TSTP Solution File: KLE026+2 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : KLE026+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n007.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 01:36:44 EDT 2022
% Result : Theorem 4.44s 4.83s
% Output : Refutation 4.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KLE026+2 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n007.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % DateTime : Thu Jun 16 14:07:11 EDT 2022
% 0.13/0.34 % CPUTime :
% 4.44/4.83 *** allocated 10000 integers for termspace/termends
% 4.44/4.83 *** allocated 10000 integers for clauses
% 4.44/4.83 *** allocated 10000 integers for justifications
% 4.44/4.83 Bliksem 1.12
% 4.44/4.83
% 4.44/4.83
% 4.44/4.83 Automatic Strategy Selection
% 4.44/4.83
% 4.44/4.83
% 4.44/4.83 Clauses:
% 4.44/4.83
% 4.44/4.83 { addition( X, Y ) = addition( Y, X ) }.
% 4.44/4.83 { addition( Z, addition( Y, X ) ) = addition( addition( Z, Y ), X ) }.
% 4.44/4.83 { addition( X, zero ) = X }.
% 4.44/4.83 { addition( X, X ) = X }.
% 4.44/4.83 { multiplication( X, multiplication( Y, Z ) ) = multiplication(
% 4.44/4.83 multiplication( X, Y ), Z ) }.
% 4.44/4.83 { multiplication( X, one ) = X }.
% 4.44/4.83 { multiplication( one, X ) = X }.
% 4.44/4.83 { multiplication( X, addition( Y, Z ) ) = addition( multiplication( X, Y )
% 4.44/4.83 , multiplication( X, Z ) ) }.
% 4.44/4.83 { multiplication( addition( X, Y ), Z ) = addition( multiplication( X, Z )
% 4.44/4.83 , multiplication( Y, Z ) ) }.
% 4.44/4.83 { multiplication( X, zero ) = zero }.
% 4.44/4.83 { multiplication( zero, X ) = zero }.
% 4.44/4.83 { ! leq( X, Y ), addition( X, Y ) = Y }.
% 4.44/4.83 { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 4.44/4.83 { ! test( X ), complement( skol1( X ), X ) }.
% 4.44/4.83 { ! complement( Y, X ), test( X ) }.
% 4.44/4.83 { ! complement( Y, X ), multiplication( X, Y ) = zero }.
% 4.44/4.83 { ! complement( Y, X ), alpha1( X, Y ) }.
% 4.44/4.83 { ! multiplication( X, Y ) = zero, ! alpha1( X, Y ), complement( Y, X ) }.
% 4.44/4.83 { ! alpha1( X, Y ), multiplication( Y, X ) = zero }.
% 4.44/4.83 { ! alpha1( X, Y ), addition( X, Y ) = one }.
% 4.44/4.83 { ! multiplication( Y, X ) = zero, ! addition( X, Y ) = one, alpha1( X, Y )
% 4.44/4.83 }.
% 4.44/4.83 { ! test( X ), ! c( X ) = Y, complement( X, Y ) }.
% 4.44/4.83 { ! test( X ), ! complement( X, Y ), c( X ) = Y }.
% 4.44/4.83 { test( X ), c( X ) = zero }.
% 4.44/4.83 { ! test( X ), ! test( Y ), c( addition( X, Y ) ) = multiplication( c( X )
% 4.44/4.83 , c( Y ) ) }.
% 4.44/4.83 { ! test( X ), ! test( Y ), c( multiplication( X, Y ) ) = addition( c( X )
% 4.44/4.83 , c( Y ) ) }.
% 4.44/4.83 { test( skol2 ) }.
% 4.44/4.83 { test( skol3 ) }.
% 4.44/4.83 { multiplication( skol2, skol4 ) = multiplication( multiplication( skol2,
% 4.44/4.83 skol4 ), skol3 ) }.
% 4.44/4.83 { ! leq( multiplication( skol2, skol4 ), multiplication( skol4, skol3 ) ) }
% 4.44/4.83 .
% 4.44/4.83
% 4.44/4.83 percentage equality = 0.490196, percentage horn = 0.966667
% 4.44/4.83 This is a problem with some equality
% 4.44/4.83
% 4.44/4.83
% 4.44/4.83
% 4.44/4.83 Options Used:
% 4.44/4.83
% 4.44/4.83 useres = 1
% 4.44/4.83 useparamod = 1
% 4.44/4.83 useeqrefl = 1
% 4.44/4.83 useeqfact = 1
% 4.44/4.83 usefactor = 1
% 4.44/4.83 usesimpsplitting = 0
% 4.44/4.83 usesimpdemod = 5
% 4.44/4.83 usesimpres = 3
% 4.44/4.83
% 4.44/4.83 resimpinuse = 1000
% 4.44/4.83 resimpclauses = 20000
% 4.44/4.83 substype = eqrewr
% 4.44/4.83 backwardsubs = 1
% 4.44/4.83 selectoldest = 5
% 4.44/4.83
% 4.44/4.83 litorderings [0] = split
% 4.44/4.83 litorderings [1] = extend the termordering, first sorting on arguments
% 4.44/4.83
% 4.44/4.83 termordering = kbo
% 4.44/4.83
% 4.44/4.83 litapriori = 0
% 4.44/4.83 termapriori = 1
% 4.44/4.83 litaposteriori = 0
% 4.44/4.83 termaposteriori = 0
% 4.44/4.83 demodaposteriori = 0
% 4.44/4.83 ordereqreflfact = 0
% 4.44/4.83
% 4.44/4.83 litselect = negord
% 4.44/4.83
% 4.44/4.83 maxweight = 15
% 4.44/4.83 maxdepth = 30000
% 4.44/4.83 maxlength = 115
% 4.44/4.83 maxnrvars = 195
% 4.44/4.83 excuselevel = 1
% 4.44/4.83 increasemaxweight = 1
% 4.44/4.83
% 4.44/4.83 maxselected = 10000000
% 4.44/4.83 maxnrclauses = 10000000
% 4.44/4.83
% 4.44/4.83 showgenerated = 0
% 4.44/4.83 showkept = 0
% 4.44/4.83 showselected = 0
% 4.44/4.83 showdeleted = 0
% 4.44/4.83 showresimp = 1
% 4.44/4.83 showstatus = 2000
% 4.44/4.83
% 4.44/4.83 prologoutput = 0
% 4.44/4.83 nrgoals = 5000000
% 4.44/4.83 totalproof = 1
% 4.44/4.83
% 4.44/4.83 Symbols occurring in the translation:
% 4.44/4.83
% 4.44/4.83 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 4.44/4.83 . [1, 2] (w:1, o:25, a:1, s:1, b:0),
% 4.44/4.83 ! [4, 1] (w:0, o:17, a:1, s:1, b:0),
% 4.44/4.83 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 4.44/4.83 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 4.44/4.83 addition [37, 2] (w:1, o:49, a:1, s:1, b:0),
% 4.44/4.83 zero [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 4.44/4.83 multiplication [40, 2] (w:1, o:51, a:1, s:1, b:0),
% 4.44/4.83 one [41, 0] (w:1, o:10, a:1, s:1, b:0),
% 4.44/4.83 leq [42, 2] (w:1, o:50, a:1, s:1, b:0),
% 4.44/4.83 test [44, 1] (w:1, o:23, a:1, s:1, b:0),
% 4.44/4.83 complement [46, 2] (w:1, o:52, a:1, s:1, b:0),
% 4.44/4.83 c [47, 1] (w:1, o:24, a:1, s:1, b:0),
% 4.44/4.83 alpha1 [49, 2] (w:1, o:53, a:1, s:1, b:1),
% 4.44/4.83 skol1 [50, 1] (w:1, o:22, a:1, s:1, b:1),
% 4.44/4.83 skol2 [51, 0] (w:1, o:14, a:1, s:1, b:1),
% 4.44/4.83 skol3 [52, 0] (w:1, o:15, a:1, s:1, b:1),
% 4.44/4.83 skol4 [53, 0] (w:1, o:16, a:1, s:1, b:1).
% 4.44/4.83
% 4.44/4.83
% 4.44/4.83 Starting Search:
% 4.44/4.83
% 4.44/4.83 *** allocated 15000 integers for clauses
% 4.44/4.83 *** allocated 22500 integers for clauses
% 4.44/4.83 *** allocated 33750 integers for clauses
% 4.44/4.83 *** allocated 50625 integers for clauses
% 4.44/4.83 *** allocated 15000 integers for termspace/termends
% 4.44/4.83 *** allocated 75937 integers for clauses
% 4.44/4.83 Resimplifying inuse:
% 4.44/4.83 Done
% 4.44/4.83
% 4.44/4.83 *** allocated 22500 integers for termspace/termends
% 4.44/4.83 *** allocated 113905 integers for clauses
% 4.44/4.83 *** allocated 33750 integers for termspace/termends
% 4.44/4.83
% 4.44/4.83 Intermediate Status:
% 4.44/4.83 Generated: 12240
% 4.44/4.83 Kept: 2007
% 4.44/4.83 Inuse: 259
% 4.44/4.83 Deleted: 38
% 4.44/4.83 Deletedinuse: 22
% 4.44/4.83
% 4.44/4.83 Resimplifying inuse:
% 4.44/4.83 Done
% 4.44/4.83
% 4.44/4.83 *** allocated 170857 integers for clauses
% 4.44/4.83 *** allocated 50625 integers for termspace/termends
% 4.44/4.83 Resimplifying inuse:
% 4.44/4.83 Done
% 4.44/4.83
% 4.44/4.83 *** allocated 256285 integers for clauses
% 4.44/4.83
% 4.44/4.83 Intermediate Status:
% 4.44/4.83 Generated: 26961
% 4.44/4.83 Kept: 4010
% 4.44/4.83 Inuse: 439
% 4.44/4.83 Deleted: 186
% 4.44/4.83 Deletedinuse: 34
% 4.44/4.83
% 4.44/4.83 Resimplifying inuse:
% 4.44/4.83 Done
% 4.44/4.83
% 4.44/4.83 *** allocated 75937 integers for termspace/termends
% 4.44/4.83 *** allocated 384427 integers for clauses
% 4.44/4.83 Resimplifying inuse:
% 4.44/4.83 Done
% 4.44/4.83
% 4.44/4.83
% 4.44/4.83 Intermediate Status:
% 4.44/4.83 Generated: 42338
% 4.44/4.83 Kept: 6021
% 4.44/4.83 Inuse: 670
% 4.44/4.83 Deleted: 242
% 4.44/4.83 Deletedinuse: 60
% 4.44/4.83
% 4.44/4.83 Resimplifying inuse:
% 4.44/4.83 Done
% 4.44/4.83
% 4.44/4.83 *** allocated 113905 integers for termspace/termends
% 4.44/4.83 Resimplifying inuse:
% 4.44/4.83 Done
% 4.44/4.83
% 4.44/4.83 *** allocated 576640 integers for clauses
% 4.44/4.83
% 4.44/4.83 Intermediate Status:
% 4.44/4.83 Generated: 57593
% 4.44/4.83 Kept: 8034
% 4.44/4.83 Inuse: 836
% 4.44/4.83 Deleted: 357
% 4.44/4.83 Deletedinuse: 162
% 4.44/4.83
% 4.44/4.83 Resimplifying inuse:
% 4.44/4.83 Done
% 4.44/4.83
% 4.44/4.83 Resimplifying inuse:
% 4.44/4.83 Done
% 4.44/4.83
% 4.44/4.83 *** allocated 170857 integers for termspace/termends
% 4.44/4.83
% 4.44/4.83 Intermediate Status:
% 4.44/4.83 Generated: 67659
% 4.44/4.83 Kept: 10058
% 4.44/4.83 Inuse: 944
% 4.44/4.83 Deleted: 432
% 4.44/4.83 Deletedinuse: 202
% 4.44/4.83
% 4.44/4.83 Resimplifying inuse:
% 4.44/4.83 Done
% 4.44/4.83
% 4.44/4.83 Resimplifying inuse:
% 4.44/4.83 Done
% 4.44/4.83
% 4.44/4.83 *** allocated 864960 integers for clauses
% 4.44/4.83
% 4.44/4.83 Intermediate Status:
% 4.44/4.83 Generated: 78160
% 4.44/4.83 Kept: 12123
% 4.44/4.83 Inuse: 1031
% 4.44/4.83 Deleted: 610
% 4.44/4.83 Deletedinuse: 355
% 4.44/4.83
% 4.44/4.83 Resimplifying inuse:
% 4.44/4.83 Done
% 4.44/4.83
% 4.44/4.83 Resimplifying inuse:
% 4.44/4.83 Done
% 4.44/4.83
% 4.44/4.83
% 4.44/4.83 Intermediate Status:
% 4.44/4.83 Generated: 96357
% 4.44/4.83 Kept: 14131
% 4.44/4.83 Inuse: 1193
% 4.44/4.83 Deleted: 752
% 4.44/4.83 Deletedinuse: 391
% 4.44/4.83
% 4.44/4.83 *** allocated 256285 integers for termspace/termends
% 4.44/4.83 Resimplifying inuse:
% 4.44/4.83 Done
% 4.44/4.83
% 4.44/4.83 Resimplifying inuse:
% 4.44/4.83 Done
% 4.44/4.83
% 4.44/4.83
% 4.44/4.83 Intermediate Status:
% 4.44/4.83 Generated: 110449
% 4.44/4.83 Kept: 16132
% 4.44/4.83 Inuse: 1309
% 4.44/4.83 Deleted: 807
% 4.44/4.83 Deletedinuse: 399
% 4.44/4.83
% 4.44/4.83 Resimplifying inuse:
% 4.44/4.83 Done
% 4.44/4.83
% 4.44/4.83 Resimplifying inuse:
% 4.44/4.83 Done
% 4.44/4.83
% 4.44/4.83
% 4.44/4.83 Intermediate Status:
% 4.44/4.83 Generated: 127570
% 4.44/4.83 Kept: 18173
% 4.44/4.83 Inuse: 1455
% 4.44/4.83 Deleted: 920
% 4.44/4.83 Deletedinuse: 411
% 4.44/4.83
% 4.44/4.83 Resimplifying inuse:
% 4.44/4.83 Done
% 4.44/4.83
% 4.44/4.83 *** allocated 1297440 integers for clauses
% 4.44/4.83 Resimplifying inuse:
% 4.44/4.83 Done
% 4.44/4.83
% 4.44/4.83 Resimplifying clauses:
% 4.44/4.83
% 4.44/4.83 Bliksems!, er is een bewijs:
% 4.44/4.83 % SZS status Theorem
% 4.44/4.83 % SZS output start Refutation
% 4.44/4.83
% 4.44/4.83 (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X ) }.
% 4.44/4.83 (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) ) ==> addition(
% 4.44/4.83 addition( Z, Y ), X ) }.
% 4.44/4.83 (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 4.44/4.83 (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 4.44/4.83 (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ),
% 4.44/4.83 multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 4.44/4.83 (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y ) ==> Y }.
% 4.44/4.83 (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X, Y ) }.
% 4.44/4.83 (16) {G0,W6,D2,L2,V2,M2} I { ! complement( Y, X ), alpha1( X, Y ) }.
% 4.44/4.83 (19) {G0,W8,D3,L2,V2,M2} I { ! alpha1( X, Y ), addition( X, Y ) ==> one }.
% 4.44/4.83 (21) {G0,W9,D3,L3,V2,M3} I { ! test( X ), ! c( X ) = Y, complement( X, Y )
% 4.44/4.83 }.
% 4.44/4.83 (26) {G0,W2,D2,L1,V0,M1} I { test( skol2 ) }.
% 4.44/4.83 (28) {G0,W9,D4,L1,V0,M1} I { multiplication( multiplication( skol2, skol4 )
% 4.44/4.83 , skol3 ) ==> multiplication( skol2, skol4 ) }.
% 4.44/4.83 (29) {G0,W7,D3,L1,V0,M1} I { ! leq( multiplication( skol2, skol4 ),
% 4.44/4.83 multiplication( skol4, skol3 ) ) }.
% 4.44/4.83 (30) {G1,W6,D3,L2,V1,M2} Q(21) { ! test( X ), complement( X, c( X ) ) }.
% 4.44/4.83 (42) {G2,W4,D3,L1,V0,M1} R(30,26) { complement( skol2, c( skol2 ) ) }.
% 4.44/4.83 (44) {G3,W4,D3,L1,V0,M1} R(42,16) { alpha1( c( skol2 ), skol2 ) }.
% 4.44/4.83 (65) {G1,W11,D4,L1,V2,M1} P(6,8) { addition( X, multiplication( Y, X ) ) =
% 4.44/4.83 multiplication( addition( one, Y ), X ) }.
% 4.44/4.83 (81) {G1,W8,D3,L2,V2,M2} P(11,0) { addition( Y, X ) ==> Y, ! leq( X, Y )
% 4.44/4.83 }.
% 4.44/4.83 (155) {G1,W14,D4,L2,V3,M2} P(1,12) { ! addition( addition( X, Y ), Z ) ==>
% 4.44/4.83 addition( Y, Z ), leq( X, addition( Y, Z ) ) }.
% 4.44/4.83 (157) {G1,W8,D3,L2,V2,M2} P(0,12) { ! addition( Y, X ) ==> Y, leq( X, Y )
% 4.44/4.83 }.
% 4.44/4.83 (524) {G1,W15,D5,L1,V1,M1} P(28,8) { multiplication( addition( X,
% 4.44/4.83 multiplication( skol2, skol4 ) ), skol3 ) ==> addition( multiplication( X
% 4.44/4.83 , skol3 ), multiplication( skol2, skol4 ) ) }.
% 4.44/4.83 (3889) {G2,W5,D3,L1,V2,M1} P(3,155);q { leq( X, addition( X, Y ) ) }.
% 4.44/4.83 (3947) {G3,W5,D3,L1,V2,M1} P(0,3889) { leq( X, addition( Y, X ) ) }.
% 4.44/4.83 (3986) {G4,W6,D2,L2,V2,M2} P(19,3947) { leq( Y, one ), ! alpha1( X, Y ) }.
% 4.44/4.83 (3995) {G2,W11,D4,L1,V0,M1} R(157,29) { ! addition( multiplication( skol4,
% 4.44/4.83 skol3 ), multiplication( skol2, skol4 ) ) ==> multiplication( skol4,
% 4.44/4.83 skol3 ) }.
% 4.44/4.83 (4273) {G5,W3,D2,L1,V0,M1} R(3986,44) { leq( skol2, one ) }.
% 4.44/4.83 (4280) {G6,W5,D3,L1,V0,M1} R(4273,81) { addition( one, skol2 ) ==> one }.
% 4.44/4.83 (19834) {G7,W11,D4,L1,V0,M1} P(65,524);d(4280);d(6) { addition(
% 4.44/4.83 multiplication( skol4, skol3 ), multiplication( skol2, skol4 ) ) ==>
% 4.44/4.83 multiplication( skol4, skol3 ) }.
% 4.44/4.83 (20012) {G8,W0,D0,L0,V0,M0} S(19834);r(3995) { }.
% 4.44/4.83
% 4.44/4.83
% 4.44/4.83 % SZS output end Refutation
% 4.44/4.83 found a proof!
% 4.44/4.83
% 4.44/4.83
% 4.44/4.83 Unprocessed initial clauses:
% 4.44/4.83
% 4.44/4.83 (20014) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X ) }.
% 4.44/4.83 (20015) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) = addition
% 4.44/4.83 ( addition( Z, Y ), X ) }.
% 4.44/4.83 (20016) {G0,W5,D3,L1,V1,M1} { addition( X, zero ) = X }.
% 4.44/4.83 (20017) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 4.44/4.83 (20018) {G0,W11,D4,L1,V3,M1} { multiplication( X, multiplication( Y, Z ) )
% 4.44/4.83 = multiplication( multiplication( X, Y ), Z ) }.
% 4.44/4.83 (20019) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 4.44/4.83 (20020) {G0,W5,D3,L1,V1,M1} { multiplication( one, X ) = X }.
% 4.44/4.83 (20021) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y, Z ) ) =
% 4.44/4.83 addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 4.44/4.83 (20022) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Y ), Z ) =
% 4.44/4.83 addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 4.44/4.83 (20023) {G0,W5,D3,L1,V1,M1} { multiplication( X, zero ) = zero }.
% 4.44/4.83 (20024) {G0,W5,D3,L1,V1,M1} { multiplication( zero, X ) = zero }.
% 4.44/4.83 (20025) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y }.
% 4.44/4.83 (20026) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 4.44/4.83 (20027) {G0,W6,D3,L2,V1,M2} { ! test( X ), complement( skol1( X ), X ) }.
% 4.44/4.83 (20028) {G0,W5,D2,L2,V2,M2} { ! complement( Y, X ), test( X ) }.
% 4.44/4.83 (20029) {G0,W8,D3,L2,V2,M2} { ! complement( Y, X ), multiplication( X, Y )
% 4.44/4.83 = zero }.
% 4.44/4.83 (20030) {G0,W6,D2,L2,V2,M2} { ! complement( Y, X ), alpha1( X, Y ) }.
% 4.44/4.83 (20031) {G0,W11,D3,L3,V2,M3} { ! multiplication( X, Y ) = zero, ! alpha1(
% 4.44/4.83 X, Y ), complement( Y, X ) }.
% 4.44/4.83 (20032) {G0,W8,D3,L2,V2,M2} { ! alpha1( X, Y ), multiplication( Y, X ) =
% 4.44/4.83 zero }.
% 4.44/4.83 (20033) {G0,W8,D3,L2,V2,M2} { ! alpha1( X, Y ), addition( X, Y ) = one }.
% 4.44/4.83 (20034) {G0,W13,D3,L3,V2,M3} { ! multiplication( Y, X ) = zero, ! addition
% 4.44/4.83 ( X, Y ) = one, alpha1( X, Y ) }.
% 4.44/4.83 (20035) {G0,W9,D3,L3,V2,M3} { ! test( X ), ! c( X ) = Y, complement( X, Y
% 4.44/4.83 ) }.
% 4.44/4.83 (20036) {G0,W9,D3,L3,V2,M3} { ! test( X ), ! complement( X, Y ), c( X ) =
% 4.44/4.83 Y }.
% 4.44/4.83 (20037) {G0,W6,D3,L2,V1,M2} { test( X ), c( X ) = zero }.
% 4.44/4.83 (20038) {G0,W14,D4,L3,V2,M3} { ! test( X ), ! test( Y ), c( addition( X, Y
% 4.44/4.83 ) ) = multiplication( c( X ), c( Y ) ) }.
% 4.44/4.83 (20039) {G0,W14,D4,L3,V2,M3} { ! test( X ), ! test( Y ), c( multiplication
% 4.44/4.83 ( X, Y ) ) = addition( c( X ), c( Y ) ) }.
% 4.44/4.83 (20040) {G0,W2,D2,L1,V0,M1} { test( skol2 ) }.
% 4.44/4.83 (20041) {G0,W2,D2,L1,V0,M1} { test( skol3 ) }.
% 4.44/4.83 (20042) {G0,W9,D4,L1,V0,M1} { multiplication( skol2, skol4 ) =
% 4.44/4.83 multiplication( multiplication( skol2, skol4 ), skol3 ) }.
% 4.44/4.83 (20043) {G0,W7,D3,L1,V0,M1} { ! leq( multiplication( skol2, skol4 ),
% 4.44/4.83 multiplication( skol4, skol3 ) ) }.
% 4.44/4.83
% 4.44/4.83
% 4.44/4.83 Total Proof:
% 4.44/4.83
% 4.44/4.83 subsumption: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X
% 4.44/4.83 ) }.
% 4.44/4.83 parent0: (20014) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X )
% 4.44/4.83 }.
% 4.44/4.83 substitution0:
% 4.44/4.83 X := X
% 4.44/4.83 Y := Y
% 4.44/4.83 end
% 4.44/4.83 permutation0:
% 4.44/4.83 0 ==> 0
% 4.44/4.83 end
% 4.44/4.83
% 4.44/4.83 subsumption: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 4.44/4.83 ==> addition( addition( Z, Y ), X ) }.
% 4.44/4.83 parent0: (20015) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) =
% 4.44/4.83 addition( addition( Z, Y ), X ) }.
% 4.44/4.83 substitution0:
% 4.44/4.83 X := X
% 4.44/4.83 Y := Y
% 4.44/4.83 Z := Z
% 4.44/4.83 end
% 4.44/4.83 permutation0:
% 4.44/4.83 0 ==> 0
% 4.44/4.83 end
% 4.44/4.83
% 4.44/4.83 subsumption: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 4.44/4.83 parent0: (20017) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 4.44/4.83 substitution0:
% 4.44/4.83 X := X
% 4.44/4.83 end
% 4.44/4.83 permutation0:
% 4.44/4.83 0 ==> 0
% 4.44/4.83 end
% 4.44/4.83
% 4.44/4.83 subsumption: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 4.44/4.83 parent0: (20020) {G0,W5,D3,L1,V1,M1} { multiplication( one, X ) = X }.
% 4.44/4.83 substitution0:
% 4.44/4.83 X := X
% 4.44/4.83 end
% 4.44/4.83 permutation0:
% 4.44/4.83 0 ==> 0
% 4.44/4.83 end
% 4.44/4.83
% 4.44/4.83 eqswap: (20061) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Z ),
% 4.44/4.83 multiplication( Y, Z ) ) = multiplication( addition( X, Y ), Z ) }.
% 4.44/4.83 parent0[0]: (20022) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Y
% 4.44/4.83 ), Z ) = addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 4.44/4.83 substitution0:
% 4.44/4.83 X := X
% 4.44/4.83 Y := Y
% 4.44/4.83 Z := Z
% 4.44/4.83 end
% 4.44/4.83
% 4.44/4.83 subsumption: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z )
% 4.44/4.83 , multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 4.44/4.83 parent0: (20061) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Z ),
% 4.44/4.83 multiplication( Y, Z ) ) = multiplication( addition( X, Y ), Z ) }.
% 4.44/4.83 substitution0:
% 4.44/4.83 X := X
% 4.44/4.83 Y := Y
% 4.44/4.83 Z := Z
% 4.44/4.83 end
% 4.44/4.83 permutation0:
% 4.44/4.83 0 ==> 0
% 4.44/4.83 end
% 4.44/4.83
% 4.44/4.83 subsumption: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 4.44/4.83 ==> Y }.
% 4.44/4.83 parent0: (20025) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y
% 4.44/4.83 }.
% 4.44/4.83 substitution0:
% 4.44/4.83 X := X
% 4.44/4.83 Y := Y
% 4.44/4.83 end
% 4.44/4.83 permutation0:
% 4.44/4.83 0 ==> 0
% 4.44/4.83 1 ==> 1
% 4.44/4.83 end
% 4.44/4.83
% 4.44/4.83 subsumption: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X
% 4.44/4.83 , Y ) }.
% 4.44/4.83 parent0: (20026) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y )
% 4.44/4.83 }.
% 4.44/4.83 substitution0:
% 4.44/4.83 X := X
% 4.44/4.83 Y := Y
% 4.44/4.83 end
% 4.44/4.83 permutation0:
% 4.44/4.83 0 ==> 0
% 4.44/4.83 1 ==> 1
% 4.44/4.83 end
% 4.44/4.83
% 4.44/4.83 subsumption: (16) {G0,W6,D2,L2,V2,M2} I { ! complement( Y, X ), alpha1( X,
% 4.44/4.83 Y ) }.
% 4.44/4.83 parent0: (20030) {G0,W6,D2,L2,V2,M2} { ! complement( Y, X ), alpha1( X, Y
% 4.44/4.83 ) }.
% 4.44/4.83 substitution0:
% 4.44/4.83 X := X
% 4.44/4.83 Y := Y
% 4.44/4.83 end
% 4.44/4.83 permutation0:
% 4.44/4.83 0 ==> 0
% 4.44/4.83 1 ==> 1
% 4.44/4.83 end
% 4.44/4.83
% 4.44/4.83 subsumption: (19) {G0,W8,D3,L2,V2,M2} I { ! alpha1( X, Y ), addition( X, Y
% 4.44/4.83 ) ==> one }.
% 4.44/4.83 parent0: (20033) {G0,W8,D3,L2,V2,M2} { ! alpha1( X, Y ), addition( X, Y )
% 4.44/4.83 = one }.
% 4.44/4.83 substitution0:
% 4.44/4.83 X := X
% 4.44/4.83 Y := Y
% 4.44/4.83 end
% 4.44/4.83 permutation0:
% 4.44/4.83 0 ==> 0
% 4.44/4.83 1 ==> 1
% 4.44/4.83 end
% 4.44/4.83
% 4.44/4.83 subsumption: (21) {G0,W9,D3,L3,V2,M3} I { ! test( X ), ! c( X ) = Y,
% 4.44/4.83 complement( X, Y ) }.
% 4.44/4.83 parent0: (20035) {G0,W9,D3,L3,V2,M3} { ! test( X ), ! c( X ) = Y,
% 4.44/4.83 complement( X, Y ) }.
% 4.44/4.83 substitution0:
% 4.44/4.83 X := X
% 4.44/4.83 Y := Y
% 4.44/4.83 end
% 4.44/4.83 permutation0:
% 4.44/4.83 0 ==> 0
% 4.44/4.83 1 ==> 1
% 4.44/4.83 2 ==> 2
% 4.44/4.83 end
% 4.44/4.83
% 4.44/4.83 subsumption: (26) {G0,W2,D2,L1,V0,M1} I { test( skol2 ) }.
% 4.44/4.83 parent0: (20040) {G0,W2,D2,L1,V0,M1} { test( skol2 ) }.
% 4.44/4.83 substitution0:
% 4.44/4.83 end
% 4.44/4.83 permutation0:
% 4.44/4.83 0 ==> 0
% 4.44/4.83 end
% 4.44/4.83
% 4.44/4.83 eqswap: (20190) {G0,W9,D4,L1,V0,M1} { multiplication( multiplication(
% 4.44/4.83 skol2, skol4 ), skol3 ) = multiplication( skol2, skol4 ) }.
% 4.44/4.83 parent0[0]: (20042) {G0,W9,D4,L1,V0,M1} { multiplication( skol2, skol4 ) =
% 4.44/4.83 multiplication( multiplication( skol2, skol4 ), skol3 ) }.
% 4.44/4.83 substitution0:
% 4.44/4.83 end
% 4.44/4.83
% 4.44/4.83 subsumption: (28) {G0,W9,D4,L1,V0,M1} I { multiplication( multiplication(
% 4.44/4.83 skol2, skol4 ), skol3 ) ==> multiplication( skol2, skol4 ) }.
% 4.44/4.83 parent0: (20190) {G0,W9,D4,L1,V0,M1} { multiplication( multiplication(
% 4.44/4.83 skol2, skol4 ), skol3 ) = multiplication( skol2, skol4 ) }.
% 4.44/4.83 substitution0:
% 4.44/4.83 end
% 4.44/4.83 permutation0:
% 4.44/4.83 0 ==> 0
% 4.44/4.83 end
% 4.44/4.83
% 4.44/4.83 subsumption: (29) {G0,W7,D3,L1,V0,M1} I { ! leq( multiplication( skol2,
% 4.44/4.83 skol4 ), multiplication( skol4, skol3 ) ) }.
% 4.44/4.83 parent0: (20043) {G0,W7,D3,L1,V0,M1} { ! leq( multiplication( skol2, skol4
% 4.44/4.83 ), multiplication( skol4, skol3 ) ) }.
% 4.44/4.83 substitution0:
% 4.44/4.83 end
% 4.44/4.83 permutation0:
% 4.44/4.83 0 ==> 0
% 4.44/4.83 end
% 4.44/4.83
% 4.44/4.83 eqswap: (20220) {G0,W9,D3,L3,V2,M3} { ! Y = c( X ), ! test( X ),
% 4.44/4.83 complement( X, Y ) }.
% 4.44/4.83 parent0[1]: (21) {G0,W9,D3,L3,V2,M3} I { ! test( X ), ! c( X ) = Y,
% 4.44/4.83 complement( X, Y ) }.
% 4.44/4.83 substitution0:
% 4.44/4.83 X := X
% 4.44/4.83 Y := Y
% 4.44/4.83 end
% 4.44/4.83
% 4.44/4.83 eqrefl: (20221) {G0,W6,D3,L2,V1,M2} { ! test( X ), complement( X, c( X ) )
% 4.44/4.83 }.
% 4.44/4.83 parent0[0]: (20220) {G0,W9,D3,L3,V2,M3} { ! Y = c( X ), ! test( X ),
% 4.44/4.83 complement( X, Y ) }.
% 4.44/4.83 substitution0:
% 4.44/4.83 X := X
% 4.44/4.83 Y := c( X )
% 4.44/4.83 end
% 4.44/4.83
% 4.44/4.83 subsumption: (30) {G1,W6,D3,L2,V1,M2} Q(21) { ! test( X ), complement( X, c
% 4.44/4.83 ( X ) ) }.
% 4.44/4.83 parent0: (20221) {G0,W6,D3,L2,V1,M2} { ! test( X ), complement( X, c( X )
% 4.44/4.83 ) }.
% 4.44/4.83 substitution0:
% 4.44/4.83 X := X
% 4.44/4.83 end
% 4.44/4.83 permutation0:
% 4.44/4.83 0 ==> 0
% 4.44/4.83 1 ==> 1
% 4.44/4.83 end
% 4.44/4.83
% 4.44/4.83 resolution: (20222) {G1,W4,D3,L1,V0,M1} { complement( skol2, c( skol2 ) )
% 4.44/4.83 }.
% 4.44/4.83 parent0[0]: (30) {G1,W6,D3,L2,V1,M2} Q(21) { ! test( X ), complement( X, c
% 4.44/4.83 ( X ) ) }.
% 4.44/4.83 parent1[0]: (26) {G0,W2,D2,L1,V0,M1} I { test( skol2 ) }.
% 4.44/4.83 substitution0:
% 4.44/4.83 X := skol2
% 4.44/4.83 end
% 4.44/4.83 substitution1:
% 4.44/4.83 end
% 4.44/4.83
% 4.44/4.83 subsumption: (42) {G2,W4,D3,L1,V0,M1} R(30,26) { complement( skol2, c(
% 4.44/4.83 skol2 ) ) }.
% 4.44/4.83 parent0: (20222) {G1,W4,D3,L1,V0,M1} { complement( skol2, c( skol2 ) ) }.
% 4.44/4.83 substitution0:
% 4.44/4.83 end
% 4.44/4.83 permutation0:
% 4.44/4.83 0 ==> 0
% 4.44/4.83 end
% 4.44/4.83
% 4.44/4.83 resolution: (20223) {G1,W4,D3,L1,V0,M1} { alpha1( c( skol2 ), skol2 ) }.
% 4.44/4.83 parent0[0]: (16) {G0,W6,D2,L2,V2,M2} I { ! complement( Y, X ), alpha1( X, Y
% 4.44/4.83 ) }.
% 4.44/4.83 parent1[0]: (42) {G2,W4,D3,L1,V0,M1} R(30,26) { complement( skol2, c( skol2
% 4.44/4.83 ) ) }.
% 4.44/4.83 substitution0:
% 4.44/4.83 X := c( skol2 )
% 4.44/4.83 Y := skol2
% 4.44/4.83 end
% 4.44/4.83 substitution1:
% 4.44/4.83 end
% 4.44/4.83
% 4.44/4.83 subsumption: (44) {G3,W4,D3,L1,V0,M1} R(42,16) { alpha1( c( skol2 ), skol2
% 4.44/4.83 ) }.
% 4.44/4.83 parent0: (20223) {G1,W4,D3,L1,V0,M1} { alpha1( c( skol2 ), skol2 ) }.
% 4.44/4.83 substitution0:
% 4.44/4.83 end
% 4.44/4.83 permutation0:
% 4.44/4.83 0 ==> 0
% 4.44/4.83 end
% 4.44/4.83
% 4.44/4.83 eqswap: (20225) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Z ), Y
% 4.44/4.83 ) ==> addition( multiplication( X, Y ), multiplication( Z, Y ) ) }.
% 4.44/4.83 parent0[0]: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ),
% 4.44/4.83 multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 4.44/4.83 substitution0:
% 4.44/4.83 X := X
% 4.44/4.83 Y := Z
% 4.44/4.83 Z := Y
% 4.44/4.83 end
% 4.44/4.83
% 4.44/4.83 paramod: (20226) {G1,W11,D4,L1,V2,M1} { multiplication( addition( one, X )
% 4.44/4.83 , Y ) ==> addition( Y, multiplication( X, Y ) ) }.
% 4.44/4.83 parent0[0]: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 4.44/4.83 parent1[0; 7]: (20225) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X
% 4.44/4.83 , Z ), Y ) ==> addition( multiplication( X, Y ), multiplication( Z, Y ) )
% 4.44/4.83 }.
% 4.44/4.83 substitution0:
% 4.44/4.83 X := Y
% 4.44/4.83 end
% 4.44/4.83 substitution1:
% 4.44/4.83 X := one
% 4.44/4.83 Y := Y
% 4.44/4.83 Z := X
% 4.44/4.83 end
% 4.44/4.83
% 4.44/4.83 eqswap: (20228) {G1,W11,D4,L1,V2,M1} { addition( Y, multiplication( X, Y )
% 4.44/4.83 ) ==> multiplication( addition( one, X ), Y ) }.
% 4.44/4.83 parent0[0]: (20226) {G1,W11,D4,L1,V2,M1} { multiplication( addition( one,
% 4.44/4.83 X ), Y ) ==> addition( Y, multiplication( X, Y ) ) }.
% 4.44/4.83 substitution0:
% 4.44/4.83 X := X
% 4.44/4.83 Y := Y
% 4.44/4.83 end
% 4.44/4.83
% 4.44/4.83 subsumption: (65) {G1,W11,D4,L1,V2,M1} P(6,8) { addition( X, multiplication
% 4.44/4.83 ( Y, X ) ) = multiplication( addition( one, Y ), X ) }.
% 4.44/4.83 parent0: (20228) {G1,W11,D4,L1,V2,M1} { addition( Y, multiplication( X, Y
% 4.44/4.83 ) ) ==> multiplication( addition( one, X ), Y ) }.
% 4.44/4.83 substitution0:
% 4.44/4.83 X := Y
% 4.44/4.83 Y := X
% 4.44/4.83 end
% 4.44/4.83 permutation0:
% 4.44/4.83 0 ==> 0
% 4.44/4.83 end
% 4.44/4.83
% 4.44/4.83 eqswap: (20230) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X, Y
% 4.44/4.83 ) }.
% 4.44/4.83 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 4.44/4.83 ==> Y }.
% 4.44/4.83 substitution0:
% 4.44/4.83 X := X
% 4.44/4.83 Y := Y
% 4.44/4.83 end
% 4.44/4.83
% 4.44/4.83 paramod: (20231) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y, X
% 4.44/4.83 ) }.
% 4.44/4.83 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 4.44/4.83 }.
% 4.44/4.83 parent1[0; 2]: (20230) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq
% 4.44/4.83 ( X, Y ) }.
% 4.44/4.83 substitution0:
% 4.44/4.83 X := Y
% 4.44/4.83 Y := X
% 4.44/4.83 end
% 4.44/4.83 substitution1:
% 4.44/4.83 X := Y
% 4.44/4.83 Y := X
% 4.44/4.83 end
% 4.44/4.83
% 4.44/4.83 eqswap: (20234) {G1,W8,D3,L2,V2,M2} { addition( X, Y ) ==> X, ! leq( Y, X
% 4.44/4.83 ) }.
% 4.44/4.83 parent0[0]: (20231) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y
% 4.44/4.83 , X ) }.
% 4.44/4.83 substitution0:
% 4.44/4.83 X := X
% 4.44/4.83 Y := Y
% 4.44/4.83 end
% 4.44/4.83
% 4.44/4.83 subsumption: (81) {G1,W8,D3,L2,V2,M2} P(11,0) { addition( Y, X ) ==> Y, !
% 4.44/4.83 leq( X, Y ) }.
% 4.44/4.83 parent0: (20234) {G1,W8,D3,L2,V2,M2} { addition( X, Y ) ==> X, ! leq( Y, X
% 4.44/4.83 ) }.
% 4.44/4.83 substitution0:
% 4.44/4.83 X := Y
% 4.44/4.83 Y := X
% 4.44/4.83 end
% 4.44/4.83 permutation0:
% 4.44/4.83 0 ==> 0
% 4.44/4.83 1 ==> 1
% 4.44/4.83 end
% 4.44/4.83
% 4.44/4.83 eqswap: (20236) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y
% 4.44/4.83 ) }.
% 4.44/4.83 parent0[0]: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 4.44/4.83 Y ) }.
% 4.44/4.83 substitution0:
% 4.44/4.83 X := X
% 4.44/4.83 Y := Y
% 4.44/4.83 end
% 4.44/4.83
% 4.44/4.83 paramod: (20237) {G1,W14,D4,L2,V3,M2} { ! addition( X, Y ) ==> addition(
% 4.44/4.83 addition( Z, X ), Y ), leq( Z, addition( X, Y ) ) }.
% 4.44/4.83 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 4.44/4.83 ==> addition( addition( Z, Y ), X ) }.
% 4.44/4.83 parent1[0; 5]: (20236) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq
% 4.44/4.83 ( X, Y ) }.
% 4.44/4.83 substitution0:
% 4.44/4.83 X := Y
% 4.44/4.83 Y := X
% 4.44/4.83 Z := Z
% 4.44/4.83 end
% 4.44/4.83 substitution1:
% 4.44/4.83 X := Z
% 4.44/4.83 Y := addition( X, Y )
% 4.44/4.83 end
% 4.44/4.83
% 4.44/4.83 eqswap: (20238) {G1,W14,D4,L2,V3,M2} { ! addition( addition( Z, X ), Y )
% 4.44/4.83 ==> addition( X, Y ), leq( Z, addition( X, Y ) ) }.
% 4.44/4.83 parent0[0]: (20237) {G1,W14,D4,L2,V3,M2} { ! addition( X, Y ) ==> addition
% 4.44/4.83 ( addition( Z, X ), Y ), leq( Z, addition( X, Y ) ) }.
% 4.44/4.83 substitution0:
% 4.44/4.83 X := X
% 4.44/4.83 Y := Y
% 4.44/4.83 Z := Z
% 4.44/4.83 end
% 4.44/4.83
% 4.44/4.83 subsumption: (155) {G1,W14,D4,L2,V3,M2} P(1,12) { ! addition( addition( X,
% 4.44/4.83 Y ), Z ) ==> addition( Y, Z ), leq( X, addition( Y, Z ) ) }.
% 4.44/4.83 parent0: (20238) {G1,W14,D4,L2,V3,M2} { ! addition( addition( Z, X ), Y )
% 4.44/4.83 ==> addition( X, Y ), leq( Z, addition( X, Y ) ) }.
% 4.44/4.83 substitution0:
% 4.44/4.83 X := Y
% 4.44/4.83 Y := Z
% 4.44/4.83 Z := X
% 4.44/4.83 end
% 4.44/4.83 permutation0:
% 4.44/4.83 0 ==> 0
% 4.44/4.83 1 ==> 1
% 4.44/4.83 end
% 4.44/4.83
% 4.44/4.83 eqswap: (20239) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y
% 4.44/4.83 ) }.
% 4.44/4.83 parent0[0]: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 4.44/4.83 Y ) }.
% 4.44/4.83 substitution0:
% 4.44/4.83 X := X
% 4.44/4.83 Y := Y
% 4.44/4.83 end
% 4.44/4.83
% 4.44/4.83 paramod: (20240) {G1,W8,D3,L2,V2,M2} { ! X ==> addition( X, Y ), leq( Y, X
% 4.44/4.83 ) }.
% 4.44/4.83 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 4.44/4.83 }.
% 4.44/4.83 parent1[0; 3]: (20239) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq
% 4.44/4.83 ( X, Y ) }.
% 4.44/4.83 substitution0:
% 4.44/4.83 X := Y
% 4.44/4.83 Y := X
% 4.44/4.83 end
% 4.44/4.83 substitution1:
% 4.44/4.83 X := Y
% 4.44/4.83 Y := X
% 4.44/4.83 end
% 4.44/4.83
% 4.44/4.83 eqswap: (20243) {G1,W8,D3,L2,V2,M2} { ! addition( X, Y ) ==> X, leq( Y, X
% 4.44/4.83 ) }.
% 4.44/4.83 parent0[0]: (20240) {G1,W8,D3,L2,V2,M2} { ! X ==> addition( X, Y ), leq( Y
% 4.44/4.83 , X ) }.
% 4.44/4.83 substitution0:
% 4.44/4.83 X := X
% 4.44/4.83 Y := Y
% 4.44/4.83 end
% 4.44/4.83
% 4.44/4.83 subsumption: (157) {G1,W8,D3,L2,V2,M2} P(0,12) { ! addition( Y, X ) ==> Y,
% 4.44/4.83 leq( X, Y ) }.
% 4.44/4.83 parent0: (20243) {G1,W8,D3,L2,V2,M2} { ! addition( X, Y ) ==> X, leq( Y, X
% 4.44/4.83 ) }.
% 4.44/4.83 substitution0:
% 4.44/4.83 X := Y
% 4.44/4.83 Y := X
% 4.44/4.83 end
% 4.44/4.83 permutation0:
% 4.44/4.83 0 ==> 0
% 4.44/4.83 1 ==> 1
% 4.44/4.83 end
% 4.44/4.83
% 4.44/4.83 eqswap: (20245) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Z ), Y
% 4.44/4.83 ) ==> addition( multiplication( X, Y ), multiplication( Z, Y ) ) }.
% 4.44/4.83 parent0[0]: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ),
% 4.44/4.83 multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 4.44/4.83 substitution0:
% 4.44/4.83 X := X
% 4.44/4.83 Y := Z
% 4.44/4.83 Z := Y
% 4.44/4.83 end
% 4.44/4.83
% 4.44/4.83 paramod: (20247) {G1,W15,D5,L1,V1,M1} { multiplication( addition( X,
% 4.44/4.83 multiplication( skol2, skol4 ) ), skol3 ) ==> addition( multiplication( X
% 4.44/4.83 , skol3 ), multiplication( skol2, skol4 ) ) }.
% 4.44/4.83 parent0[0]: (28) {G0,W9,D4,L1,V0,M1} I { multiplication( multiplication(
% 4.44/4.83 skol2, skol4 ), skol3 ) ==> multiplication( skol2, skol4 ) }.
% 4.44/4.83 parent1[0; 12]: (20245) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X
% 4.44/4.83 , Z ), Y ) ==> addition( multiplication( X, Y ), multiplication( Z, Y ) )
% 4.44/4.83 }.
% 4.44/4.83 substitution0:
% 4.44/4.83 end
% 4.44/4.83 substitution1:
% 4.44/4.83 X := X
% 4.44/4.83 Y := skol3
% 4.44/4.83 Z := multiplication( skol2, skol4 )
% 4.44/4.83 end
% 4.44/4.83
% 4.44/4.83 subsumption: (524) {G1,W15,D5,L1,V1,M1} P(28,8) { multiplication( addition
% 4.44/4.83 ( X, multiplication( skol2, skol4 ) ), skol3 ) ==> addition(
% 4.44/4.83 multiplication( X, skol3 ), multiplication( skol2, skol4 ) ) }.
% 4.44/4.83 parent0: (20247) {G1,W15,D5,L1,V1,M1} { multiplication( addition( X,
% 4.44/4.83 multiplication( skol2, skol4 ) ), skol3 ) ==> addition( multiplication( X
% 4.44/4.83 , skol3 ), multiplication( skol2, skol4 ) ) }.
% 4.44/4.83 substitution0:
% 4.44/4.83 X := X
% 4.44/4.83 end
% 4.44/4.83 permutation0:
% 4.44/4.83 0 ==> 0
% 4.44/4.83 end
% 4.44/4.83
% 4.44/4.83 eqswap: (20251) {G1,W14,D4,L2,V3,M2} { ! addition( Y, Z ) ==> addition(
% 4.44/4.83 addition( X, Y ), Z ), leq( X, addition( Y, Z ) ) }.
% 4.44/4.83 parent0[0]: (155) {G1,W14,D4,L2,V3,M2} P(1,12) { ! addition( addition( X, Y
% 4.44/4.83 ), Z ) ==> addition( Y, Z ), leq( X, addition( Y, Z ) ) }.
% 4.44/4.83 substitution0:
% 4.44/4.83 X := X
% 4.44/4.83 Y := Y
% 4.44/4.83 Z := Z
% 4.44/4.83 end
% 4.44/4.83
% 4.44/4.83 paramod: (20254) {G1,W12,D3,L2,V2,M2} { ! addition( X, Y ) ==> addition( X
% 4.44/4.83 , Y ), leq( X, addition( X, Y ) ) }.
% 4.44/4.83 parent0[0]: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 4.44/4.83 parent1[0; 6]: (20251) {G1,W14,D4,L2,V3,M2} { ! addition( Y, Z ) ==>
% 4.44/4.83 addition( addition( X, Y ), Z ), leq( X, addition( Y, Z ) ) }.
% 4.44/4.83 substitution0:
% 4.44/4.83 X := X
% 4.44/4.83 end
% 4.44/4.83 substitution1:
% 4.44/4.83 X := X
% 4.44/4.83 Y := X
% 4.44/4.83 Z := Y
% 4.44/4.83 end
% 4.44/4.83
% 4.44/4.83 eqrefl: (20257) {G0,W5,D3,L1,V2,M1} { leq( X, addition( X, Y ) ) }.
% 4.44/4.83 parent0[0]: (20254) {G1,W12,D3,L2,V2,M2} { ! addition( X, Y ) ==> addition
% 4.44/4.83 ( X, Y ), leq( X, addition( X, Y ) ) }.
% 4.44/4.83 substitution0:
% 4.44/4.83 X := X
% 4.44/4.83 Y := Y
% 4.44/4.83 end
% 4.44/4.83
% 4.44/4.83 subsumption: (3889) {G2,W5,D3,L1,V2,M1} P(3,155);q { leq( X, addition( X, Y
% 4.44/4.83 ) ) }.
% 4.44/4.83 parent0: (20257) {G0,W5,D3,L1,V2,M1} { leq( X, addition( X, Y ) ) }.
% 4.44/4.83 substitution0:
% 4.44/4.83 X := X
% 4.44/4.83 Y := Y
% 4.44/4.83 end
% 4.44/4.83 permutation0:
% 4.44/4.83 0 ==> 0
% 4.44/4.83 end
% 4.44/4.83
% 4.44/4.83 paramod: (20258) {G1,W5,D3,L1,V2,M1} { leq( X, addition( Y, X ) ) }.
% 4.44/4.83 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 4.44/4.83 }.
% 4.44/4.83 parent1[0; 2]: (3889) {G2,W5,D3,L1,V2,M1} P(3,155);q { leq( X, addition( X
% 4.44/4.83 , Y ) ) }.
% 4.44/4.83 substitution0:
% 4.44/4.83 X := X
% 4.44/4.83 Y := Y
% 4.44/4.83 end
% 4.44/4.83 substitution1:
% 4.44/4.83 X := X
% 4.44/4.83 Y := Y
% 4.44/4.83 end
% 4.44/4.83
% 4.44/4.83 subsumption: (3947) {G3,W5,D3,L1,V2,M1} P(0,3889) { leq( X, addition( Y, X
% 4.44/4.83 ) ) }.
% 4.44/4.83 parent0: (20258) {G1,W5,D3,L1,V2,M1} { leq( X, addition( Y, X ) ) }.
% 4.44/4.83 substitution0:
% 4.44/4.83 X := X
% 4.44/4.83 Y := Y
% 4.44/4.83 end
% 4.44/4.83 permutation0:
% 4.44/4.83 0 ==> 0
% 4.44/4.83 end
% 4.44/4.83
% 4.44/4.83 paramod: (20261) {G1,W6,D2,L2,V2,M2} { leq( X, one ), ! alpha1( Y, X ) }.
% 4.44/4.83 parent0[1]: (19) {G0,W8,D3,L2,V2,M2} I { ! alpha1( X, Y ), addition( X, Y )
% 4.44/4.83 ==> one }.
% 4.44/4.83 parent1[0; 2]: (3947) {G3,W5,D3,L1,V2,M1} P(0,3889) { leq( X, addition( Y,
% 4.44/4.83 X ) ) }.
% 4.44/4.83 substitution0:
% 4.44/4.83 X := Y
% 4.44/4.83 Y := X
% 4.44/4.83 end
% 4.44/4.83 substitution1:
% 4.44/4.83 X := X
% 4.44/4.83 Y := Y
% 4.44/4.83 end
% 4.44/4.83
% 4.44/4.83 subsumption: (3986) {G4,W6,D2,L2,V2,M2} P(19,3947) { leq( Y, one ), !
% 4.44/4.83 alpha1( X, Y ) }.
% 4.44/4.83 parent0: (20261) {G1,W6,D2,L2,V2,M2} { leq( X, one ), ! alpha1( Y, X ) }.
% 4.44/4.83 substitution0:
% 4.44/4.83 X := Y
% 4.44/4.83 Y := X
% 4.44/4.83 end
% 4.44/4.83 permutation0:
% 4.44/4.83 0 ==> 0
% 4.44/4.83 1 ==> 1
% 4.44/4.83 end
% 4.44/4.83
% 4.44/4.83 eqswap: (20262) {G1,W8,D3,L2,V2,M2} { ! X ==> addition( X, Y ), leq( Y, X
% 4.44/4.83 ) }.
% 4.44/4.83 parent0[0]: (157) {G1,W8,D3,L2,V2,M2} P(0,12) { ! addition( Y, X ) ==> Y,
% 4.44/4.83 leq( X, Y ) }.
% 4.44/4.83 substitution0:
% 4.44/4.83 X := Y
% 4.44/4.83 Y := X
% 4.44/4.83 end
% 4.44/4.83
% 4.44/4.83 resolution: (20263) {G1,W11,D4,L1,V0,M1} { ! multiplication( skol4, skol3
% 4.44/4.83 ) ==> addition( multiplication( skol4, skol3 ), multiplication( skol2,
% 4.44/4.83 skol4 ) ) }.
% 4.44/4.83 parent0[0]: (29) {G0,W7,D3,L1,V0,M1} I { ! leq( multiplication( skol2,
% 4.44/4.83 skol4 ), multiplication( skol4, skol3 ) ) }.
% 4.44/4.83 parent1[1]: (20262) {G1,W8,D3,L2,V2,M2} { ! X ==> addition( X, Y ), leq( Y
% 4.44/4.83 , X ) }.
% 4.44/4.83 substitution0:
% 4.44/4.83 end
% 4.44/4.83 substitution1:
% 4.44/4.83 X := multiplication( skol4, skol3 )
% 4.44/4.83 Y := multiplication( skol2, skol4 )
% 4.44/4.83 end
% 4.44/4.83
% 4.44/4.83 eqswap: (20264) {G1,W11,D4,L1,V0,M1} { ! addition( multiplication( skol4,
% 4.44/4.83 skol3 ), multiplication( skol2, skol4 ) ) ==> multiplication( skol4,
% 4.44/4.83 skol3 ) }.
% 4.44/4.83 parent0[0]: (20263) {G1,W11,D4,L1,V0,M1} { ! multiplication( skol4, skol3
% 4.44/4.83 ) ==> addition( multiplication( skol4, skol3 ), multiplication( skol2,
% 4.44/4.83 skol4 ) ) }.
% 4.44/4.83 substitution0:
% 4.44/4.83 end
% 4.44/4.83
% 4.44/4.83 subsumption: (3995) {G2,W11,D4,L1,V0,M1} R(157,29) { ! addition(
% 4.44/4.83 multiplication( skol4, skol3 ), multiplication( skol2, skol4 ) ) ==>
% 4.44/4.83 multiplication( skol4, skol3 ) }.
% 4.44/4.83 parent0: (20264) {G1,W11,D4,L1,V0,M1} { ! addition( multiplication( skol4
% 4.44/4.83 , skol3 ), multiplication( skol2, skol4 ) ) ==> multiplication( skol4,
% 4.44/4.83 skol3 ) }.
% 4.44/4.83 substitution0:
% 4.44/4.83 end
% 4.44/4.83 permutation0:
% 4.44/4.83 0 ==> 0
% 4.44/4.83 end
% 4.44/4.83
% 4.44/4.83 resolution: (20265) {G4,W3,D2,L1,V0,M1} { leq( skol2, one ) }.
% 4.44/4.83 parent0[1]: (3986) {G4,W6,D2,L2,V2,M2} P(19,3947) { leq( Y, one ), ! alpha1
% 4.44/4.83 ( X, Y ) }.
% 4.44/4.83 parent1[0]: (44) {G3,W4,D3,L1,V0,M1} R(42,16) { alpha1( c( skol2 ), skol2 )
% 4.44/4.83 }.
% 4.44/4.83 substitution0:
% 4.44/4.83 X := c( skol2 )
% 4.44/4.83 Y := skol2
% 4.44/4.83 end
% 4.44/4.83 substitution1:
% 4.44/4.83 end
% 4.44/4.83
% 4.44/4.83 subsumption: (4273) {G5,W3,D2,L1,V0,M1} R(3986,44) { leq( skol2, one ) }.
% 4.44/4.83 parent0: (20265) {G4,W3,D2,L1,V0,M1} { leq( skol2, one ) }.
% 4.44/4.83 substitution0:
% 4.44/4.83 end
% 4.44/4.83 permutation0:
% 4.44/4.83 0 ==> 0
% 4.44/4.83 end
% 4.44/4.83
% 4.44/4.83 eqswap: (20266) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y, X
% 4.44/4.83 ) }.
% 4.44/4.83 parent0[0]: (81) {G1,W8,D3,L2,V2,M2} P(11,0) { addition( Y, X ) ==> Y, !
% 4.44/4.83 leq( X, Y ) }.
% 4.44/4.83 substitution0:
% 4.44/4.83 X := Y
% 4.44/4.83 Y := X
% 4.44/4.83 end
% 4.44/4.83
% 4.44/4.83 resolution: (20267) {G2,W5,D3,L1,V0,M1} { one ==> addition( one, skol2 )
% 4.44/4.83 }.
% 4.44/4.83 parent0[1]: (20266) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y
% 4.44/4.83 , X ) }.
% 4.44/4.83 parent1[0]: (4273) {G5,W3,D2,L1,V0,M1} R(3986,44) { leq( skol2, one ) }.
% 4.44/4.83 substitution0:
% 4.44/4.83 X := one
% 4.44/4.83 Y := skol2
% 4.44/4.83 end
% 4.44/4.83 substitution1:
% 4.44/4.83 end
% 4.44/4.83
% 4.44/4.83 eqswap: (20268) {G2,W5,D3,L1,V0,M1} { addition( one, skol2 ) ==> one }.
% 4.44/4.83 parent0[0]: (20267) {G2,W5,D3,L1,V0,M1} { one ==> addition( one, skol2 )
% 4.44/4.83 }.
% 4.44/4.83 substitution0:
% 4.44/4.83 end
% 4.44/4.83
% 4.44/4.83 subsumption: (4280) {G6,W5,D3,L1,V0,M1} R(4273,81) { addition( one, skol2 )
% 4.44/4.83 ==> one }.
% 4.44/4.83 parent0: (20268) {G2,W5,D3,L1,V0,M1} { addition( one, skol2 ) ==> one }.
% 4.44/4.83 substitution0:
% 4.44/4.83 end
% 4.44/4.83 permutation0:
% 4.44/4.83 0 ==> 0
% 4.44/4.83 end
% 4.44/4.83
% 4.44/4.83 eqswap: (20270) {G1,W15,D5,L1,V1,M1} { addition( multiplication( X, skol3
% 4.44/4.83 ), multiplication( skol2, skol4 ) ) ==> multiplication( addition( X,
% 4.44/4.83 multiplication( skol2, skol4 ) ), skol3 ) }.
% 4.44/4.83 parent0[0]: (524) {G1,W15,D5,L1,V1,M1} P(28,8) { multiplication( addition(
% 4.44/4.83 X, multiplication( skol2, skol4 ) ), skol3 ) ==> addition( multiplication
% 4.44/4.83 ( X, skol3 ), multiplication( skol2, skol4 ) ) }.
% 4.44/4.83 substitution0:
% 4.44/4.83 X := X
% 4.44/4.83 end
% 4.44/4.83
% 4.44/4.83 paramod: (20279) {G2,W15,D5,L1,V0,M1} { addition( multiplication( skol4,
% 4.44/4.83 skol3 ), multiplication( skol2, skol4 ) ) ==> multiplication(
% 4.44/4.83 multiplication( addition( one, skol2 ), skol4 ), skol3 ) }.
% 4.44/4.83 parent0[0]: (65) {G1,W11,D4,L1,V2,M1} P(6,8) { addition( X, multiplication
% 4.44/4.83 ( Y, X ) ) = multiplication( addition( one, Y ), X ) }.
% 4.44/4.83 parent1[0; 9]: (20270) {G1,W15,D5,L1,V1,M1} { addition( multiplication( X
% 4.44/4.83 , skol3 ), multiplication( skol2, skol4 ) ) ==> multiplication( addition
% 4.44/4.83 ( X, multiplication( skol2, skol4 ) ), skol3 ) }.
% 4.44/4.83 substitution0:
% 4.44/4.83 X := skol4
% 4.44/4.83 Y := skol2
% 4.44/4.83 end
% 4.44/4.83 substitution1:
% 4.44/4.83 X := skol4
% 4.44/4.83 end
% 4.44/4.83
% 4.44/4.83 paramod: (20280) {G3,W13,D4,L1,V0,M1} { addition( multiplication( skol4,
% 4.44/4.83 skol3 ), multiplication( skol2, skol4 ) ) ==> multiplication(
% 4.44/4.83 multiplication( one, skol4 ), skol3 ) }.
% 4.44/4.83 parent0[0]: (4280) {G6,W5,D3,L1,V0,M1} R(4273,81) { addition( one, skol2 )
% 4.44/4.83 ==> one }.
% 4.44/4.83 parent1[0; 10]: (20279) {G2,W15,D5,L1,V0,M1} { addition( multiplication(
% 4.44/4.83 skol4, skol3 ), multiplication( skol2, skol4 ) ) ==> multiplication(
% 4.44/4.83 multiplication( addition( one, skol2 ), skol4 ), skol3 ) }.
% 4.44/4.83 substitution0:
% 4.44/4.83 end
% 4.44/4.83 substitution1:
% 4.44/4.83 end
% 4.44/4.83
% 4.44/4.83 paramod: (20281) {G1,W11,D4,L1,V0,M1} { addition( multiplication( skol4,
% 4.44/4.83 skol3 ), multiplication( skol2, skol4 ) ) ==> multiplication( skol4,
% 4.44/4.83 skol3 ) }.
% 4.44/4.83 parent0[0]: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 4.44/4.83 parent1[0; 9]: (20280) {G3,W13,D4,L1,V0,M1} { addition( multiplication(
% 4.44/4.83 skol4, skol3 ), multiplication( skol2, skol4 ) ) ==> multiplication(
% 4.44/4.83 multiplication( one, skol4 ), skol3 ) }.
% 4.44/4.83 substitution0:
% 4.44/4.83 X := skol4
% 4.44/4.83 end
% 4.44/4.83 substitution1:
% 4.44/4.83 end
% 4.44/4.83
% 4.44/4.83 subsumption: (19834) {G7,W11,D4,L1,V0,M1} P(65,524);d(4280);d(6) { addition
% 4.44/4.83 ( multiplication( skol4, skol3 ), multiplication( skol2, skol4 ) ) ==>
% 4.44/4.83 multiplication( skol4, skol3 ) }.
% 4.44/4.83 parent0: (20281) {G1,W11,D4,L1,V0,M1} { addition( multiplication( skol4,
% 4.44/4.83 skol3 ), multiplication( skol2, skol4 ) ) ==> multiplication( skol4,
% 4.44/4.83 skol3 ) }.
% 4.44/4.83 substitution0:
% 4.44/4.83 end
% 4.44/4.83 permutation0:
% 4.44/4.83 0 ==> 0
% 4.44/4.83 end
% 4.44/4.83
% 4.44/4.83 resolution: (20285) {G3,W0,D0,L0,V0,M0} { }.
% 4.44/4.83 parent0[0]: (3995) {G2,W11,D4,L1,V0,M1} R(157,29) { ! addition(
% 4.44/4.83 multiplication( skol4, skol3 ), multiplication( skol2, skol4 ) ) ==>
% 4.44/4.83 multiplication( skol4, skol3 ) }.
% 4.44/4.83 parent1[0]: (19834) {G7,W11,D4,L1,V0,M1} P(65,524);d(4280);d(6) { addition
% 4.44/4.83 ( multiplication( skol4, skol3 ), multiplication( skol2, skol4 ) ) ==>
% 4.44/4.83 multiplication( skol4, skol3 ) }.
% 4.44/4.83 substitution0:
% 4.44/4.83 end
% 4.44/4.83 substitution1:
% 4.44/4.83 end
% 4.44/4.83
% 4.44/4.83 subsumption: (20012) {G8,W0,D0,L0,V0,M0} S(19834);r(3995) { }.
% 4.44/4.83 parent0: (20285) {G3,W0,D0,L0,V0,M0} { }.
% 4.44/4.83 substitution0:
% 4.44/4.83 end
% 4.44/4.83 permutation0:
% 4.44/4.83 end
% 4.44/4.83
% 4.44/4.83 Proof check complete!
% 4.44/4.83
% 4.44/4.83 Memory use:
% 4.44/4.83
% 4.44/4.83 space for terms: 245517
% 4.44/4.83 space for clauses: 926704
% 4.44/4.83
% 4.44/4.83
% 4.44/4.83 clauses generated: 146677
% 4.44/4.83 clauses kept: 20013
% 4.44/4.83 clauses selected: 1517
% 4.44/4.83 clauses deleted: 998
% 4.44/4.83 clauses inuse deleted: 423
% 4.44/4.83
% 4.44/4.83 subsentry: 831062
% 4.44/4.83 literals s-matched: 470887
% 4.44/4.83 literals matched: 466783
% 4.44/4.83 full subsumption: 193600
% 4.44/4.83
% 4.44/4.83 checksum: 2004309600
% 4.44/4.83
% 4.44/4.83
% 4.44/4.83 Bliksem ended
%------------------------------------------------------------------------------