TSTP Solution File: KLE048+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : KLE048+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Sun Jul 17 01:36:53 EDT 2022
% Result : Theorem 2.35s 2.72s
% Output : Refutation 2.35s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : KLE048+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.14 % Command : bliksem %s
% 0.14/0.36 % Computer : n010.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 12:13:53 EDT 2022
% 0.14/0.36 % CPUTime :
% 2.35/2.72 *** allocated 10000 integers for termspace/termends
% 2.35/2.72 *** allocated 10000 integers for clauses
% 2.35/2.72 *** allocated 10000 integers for justifications
% 2.35/2.72 Bliksem 1.12
% 2.35/2.72
% 2.35/2.72
% 2.35/2.72 Automatic Strategy Selection
% 2.35/2.72
% 2.35/2.72
% 2.35/2.72 Clauses:
% 2.35/2.72
% 2.35/2.72 { addition( X, Y ) = addition( Y, X ) }.
% 2.35/2.72 { addition( Z, addition( Y, X ) ) = addition( addition( Z, Y ), X ) }.
% 2.35/2.72 { addition( X, zero ) = X }.
% 2.35/2.72 { addition( X, X ) = X }.
% 2.35/2.72 { multiplication( X, multiplication( Y, Z ) ) = multiplication(
% 2.35/2.72 multiplication( X, Y ), Z ) }.
% 2.35/2.72 { multiplication( X, one ) = X }.
% 2.35/2.72 { multiplication( one, X ) = X }.
% 2.35/2.72 { multiplication( X, addition( Y, Z ) ) = addition( multiplication( X, Y )
% 2.35/2.72 , multiplication( X, Z ) ) }.
% 2.35/2.72 { multiplication( addition( X, Y ), Z ) = addition( multiplication( X, Z )
% 2.35/2.72 , multiplication( Y, Z ) ) }.
% 2.35/2.72 { multiplication( X, zero ) = zero }.
% 2.35/2.72 { multiplication( zero, X ) = zero }.
% 2.35/2.72 { ! leq( X, Y ), addition( X, Y ) = Y }.
% 2.35/2.72 { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 2.35/2.72 { leq( addition( one, multiplication( X, star( X ) ) ), star( X ) ) }.
% 2.35/2.72 { leq( addition( one, multiplication( star( X ), X ) ), star( X ) ) }.
% 2.35/2.72 { ! leq( addition( multiplication( X, Y ), Z ), Y ), leq( multiplication(
% 2.35/2.72 star( X ), Z ), Y ) }.
% 2.35/2.72 { ! leq( addition( multiplication( X, Y ), Z ), X ), leq( multiplication( Z
% 2.35/2.72 , star( Y ) ), X ) }.
% 2.35/2.72 { ! test( X ), complement( skol1( X ), X ) }.
% 2.35/2.72 { ! complement( Y, X ), test( X ) }.
% 2.35/2.72 { ! complement( Y, X ), multiplication( X, Y ) = zero }.
% 2.35/2.72 { ! complement( Y, X ), alpha1( X, Y ) }.
% 2.35/2.72 { ! multiplication( X, Y ) = zero, ! alpha1( X, Y ), complement( Y, X ) }.
% 2.35/2.72 { ! alpha1( X, Y ), multiplication( Y, X ) = zero }.
% 2.35/2.72 { ! alpha1( X, Y ), addition( X, Y ) = one }.
% 2.35/2.72 { ! multiplication( Y, X ) = zero, ! addition( X, Y ) = one, alpha1( X, Y )
% 2.35/2.72 }.
% 2.35/2.72 { ! test( X ), ! c( X ) = Y, complement( X, Y ) }.
% 2.35/2.72 { ! test( X ), ! complement( X, Y ), c( X ) = Y }.
% 2.35/2.72 { test( X ), c( X ) = zero }.
% 2.35/2.72 { test( skol2 ) }.
% 2.35/2.72 { ! star( skol2 ) = one }.
% 2.35/2.72
% 2.35/2.72 percentage equality = 0.469388, percentage horn = 0.966667
% 2.35/2.72 This is a problem with some equality
% 2.35/2.72
% 2.35/2.72
% 2.35/2.72
% 2.35/2.72 Options Used:
% 2.35/2.72
% 2.35/2.72 useres = 1
% 2.35/2.72 useparamod = 1
% 2.35/2.72 useeqrefl = 1
% 2.35/2.72 useeqfact = 1
% 2.35/2.72 usefactor = 1
% 2.35/2.72 usesimpsplitting = 0
% 2.35/2.72 usesimpdemod = 5
% 2.35/2.72 usesimpres = 3
% 2.35/2.72
% 2.35/2.72 resimpinuse = 1000
% 2.35/2.72 resimpclauses = 20000
% 2.35/2.72 substype = eqrewr
% 2.35/2.72 backwardsubs = 1
% 2.35/2.72 selectoldest = 5
% 2.35/2.72
% 2.35/2.72 litorderings [0] = split
% 2.35/2.72 litorderings [1] = extend the termordering, first sorting on arguments
% 2.35/2.72
% 2.35/2.72 termordering = kbo
% 2.35/2.72
% 2.35/2.72 litapriori = 0
% 2.35/2.72 termapriori = 1
% 2.35/2.72 litaposteriori = 0
% 2.35/2.72 termaposteriori = 0
% 2.35/2.72 demodaposteriori = 0
% 2.35/2.72 ordereqreflfact = 0
% 2.35/2.72
% 2.35/2.72 litselect = negord
% 2.35/2.72
% 2.35/2.72 maxweight = 15
% 2.35/2.72 maxdepth = 30000
% 2.35/2.72 maxlength = 115
% 2.35/2.72 maxnrvars = 195
% 2.35/2.72 excuselevel = 1
% 2.35/2.72 increasemaxweight = 1
% 2.35/2.72
% 2.35/2.72 maxselected = 10000000
% 2.35/2.72 maxnrclauses = 10000000
% 2.35/2.72
% 2.35/2.72 showgenerated = 0
% 2.35/2.72 showkept = 0
% 2.35/2.72 showselected = 0
% 2.35/2.72 showdeleted = 0
% 2.35/2.72 showresimp = 1
% 2.35/2.72 showstatus = 2000
% 2.35/2.72
% 2.35/2.72 prologoutput = 0
% 2.35/2.72 nrgoals = 5000000
% 2.35/2.72 totalproof = 1
% 2.35/2.72
% 2.35/2.72 Symbols occurring in the translation:
% 2.35/2.72
% 2.35/2.72 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 2.35/2.72 . [1, 2] (w:1, o:23, a:1, s:1, b:0),
% 2.35/2.72 ! [4, 1] (w:0, o:14, a:1, s:1, b:0),
% 2.35/2.72 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 2.35/2.72 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 2.35/2.72 addition [37, 2] (w:1, o:47, a:1, s:1, b:0),
% 2.35/2.72 zero [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 2.35/2.72 multiplication [40, 2] (w:1, o:49, a:1, s:1, b:0),
% 2.35/2.72 one [41, 0] (w:1, o:10, a:1, s:1, b:0),
% 2.35/2.72 leq [42, 2] (w:1, o:48, a:1, s:1, b:0),
% 2.35/2.72 star [43, 1] (w:1, o:19, a:1, s:1, b:0),
% 2.35/2.72 test [45, 1] (w:1, o:21, a:1, s:1, b:0),
% 2.35/2.72 complement [47, 2] (w:1, o:50, a:1, s:1, b:0),
% 2.35/2.72 c [48, 1] (w:1, o:22, a:1, s:1, b:0),
% 2.35/2.72 alpha1 [49, 2] (w:1, o:51, a:1, s:1, b:1),
% 2.35/2.72 skol1 [50, 1] (w:1, o:20, a:1, s:1, b:1),
% 2.35/2.72 skol2 [51, 0] (w:1, o:13, a:1, s:1, b:1).
% 2.35/2.72
% 2.35/2.72
% 2.35/2.72 Starting Search:
% 2.35/2.72
% 2.35/2.72 *** allocated 15000 integers for clauses
% 2.35/2.72 *** allocated 22500 integers for clauses
% 2.35/2.72 *** allocated 33750 integers for clauses
% 2.35/2.72 *** allocated 50625 integers for clauses
% 2.35/2.72 *** allocated 15000 integers for termspace/termends
% 2.35/2.72 *** allocated 75937 integers for clauses
% 2.35/2.72 Resimplifying inuse:
% 2.35/2.72 Done
% 2.35/2.72
% 2.35/2.72 *** allocated 22500 integers for termspace/termends
% 2.35/2.72 *** allocated 113905 integers for clauses
% 2.35/2.72 *** allocated 33750 integers for termspace/termends
% 2.35/2.72
% 2.35/2.72 Intermediate Status:
% 2.35/2.72 Generated: 11354
% 2.35/2.72 Kept: 2102
% 2.35/2.72 Inuse: 224
% 2.35/2.72 Deleted: 55
% 2.35/2.72 Deletedinuse: 27
% 2.35/2.72
% 2.35/2.72 Resimplifying inuse:
% 2.35/2.72 Done
% 2.35/2.72
% 2.35/2.72 *** allocated 170857 integers for clauses
% 2.35/2.72 *** allocated 50625 integers for termspace/termends
% 2.35/2.72 Resimplifying inuse:
% 2.35/2.72 Done
% 2.35/2.72
% 2.35/2.72 *** allocated 256285 integers for clauses
% 2.35/2.72
% 2.35/2.72 Intermediate Status:
% 2.35/2.72 Generated: 25155
% 2.35/2.72 Kept: 4105
% 2.35/2.72 Inuse: 393
% 2.35/2.72 Deleted: 136
% 2.35/2.72 Deletedinuse: 50
% 2.35/2.72
% 2.35/2.72 Resimplifying inuse:
% 2.35/2.72 Done
% 2.35/2.72
% 2.35/2.72 *** allocated 75937 integers for termspace/termends
% 2.35/2.72 Resimplifying inuse:
% 2.35/2.72 Done
% 2.35/2.72
% 2.35/2.72 *** allocated 384427 integers for clauses
% 2.35/2.72 *** allocated 113905 integers for termspace/termends
% 2.35/2.72
% 2.35/2.72 Intermediate Status:
% 2.35/2.72 Generated: 40072
% 2.35/2.72 Kept: 6106
% 2.35/2.72 Inuse: 489
% 2.35/2.72 Deleted: 241
% 2.35/2.72 Deletedinuse: 99
% 2.35/2.72
% 2.35/2.72 Resimplifying inuse:
% 2.35/2.72 Done
% 2.35/2.72
% 2.35/2.72 Resimplifying inuse:
% 2.35/2.72 Done
% 2.35/2.72
% 2.35/2.72 *** allocated 576640 integers for clauses
% 2.35/2.72
% 2.35/2.72 Intermediate Status:
% 2.35/2.72 Generated: 53542
% 2.35/2.72 Kept: 8106
% 2.35/2.72 Inuse: 623
% 2.35/2.72 Deleted: 276
% 2.35/2.72 Deletedinuse: 107
% 2.35/2.72
% 2.35/2.72 Resimplifying inuse:
% 2.35/2.72 Done
% 2.35/2.72
% 2.35/2.72 Resimplifying inuse:
% 2.35/2.72 Done
% 2.35/2.72
% 2.35/2.72 *** allocated 170857 integers for termspace/termends
% 2.35/2.72
% 2.35/2.72 Intermediate Status:
% 2.35/2.72 Generated: 68469
% 2.35/2.72 Kept: 10126
% 2.35/2.72 Inuse: 699
% 2.35/2.72 Deleted: 284
% 2.35/2.72 Deletedinuse: 110
% 2.35/2.72
% 2.35/2.72 Resimplifying inuse:
% 2.35/2.72 Done
% 2.35/2.72
% 2.35/2.72
% 2.35/2.72 Bliksems!, er is een bewijs:
% 2.35/2.72 % SZS status Theorem
% 2.35/2.72 % SZS output start Refutation
% 2.35/2.72
% 2.35/2.72 (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X ) }.
% 2.35/2.72 (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) ) ==> addition(
% 2.35/2.72 addition( Z, Y ), X ) }.
% 2.35/2.72 (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 2.35/2.72 (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 2.35/2.72 (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 2.35/2.72 (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ),
% 2.35/2.72 multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 2.35/2.72 (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y ) ==> Y }.
% 2.35/2.72 (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X, Y ) }.
% 2.35/2.72 (14) {G0,W9,D5,L1,V1,M1} I { leq( addition( one, multiplication( star( X )
% 2.35/2.72 , X ) ), star( X ) ) }.
% 2.35/2.72 (15) {G0,W13,D4,L2,V3,M2} I { ! leq( addition( multiplication( X, Y ), Z )
% 2.35/2.72 , Y ), leq( multiplication( star( X ), Z ), Y ) }.
% 2.35/2.72 (17) {G0,W6,D3,L2,V1,M2} I { ! test( X ), complement( skol1( X ), X ) }.
% 2.35/2.72 (20) {G0,W6,D2,L2,V2,M2} I { ! complement( Y, X ), alpha1( X, Y ) }.
% 2.35/2.72 (23) {G0,W8,D3,L2,V2,M2} I { ! alpha1( X, Y ), addition( X, Y ) ==> one }.
% 2.35/2.72 (28) {G0,W2,D2,L1,V0,M1} I { test( skol2 ) }.
% 2.35/2.72 (29) {G0,W4,D3,L1,V0,M1} I { ! star( skol2 ) ==> one }.
% 2.35/2.72 (33) {G1,W9,D4,L1,V2,M1} P(3,1) { addition( addition( Y, X ), X ) ==>
% 2.35/2.72 addition( Y, X ) }.
% 2.35/2.72 (80) {G1,W4,D3,L1,V0,M1} R(17,28) { complement( skol1( skol2 ), skol2 ) }.
% 2.35/2.72 (81) {G2,W4,D3,L1,V0,M1} R(80,20) { alpha1( skol2, skol1( skol2 ) ) }.
% 2.35/2.72 (94) {G1,W8,D3,L2,V2,M2} P(11,0) { addition( Y, X ) ==> Y, ! leq( X, Y )
% 2.35/2.72 }.
% 2.35/2.72 (164) {G1,W3,D2,L1,V1,M1} R(12,3) { leq( X, X ) }.
% 2.35/2.72 (167) {G1,W16,D4,L2,V3,M2} P(8,12) { ! multiplication( addition( X, Z ), Y
% 2.35/2.72 ) ==> multiplication( Z, Y ), leq( multiplication( X, Y ),
% 2.35/2.72 multiplication( Z, Y ) ) }.
% 2.35/2.72 (169) {G1,W14,D4,L2,V3,M2} P(1,12) { ! addition( addition( X, Y ), Z ) ==>
% 2.35/2.72 addition( Y, Z ), leq( X, addition( Y, Z ) ) }.
% 2.35/2.72 (217) {G1,W9,D5,L1,V1,M1} P(0,14) { leq( addition( multiplication( star( X
% 2.35/2.72 ), X ), one ), star( X ) ) }.
% 2.35/2.72 (235) {G1,W15,D5,L2,V3,M2} R(15,11) { ! leq( addition( multiplication( X, Y
% 2.35/2.72 ), Z ), Y ), addition( multiplication( star( X ), Z ), Y ) ==> Y }.
% 2.35/2.72 (237) {G1,W14,D4,L3,V3,M3} P(11,15) { ! leq( Z, Y ), leq( multiplication(
% 2.35/2.72 star( X ), Z ), Y ), ! leq( multiplication( X, Y ), Z ) }.
% 2.35/2.72 (414) {G3,W6,D4,L1,V0,M1} R(23,81) { addition( skol2, skol1( skol2 ) ) ==>
% 2.35/2.72 one }.
% 2.35/2.72 (2270) {G4,W6,D4,L1,V0,M1} P(414,0) { addition( skol1( skol2 ), skol2 ) ==>
% 2.35/2.72 one }.
% 2.35/2.72 (2311) {G5,W5,D3,L1,V0,M1} P(2270,33) { addition( one, skol2 ) ==> one }.
% 2.35/2.72 (2376) {G6,W5,D3,L1,V0,M1} P(2311,0) { addition( skol2, one ) ==> one }.
% 2.35/2.72 (6098) {G7,W5,D3,L1,V1,M1} P(2376,167);q;d(6) { leq( multiplication( skol2
% 2.35/2.72 , X ), X ) }.
% 2.35/2.72 (6190) {G7,W5,D3,L1,V1,M1} P(2376,169);q { leq( skol2, addition( one, X ) )
% 2.35/2.72 }.
% 2.35/2.72 (6424) {G8,W6,D2,L2,V1,M2} P(11,6190) { leq( skol2, X ), ! leq( one, X )
% 2.35/2.72 }.
% 2.35/2.72 (10137) {G2,W7,D3,L2,V1,M2} P(235,217);d(5);d(3) { leq( one, star( X ) ), !
% 2.35/2.72 leq( X, one ) }.
% 2.35/2.72 (10180) {G9,W4,D3,L1,V0,M1} R(10137,6424);r(164) { leq( one, star( skol2 )
% 2.35/2.72 ) }.
% 2.35/2.72 (10299) {G10,W7,D4,L1,V0,M1} R(10180,11) { addition( one, star( skol2 ) )
% 2.35/2.72 ==> star( skol2 ) }.
% 2.35/2.72 (10364) {G8,W6,D4,L1,V1,M1} R(237,6098);r(164) { leq( multiplication( star
% 2.35/2.72 ( skol2 ), X ), X ) }.
% 2.35/2.72 (10596) {G9,W4,D3,L1,V0,M1} P(5,10364) { leq( star( skol2 ), one ) }.
% 2.35/2.72 (10599) {G11,W0,D0,L0,V0,M0} R(10596,94);d(10299);r(29) { }.
% 2.35/2.72
% 2.35/2.72
% 2.35/2.72 % SZS output end Refutation
% 2.35/2.72 found a proof!
% 2.35/2.72
% 2.35/2.72
% 2.35/2.72 Unprocessed initial clauses:
% 2.35/2.72
% 2.35/2.72 (10601) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X ) }.
% 2.35/2.72 (10602) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) = addition
% 2.35/2.72 ( addition( Z, Y ), X ) }.
% 2.35/2.72 (10603) {G0,W5,D3,L1,V1,M1} { addition( X, zero ) = X }.
% 2.35/2.72 (10604) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 2.35/2.72 (10605) {G0,W11,D4,L1,V3,M1} { multiplication( X, multiplication( Y, Z ) )
% 2.35/2.72 = multiplication( multiplication( X, Y ), Z ) }.
% 2.35/2.72 (10606) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 2.35/2.72 (10607) {G0,W5,D3,L1,V1,M1} { multiplication( one, X ) = X }.
% 2.35/2.72 (10608) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y, Z ) ) =
% 2.35/2.72 addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 2.35/2.72 (10609) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Y ), Z ) =
% 2.35/2.72 addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 2.35/2.72 (10610) {G0,W5,D3,L1,V1,M1} { multiplication( X, zero ) = zero }.
% 2.35/2.72 (10611) {G0,W5,D3,L1,V1,M1} { multiplication( zero, X ) = zero }.
% 2.35/2.72 (10612) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y }.
% 2.35/2.72 (10613) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 2.35/2.72 (10614) {G0,W9,D5,L1,V1,M1} { leq( addition( one, multiplication( X, star
% 2.35/2.72 ( X ) ) ), star( X ) ) }.
% 2.35/2.72 (10615) {G0,W9,D5,L1,V1,M1} { leq( addition( one, multiplication( star( X
% 2.35/2.72 ), X ) ), star( X ) ) }.
% 2.35/2.72 (10616) {G0,W13,D4,L2,V3,M2} { ! leq( addition( multiplication( X, Y ), Z
% 2.35/2.72 ), Y ), leq( multiplication( star( X ), Z ), Y ) }.
% 2.35/2.72 (10617) {G0,W13,D4,L2,V3,M2} { ! leq( addition( multiplication( X, Y ), Z
% 2.35/2.72 ), X ), leq( multiplication( Z, star( Y ) ), X ) }.
% 2.35/2.72 (10618) {G0,W6,D3,L2,V1,M2} { ! test( X ), complement( skol1( X ), X ) }.
% 2.35/2.72 (10619) {G0,W5,D2,L2,V2,M2} { ! complement( Y, X ), test( X ) }.
% 2.35/2.72 (10620) {G0,W8,D3,L2,V2,M2} { ! complement( Y, X ), multiplication( X, Y )
% 2.35/2.72 = zero }.
% 2.35/2.72 (10621) {G0,W6,D2,L2,V2,M2} { ! complement( Y, X ), alpha1( X, Y ) }.
% 2.35/2.72 (10622) {G0,W11,D3,L3,V2,M3} { ! multiplication( X, Y ) = zero, ! alpha1(
% 2.35/2.72 X, Y ), complement( Y, X ) }.
% 2.35/2.72 (10623) {G0,W8,D3,L2,V2,M2} { ! alpha1( X, Y ), multiplication( Y, X ) =
% 2.35/2.72 zero }.
% 2.35/2.72 (10624) {G0,W8,D3,L2,V2,M2} { ! alpha1( X, Y ), addition( X, Y ) = one }.
% 2.35/2.72 (10625) {G0,W13,D3,L3,V2,M3} { ! multiplication( Y, X ) = zero, ! addition
% 2.35/2.72 ( X, Y ) = one, alpha1( X, Y ) }.
% 2.35/2.72 (10626) {G0,W9,D3,L3,V2,M3} { ! test( X ), ! c( X ) = Y, complement( X, Y
% 2.35/2.72 ) }.
% 2.35/2.72 (10627) {G0,W9,D3,L3,V2,M3} { ! test( X ), ! complement( X, Y ), c( X ) =
% 2.35/2.72 Y }.
% 2.35/2.72 (10628) {G0,W6,D3,L2,V1,M2} { test( X ), c( X ) = zero }.
% 2.35/2.72 (10629) {G0,W2,D2,L1,V0,M1} { test( skol2 ) }.
% 2.35/2.72 (10630) {G0,W4,D3,L1,V0,M1} { ! star( skol2 ) = one }.
% 2.35/2.72
% 2.35/2.72
% 2.35/2.72 Total Proof:
% 2.35/2.72
% 2.35/2.72 subsumption: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X
% 2.35/2.72 ) }.
% 2.35/2.72 parent0: (10601) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X )
% 2.35/2.72 }.
% 2.35/2.72 substitution0:
% 2.35/2.72 X := X
% 2.35/2.72 Y := Y
% 2.35/2.72 end
% 2.35/2.72 permutation0:
% 2.35/2.72 0 ==> 0
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 subsumption: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 2.35/2.72 ==> addition( addition( Z, Y ), X ) }.
% 2.35/2.72 parent0: (10602) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) =
% 2.35/2.72 addition( addition( Z, Y ), X ) }.
% 2.35/2.72 substitution0:
% 2.35/2.72 X := X
% 2.35/2.72 Y := Y
% 2.35/2.72 Z := Z
% 2.35/2.72 end
% 2.35/2.72 permutation0:
% 2.35/2.72 0 ==> 0
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 subsumption: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 2.35/2.72 parent0: (10604) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 2.35/2.72 substitution0:
% 2.35/2.72 X := X
% 2.35/2.72 end
% 2.35/2.72 permutation0:
% 2.35/2.72 0 ==> 0
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 subsumption: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 2.35/2.72 parent0: (10606) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 2.35/2.72 substitution0:
% 2.35/2.72 X := X
% 2.35/2.72 end
% 2.35/2.72 permutation0:
% 2.35/2.72 0 ==> 0
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 subsumption: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 2.35/2.72 parent0: (10607) {G0,W5,D3,L1,V1,M1} { multiplication( one, X ) = X }.
% 2.35/2.72 substitution0:
% 2.35/2.72 X := X
% 2.35/2.72 end
% 2.35/2.72 permutation0:
% 2.35/2.72 0 ==> 0
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 eqswap: (10653) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Z ),
% 2.35/2.72 multiplication( Y, Z ) ) = multiplication( addition( X, Y ), Z ) }.
% 2.35/2.72 parent0[0]: (10609) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Y
% 2.35/2.72 ), Z ) = addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 2.35/2.72 substitution0:
% 2.35/2.72 X := X
% 2.35/2.72 Y := Y
% 2.35/2.72 Z := Z
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 subsumption: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z )
% 2.35/2.72 , multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 2.35/2.72 parent0: (10653) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Z ),
% 2.35/2.72 multiplication( Y, Z ) ) = multiplication( addition( X, Y ), Z ) }.
% 2.35/2.72 substitution0:
% 2.35/2.72 X := X
% 2.35/2.72 Y := Y
% 2.35/2.72 Z := Z
% 2.35/2.72 end
% 2.35/2.72 permutation0:
% 2.35/2.72 0 ==> 0
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 subsumption: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 2.35/2.72 ==> Y }.
% 2.35/2.72 parent0: (10612) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y
% 2.35/2.72 }.
% 2.35/2.72 substitution0:
% 2.35/2.72 X := X
% 2.35/2.72 Y := Y
% 2.35/2.72 end
% 2.35/2.72 permutation0:
% 2.35/2.72 0 ==> 0
% 2.35/2.72 1 ==> 1
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 subsumption: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X
% 2.35/2.72 , Y ) }.
% 2.35/2.72 parent0: (10613) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y )
% 2.35/2.72 }.
% 2.35/2.72 substitution0:
% 2.35/2.72 X := X
% 2.35/2.72 Y := Y
% 2.35/2.72 end
% 2.35/2.72 permutation0:
% 2.35/2.72 0 ==> 0
% 2.35/2.72 1 ==> 1
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 subsumption: (14) {G0,W9,D5,L1,V1,M1} I { leq( addition( one,
% 2.35/2.72 multiplication( star( X ), X ) ), star( X ) ) }.
% 2.35/2.72 parent0: (10615) {G0,W9,D5,L1,V1,M1} { leq( addition( one, multiplication
% 2.35/2.72 ( star( X ), X ) ), star( X ) ) }.
% 2.35/2.72 substitution0:
% 2.35/2.72 X := X
% 2.35/2.72 end
% 2.35/2.72 permutation0:
% 2.35/2.72 0 ==> 0
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 subsumption: (15) {G0,W13,D4,L2,V3,M2} I { ! leq( addition( multiplication
% 2.35/2.72 ( X, Y ), Z ), Y ), leq( multiplication( star( X ), Z ), Y ) }.
% 2.35/2.72 parent0: (10616) {G0,W13,D4,L2,V3,M2} { ! leq( addition( multiplication( X
% 2.35/2.72 , Y ), Z ), Y ), leq( multiplication( star( X ), Z ), Y ) }.
% 2.35/2.72 substitution0:
% 2.35/2.72 X := X
% 2.35/2.72 Y := Y
% 2.35/2.72 Z := Z
% 2.35/2.72 end
% 2.35/2.72 permutation0:
% 2.35/2.72 0 ==> 0
% 2.35/2.72 1 ==> 1
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 subsumption: (17) {G0,W6,D3,L2,V1,M2} I { ! test( X ), complement( skol1( X
% 2.35/2.72 ), X ) }.
% 2.35/2.72 parent0: (10618) {G0,W6,D3,L2,V1,M2} { ! test( X ), complement( skol1( X )
% 2.35/2.72 , X ) }.
% 2.35/2.72 substitution0:
% 2.35/2.72 X := X
% 2.35/2.72 end
% 2.35/2.72 permutation0:
% 2.35/2.72 0 ==> 0
% 2.35/2.72 1 ==> 1
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 subsumption: (20) {G0,W6,D2,L2,V2,M2} I { ! complement( Y, X ), alpha1( X,
% 2.35/2.72 Y ) }.
% 2.35/2.72 parent0: (10621) {G0,W6,D2,L2,V2,M2} { ! complement( Y, X ), alpha1( X, Y
% 2.35/2.72 ) }.
% 2.35/2.72 substitution0:
% 2.35/2.72 X := X
% 2.35/2.72 Y := Y
% 2.35/2.72 end
% 2.35/2.72 permutation0:
% 2.35/2.72 0 ==> 0
% 2.35/2.72 1 ==> 1
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 subsumption: (23) {G0,W8,D3,L2,V2,M2} I { ! alpha1( X, Y ), addition( X, Y
% 2.35/2.72 ) ==> one }.
% 2.35/2.72 parent0: (10624) {G0,W8,D3,L2,V2,M2} { ! alpha1( X, Y ), addition( X, Y )
% 2.35/2.72 = one }.
% 2.35/2.72 substitution0:
% 2.35/2.72 X := X
% 2.35/2.72 Y := Y
% 2.35/2.72 end
% 2.35/2.72 permutation0:
% 2.35/2.72 0 ==> 0
% 2.35/2.72 1 ==> 1
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 subsumption: (28) {G0,W2,D2,L1,V0,M1} I { test( skol2 ) }.
% 2.35/2.72 parent0: (10629) {G0,W2,D2,L1,V0,M1} { test( skol2 ) }.
% 2.35/2.72 substitution0:
% 2.35/2.72 end
% 2.35/2.72 permutation0:
% 2.35/2.72 0 ==> 0
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 subsumption: (29) {G0,W4,D3,L1,V0,M1} I { ! star( skol2 ) ==> one }.
% 2.35/2.72 parent0: (10630) {G0,W4,D3,L1,V0,M1} { ! star( skol2 ) = one }.
% 2.35/2.72 substitution0:
% 2.35/2.72 end
% 2.35/2.72 permutation0:
% 2.35/2.72 0 ==> 0
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 eqswap: (10788) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z ) ==>
% 2.35/2.72 addition( X, addition( Y, Z ) ) }.
% 2.35/2.72 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 2.35/2.72 ==> addition( addition( Z, Y ), X ) }.
% 2.35/2.72 substitution0:
% 2.35/2.72 X := Z
% 2.35/2.72 Y := Y
% 2.35/2.72 Z := X
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 paramod: (10794) {G1,W9,D4,L1,V2,M1} { addition( addition( X, Y ), Y ) ==>
% 2.35/2.72 addition( X, Y ) }.
% 2.35/2.72 parent0[0]: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 2.35/2.72 parent1[0; 8]: (10788) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y ),
% 2.35/2.72 Z ) ==> addition( X, addition( Y, Z ) ) }.
% 2.35/2.72 substitution0:
% 2.35/2.72 X := Y
% 2.35/2.72 end
% 2.35/2.72 substitution1:
% 2.35/2.72 X := X
% 2.35/2.72 Y := Y
% 2.35/2.72 Z := Y
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 subsumption: (33) {G1,W9,D4,L1,V2,M1} P(3,1) { addition( addition( Y, X ),
% 2.35/2.72 X ) ==> addition( Y, X ) }.
% 2.35/2.72 parent0: (10794) {G1,W9,D4,L1,V2,M1} { addition( addition( X, Y ), Y ) ==>
% 2.35/2.72 addition( X, Y ) }.
% 2.35/2.72 substitution0:
% 2.35/2.72 X := Y
% 2.35/2.72 Y := X
% 2.35/2.72 end
% 2.35/2.72 permutation0:
% 2.35/2.72 0 ==> 0
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 resolution: (10799) {G1,W4,D3,L1,V0,M1} { complement( skol1( skol2 ),
% 2.35/2.72 skol2 ) }.
% 2.35/2.72 parent0[0]: (17) {G0,W6,D3,L2,V1,M2} I { ! test( X ), complement( skol1( X
% 2.35/2.72 ), X ) }.
% 2.35/2.72 parent1[0]: (28) {G0,W2,D2,L1,V0,M1} I { test( skol2 ) }.
% 2.35/2.72 substitution0:
% 2.35/2.72 X := skol2
% 2.35/2.72 end
% 2.35/2.72 substitution1:
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 subsumption: (80) {G1,W4,D3,L1,V0,M1} R(17,28) { complement( skol1( skol2 )
% 2.35/2.72 , skol2 ) }.
% 2.35/2.72 parent0: (10799) {G1,W4,D3,L1,V0,M1} { complement( skol1( skol2 ), skol2 )
% 2.35/2.72 }.
% 2.35/2.72 substitution0:
% 2.35/2.72 end
% 2.35/2.72 permutation0:
% 2.35/2.72 0 ==> 0
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 resolution: (10800) {G1,W4,D3,L1,V0,M1} { alpha1( skol2, skol1( skol2 ) )
% 2.35/2.72 }.
% 2.35/2.72 parent0[0]: (20) {G0,W6,D2,L2,V2,M2} I { ! complement( Y, X ), alpha1( X, Y
% 2.35/2.72 ) }.
% 2.35/2.72 parent1[0]: (80) {G1,W4,D3,L1,V0,M1} R(17,28) { complement( skol1( skol2 )
% 2.35/2.72 , skol2 ) }.
% 2.35/2.72 substitution0:
% 2.35/2.72 X := skol2
% 2.35/2.72 Y := skol1( skol2 )
% 2.35/2.72 end
% 2.35/2.72 substitution1:
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 subsumption: (81) {G2,W4,D3,L1,V0,M1} R(80,20) { alpha1( skol2, skol1(
% 2.35/2.72 skol2 ) ) }.
% 2.35/2.72 parent0: (10800) {G1,W4,D3,L1,V0,M1} { alpha1( skol2, skol1( skol2 ) ) }.
% 2.35/2.72 substitution0:
% 2.35/2.72 end
% 2.35/2.72 permutation0:
% 2.35/2.72 0 ==> 0
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 eqswap: (10801) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X, Y
% 2.35/2.72 ) }.
% 2.35/2.72 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 2.35/2.72 ==> Y }.
% 2.35/2.72 substitution0:
% 2.35/2.72 X := X
% 2.35/2.72 Y := Y
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 paramod: (10802) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y, X
% 2.35/2.72 ) }.
% 2.35/2.72 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 2.35/2.72 }.
% 2.35/2.72 parent1[0; 2]: (10801) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq
% 2.35/2.72 ( X, Y ) }.
% 2.35/2.72 substitution0:
% 2.35/2.72 X := Y
% 2.35/2.72 Y := X
% 2.35/2.72 end
% 2.35/2.72 substitution1:
% 2.35/2.72 X := Y
% 2.35/2.72 Y := X
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 eqswap: (10805) {G1,W8,D3,L2,V2,M2} { addition( X, Y ) ==> X, ! leq( Y, X
% 2.35/2.72 ) }.
% 2.35/2.72 parent0[0]: (10802) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y
% 2.35/2.72 , X ) }.
% 2.35/2.72 substitution0:
% 2.35/2.72 X := X
% 2.35/2.72 Y := Y
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 subsumption: (94) {G1,W8,D3,L2,V2,M2} P(11,0) { addition( Y, X ) ==> Y, !
% 2.35/2.72 leq( X, Y ) }.
% 2.35/2.72 parent0: (10805) {G1,W8,D3,L2,V2,M2} { addition( X, Y ) ==> X, ! leq( Y, X
% 2.35/2.72 ) }.
% 2.35/2.72 substitution0:
% 2.35/2.72 X := Y
% 2.35/2.72 Y := X
% 2.35/2.72 end
% 2.35/2.72 permutation0:
% 2.35/2.72 0 ==> 0
% 2.35/2.72 1 ==> 1
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 eqswap: (10806) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y
% 2.35/2.72 ) }.
% 2.35/2.72 parent0[0]: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 2.35/2.72 Y ) }.
% 2.35/2.72 substitution0:
% 2.35/2.72 X := X
% 2.35/2.72 Y := Y
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 eqswap: (10807) {G0,W5,D3,L1,V1,M1} { X ==> addition( X, X ) }.
% 2.35/2.72 parent0[0]: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 2.35/2.72 substitution0:
% 2.35/2.72 X := X
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 resolution: (10808) {G1,W3,D2,L1,V1,M1} { leq( X, X ) }.
% 2.35/2.72 parent0[0]: (10806) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X
% 2.35/2.72 , Y ) }.
% 2.35/2.72 parent1[0]: (10807) {G0,W5,D3,L1,V1,M1} { X ==> addition( X, X ) }.
% 2.35/2.72 substitution0:
% 2.35/2.72 X := X
% 2.35/2.72 Y := X
% 2.35/2.72 end
% 2.35/2.72 substitution1:
% 2.35/2.72 X := X
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 subsumption: (164) {G1,W3,D2,L1,V1,M1} R(12,3) { leq( X, X ) }.
% 2.35/2.72 parent0: (10808) {G1,W3,D2,L1,V1,M1} { leq( X, X ) }.
% 2.35/2.72 substitution0:
% 2.35/2.72 X := X
% 2.35/2.72 end
% 2.35/2.72 permutation0:
% 2.35/2.72 0 ==> 0
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 eqswap: (10810) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y
% 2.35/2.72 ) }.
% 2.35/2.72 parent0[0]: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 2.35/2.72 Y ) }.
% 2.35/2.72 substitution0:
% 2.35/2.72 X := X
% 2.35/2.72 Y := Y
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 paramod: (10811) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Y ) ==>
% 2.35/2.72 multiplication( addition( Z, X ), Y ), leq( multiplication( Z, Y ),
% 2.35/2.72 multiplication( X, Y ) ) }.
% 2.35/2.72 parent0[0]: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ),
% 2.35/2.72 multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 2.35/2.72 parent1[0; 5]: (10810) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq
% 2.35/2.72 ( X, Y ) }.
% 2.35/2.72 substitution0:
% 2.35/2.72 X := Z
% 2.35/2.72 Y := X
% 2.35/2.72 Z := Y
% 2.35/2.72 end
% 2.35/2.72 substitution1:
% 2.35/2.72 X := multiplication( Z, Y )
% 2.35/2.72 Y := multiplication( X, Y )
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 eqswap: (10812) {G1,W16,D4,L2,V3,M2} { ! multiplication( addition( Z, X )
% 2.35/2.72 , Y ) ==> multiplication( X, Y ), leq( multiplication( Z, Y ),
% 2.35/2.72 multiplication( X, Y ) ) }.
% 2.35/2.72 parent0[0]: (10811) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Y ) ==>
% 2.35/2.72 multiplication( addition( Z, X ), Y ), leq( multiplication( Z, Y ),
% 2.35/2.72 multiplication( X, Y ) ) }.
% 2.35/2.72 substitution0:
% 2.35/2.72 X := X
% 2.35/2.72 Y := Y
% 2.35/2.72 Z := Z
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 subsumption: (167) {G1,W16,D4,L2,V3,M2} P(8,12) { ! multiplication(
% 2.35/2.72 addition( X, Z ), Y ) ==> multiplication( Z, Y ), leq( multiplication( X
% 2.35/2.72 , Y ), multiplication( Z, Y ) ) }.
% 2.35/2.72 parent0: (10812) {G1,W16,D4,L2,V3,M2} { ! multiplication( addition( Z, X )
% 2.35/2.72 , Y ) ==> multiplication( X, Y ), leq( multiplication( Z, Y ),
% 2.35/2.72 multiplication( X, Y ) ) }.
% 2.35/2.72 substitution0:
% 2.35/2.72 X := Z
% 2.35/2.72 Y := Y
% 2.35/2.72 Z := X
% 2.35/2.72 end
% 2.35/2.72 permutation0:
% 2.35/2.72 0 ==> 0
% 2.35/2.72 1 ==> 1
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 eqswap: (10814) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y
% 2.35/2.72 ) }.
% 2.35/2.72 parent0[0]: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 2.35/2.72 Y ) }.
% 2.35/2.72 substitution0:
% 2.35/2.72 X := X
% 2.35/2.72 Y := Y
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 paramod: (10815) {G1,W14,D4,L2,V3,M2} { ! addition( X, Y ) ==> addition(
% 2.35/2.72 addition( Z, X ), Y ), leq( Z, addition( X, Y ) ) }.
% 2.35/2.72 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 2.35/2.72 ==> addition( addition( Z, Y ), X ) }.
% 2.35/2.72 parent1[0; 5]: (10814) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq
% 2.35/2.72 ( X, Y ) }.
% 2.35/2.72 substitution0:
% 2.35/2.72 X := Y
% 2.35/2.72 Y := X
% 2.35/2.72 Z := Z
% 2.35/2.72 end
% 2.35/2.72 substitution1:
% 2.35/2.72 X := Z
% 2.35/2.72 Y := addition( X, Y )
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 eqswap: (10816) {G1,W14,D4,L2,V3,M2} { ! addition( addition( Z, X ), Y )
% 2.35/2.72 ==> addition( X, Y ), leq( Z, addition( X, Y ) ) }.
% 2.35/2.72 parent0[0]: (10815) {G1,W14,D4,L2,V3,M2} { ! addition( X, Y ) ==> addition
% 2.35/2.72 ( addition( Z, X ), Y ), leq( Z, addition( X, Y ) ) }.
% 2.35/2.72 substitution0:
% 2.35/2.72 X := X
% 2.35/2.72 Y := Y
% 2.35/2.72 Z := Z
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 subsumption: (169) {G1,W14,D4,L2,V3,M2} P(1,12) { ! addition( addition( X,
% 2.35/2.72 Y ), Z ) ==> addition( Y, Z ), leq( X, addition( Y, Z ) ) }.
% 2.35/2.72 parent0: (10816) {G1,W14,D4,L2,V3,M2} { ! addition( addition( Z, X ), Y )
% 2.35/2.72 ==> addition( X, Y ), leq( Z, addition( X, Y ) ) }.
% 2.35/2.72 substitution0:
% 2.35/2.72 X := Y
% 2.35/2.72 Y := Z
% 2.35/2.72 Z := X
% 2.35/2.72 end
% 2.35/2.72 permutation0:
% 2.35/2.72 0 ==> 0
% 2.35/2.72 1 ==> 1
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 paramod: (10817) {G1,W9,D5,L1,V1,M1} { leq( addition( multiplication( star
% 2.35/2.72 ( X ), X ), one ), star( X ) ) }.
% 2.35/2.72 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 2.35/2.72 }.
% 2.35/2.72 parent1[0; 1]: (14) {G0,W9,D5,L1,V1,M1} I { leq( addition( one,
% 2.35/2.72 multiplication( star( X ), X ) ), star( X ) ) }.
% 2.35/2.72 substitution0:
% 2.35/2.72 X := one
% 2.35/2.72 Y := multiplication( star( X ), X )
% 2.35/2.72 end
% 2.35/2.72 substitution1:
% 2.35/2.72 X := X
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 subsumption: (217) {G1,W9,D5,L1,V1,M1} P(0,14) { leq( addition(
% 2.35/2.72 multiplication( star( X ), X ), one ), star( X ) ) }.
% 2.35/2.72 parent0: (10817) {G1,W9,D5,L1,V1,M1} { leq( addition( multiplication( star
% 2.35/2.72 ( X ), X ), one ), star( X ) ) }.
% 2.35/2.72 substitution0:
% 2.35/2.72 X := X
% 2.35/2.72 end
% 2.35/2.72 permutation0:
% 2.35/2.72 0 ==> 0
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 eqswap: (10819) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X, Y
% 2.35/2.72 ) }.
% 2.35/2.72 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 2.35/2.72 ==> Y }.
% 2.35/2.72 substitution0:
% 2.35/2.72 X := X
% 2.35/2.72 Y := Y
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 resolution: (10820) {G1,W15,D5,L2,V3,M2} { X ==> addition( multiplication
% 2.35/2.72 ( star( Y ), Z ), X ), ! leq( addition( multiplication( Y, X ), Z ), X )
% 2.35/2.72 }.
% 2.35/2.72 parent0[1]: (10819) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X
% 2.35/2.72 , Y ) }.
% 2.35/2.72 parent1[1]: (15) {G0,W13,D4,L2,V3,M2} I { ! leq( addition( multiplication(
% 2.35/2.72 X, Y ), Z ), Y ), leq( multiplication( star( X ), Z ), Y ) }.
% 2.35/2.72 substitution0:
% 2.35/2.72 X := multiplication( star( Y ), Z )
% 2.35/2.72 Y := X
% 2.35/2.72 end
% 2.35/2.72 substitution1:
% 2.35/2.72 X := Y
% 2.35/2.72 Y := X
% 2.35/2.72 Z := Z
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 eqswap: (10821) {G1,W15,D5,L2,V3,M2} { addition( multiplication( star( Y )
% 2.35/2.72 , Z ), X ) ==> X, ! leq( addition( multiplication( Y, X ), Z ), X ) }.
% 2.35/2.72 parent0[0]: (10820) {G1,W15,D5,L2,V3,M2} { X ==> addition( multiplication
% 2.35/2.72 ( star( Y ), Z ), X ), ! leq( addition( multiplication( Y, X ), Z ), X )
% 2.35/2.72 }.
% 2.35/2.72 substitution0:
% 2.35/2.72 X := X
% 2.35/2.72 Y := Y
% 2.35/2.72 Z := Z
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 subsumption: (235) {G1,W15,D5,L2,V3,M2} R(15,11) { ! leq( addition(
% 2.35/2.72 multiplication( X, Y ), Z ), Y ), addition( multiplication( star( X ), Z
% 2.35/2.72 ), Y ) ==> Y }.
% 2.35/2.72 parent0: (10821) {G1,W15,D5,L2,V3,M2} { addition( multiplication( star( Y
% 2.35/2.72 ), Z ), X ) ==> X, ! leq( addition( multiplication( Y, X ), Z ), X ) }.
% 2.35/2.72 substitution0:
% 2.35/2.72 X := Y
% 2.35/2.72 Y := X
% 2.35/2.72 Z := Z
% 2.35/2.72 end
% 2.35/2.72 permutation0:
% 2.35/2.72 0 ==> 1
% 2.35/2.72 1 ==> 0
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 paramod: (10823) {G1,W14,D4,L3,V3,M3} { ! leq( Z, Y ), ! leq(
% 2.35/2.72 multiplication( X, Y ), Z ), leq( multiplication( star( X ), Z ), Y ) }.
% 2.35/2.72 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 2.35/2.72 ==> Y }.
% 2.35/2.72 parent1[0; 2]: (15) {G0,W13,D4,L2,V3,M2} I { ! leq( addition(
% 2.35/2.72 multiplication( X, Y ), Z ), Y ), leq( multiplication( star( X ), Z ), Y
% 2.35/2.72 ) }.
% 2.35/2.72 substitution0:
% 2.35/2.72 X := multiplication( X, Y )
% 2.35/2.72 Y := Z
% 2.35/2.72 end
% 2.35/2.72 substitution1:
% 2.35/2.72 X := X
% 2.35/2.72 Y := Y
% 2.35/2.72 Z := Z
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 subsumption: (237) {G1,W14,D4,L3,V3,M3} P(11,15) { ! leq( Z, Y ), leq(
% 2.35/2.72 multiplication( star( X ), Z ), Y ), ! leq( multiplication( X, Y ), Z )
% 2.35/2.72 }.
% 2.35/2.72 parent0: (10823) {G1,W14,D4,L3,V3,M3} { ! leq( Z, Y ), ! leq(
% 2.35/2.72 multiplication( X, Y ), Z ), leq( multiplication( star( X ), Z ), Y ) }.
% 2.35/2.72 substitution0:
% 2.35/2.72 X := X
% 2.35/2.72 Y := Y
% 2.35/2.72 Z := Z
% 2.35/2.72 end
% 2.35/2.72 permutation0:
% 2.35/2.72 0 ==> 0
% 2.35/2.72 1 ==> 2
% 2.35/2.72 2 ==> 1
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 eqswap: (10824) {G0,W8,D3,L2,V2,M2} { one ==> addition( X, Y ), ! alpha1(
% 2.35/2.72 X, Y ) }.
% 2.35/2.72 parent0[1]: (23) {G0,W8,D3,L2,V2,M2} I { ! alpha1( X, Y ), addition( X, Y )
% 2.35/2.72 ==> one }.
% 2.35/2.72 substitution0:
% 2.35/2.72 X := X
% 2.35/2.72 Y := Y
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 resolution: (10825) {G1,W6,D4,L1,V0,M1} { one ==> addition( skol2, skol1(
% 2.35/2.72 skol2 ) ) }.
% 2.35/2.72 parent0[1]: (10824) {G0,W8,D3,L2,V2,M2} { one ==> addition( X, Y ), !
% 2.35/2.72 alpha1( X, Y ) }.
% 2.35/2.72 parent1[0]: (81) {G2,W4,D3,L1,V0,M1} R(80,20) { alpha1( skol2, skol1( skol2
% 2.35/2.72 ) ) }.
% 2.35/2.72 substitution0:
% 2.35/2.72 X := skol2
% 2.35/2.72 Y := skol1( skol2 )
% 2.35/2.72 end
% 2.35/2.72 substitution1:
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 eqswap: (10826) {G1,W6,D4,L1,V0,M1} { addition( skol2, skol1( skol2 ) )
% 2.35/2.72 ==> one }.
% 2.35/2.72 parent0[0]: (10825) {G1,W6,D4,L1,V0,M1} { one ==> addition( skol2, skol1(
% 2.35/2.72 skol2 ) ) }.
% 2.35/2.72 substitution0:
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 subsumption: (414) {G3,W6,D4,L1,V0,M1} R(23,81) { addition( skol2, skol1(
% 2.35/2.72 skol2 ) ) ==> one }.
% 2.35/2.72 parent0: (10826) {G1,W6,D4,L1,V0,M1} { addition( skol2, skol1( skol2 ) )
% 2.35/2.72 ==> one }.
% 2.35/2.72 substitution0:
% 2.35/2.72 end
% 2.35/2.72 permutation0:
% 2.35/2.72 0 ==> 0
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 eqswap: (10827) {G3,W6,D4,L1,V0,M1} { one ==> addition( skol2, skol1(
% 2.35/2.72 skol2 ) ) }.
% 2.35/2.72 parent0[0]: (414) {G3,W6,D4,L1,V0,M1} R(23,81) { addition( skol2, skol1(
% 2.35/2.72 skol2 ) ) ==> one }.
% 2.35/2.72 substitution0:
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 paramod: (10828) {G1,W6,D4,L1,V0,M1} { one ==> addition( skol1( skol2 ),
% 2.35/2.72 skol2 ) }.
% 2.35/2.72 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 2.35/2.72 }.
% 2.35/2.72 parent1[0; 2]: (10827) {G3,W6,D4,L1,V0,M1} { one ==> addition( skol2,
% 2.35/2.72 skol1( skol2 ) ) }.
% 2.35/2.72 substitution0:
% 2.35/2.72 X := skol2
% 2.35/2.72 Y := skol1( skol2 )
% 2.35/2.72 end
% 2.35/2.72 substitution1:
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 eqswap: (10831) {G1,W6,D4,L1,V0,M1} { addition( skol1( skol2 ), skol2 )
% 2.35/2.72 ==> one }.
% 2.35/2.72 parent0[0]: (10828) {G1,W6,D4,L1,V0,M1} { one ==> addition( skol1( skol2 )
% 2.35/2.72 , skol2 ) }.
% 2.35/2.72 substitution0:
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 subsumption: (2270) {G4,W6,D4,L1,V0,M1} P(414,0) { addition( skol1( skol2 )
% 2.35/2.72 , skol2 ) ==> one }.
% 2.35/2.72 parent0: (10831) {G1,W6,D4,L1,V0,M1} { addition( skol1( skol2 ), skol2 )
% 2.35/2.72 ==> one }.
% 2.35/2.72 substitution0:
% 2.35/2.72 end
% 2.35/2.72 permutation0:
% 2.35/2.72 0 ==> 0
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 eqswap: (10833) {G1,W9,D4,L1,V2,M1} { addition( X, Y ) ==> addition(
% 2.35/2.72 addition( X, Y ), Y ) }.
% 2.35/2.72 parent0[0]: (33) {G1,W9,D4,L1,V2,M1} P(3,1) { addition( addition( Y, X ), X
% 2.35/2.72 ) ==> addition( Y, X ) }.
% 2.35/2.72 substitution0:
% 2.35/2.72 X := Y
% 2.35/2.72 Y := X
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 paramod: (10835) {G2,W8,D4,L1,V0,M1} { addition( skol1( skol2 ), skol2 )
% 2.35/2.72 ==> addition( one, skol2 ) }.
% 2.35/2.72 parent0[0]: (2270) {G4,W6,D4,L1,V0,M1} P(414,0) { addition( skol1( skol2 )
% 2.35/2.72 , skol2 ) ==> one }.
% 2.35/2.72 parent1[0; 6]: (10833) {G1,W9,D4,L1,V2,M1} { addition( X, Y ) ==> addition
% 2.35/2.72 ( addition( X, Y ), Y ) }.
% 2.35/2.72 substitution0:
% 2.35/2.72 end
% 2.35/2.72 substitution1:
% 2.35/2.72 X := skol1( skol2 )
% 2.35/2.72 Y := skol2
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 paramod: (10836) {G3,W5,D3,L1,V0,M1} { one ==> addition( one, skol2 ) }.
% 2.35/2.72 parent0[0]: (2270) {G4,W6,D4,L1,V0,M1} P(414,0) { addition( skol1( skol2 )
% 2.35/2.72 , skol2 ) ==> one }.
% 2.35/2.72 parent1[0; 1]: (10835) {G2,W8,D4,L1,V0,M1} { addition( skol1( skol2 ),
% 2.35/2.72 skol2 ) ==> addition( one, skol2 ) }.
% 2.35/2.72 substitution0:
% 2.35/2.72 end
% 2.35/2.72 substitution1:
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 eqswap: (10838) {G3,W5,D3,L1,V0,M1} { addition( one, skol2 ) ==> one }.
% 2.35/2.72 parent0[0]: (10836) {G3,W5,D3,L1,V0,M1} { one ==> addition( one, skol2 )
% 2.35/2.72 }.
% 2.35/2.72 substitution0:
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 subsumption: (2311) {G5,W5,D3,L1,V0,M1} P(2270,33) { addition( one, skol2 )
% 2.35/2.72 ==> one }.
% 2.35/2.72 parent0: (10838) {G3,W5,D3,L1,V0,M1} { addition( one, skol2 ) ==> one }.
% 2.35/2.72 substitution0:
% 2.35/2.72 end
% 2.35/2.72 permutation0:
% 2.35/2.72 0 ==> 0
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 eqswap: (10840) {G5,W5,D3,L1,V0,M1} { one ==> addition( one, skol2 ) }.
% 2.35/2.72 parent0[0]: (2311) {G5,W5,D3,L1,V0,M1} P(2270,33) { addition( one, skol2 )
% 2.35/2.72 ==> one }.
% 2.35/2.72 substitution0:
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 paramod: (10841) {G1,W5,D3,L1,V0,M1} { one ==> addition( skol2, one ) }.
% 2.35/2.72 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 2.35/2.72 }.
% 2.35/2.72 parent1[0; 2]: (10840) {G5,W5,D3,L1,V0,M1} { one ==> addition( one, skol2
% 2.35/2.72 ) }.
% 2.35/2.72 substitution0:
% 2.35/2.72 X := one
% 2.35/2.72 Y := skol2
% 2.35/2.72 end
% 2.35/2.72 substitution1:
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 eqswap: (10844) {G1,W5,D3,L1,V0,M1} { addition( skol2, one ) ==> one }.
% 2.35/2.72 parent0[0]: (10841) {G1,W5,D3,L1,V0,M1} { one ==> addition( skol2, one )
% 2.35/2.72 }.
% 2.35/2.72 substitution0:
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 subsumption: (2376) {G6,W5,D3,L1,V0,M1} P(2311,0) { addition( skol2, one )
% 2.35/2.72 ==> one }.
% 2.35/2.72 parent0: (10844) {G1,W5,D3,L1,V0,M1} { addition( skol2, one ) ==> one }.
% 2.35/2.72 substitution0:
% 2.35/2.72 end
% 2.35/2.72 permutation0:
% 2.35/2.72 0 ==> 0
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 eqswap: (10846) {G1,W16,D4,L2,V3,M2} { ! multiplication( Y, Z ) ==>
% 2.35/2.72 multiplication( addition( X, Y ), Z ), leq( multiplication( X, Z ),
% 2.35/2.72 multiplication( Y, Z ) ) }.
% 2.35/2.72 parent0[0]: (167) {G1,W16,D4,L2,V3,M2} P(8,12) { ! multiplication( addition
% 2.35/2.72 ( X, Z ), Y ) ==> multiplication( Z, Y ), leq( multiplication( X, Y ),
% 2.35/2.72 multiplication( Z, Y ) ) }.
% 2.35/2.72 substitution0:
% 2.35/2.72 X := X
% 2.35/2.72 Y := Z
% 2.35/2.72 Z := Y
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 paramod: (10848) {G2,W14,D3,L2,V1,M2} { ! multiplication( one, X ) ==>
% 2.35/2.72 multiplication( one, X ), leq( multiplication( skol2, X ), multiplication
% 2.35/2.72 ( one, X ) ) }.
% 2.35/2.72 parent0[0]: (2376) {G6,W5,D3,L1,V0,M1} P(2311,0) { addition( skol2, one )
% 2.35/2.72 ==> one }.
% 2.35/2.72 parent1[0; 6]: (10846) {G1,W16,D4,L2,V3,M2} { ! multiplication( Y, Z ) ==>
% 2.35/2.72 multiplication( addition( X, Y ), Z ), leq( multiplication( X, Z ),
% 2.35/2.72 multiplication( Y, Z ) ) }.
% 2.35/2.72 substitution0:
% 2.35/2.72 end
% 2.35/2.72 substitution1:
% 2.35/2.72 X := skol2
% 2.35/2.72 Y := one
% 2.35/2.72 Z := X
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 eqrefl: (10849) {G0,W7,D3,L1,V1,M1} { leq( multiplication( skol2, X ),
% 2.35/2.72 multiplication( one, X ) ) }.
% 2.35/2.72 parent0[0]: (10848) {G2,W14,D3,L2,V1,M2} { ! multiplication( one, X ) ==>
% 2.35/2.72 multiplication( one, X ), leq( multiplication( skol2, X ), multiplication
% 2.35/2.72 ( one, X ) ) }.
% 2.35/2.72 substitution0:
% 2.35/2.72 X := X
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 paramod: (10850) {G1,W5,D3,L1,V1,M1} { leq( multiplication( skol2, X ), X
% 2.35/2.72 ) }.
% 2.35/2.72 parent0[0]: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 2.35/2.72 parent1[0; 4]: (10849) {G0,W7,D3,L1,V1,M1} { leq( multiplication( skol2, X
% 2.35/2.72 ), multiplication( one, X ) ) }.
% 2.35/2.72 substitution0:
% 2.35/2.72 X := X
% 2.35/2.72 end
% 2.35/2.72 substitution1:
% 2.35/2.72 X := X
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 subsumption: (6098) {G7,W5,D3,L1,V1,M1} P(2376,167);q;d(6) { leq(
% 2.35/2.72 multiplication( skol2, X ), X ) }.
% 2.35/2.72 parent0: (10850) {G1,W5,D3,L1,V1,M1} { leq( multiplication( skol2, X ), X
% 2.35/2.72 ) }.
% 2.35/2.72 substitution0:
% 2.35/2.72 X := X
% 2.35/2.72 end
% 2.35/2.72 permutation0:
% 2.35/2.72 0 ==> 0
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 eqswap: (10852) {G1,W14,D4,L2,V3,M2} { ! addition( Y, Z ) ==> addition(
% 2.35/2.72 addition( X, Y ), Z ), leq( X, addition( Y, Z ) ) }.
% 2.35/2.72 parent0[0]: (169) {G1,W14,D4,L2,V3,M2} P(1,12) { ! addition( addition( X, Y
% 2.35/2.72 ), Z ) ==> addition( Y, Z ), leq( X, addition( Y, Z ) ) }.
% 2.35/2.72 substitution0:
% 2.35/2.72 X := X
% 2.35/2.72 Y := Y
% 2.35/2.72 Z := Z
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 paramod: (10854) {G2,W12,D3,L2,V1,M2} { ! addition( one, X ) ==> addition
% 2.35/2.72 ( one, X ), leq( skol2, addition( one, X ) ) }.
% 2.35/2.72 parent0[0]: (2376) {G6,W5,D3,L1,V0,M1} P(2311,0) { addition( skol2, one )
% 2.35/2.72 ==> one }.
% 2.35/2.72 parent1[0; 6]: (10852) {G1,W14,D4,L2,V3,M2} { ! addition( Y, Z ) ==>
% 2.35/2.72 addition( addition( X, Y ), Z ), leq( X, addition( Y, Z ) ) }.
% 2.35/2.72 substitution0:
% 2.35/2.72 end
% 2.35/2.72 substitution1:
% 2.35/2.72 X := skol2
% 2.35/2.72 Y := one
% 2.35/2.72 Z := X
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 eqrefl: (10857) {G0,W5,D3,L1,V1,M1} { leq( skol2, addition( one, X ) ) }.
% 2.35/2.72 parent0[0]: (10854) {G2,W12,D3,L2,V1,M2} { ! addition( one, X ) ==>
% 2.35/2.72 addition( one, X ), leq( skol2, addition( one, X ) ) }.
% 2.35/2.72 substitution0:
% 2.35/2.72 X := X
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 subsumption: (6190) {G7,W5,D3,L1,V1,M1} P(2376,169);q { leq( skol2,
% 2.35/2.72 addition( one, X ) ) }.
% 2.35/2.72 parent0: (10857) {G0,W5,D3,L1,V1,M1} { leq( skol2, addition( one, X ) )
% 2.35/2.72 }.
% 2.35/2.72 substitution0:
% 2.35/2.72 X := X
% 2.35/2.72 end
% 2.35/2.72 permutation0:
% 2.35/2.72 0 ==> 0
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 paramod: (10859) {G1,W6,D2,L2,V1,M2} { leq( skol2, X ), ! leq( one, X )
% 2.35/2.72 }.
% 2.35/2.72 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 2.35/2.72 ==> Y }.
% 2.35/2.72 parent1[0; 2]: (6190) {G7,W5,D3,L1,V1,M1} P(2376,169);q { leq( skol2,
% 2.35/2.72 addition( one, X ) ) }.
% 2.35/2.72 substitution0:
% 2.35/2.72 X := one
% 2.35/2.72 Y := X
% 2.35/2.72 end
% 2.35/2.72 substitution1:
% 2.35/2.72 X := X
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 subsumption: (6424) {G8,W6,D2,L2,V1,M2} P(11,6190) { leq( skol2, X ), ! leq
% 2.35/2.72 ( one, X ) }.
% 2.35/2.72 parent0: (10859) {G1,W6,D2,L2,V1,M2} { leq( skol2, X ), ! leq( one, X )
% 2.35/2.72 }.
% 2.35/2.72 substitution0:
% 2.35/2.72 X := X
% 2.35/2.72 end
% 2.35/2.72 permutation0:
% 2.35/2.72 0 ==> 0
% 2.35/2.72 1 ==> 1
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 paramod: (10863) {G2,W11,D4,L2,V1,M2} { leq( one, star( X ) ), ! leq(
% 2.35/2.72 addition( multiplication( X, one ), X ), one ) }.
% 2.35/2.72 parent0[1]: (235) {G1,W15,D5,L2,V3,M2} R(15,11) { ! leq( addition(
% 2.35/2.72 multiplication( X, Y ), Z ), Y ), addition( multiplication( star( X ), Z
% 2.35/2.72 ), Y ) ==> Y }.
% 2.35/2.72 parent1[0; 1]: (217) {G1,W9,D5,L1,V1,M1} P(0,14) { leq( addition(
% 2.35/2.72 multiplication( star( X ), X ), one ), star( X ) ) }.
% 2.35/2.72 substitution0:
% 2.35/2.72 X := X
% 2.35/2.72 Y := one
% 2.35/2.72 Z := X
% 2.35/2.72 end
% 2.35/2.72 substitution1:
% 2.35/2.72 X := X
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 paramod: (10864) {G1,W9,D3,L2,V1,M2} { ! leq( addition( X, X ), one ), leq
% 2.35/2.72 ( one, star( X ) ) }.
% 2.35/2.72 parent0[0]: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 2.35/2.72 parent1[1; 3]: (10863) {G2,W11,D4,L2,V1,M2} { leq( one, star( X ) ), ! leq
% 2.35/2.72 ( addition( multiplication( X, one ), X ), one ) }.
% 2.35/2.72 substitution0:
% 2.35/2.72 X := X
% 2.35/2.72 end
% 2.35/2.72 substitution1:
% 2.35/2.72 X := X
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 paramod: (10865) {G1,W7,D3,L2,V1,M2} { ! leq( X, one ), leq( one, star( X
% 2.35/2.72 ) ) }.
% 2.35/2.72 parent0[0]: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 2.35/2.72 parent1[0; 2]: (10864) {G1,W9,D3,L2,V1,M2} { ! leq( addition( X, X ), one
% 2.35/2.72 ), leq( one, star( X ) ) }.
% 2.35/2.72 substitution0:
% 2.35/2.72 X := X
% 2.35/2.72 end
% 2.35/2.72 substitution1:
% 2.35/2.72 X := X
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 subsumption: (10137) {G2,W7,D3,L2,V1,M2} P(235,217);d(5);d(3) { leq( one,
% 2.35/2.72 star( X ) ), ! leq( X, one ) }.
% 2.35/2.72 parent0: (10865) {G1,W7,D3,L2,V1,M2} { ! leq( X, one ), leq( one, star( X
% 2.35/2.72 ) ) }.
% 2.35/2.72 substitution0:
% 2.35/2.72 X := X
% 2.35/2.72 end
% 2.35/2.72 permutation0:
% 2.35/2.72 0 ==> 1
% 2.35/2.72 1 ==> 0
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 resolution: (10866) {G3,W7,D3,L2,V0,M2} { leq( one, star( skol2 ) ), ! leq
% 2.35/2.72 ( one, one ) }.
% 2.35/2.72 parent0[1]: (10137) {G2,W7,D3,L2,V1,M2} P(235,217);d(5);d(3) { leq( one,
% 2.35/2.72 star( X ) ), ! leq( X, one ) }.
% 2.35/2.72 parent1[0]: (6424) {G8,W6,D2,L2,V1,M2} P(11,6190) { leq( skol2, X ), ! leq
% 2.35/2.72 ( one, X ) }.
% 2.35/2.72 substitution0:
% 2.35/2.72 X := skol2
% 2.35/2.72 end
% 2.35/2.72 substitution1:
% 2.35/2.72 X := one
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 resolution: (10867) {G2,W4,D3,L1,V0,M1} { leq( one, star( skol2 ) ) }.
% 2.35/2.72 parent0[1]: (10866) {G3,W7,D3,L2,V0,M2} { leq( one, star( skol2 ) ), ! leq
% 2.35/2.72 ( one, one ) }.
% 2.35/2.72 parent1[0]: (164) {G1,W3,D2,L1,V1,M1} R(12,3) { leq( X, X ) }.
% 2.35/2.72 substitution0:
% 2.35/2.72 end
% 2.35/2.72 substitution1:
% 2.35/2.72 X := one
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 subsumption: (10180) {G9,W4,D3,L1,V0,M1} R(10137,6424);r(164) { leq( one,
% 2.35/2.72 star( skol2 ) ) }.
% 2.35/2.72 parent0: (10867) {G2,W4,D3,L1,V0,M1} { leq( one, star( skol2 ) ) }.
% 2.35/2.72 substitution0:
% 2.35/2.72 end
% 2.35/2.72 permutation0:
% 2.35/2.72 0 ==> 0
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 eqswap: (10868) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X, Y
% 2.35/2.72 ) }.
% 2.35/2.72 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 2.35/2.72 ==> Y }.
% 2.35/2.72 substitution0:
% 2.35/2.72 X := X
% 2.35/2.72 Y := Y
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 resolution: (10869) {G1,W7,D4,L1,V0,M1} { star( skol2 ) ==> addition( one
% 2.35/2.72 , star( skol2 ) ) }.
% 2.35/2.72 parent0[1]: (10868) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X
% 2.35/2.72 , Y ) }.
% 2.35/2.72 parent1[0]: (10180) {G9,W4,D3,L1,V0,M1} R(10137,6424);r(164) { leq( one,
% 2.35/2.72 star( skol2 ) ) }.
% 2.35/2.72 substitution0:
% 2.35/2.72 X := one
% 2.35/2.72 Y := star( skol2 )
% 2.35/2.72 end
% 2.35/2.72 substitution1:
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 eqswap: (10870) {G1,W7,D4,L1,V0,M1} { addition( one, star( skol2 ) ) ==>
% 2.35/2.72 star( skol2 ) }.
% 2.35/2.72 parent0[0]: (10869) {G1,W7,D4,L1,V0,M1} { star( skol2 ) ==> addition( one
% 2.35/2.72 , star( skol2 ) ) }.
% 2.35/2.72 substitution0:
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 subsumption: (10299) {G10,W7,D4,L1,V0,M1} R(10180,11) { addition( one, star
% 2.35/2.72 ( skol2 ) ) ==> star( skol2 ) }.
% 2.35/2.72 parent0: (10870) {G1,W7,D4,L1,V0,M1} { addition( one, star( skol2 ) ) ==>
% 2.35/2.72 star( skol2 ) }.
% 2.35/2.72 substitution0:
% 2.35/2.72 end
% 2.35/2.72 permutation0:
% 2.35/2.72 0 ==> 0
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 resolution: (10872) {G2,W9,D4,L2,V1,M2} { ! leq( X, X ), leq(
% 2.35/2.72 multiplication( star( skol2 ), X ), X ) }.
% 2.35/2.72 parent0[2]: (237) {G1,W14,D4,L3,V3,M3} P(11,15) { ! leq( Z, Y ), leq(
% 2.35/2.72 multiplication( star( X ), Z ), Y ), ! leq( multiplication( X, Y ), Z )
% 2.35/2.72 }.
% 2.35/2.72 parent1[0]: (6098) {G7,W5,D3,L1,V1,M1} P(2376,167);q;d(6) { leq(
% 2.35/2.72 multiplication( skol2, X ), X ) }.
% 2.35/2.72 substitution0:
% 2.35/2.72 X := skol2
% 2.35/2.72 Y := X
% 2.35/2.72 Z := X
% 2.35/2.72 end
% 2.35/2.72 substitution1:
% 2.35/2.72 X := X
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 resolution: (10873) {G2,W6,D4,L1,V1,M1} { leq( multiplication( star( skol2
% 2.35/2.72 ), X ), X ) }.
% 2.35/2.72 parent0[0]: (10872) {G2,W9,D4,L2,V1,M2} { ! leq( X, X ), leq(
% 2.35/2.72 multiplication( star( skol2 ), X ), X ) }.
% 2.35/2.72 parent1[0]: (164) {G1,W3,D2,L1,V1,M1} R(12,3) { leq( X, X ) }.
% 2.35/2.72 substitution0:
% 2.35/2.72 X := X
% 2.35/2.72 end
% 2.35/2.72 substitution1:
% 2.35/2.72 X := X
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 subsumption: (10364) {G8,W6,D4,L1,V1,M1} R(237,6098);r(164) { leq(
% 2.35/2.72 multiplication( star( skol2 ), X ), X ) }.
% 2.35/2.72 parent0: (10873) {G2,W6,D4,L1,V1,M1} { leq( multiplication( star( skol2 )
% 2.35/2.72 , X ), X ) }.
% 2.35/2.72 substitution0:
% 2.35/2.72 X := X
% 2.35/2.72 end
% 2.35/2.72 permutation0:
% 2.35/2.72 0 ==> 0
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 paramod: (10875) {G1,W4,D3,L1,V0,M1} { leq( star( skol2 ), one ) }.
% 2.35/2.72 parent0[0]: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 2.35/2.72 parent1[0; 1]: (10364) {G8,W6,D4,L1,V1,M1} R(237,6098);r(164) { leq(
% 2.35/2.72 multiplication( star( skol2 ), X ), X ) }.
% 2.35/2.72 substitution0:
% 2.35/2.72 X := star( skol2 )
% 2.35/2.72 end
% 2.35/2.72 substitution1:
% 2.35/2.72 X := one
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 subsumption: (10596) {G9,W4,D3,L1,V0,M1} P(5,10364) { leq( star( skol2 ),
% 2.35/2.72 one ) }.
% 2.35/2.72 parent0: (10875) {G1,W4,D3,L1,V0,M1} { leq( star( skol2 ), one ) }.
% 2.35/2.72 substitution0:
% 2.35/2.72 end
% 2.35/2.72 permutation0:
% 2.35/2.72 0 ==> 0
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 eqswap: (10876) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y, X
% 2.35/2.72 ) }.
% 2.35/2.72 parent0[0]: (94) {G1,W8,D3,L2,V2,M2} P(11,0) { addition( Y, X ) ==> Y, !
% 2.35/2.72 leq( X, Y ) }.
% 2.35/2.72 substitution0:
% 2.35/2.72 X := Y
% 2.35/2.72 Y := X
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 eqswap: (10878) {G0,W4,D3,L1,V0,M1} { ! one ==> star( skol2 ) }.
% 2.35/2.72 parent0[0]: (29) {G0,W4,D3,L1,V0,M1} I { ! star( skol2 ) ==> one }.
% 2.35/2.72 substitution0:
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 resolution: (10879) {G2,W6,D4,L1,V0,M1} { one ==> addition( one, star(
% 2.35/2.72 skol2 ) ) }.
% 2.35/2.72 parent0[1]: (10876) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y
% 2.35/2.72 , X ) }.
% 2.35/2.72 parent1[0]: (10596) {G9,W4,D3,L1,V0,M1} P(5,10364) { leq( star( skol2 ),
% 2.35/2.72 one ) }.
% 2.35/2.72 substitution0:
% 2.35/2.72 X := one
% 2.35/2.72 Y := star( skol2 )
% 2.35/2.72 end
% 2.35/2.72 substitution1:
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 paramod: (10880) {G3,W4,D3,L1,V0,M1} { one ==> star( skol2 ) }.
% 2.35/2.72 parent0[0]: (10299) {G10,W7,D4,L1,V0,M1} R(10180,11) { addition( one, star
% 2.35/2.72 ( skol2 ) ) ==> star( skol2 ) }.
% 2.35/2.72 parent1[0; 2]: (10879) {G2,W6,D4,L1,V0,M1} { one ==> addition( one, star(
% 2.35/2.72 skol2 ) ) }.
% 2.35/2.72 substitution0:
% 2.35/2.72 end
% 2.35/2.72 substitution1:
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 resolution: (10881) {G1,W0,D0,L0,V0,M0} { }.
% 2.35/2.72 parent0[0]: (10878) {G0,W4,D3,L1,V0,M1} { ! one ==> star( skol2 ) }.
% 2.35/2.72 parent1[0]: (10880) {G3,W4,D3,L1,V0,M1} { one ==> star( skol2 ) }.
% 2.35/2.72 substitution0:
% 2.35/2.72 end
% 2.35/2.72 substitution1:
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 subsumption: (10599) {G11,W0,D0,L0,V0,M0} R(10596,94);d(10299);r(29) { }.
% 2.35/2.72 parent0: (10881) {G1,W0,D0,L0,V0,M0} { }.
% 2.35/2.72 substitution0:
% 2.35/2.72 end
% 2.35/2.72 permutation0:
% 2.35/2.72 end
% 2.35/2.72
% 2.35/2.72 Proof check complete!
% 2.35/2.72
% 2.35/2.72 Memory use:
% 2.35/2.72
% 2.35/2.72 space for terms: 130564
% 2.35/2.72 space for clauses: 496666
% 2.35/2.72
% 2.35/2.72
% 2.35/2.72 clauses generated: 71686
% 2.35/2.72 clauses kept: 10600
% 2.35/2.72 clauses selected: 723
% 2.35/2.72 clauses deleted: 291
% 2.35/2.72 clauses inuse deleted: 115
% 2.35/2.72
% 2.35/2.72 subsentry: 296349
% 2.35/2.72 literals s-matched: 158453
% 2.35/2.72 literals matched: 157227
% 2.35/2.72 full subsumption: 40647
% 2.35/2.72
% 2.35/2.72 checksum: -1205797901
% 2.35/2.72
% 2.35/2.72
% 2.35/2.72 Bliksem ended
%------------------------------------------------------------------------------