s:1, b:0),
% 2.33/2.77 leq [43, 2] (w:1, o:45, a:1, s:1, b:0),
% 2.33/2.77 strong_iteration [44, 1] (w:1, o:19, a:1, s:1, b:0),
% 2.33/2.77 skol1 [46, 0] (w:1, o:12, a:1, s:1, b:1).
% 2.33/2.77
% 2.33/2.77
% 2.33/2.77 Starting Search:
% 2.33/2.77
% 2.33/2.77 *** allocated 15000 integers for clauses
% 2.33/2.77 *** allocated 22500 integers for clauses
% 2.33/2.77 *** allocated 33750 integers for clauses
% 2.33/2.77 *** allocated 50625 integers for clauses
% 2.33/2.77 *** allocated 75937 integers for clauses
% 2.33/2.77 *** allocated 15000 integers for termspace/termends
% 2.33/2.77 Resimplifying inuse:
% 2.33/2.77 Done
% 2.33/2.77
% 2.33/2.77 *** allocated 22500 integers for termspace/termends
% 2.33/2.77 *** allocated 113905 integers for clauses
% 2.33/2.77 *** allocated 33750 integers for termspace/termends
% 2.33/2.77
% 2.33/2.77 Intermediate Status:
% 2.33/2.77 Generated: 15767
% 2.33/2.77 Kept: 2009
% 2.33/2.77 Inuse: 243
% 2.33/2.77 Deleted: 29
% 2.33/2.77 Deletedinuse: 4
% 2.33/2.77
% 2.33/2.77 Resimplifying inuse:
% 2.33/2.77 Done
% 2.33/2.77
% 2.33/2.77 *** allocated 170857 integers for clauses
% 2.33/2.77 *** allocated 50625 integers for termspace/termends
% 2.33/2.77 Resimplifying inuse:
% 2.33/2.77 Done
% 2.33/2.77
% 2.33/2.77 *** allocated 256285 integers for clauses
% 2.33/2.77
% 2.33/2.77 Intermediate Status:
% 2.33/2.77 Generated: 37813
% 2.33/2.77 Kept: 4011
% 2.33/2.77 Inuse: 422
% 2.33/2.77 Deleted: 50
% 2.33/2.77 Deletedinuse: 5
% 2.33/2.77
% 2.33/2.77 Resimplifying inuse:
% 2.33/2.77 Done
% 2.33/2.77
% 2.33/2.77 *** allocated 75937 integers for termspace/termends
% 2.33/2.77 *** allocated 384427 integers for clauses
% 2.33/2.77 Resimplifying inuse:
% 2.33/2.77 Done
% 2.33/2.77
% 2.33/2.77
% 2.33/2.77 Intermediate Status:
% 2.33/2.77 Generated: 55871
% 2.33/2.77 Kept: 6015
% 2.33/2.77 Inuse: 558
% 2.33/2.77 Deleted: 73
% 2.33/2.77 Deletedinuse: 9
% 2.33/2.77
% 2.33/2.77 Resimplifying inuse:
% 2.33/2.77 Done
% 2.33/2.77
% 2.33/2.77 *** allocated 113905 integers for termspace/termends
% 2.33/2.77 *** allocated 576640 integers for clauses
% 2.33/2.77 Resimplifying inuse:
% 2.33/2.77 Done
% 2.33/2.77
% 2.33/2.77
% 2.33/2.77 Intermediate Status:
% 2.33/2.77 Generated: 76952
% 2.33/2.77 Kept: 8042
% 2.33/2.77 Inuse: 701
% 2.33/2.77 Deleted: 83
% 2.33/2.77 Deletedinuse: 11
% 2.33/2.77
% 2.33/2.77 Resimplifying inuse:
% 2.33/2.77 Done
% 2.33/2.77
% 2.33/2.77 Resimplifying inuse:
% 2.33/2.77 Done
% 2.33/2.77
% 2.33/2.77 *** allocated 170857 integers for termspace/termends
% 2.33/2.77
% 2.33/2.77 Intermediate Status:
% 2.33/2.77 Generated: 92211
% 2.33/2.77 Kept: 10050
% 2.33/2.77 Inuse: 778
% 2.33/2.77 Deleted: 99
% 2.33/2.77 Deletedinuse: 11
% 2.33/2.77
% 2.33/2.77 Resimplifying inuse:
% 2.33/2.77 Done
% 2.33/2.77
% 2.33/2.77 *** allocated 864960 integers for clauses
% 2.33/2.77 Resimplifying inuse:
% 2.33/2.77 Done
% 2.33/2.77
% 2.33/2.77
% 2.33/2.77 Intermediate Status:
% 2.33/2.77 Generated: 119671
% 2.33/2.77 Kept: 12062
% 2.33/2.77 Inuse: 900
% 2.33/2.78 Deleted: 236
% 2.33/2.78 Deletedinuse: 111
% 2.33/2.78
% 2.33/2.78 Resimplifying inuse:
% 2.33/2.78 Done
% 2.33/2.78
% 2.33/2.78
% 2.33/2.78 Bliksems!, er is een bewijs:
% 2.33/2.78 % SZS status Theorem
% 2.33/2.78 % SZS output start Refutation
% 2.33/2.78
% 2.33/2.78 (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X ) }.
% 2.33/2.78 (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) ) ==> addition(
% 2.33/2.78 addition( Z, Y ), X ) }.
% 2.33/2.78 (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 2.33/2.78 (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 2.33/2.78 (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 2.33/2.78 (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 2.33/2.78 (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 2.33/2.78 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 2.33/2.78 (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ),
% 2.33/2.78 multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 2.33/2.78 (11) {G0,W9,D5,L1,V1,M1} I { addition( one, multiplication( star( X ), X )
% 2.33/2.78 ) ==> star( X ) }.
% 2.33/2.78 (15) {G0,W13,D4,L2,V3,M2} I { ! leq( Z, addition( multiplication( X, Z ), Y
% 2.33/2.78 ) ), leq( Z, multiplication( strong_iteration( X ), Y ) ) }.
% 2.33/2.78 (17) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y ) ==> Y }.
% 2.33/2.78 (18) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X, Y ) }.
% 2.33/2.78 (19) {G0,W6,D4,L1,V0,M1} I { ! strong_iteration( star( skol1 ) ) ==>
% 2.33/2.78 strong_iteration( one ) }.
% 2.33/2.78 (20) {G1,W5,D3,L1,V1,M1} P(0,2) { addition( zero, X ) ==> X }.
% 2.33/2.78 (22) {G1,W3,D2,L1,V1,M1} R(18,3) { leq( X, X ) }.
% 2.33/2.78 (25) {G1,W14,D4,L2,V3,M2} P(1,18) { ! addition( addition( X, Y ), Z ) ==>
% 2.33/2.78 addition( Y, Z ), leq( X, addition( Y, Z ) ) }.
% 2.33/2.78 (26) {G1,W11,D4,L1,V3,M1} P(1,0) { addition( addition( X, Y ), Z ) =
% 2.33/2.78 addition( addition( Y, Z ), X ) }.
% 2.33/2.78 (35) {G1,W12,D4,L2,V3,M2} P(17,1) { addition( addition( Z, X ), Y ) ==>
% 2.33/2.78 addition( Z, Y ), ! leq( X, Y ) }.
% 2.33/2.78 (36) {G1,W8,D3,L2,V2,M2} P(17,0) { addition( Y, X ) ==> Y, ! leq( X, Y )
% 2.33/2.78 }.
% 2.33/2.78 (73) {G1,W16,D4,L2,V3,M2} P(7,18) { ! multiplication( X, addition( Y, Z ) )
% 2.33/2.78 ==> multiplication( X, Z ), leq( multiplication( X, Y ), multiplication
% 2.33/2.78 ( X, Z ) ) }.
% 2.33/2.78 (108) {G1,W11,D4,L1,V2,M1} P(6,8) { addition( multiplication( Y, X ), X ) =
% 2.33/2.78 multiplication( addition( Y, one ), X ) }.
% 2.33/2.78 (149) {G1,W9,D5,L1,V1,M1} P(11,0) { addition( multiplication( star( X ), X
% 2.33/2.78 ), one ) ==> star( X ) }.
% 2.33/2.78 (297) {G2,W5,D3,L1,V2,M1} P(3,25);q { leq( X, addition( X, Y ) ) }.
% 2.33/2.78 (313) {G3,W5,D3,L1,V2,M1} P(0,297) { leq( X, addition( Y, X ) ) }.
% 2.33/2.78 (339) {G4,W7,D4,L1,V3,M1} P(26,313) { leq( Z, addition( addition( Y, Z ), X
% 2.33/2.78 ) ) }.
% 2.33/2.78 (562) {G5,W8,D3,L2,V3,M2} P(35,339) { leq( Y, addition( X, Z ) ), ! leq( Y
% 2.33/2.78 , Z ) }.
% 2.33/2.78 (1933) {G2,W7,D3,L1,V2,M1} P(20,73);q { leq( multiplication( Y, zero ),
% 2.33/2.78 multiplication( Y, X ) ) }.
% 2.33/2.78 (2047) {G3,W5,D3,L1,V1,M1} P(5,1933) { leq( multiplication( X, zero ), X )
% 2.33/2.78 }.
% 2.33/2.78 (2051) {G4,W7,D4,L1,V1,M1} R(2047,36) { addition( X, multiplication( X,
% 2.33/2.78 zero ) ) ==> X }.
% 2.33/2.78 (2055) {G4,W7,D4,L1,V1,M1} R(2047,17) { addition( multiplication( X, zero )
% 2.33/2.78 , X ) ==> X }.
% 2.33/2.78 (2439) {G6,W8,D3,L2,V2,M2} P(2051,562) { leq( Y, X ), ! leq( Y,
% 2.33/2.78 multiplication( X, zero ) ) }.
% 2.33/2.78 (3539) {G5,W8,D5,L1,V3,M1} P(108,15);r(339) { leq( Y, multiplication(
% 2.33/2.78 strong_iteration( addition( X, one ) ), Z ) ) }.
% 2.33/2.78 (9185) {G7,W6,D4,L1,V2,M1} R(3539,2439) { leq( X, strong_iteration(
% 2.33/2.78 addition( Y, one ) ) ) }.
% 2.33/2.78 (9234) {G8,W5,D4,L1,V2,M1} P(149,9185) { leq( Y, strong_iteration( star( X
% 2.33/2.78 ) ) ) }.
% 2.33/2.78 (9235) {G8,W4,D3,L1,V1,M1} P(2055,9185) { leq( X, strong_iteration( one ) )
% 2.33/2.78 }.
% 2.33/2.78 (9315) {G9,W7,D4,L1,V1,M1} R(9235,36) { addition( strong_iteration( one ),
% 2.33/2.78 X ) ==> strong_iteration( one ) }.
% 2.33/2.78 (9837) {G10,W8,D3,L2,V1,M2} P(9315,17) { ! leq( strong_iteration( one ), X
% 2.33/2.78 ), strong_iteration( one ) = X }.
% 2.33/2.78 (12347) {G11,W6,D4,L1,V1,M1} R(9837,9234) { strong_iteration( star( X ) )
% 2.33/2.78 ==> strong_iteration( one ) }.
% 2.33/2.78 (12444) {G12,W0,D0,L0,V0,M0} P(9837,19);q;d(12347);r(22) { }.
% 2.33/2.78
% 2.33/2.78
% 2.33/2.78 % SZS output end Refutation
% 2.33/2.78 found a proof!
% 2.33/2.78
% 2.33/2.78
% 2.33/2.78 Unprocessed initial clauses:
% 2.33/2.78
% 2.33/2.78 (12446) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X ) }.
% 2.33/2.78 (12447) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) = addition
% 2.33/2.78 ( addition( Z, Y ), X ) }.
% 2.33/2.78 (12448) {G0,W5,D3,L1,V1,M1} { addition( X, zero ) = X }.
% 2.33/2.78 (12449) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 2.33/2.78 (12450) {G0,W11,D4,L1,V3,M1} { multiplication( X, multiplication( Y, Z ) )
% 2.33/2.78 = multiplication( multiplication( X, Y ), Z ) }.
% 2.33/2.78 (12451) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 2.33/2.78 (12452) {G0,W5,D3,L1,V1,M1} { multiplication( one, X ) = X }.
% 2.33/2.78 (12453) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y, Z ) ) =
% 2.33/2.78 addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 2.33/2.78 (12454) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Y ), Z ) =
% 2.33/2.78 addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 2.33/2.78 (12455) {G0,W5,D3,L1,V1,M1} { multiplication( zero, X ) = zero }.
% 2.33/2.78 (12456) {G0,W9,D5,L1,V1,M1} { addition( one, multiplication( X, star( X )
% 2.33/2.78 ) ) = star( X ) }.
% 2.33/2.78 (12457) {G0,W9,D5,L1,V1,M1} { addition( one, multiplication( star( X ), X
% 2.33/2.78 ) ) = star( X ) }.
% 2.33/2.78 (12458) {G0,W13,D4,L2,V3,M2} { ! leq( addition( multiplication( X, Z ), Y
% 2.33/2.78 ), Z ), leq( multiplication( star( X ), Y ), Z ) }.
% 2.33/2.78 (12459) {G0,W13,D4,L2,V3,M2} { ! leq( addition( multiplication( Z, X ), Y
% 2.33/2.78 ), Z ), leq( multiplication( Y, star( X ) ), Z ) }.
% 2.33/2.78 (12460) {G0,W9,D5,L1,V1,M1} { strong_iteration( X ) = addition(
% 2.33/2.78 multiplication( X, strong_iteration( X ) ), one ) }.
% 2.33/2.78 (12461) {G0,W13,D4,L2,V3,M2} { ! leq( Z, addition( multiplication( X, Z )
% 2.33/2.78 , Y ) ), leq( Z, multiplication( strong_iteration( X ), Y ) ) }.
% 2.33/2.78 (12462) {G0,W10,D5,L1,V1,M1} { strong_iteration( X ) = addition( star( X )
% 2.33/2.78 , multiplication( strong_iteration( X ), zero ) ) }.
% 2.33/2.78 (12463) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y }.
% 2.33/2.78 (12464) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 2.33/2.78 (12465) {G0,W6,D4,L1,V0,M1} { ! strong_iteration( star( skol1 ) ) =
% 2.33/2.78 strong_iteration( one ) }.
% 2.33/2.78
% 2.33/2.78
% 2.33/2.78 Total Proof:
% 2.33/2.78
% 2.33/2.78 subsumption: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X
% 2.33/2.78 ) }.
% 2.33/2.78 parent0: (12446) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X )
% 2.33/2.78 }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := X
% 2.33/2.78 Y := Y
% 2.33/2.78 end
% 2.33/2.78 permutation0:
% 2.33/2.78 0 ==> 0
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 subsumption: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 2.33/2.78 ==> addition( addition( Z, Y ), X ) }.
% 2.33/2.78 parent0: (12447) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) =
% 2.33/2.78 addition( addition( Z, Y ), X ) }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := X
% 2.33/2.78 Y := Y
% 2.33/2.78 Z := Z
% 2.33/2.78 end
% 2.33/2.78 permutation0:
% 2.33/2.78 0 ==> 0
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 subsumption: (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 2.33/2.78 parent0: (12448) {G0,W5,D3,L1,V1,M1} { addition( X, zero ) = X }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := X
% 2.33/2.78 end
% 2.33/2.78 permutation0:
% 2.33/2.78 0 ==> 0
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 subsumption: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 2.33/2.78 parent0: (12449) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := X
% 2.33/2.78 end
% 2.33/2.78 permutation0:
% 2.33/2.78 0 ==> 0
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 subsumption: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 2.33/2.78 parent0: (12451) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := X
% 2.33/2.78 end
% 2.33/2.78 permutation0:
% 2.33/2.78 0 ==> 0
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 subsumption: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 2.33/2.78 parent0: (12452) {G0,W5,D3,L1,V1,M1} { multiplication( one, X ) = X }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := X
% 2.33/2.78 end
% 2.33/2.78 permutation0:
% 2.33/2.78 0 ==> 0
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 eqswap: (12489) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Y ),
% 2.33/2.78 multiplication( X, Z ) ) = multiplication( X, addition( Y, Z ) ) }.
% 2.33/2.78 parent0[0]: (12453) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y
% 2.33/2.78 , Z ) ) = addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := X
% 2.33/2.78 Y := Y
% 2.33/2.78 Z := Z
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 subsumption: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y )
% 2.33/2.78 , multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 2.33/2.78 parent0: (12489) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Y ),
% 2.33/2.78 multiplication( X, Z ) ) = multiplication( X, addition( Y, Z ) ) }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := X
% 2.33/2.78 Y := Y
% 2.33/2.78 Z := Z
% 2.33/2.78 end
% 2.33/2.78 permutation0:
% 2.33/2.78 0 ==> 0
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 eqswap: (12497) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Z ),
% 2.33/2.78 multiplication( Y, Z ) ) = multiplication( addition( X, Y ), Z ) }.
% 2.33/2.78 parent0[0]: (12454) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Y
% 2.33/2.78 ), Z ) = addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := X
% 2.33/2.78 Y := Y
% 2.33/2.78 Z := Z
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 subsumption: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z )
% 2.33/2.78 , multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 2.33/2.78 parent0: (12497) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Z ),
% 2.33/2.78 multiplication( Y, Z ) ) = multiplication( addition( X, Y ), Z ) }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := X
% 2.33/2.78 Y := Y
% 2.33/2.78 Z := Z
% 2.33/2.78 end
% 2.33/2.78 permutation0:
% 2.33/2.78 0 ==> 0
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 subsumption: (11) {G0,W9,D5,L1,V1,M1} I { addition( one, multiplication(
% 2.33/2.78 star( X ), X ) ) ==> star( X ) }.
% 2.33/2.78 parent0: (12457) {G0,W9,D5,L1,V1,M1} { addition( one, multiplication( star
% 2.33/2.78 ( X ), X ) ) = star( X ) }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := X
% 2.33/2.78 end
% 2.33/2.78 permutation0:
% 2.33/2.78 0 ==> 0
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 subsumption: (15) {G0,W13,D4,L2,V3,M2} I { ! leq( Z, addition(
% 2.33/2.78 multiplication( X, Z ), Y ) ), leq( Z, multiplication( strong_iteration(
% 2.33/2.78 X ), Y ) ) }.
% 2.33/2.78 parent0: (12461) {G0,W13,D4,L2,V3,M2} { ! leq( Z, addition( multiplication
% 2.33/2.78 ( X, Z ), Y ) ), leq( Z, multiplication( strong_iteration( X ), Y ) ) }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := X
% 2.33/2.78 Y := Y
% 2.33/2.78 Z := Z
% 2.33/2.78 end
% 2.33/2.78 permutation0:
% 2.33/2.78 0 ==> 0
% 2.33/2.78 1 ==> 1
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 subsumption: (17) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 2.33/2.78 ==> Y }.
% 2.33/2.78 parent0: (12463) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y
% 2.33/2.78 }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := X
% 2.33/2.78 Y := Y
% 2.33/2.78 end
% 2.33/2.78 permutation0:
% 2.33/2.78 0 ==> 0
% 2.33/2.78 1 ==> 1
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 subsumption: (18) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X
% 2.33/2.78 , Y ) }.
% 2.33/2.78 parent0: (12464) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y )
% 2.33/2.78 }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := X
% 2.33/2.78 Y := Y
% 2.33/2.78 end
% 2.33/2.78 permutation0:
% 2.33/2.78 0 ==> 0
% 2.33/2.78 1 ==> 1
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 subsumption: (19) {G0,W6,D4,L1,V0,M1} I { ! strong_iteration( star( skol1 )
% 2.33/2.78 ) ==> strong_iteration( one ) }.
% 2.33/2.78 parent0: (12465) {G0,W6,D4,L1,V0,M1} { ! strong_iteration( star( skol1 ) )
% 2.33/2.78 = strong_iteration( one ) }.
% 2.33/2.78 substitution0:
% 2.33/2.78 end
% 2.33/2.78 permutation0:
% 2.33/2.78 0 ==> 0
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 eqswap: (12566) {G0,W5,D3,L1,V1,M1} { X ==> addition( X, zero ) }.
% 2.33/2.78 parent0[0]: (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := X
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 paramod: (12567) {G1,W5,D3,L1,V1,M1} { X ==> addition( zero, X ) }.
% 2.33/2.78 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 2.33/2.78 }.
% 2.33/2.78 parent1[0; 2]: (12566) {G0,W5,D3,L1,V1,M1} { X ==> addition( X, zero ) }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := X
% 2.33/2.78 Y := zero
% 2.33/2.78 end
% 2.33/2.78 substitution1:
% 2.33/2.78 X := X
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 eqswap: (12570) {G1,W5,D3,L1,V1,M1} { addition( zero, X ) ==> X }.
% 2.33/2.78 parent0[0]: (12567) {G1,W5,D3,L1,V1,M1} { X ==> addition( zero, X ) }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := X
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 subsumption: (20) {G1,W5,D3,L1,V1,M1} P(0,2) { addition( zero, X ) ==> X
% 2.33/2.78 }.
% 2.33/2.78 parent0: (12570) {G1,W5,D3,L1,V1,M1} { addition( zero, X ) ==> X }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := X
% 2.33/2.78 end
% 2.33/2.78 permutation0:
% 2.33/2.78 0 ==> 0
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 eqswap: (12571) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y
% 2.33/2.78 ) }.
% 2.33/2.78 parent0[0]: (18) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 2.33/2.78 Y ) }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := X
% 2.33/2.78 Y := Y
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 eqswap: (12572) {G0,W5,D3,L1,V1,M1} { X ==> addition( X, X ) }.
% 2.33/2.78 parent0[0]: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := X
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 resolution: (12573) {G1,W3,D2,L1,V1,M1} { leq( X, X ) }.
% 2.33/2.78 parent0[0]: (12571) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X
% 2.33/2.78 , Y ) }.
% 2.33/2.78 parent1[0]: (12572) {G0,W5,D3,L1,V1,M1} { X ==> addition( X, X ) }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := X
% 2.33/2.78 Y := X
% 2.33/2.78 end
% 2.33/2.78 substitution1:
% 2.33/2.78 X := X
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 subsumption: (22) {G1,W3,D2,L1,V1,M1} R(18,3) { leq( X, X ) }.
% 2.33/2.78 parent0: (12573) {G1,W3,D2,L1,V1,M1} { leq( X, X ) }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := X
% 2.33/2.78 end
% 2.33/2.78 permutation0:
% 2.33/2.78 0 ==> 0
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 eqswap: (12575) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y
% 2.33/2.78 ) }.
% 2.33/2.78 parent0[0]: (18) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 2.33/2.78 Y ) }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := X
% 2.33/2.78 Y := Y
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 paramod: (12576) {G1,W14,D4,L2,V3,M2} { ! addition( X, Y ) ==> addition(
% 2.33/2.78 addition( Z, X ), Y ), leq( Z, addition( X, Y ) ) }.
% 2.33/2.78 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 2.33/2.78 ==> addition( addition( Z, Y ), X ) }.
% 2.33/2.78 parent1[0; 5]: (12575) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq
% 2.33/2.78 ( X, Y ) }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := Y
% 2.33/2.78 Y := X
% 2.33/2.78 Z := Z
% 2.33/2.78 end
% 2.33/2.78 substitution1:
% 2.33/2.78 X := Z
% 2.33/2.78 Y := addition( X, Y )
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 eqswap: (12577) {G1,W14,D4,L2,V3,M2} { ! addition( addition( Z, X ), Y )
% 2.33/2.78 ==> addition( X, Y ), leq( Z, addition( X, Y ) ) }.
% 2.33/2.78 parent0[0]: (12576) {G1,W14,D4,L2,V3,M2} { ! addition( X, Y ) ==> addition
% 2.33/2.78 ( addition( Z, X ), Y ), leq( Z, addition( X, Y ) ) }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := X
% 2.33/2.78 Y := Y
% 2.33/2.78 Z := Z
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 subsumption: (25) {G1,W14,D4,L2,V3,M2} P(1,18) { ! addition( addition( X, Y
% 2.33/2.78 ), Z ) ==> addition( Y, Z ), leq( X, addition( Y, Z ) ) }.
% 2.33/2.78 parent0: (12577) {G1,W14,D4,L2,V3,M2} { ! addition( addition( Z, X ), Y )
% 2.33/2.78 ==> addition( X, Y ), leq( Z, addition( X, Y ) ) }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := Y
% 2.33/2.78 Y := Z
% 2.33/2.78 Z := X
% 2.33/2.78 end
% 2.33/2.78 permutation0:
% 2.33/2.78 0 ==> 0
% 2.33/2.78 1 ==> 1
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 eqswap: (12578) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z ) ==>
% 2.33/2.78 addition( X, addition( Y, Z ) ) }.
% 2.33/2.78 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 2.33/2.78 ==> addition( addition( Z, Y ), X ) }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := Z
% 2.33/2.78 Y := Y
% 2.33/2.78 Z := X
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 paramod: (12581) {G1,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z )
% 2.33/2.78 ==> addition( addition( Y, Z ), X ) }.
% 2.33/2.78 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 2.33/2.78 }.
% 2.33/2.78 parent1[0; 6]: (12578) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y ),
% 2.33/2.78 Z ) ==> addition( X, addition( Y, Z ) ) }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := X
% 2.33/2.78 Y := addition( Y, Z )
% 2.33/2.78 end
% 2.33/2.78 substitution1:
% 2.33/2.78 X := X
% 2.33/2.78 Y := Y
% 2.33/2.78 Z := Z
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 subsumption: (26) {G1,W11,D4,L1,V3,M1} P(1,0) { addition( addition( X, Y )
% 2.33/2.78 , Z ) = addition( addition( Y, Z ), X ) }.
% 2.33/2.78 parent0: (12581) {G1,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z )
% 2.33/2.78 ==> addition( addition( Y, Z ), X ) }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := X
% 2.33/2.78 Y := Y
% 2.33/2.78 Z := Z
% 2.33/2.78 end
% 2.33/2.78 permutation0:
% 2.33/2.78 0 ==> 0
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 eqswap: (12596) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z ) ==>
% 2.33/2.78 addition( X, addition( Y, Z ) ) }.
% 2.33/2.78 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 2.33/2.78 ==> addition( addition( Z, Y ), X ) }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := Z
% 2.33/2.78 Y := Y
% 2.33/2.78 Z := X
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 paramod: (12602) {G1,W12,D4,L2,V3,M2} { addition( addition( X, Y ), Z )
% 2.33/2.78 ==> addition( X, Z ), ! leq( Y, Z ) }.
% 2.33/2.78 parent0[1]: (17) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 2.33/2.78 ==> Y }.
% 2.33/2.78 parent1[0; 8]: (12596) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y ),
% 2.33/2.78 Z ) ==> addition( X, addition( Y, Z ) ) }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := Y
% 2.33/2.78 Y := Z
% 2.33/2.78 end
% 2.33/2.78 substitution1:
% 2.33/2.78 X := X
% 2.33/2.78 Y := Y
% 2.33/2.78 Z := Z
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 subsumption: (35) {G1,W12,D4,L2,V3,M2} P(17,1) { addition( addition( Z, X )
% 2.33/2.78 , Y ) ==> addition( Z, Y ), ! leq( X, Y ) }.
% 2.33/2.78 parent0: (12602) {G1,W12,D4,L2,V3,M2} { addition( addition( X, Y ), Z )
% 2.33/2.78 ==> addition( X, Z ), ! leq( Y, Z ) }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := Z
% 2.33/2.78 Y := X
% 2.33/2.78 Z := Y
% 2.33/2.78 end
% 2.33/2.78 permutation0:
% 2.33/2.78 0 ==> 0
% 2.33/2.78 1 ==> 1
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 eqswap: (12649) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X, Y
% 2.33/2.78 ) }.
% 2.33/2.78 parent0[1]: (17) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 2.33/2.78 ==> Y }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := X
% 2.33/2.78 Y := Y
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 paramod: (12650) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y, X
% 2.33/2.78 ) }.
% 2.33/2.78 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 2.33/2.78 }.
% 2.33/2.78 parent1[0; 2]: (12649) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq
% 2.33/2.78 ( X, Y ) }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := Y
% 2.33/2.78 Y := X
% 2.33/2.78 end
% 2.33/2.78 substitution1:
% 2.33/2.78 X := Y
% 2.33/2.78 Y := X
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 eqswap: (12653) {G1,W8,D3,L2,V2,M2} { addition( X, Y ) ==> X, ! leq( Y, X
% 2.33/2.78 ) }.
% 2.33/2.78 parent0[0]: (12650) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y
% 2.33/2.78 , X ) }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := X
% 2.33/2.78 Y := Y
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 subsumption: (36) {G1,W8,D3,L2,V2,M2} P(17,0) { addition( Y, X ) ==> Y, !
% 2.33/2.78 leq( X, Y ) }.
% 2.33/2.78 parent0: (12653) {G1,W8,D3,L2,V2,M2} { addition( X, Y ) ==> X, ! leq( Y, X
% 2.33/2.78 ) }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := Y
% 2.33/2.78 Y := X
% 2.33/2.78 end
% 2.33/2.78 permutation0:
% 2.33/2.78 0 ==> 0
% 2.33/2.78 1 ==> 1
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 eqswap: (12655) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y
% 2.33/2.78 ) }.
% 2.33/2.78 parent0[0]: (18) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 2.33/2.78 Y ) }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := X
% 2.33/2.78 Y := Y
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 paramod: (12656) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Y ) ==>
% 2.33/2.78 multiplication( X, addition( Z, Y ) ), leq( multiplication( X, Z ),
% 2.33/2.78 multiplication( X, Y ) ) }.
% 2.33/2.78 parent0[0]: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 2.33/2.78 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 2.33/2.78 parent1[0; 5]: (12655) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq
% 2.33/2.78 ( X, Y ) }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := X
% 2.33/2.78 Y := Z
% 2.33/2.78 Z := Y
% 2.33/2.78 end
% 2.33/2.78 substitution1:
% 2.33/2.78 X := multiplication( X, Z )
% 2.33/2.78 Y := multiplication( X, Y )
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 eqswap: (12657) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, addition( Z, Y
% 2.33/2.78 ) ) ==> multiplication( X, Y ), leq( multiplication( X, Z ),
% 2.33/2.78 multiplication( X, Y ) ) }.
% 2.33/2.78 parent0[0]: (12656) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Y ) ==>
% 2.33/2.78 multiplication( X, addition( Z, Y ) ), leq( multiplication( X, Z ),
% 2.33/2.78 multiplication( X, Y ) ) }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := X
% 2.33/2.78 Y := Y
% 2.33/2.78 Z := Z
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 subsumption: (73) {G1,W16,D4,L2,V3,M2} P(7,18) { ! multiplication( X,
% 2.33/2.78 addition( Y, Z ) ) ==> multiplication( X, Z ), leq( multiplication( X, Y
% 2.33/2.78 ), multiplication( X, Z ) ) }.
% 2.33/2.78 parent0: (12657) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, addition( Z,
% 2.33/2.78 Y ) ) ==> multiplication( X, Y ), leq( multiplication( X, Z ),
% 2.33/2.78 multiplication( X, Y ) ) }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := X
% 2.33/2.78 Y := Z
% 2.33/2.78 Z := Y
% 2.33/2.78 end
% 2.33/2.78 permutation0:
% 2.33/2.78 0 ==> 0
% 2.33/2.78 1 ==> 1
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 eqswap: (12659) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Z ), Y
% 2.33/2.78 ) ==> addition( multiplication( X, Y ), multiplication( Z, Y ) ) }.
% 2.33/2.78 parent0[0]: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ),
% 2.33/2.78 multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := X
% 2.33/2.78 Y := Z
% 2.33/2.78 Z := Y
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 paramod: (12661) {G1,W11,D4,L1,V2,M1} { multiplication( addition( X, one )
% 2.33/2.78 , Y ) ==> addition( multiplication( X, Y ), Y ) }.
% 2.33/2.78 parent0[0]: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 2.33/2.78 parent1[0; 10]: (12659) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X
% 2.33/2.78 , Z ), Y ) ==> addition( multiplication( X, Y ), multiplication( Z, Y ) )
% 2.33/2.78 }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := Y
% 2.33/2.78 end
% 2.33/2.78 substitution1:
% 2.33/2.78 X := X
% 2.33/2.78 Y := Y
% 2.33/2.78 Z := one
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 eqswap: (12663) {G1,W11,D4,L1,V2,M1} { addition( multiplication( X, Y ), Y
% 2.33/2.78 ) ==> multiplication( addition( X, one ), Y ) }.
% 2.33/2.78 parent0[0]: (12661) {G1,W11,D4,L1,V2,M1} { multiplication( addition( X,
% 2.33/2.78 one ), Y ) ==> addition( multiplication( X, Y ), Y ) }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := X
% 2.33/2.78 Y := Y
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 subsumption: (108) {G1,W11,D4,L1,V2,M1} P(6,8) { addition( multiplication(
% 2.33/2.78 Y, X ), X ) = multiplication( addition( Y, one ), X ) }.
% 2.33/2.78 parent0: (12663) {G1,W11,D4,L1,V2,M1} { addition( multiplication( X, Y ),
% 2.33/2.78 Y ) ==> multiplication( addition( X, one ), Y ) }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := Y
% 2.33/2.78 Y := X
% 2.33/2.78 end
% 2.33/2.78 permutation0:
% 2.33/2.78 0 ==> 0
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 eqswap: (12664) {G0,W9,D5,L1,V1,M1} { star( X ) ==> addition( one,
% 2.33/2.78 multiplication( star( X ), X ) ) }.
% 2.33/2.78 parent0[0]: (11) {G0,W9,D5,L1,V1,M1} I { addition( one, multiplication(
% 2.33/2.78 star( X ), X ) ) ==> star( X ) }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := X
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 paramod: (12665) {G1,W9,D5,L1,V1,M1} { star( X ) ==> addition(
% 2.33/2.78 multiplication( star( X ), X ), one ) }.
% 2.33/2.78 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 2.33/2.78 }.
% 2.33/2.78 parent1[0; 3]: (12664) {G0,W9,D5,L1,V1,M1} { star( X ) ==> addition( one,
% 2.33/2.78 multiplication( star( X ), X ) ) }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := one
% 2.33/2.78 Y := multiplication( star( X ), X )
% 2.33/2.78 end
% 2.33/2.78 substitution1:
% 2.33/2.78 X := X
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 eqswap: (12668) {G1,W9,D5,L1,V1,M1} { addition( multiplication( star( X )
% 2.33/2.78 , X ), one ) ==> star( X ) }.
% 2.33/2.78 parent0[0]: (12665) {G1,W9,D5,L1,V1,M1} { star( X ) ==> addition(
% 2.33/2.78 multiplication( star( X ), X ), one ) }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := X
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 subsumption: (149) {G1,W9,D5,L1,V1,M1} P(11,0) { addition( multiplication(
% 2.33/2.78 star( X ), X ), one ) ==> star( X ) }.
% 2.33/2.78 parent0: (12668) {G1,W9,D5,L1,V1,M1} { addition( multiplication( star( X )
% 2.33/2.78 , X ), one ) ==> star( X ) }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := X
% 2.33/2.78 end
% 2.33/2.78 permutation0:
% 2.33/2.78 0 ==> 0
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 eqswap: (12670) {G1,W14,D4,L2,V3,M2} { ! addition( Y, Z ) ==> addition(
% 2.33/2.78 addition( X, Y ), Z ), leq( X, addition( Y, Z ) ) }.
% 2.33/2.78 parent0[0]: (25) {G1,W14,D4,L2,V3,M2} P(1,18) { ! addition( addition( X, Y
% 2.33/2.78 ), Z ) ==> addition( Y, Z ), leq( X, addition( Y, Z ) ) }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := X
% 2.33/2.78 Y := Y
% 2.33/2.78 Z := Z
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 paramod: (12673) {G1,W12,D3,L2,V2,M2} { ! addition( X, Y ) ==> addition( X
% 2.33/2.78 , Y ), leq( X, addition( X, Y ) ) }.
% 2.33/2.78 parent0[0]: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 2.33/2.78 parent1[0; 6]: (12670) {G1,W14,D4,L2,V3,M2} { ! addition( Y, Z ) ==>
% 2.33/2.78 addition( addition( X, Y ), Z ), leq( X, addition( Y, Z ) ) }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := X
% 2.33/2.78 end
% 2.33/2.78 substitution1:
% 2.33/2.78 X := X
% 2.33/2.78 Y := X
% 2.33/2.78 Z := Y
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 eqrefl: (12676) {G0,W5,D3,L1,V2,M1} { leq( X, addition( X, Y ) ) }.
% 2.33/2.78 parent0[0]: (12673) {G1,W12,D3,L2,V2,M2} { ! addition( X, Y ) ==> addition
% 2.33/2.78 ( X, Y ), leq( X, addition( X, Y ) ) }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := X
% 2.33/2.78 Y := Y
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 subsumption: (297) {G2,W5,D3,L1,V2,M1} P(3,25);q { leq( X, addition( X, Y )
% 2.33/2.78 ) }.
% 2.33/2.78 parent0: (12676) {G0,W5,D3,L1,V2,M1} { leq( X, addition( X, Y ) ) }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := X
% 2.33/2.78 Y := Y
% 2.33/2.78 end
% 2.33/2.78 permutation0:
% 2.33/2.78 0 ==> 0
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 paramod: (12677) {G1,W5,D3,L1,V2,M1} { leq( X, addition( Y, X ) ) }.
% 2.33/2.78 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 2.33/2.78 }.
% 2.33/2.78 parent1[0; 2]: (297) {G2,W5,D3,L1,V2,M1} P(3,25);q { leq( X, addition( X, Y
% 2.33/2.78 ) ) }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := X
% 2.33/2.78 Y := Y
% 2.33/2.78 end
% 2.33/2.78 substitution1:
% 2.33/2.78 X := X
% 2.33/2.78 Y := Y
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 subsumption: (313) {G3,W5,D3,L1,V2,M1} P(0,297) { leq( X, addition( Y, X )
% 2.33/2.78 ) }.
% 2.33/2.78 parent0: (12677) {G1,W5,D3,L1,V2,M1} { leq( X, addition( Y, X ) ) }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := X
% 2.33/2.78 Y := Y
% 2.33/2.78 end
% 2.33/2.78 permutation0:
% 2.33/2.78 0 ==> 0
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 eqswap: (12679) {G1,W11,D4,L1,V3,M1} { addition( addition( Y, Z ), X ) =
% 2.33/2.78 addition( addition( X, Y ), Z ) }.
% 2.33/2.78 parent0[0]: (26) {G1,W11,D4,L1,V3,M1} P(1,0) { addition( addition( X, Y ),
% 2.33/2.78 Z ) = addition( addition( Y, Z ), X ) }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := X
% 2.33/2.78 Y := Y
% 2.33/2.78 Z := Z
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 paramod: (12680) {G2,W7,D4,L1,V3,M1} { leq( X, addition( addition( X, Y )
% 2.33/2.78 , Z ) ) }.
% 2.33/2.78 parent0[0]: (12679) {G1,W11,D4,L1,V3,M1} { addition( addition( Y, Z ), X )
% 2.33/2.78 = addition( addition( X, Y ), Z ) }.
% 2.33/2.78 parent1[0; 2]: (313) {G3,W5,D3,L1,V2,M1} P(0,297) { leq( X, addition( Y, X
% 2.33/2.78 ) ) }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := X
% 2.33/2.78 Y := Y
% 2.33/2.78 Z := Z
% 2.33/2.78 end
% 2.33/2.78 substitution1:
% 2.33/2.78 X := X
% 2.33/2.78 Y := addition( Y, Z )
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 paramod: (12681) {G2,W7,D4,L1,V3,M1} { leq( X, addition( addition( Z, X )
% 2.33/2.78 , Y ) ) }.
% 2.33/2.78 parent0[0]: (12679) {G1,W11,D4,L1,V3,M1} { addition( addition( Y, Z ), X )
% 2.33/2.78 = addition( addition( X, Y ), Z ) }.
% 2.33/2.78 parent1[0; 2]: (12680) {G2,W7,D4,L1,V3,M1} { leq( X, addition( addition( X
% 2.33/2.78 , Y ), Z ) ) }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := Z
% 2.33/2.78 Y := X
% 2.33/2.78 Z := Y
% 2.33/2.78 end
% 2.33/2.78 substitution1:
% 2.33/2.78 X := X
% 2.33/2.78 Y := Y
% 2.33/2.78 Z := Z
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 subsumption: (339) {G4,W7,D4,L1,V3,M1} P(26,313) { leq( Z, addition(
% 2.33/2.78 addition( Y, Z ), X ) ) }.
% 2.33/2.78 parent0: (12681) {G2,W7,D4,L1,V3,M1} { leq( X, addition( addition( Z, X )
% 2.33/2.78 , Y ) ) }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := Z
% 2.33/2.78 Y := X
% 2.33/2.78 Z := Y
% 2.33/2.78 end
% 2.33/2.78 permutation0:
% 2.33/2.78 0 ==> 0
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 paramod: (12684) {G2,W8,D3,L2,V3,M2} { leq( X, addition( Y, Z ) ), ! leq(
% 2.33/2.78 X, Z ) }.
% 2.33/2.78 parent0[0]: (35) {G1,W12,D4,L2,V3,M2} P(17,1) { addition( addition( Z, X )
% 2.33/2.78 , Y ) ==> addition( Z, Y ), ! leq( X, Y ) }.
% 2.33/2.78 parent1[0; 2]: (339) {G4,W7,D4,L1,V3,M1} P(26,313) { leq( Z, addition(
% 2.33/2.78 addition( Y, Z ), X ) ) }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := X
% 2.33/2.78 Y := Z
% 2.33/2.78 Z := Y
% 2.33/2.78 end
% 2.33/2.78 substitution1:
% 2.33/2.78 X := Z
% 2.33/2.78 Y := Y
% 2.33/2.78 Z := X
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 subsumption: (562) {G5,W8,D3,L2,V3,M2} P(35,339) { leq( Y, addition( X, Z )
% 2.33/2.78 ), ! leq( Y, Z ) }.
% 2.33/2.78 parent0: (12684) {G2,W8,D3,L2,V3,M2} { leq( X, addition( Y, Z ) ), ! leq(
% 2.33/2.78 X, Z ) }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := Y
% 2.33/2.78 Y := X
% 2.33/2.78 Z := Z
% 2.33/2.78 end
% 2.33/2.78 permutation0:
% 2.33/2.78 0 ==> 0
% 2.33/2.78 1 ==> 1
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 eqswap: (12688) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Z ) ==>
% 2.33/2.78 multiplication( X, addition( Y, Z ) ), leq( multiplication( X, Y ),
% 2.33/2.78 multiplication( X, Z ) ) }.
% 2.33/2.78 parent0[0]: (73) {G1,W16,D4,L2,V3,M2} P(7,18) { ! multiplication( X,
% 2.33/2.78 addition( Y, Z ) ) ==> multiplication( X, Z ), leq( multiplication( X, Y
% 2.33/2.78 ), multiplication( X, Z ) ) }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := X
% 2.33/2.78 Y := Y
% 2.33/2.78 Z := Z
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 paramod: (12689) {G2,W14,D3,L2,V2,M2} { ! multiplication( X, Y ) ==>
% 2.33/2.78 multiplication( X, Y ), leq( multiplication( X, zero ), multiplication( X
% 2.33/2.78 , Y ) ) }.
% 2.33/2.78 parent0[0]: (20) {G1,W5,D3,L1,V1,M1} P(0,2) { addition( zero, X ) ==> X }.
% 2.33/2.78 parent1[0; 7]: (12688) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Z ) ==>
% 2.33/2.78 multiplication( X, addition( Y, Z ) ), leq( multiplication( X, Y ),
% 2.33/2.78 multiplication( X, Z ) ) }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := Y
% 2.33/2.78 end
% 2.33/2.78 substitution1:
% 2.33/2.78 X := X
% 2.33/2.78 Y := zero
% 2.33/2.78 Z := Y
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 eqrefl: (12690) {G0,W7,D3,L1,V2,M1} { leq( multiplication( X, zero ),
% 2.33/2.78 multiplication( X, Y ) ) }.
% 2.33/2.78 parent0[0]: (12689) {G2,W14,D3,L2,V2,M2} { ! multiplication( X, Y ) ==>
% 2.33/2.78 multiplication( X, Y ), leq( multiplication( X, zero ), multiplication( X
% 2.33/2.78 , Y ) ) }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := X
% 2.33/2.78 Y := Y
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 subsumption: (1933) {G2,W7,D3,L1,V2,M1} P(20,73);q { leq( multiplication( Y
% 2.33/2.78 , zero ), multiplication( Y, X ) ) }.
% 2.33/2.78 parent0: (12690) {G0,W7,D3,L1,V2,M1} { leq( multiplication( X, zero ),
% 2.33/2.78 multiplication( X, Y ) ) }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := Y
% 2.33/2.78 Y := X
% 2.33/2.78 end
% 2.33/2.78 permutation0:
% 2.33/2.78 0 ==> 0
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 paramod: (12692) {G1,W5,D3,L1,V1,M1} { leq( multiplication( X, zero ), X )
% 2.33/2.78 }.
% 2.33/2.78 parent0[0]: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 2.33/2.78 parent1[0; 4]: (1933) {G2,W7,D3,L1,V2,M1} P(20,73);q { leq( multiplication
% 2.33/2.78 ( Y, zero ), multiplication( Y, X ) ) }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := X
% 2.33/2.78 end
% 2.33/2.78 substitution1:
% 2.33/2.78 X := one
% 2.33/2.78 Y := X
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 subsumption: (2047) {G3,W5,D3,L1,V1,M1} P(5,1933) { leq( multiplication( X
% 2.33/2.78 , zero ), X ) }.
% 2.33/2.78 parent0: (12692) {G1,W5,D3,L1,V1,M1} { leq( multiplication( X, zero ), X )
% 2.33/2.78 }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := X
% 2.33/2.78 end
% 2.33/2.78 permutation0:
% 2.33/2.78 0 ==> 0
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 eqswap: (12693) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y, X
% 2.33/2.78 ) }.
% 2.33/2.78 parent0[0]: (36) {G1,W8,D3,L2,V2,M2} P(17,0) { addition( Y, X ) ==> Y, !
% 2.33/2.78 leq( X, Y ) }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := Y
% 2.33/2.78 Y := X
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 resolution: (12694) {G2,W7,D4,L1,V1,M1} { X ==> addition( X,
% 2.33/2.78 multiplication( X, zero ) ) }.
% 2.33/2.78 parent0[1]: (12693) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y
% 2.33/2.78 , X ) }.
% 2.33/2.78 parent1[0]: (2047) {G3,W5,D3,L1,V1,M1} P(5,1933) { leq( multiplication( X,
% 2.33/2.78 zero ), X ) }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := X
% 2.33/2.78 Y := multiplication( X, zero )
% 2.33/2.78 end
% 2.33/2.78 substitution1:
% 2.33/2.78 X := X
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 eqswap: (12695) {G2,W7,D4,L1,V1,M1} { addition( X, multiplication( X, zero
% 2.33/2.78 ) ) ==> X }.
% 2.33/2.78 parent0[0]: (12694) {G2,W7,D4,L1,V1,M1} { X ==> addition( X,
% 2.33/2.78 multiplication( X, zero ) ) }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := X
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 subsumption: (2051) {G4,W7,D4,L1,V1,M1} R(2047,36) { addition( X,
% 2.33/2.78 multiplication( X, zero ) ) ==> X }.
% 2.33/2.78 parent0: (12695) {G2,W7,D4,L1,V1,M1} { addition( X, multiplication( X,
% 2.33/2.78 zero ) ) ==> X }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := X
% 2.33/2.78 end
% 2.33/2.78 permutation0:
% 2.33/2.78 0 ==> 0
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 eqswap: (12696) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X, Y
% 2.33/2.78 ) }.
% 2.33/2.78 parent0[1]: (17) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 2.33/2.78 ==> Y }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := X
% 2.33/2.78 Y := Y
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 resolution: (12697) {G1,W7,D4,L1,V1,M1} { X ==> addition( multiplication(
% 2.33/2.78 X, zero ), X ) }.
% 2.33/2.78 parent0[1]: (12696) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X
% 2.33/2.78 , Y ) }.
% 2.33/2.78 parent1[0]: (2047) {G3,W5,D3,L1,V1,M1} P(5,1933) { leq( multiplication( X,
% 2.33/2.78 zero ), X ) }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := multiplication( X, zero )
% 2.33/2.78 Y := X
% 2.33/2.78 end
% 2.33/2.78 substitution1:
% 2.33/2.78 X := X
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 eqswap: (12698) {G1,W7,D4,L1,V1,M1} { addition( multiplication( X, zero )
% 2.33/2.78 , X ) ==> X }.
% 2.33/2.78 parent0[0]: (12697) {G1,W7,D4,L1,V1,M1} { X ==> addition( multiplication(
% 2.33/2.78 X, zero ), X ) }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := X
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 subsumption: (2055) {G4,W7,D4,L1,V1,M1} R(2047,17) { addition(
% 2.33/2.78 multiplication( X, zero ), X ) ==> X }.
% 2.33/2.78 parent0: (12698) {G1,W7,D4,L1,V1,M1} { addition( multiplication( X, zero )
% 2.33/2.78 , X ) ==> X }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := X
% 2.33/2.78 end
% 2.33/2.78 permutation0:
% 2.33/2.78 0 ==> 0
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 paramod: (12700) {G5,W8,D3,L2,V2,M2} { leq( X, Y ), ! leq( X,
% 2.33/2.78 multiplication( Y, zero ) ) }.
% 2.33/2.78 parent0[0]: (2051) {G4,W7,D4,L1,V1,M1} R(2047,36) { addition( X,
% 2.33/2.78 multiplication( X, zero ) ) ==> X }.
% 2.33/2.78 parent1[0; 2]: (562) {G5,W8,D3,L2,V3,M2} P(35,339) { leq( Y, addition( X, Z
% 2.33/2.78 ) ), ! leq( Y, Z ) }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := Y
% 2.33/2.78 end
% 2.33/2.78 substitution1:
% 2.33/2.78 X := Y
% 2.33/2.78 Y := X
% 2.33/2.78 Z := multiplication( Y, zero )
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 subsumption: (2439) {G6,W8,D3,L2,V2,M2} P(2051,562) { leq( Y, X ), ! leq( Y
% 2.33/2.78 , multiplication( X, zero ) ) }.
% 2.33/2.78 parent0: (12700) {G5,W8,D3,L2,V2,M2} { leq( X, Y ), ! leq( X,
% 2.33/2.78 multiplication( Y, zero ) ) }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := Y
% 2.33/2.78 Y := X
% 2.33/2.78 end
% 2.33/2.78 permutation0:
% 2.33/2.78 0 ==> 0
% 2.33/2.78 1 ==> 1
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 eqswap: (12701) {G1,W11,D4,L1,V2,M1} { multiplication( addition( X, one )
% 2.33/2.78 , Y ) = addition( multiplication( X, Y ), Y ) }.
% 2.33/2.78 parent0[0]: (108) {G1,W11,D4,L1,V2,M1} P(6,8) { addition( multiplication( Y
% 2.33/2.78 , X ), X ) = multiplication( addition( Y, one ), X ) }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := Y
% 2.33/2.78 Y := X
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 paramod: (12702) {G1,W17,D5,L2,V3,M2} { ! leq( X, addition( addition(
% 2.33/2.78 multiplication( Y, X ), X ), Z ) ), leq( X, multiplication(
% 2.33/2.78 strong_iteration( addition( Y, one ) ), Z ) ) }.
% 2.33/2.78 parent0[0]: (12701) {G1,W11,D4,L1,V2,M1} { multiplication( addition( X,
% 2.33/2.78 one ), Y ) = addition( multiplication( X, Y ), Y ) }.
% 2.33/2.78 parent1[0; 4]: (15) {G0,W13,D4,L2,V3,M2} I { ! leq( Z, addition(
% 2.33/2.78 multiplication( X, Z ), Y ) ), leq( Z, multiplication( strong_iteration(
% 2.33/2.78 X ), Y ) ) }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := Y
% 2.33/2.78 Y := X
% 2.33/2.78 end
% 2.33/2.78 substitution1:
% 2.33/2.78 X := addition( Y, one )
% 2.33/2.78 Y := Z
% 2.33/2.78 Z := X
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 resolution: (12703) {G2,W8,D5,L1,V3,M1} { leq( X, multiplication(
% 2.33/2.78 strong_iteration( addition( Y, one ) ), Z ) ) }.
% 2.33/2.78 parent0[0]: (12702) {G1,W17,D5,L2,V3,M2} { ! leq( X, addition( addition(
% 2.33/2.78 multiplication( Y, X ), X ), Z ) ), leq( X, multiplication(
% 2.33/2.78 strong_iteration( addition( Y, one ) ), Z ) ) }.
% 2.33/2.78 parent1[0]: (339) {G4,W7,D4,L1,V3,M1} P(26,313) { leq( Z, addition(
% 2.33/2.78 addition( Y, Z ), X ) ) }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := X
% 2.33/2.78 Y := Y
% 2.33/2.78 Z := Z
% 2.33/2.78 end
% 2.33/2.78 substitution1:
% 2.33/2.78 X := Z
% 2.33/2.78 Y := multiplication( Y, X )
% 2.33/2.78 Z := X
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 subsumption: (3539) {G5,W8,D5,L1,V3,M1} P(108,15);r(339) { leq( Y,
% 2.33/2.78 multiplication( strong_iteration( addition( X, one ) ), Z ) ) }.
% 2.33/2.78 parent0: (12703) {G2,W8,D5,L1,V3,M1} { leq( X, multiplication(
% 2.33/2.78 strong_iteration( addition( Y, one ) ), Z ) ) }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := Y
% 2.33/2.78 Y := X
% 2.33/2.78 Z := Z
% 2.33/2.78 end
% 2.33/2.78 permutation0:
% 2.33/2.78 0 ==> 0
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 resolution: (12704) {G6,W6,D4,L1,V2,M1} { leq( X, strong_iteration(
% 2.33/2.78 addition( Y, one ) ) ) }.
% 2.33/2.78 parent0[1]: (2439) {G6,W8,D3,L2,V2,M2} P(2051,562) { leq( Y, X ), ! leq( Y
% 2.33/2.78 , multiplication( X, zero ) ) }.
% 2.33/2.78 parent1[0]: (3539) {G5,W8,D5,L1,V3,M1} P(108,15);r(339) { leq( Y,
% 2.33/2.78 multiplication( strong_iteration( addition( X, one ) ), Z ) ) }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := strong_iteration( addition( Y, one ) )
% 2.33/2.78 Y := X
% 2.33/2.78 end
% 2.33/2.78 substitution1:
% 2.33/2.78 X := Y
% 2.33/2.78 Y := X
% 2.33/2.78 Z := zero
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 subsumption: (9185) {G7,W6,D4,L1,V2,M1} R(3539,2439) { leq( X,
% 2.33/2.78 strong_iteration( addition( Y, one ) ) ) }.
% 2.33/2.78 parent0: (12704) {G6,W6,D4,L1,V2,M1} { leq( X, strong_iteration( addition
% 2.33/2.78 ( Y, one ) ) ) }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := X
% 2.33/2.78 Y := Y
% 2.33/2.78 end
% 2.33/2.78 permutation0:
% 2.33/2.78 0 ==> 0
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 paramod: (12706) {G2,W5,D4,L1,V2,M1} { leq( X, strong_iteration( star( Y )
% 2.33/2.78 ) ) }.
% 2.33/2.78 parent0[0]: (149) {G1,W9,D5,L1,V1,M1} P(11,0) { addition( multiplication(
% 2.33/2.78 star( X ), X ), one ) ==> star( X ) }.
% 2.33/2.78 parent1[0; 3]: (9185) {G7,W6,D4,L1,V2,M1} R(3539,2439) { leq( X,
% 2.33/2.78 strong_iteration( addition( Y, one ) ) ) }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := Y
% 2.33/2.78 end
% 2.33/2.78 substitution1:
% 2.33/2.78 X := X
% 2.33/2.78 Y := multiplication( star( Y ), Y )
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 subsumption: (9234) {G8,W5,D4,L1,V2,M1} P(149,9185) { leq( Y,
% 2.33/2.78 strong_iteration( star( X ) ) ) }.
% 2.33/2.78 parent0: (12706) {G2,W5,D4,L1,V2,M1} { leq( X, strong_iteration( star( Y )
% 2.33/2.78 ) ) }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := Y
% 2.33/2.78 Y := X
% 2.33/2.78 end
% 2.33/2.78 permutation0:
% 2.33/2.78 0 ==> 0
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 paramod: (12708) {G5,W4,D3,L1,V1,M1} { leq( X, strong_iteration( one ) )
% 2.33/2.78 }.
% 2.33/2.78 parent0[0]: (2055) {G4,W7,D4,L1,V1,M1} R(2047,17) { addition(
% 2.33/2.78 multiplication( X, zero ), X ) ==> X }.
% 2.33/2.78 parent1[0; 3]: (9185) {G7,W6,D4,L1,V2,M1} R(3539,2439) { leq( X,
% 2.33/2.78 strong_iteration( addition( Y, one ) ) ) }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := one
% 2.33/2.78 end
% 2.33/2.78 substitution1:
% 2.33/2.78 X := X
% 2.33/2.78 Y := multiplication( one, zero )
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 subsumption: (9235) {G8,W4,D3,L1,V1,M1} P(2055,9185) { leq( X,
% 2.33/2.78 strong_iteration( one ) ) }.
% 2.33/2.78 parent0: (12708) {G5,W4,D3,L1,V1,M1} { leq( X, strong_iteration( one ) )
% 2.33/2.78 }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := X
% 2.33/2.78 end
% 2.33/2.78 permutation0:
% 2.33/2.78 0 ==> 0
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 eqswap: (12709) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y, X
% 2.33/2.78 ) }.
% 2.33/2.78 parent0[0]: (36) {G1,W8,D3,L2,V2,M2} P(17,0) { addition( Y, X ) ==> Y, !
% 2.33/2.78 leq( X, Y ) }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := Y
% 2.33/2.78 Y := X
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 resolution: (12710) {G2,W7,D4,L1,V1,M1} { strong_iteration( one ) ==>
% 2.33/2.78 addition( strong_iteration( one ), X ) }.
% 2.33/2.78 parent0[1]: (12709) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y
% 2.33/2.78 , X ) }.
% 2.33/2.78 parent1[0]: (9235) {G8,W4,D3,L1,V1,M1} P(2055,9185) { leq( X,
% 2.33/2.78 strong_iteration( one ) ) }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := strong_iteration( one )
% 2.33/2.78 Y := X
% 2.33/2.78 end
% 2.33/2.78 substitution1:
% 2.33/2.78 X := X
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 eqswap: (12711) {G2,W7,D4,L1,V1,M1} { addition( strong_iteration( one ), X
% 2.33/2.78 ) ==> strong_iteration( one ) }.
% 2.33/2.78 parent0[0]: (12710) {G2,W7,D4,L1,V1,M1} { strong_iteration( one ) ==>
% 2.33/2.78 addition( strong_iteration( one ), X ) }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := X
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 subsumption: (9315) {G9,W7,D4,L1,V1,M1} R(9235,36) { addition(
% 2.33/2.78 strong_iteration( one ), X ) ==> strong_iteration( one ) }.
% 2.33/2.78 parent0: (12711) {G2,W7,D4,L1,V1,M1} { addition( strong_iteration( one ),
% 2.33/2.78 X ) ==> strong_iteration( one ) }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := X
% 2.33/2.78 end
% 2.33/2.78 permutation0:
% 2.33/2.78 0 ==> 0
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 eqswap: (12712) {G9,W7,D4,L1,V1,M1} { strong_iteration( one ) ==> addition
% 2.33/2.78 ( strong_iteration( one ), X ) }.
% 2.33/2.78 parent0[0]: (9315) {G9,W7,D4,L1,V1,M1} R(9235,36) { addition(
% 2.33/2.78 strong_iteration( one ), X ) ==> strong_iteration( one ) }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := X
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 paramod: (12714) {G1,W8,D3,L2,V1,M2} { strong_iteration( one ) ==> X, !
% 2.33/2.78 leq( strong_iteration( one ), X ) }.
% 2.33/2.78 parent0[1]: (17) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 2.33/2.78 ==> Y }.
% 2.33/2.78 parent1[0; 3]: (12712) {G9,W7,D4,L1,V1,M1} { strong_iteration( one ) ==>
% 2.33/2.78 addition( strong_iteration( one ), X ) }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := strong_iteration( one )
% 2.33/2.78 Y := X
% 2.33/2.78 end
% 2.33/2.78 substitution1:
% 2.33/2.78 X := X
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 subsumption: (9837) {G10,W8,D3,L2,V1,M2} P(9315,17) { ! leq(
% 2.33/2.78 strong_iteration( one ), X ), strong_iteration( one ) = X }.
% 2.33/2.78 parent0: (12714) {G1,W8,D3,L2,V1,M2} { strong_iteration( one ) ==> X, !
% 2.33/2.78 leq( strong_iteration( one ), X ) }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := X
% 2.33/2.78 end
% 2.33/2.78 permutation0:
% 2.33/2.78 0 ==> 1
% 2.33/2.78 1 ==> 0
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 eqswap: (12716) {G10,W8,D3,L2,V1,M2} { X = strong_iteration( one ), ! leq
% 2.33/2.78 ( strong_iteration( one ), X ) }.
% 2.33/2.78 parent0[1]: (9837) {G10,W8,D3,L2,V1,M2} P(9315,17) { ! leq(
% 2.33/2.78 strong_iteration( one ), X ), strong_iteration( one ) = X }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := X
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 resolution: (12717) {G9,W6,D4,L1,V1,M1} { strong_iteration( star( X ) ) =
% 2.33/2.78 strong_iteration( one ) }.
% 2.33/2.78 parent0[1]: (12716) {G10,W8,D3,L2,V1,M2} { X = strong_iteration( one ), !
% 2.33/2.78 leq( strong_iteration( one ), X ) }.
% 2.33/2.78 parent1[0]: (9234) {G8,W5,D4,L1,V2,M1} P(149,9185) { leq( Y,
% 2.33/2.78 strong_iteration( star( X ) ) ) }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := strong_iteration( star( X ) )
% 2.33/2.78 end
% 2.33/2.78 substitution1:
% 2.33/2.78 X := X
% 2.33/2.78 Y := strong_iteration( one )
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 subsumption: (12347) {G11,W6,D4,L1,V1,M1} R(9837,9234) { strong_iteration(
% 2.33/2.78 star( X ) ) ==> strong_iteration( one ) }.
% 2.33/2.78 parent0: (12717) {G9,W6,D4,L1,V1,M1} { strong_iteration( star( X ) ) =
% 2.33/2.78 strong_iteration( one ) }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := X
% 2.33/2.78 end
% 2.33/2.78 permutation0:
% 2.33/2.78 0 ==> 0
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 *** allocated 256285 integers for termspace/termends
% 2.33/2.78 eqswap: (12719) {G10,W8,D3,L2,V1,M2} { X = strong_iteration( one ), ! leq
% 2.33/2.78 ( strong_iteration( one ), X ) }.
% 2.33/2.78 parent0[1]: (9837) {G10,W8,D3,L2,V1,M2} P(9315,17) { ! leq(
% 2.33/2.78 strong_iteration( one ), X ), strong_iteration( one ) = X }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := X
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 eqswap: (12720) {G0,W6,D4,L1,V0,M1} { ! strong_iteration( one ) ==>
% 2.33/2.78 strong_iteration( star( skol1 ) ) }.
% 2.33/2.78 parent0[0]: (19) {G0,W6,D4,L1,V0,M1} I { ! strong_iteration( star( skol1 )
% 2.33/2.78 ) ==> strong_iteration( one ) }.
% 2.33/2.78 substitution0:
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 paramod: (12724) {G1,W11,D4,L2,V0,M2} { ! strong_iteration( one ) ==>
% 2.33/2.78 strong_iteration( one ), ! leq( strong_iteration( one ), strong_iteration
% 2.33/2.78 ( star( skol1 ) ) ) }.
% 2.33/2.78 parent0[0]: (12719) {G10,W8,D3,L2,V1,M2} { X = strong_iteration( one ), !
% 2.33/2.78 leq( strong_iteration( one ), X ) }.
% 2.33/2.78 parent1[0; 4]: (12720) {G0,W6,D4,L1,V0,M1} { ! strong_iteration( one ) ==>
% 2.33/2.78 strong_iteration( star( skol1 ) ) }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := strong_iteration( star( skol1 ) )
% 2.33/2.78 end
% 2.33/2.78 substitution1:
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 eqrefl: (13689) {G0,W6,D4,L1,V0,M1} { ! leq( strong_iteration( one ),
% 2.33/2.78 strong_iteration( star( skol1 ) ) ) }.
% 2.33/2.78 parent0[0]: (12724) {G1,W11,D4,L2,V0,M2} { ! strong_iteration( one ) ==>
% 2.33/2.78 strong_iteration( one ), ! leq( strong_iteration( one ), strong_iteration
% 2.33/2.78 ( star( skol1 ) ) ) }.
% 2.33/2.78 substitution0:
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 paramod: (13690) {G1,W5,D3,L1,V0,M1} { ! leq( strong_iteration( one ),
% 2.33/2.78 strong_iteration( one ) ) }.
% 2.33/2.78 parent0[0]: (12347) {G11,W6,D4,L1,V1,M1} R(9837,9234) { strong_iteration(
% 2.33/2.78 star( X ) ) ==> strong_iteration( one ) }.
% 2.33/2.78 parent1[0; 4]: (13689) {G0,W6,D4,L1,V0,M1} { ! leq( strong_iteration( one
% 2.33/2.78 ), strong_iteration( star( skol1 ) ) ) }.
% 2.33/2.78 substitution0:
% 2.33/2.78 X := skol1
% 2.33/2.78 end
% 2.33/2.78 substitution1:
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 resolution: (13691) {G2,W0,D0,L0,V0,M0} { }.
% 2.33/2.78 parent0[0]: (13690) {G1,W5,D3,L1,V0,M1} { ! leq( strong_iteration( one ),
% 2.33/2.78 strong_iteration( one ) ) }.
% 2.33/2.78 parent1[0]: (22) {G1,W3,D2,L1,V1,M1} R(18,3) { leq( X, X ) }.
% 2.33/2.78 substitution0:
% 2.33/2.78 end
% 2.33/2.78 substitution1:
% 2.33/2.78 X := strong_iteration( one )
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 subsumption: (12444) {G12,W0,D0,L0,V0,M0} P(9837,19);q;d(12347);r(22) {
% 2.33/2.78 }.
% 2.33/2.78 parent0: (13691) {G2,W0,D0,L0,V0,M0} { }.
% 2.33/2.78 substitution0:
% 2.33/2.78 end
% 2.33/2.78 permutation0:
% 2.33/2.78 end
% 2.33/2.78
% 2.33/2.78 Proof check complete!
% 2.33/2.78
% 2.33/2.78 Memory use:
% 2.33/2.78
% 2.33/2.78 space for terms: 154119
% 2.33/2.78 space for clauses: 671106
% 2.33/2.78
% 2.33/2.78
% 2.33/2.78 clauses generated: 128874
% 2.33/2.78 clauses kept: 12445
% 2.33/2.78 clauses selected: 910
% 2.33/2.78 clauses deleted: 272
% 2.33/2.78 clauses inuse deleted: 139
% 2.33/2.78
% 2.33/2.78 subsentry: 406513
% 2.33/2.78 literals s-matched: 235598
% 2.33/2.78 literals matched: 228478
% 2.33/2.78 full subsumption: 44167
% 2.33/2.78
% 2.33/2.78 checksum: 624444326
% 2.33/2.78
% 2.33/2.78
% 2.33/2.78 Bliksem ended
%------------------------------------------------------------------------------