TSTP Solution File: KLE026+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : KLE026+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n009.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 01:36:43 EDT 2022
% Result : Theorem 3.07s 3.48s
% Output : Refutation 3.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KLE026+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % DateTime : Thu Jun 16 14:53:37 EDT 2022
% 0.12/0.34 % CPUTime :
% 3.07/3.48 *** allocated 10000 integers for termspace/termends
% 3.07/3.48 *** allocated 10000 integers for clauses
% 3.07/3.48 *** allocated 10000 integers for justifications
% 3.07/3.48 Bliksem 1.12
% 3.07/3.48
% 3.07/3.48
% 3.07/3.48 Automatic Strategy Selection
% 3.07/3.48
% 3.07/3.48
% 3.07/3.48 Clauses:
% 3.07/3.48
% 3.07/3.48 { addition( X, Y ) = addition( Y, X ) }.
% 3.07/3.48 { addition( Z, addition( Y, X ) ) = addition( addition( Z, Y ), X ) }.
% 3.07/3.48 { addition( X, zero ) = X }.
% 3.07/3.48 { addition( X, X ) = X }.
% 3.07/3.48 { multiplication( X, multiplication( Y, Z ) ) = multiplication(
% 3.07/3.48 multiplication( X, Y ), Z ) }.
% 3.07/3.48 { multiplication( X, one ) = X }.
% 3.07/3.48 { multiplication( one, X ) = X }.
% 3.07/3.48 { multiplication( X, addition( Y, Z ) ) = addition( multiplication( X, Y )
% 3.07/3.48 , multiplication( X, Z ) ) }.
% 3.07/3.48 { multiplication( addition( X, Y ), Z ) = addition( multiplication( X, Z )
% 3.07/3.48 , multiplication( Y, Z ) ) }.
% 3.07/3.48 { multiplication( X, zero ) = zero }.
% 3.07/3.48 { multiplication( zero, X ) = zero }.
% 3.07/3.48 { ! leq( X, Y ), addition( X, Y ) = Y }.
% 3.07/3.48 { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 3.07/3.48 { ! test( X ), complement( skol1( X ), X ) }.
% 3.07/3.48 { ! complement( Y, X ), test( X ) }.
% 3.07/3.48 { ! complement( Y, X ), multiplication( X, Y ) = zero }.
% 3.07/3.48 { ! complement( Y, X ), alpha1( X, Y ) }.
% 3.07/3.48 { ! multiplication( X, Y ) = zero, ! alpha1( X, Y ), complement( Y, X ) }.
% 3.07/3.48 { ! alpha1( X, Y ), multiplication( Y, X ) = zero }.
% 3.07/3.48 { ! alpha1( X, Y ), addition( X, Y ) = one }.
% 3.07/3.48 { ! multiplication( Y, X ) = zero, ! addition( X, Y ) = one, alpha1( X, Y )
% 3.07/3.48 }.
% 3.07/3.48 { ! test( X ), ! c( X ) = Y, complement( X, Y ) }.
% 3.07/3.48 { ! test( X ), ! complement( X, Y ), c( X ) = Y }.
% 3.07/3.48 { test( X ), c( X ) = zero }.
% 3.07/3.48 { test( skol2 ) }.
% 3.07/3.48 { test( skol3 ) }.
% 3.07/3.48 { multiplication( skol2, skol4 ) = multiplication( multiplication( skol2,
% 3.07/3.48 skol4 ), skol3 ) }.
% 3.07/3.48 { ! leq( multiplication( skol2, skol4 ), multiplication( skol4, skol3 ) ) }
% 3.07/3.48 .
% 3.07/3.48
% 3.07/3.48 percentage equality = 0.511111, percentage horn = 0.964286
% 3.07/3.48 This is a problem with some equality
% 3.07/3.48
% 3.07/3.48
% 3.07/3.48
% 3.07/3.48 Options Used:
% 3.07/3.48
% 3.07/3.48 useres = 1
% 3.07/3.48 useparamod = 1
% 3.07/3.48 useeqrefl = 1
% 3.07/3.48 useeqfact = 1
% 3.07/3.48 usefactor = 1
% 3.07/3.48 usesimpsplitting = 0
% 3.07/3.48 usesimpdemod = 5
% 3.07/3.48 usesimpres = 3
% 3.07/3.48
% 3.07/3.48 resimpinuse = 1000
% 3.07/3.48 resimpclauses = 20000
% 3.07/3.48 substype = eqrewr
% 3.07/3.48 backwardsubs = 1
% 3.07/3.48 selectoldest = 5
% 3.07/3.48
% 3.07/3.48 litorderings [0] = split
% 3.07/3.48 litorderings [1] = extend the termordering, first sorting on arguments
% 3.07/3.48
% 3.07/3.48 termordering = kbo
% 3.07/3.48
% 3.07/3.48 litapriori = 0
% 3.07/3.48 termapriori = 1
% 3.07/3.48 litaposteriori = 0
% 3.07/3.48 termaposteriori = 0
% 3.07/3.48 demodaposteriori = 0
% 3.07/3.48 ordereqreflfact = 0
% 3.07/3.48
% 3.07/3.48 litselect = negord
% 3.07/3.48
% 3.07/3.48 maxweight = 15
% 3.07/3.48 maxdepth = 30000
% 3.07/3.48 maxlength = 115
% 3.07/3.48 maxnrvars = 195
% 3.07/3.48 excuselevel = 1
% 3.07/3.48 increasemaxweight = 1
% 3.07/3.48
% 3.07/3.48 maxselected = 10000000
% 3.07/3.48 maxnrclauses = 10000000
% 3.07/3.48
% 3.07/3.48 showgenerated = 0
% 3.07/3.48 showkept = 0
% 3.07/3.48 showselected = 0
% 3.07/3.48 showdeleted = 0
% 3.07/3.48 showresimp = 1
% 3.07/3.48 showstatus = 2000
% 3.07/3.48
% 3.07/3.48 prologoutput = 0
% 3.07/3.48 nrgoals = 5000000
% 3.07/3.48 totalproof = 1
% 3.07/3.48
% 3.07/3.48 Symbols occurring in the translation:
% 3.07/3.48
% 3.07/3.48 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 3.07/3.48 . [1, 2] (w:1, o:25, a:1, s:1, b:0),
% 3.07/3.48 ! [4, 1] (w:0, o:17, a:1, s:1, b:0),
% 3.07/3.48 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 3.07/3.48 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 3.07/3.48 addition [37, 2] (w:1, o:49, a:1, s:1, b:0),
% 3.07/3.48 zero [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 3.07/3.48 multiplication [40, 2] (w:1, o:51, a:1, s:1, b:0),
% 3.07/3.48 one [41, 0] (w:1, o:10, a:1, s:1, b:0),
% 3.07/3.48 leq [42, 2] (w:1, o:50, a:1, s:1, b:0),
% 3.07/3.48 test [44, 1] (w:1, o:23, a:1, s:1, b:0),
% 3.07/3.48 complement [46, 2] (w:1, o:52, a:1, s:1, b:0),
% 3.07/3.48 c [47, 1] (w:1, o:24, a:1, s:1, b:0),
% 3.07/3.48 alpha1 [49, 2] (w:1, o:53, a:1, s:1, b:1),
% 3.07/3.48 skol1 [50, 1] (w:1, o:22, a:1, s:1, b:1),
% 3.07/3.48 skol2 [51, 0] (w:1, o:14, a:1, s:1, b:1),
% 3.07/3.48 skol3 [52, 0] (w:1, o:15, a:1, s:1, b:1),
% 3.07/3.48 skol4 [53, 0] (w:1, o:16, a:1, s:1, b:1).
% 3.07/3.48
% 3.07/3.48
% 3.07/3.48 Starting Search:
% 3.07/3.48
% 3.07/3.48 *** allocated 15000 integers for clauses
% 3.07/3.48 *** allocated 22500 integers for clauses
% 3.07/3.48 *** allocated 33750 integers for clauses
% 3.07/3.48 *** allocated 50625 integers for clauses
% 3.07/3.48 *** allocated 75937 integers for clauses
% 3.07/3.48 *** allocated 15000 integers for termspace/termends
% 3.07/3.48 Resimplifying inuse:
% 3.07/3.48 Done
% 3.07/3.48
% 3.07/3.48 *** allocated 22500 integers for termspace/termends
% 3.07/3.48 *** allocated 113905 integers for clauses
% 3.07/3.48 *** allocated 33750 integers for termspace/termends
% 3.07/3.48
% 3.07/3.48 Intermediate Status:
% 3.07/3.48 Generated: 13298
% 3.07/3.48 Kept: 2003
% 3.07/3.48 Inuse: 263
% 3.07/3.48 Deleted: 43
% 3.07/3.48 Deletedinuse: 22
% 3.07/3.48
% 3.07/3.48 Resimplifying inuse:
% 3.07/3.48 Done
% 3.07/3.48
% 3.07/3.48 *** allocated 170857 integers for clauses
% 3.07/3.48 *** allocated 50625 integers for termspace/termends
% 3.07/3.48 Resimplifying inuse:
% 3.07/3.48 Done
% 3.07/3.48
% 3.07/3.48 *** allocated 256285 integers for clauses
% 3.07/3.48
% 3.07/3.48 Intermediate Status:
% 3.07/3.48 Generated: 28187
% 3.07/3.48 Kept: 4010
% 3.07/3.48 Inuse: 468
% 3.07/3.48 Deleted: 199
% 3.07/3.48 Deletedinuse: 37
% 3.07/3.48
% 3.07/3.48 Resimplifying inuse:
% 3.07/3.48 Done
% 3.07/3.48
% 3.07/3.48 *** allocated 75937 integers for termspace/termends
% 3.07/3.48 Resimplifying inuse:
% 3.07/3.48 Done
% 3.07/3.48
% 3.07/3.48 *** allocated 384427 integers for clauses
% 3.07/3.48
% 3.07/3.48 Intermediate Status:
% 3.07/3.48 Generated: 43818
% 3.07/3.48 Kept: 6010
% 3.07/3.48 Inuse: 687
% 3.07/3.48 Deleted: 246
% 3.07/3.48 Deletedinuse: 63
% 3.07/3.48
% 3.07/3.48 Resimplifying inuse:
% 3.07/3.48 Done
% 3.07/3.48
% 3.07/3.48 *** allocated 113905 integers for termspace/termends
% 3.07/3.48 Resimplifying inuse:
% 3.07/3.48 Done
% 3.07/3.48
% 3.07/3.48 *** allocated 576640 integers for clauses
% 3.07/3.48
% 3.07/3.48 Intermediate Status:
% 3.07/3.48 Generated: 58382
% 3.07/3.48 Kept: 8026
% 3.07/3.48 Inuse: 845
% 3.07/3.48 Deleted: 360
% 3.07/3.48 Deletedinuse: 165
% 3.07/3.48
% 3.07/3.48 Resimplifying inuse:
% 3.07/3.48 Done
% 3.07/3.48
% 3.07/3.48 Resimplifying inuse:
% 3.07/3.48 Done
% 3.07/3.48
% 3.07/3.48 *** allocated 170857 integers for termspace/termends
% 3.07/3.48
% 3.07/3.48 Intermediate Status:
% 3.07/3.48 Generated: 67731
% 3.07/3.48 Kept: 10047
% 3.07/3.48 Inuse: 947
% 3.07/3.48 Deleted: 445
% 3.07/3.48 Deletedinuse: 209
% 3.07/3.48
% 3.07/3.48 Resimplifying inuse:
% 3.07/3.48 Done
% 3.07/3.48
% 3.07/3.48 Resimplifying inuse:
% 3.07/3.48 Done
% 3.07/3.48
% 3.07/3.48 *** allocated 864960 integers for clauses
% 3.07/3.48
% 3.07/3.48 Intermediate Status:
% 3.07/3.48 Generated: 79569
% 3.07/3.48 Kept: 12053
% 3.07/3.48 Inuse: 1039
% 3.07/3.48 Deleted: 608
% 3.07/3.48 Deletedinuse: 347
% 3.07/3.48
% 3.07/3.48 Resimplifying inuse:
% 3.07/3.48 Done
% 3.07/3.48
% 3.07/3.48 Resimplifying inuse:
% 3.07/3.48 Done
% 3.07/3.48
% 3.07/3.48
% 3.07/3.48 Intermediate Status:
% 3.07/3.48 Generated: 98617
% 3.07/3.48 Kept: 14073
% 3.07/3.48 Inuse: 1203
% 3.07/3.48 Deleted: 748
% 3.07/3.48 Deletedinuse: 380
% 3.07/3.48
% 3.07/3.48 *** allocated 256285 integers for termspace/termends
% 3.07/3.48 Resimplifying inuse:
% 3.07/3.48 Done
% 3.07/3.48
% 3.07/3.48 Resimplifying inuse:
% 3.07/3.48 Done
% 3.07/3.48
% 3.07/3.48
% 3.07/3.48 Bliksems!, er is een bewijs:
% 3.07/3.48 % SZS status Theorem
% 3.07/3.48 % SZS output start Refutation
% 3.07/3.48
% 3.07/3.48 (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X ) }.
% 3.07/3.48 (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) ) ==> addition(
% 3.07/3.48 addition( Z, Y ), X ) }.
% 3.07/3.48 (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 3.07/3.48 (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 3.07/3.48 (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ),
% 3.07/3.48 multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 3.07/3.48 (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y ) ==> Y }.
% 3.07/3.48 (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X, Y ) }.
% 3.07/3.48 (16) {G0,W6,D2,L2,V2,M2} I { ! complement( Y, X ), alpha1( X, Y ) }.
% 3.07/3.48 (19) {G0,W8,D3,L2,V2,M2} I { ! alpha1( X, Y ), addition( X, Y ) ==> one }.
% 3.07/3.48 (21) {G0,W9,D3,L3,V2,M3} I { ! test( X ), ! c( X ) = Y, complement( X, Y )
% 3.07/3.48 }.
% 3.07/3.48 (24) {G0,W2,D2,L1,V0,M1} I { test( skol2 ) }.
% 3.07/3.48 (26) {G0,W9,D4,L1,V0,M1} I { multiplication( multiplication( skol2, skol4 )
% 3.07/3.48 , skol3 ) ==> multiplication( skol2, skol4 ) }.
% 3.07/3.48 (27) {G0,W7,D3,L1,V0,M1} I { ! leq( multiplication( skol2, skol4 ),
% 3.07/3.48 multiplication( skol4, skol3 ) ) }.
% 3.07/3.48 (28) {G1,W6,D3,L2,V1,M2} Q(21) { ! test( X ), complement( X, c( X ) ) }.
% 3.07/3.48 (38) {G2,W4,D3,L1,V0,M1} R(28,24) { complement( skol2, c( skol2 ) ) }.
% 3.07/3.48 (40) {G3,W4,D3,L1,V0,M1} R(38,16) { alpha1( c( skol2 ), skol2 ) }.
% 3.07/3.48 (62) {G1,W11,D4,L1,V2,M1} P(6,8) { addition( multiplication( Y, X ), X ) =
% 3.07/3.48 multiplication( addition( Y, one ), X ) }.
% 3.07/3.48 (151) {G1,W14,D4,L2,V3,M2} P(1,12) { ! addition( addition( X, Y ), Z ) ==>
% 3.07/3.48 addition( Y, Z ), leq( X, addition( Y, Z ) ) }.
% 3.07/3.48 (442) {G1,W15,D5,L1,V1,M1} P(26,8) { multiplication( addition(
% 3.07/3.48 multiplication( skol2, skol4 ), X ), skol3 ) ==> addition( multiplication
% 3.07/3.48 ( skol2, skol4 ), multiplication( X, skol3 ) ) }.
% 3.07/3.48 (457) {G1,W11,D4,L1,V0,M1} R(27,12) { ! addition( multiplication( skol2,
% 3.07/3.48 skol4 ), multiplication( skol4, skol3 ) ) ==> multiplication( skol4,
% 3.07/3.48 skol3 ) }.
% 3.07/3.48 (3568) {G2,W5,D3,L1,V2,M1} P(3,151);q { leq( X, addition( X, Y ) ) }.
% 3.07/3.48 (3626) {G3,W5,D3,L1,V2,M1} P(0,3568) { leq( X, addition( Y, X ) ) }.
% 3.07/3.48 (3671) {G4,W6,D2,L2,V2,M2} P(19,3626) { leq( Y, one ), ! alpha1( X, Y ) }.
% 3.07/3.48 (4120) {G5,W3,D2,L1,V0,M1} R(3671,40) { leq( skol2, one ) }.
% 3.07/3.48 (4129) {G6,W5,D3,L1,V0,M1} R(4120,11) { addition( skol2, one ) ==> one }.
% 3.07/3.48 (15036) {G7,W11,D4,L1,V0,M1} P(62,442);d(4129);d(6) { addition(
% 3.07/3.48 multiplication( skol2, skol4 ), multiplication( skol4, skol3 ) ) ==>
% 3.07/3.48 multiplication( skol4, skol3 ) }.
% 3.07/3.48 (15721) {G8,W0,D0,L0,V0,M0} S(457);d(15036);q { }.
% 3.07/3.48
% 3.07/3.48
% 3.07/3.48 % SZS output end Refutation
% 3.07/3.48 found a proof!
% 3.07/3.48
% 3.07/3.48
% 3.07/3.48 Unprocessed initial clauses:
% 3.07/3.48
% 3.07/3.48 (15723) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X ) }.
% 3.07/3.48 (15724) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) = addition
% 3.07/3.48 ( addition( Z, Y ), X ) }.
% 3.07/3.48 (15725) {G0,W5,D3,L1,V1,M1} { addition( X, zero ) = X }.
% 3.07/3.48 (15726) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 3.07/3.48 (15727) {G0,W11,D4,L1,V3,M1} { multiplication( X, multiplication( Y, Z ) )
% 3.07/3.48 = multiplication( multiplication( X, Y ), Z ) }.
% 3.07/3.48 (15728) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 3.07/3.48 (15729) {G0,W5,D3,L1,V1,M1} { multiplication( one, X ) = X }.
% 3.07/3.48 (15730) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y, Z ) ) =
% 3.07/3.48 addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 3.07/3.48 (15731) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Y ), Z ) =
% 3.07/3.48 addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 3.07/3.48 (15732) {G0,W5,D3,L1,V1,M1} { multiplication( X, zero ) = zero }.
% 3.07/3.48 (15733) {G0,W5,D3,L1,V1,M1} { multiplication( zero, X ) = zero }.
% 3.07/3.48 (15734) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y }.
% 3.07/3.48 (15735) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 3.07/3.48 (15736) {G0,W6,D3,L2,V1,M2} { ! test( X ), complement( skol1( X ), X ) }.
% 3.07/3.48 (15737) {G0,W5,D2,L2,V2,M2} { ! complement( Y, X ), test( X ) }.
% 3.07/3.48 (15738) {G0,W8,D3,L2,V2,M2} { ! complement( Y, X ), multiplication( X, Y )
% 3.07/3.48 = zero }.
% 3.07/3.48 (15739) {G0,W6,D2,L2,V2,M2} { ! complement( Y, X ), alpha1( X, Y ) }.
% 3.07/3.48 (15740) {G0,W11,D3,L3,V2,M3} { ! multiplication( X, Y ) = zero, ! alpha1(
% 3.07/3.48 X, Y ), complement( Y, X ) }.
% 3.07/3.48 (15741) {G0,W8,D3,L2,V2,M2} { ! alpha1( X, Y ), multiplication( Y, X ) =
% 3.07/3.48 zero }.
% 3.07/3.48 (15742) {G0,W8,D3,L2,V2,M2} { ! alpha1( X, Y ), addition( X, Y ) = one }.
% 3.07/3.48 (15743) {G0,W13,D3,L3,V2,M3} { ! multiplication( Y, X ) = zero, ! addition
% 3.07/3.48 ( X, Y ) = one, alpha1( X, Y ) }.
% 3.07/3.48 (15744) {G0,W9,D3,L3,V2,M3} { ! test( X ), ! c( X ) = Y, complement( X, Y
% 3.07/3.48 ) }.
% 3.07/3.48 (15745) {G0,W9,D3,L3,V2,M3} { ! test( X ), ! complement( X, Y ), c( X ) =
% 3.07/3.48 Y }.
% 3.07/3.48 (15746) {G0,W6,D3,L2,V1,M2} { test( X ), c( X ) = zero }.
% 3.07/3.48 (15747) {G0,W2,D2,L1,V0,M1} { test( skol2 ) }.
% 3.07/3.48 (15748) {G0,W2,D2,L1,V0,M1} { test( skol3 ) }.
% 3.07/3.48 (15749) {G0,W9,D4,L1,V0,M1} { multiplication( skol2, skol4 ) =
% 3.07/3.48 multiplication( multiplication( skol2, skol4 ), skol3 ) }.
% 3.07/3.48 (15750) {G0,W7,D3,L1,V0,M1} { ! leq( multiplication( skol2, skol4 ),
% 3.07/3.48 multiplication( skol4, skol3 ) ) }.
% 3.07/3.48
% 3.07/3.48
% 3.07/3.48 Total Proof:
% 3.07/3.48
% 3.07/3.48 subsumption: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X
% 3.07/3.48 ) }.
% 3.07/3.48 parent0: (15723) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X )
% 3.07/3.48 }.
% 3.07/3.48 substitution0:
% 3.07/3.48 X := X
% 3.07/3.48 Y := Y
% 3.07/3.48 end
% 3.07/3.48 permutation0:
% 3.07/3.48 0 ==> 0
% 3.07/3.48 end
% 3.07/3.48
% 3.07/3.48 subsumption: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 3.07/3.48 ==> addition( addition( Z, Y ), X ) }.
% 3.07/3.48 parent0: (15724) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) =
% 3.07/3.48 addition( addition( Z, Y ), X ) }.
% 3.07/3.48 substitution0:
% 3.07/3.48 X := X
% 3.07/3.48 Y := Y
% 3.07/3.48 Z := Z
% 3.07/3.48 end
% 3.07/3.48 permutation0:
% 3.07/3.48 0 ==> 0
% 3.07/3.48 end
% 3.07/3.48
% 3.07/3.48 subsumption: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 3.07/3.48 parent0: (15726) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 3.07/3.48 substitution0:
% 3.07/3.48 X := X
% 3.07/3.48 end
% 3.07/3.48 permutation0:
% 3.07/3.48 0 ==> 0
% 3.07/3.48 end
% 3.07/3.48
% 3.07/3.48 subsumption: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 3.07/3.48 parent0: (15729) {G0,W5,D3,L1,V1,M1} { multiplication( one, X ) = X }.
% 3.07/3.48 substitution0:
% 3.07/3.48 X := X
% 3.07/3.48 end
% 3.07/3.48 permutation0:
% 3.07/3.48 0 ==> 0
% 3.07/3.48 end
% 3.07/3.48
% 3.07/3.48 eqswap: (15768) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Z ),
% 3.07/3.48 multiplication( Y, Z ) ) = multiplication( addition( X, Y ), Z ) }.
% 3.07/3.48 parent0[0]: (15731) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Y
% 3.07/3.48 ), Z ) = addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 3.07/3.48 substitution0:
% 3.07/3.48 X := X
% 3.07/3.48 Y := Y
% 3.07/3.48 Z := Z
% 3.07/3.48 end
% 3.07/3.48
% 3.07/3.48 subsumption: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z )
% 3.07/3.48 , multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 3.07/3.48 parent0: (15768) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Z ),
% 3.07/3.48 multiplication( Y, Z ) ) = multiplication( addition( X, Y ), Z ) }.
% 3.07/3.48 substitution0:
% 3.07/3.48 X := X
% 3.07/3.48 Y := Y
% 3.07/3.48 Z := Z
% 3.07/3.48 end
% 3.07/3.48 permutation0:
% 3.07/3.48 0 ==> 0
% 3.07/3.48 end
% 3.07/3.48
% 3.07/3.48 subsumption: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 3.07/3.48 ==> Y }.
% 3.07/3.48 parent0: (15734) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y
% 3.07/3.48 }.
% 3.07/3.48 substitution0:
% 3.07/3.48 X := X
% 3.07/3.48 Y := Y
% 3.07/3.48 end
% 3.07/3.48 permutation0:
% 3.07/3.48 0 ==> 0
% 3.07/3.48 1 ==> 1
% 3.07/3.48 end
% 3.07/3.48
% 3.07/3.48 subsumption: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X
% 3.07/3.48 , Y ) }.
% 3.07/3.48 parent0: (15735) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y )
% 3.07/3.48 }.
% 3.07/3.48 substitution0:
% 3.07/3.48 X := X
% 3.07/3.48 Y := Y
% 3.07/3.48 end
% 3.07/3.48 permutation0:
% 3.07/3.48 0 ==> 0
% 3.07/3.48 1 ==> 1
% 3.07/3.48 end
% 3.07/3.48
% 3.07/3.48 subsumption: (16) {G0,W6,D2,L2,V2,M2} I { ! complement( Y, X ), alpha1( X,
% 3.07/3.48 Y ) }.
% 3.07/3.48 parent0: (15739) {G0,W6,D2,L2,V2,M2} { ! complement( Y, X ), alpha1( X, Y
% 3.07/3.48 ) }.
% 3.07/3.48 substitution0:
% 3.07/3.48 X := X
% 3.07/3.48 Y := Y
% 3.07/3.48 end
% 3.07/3.48 permutation0:
% 3.07/3.48 0 ==> 0
% 3.07/3.48 1 ==> 1
% 3.07/3.48 end
% 3.07/3.48
% 3.07/3.48 subsumption: (19) {G0,W8,D3,L2,V2,M2} I { ! alpha1( X, Y ), addition( X, Y
% 3.07/3.48 ) ==> one }.
% 3.07/3.48 parent0: (15742) {G0,W8,D3,L2,V2,M2} { ! alpha1( X, Y ), addition( X, Y )
% 3.07/3.48 = one }.
% 3.07/3.48 substitution0:
% 3.07/3.48 X := X
% 3.07/3.48 Y := Y
% 3.07/3.48 end
% 3.07/3.48 permutation0:
% 3.07/3.48 0 ==> 0
% 3.07/3.48 1 ==> 1
% 3.07/3.48 end
% 3.07/3.48
% 3.07/3.48 subsumption: (21) {G0,W9,D3,L3,V2,M3} I { ! test( X ), ! c( X ) = Y,
% 3.07/3.48 complement( X, Y ) }.
% 3.07/3.48 parent0: (15744) {G0,W9,D3,L3,V2,M3} { ! test( X ), ! c( X ) = Y,
% 3.07/3.48 complement( X, Y ) }.
% 3.07/3.48 substitution0:
% 3.07/3.48 X := X
% 3.07/3.48 Y := Y
% 3.07/3.48 end
% 3.07/3.48 permutation0:
% 3.07/3.48 0 ==> 0
% 3.07/3.48 1 ==> 1
% 3.07/3.48 2 ==> 2
% 3.07/3.48 end
% 3.07/3.48
% 3.07/3.48 subsumption: (24) {G0,W2,D2,L1,V0,M1} I { test( skol2 ) }.
% 3.07/3.48 parent0: (15747) {G0,W2,D2,L1,V0,M1} { test( skol2 ) }.
% 3.07/3.48 substitution0:
% 3.07/3.48 end
% 3.07/3.48 permutation0:
% 3.07/3.48 0 ==> 0
% 3.07/3.48 end
% 3.07/3.48
% 3.07/3.48 eqswap: (15885) {G0,W9,D4,L1,V0,M1} { multiplication( multiplication(
% 3.07/3.48 skol2, skol4 ), skol3 ) = multiplication( skol2, skol4 ) }.
% 3.07/3.48 parent0[0]: (15749) {G0,W9,D4,L1,V0,M1} { multiplication( skol2, skol4 ) =
% 3.07/3.48 multiplication( multiplication( skol2, skol4 ), skol3 ) }.
% 3.07/3.48 substitution0:
% 3.07/3.48 end
% 3.07/3.48
% 3.07/3.48 subsumption: (26) {G0,W9,D4,L1,V0,M1} I { multiplication( multiplication(
% 3.07/3.48 skol2, skol4 ), skol3 ) ==> multiplication( skol2, skol4 ) }.
% 3.07/3.48 parent0: (15885) {G0,W9,D4,L1,V0,M1} { multiplication( multiplication(
% 3.07/3.48 skol2, skol4 ), skol3 ) = multiplication( skol2, skol4 ) }.
% 3.07/3.48 substitution0:
% 3.07/3.48 end
% 3.07/3.48 permutation0:
% 3.07/3.48 0 ==> 0
% 3.07/3.48 end
% 3.07/3.48
% 3.07/3.48 subsumption: (27) {G0,W7,D3,L1,V0,M1} I { ! leq( multiplication( skol2,
% 3.07/3.48 skol4 ), multiplication( skol4, skol3 ) ) }.
% 3.07/3.48 parent0: (15750) {G0,W7,D3,L1,V0,M1} { ! leq( multiplication( skol2, skol4
% 3.07/3.48 ), multiplication( skol4, skol3 ) ) }.
% 3.07/3.48 substitution0:
% 3.07/3.48 end
% 3.07/3.48 permutation0:
% 3.07/3.48 0 ==> 0
% 3.07/3.48 end
% 3.07/3.48
% 3.07/3.48 eqswap: (15909) {G0,W9,D3,L3,V2,M3} { ! Y = c( X ), ! test( X ),
% 3.07/3.48 complement( X, Y ) }.
% 3.07/3.48 parent0[1]: (21) {G0,W9,D3,L3,V2,M3} I { ! test( X ), ! c( X ) = Y,
% 3.07/3.48 complement( X, Y ) }.
% 3.07/3.48 substitution0:
% 3.07/3.48 X := X
% 3.07/3.48 Y := Y
% 3.07/3.48 end
% 3.07/3.48
% 3.07/3.48 eqrefl: (15910) {G0,W6,D3,L2,V1,M2} { ! test( X ), complement( X, c( X ) )
% 3.07/3.48 }.
% 3.07/3.48 parent0[0]: (15909) {G0,W9,D3,L3,V2,M3} { ! Y = c( X ), ! test( X ),
% 3.07/3.48 complement( X, Y ) }.
% 3.07/3.48 substitution0:
% 3.07/3.48 X := X
% 3.07/3.48 Y := c( X )
% 3.07/3.48 end
% 3.07/3.48
% 3.07/3.48 subsumption: (28) {G1,W6,D3,L2,V1,M2} Q(21) { ! test( X ), complement( X, c
% 3.07/3.48 ( X ) ) }.
% 3.07/3.48 parent0: (15910) {G0,W6,D3,L2,V1,M2} { ! test( X ), complement( X, c( X )
% 3.07/3.48 ) }.
% 3.07/3.48 substitution0:
% 3.07/3.48 X := X
% 3.07/3.48 end
% 3.07/3.48 permutation0:
% 3.07/3.48 0 ==> 0
% 3.07/3.48 1 ==> 1
% 3.07/3.48 end
% 3.07/3.48
% 3.07/3.48 resolution: (15911) {G1,W4,D3,L1,V0,M1} { complement( skol2, c( skol2 ) )
% 3.07/3.48 }.
% 3.07/3.48 parent0[0]: (28) {G1,W6,D3,L2,V1,M2} Q(21) { ! test( X ), complement( X, c
% 3.07/3.48 ( X ) ) }.
% 3.07/3.48 parent1[0]: (24) {G0,W2,D2,L1,V0,M1} I { test( skol2 ) }.
% 3.07/3.48 substitution0:
% 3.07/3.48 X := skol2
% 3.07/3.48 end
% 3.07/3.48 substitution1:
% 3.07/3.48 end
% 3.07/3.48
% 3.07/3.48 subsumption: (38) {G2,W4,D3,L1,V0,M1} R(28,24) { complement( skol2, c(
% 3.07/3.48 skol2 ) ) }.
% 3.07/3.48 parent0: (15911) {G1,W4,D3,L1,V0,M1} { complement( skol2, c( skol2 ) ) }.
% 3.07/3.48 substitution0:
% 3.07/3.48 end
% 3.07/3.48 permutation0:
% 3.07/3.48 0 ==> 0
% 3.07/3.48 end
% 3.07/3.48
% 3.07/3.48 resolution: (15912) {G1,W4,D3,L1,V0,M1} { alpha1( c( skol2 ), skol2 ) }.
% 3.07/3.48 parent0[0]: (16) {G0,W6,D2,L2,V2,M2} I { ! complement( Y, X ), alpha1( X, Y
% 3.07/3.48 ) }.
% 3.07/3.48 parent1[0]: (38) {G2,W4,D3,L1,V0,M1} R(28,24) { complement( skol2, c( skol2
% 3.07/3.48 ) ) }.
% 3.07/3.48 substitution0:
% 3.07/3.48 X := c( skol2 )
% 3.07/3.48 Y := skol2
% 3.07/3.48 end
% 3.07/3.48 substitution1:
% 3.07/3.48 end
% 3.07/3.48
% 3.07/3.48 subsumption: (40) {G3,W4,D3,L1,V0,M1} R(38,16) { alpha1( c( skol2 ), skol2
% 3.07/3.48 ) }.
% 3.07/3.48 parent0: (15912) {G1,W4,D3,L1,V0,M1} { alpha1( c( skol2 ), skol2 ) }.
% 3.07/3.48 substitution0:
% 3.07/3.48 end
% 3.07/3.48 permutation0:
% 3.07/3.48 0 ==> 0
% 3.07/3.48 end
% 3.07/3.48
% 3.07/3.48 eqswap: (15914) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Z ), Y
% 3.07/3.48 ) ==> addition( multiplication( X, Y ), multiplication( Z, Y ) ) }.
% 3.07/3.48 parent0[0]: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ),
% 3.07/3.48 multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 3.07/3.48 substitution0:
% 3.07/3.48 X := X
% 3.07/3.48 Y := Z
% 3.07/3.48 Z := Y
% 3.07/3.48 end
% 3.07/3.48
% 3.07/3.48 paramod: (15916) {G1,W11,D4,L1,V2,M1} { multiplication( addition( X, one )
% 3.07/3.48 , Y ) ==> addition( multiplication( X, Y ), Y ) }.
% 3.07/3.48 parent0[0]: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 3.07/3.48 parent1[0; 10]: (15914) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X
% 3.07/3.48 , Z ), Y ) ==> addition( multiplication( X, Y ), multiplication( Z, Y ) )
% 3.07/3.48 }.
% 3.07/3.48 substitution0:
% 3.07/3.48 X := Y
% 3.07/3.48 end
% 3.07/3.48 substitution1:
% 3.07/3.48 X := X
% 3.07/3.48 Y := Y
% 3.07/3.48 Z := one
% 3.07/3.48 end
% 3.07/3.48
% 3.07/3.48 eqswap: (15918) {G1,W11,D4,L1,V2,M1} { addition( multiplication( X, Y ), Y
% 3.07/3.48 ) ==> multiplication( addition( X, one ), Y ) }.
% 3.07/3.48 parent0[0]: (15916) {G1,W11,D4,L1,V2,M1} { multiplication( addition( X,
% 3.07/3.48 one ), Y ) ==> addition( multiplication( X, Y ), Y ) }.
% 3.07/3.48 substitution0:
% 3.07/3.48 X := X
% 3.07/3.48 Y := Y
% 3.07/3.48 end
% 3.07/3.48
% 3.07/3.48 subsumption: (62) {G1,W11,D4,L1,V2,M1} P(6,8) { addition( multiplication( Y
% 3.07/3.48 , X ), X ) = multiplication( addition( Y, one ), X ) }.
% 3.07/3.48 parent0: (15918) {G1,W11,D4,L1,V2,M1} { addition( multiplication( X, Y ),
% 3.07/3.48 Y ) ==> multiplication( addition( X, one ), Y ) }.
% 3.07/3.48 substitution0:
% 3.07/3.48 X := Y
% 3.07/3.48 Y := X
% 3.07/3.48 end
% 3.07/3.48 permutation0:
% 3.07/3.48 0 ==> 0
% 3.07/3.48 end
% 3.07/3.48
% 3.07/3.48 eqswap: (15920) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y
% 3.07/3.48 ) }.
% 3.07/3.48 parent0[0]: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 3.07/3.48 Y ) }.
% 3.07/3.48 substitution0:
% 3.07/3.48 X := X
% 3.07/3.48 Y := Y
% 3.07/3.48 end
% 3.07/3.48
% 3.07/3.48 paramod: (15921) {G1,W14,D4,L2,V3,M2} { ! addition( X, Y ) ==> addition(
% 3.07/3.48 addition( Z, X ), Y ), leq( Z, addition( X, Y ) ) }.
% 3.07/3.48 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 3.07/3.48 ==> addition( addition( Z, Y ), X ) }.
% 3.07/3.48 parent1[0; 5]: (15920) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq
% 3.07/3.48 ( X, Y ) }.
% 3.07/3.48 substitution0:
% 3.07/3.48 X := Y
% 3.07/3.48 Y := X
% 3.07/3.48 Z := Z
% 3.07/3.48 end
% 3.07/3.48 substitution1:
% 3.07/3.48 X := Z
% 3.07/3.48 Y := addition( X, Y )
% 3.07/3.48 end
% 3.07/3.48
% 3.07/3.48 eqswap: (15922) {G1,W14,D4,L2,V3,M2} { ! addition( addition( Z, X ), Y )
% 3.07/3.48 ==> addition( X, Y ), leq( Z, addition( X, Y ) ) }.
% 3.07/3.48 parent0[0]: (15921) {G1,W14,D4,L2,V3,M2} { ! addition( X, Y ) ==> addition
% 3.07/3.48 ( addition( Z, X ), Y ), leq( Z, addition( X, Y ) ) }.
% 3.07/3.48 substitution0:
% 3.07/3.48 X := X
% 3.07/3.48 Y := Y
% 3.07/3.48 Z := Z
% 3.07/3.48 end
% 3.07/3.48
% 3.07/3.48 subsumption: (151) {G1,W14,D4,L2,V3,M2} P(1,12) { ! addition( addition( X,
% 3.07/3.48 Y ), Z ) ==> addition( Y, Z ), leq( X, addition( Y, Z ) ) }.
% 3.07/3.48 parent0: (15922) {G1,W14,D4,L2,V3,M2} { ! addition( addition( Z, X ), Y )
% 3.07/3.48 ==> addition( X, Y ), leq( Z, addition( X, Y ) ) }.
% 3.07/3.48 substitution0:
% 3.07/3.48 X := Y
% 3.07/3.48 Y := Z
% 3.07/3.48 Z := X
% 3.07/3.48 end
% 3.07/3.48 permutation0:
% 3.07/3.48 0 ==> 0
% 3.07/3.48 1 ==> 1
% 3.07/3.48 end
% 3.07/3.48
% 3.07/3.48 eqswap: (15924) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Z ), Y
% 3.07/3.48 ) ==> addition( multiplication( X, Y ), multiplication( Z, Y ) ) }.
% 3.07/3.48 parent0[0]: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ),
% 3.07/3.48 multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 3.07/3.48 substitution0:
% 3.07/3.48 X := X
% 3.07/3.48 Y := Z
% 3.07/3.48 Z := Y
% 3.07/3.48 end
% 3.07/3.48
% 3.07/3.48 paramod: (15925) {G1,W15,D5,L1,V1,M1} { multiplication( addition(
% 3.07/3.48 multiplication( skol2, skol4 ), X ), skol3 ) ==> addition( multiplication
% 3.07/3.48 ( skol2, skol4 ), multiplication( X, skol3 ) ) }.
% 3.07/3.48 parent0[0]: (26) {G0,W9,D4,L1,V0,M1} I { multiplication( multiplication(
% 3.07/3.48 skol2, skol4 ), skol3 ) ==> multiplication( skol2, skol4 ) }.
% 3.07/3.48 parent1[0; 9]: (15924) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X
% 3.07/3.48 , Z ), Y ) ==> addition( multiplication( X, Y ), multiplication( Z, Y ) )
% 3.07/3.48 }.
% 3.07/3.48 substitution0:
% 3.07/3.48 end
% 3.07/3.48 substitution1:
% 3.07/3.48 X := multiplication( skol2, skol4 )
% 3.07/3.48 Y := skol3
% 3.07/3.48 Z := X
% 3.07/3.48 end
% 3.07/3.48
% 3.07/3.48 subsumption: (442) {G1,W15,D5,L1,V1,M1} P(26,8) { multiplication( addition
% 3.07/3.48 ( multiplication( skol2, skol4 ), X ), skol3 ) ==> addition(
% 3.07/3.48 multiplication( skol2, skol4 ), multiplication( X, skol3 ) ) }.
% 3.07/3.48 parent0: (15925) {G1,W15,D5,L1,V1,M1} { multiplication( addition(
% 3.07/3.48 multiplication( skol2, skol4 ), X ), skol3 ) ==> addition( multiplication
% 3.07/3.48 ( skol2, skol4 ), multiplication( X, skol3 ) ) }.
% 3.07/3.48 substitution0:
% 3.07/3.48 X := X
% 3.07/3.48 end
% 3.07/3.48 permutation0:
% 3.07/3.48 0 ==> 0
% 3.07/3.48 end
% 3.07/3.48
% 3.07/3.48 eqswap: (15929) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y
% 3.07/3.48 ) }.
% 3.07/3.48 parent0[0]: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 3.07/3.48 Y ) }.
% 3.07/3.48 substitution0:
% 3.07/3.48 X := X
% 3.07/3.48 Y := Y
% 3.07/3.48 end
% 3.07/3.48
% 3.07/3.48 resolution: (15930) {G1,W11,D4,L1,V0,M1} { ! multiplication( skol4, skol3
% 3.07/3.48 ) ==> addition( multiplication( skol2, skol4 ), multiplication( skol4,
% 3.07/3.48 skol3 ) ) }.
% 3.07/3.48 parent0[0]: (27) {G0,W7,D3,L1,V0,M1} I { ! leq( multiplication( skol2,
% 3.07/3.48 skol4 ), multiplication( skol4, skol3 ) ) }.
% 3.07/3.48 parent1[1]: (15929) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X
% 3.07/3.48 , Y ) }.
% 3.07/3.48 substitution0:
% 3.07/3.48 end
% 3.07/3.48 substitution1:
% 3.07/3.48 X := multiplication( skol2, skol4 )
% 3.07/3.48 Y := multiplication( skol4, skol3 )
% 3.07/3.48 end
% 3.07/3.48
% 3.07/3.48 eqswap: (15931) {G1,W11,D4,L1,V0,M1} { ! addition( multiplication( skol2,
% 3.07/3.48 skol4 ), multiplication( skol4, skol3 ) ) ==> multiplication( skol4,
% 3.07/3.48 skol3 ) }.
% 3.07/3.48 parent0[0]: (15930) {G1,W11,D4,L1,V0,M1} { ! multiplication( skol4, skol3
% 3.07/3.48 ) ==> addition( multiplication( skol2, skol4 ), multiplication( skol4,
% 3.07/3.48 skol3 ) ) }.
% 3.07/3.48 substitution0:
% 3.07/3.48 end
% 3.07/3.48
% 3.07/3.48 subsumption: (457) {G1,W11,D4,L1,V0,M1} R(27,12) { ! addition(
% 3.07/3.48 multiplication( skol2, skol4 ), multiplication( skol4, skol3 ) ) ==>
% 3.07/3.48 multiplication( skol4, skol3 ) }.
% 3.07/3.48 parent0: (15931) {G1,W11,D4,L1,V0,M1} { ! addition( multiplication( skol2
% 3.07/3.48 , skol4 ), multiplication( skol4, skol3 ) ) ==> multiplication( skol4,
% 3.07/3.48 skol3 ) }.
% 3.07/3.48 substitution0:
% 3.07/3.48 end
% 3.07/3.48 permutation0:
% 3.07/3.48 0 ==> 0
% 3.07/3.48 end
% 3.07/3.48
% 3.07/3.48 eqswap: (15933) {G1,W14,D4,L2,V3,M2} { ! addition( Y, Z ) ==> addition(
% 3.07/3.48 addition( X, Y ), Z ), leq( X, addition( Y, Z ) ) }.
% 3.07/3.48 parent0[0]: (151) {G1,W14,D4,L2,V3,M2} P(1,12) { ! addition( addition( X, Y
% 3.07/3.48 ), Z ) ==> addition( Y, Z ), leq( X, addition( Y, Z ) ) }.
% 3.07/3.48 substitution0:
% 3.07/3.48 X := X
% 3.07/3.48 Y := Y
% 3.07/3.48 Z := Z
% 3.07/3.48 end
% 3.07/3.48
% 3.07/3.48 paramod: (15936) {G1,W12,D3,L2,V2,M2} { ! addition( X, Y ) ==> addition( X
% 3.07/3.48 , Y ), leq( X, addition( X, Y ) ) }.
% 3.07/3.48 parent0[0]: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 3.07/3.48 parent1[0; 6]: (15933) {G1,W14,D4,L2,V3,M2} { ! addition( Y, Z ) ==>
% 3.07/3.48 addition( addition( X, Y ), Z ), leq( X, addition( Y, Z ) ) }.
% 3.07/3.48 substitution0:
% 3.07/3.48 X := X
% 3.07/3.48 end
% 3.07/3.48 substitution1:
% 3.07/3.48 X := X
% 3.07/3.48 Y := X
% 3.07/3.48 Z := Y
% 3.07/3.48 end
% 3.07/3.48
% 3.07/3.48 eqrefl: (15939) {G0,W5,D3,L1,V2,M1} { leq( X, addition( X, Y ) ) }.
% 3.07/3.48 parent0[0]: (15936) {G1,W12,D3,L2,V2,M2} { ! addition( X, Y ) ==> addition
% 3.07/3.48 ( X, Y ), leq( X, addition( X, Y ) ) }.
% 3.07/3.48 substitution0:
% 3.07/3.48 X := X
% 3.07/3.48 Y := Y
% 3.07/3.48 end
% 3.07/3.48
% 3.07/3.48 subsumption: (3568) {G2,W5,D3,L1,V2,M1} P(3,151);q { leq( X, addition( X, Y
% 3.07/3.48 ) ) }.
% 3.07/3.48 parent0: (15939) {G0,W5,D3,L1,V2,M1} { leq( X, addition( X, Y ) ) }.
% 3.07/3.48 substitution0:
% 3.07/3.48 X := X
% 3.07/3.48 Y := Y
% 3.07/3.48 end
% 3.07/3.48 permutation0:
% 3.07/3.48 0 ==> 0
% 3.07/3.48 end
% 3.07/3.48
% 3.07/3.48 paramod: (15940) {G1,W5,D3,L1,V2,M1} { leq( X, addition( Y, X ) ) }.
% 3.07/3.48 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 3.07/3.48 }.
% 3.07/3.48 parent1[0; 2]: (3568) {G2,W5,D3,L1,V2,M1} P(3,151);q { leq( X, addition( X
% 3.07/3.48 , Y ) ) }.
% 3.07/3.48 substitution0:
% 3.07/3.48 X := X
% 3.07/3.48 Y := Y
% 3.07/3.48 end
% 3.07/3.48 substitution1:
% 3.07/3.48 X := X
% 3.07/3.48 Y := Y
% 3.07/3.48 end
% 3.07/3.48
% 3.07/3.48 subsumption: (3626) {G3,W5,D3,L1,V2,M1} P(0,3568) { leq( X, addition( Y, X
% 3.07/3.48 ) ) }.
% 3.07/3.48 parent0: (15940) {G1,W5,D3,L1,V2,M1} { leq( X, addition( Y, X ) ) }.
% 3.07/3.48 substitution0:
% 3.07/3.48 X := X
% 3.07/3.48 Y := Y
% 3.07/3.48 end
% 3.07/3.48 permutation0:
% 3.07/3.48 0 ==> 0
% 3.07/3.48 end
% 3.07/3.48
% 3.07/3.48 paramod: (15943) {G1,W6,D2,L2,V2,M2} { leq( X, one ), ! alpha1( Y, X ) }.
% 3.07/3.48 parent0[1]: (19) {G0,W8,D3,L2,V2,M2} I { ! alpha1( X, Y ), addition( X, Y )
% 3.07/3.48 ==> one }.
% 3.07/3.48 parent1[0; 2]: (3626) {G3,W5,D3,L1,V2,M1} P(0,3568) { leq( X, addition( Y,
% 3.07/3.48 X ) ) }.
% 3.07/3.48 substitution0:
% 3.07/3.48 X := Y
% 3.07/3.48 Y := X
% 3.07/3.48 end
% 3.07/3.48 substitution1:
% 3.07/3.48 X := X
% 3.07/3.48 Y := Y
% 3.07/3.48 end
% 3.07/3.48
% 3.07/3.48 subsumption: (3671) {G4,W6,D2,L2,V2,M2} P(19,3626) { leq( Y, one ), !
% 3.07/3.48 alpha1( X, Y ) }.
% 3.07/3.48 parent0: (15943) {G1,W6,D2,L2,V2,M2} { leq( X, one ), ! alpha1( Y, X ) }.
% 3.07/3.48 substitution0:
% 3.07/3.48 X := Y
% 3.07/3.48 Y := X
% 3.07/3.48 end
% 3.07/3.48 permutation0:
% 3.07/3.48 0 ==> 0
% 3.07/3.48 1 ==> 1
% 3.07/3.48 end
% 3.07/3.48
% 3.07/3.48 resolution: (15944) {G4,W3,D2,L1,V0,M1} { leq( skol2, one ) }.
% 3.07/3.48 parent0[1]: (3671) {G4,W6,D2,L2,V2,M2} P(19,3626) { leq( Y, one ), ! alpha1
% 3.07/3.48 ( X, Y ) }.
% 3.07/3.48 parent1[0]: (40) {G3,W4,D3,L1,V0,M1} R(38,16) { alpha1( c( skol2 ), skol2 )
% 3.07/3.48 }.
% 3.07/3.48 substitution0:
% 3.07/3.48 X := c( skol2 )
% 3.07/3.48 Y := skol2
% 3.07/3.48 end
% 3.07/3.48 substitution1:
% 3.07/3.48 end
% 3.07/3.48
% 3.07/3.48 subsumption: (4120) {G5,W3,D2,L1,V0,M1} R(3671,40) { leq( skol2, one ) }.
% 3.07/3.48 parent0: (15944) {G4,W3,D2,L1,V0,M1} { leq( skol2, one ) }.
% 3.07/3.48 substitution0:
% 3.07/3.48 end
% 3.07/3.48 permutation0:
% 3.07/3.48 0 ==> 0
% 3.07/3.48 end
% 3.07/3.48
% 3.07/3.48 eqswap: (15945) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X, Y
% 3.07/3.48 ) }.
% 3.07/3.48 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 3.07/3.48 ==> Y }.
% 3.07/3.48 substitution0:
% 3.07/3.48 X := X
% 3.07/3.48 Y := Y
% 3.07/3.48 end
% 3.07/3.48
% 3.07/3.48 resolution: (15946) {G1,W5,D3,L1,V0,M1} { one ==> addition( skol2, one )
% 3.07/3.48 }.
% 3.07/3.48 parent0[1]: (15945) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X
% 3.07/3.48 , Y ) }.
% 3.07/3.48 parent1[0]: (4120) {G5,W3,D2,L1,V0,M1} R(3671,40) { leq( skol2, one ) }.
% 3.07/3.48 substitution0:
% 3.07/3.48 X := skol2
% 3.07/3.48 Y := one
% 3.07/3.48 end
% 3.07/3.48 substitution1:
% 3.07/3.48 end
% 3.07/3.48
% 3.07/3.48 eqswap: (15947) {G1,W5,D3,L1,V0,M1} { addition( skol2, one ) ==> one }.
% 3.07/3.48 parent0[0]: (15946) {G1,W5,D3,L1,V0,M1} { one ==> addition( skol2, one )
% 3.07/3.48 }.
% 3.07/3.48 substitution0:
% 3.07/3.48 end
% 3.07/3.48
% 3.07/3.48 subsumption: (4129) {G6,W5,D3,L1,V0,M1} R(4120,11) { addition( skol2, one )
% 3.07/3.48 ==> one }.
% 3.07/3.48 parent0: (15947) {G1,W5,D3,L1,V0,M1} { addition( skol2, one ) ==> one }.
% 3.07/3.48 substitution0:
% 3.07/3.48 end
% 3.07/3.48 permutation0:
% 3.07/3.48 0 ==> 0
% 3.07/3.48 end
% 3.07/3.48
% 3.07/3.48 eqswap: (15949) {G1,W15,D5,L1,V1,M1} { addition( multiplication( skol2,
% 3.07/3.48 skol4 ), multiplication( X, skol3 ) ) ==> multiplication( addition(
% 3.07/3.48 multiplication( skol2, skol4 ), X ), skol3 ) }.
% 3.07/3.48 parent0[0]: (442) {G1,W15,D5,L1,V1,M1} P(26,8) { multiplication( addition(
% 3.07/3.48 multiplication( skol2, skol4 ), X ), skol3 ) ==> addition( multiplication
% 3.07/3.48 ( skol2, skol4 ), multiplication( X, skol3 ) ) }.
% 3.07/3.48 substitution0:
% 3.07/3.48 X := X
% 3.07/3.48 end
% 3.07/3.48
% 3.07/3.48 paramod: (15958) {G2,W15,D5,L1,V0,M1} { addition( multiplication( skol2,
% 3.07/3.48 skol4 ), multiplication( skol4, skol3 ) ) ==> multiplication(
% 3.07/3.48 multiplication( addition( skol2, one ), skol4 ), skol3 ) }.
% 3.07/3.48 parent0[0]: (62) {G1,W11,D4,L1,V2,M1} P(6,8) { addition( multiplication( Y
% 3.07/3.48 , X ), X ) = multiplication( addition( Y, one ), X ) }.
% 3.07/3.48 parent1[0; 9]: (15949) {G1,W15,D5,L1,V1,M1} { addition( multiplication(
% 3.07/3.48 skol2, skol4 ), multiplication( X, skol3 ) ) ==> multiplication( addition
% 3.07/3.48 ( multiplication( skol2, skol4 ), X ), skol3 ) }.
% 3.07/3.48 substitution0:
% 3.07/3.48 X := skol4
% 3.07/3.48 Y := skol2
% 3.07/3.48 end
% 3.07/3.48 substitution1:
% 3.07/3.48 X := skol4
% 3.07/3.48 end
% 3.07/3.48
% 3.07/3.48 paramod: (15959) {G3,W13,D4,L1,V0,M1} { addition( multiplication( skol2,
% 3.07/3.48 skol4 ), multiplication( skol4, skol3 ) ) ==> multiplication(
% 3.07/3.48 multiplication( one, skol4 ), skol3 ) }.
% 3.07/3.48 parent0[0]: (4129) {G6,W5,D3,L1,V0,M1} R(4120,11) { addition( skol2, one )
% 3.07/3.48 ==> one }.
% 3.07/3.48 parent1[0; 10]: (15958) {G2,W15,D5,L1,V0,M1} { addition( multiplication(
% 3.07/3.48 skol2, skol4 ), multiplication( skol4, skol3 ) ) ==> multiplication(
% 3.07/3.48 multiplication( addition( skol2, one ), skol4 ), skol3 ) }.
% 3.07/3.48 substitution0:
% 3.07/3.48 end
% 3.07/3.48 substitution1:
% 3.07/3.48 end
% 3.07/3.48
% 3.07/3.48 paramod: (15960) {G1,W11,D4,L1,V0,M1} { addition( multiplication( skol2,
% 3.07/3.48 skol4 ), multiplication( skol4, skol3 ) ) ==> multiplication( skol4,
% 3.07/3.48 skol3 ) }.
% 3.07/3.48 parent0[0]: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 3.07/3.48 parent1[0; 9]: (15959) {G3,W13,D4,L1,V0,M1} { addition( multiplication(
% 3.07/3.48 skol2, skol4 ), multiplication( skol4, skol3 ) ) ==> multiplication(
% 3.07/3.48 multiplication( one, skol4 ), skol3 ) }.
% 3.07/3.48 substitution0:
% 3.07/3.48 X := skol4
% 3.07/3.48 end
% 3.07/3.48 substitution1:
% 3.07/3.48 end
% 3.07/3.48
% 3.07/3.48 subsumption: (15036) {G7,W11,D4,L1,V0,M1} P(62,442);d(4129);d(6) { addition
% 3.07/3.48 ( multiplication( skol2, skol4 ), multiplication( skol4, skol3 ) ) ==>
% 3.07/3.48 multiplication( skol4, skol3 ) }.
% 3.07/3.48 parent0: (15960) {G1,W11,D4,L1,V0,M1} { addition( multiplication( skol2,
% 3.07/3.48 skol4 ), multiplication( skol4, skol3 ) ) ==> multiplication( skol4,
% 3.07/3.48 skol3 ) }.
% 3.07/3.48 substitution0:
% 3.07/3.48 end
% 3.07/3.48 permutation0:
% 3.07/3.48 0 ==> 0
% 3.07/3.48 end
% 3.07/3.48
% 3.07/3.48 paramod: (15964) {G2,W7,D3,L1,V0,M1} { ! multiplication( skol4, skol3 )
% 3.07/3.48 ==> multiplication( skol4, skol3 ) }.
% 3.07/3.48 parent0[0]: (15036) {G7,W11,D4,L1,V0,M1} P(62,442);d(4129);d(6) { addition
% 3.07/3.48 ( multiplication( skol2, skol4 ), multiplication( skol4, skol3 ) ) ==>
% 3.07/3.48 multiplication( skol4, skol3 ) }.
% 3.07/3.48 parent1[0; 2]: (457) {G1,W11,D4,L1,V0,M1} R(27,12) { ! addition(
% 3.07/3.48 multiplication( skol2, skol4 ), multiplication( skol4, skol3 ) ) ==>
% 3.07/3.48 multiplication( skol4, skol3 ) }.
% 3.07/3.48 substitution0:
% 3.07/3.48 end
% 3.07/3.48 substitution1:
% 3.07/3.48 end
% 3.07/3.48
% 3.07/3.48 eqrefl: (15965) {G0,W0,D0,L0,V0,M0} { }.
% 3.07/3.48 parent0[0]: (15964) {G2,W7,D3,L1,V0,M1} { ! multiplication( skol4, skol3 )
% 3.07/3.48 ==> multiplication( skol4, skol3 ) }.
% 3.07/3.48 substitution0:
% 3.07/3.48 end
% 3.07/3.48
% 3.07/3.48 subsumption: (15721) {G8,W0,D0,L0,V0,M0} S(457);d(15036);q { }.
% 3.07/3.48 parent0: (15965) {G0,W0,D0,L0,V0,M0} { }.
% 3.07/3.48 substitution0:
% 3.07/3.48 end
% 3.07/3.48 permutation0:
% 3.07/3.48 end
% 3.07/3.48
% 3.07/3.48 Proof check complete!
% 3.07/3.48
% 3.07/3.48 Memory use:
% 3.07/3.48
% 3.07/3.48 space for terms: 189080
% 3.07/3.48 space for clauses: 743090
% 3.07/3.48
% 3.07/3.48
% 3.07/3.48 clauses generated: 107281
% 3.07/3.48 clauses kept: 15722
% 3.07/3.48 clauses selected: 1291
% 3.07/3.48 clauses deleted: 782
% 3.07/3.48 clauses inuse deleted: 387
% 3.07/3.48
% 3.07/3.48 subsentry: 501260
% 3.07/3.48 literals s-matched: 292712
% 3.07/3.48 literals matched: 289825
% 3.07/3.48 full subsumption: 109430
% 3.07/3.48
% 3.07/3.48 checksum: 1685830946
% 3.07/3.48
% 3.07/3.48
% 3.07/3.48 Bliksem ended
%------------------------------------------------------------------------------