%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : KLE170+1.002 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n032.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 01:37:38 EDT 2022
% Result : Theorem 2.17s 2.59s
% Output : Refutation 2.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : KLE170+1.002 : TPTP v8.1.0. Released v5.2.0.
% 0.04/0.13 % Command : bliksem %s
% 0.12/0.34 % Computer : n032.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % DateTime : Thu Jun 16 13:53:15 EDT 2022
% 0.12/0.34 % CPUTime :
% 2.17/2.59 *** allocated 10000 integers for termspace/termends
% 2.17/2.59 *** allocated 10000 integers for clauses
% 2.17/2.59 *** allocated 10000 integers for justifications
% 2.17/2.59 Bliksem 1.12
% 2.17/2.59
% 2.17/2.59
% 2.17/2.59 Automatic Strategy Selection
% 2.17/2.59
% 2.17/2.59
% 2.17/2.59 Clauses:
% 2.17/2.59
% 2.17/2.59 { addition( X, Y ) = addition( Y, X ) }.
% 2.17/2.59 { addition( Z, addition( Y, X ) ) = addition( addition( Z, Y ), X ) }.
% 2.17/2.59 { addition( X, zero ) = X }.
% 2.17/2.59 { addition( X, X ) = X }.
% 2.17/2.59 { multiplication( X, multiplication( Y, Z ) ) = multiplication(
% 2.17/2.59 multiplication( X, Y ), Z ) }.
% 2.17/2.59 { multiplication( X, one ) = X }.
% 2.17/2.59 { multiplication( one, X ) = X }.
% 2.17/2.59 { multiplication( X, addition( Y, Z ) ) = addition( multiplication( X, Y )
% 2.17/2.59 , multiplication( X, Z ) ) }.
% 2.17/2.59 { multiplication( addition( X, Y ), Z ) = addition( multiplication( X, Z )
% 2.17/2.59 , multiplication( Y, Z ) ) }.
% 2.17/2.59 { multiplication( X, zero ) = zero }.
% 2.17/2.59 { multiplication( zero, X ) = zero }.
% 2.17/2.59 { ! leq( X, Y ), addition( X, Y ) = Y }.
% 2.17/2.59 { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 2.17/2.59 { leq( addition( one, multiplication( X, star( X ) ) ), star( X ) ) }.
% 2.17/2.59 { leq( addition( one, multiplication( star( X ), X ) ), star( X ) ) }.
% 2.17/2.59 { ! leq( addition( multiplication( X, Y ), Z ), Y ), leq( multiplication(
% 2.17/2.59 star( X ), Z ), Y ) }.
% 2.17/2.59 { ! leq( addition( multiplication( X, Y ), Z ), X ), leq( multiplication( Z
% 2.17/2.59 , star( Y ) ), X ) }.
% 2.17/2.59 { ! leq( multiplication( a, a ), star( a ) ) }.
% 2.17/2.59
% 2.17/2.59 percentage equality = 0.590909, percentage horn = 1.000000
% 2.17/2.59 This is a problem with some equality
% 2.17/2.59
% 2.17/2.59
% 2.17/2.59
% 2.17/2.59 Options Used:
% 2.17/2.59
% 2.17/2.59 useres = 1
% 2.17/2.59 useparamod = 1
% 2.17/2.59 useeqrefl = 1
% 2.17/2.59 useeqfact = 1
% 2.17/2.59 usefactor = 1
% 2.17/2.59 usesimpsplitting = 0
% 2.17/2.59 usesimpdemod = 5
% 2.17/2.59 usesimpres = 3
% 2.17/2.59
% 2.17/2.59 resimpinuse = 1000
% 2.17/2.59 resimpclauses = 20000
% 2.17/2.59 substype = eqrewr
% 2.17/2.59 backwardsubs = 1
% 2.17/2.59 selectoldest = 5
% 2.17/2.59
% 2.17/2.59 litorderings [0] = split
% 2.17/2.59 litorderings [1] = extend the termordering, first sorting on arguments
% 2.17/2.59
% 2.17/2.59 termordering = kbo
% 2.17/2.59
% 2.17/2.59 litapriori = 0
% 2.17/2.59 termapriori = 1
% 2.17/2.59 litaposteriori = 0
% 2.17/2.59 termaposteriori = 0
% 2.17/2.59 demodaposteriori = 0
% 2.17/2.59 ordereqreflfact = 0
% 2.17/2.59
% 2.17/2.59 litselect = negord
% 2.17/2.59
% 2.17/2.59 maxweight = 15
% 2.17/2.59 maxdepth = 30000
% 2.17/2.59 maxlength = 115
% 2.17/2.59 maxnrvars = 195
% 2.17/2.59 excuselevel = 1
% 2.17/2.59 increasemaxweight = 1
% 2.17/2.59
% 2.17/2.59 maxselected = 10000000
% 2.17/2.59 maxnrclauses = 10000000
% 2.17/2.59
% 2.17/2.59 showgenerated = 0
% 2.17/2.59 showkept = 0
% 2.17/2.59 showselected = 0
% 2.17/2.59 showdeleted = 0
% 2.17/2.59 showresimp = 1
% 2.17/2.59 showstatus = 2000
% 2.17/2.59
% 2.17/2.59 prologoutput = 0
% 2.17/2.59 nrgoals = 5000000
% 2.17/2.59 totalproof = 1
% 2.17/2.59
% 2.17/2.59 Symbols occurring in the translation:
% 2.17/2.59
% 2.17/2.59 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 2.17/2.59 . [1, 2] (w:1, o:18, a:1, s:1, b:0),
% 2.17/2.59 ! [4, 1] (w:0, o:12, a:1, s:1, b:0),
% 2.17/2.59 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 2.17/2.59 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 2.17/2.59 addition [37, 2] (w:1, o:42, a:1, s:1, b:0),
% 2.17/2.59 zero [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 2.17/2.59 multiplication [40, 2] (w:1, o:44, a:1, s:1, b:0),
% 2.17/2.59 one [41, 0] (w:1, o:10, a:1, s:1, b:0),
% 2.17/2.59 leq [42, 2] (w:1, o:43, a:1, s:1, b:0),
% 2.17/2.59 star [43, 1] (w:1, o:17, a:1, s:1, b:0),
% 2.17/2.59 a [44, 0] (w:1, o:11, a:1, s:1, b:0).
% 2.17/2.59
% 2.17/2.59
% 2.17/2.59 Starting Search:
% 2.17/2.59
% 2.17/2.59 *** allocated 15000 integers for clauses
% 2.17/2.59 *** allocated 22500 integers for clauses
% 2.17/2.59 *** allocated 33750 integers for clauses
% 2.17/2.59 *** allocated 50625 integers for clauses
% 2.17/2.59 *** allocated 15000 integers for termspace/termends
% 2.17/2.59 *** allocated 75937 integers for clauses
% 2.17/2.59 Resimplifying inuse:
% 2.17/2.59 Done
% 2.17/2.59
% 2.17/2.59 *** allocated 22500 integers for termspace/termends
% 2.17/2.59 *** allocated 113905 integers for clauses
% 2.17/2.59 *** allocated 33750 integers for termspace/termends
% 2.17/2.59
% 2.17/2.59 Intermediate Status:
% 2.17/2.59 Generated: 16601
% 2.17/2.59 Kept: 2025
% 2.17/2.59 Inuse: 236
% 2.17/2.59 Deleted: 34
% 2.17/2.59 Deletedinuse: 19
% 2.17/2.59
% 2.17/2.59 Resimplifying inuse:
% 2.17/2.59 Done
% 2.17/2.59
% 2.17/2.59 *** allocated 170857 integers for clauses
% 2.17/2.59 *** allocated 50625 integers for termspace/termends
% 2.17/2.59 Resimplifying inuse:
% 2.17/2.59 Done
% 2.17/2.59
% 2.17/2.59 *** allocated 256285 integers for clauses
% 2.17/2.59 *** allocated 75937 integers for termspace/termends
% 2.17/2.59
% 2.17/2.59 Intermediate Status:
% 2.17/2.59 Generated: 37315
% 2.17/2.59 Kept: 4028
% 2.17/2.59 Inuse: 417
% 2.17/2.59 Deleted: 56
% 2.17/2.59 Deletedinuse: 19
% 2.17/2.59
% 2.17/2.59 Resimplifying inuse:
% 2.17/2.59 Done
% 2.17/2.59
% 2.17/2.59 *** allocated 384427 integers for clauses
% 2.17/2.59 Resimplifying inuse:
% 2.17/2.59 Done
% 2.17/2.59
% 2.17/2.59 *** allocated 113905 integers for termspace/termends
% 2.17/2.59
% 2.17/2.59 Intermediate Status:
% 2.17/2.59 Generated: 63323
% 2.17/2.59 Kept: 6141
% 2.17/2.59 Inuse: 599
% 2.17/2.59 Deleted: 83
% 2.17/2.59 Deletedinuse: 19
% 2.17/2.59
% 2.17/2.59 Resimplifying inuse:
% 2.17/2.59 Done
% 2.17/2.59
% 2.17/2.59 Resimplifying inuse:
% 2.17/2.59 Done
% 2.17/2.59
% 2.17/2.59 *** allocated 576640 integers for clauses
% 2.17/2.59 *** allocated 170857 integers for termspace/termends
% 2.17/2.59
% 2.17/2.59 Intermediate Status:
% 2.17/2.59 Generated: 101915
% 2.17/2.59 Kept: 8737
% 2.17/2.59 Inuse: 613
% 2.17/2.59 Deleted: 88
% 2.17/2.59 Deletedinuse: 24
% 2.17/2.59
% 2.17/2.59 Resimplifying inuse:
% 2.17/2.59 Done
% 2.17/2.59
% 2.17/2.59 Resimplifying inuse:
% 2.17/2.59 Done
% 2.17/2.59
% 2.17/2.59
% 2.17/2.59 Intermediate Status:
% 2.17/2.59 Generated: 132757
% 2.17/2.59 Kept: 10748
% 2.17/2.59 Inuse: 692
% 2.17/2.59 Deleted: 97
% 2.17/2.59 Deletedinuse: 24
% 2.17/2.59
% 2.17/2.59 Resimplifying inuse:
% 2.17/2.59 Done
% 2.17/2.59
% 2.17/2.59
% 2.17/2.59 Bliksems!, er is een bewijs:
% 2.17/2.59 % SZS status Theorem
% 2.17/2.59 % SZS output start Refutation
% 2.17/2.59
% 2.17/2.59 (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X ) }.
% 2.17/2.59 (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) ) ==> addition(
% 2.17/2.59 addition( Z, Y ), X ) }.
% 2.17/2.59 (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 2.17/2.59 (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 2.17/2.59 (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 2.17/2.59 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 2.17/2.59 (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y ) ==> Y }.
% 2.17/2.59 (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X, Y ) }.
% 2.17/2.59 (13) {G0,W9,D5,L1,V1,M1} I { leq( addition( one, multiplication( X, star( X
% 2.17/2.59 ) ) ), star( X ) ) }.
% 2.17/2.59 (14) {G0,W9,D5,L1,V1,M1} I { leq( addition( one, multiplication( star( X )
% 2.17/2.59 , X ) ), star( X ) ) }.
% 2.17/2.59 (17) {G0,W6,D3,L1,V0,M1} I { ! leq( multiplication( a, a ), star( a ) ) }.
% 2.17/2.59 (24) {G1,W14,D4,L2,V3,M2} P(1,12) { ! addition( addition( X, Y ), Z ) ==>
% 2.17/2.59 addition( Y, Z ), leq( X, addition( Y, Z ) ) }.
% 2.17/2.59 (25) {G1,W11,D4,L1,V3,M1} P(1,0) { addition( addition( X, Y ), Z ) =
% 2.17/2.59 addition( addition( Y, Z ), X ) }.
% 2.17/2.59 (35) {G1,W12,D4,L2,V3,M2} P(11,1) { addition( addition( Z, X ), Y ) ==>
% 2.17/2.59 addition( Z, Y ), ! leq( X, Y ) }.
% 2.17/2.59 (37) {G1,W8,D3,L2,V2,M2} P(11,0) { addition( Y, X ) ==> Y, ! leq( X, Y )
% 2.17/2.59 }.
% 2.17/2.59 (59) {G1,W16,D4,L2,V3,M2} P(7,12) { ! multiplication( X, addition( Y, Z ) )
% 2.17/2.59 ==> multiplication( X, Z ), leq( multiplication( X, Y ), multiplication
% 2.17/2.59 ( X, Z ) ) }.
% 2.17/2.60 (217) {G2,W5,D3,L1,V2,M1} P(3,24);q { leq( X, addition( X, Y ) ) }.
% 2.17/2.60 (228) {G3,W7,D4,L1,V3,M1} P(1,217) { leq( X, addition( addition( X, Y ), Z
% 2.17/2.60 ) ) }.
% 2.17/2.60 (229) {G3,W5,D3,L1,V2,M1} P(0,217) { leq( X, addition( Y, X ) ) }.
% 2.17/2.60 (252) {G4,W7,D4,L1,V3,M1} P(25,229) { leq( Z, addition( addition( Y, Z ), X
% 2.17/2.60 ) ) }.
% 2.17/2.60 (325) {G5,W8,D3,L2,V3,M2} P(11,252) { leq( Y, Z ), ! leq( addition( X, Y )
% 2.17/2.60 , Z ) }.
% 2.17/2.60 (335) {G4,W8,D3,L2,V3,M2} P(11,228) { leq( X, Z ), ! leq( addition( X, Y )
% 2.17/2.60 , Z ) }.
% 2.17/2.60 (508) {G5,W8,D3,L2,V3,M2} P(35,252) { leq( Y, addition( X, Z ) ), ! leq( Y
% 2.17/2.60 , Z ) }.
% 2.17/2.60 (570) {G6,W9,D2,L3,V3,M3} P(37,508) { leq( Z, X ), ! leq( Z, Y ), ! leq( Y
% 2.17/2.60 , X ) }.
% 2.17/2.60 (646) {G5,W4,D3,L1,V1,M1} R(335,14) { leq( one, star( X ) ) }.
% 2.17/2.60 (663) {G6,W7,D4,L1,V1,M1} R(646,11) { addition( one, star( X ) ) ==> star(
% 2.17/2.60 X ) }.
% 2.17/2.60 (825) {G6,W7,D4,L1,V1,M1} R(325,13) { leq( multiplication( X, star( X ) ),
% 2.17/2.60 star( X ) ) }.
% 2.17/2.60 (828) {G6,W8,D4,L1,V1,M1} R(325,17) { ! leq( addition( X, multiplication( a
% 2.17/2.60 , a ) ), star( a ) ) }.
% 2.17/2.60 (1464) {G7,W6,D4,L1,V2,M1} P(663,59);q;d(5) { leq( Y, multiplication( Y,
% 2.17/2.60 star( X ) ) ) }.
% 2.17/2.60 (3810) {G7,W8,D4,L1,V1,M1} P(7,828) { ! leq( multiplication( a, addition( X
% 2.17/2.60 , a ) ), star( a ) ) }.
% 2.17/2.60 (3844) {G8,W9,D3,L2,V1,M2} P(37,3810) { ! leq( multiplication( a, X ), star
% 2.17/2.60 ( a ) ), ! leq( a, X ) }.
% 2.17/2.60 (10812) {G9,W12,D3,L3,V2,M3} R(3844,570) { ! leq( multiplication( a, X ),
% 2.17/2.60 star( a ) ), ! leq( a, Y ), ! leq( Y, X ) }.
% 2.17/2.60 (10854) {G10,W6,D4,L1,V0,M1} F(10812);r(825) { ! leq( a, multiplication( a
% 2.17/2.60 , star( a ) ) ) }.
% 2.17/2.60 (10890) {G11,W0,D0,L0,V0,M0} S(10854);r(1464) { }.
% 2.17/2.60
% 2.17/2.60
% 2.17/2.60 % SZS output end Refutation
% 2.17/2.60 found a proof!
% 2.17/2.60
% 2.17/2.60
% 2.17/2.60 Unprocessed initial clauses:
% 2.17/2.60
% 2.17/2.60 (10892) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X ) }.
% 2.17/2.60 (10893) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) = addition
% 2.17/2.60 ( addition( Z, Y ), X ) }.
% 2.17/2.60 (10894) {G0,W5,D3,L1,V1,M1} { addition( X, zero ) = X }.
% 2.17/2.60 (10895) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 2.17/2.60 (10896) {G0,W11,D4,L1,V3,M1} { multiplication( X, multiplication( Y, Z ) )
% 2.17/2.60 = multiplication( multiplication( X, Y ), Z ) }.
% 2.17/2.60 (10897) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 2.17/2.60 (10898) {G0,W5,D3,L1,V1,M1} { multiplication( one, X ) = X }.
% 2.17/2.60 (10899) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y, Z ) ) =
% 2.17/2.60 addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 2.17/2.60 (10900) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Y ), Z ) =
% 2.17/2.60 addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 2.17/2.60 (10901) {G0,W5,D3,L1,V1,M1} { multiplication( X, zero ) = zero }.
% 2.17/2.60 (10902) {G0,W5,D3,L1,V1,M1} { multiplication( zero, X ) = zero }.
% 2.17/2.60 (10903) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y }.
% 2.17/2.60 (10904) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 2.17/2.60 (10905) {G0,W9,D5,L1,V1,M1} { leq( addition( one, multiplication( X, star
% 2.17/2.60 ( X ) ) ), star( X ) ) }.
% 2.17/2.60 (10906) {G0,W9,D5,L1,V1,M1} { leq( addition( one, multiplication( star( X
% 2.17/2.60 ), X ) ), star( X ) ) }.
% 2.17/2.60 (10907) {G0,W13,D4,L2,V3,M2} { ! leq( addition( multiplication( X, Y ), Z
% 2.17/2.60 ), Y ), leq( multiplication( star( X ), Z ), Y ) }.
% 2.17/2.60 (10908) {G0,W13,D4,L2,V3,M2} { ! leq( addition( multiplication( X, Y ), Z
% 2.17/2.60 ), X ), leq( multiplication( Z, star( Y ) ), X ) }.
% 2.17/2.60 (10909) {G0,W6,D3,L1,V0,M1} { ! leq( multiplication( a, a ), star( a ) )
% 2.17/2.60 }.
% 2.17/2.60
% 2.17/2.60
% 2.17/2.60 Total Proof:
% 2.17/2.60
% 2.17/2.60 subsumption: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X
% 2.17/2.60 ) }.
% 2.17/2.60 parent0: (10892) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X )
% 2.17/2.60 }.
% 2.17/2.60 substitution0:
% 2.17/2.60 X := X
% 2.17/2.60 Y := Y
% 2.17/2.60 end
% 2.17/2.60 permutation0:
% 2.17/2.60 0 ==> 0
% 2.17/2.60 end
% 2.17/2.60
% 2.17/2.60 subsumption: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 2.17/2.60 ==> addition( addition( Z, Y ), X ) }.
% 2.17/2.60 parent0: (10893) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) =
% 2.17/2.60 addition( addition( Z, Y ), X ) }.
% 2.17/2.60 substitution0:
% 2.17/2.60 X := X
% 2.17/2.60 Y := Y
% 2.17/2.60 Z := Z
% 2.17/2.60 end
% 2.17/2.60 permutation0:
% 2.17/2.60 0 ==> 0
% 2.17/2.60 end
% 2.17/2.60
% 2.17/2.60 subsumption: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 2.17/2.60 parent0: (10895) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 2.17/2.60 substitution0:
% 2.17/2.60 X := X
% 2.17/2.60 end
% 2.17/2.60 permutation0:
% 2.17/2.60 0 ==> 0
% 2.17/2.60 end
% 2.17/2.60
% 2.17/2.60 subsumption: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 2.17/2.60 parent0: (10897) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 2.17/2.60 substitution0:
% 2.17/2.60 X := X
% 2.17/2.60 end
% 2.17/2.60 permutation0:
% 2.17/2.60 0 ==> 0
% 2.17/2.60 end
% 2.17/2.60
% 2.17/2.60 eqswap: (10925) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Y ),
% 2.17/2.60 multiplication( X, Z ) ) = multiplication( X, addition( Y, Z ) ) }.
% 2.17/2.60 parent0[0]: (10899) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y
% 2.17/2.60 , Z ) ) = addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 2.17/2.60 substitution0:
% 2.17/2.60 X := X
% 2.17/2.60 Y := Y
% 2.17/2.60 Z := Z
% 2.17/2.60 end
% 2.17/2.60
% 2.17/2.60 subsumption: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y )
% 2.17/2.60 , multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 2.17/2.60 parent0: (10925) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Y ),
% 2.17/2.60 multiplication( X, Z ) ) = multiplication( X, addition( Y, Z ) ) }.
% 2.17/2.60 substitution0:
% 2.17/2.60 X := X
% 2.17/2.60 Y := Y
% 2.17/2.60 Z := Z
% 2.17/2.60 end
% 2.17/2.60 permutation0:
% 2.17/2.60 0 ==> 0
% 2.17/2.60 end
% 2.17/2.60
% 2.17/2.60 subsumption: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 2.17/2.60 ==> Y }.
% 2.17/2.60 parent0: (10903) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y
% 2.17/2.60 }.
% 2.17/2.60 substitution0:
% 2.17/2.60 X := X
% 2.17/2.60 Y := Y
% 2.17/2.60 end
% 2.17/2.60 permutation0:
% 2.17/2.60 0 ==> 0
% 2.17/2.60 1 ==> 1
% 2.17/2.60 end
% 2.17/2.60
% 2.17/2.60 subsumption: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X
% 2.17/2.60 , Y ) }.
% 2.17/2.60 parent0: (10904) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y )
% 2.17/2.60 }.
% 2.17/2.60 substitution0:
% 2.17/2.60 X := X
% 2.17/2.60 Y := Y
% 2.17/2.60 end
% 2.17/2.60 permutation0:
% 2.17/2.60 0 ==> 0
% 2.17/2.60 1 ==> 1
% 2.17/2.60 end
% 2.17/2.60
% 2.17/2.60 subsumption: (13) {G0,W9,D5,L1,V1,M1} I { leq( addition( one,
% 2.17/2.60 multiplication( X, star( X ) ) ), star( X ) ) }.
% 2.17/2.60 parent0: (10905) {G0,W9,D5,L1,V1,M1} { leq( addition( one, multiplication
% 2.17/2.60 ( X, star( X ) ) ), star( X ) ) }.
% 2.17/2.60 substitution0:
% 2.17/2.60 X := X
% 2.17/2.60 end
% 2.17/2.60 permutation0:
% 2.17/2.60 0 ==> 0
% 2.17/2.60 end
% 2.17/2.60
% 2.17/2.60 subsumption: (14) {G0,W9,D5,L1,V1,M1} I { leq( addition( one,
% 2.17/2.60 multiplication( star( X ), X ) ), star( X ) ) }.
% 2.17/2.60 parent0: (10906) {G0,W9,D5,L1,V1,M1} { leq( addition( one, multiplication
% 2.17/2.60 ( star( X ), X ) ), star( X ) ) }.
% 2.17/2.60 substitution0:
% 2.17/2.60 X := X
% 2.17/2.60 end
% 2.17/2.60 permutation0:
% 2.17/2.60 0 ==> 0
% 2.17/2.60 end
% 2.17/2.60
% 2.17/2.60 subsumption: (17) {G0,W6,D3,L1,V0,M1} I { ! leq( multiplication( a, a ),
% 2.17/2.60 star( a ) ) }.
% 2.17/2.60 parent0: (10909) {G0,W6,D3,L1,V0,M1} { ! leq( multiplication( a, a ), star
% 2.17/2.60 ( a ) ) }.
% 2.17/2.60 substitution0:
% 2.17/2.60 end
% 2.17/2.60 permutation0:
% 2.17/2.60 0 ==> 0
% 2.17/2.60 end
% 2.17/2.60
% 2.17/2.60 eqswap: (10986) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y
% 2.17/2.60 ) }.
% 2.17/2.60 parent0[0]: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 2.17/2.60 Y ) }.
% 2.17/2.60 substitution0:
% 2.17/2.60 X := X
% 2.17/2.60 Y := Y
% 2.17/2.60 end
% 2.17/2.60
% 2.17/2.60 paramod: (10987) {G1,W14,D4,L2,V3,M2} { ! addition( X, Y ) ==> addition(
% 2.17/2.60 addition( Z, X ), Y ), leq( Z, addition( X, Y ) ) }.
% 2.17/2.60 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 2.17/2.60 ==> addition( addition( Z, Y ), X ) }.
% 2.17/2.60 parent1[0; 5]: (10986) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq
% 2.17/2.60 ( X, Y ) }.
% 2.17/2.60 substitution0:
% 2.17/2.60 X := Y
% 2.17/2.60 Y := X
% 2.17/2.60 Z := Z
% 2.17/2.60 end
% 2.17/2.60 substitution1:
% 2.17/2.60 X := Z
% 2.17/2.60 Y := addition( X, Y )
% 2.17/2.60 end
% 2.17/2.60
% 2.17/2.60 eqswap: (10988) {G1,W14,D4,L2,V3,M2} { ! addition( addition( Z, X ), Y )
% 2.17/2.60 ==> addition( X, Y ), leq( Z, addition( X, Y ) ) }.
% 2.17/2.60 parent0[0]: (10987) {G1,W14,D4,L2,V3,M2} { ! addition( X, Y ) ==> addition
% 2.17/2.60 ( addition( Z, X ), Y ), leq( Z, addition( X, Y ) ) }.
% 2.17/2.60 substitution0:
% 2.17/2.60 X := X
% 2.17/2.60 Y := Y
% 2.17/2.60 Z := Z
% 2.17/2.60 end
% 2.17/2.60
% 2.17/2.60 subsumption: (24) {G1,W14,D4,L2,V3,M2} P(1,12) { ! addition( addition( X, Y
% 2.17/2.60 ), Z ) ==> addition( Y, Z ), leq( X, addition( Y, Z ) ) }.
% 2.17/2.60 parent0: (10988) {G1,W14,D4,L2,V3,M2} { ! addition( addition( Z, X ), Y )
% 2.17/2.60 ==> addition( X, Y ), leq( Z, addition( X, Y ) ) }.
% 2.17/2.60 substitution0:
% 2.17/2.60 X := Y
% 2.17/2.60 Y := Z
% 2.17/2.60 Z := X
% 2.17/2.60 end
% 2.17/2.60 permutation0:
% 2.17/2.60 0 ==> 0
% 2.17/2.60 1 ==> 1
% 2.17/2.60 end
% 2.17/2.60
% 2.17/2.60 eqswap: (10989) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z ) ==>
% 2.17/2.60 addition( X, addition( Y, Z ) ) }.
% 2.17/2.60 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 2.17/2.60 ==> addition( addition( Z, Y ), X ) }.
% 2.17/2.60 substitution0:
% 2.17/2.60 X := Z
% 2.17/2.60 Y := Y
% 2.17/2.60 Z := X
% 2.17/2.60 end
% 2.17/2.60
% 2.17/2.60 paramod: (10992) {G1,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z )
% 2.17/2.60 ==> addition( addition( Y, Z ), X ) }.
% 2.17/2.60 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 2.17/2.60 }.
% 2.17/2.60 parent1[0; 6]: (10989) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y ),
% 2.17/2.60 Z ) ==> addition( X, addition( Y, Z ) ) }.
% 2.17/2.60 substitution0:
% 2.17/2.60 X := X
% 2.17/2.60 Y := addition( Y, Z )
% 2.17/2.60 end
% 2.17/2.60 substitution1:
% 2.17/2.60 X := X
% 2.17/2.60 Y := Y
% 2.17/2.60 Z := Z
% 2.17/2.60 end
% 2.17/2.60
% 2.17/2.60 subsumption: (25) {G1,W11,D4,L1,V3,M1} P(1,0) { addition( addition( X, Y )
% 2.17/2.60 , Z ) = addition( addition( Y, Z ), X ) }.
% 2.17/2.60 parent0: (10992) {G1,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z )
% 2.17/2.60 ==> addition( addition( Y, Z ), X ) }.
% 2.17/2.60 substitution0:
% 2.17/2.60 X := X
% 2.17/2.60 Y := Y
% 2.17/2.60 Z := Z
% 2.17/2.60 end
% 2.17/2.60 permutation0:
% 2.17/2.60 0 ==> 0
% 2.17/2.60 end
% 2.17/2.60
% 2.17/2.60 eqswap: (11007) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z ) ==>
% 2.17/2.60 addition( X, addition( Y, Z ) ) }.
% 2.17/2.60 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 2.17/2.60 ==> addition( addition( Z, Y ), X ) }.
% 2.17/2.60 substitution0:
% 2.17/2.60 X := Z
% 2.17/2.60 Y := Y
% 2.17/2.60 Z := X
% 2.17/2.60 end
% 2.17/2.60
% 2.17/2.60 paramod: (11013) {G1,W12,D4,L2,V3,M2} { addition( addition( X, Y ), Z )
% 2.17/2.60 ==> addition( X, Z ), ! leq( Y, Z ) }.
% 2.17/2.60 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 2.17/2.60 ==> Y }.
% 2.17/2.60 parent1[0; 8]: (11007) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y ),
% 2.17/2.60 Z ) ==> addition( X, addition( Y, Z ) ) }.
% 2.17/2.60 substitution0:
% 2.17/2.60 X := Y
% 2.17/2.60 Y := Z
% 2.17/2.60 end
% 2.17/2.60 substitution1:
% 2.17/2.60 X := X
% 2.17/2.60 Y := Y
% 2.17/2.60 Z := Z
% 2.17/2.60 end
% 2.17/2.60
% 2.17/2.60 subsumption: (35) {G1,W12,D4,L2,V3,M2} P(11,1) { addition( addition( Z, X )
% 2.17/2.60 , Y ) ==> addition( Z, Y ), ! leq( X, Y ) }.
% 2.17/2.60 parent0: (11013) {G1,W12,D4,L2,V3,M2} { addition( addition( X, Y ), Z )
% 2.17/2.60 ==> addition( X, Z ), ! leq( Y, Z ) }.
% 2.17/2.60 substitution0:
% 2.17/2.60 X := Z
% 2.17/2.60 Y := X
% 2.17/2.60 Z := Y
% 2.17/2.60 end
% 2.17/2.60 permutation0:
% 2.17/2.60 0 ==> 0
% 2.17/2.60 1 ==> 1
% 2.17/2.60 end
% 2.17/2.60
% 2.17/2.60 eqswap: (11060) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X, Y
% 2.17/2.60 ) }.
% 2.17/2.60 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 2.17/2.60 ==> Y }.
% 2.17/2.60 substitution0:
% 2.17/2.60 X := X
% 2.17/2.60 Y := Y
% 2.17/2.60 end
% 2.17/2.60
% 2.17/2.60 paramod: (11061) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y, X
% 2.17/2.60 ) }.
% 2.17/2.60 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 2.17/2.60 }.
% 2.17/2.60 parent1[0; 2]: (11060) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq
% 2.17/2.60 ( X, Y ) }.
% 2.17/2.60 substitution0:
% 2.17/2.60 X := Y
% 2.17/2.60 Y := X
% 2.17/2.60 end
% 2.17/2.60 substitution1:
% 2.17/2.60 X := Y
% 2.17/2.60 Y := X
% 2.17/2.60 end
% 2.17/2.60
% 2.17/2.60 eqswap: (11064) {G1,W8,D3,L2,V2,M2} { addition( X, Y ) ==> X, ! leq( Y, X
% 2.17/2.60 ) }.
% 2.17/2.60 parent0[0]: (11061) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y
% 2.17/2.60 , X ) }.
% 2.17/2.60 substitution0:
% 2.17/2.60 X := X
% 2.17/2.60 Y := Y
% 2.17/2.60 end
% 2.17/2.60
% 2.17/2.60 subsumption: (37) {G1,W8,D3,L2,V2,M2} P(11,0) { addition( Y, X ) ==> Y, !
% 2.17/2.60 leq( X, Y ) }.
% 2.17/2.60 parent0: (11064) {G1,W8,D3,L2,V2,M2} { addition( X, Y ) ==> X, ! leq( Y, X
% 2.17/2.60 ) }.
% 2.17/2.60 substitution0:
% 2.17/2.60 X := Y
% 2.17/2.60 Y := X
% 2.17/2.60 end
% 2.17/2.60 permutation0:
% 2.17/2.60 0 ==> 0
% 2.17/2.60 1 ==> 1
% 2.17/2.60 end
% 2.17/2.60
% 2.17/2.60 eqswap: (11066) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y
% 2.17/2.60 ) }.
% 2.17/2.60 parent0[0]: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 2.17/2.60 Y ) }.
% 2.17/2.60 substitution0:
% 2.17/2.60 X := X
% 2.17/2.60 Y := Y
% 2.17/2.60 end
% 2.17/2.60
% 2.17/2.60 paramod: (11067) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Y ) ==>
% 2.17/2.60 multiplication( X, addition( Z, Y ) ), leq( multiplication( X, Z ),
% 2.17/2.60 multiplication( X, Y ) ) }.
% 2.17/2.60 parent0[0]: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 2.17/2.60 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 2.17/2.60 parent1[0; 5]: (11066) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq
% 2.17/2.60 ( X, Y ) }.
% 2.17/2.60 substitution0:
% 2.17/2.60 X := X
% 2.17/2.60 Y := Z
% 2.17/2.60 Z := Y
% 2.17/2.60 end
% 2.17/2.60 substitution1:
% 2.17/2.60 X := multiplication( X, Z )
% 2.17/2.60 Y := multiplication( X, Y )
% 2.17/2.60 end
% 2.17/2.60
% 2.17/2.60 eqswap: (11068) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, addition( Z, Y
% 2.17/2.60 ) ) ==> multiplication( X, Y ), leq( multiplication( X, Z ),
% 2.17/2.60 multiplication( X, Y ) ) }.
% 2.17/2.60 parent0[0]: (11067) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Y ) ==>
% 2.17/2.60 multiplication( X, addition( Z, Y ) ), leq( multiplication( X, Z ),
% 2.17/2.60 multiplication( X, Y ) ) }.
% 2.17/2.60 substitution0:
% 2.17/2.60 X := X
% 2.17/2.60 Y := Y
% 2.17/2.60 Z := Z
% 2.17/2.60 end
% 2.17/2.60
% 2.17/2.60 subsumption: (59) {G1,W16,D4,L2,V3,M2} P(7,12) { ! multiplication( X,
% 2.17/2.60 addition( Y, Z ) ) ==> multiplication( X, Z ), leq( multiplication( X, Y
% 2.17/2.60 ), multiplication( X, Z ) ) }.
% 2.17/2.60 parent0: (11068) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, addition( Z,
% 2.17/2.60 Y ) ) ==> multiplication( X, Y ), leq( multiplication( X, Z ),
% 2.17/2.60 multiplication( X, Y ) ) }.
% 2.17/2.60 substitution0:
% 2.17/2.60 X := X
% 2.17/2.60 Y := Z
% 2.17/2.60 Z := Y
% 2.17/2.60 end
% 2.17/2.60 permutation0:
% 2.17/2.60 0 ==> 0
% 2.17/2.60 1 ==> 1
% 2.17/2.60 end
% 2.17/2.60
% 2.17/2.60 eqswap: (11070) {G1,W14,D4,L2,V3,M2} { ! addition( Y, Z ) ==> addition(
% 2.17/2.60 addition( X, Y ), Z ), leq( X, addition( Y, Z ) ) }.
% 2.17/2.60 parent0[0]: (24) {G1,W14,D4,L2,V3,M2} P(1,12) { ! addition( addition( X, Y
% 2.17/2.60 ), Z ) ==> addition( Y, Z ), leq( X, addition( Y, Z ) ) }.
% 2.17/2.60 substitution0:
% 2.17/2.60 X := X
% 2.17/2.60 Y := Y
% 2.17/2.60 Z := Z
% 2.17/2.60 end
% 2.17/2.60
% 2.17/2.60 paramod: (11073) {G1,W12,D3,L2,V2,M2} { ! addition( X, Y ) ==> addition( X
% 2.17/2.60 , Y ), leq( X, addition( X, Y ) ) }.
% 2.17/2.60 parent0[0]: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 2.17/2.60 parent1[0; 6]: (11070) {G1,W14,D4,L2,V3,M2} { ! addition( Y, Z ) ==>
% 2.17/2.60 addition( addition( X, Y ), Z ), leq( X, addition( Y, Z ) ) }.
% 2.17/2.60 substitution0:
% 2.17/2.60 X := X
% 2.17/2.60 end
% 2.17/2.60 substitution1:
% 2.17/2.60 X := X
% 2.17/2.60 Y := X
% 2.17/2.60 Z := Y
% 2.17/2.60 end
% 2.17/2.60
% 2.17/2.60 eqrefl: (11076) {G0,W5,D3,L1,V2,M1} { leq( X, addition( X, Y ) ) }.
% 2.17/2.60 parent0[0]: (11073) {G1,W12,D3,L2,V2,M2} { ! addition( X, Y ) ==> addition
% 2.17/2.60 ( X, Y ), leq( X, addition( X, Y ) ) }.
% 2.17/2.60 substitution0:
% 2.17/2.60 X := X
% 2.17/2.60 Y := Y
% 2.17/2.60 end
% 2.17/2.60
% 2.17/2.60 subsumption: (217) {G2,W5,D3,L1,V2,M1} P(3,24);q { leq( X, addition( X, Y )
% 2.17/2.60 ) }.
% 2.17/2.60 parent0: (11076) {G0,W5,D3,L1,V2,M1} { leq( X, addition( X, Y ) ) }.
% 2.17/2.60 substitution0:
% 2.17/2.60 X := X
% 2.17/2.60 Y := Y
% 2.17/2.60 end
% 2.17/2.60 permutation0:
% 2.17/2.60 0 ==> 0
% 2.17/2.60 end
% 2.17/2.60
% 2.17/2.60 paramod: (11078) {G1,W7,D4,L1,V3,M1} { leq( X, addition( addition( X, Y )
% 2.17/2.60 , Z ) ) }.
% 2.17/2.60 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 2.17/2.60 ==> addition( addition( Z, Y ), X ) }.
% 2.17/2.60 parent1[0; 2]: (217) {G2,W5,D3,L1,V2,M1} P(3,24);q { leq( X, addition( X, Y
% 2.17/2.60 ) ) }.
% 2.17/2.60 substitution0:
% 2.17/2.60 X := Z
% 2.17/2.60 Y := Y
% 2.17/2.60 Z := X
% 2.17/2.60 end
% 2.17/2.60 substitution1:
% 2.17/2.60 X := X
% 2.17/2.60 Y := addition( Y, Z )
% 2.17/2.60 end
% 2.17/2.60
% 2.17/2.60 subsumption: (228) {G3,W7,D4,L1,V3,M1} P(1,217) { leq( X, addition(
% 2.17/2.60 addition( X, Y ), Z ) ) }.
% 2.17/2.60 parent0: (11078) {G1,W7,D4,L1,V3,M1} { leq( X, addition( addition( X, Y )
% 2.17/2.60 , Z ) ) }.
% 2.17/2.60 substitution0:
% 2.17/2.60 X := X
% 2.17/2.60 Y := Y
% 2.17/2.60 Z := Z
% 2.17/2.60 end
% 2.17/2.60 permutation0:
% 2.17/2.60 0 ==> 0
% 2.17/2.60 end
% 2.17/2.60
% 2.17/2.60 paramod: (11079) {G1,W5,D3,L1,V2,M1} { leq( X, addition( Y, X ) ) }.
% 2.17/2.60 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 2.17/2.60 }.
% 2.17/2.60 parent1[0; 2]: (217) {G2,W5,D3,L1,V2,M1} P(3,24);q { leq( X, addition( X, Y
% 2.17/2.60 ) ) }.
% 2.17/2.60 substitution0:
% 2.17/2.60 X := X
% 2.17/2.60 Y := Y
% 2.17/2.60 end
% 2.17/2.60 substitution1:
% 2.17/2.60 X := X
% 2.17/2.60 Y := Y
% 2.17/2.60 end
% 2.17/2.60
% 2.17/2.60 subsumption: (229) {G3,W5,D3,L1,V2,M1} P(0,217) { leq( X, addition( Y, X )
% 2.17/2.60 ) }.
% 2.17/2.60 parent0: (11079) {G1,W5,D3,L1,V2,M1} { leq( X, addition( Y, X ) ) }.
% 2.17/2.60 substitution0:
% 2.17/2.60 X := X
% 2.17/2.60 Y := Y
% 2.17/2.60 end
% 2.17/2.60 permutation0:
% 2.17/2.60 0 ==> 0
% 2.17/2.60 end
% 2.17/2.60
% 2.17/2.60 eqswap: (11081) {G1,W11,D4,L1,V3,M1} { addition( addition( Y, Z ), X ) =
% 2.17/2.60 addition( addition( X, Y ), Z ) }.
% 2.17/2.60 parent0[0]: (25) {G1,W11,D4,L1,V3,M1} P(1,0) { addition( addition( X, Y ),
% 2.17/2.60 Z ) = addition( addition( Y, Z ), X ) }.
% 2.17/2.60 substitution0:
% 2.17/2.60 X := X
% 2.17/2.60 Y := Y
% 2.17/2.60 Z := Z
% 2.17/2.60 end
% 2.17/2.60
% 2.17/2.60 paramod: (11082) {G2,W7,D4,L1,V3,M1} { leq( X, addition( addition( X, Y )
% 2.17/2.60 , Z ) ) }.
% 2.17/2.60 parent0[0]: (11081) {G1,W11,D4,L1,V3,M1} { addition( addition( Y, Z ), X )
% 2.17/2.60 = addition( addition( X, Y ), Z ) }.
% 2.17/2.60 parent1[0; 2]: (229) {G3,W5,D3,L1,V2,M1} P(0,217) { leq( X, addition( Y, X
% 2.17/2.60 ) ) }.
% 2.17/2.60 substitution0:
% 2.17/2.60 X := X
% 2.17/2.60 Y := Y
% 2.17/2.60 Z := Z
% 2.17/2.60 end
% 2.17/2.60 substitution1:
% 2.17/2.60 X := X
% 2.17/2.60 Y := addition( Y, Z )
% 2.17/2.60 end
% 2.17/2.60
% 2.17/2.60 paramod: (11083) {G2,W7,D4,L1,V3,M1} { leq( X, addition( addition( Z, X )
% 2.17/2.60 , Y ) ) }.
% 2.17/2.60 parent0[0]: (11081) {G1,W11,D4,L1,V3,M1} { addition( addition( Y, Z ), X )
% 2.17/2.60 = addition( addition( X, Y ), Z ) }.
% 2.17/2.60 parent1[0; 2]: (11082) {G2,W7,D4,L1,V3,M1} { leq( X, addition( addition( X
% 2.17/2.60 , Y ), Z ) ) }.
% 2.17/2.60 substitution0:
% 2.17/2.60 X := Z
% 2.17/2.60 Y := X
% 2.17/2.60 Z := Y
% 2.17/2.60 end
% 2.17/2.60 substitution1:
% 2.17/2.60 X := X
% 2.17/2.60 Y := Y
% 2.17/2.60 Z := Z
% 2.17/2.60 end
% 2.17/2.60
% 2.17/2.60 subsumption: (252) {G4,W7,D4,L1,V3,M1} P(25,229) { leq( Z, addition(
% 2.17/2.60 addition( Y, Z ), X ) ) }.
% 2.17/2.60 parent0: (11083) {G2,W7,D4,L1,V3,M1} { leq( X, addition( addition( Z, X )
% 2.17/2.60 , Y ) ) }.
% 2.17/2.60 substitution0:
% 2.17/2.60 X := Z
% 2.17/2.60 Y := X
% 2.17/2.60 Z := Y
% 2.17/2.60 end
% 2.17/2.60 permutation0:
% 2.17/2.60 0 ==> 0
% 2.17/2.60 end
% 2.17/2.60
% 2.17/2.60 paramod: (11086) {G1,W8,D3,L2,V3,M2} { leq( X, Z ), ! leq( addition( Y, X
% 2.17/2.60 ), Z ) }.
% 2.17/2.60 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 2.17/2.60 ==> Y }.
% 2.17/2.60 parent1[0; 2]: (252) {G4,W7,D4,L1,V3,M1} P(25,229) { leq( Z, addition(
% 2.17/2.60 addition( Y, Z ), X ) ) }.
% 2.17/2.60 substitution0:
% 2.17/2.60 X := addition( Y, X )
% 2.17/2.60 Y := Z
% 2.17/2.60 end
% 2.17/2.60 substitution1:
% 2.17/2.60 X := Z
% 2.17/2.60 Y := Y
% 2.17/2.60 Z := X
% 2.17/2.60 end
% 2.17/2.60
% 2.17/2.60 subsumption: (325) {G5,W8,D3,L2,V3,M2} P(11,252) { leq( Y, Z ), ! leq(
% 2.17/2.60 addition( X, Y ), Z ) }.
% 2.17/2.60 parent0: (11086) {G1,W8,D3,L2,V3,M2} { leq( X, Z ), ! leq( addition( Y, X
% 2.17/2.60 ), Z ) }.
% 2.17/2.60 substitution0:
% 2.17/2.60 X := Y
% 2.17/2.60 Y := X
% 2.17/2.60 Z := Z
% 2.17/2.60 end
% 2.17/2.60 permutation0:
% 2.17/2.60 0 ==> 0
% 2.17/2.60 1 ==> 1
% 2.17/2.60 end
% 2.17/2.60
% 2.17/2.60 paramod: (11091) {G1,W8,D3,L2,V3,M2} { leq( X, Z ), ! leq( addition( X, Y
% 2.17/2.60 ), Z ) }.
% 2.17/2.60 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 2.17/2.60 ==> Y }.
% 2.17/2.60 parent1[0; 2]: (228) {G3,W7,D4,L1,V3,M1} P(1,217) { leq( X, addition(
% 2.17/2.60 addition( X, Y ), Z ) ) }.
% 2.17/2.60 substitution0:
% 2.17/2.60 X := addition( X, Y )
% 2.17/2.60 Y := Z
% 2.17/2.60 end
% 2.17/2.60 substitution1:
% 2.17/2.60 X := X
% 2.17/2.60 Y := Y
% 2.17/2.60 Z := Z
% 2.17/2.60 end
% 2.17/2.60
% 2.17/2.60 subsumption: (335) {G4,W8,D3,L2,V3,M2} P(11,228) { leq( X, Z ), ! leq(
% 2.17/2.60 addition( X, Y ), Z ) }.
% 2.17/2.60 parent0: (11091) {G1,W8,D3,L2,V3,M2} { leq( X, Z ), ! leq( addition( X, Y
% 2.17/2.60 ), Z ) }.
% 2.17/2.60 substitution0:
% 2.17/2.60 X := X
% 2.17/2.60 Y := Y
% 2.17/2.60 Z := Z
% 2.17/2.60 end
% 2.17/2.60 permutation0:
% 2.17/2.60 0 ==> 0
% 2.17/2.60 1 ==> 1
% 2.17/2.60 end
% 2.17/2.60
% 2.17/2.60 paramod: (11096) {G2,W8,D3,L2,V3,M2} { leq( X, addition( Y, Z ) ), ! leq(
% 2.17/2.60 X, Z ) }.
% 2.17/2.60 parent0[0]: (35) {G1,W12,D4,L2,V3,M2} P(11,1) { addition( addition( Z, X )
% 2.17/2.60 , Y ) ==> addition( Z, Y ), ! leq( X, Y ) }.
% 2.17/2.60 parent1[0; 2]: (252) {G4,W7,D4,L1,V3,M1} P(25,229) { leq( Z, addition(
% 2.17/2.60 addition( Y, Z ), X ) ) }.
% 2.17/2.60 substitution0:
% 2.17/2.60 X := X
% 2.17/2.60 Y := Z
% 2.17/2.60 Z := Y
% 2.17/2.60 end
% 2.17/2.60 substitution1:
% 2.17/2.60 X := Z
% 2.17/2.60 Y := Y
% 2.17/2.60 Z := X
% 2.17/2.60 end
% 2.17/2.60
% 2.17/2.60 subsumption: (508) {G5,W8,D3,L2,V3,M2} P(35,252) { leq( Y, addition( X, Z )
% 2.17/2.60 ), ! leq( Y, Z ) }.
% 2.17/2.60 parent0: (11096) {G2,W8,D3,L2,V3,M2} { leq( X, addition( Y, Z ) ), ! leq(
% 2.17/2.60 X, Z ) }.
% 2.17/2.60 substitution0:
% 2.17/2.60 X := Y
% 2.17/2.60 Y := X
% 2.17/2.60 Z := Z
% 2.17/2.60 end
% 2.17/2.60 permutation0:
% 2.17/2.60 0 ==> 0
% 2.17/2.60 1 ==> 1
% 2.17/2.60 end
% 2.17/2.60
% 2.17/2.60 paramod: (11100) {G2,W9,D2,L3,V3,M3} { leq( X, Y ), ! leq( Z, Y ), ! leq(
% 2.17/2.60 X, Z ) }.
% 2.17/2.60 parent0[0]: (37) {G1,W8,D3,L2,V2,M2} P(11,0) { addition( Y, X ) ==> Y, !
% 2.17/2.60 leq( X, Y ) }.
% 2.17/2.60 parent1[0; 2]: (508) {G5,W8,D3,L2,V3,M2} P(35,252) { leq( Y, addition( X, Z
% 2.17/2.60 ) ), ! leq( Y, Z ) }.
% 2.17/2.60 substitution0:
% 2.17/2.60 X := Z
% 2.17/2.60 Y := Y
% 2.17/2.60 end
% 2.17/2.60 substitution1:
% 2.17/2.60 X := Y
% 2.17/2.60 Y := X
% 2.17/2.60 Z := Z
% 2.17/2.60 end
% 2.17/2.60
% 2.17/2.60 subsumption: (570) {G6,W9,D2,L3,V3,M3} P(37,508) { leq( Z, X ), ! leq( Z, Y
% 2.17/2.60 ), ! leq( Y, X ) }.
% 2.17/2.60 parent0: (11100) {G2,W9,D2,L3,V3,M3} { leq( X, Y ), ! leq( Z, Y ), ! leq(
% 2.17/2.60 X, Z ) }.
% 2.17/2.60 substitution0:
% 2.17/2.60 X := Z
% 2.17/2.60 Y := X
% 2.17/2.60 Z := Y
% 2.17/2.60 end
% 2.17/2.60 permutation0:
% 2.17/2.60 0 ==> 0
% 2.17/2.60 1 ==> 2
% 2.17/2.60 2 ==> 1
% 2.17/2.60 end
% 2.17/2.60
% 2.17/2.60 resolution: (11102) {G1,W4,D3,L1,V1,M1} { leq( one, star( X ) ) }.
% 2.17/2.60 parent0[1]: (335) {G4,W8,D3,L2,V3,M2} P(11,228) { leq( X, Z ), ! leq(
% 2.17/2.60 addition( X, Y ), Z ) }.
% 2.17/2.60 parent1[0]: (14) {G0,W9,D5,L1,V1,M1} I { leq( addition( one, multiplication
% 2.17/2.60 ( star( X ), X ) ), star( X ) ) }.
% 2.17/2.60 substitution0:
% 2.17/2.60 X := one
% 2.17/2.60 Y := multiplication( star( X ), X )
% 2.17/2.60 Z := star( X )
% 2.17/2.60 end
% 2.17/2.60 substitution1:
% 2.17/2.60 X := X
% 2.17/2.60 end
% 2.17/2.60
% 2.17/2.60 subsumption: (646) {G5,W4,D3,L1,V1,M1} R(335,14) { leq( one, star( X ) )
% 2.17/2.60 }.
% 2.17/2.60 parent0: (11102) {G1,W4,D3,L1,V1,M1} { leq( one, star( X ) ) }.
% 2.17/2.60 substitution0:
% 2.17/2.60 X := X
% 2.17/2.60 end
% 2.17/2.60 permutation0:
% 2.17/2.60 0 ==> 0
% 2.17/2.60 end
% 2.17/2.60
% 2.17/2.60 eqswap: (11103) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X, Y
% 2.17/2.60 ) }.
% 2.17/2.60 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 2.17/2.60 ==> Y }.
% 2.17/2.60 substitution0:
% 2.17/2.60 X := X
% 2.17/2.60 Y := Y
% 2.17/2.60 end
% 2.17/2.60
% 2.17/2.60 resolution: (11104) {G1,W7,D4,L1,V1,M1} { star( X ) ==> addition( one,
% 2.17/2.60 star( X ) ) }.
% 2.17/2.60 parent0[1]: (11103) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X
% 2.17/2.60 , Y ) }.
% 2.17/2.60 parent1[0]: (646) {G5,W4,D3,L1,V1,M1} R(335,14) { leq( one, star( X ) ) }.
% 2.17/2.60 substitution0:
% 2.17/2.60 X := one
% 2.17/2.60 Y := star( X )
% 2.17/2.60 end
% 2.17/2.60 substitution1:
% 2.17/2.60 X := X
% 2.17/2.60 end
% 2.17/2.60
% 2.17/2.60 eqswap: (11105) {G1,W7,D4,L1,V1,M1} { addition( one, star( X ) ) ==> star
% 2.17/2.60 ( X ) }.
% 2.17/2.60 parent0[0]: (11104) {G1,W7,D4,L1,V1,M1} { star( X ) ==> addition( one,
% 2.17/2.60 star( X ) ) }.
% 2.17/2.60 substitution0:
% 2.17/2.60 X := X
% 2.17/2.60 end
% 2.17/2.60
% 2.17/2.60 subsumption: (663) {G6,W7,D4,L1,V1,M1} R(646,11) { addition( one, star( X )
% 2.17/2.60 ) ==> star( X ) }.
% 2.17/2.60 parent0: (11105) {G1,W7,D4,L1,V1,M1} { addition( one, star( X ) ) ==> star
% 2.17/2.60 ( X ) }.
% 2.17/2.60 substitution0:
% 2.17/2.60 X := X
% 2.17/2.60 end
% 2.17/2.60 permutation0:
% 2.17/2.60 0 ==> 0
% 2.17/2.60 end
% 2.17/2.60
% 2.17/2.60 resolution: (11106) {G1,W7,D4,L1,V1,M1} { leq( multiplication( X, star( X
% 2.17/2.60 ) ), star( X ) ) }.
% 2.17/2.60 parent0[1]: (325) {G5,W8,D3,L2,V3,M2} P(11,252) { leq( Y, Z ), ! leq(
% 2.17/2.60 addition( X, Y ), Z ) }.
% 2.17/2.60 parent1[0]: (13) {G0,W9,D5,L1,V1,M1} I { leq( addition( one, multiplication
% 2.17/2.60 ( X, star( X ) ) ), star( X ) ) }.
% 2.17/2.60 substitution0:
% 2.17/2.60 X := one
% 2.17/2.60 Y := multiplication( X, star( X ) )
% 2.17/2.60 Z := star( X )
% 2.17/2.60 end
% 2.17/2.60 substitution1:
% 2.17/2.60 X := X
% 2.17/2.60 end
% 2.17/2.60
% 2.17/2.60 subsumption: (825) {G6,W7,D4,L1,V1,M1} R(325,13) { leq( multiplication( X,
% 2.17/2.60 star( X ) ), star( X ) ) }.
% 2.17/2.60 parent0: (11106) {G1,W7,D4,L1,V1,M1} { leq( multiplication( X, star( X ) )
% 2.17/2.60 , star( X ) ) }.
% 2.17/2.60 substitution0:
% 2.17/2.60 X := X
% 2.17/2.60 end
% 2.17/2.60 permutation0:
% 2.17/2.60 0 ==> 0
% 2.17/2.60 end
% 2.17/2.60
% 2.17/2.60 resolution: (11107) {G1,W8,D4,L1,V1,M1} { ! leq( addition( X,
% 2.17/2.60 multiplication( a, a ) ), star( a ) ) }.
% 2.17/2.60 parent0[0]: (17) {G0,W6,D3,L1,V0,M1} I { ! leq( multiplication( a, a ),
% 2.17/2.60 star( a ) ) }.
% 2.17/2.60 parent1[0]: (325) {G5,W8,D3,L2,V3,M2} P(11,252) { leq( Y, Z ), ! leq(
% 2.17/2.60 addition( X, Y ), Z ) }.
% 2.17/2.60 substitution0:
% 2.17/2.60 end
% 2.17/2.60 substitution1:
% 2.17/2.60 X := X
% 2.17/2.60 Y := multiplication( a, a )
% 2.17/2.60 Z := star( a )
% 2.17/2.60 end
% 2.17/2.60
% 2.17/2.60 subsumption: (828) {G6,W8,D4,L1,V1,M1} R(325,17) { ! leq( addition( X,
% 2.17/2.60 multiplication( a, a ) ), star( a ) ) }.
% 2.17/2.60 parent0: (11107) {G1,W8,D4,L1,V1,M1} { ! leq( addition( X, multiplication
% 2.17/2.60 ( a, a ) ), star( a ) ) }.
% 2.17/2.60 substitution0:
% 2.17/2.60 X := X
% 2.17/2.60 end
% 2.17/2.60 permutation0:
% 2.17/2.60 0 ==> 0
% 2.17/2.60 end
% 2.17/2.60
% 2.17/2.60 eqswap: (11109) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Z ) ==>
% 2.17/2.60 multiplication( X, addition( Y, Z ) ), leq( multiplication( X, Y ),
% 2.17/2.60 multiplication( X, Z ) ) }.
% 2.17/2.60 parent0[0]: (59) {G1,W16,D4,L2,V3,M2} P(7,12) { ! multiplication( X,
% 2.17/2.60 addition( Y, Z ) ) ==> multiplication( X, Z ), leq( multiplication( X, Y
% 2.17/2.60 ), multiplication( X, Z ) ) }.
% 2.17/2.60 substitution0:
% 2.17/2.60 X := X
% 2.17/2.60 Y := Y
% 2.17/2.60 Z := Z
% 2.17/2.60 end
% 2.17/2.60
% 2.17/2.60 paramod: (11111) {G2,W17,D4,L2,V2,M2} { ! multiplication( X, star( Y ) )
% 2.17/2.60 ==> multiplication( X, star( Y ) ), leq( multiplication( X, one ),
% 2.17/2.60 multiplication( X, star( Y ) ) ) }.
% 2.17/2.60 parent0[0]: (663) {G6,W7,D4,L1,V1,M1} R(646,11) { addition( one, star( X )
% 2.17/2.60 ) ==> star( X ) }.
% 2.17/2.60 parent1[0; 8]: (11109) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Z ) ==>
% 2.17/2.60 multiplication( X, addition( Y, Z ) ), leq( multiplication( X, Y ),
% 2.17/2.60 multiplication( X, Z ) ) }.
% 2.17/2.60 substitution0:
% 2.17/2.60 X := Y
% 2.17/2.60 end
% 2.17/2.60 substitution1:
% 2.17/2.60 X := X
% 2.17/2.60 Y := one
% 2.17/2.60 Z := star( Y )
% 2.17/2.60 end
% 2.17/2.60
% 2.17/2.60 eqrefl: (11112) {G0,W8,D4,L1,V2,M1} { leq( multiplication( X, one ),
% 2.17/2.60 multiplication( X, star( Y ) ) ) }.
% 2.17/2.60 parent0[0]: (11111) {G2,W17,D4,L2,V2,M2} { ! multiplication( X, star( Y )
% 2.17/2.60 ) ==> multiplication( X, star( Y ) ), leq( multiplication( X, one ),
% 2.17/2.60 multiplication( X, star( Y ) ) ) }.
% 2.17/2.60 substitution0:
% 2.17/2.60 X := X
% 2.17/2.60 Y := Y
% 2.17/2.60 end
% 2.17/2.60
% 2.17/2.60 paramod: (11113) {G1,W6,D4,L1,V2,M1} { leq( X, multiplication( X, star( Y
% 2.17/2.60 ) ) ) }.
% 2.17/2.60 parent0[0]: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 2.17/2.60 parent1[0; 1]: (11112) {G0,W8,D4,L1,V2,M1} { leq( multiplication( X, one )
% 2.17/2.60 , multiplication( X, star( Y ) ) ) }.
% 2.17/2.60 substitution0:
% 2.17/2.60 X := X
% 2.17/2.60 end
% 2.17/2.60 substitution1:
% 2.17/2.60 X := X
% 2.17/2.60 Y := Y
% 2.17/2.60 end
% 2.17/2.60
% 2.17/2.60 subsumption: (1464) {G7,W6,D4,L1,V2,M1} P(663,59);q;d(5) { leq( Y,
% 2.17/2.60 multiplication( Y, star( X ) ) ) }.
% 2.17/2.60 parent0: (11113) {G1,W6,D4,L1,V2,M1} { leq( X, multiplication( X, star( Y
% 2.17/2.60 ) ) ) }.
% 2.17/2.60 substitution0:
% 2.17/2.60 X := Y
% 2.17/2.60 Y := X
% 2.17/2.60 end
% 2.17/2.60 permutation0:
% 2.17/2.60 0 ==> 0
% 2.17/2.60 end
% 2.17/2.60
% 2.17/2.60 paramod: (11115) {G1,W8,D4,L1,V1,M1} { ! leq( multiplication( a, addition
% 2.17/2.60 ( X, a ) ), star( a ) ) }.
% 2.17/2.60 parent0[0]: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 2.17/2.60 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 2.17/2.60 parent1[0; 2]: (828) {G6,W8,D4,L1,V1,M1} R(325,17) { ! leq( addition( X,
% 2.17/2.60 multiplication( a, a ) ), star( a ) ) }.
% 2.17/2.60 substitution0:
% 2.17/2.60 X := a
% 2.17/2.60 Y := X
% 2.17/2.60 Z := a
% 2.17/2.60 end
% 2.17/2.60 substitution1:
% 2.17/2.60 X := multiplication( a, X )
% 2.17/2.60 end
% 2.17/2.60
% 2.17/2.60 subsumption: (3810) {G7,W8,D4,L1,V1,M1} P(7,828) { ! leq( multiplication( a
% 2.17/2.60 , addition( X, a ) ), star( a ) ) }.
% 2.17/2.60 parent0: (11115) {G1,W8,D4,L1,V1,M1} { ! leq( multiplication( a, addition
% 2.17/2.60 ( X, a ) ), star( a ) ) }.
% 2.17/2.60 substitution0:
% 2.17/2.60 X := X
% 2.17/2.60 end
% 2.17/2.60 permutation0:
% 2.17/2.60 0 ==> 0
% 2.17/2.60 end
% 2.17/2.60
% 2.17/2.60 paramod: (11117) {G2,W9,D3,L2,V1,M2} { ! leq( multiplication( a, X ), star
% 2.17/2.60 ( a ) ), ! leq( a, X ) }.
% 2.17/2.60 parent0[0]: (37) {G1,W8,D3,L2,V2,M2} P(11,0) { addition( Y, X ) ==> Y, !
% 2.17/2.60 leq( X, Y ) }.
% 2.17/2.60 parent1[0; 4]: (3810) {G7,W8,D4,L1,V1,M1} P(7,828) { ! leq( multiplication
% 2.17/2.60 ( a, addition( X, a ) ), star( a ) ) }.
% 2.17/2.60 substitution0:
% 2.17/2.60 X := a
% 2.17/2.60 Y := X
% 2.17/2.60 end
% 2.17/2.60 substitution1:
% 2.17/2.60 X := X
% 2.17/2.60 end
% 2.17/2.60
% 2.17/2.60 subsumption: (3844) {G8,W9,D3,L2,V1,M2} P(37,3810) { ! leq( multiplication
% 2.17/2.60 ( a, X ), star( a ) ), ! leq( a, X ) }.
% 2.17/2.60 parent0: (11117) {G2,W9,D3,L2,V1,M2} { ! leq( multiplication( a, X ), star
% 2.17/2.60 ( a ) ), ! leq( a, X ) }.
% 2.17/2.60 substitution0:
% 2.17/2.60 X := X
% 2.17/2.60 end
% 2.17/2.60 permutation0:
% 2.17/2.60 0 ==> 0
% 2.17/2.60 1 ==> 1
% 2.17/2.60 end
% 2.17/2.60
% 2.17/2.60 resolution: (11119) {G7,W12,D3,L3,V2,M3} { ! leq( multiplication( a, X ),
% 2.17/2.60 star( a ) ), ! leq( a, Y ), ! leq( Y, X ) }.
% 2.17/2.60 parent0[1]: (3844) {G8,W9,D3,L2,V1,M2} P(37,3810) { ! leq( multiplication(
% 2.17/2.60 a, X ), star( a ) ), ! leq( a, X ) }.
% 2.17/2.60 parent1[0]: (570) {G6,W9,D2,L3,V3,M3} P(37,508) { leq( Z, X ), ! leq( Z, Y
% 2.17/2.60 ), ! leq( Y, X ) }.
% 2.17/2.60 substitution0:
% 2.17/2.60 X := X
% 2.17/2.60 end
% 2.17/2.60 substitution1:
% 2.17/2.60 X := X
% 2.17/2.60 Y := Y
% 2.17/2.60 Z := a
% 2.17/2.60 end
% 2.17/2.60
% 2.17/2.60 subsumption: (10812) {G9,W12,D3,L3,V2,M3} R(3844,570) { ! leq(
% 2.17/2.60 multiplication( a, X ), star( a ) ), ! leq( a, Y ), ! leq( Y, X ) }.
% 2.17/2.60 parent0: (11119) {G7,W12,D3,L3,V2,M3} { ! leq( multiplication( a, X ),
% 2.17/2.60 star( a ) ), ! leq( a, Y ), ! leq( Y, X ) }.
% 2.17/2.60 substitution0:
% 2.17/2.60 X := X
% 2.17/2.60 Y := Y
% 2.17/2.60 end
% 2.17/2.60 permutation0:
% 2.17/2.60 0 ==> 0
% 2.17/2.60 1 ==> 1
% 2.17/2.60 2 ==> 2
% 2.17/2.60 end
% 2.17/2.60
% 2.17/2.60 factor: (11123) {G9,W13,D4,L2,V0,M2} { ! leq( multiplication( a, star( a )
% 2.17/2.60 ), star( a ) ), ! leq( a, multiplication( a, star( a ) ) ) }.
% 2.17/2.60 parent0[0, 2]: (10812) {G9,W12,D3,L3,V2,M3} R(3844,570) { ! leq(
% 2.17/2.60 multiplication( a, X ), star( a ) ), ! leq( a, Y ), ! leq( Y, X ) }.
% 2.17/2.60 substitution0:
% 2.17/2.60 X := star( a )
% 2.17/2.60 Y := multiplication( a, star( a ) )
% 2.17/2.60 end
% 2.17/2.60
% 2.17/2.60 resolution: (11125) {G7,W6,D4,L1,V0,M1} { ! leq( a, multiplication( a,
% 2.17/2.60 star( a ) ) ) }.
% 2.17/2.60 parent0[0]: (11123) {G9,W13,D4,L2,V0,M2} { ! leq( multiplication( a, star
% 2.17/2.60 ( a ) ), star( a ) ), ! leq( a, multiplication( a, star( a ) ) ) }.
% 2.17/2.60 parent1[0]: (825) {G6,W7,D4,L1,V1,M1} R(325,13) { leq( multiplication( X,
% 2.17/2.60 star( X ) ), star( X ) ) }.
% 2.17/2.60 substitution0:
% 2.17/2.60 end
% 2.17/2.60 substitution1:
% 2.17/2.60 X := a
% 2.17/2.60 end
% 2.17/2.60
% 2.17/2.60 subsumption: (10854) {G10,W6,D4,L1,V0,M1} F(10812);r(825) { ! leq( a,
% 2.17/2.60 multiplication( a, star( a ) ) ) }.
% 2.17/2.60 parent0: (11125) {G7,W6,D4,L1,V0,M1} { ! leq( a, multiplication( a, star(
% 2.17/2.60 a ) ) ) }.
% 2.17/2.60 substitution0:
% 2.17/2.60 end
% 2.17/2.60 permutation0:
% 2.17/2.60 0 ==> 0
% 2.17/2.60 end
% 2.17/2.60
% 2.17/2.60 resolution: (11126) {G8,W0,D0,L0,V0,M0} { }.
% 2.17/2.60 parent0[0]: (10854) {G10,W6,D4,L1,V0,M1} F(10812);r(825) { ! leq( a,
% 2.17/2.60 multiplication( a, star( a ) ) ) }.
% 2.17/2.60 parent1[0]: (1464) {G7,W6,D4,L1,V2,M1} P(663,59);q;d(5) { leq( Y,
% 2.17/2.60 multiplication( Y, star( X ) ) ) }.
% 2.17/2.60 substitution0:
% 2.17/2.60 end
% 2.17/2.60 substitution1:
% 2.17/2.60 X := a
% 2.17/2.60 Y := a
% 2.17/2.60 end
% 2.17/2.60
% 2.17/2.60 subsumption: (10890) {G11,W0,D0,L0,V0,M0} S(10854);r(1464) { }.
% 2.17/2.60 parent0: (11126) {G8,W0,D0,L0,V0,M0} { }.
% 2.17/2.60 substitution0:
% 2.17/2.60 end
% 2.17/2.60 permutation0:
% 2.17/2.60 end
% 2.17/2.60
% 2.17/2.60 Proof check complete!
% 2.17/2.60
% 2.17/2.60 Memory use:
% 2.17/2.60
% 2.17/2.60 space for terms: 152386
% 2.17/2.60 space for clauses: 516200
% 2.17/2.60
% 2.17/2.60
% 2.17/2.60 clauses generated: 136048
% 2.17/2.60 clauses kept: 10891
% 2.17/2.60 clauses selected: 701
% 2.17/2.60 clauses deleted: 113
% 2.17/2.60 clauses inuse deleted: 24
% 2.17/2.60
% 2.17/2.60 subsentry: 595095
% 2.17/2.60 literals s-matched: 340133
% 2.17/2.60 literals matched: 334477
% 2.17/2.60 full subsumption: 121076
% 2.17/2.60
% 2.17/2.60 checksum: -1172794790
% 2.17/2.60
% 2.17/2.60
% 2.17/2.60 Bliksem ended
%------------------------------------------------------------------------------