TSTP Solution File: KLE027+4 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : KLE027+4 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n011.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 01:36:45 EDT 2022
% Result : Theorem 5.44s 5.83s
% Output : Refutation 5.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : KLE027+4 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.13 % Command : bliksem %s
% 0.12/0.34 % Computer : n011.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % DateTime : Thu Jun 16 09:33:21 EDT 2022
% 0.12/0.34 % CPUTime :
% 5.44/5.83 *** allocated 10000 integers for termspace/termends
% 5.44/5.83 *** allocated 10000 integers for clauses
% 5.44/5.83 *** allocated 10000 integers for justifications
% 5.44/5.83 Bliksem 1.12
% 5.44/5.83
% 5.44/5.83
% 5.44/5.83 Automatic Strategy Selection
% 5.44/5.83
% 5.44/5.83
% 5.44/5.83 Clauses:
% 5.44/5.83
% 5.44/5.83 { addition( X, Y ) = addition( Y, X ) }.
% 5.44/5.83 { addition( Z, addition( Y, X ) ) = addition( addition( Z, Y ), X ) }.
% 5.44/5.83 { addition( X, zero ) = X }.
% 5.44/5.83 { addition( X, X ) = X }.
% 5.44/5.83 { multiplication( X, multiplication( Y, Z ) ) = multiplication(
% 5.44/5.83 multiplication( X, Y ), Z ) }.
% 5.44/5.83 { multiplication( X, one ) = X }.
% 5.44/5.83 { multiplication( one, X ) = X }.
% 5.44/5.83 { multiplication( X, addition( Y, Z ) ) = addition( multiplication( X, Y )
% 5.44/5.83 , multiplication( X, Z ) ) }.
% 5.44/5.83 { multiplication( addition( X, Y ), Z ) = addition( multiplication( X, Z )
% 5.44/5.83 , multiplication( Y, Z ) ) }.
% 5.44/5.83 { multiplication( X, zero ) = zero }.
% 5.44/5.83 { multiplication( zero, X ) = zero }.
% 5.44/5.83 { ! leq( X, Y ), addition( X, Y ) = Y }.
% 5.44/5.83 { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 5.44/5.83 { ! test( X ), complement( skol1( X ), X ) }.
% 5.44/5.83 { ! complement( Y, X ), test( X ) }.
% 5.44/5.83 { ! complement( Y, X ), multiplication( X, Y ) = zero }.
% 5.44/5.83 { ! complement( Y, X ), alpha1( X, Y ) }.
% 5.44/5.83 { ! multiplication( X, Y ) = zero, ! alpha1( X, Y ), complement( Y, X ) }.
% 5.44/5.83 { ! alpha1( X, Y ), multiplication( Y, X ) = zero }.
% 5.44/5.83 { ! alpha1( X, Y ), addition( X, Y ) = one }.
% 5.44/5.83 { ! multiplication( Y, X ) = zero, ! addition( X, Y ) = one, alpha1( X, Y )
% 5.44/5.83 }.
% 5.44/5.83 { ! test( X ), ! c( X ) = Y, complement( X, Y ) }.
% 5.44/5.83 { ! test( X ), ! complement( X, Y ), c( X ) = Y }.
% 5.44/5.83 { test( X ), c( X ) = zero }.
% 5.44/5.83 { ! test( X ), ! test( Y ), c( addition( X, Y ) ) = multiplication( c( X )
% 5.44/5.83 , c( Y ) ) }.
% 5.44/5.83 { ! test( X ), ! test( Y ), c( multiplication( X, Y ) ) = addition( c( X )
% 5.44/5.83 , c( Y ) ) }.
% 5.44/5.83 { test( skol2 ) }.
% 5.44/5.83 { test( skol3 ) }.
% 5.44/5.83 { ! leq( addition( multiplication( skol2, addition( multiplication( skol2,
% 5.44/5.83 skol4 ), multiplication( c( skol2 ), skol5 ) ) ), multiplication( c(
% 5.44/5.83 skol2 ), skol6 ) ), addition( multiplication( skol2, skol4 ),
% 5.44/5.83 multiplication( c( skol2 ), skol6 ) ) ), ! leq( addition( multiplication
% 5.44/5.83 ( skol2, skol4 ), multiplication( c( skol2 ), skol6 ) ), addition(
% 5.44/5.83 multiplication( skol2, addition( multiplication( skol2, skol4 ),
% 5.44/5.83 multiplication( c( skol2 ), skol5 ) ) ), multiplication( c( skol2 ),
% 5.44/5.83 skol6 ) ) ) }.
% 5.44/5.83
% 5.44/5.83 percentage equality = 0.470588, percentage horn = 0.965517
% 5.44/5.83 This is a problem with some equality
% 5.44/5.83
% 5.44/5.83
% 5.44/5.83
% 5.44/5.83 Options Used:
% 5.44/5.83
% 5.44/5.83 useres = 1
% 5.44/5.83 useparamod = 1
% 5.44/5.83 useeqrefl = 1
% 5.44/5.83 useeqfact = 1
% 5.44/5.83 usefactor = 1
% 5.44/5.83 usesimpsplitting = 0
% 5.44/5.83 usesimpdemod = 5
% 5.44/5.83 usesimpres = 3
% 5.44/5.83
% 5.44/5.83 resimpinuse = 1000
% 5.44/5.83 resimpclauses = 20000
% 5.44/5.83 substype = eqrewr
% 5.44/5.83 backwardsubs = 1
% 5.44/5.83 selectoldest = 5
% 5.44/5.83
% 5.44/5.83 litorderings [0] = split
% 5.44/5.83 litorderings [1] = extend the termordering, first sorting on arguments
% 5.44/5.83
% 5.44/5.83 termordering = kbo
% 5.44/5.83
% 5.44/5.83 litapriori = 0
% 5.44/5.83 termapriori = 1
% 5.44/5.83 litaposteriori = 0
% 5.44/5.83 termaposteriori = 0
% 5.44/5.83 demodaposteriori = 0
% 5.44/5.83 ordereqreflfact = 0
% 5.44/5.83
% 5.44/5.83 litselect = negord
% 5.44/5.83
% 5.44/5.83 maxweight = 15
% 5.44/5.83 maxdepth = 30000
% 5.44/5.83 maxlength = 115
% 5.44/5.83 maxnrvars = 195
% 5.44/5.83 excuselevel = 1
% 5.44/5.83 increasemaxweight = 1
% 5.44/5.83
% 5.44/5.83 maxselected = 10000000
% 5.44/5.83 maxnrclauses = 10000000
% 5.44/5.83
% 5.44/5.83 showgenerated = 0
% 5.44/5.83 showkept = 0
% 5.44/5.83 showselected = 0
% 5.44/5.83 showdeleted = 0
% 5.44/5.83 showresimp = 1
% 5.44/5.83 showstatus = 2000
% 5.44/5.83
% 5.44/5.83 prologoutput = 0
% 5.44/5.83 nrgoals = 5000000
% 5.44/5.83 totalproof = 1
% 5.44/5.83
% 5.44/5.83 Symbols occurring in the translation:
% 5.44/5.83
% 5.44/5.83 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 5.44/5.83 . [1, 2] (w:1, o:29, a:1, s:1, b:0),
% 5.44/5.83 ! [4, 1] (w:0, o:21, a:1, s:1, b:0),
% 5.44/5.83 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 5.44/5.83 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 5.44/5.83 addition [37, 2] (w:1, o:53, a:1, s:1, b:0),
% 5.44/5.83 zero [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 5.44/5.83 multiplication [40, 2] (w:1, o:55, a:1, s:1, b:0),
% 5.44/5.83 one [41, 0] (w:1, o:10, a:1, s:1, b:0),
% 5.44/5.83 leq [42, 2] (w:1, o:54, a:1, s:1, b:0),
% 5.44/5.83 test [44, 1] (w:1, o:27, a:1, s:1, b:0),
% 5.44/5.83 complement [46, 2] (w:1, o:56, a:1, s:1, b:0),
% 5.44/5.83 c [47, 1] (w:1, o:28, a:1, s:1, b:0),
% 5.44/5.83 alpha1 [51, 2] (w:1, o:57, a:1, s:1, b:1),
% 5.44/5.83 skol1 [52, 1] (w:1, o:26, a:1, s:1, b:1),
% 5.44/5.83 skol2 [53, 0] (w:1, o:16, a:1, s:1, b:1),
% 5.44/5.83 skol3 [54, 0] (w:1, o:17, a:1, s:1, b:1),
% 5.44/5.83 skol4 [55, 0] (w:1, o:18, a:1, s:1, b:1),
% 5.44/5.83 skol5 [56, 0] (w:1, o:19, a:1, s:1, b:1),
% 5.44/5.83 skol6 [57, 0] (w:1, o:20, a:1, s:1, b:1).
% 5.44/5.83
% 5.44/5.83
% 5.44/5.83 Starting Search:
% 5.44/5.83
% 5.44/5.83 *** allocated 15000 integers for clauses
% 5.44/5.83 *** allocated 22500 integers for clauses
% 5.44/5.83 *** allocated 33750 integers for clauses
% 5.44/5.83 *** allocated 50625 integers for clauses
% 5.44/5.83 *** allocated 15000 integers for termspace/termends
% 5.44/5.83 *** allocated 75937 integers for clauses
% 5.44/5.83 Resimplifying inuse:
% 5.44/5.83 Done
% 5.44/5.83
% 5.44/5.83 *** allocated 22500 integers for termspace/termends
% 5.44/5.83 *** allocated 113905 integers for clauses
% 5.44/5.83 *** allocated 33750 integers for termspace/termends
% 5.44/5.83
% 5.44/5.83 Intermediate Status:
% 5.44/5.83 Generated: 13893
% 5.44/5.83 Kept: 2029
% 5.44/5.83 Inuse: 261
% 5.44/5.83 Deleted: 42
% 5.44/5.83 Deletedinuse: 22
% 5.44/5.83
% 5.44/5.83 *** allocated 170857 integers for clauses
% 5.44/5.83 Resimplifying inuse:
% 5.44/5.83 Done
% 5.44/5.83
% 5.44/5.83 *** allocated 50625 integers for termspace/termends
% 5.44/5.83 Resimplifying inuse:
% 5.44/5.83 Done
% 5.44/5.83
% 5.44/5.83 *** allocated 256285 integers for clauses
% 5.44/5.83
% 5.44/5.83 Intermediate Status:
% 5.44/5.83 Generated: 28610
% 5.44/5.83 Kept: 4059
% 5.44/5.83 Inuse: 453
% 5.44/5.83 Deleted: 161
% 5.44/5.83 Deletedinuse: 35
% 5.44/5.83
% 5.44/5.83 Resimplifying inuse:
% 5.44/5.83 Done
% 5.44/5.83
% 5.44/5.83 *** allocated 75937 integers for termspace/termends
% 5.44/5.83 *** allocated 384427 integers for clauses
% 5.44/5.83 Resimplifying inuse:
% 5.44/5.83 Done
% 5.44/5.83
% 5.44/5.83
% 5.44/5.83 Intermediate Status:
% 5.44/5.83 Generated: 44020
% 5.44/5.83 Kept: 6065
% 5.44/5.83 Inuse: 684
% 5.44/5.83 Deleted: 288
% 5.44/5.83 Deletedinuse: 104
% 5.44/5.83
% 5.44/5.83 Resimplifying inuse:
% 5.44/5.83 Done
% 5.44/5.83
% 5.44/5.83 *** allocated 113905 integers for termspace/termends
% 5.44/5.83 Resimplifying inuse:
% 5.44/5.83 Done
% 5.44/5.83
% 5.44/5.83 *** allocated 576640 integers for clauses
% 5.44/5.83
% 5.44/5.83 Intermediate Status:
% 5.44/5.83 Generated: 60694
% 5.44/5.83 Kept: 8072
% 5.44/5.83 Inuse: 810
% 5.44/5.83 Deleted: 308
% 5.44/5.83 Deletedinuse: 110
% 5.44/5.83
% 5.44/5.83 Resimplifying inuse:
% 5.44/5.83 Done
% 5.44/5.83
% 5.44/5.83 *** allocated 170857 integers for termspace/termends
% 5.44/5.83 Resimplifying inuse:
% 5.44/5.83 Done
% 5.44/5.83
% 5.44/5.83
% 5.44/5.83 Intermediate Status:
% 5.44/5.83 Generated: 69790
% 5.44/5.83 Kept: 10133
% 5.44/5.83 Inuse: 887
% 5.44/5.83 Deleted: 495
% 5.44/5.83 Deletedinuse: 277
% 5.44/5.83
% 5.44/5.83 Resimplifying inuse:
% 5.44/5.83 Done
% 5.44/5.83
% 5.44/5.83 Resimplifying inuse:
% 5.44/5.83 Done
% 5.44/5.83
% 5.44/5.83 *** allocated 864960 integers for clauses
% 5.44/5.83
% 5.44/5.83 Intermediate Status:
% 5.44/5.83 Generated: 82954
% 5.44/5.83 Kept: 12135
% 5.44/5.83 Inuse: 990
% 5.44/5.83 Deleted: 567
% 5.44/5.83 Deletedinuse: 294
% 5.44/5.83
% 5.44/5.83 Resimplifying inuse:
% 5.44/5.83 Done
% 5.44/5.83
% 5.44/5.83 Resimplifying inuse:
% 5.44/5.83 Done
% 5.44/5.83
% 5.44/5.83 *** allocated 256285 integers for termspace/termends
% 5.44/5.83
% 5.44/5.83 Intermediate Status:
% 5.44/5.83 Generated: 96321
% 5.44/5.83 Kept: 14144
% 5.44/5.83 Inuse: 1084
% 5.44/5.83 Deleted: 700
% 5.44/5.83 Deletedinuse: 335
% 5.44/5.83
% 5.44/5.83 Resimplifying inuse:
% 5.44/5.83 Done
% 5.44/5.83
% 5.44/5.83 Resimplifying inuse:
% 5.44/5.83 Done
% 5.44/5.83
% 5.44/5.83
% 5.44/5.83 Intermediate Status:
% 5.44/5.83 Generated: 115921
% 5.44/5.83 Kept: 16275
% 5.44/5.83 Inuse: 1211
% 5.44/5.83 Deleted: 793
% 5.44/5.83 Deletedinuse: 345
% 5.44/5.83
% 5.44/5.83 Resimplifying inuse:
% 5.44/5.83 Done
% 5.44/5.83
% 5.44/5.83
% 5.44/5.83 Intermediate Status:
% 5.44/5.83 Generated: 136964
% 5.44/5.83 Kept: 18308
% 5.44/5.83 Inuse: 1315
% 5.44/5.83 Deleted: 956
% 5.44/5.83 Deletedinuse: 345
% 5.44/5.83
% 5.44/5.83 Resimplifying inuse:
% 5.44/5.83 Done
% 5.44/5.83
% 5.44/5.83 *** allocated 1297440 integers for clauses
% 5.44/5.83 Resimplifying inuse:
% 5.44/5.83 Done
% 5.44/5.83
% 5.44/5.83 Resimplifying clauses:
% 5.44/5.83
% 5.44/5.83 Bliksems!, er is een bewijs:
% 5.44/5.83 % SZS status Theorem
% 5.44/5.83 % SZS output start Refutation
% 5.44/5.83
% 5.44/5.83 (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X ) }.
% 5.44/5.83 (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 5.44/5.83 (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 5.44/5.83 (4) {G0,W11,D4,L1,V3,M1} I { multiplication( X, multiplication( Y, Z ) )
% 5.44/5.83 ==> multiplication( multiplication( X, Y ), Z ) }.
% 5.44/5.83 (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 5.44/5.83 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 5.44/5.83 (10) {G0,W5,D3,L1,V1,M1} I { multiplication( zero, X ) ==> zero }.
% 5.44/5.83 (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X, Y ) }.
% 5.44/5.83 (13) {G0,W6,D3,L2,V1,M2} I { ! test( X ), complement( skol1( X ), X ) }.
% 5.44/5.83 (14) {G0,W5,D2,L2,V2,M2} I { ! complement( Y, X ), test( X ) }.
% 5.44/5.83 (15) {G0,W8,D3,L2,V2,M2} I { ! complement( Y, X ), multiplication( X, Y )
% 5.44/5.83 ==> zero }.
% 5.44/5.83 (16) {G0,W6,D2,L2,V2,M2} I { ! complement( Y, X ), alpha1( X, Y ) }.
% 5.44/5.83 (17) {G0,W11,D3,L3,V2,M3} I { ! multiplication( X, Y ) ==> zero, ! alpha1(
% 5.44/5.83 X, Y ), complement( Y, X ) }.
% 5.44/5.83 (18) {G0,W8,D3,L2,V2,M2} I { ! alpha1( X, Y ), multiplication( Y, X ) ==>
% 5.44/5.83 zero }.
% 5.44/5.83 (19) {G0,W8,D3,L2,V2,M2} I { ! alpha1( X, Y ), addition( X, Y ) ==> one }.
% 5.44/5.83 (20) {G0,W13,D3,L3,V2,M3} I { ! multiplication( Y, X ) ==> zero, ! addition
% 5.44/5.83 ( X, Y ) ==> one, alpha1( X, Y ) }.
% 5.44/5.83 (22) {G0,W9,D3,L3,V2,M3} I { ! test( X ), ! complement( X, Y ), c( X ) = Y
% 5.44/5.83 }.
% 5.44/5.83 (24) {G0,W14,D4,L3,V2,M3} I { ! test( X ), ! test( Y ), multiplication( c(
% 5.44/5.83 X ), c( Y ) ) ==> c( addition( X, Y ) ) }.
% 5.44/5.83 (26) {G0,W2,D2,L1,V0,M1} I { test( skol2 ) }.
% 5.44/5.83 (28) {G0,W48,D7,L2,V0,M2} I { ! leq( addition( multiplication( skol2,
% 5.44/5.83 addition( multiplication( skol2, skol4 ), multiplication( c( skol2 ),
% 5.44/5.83 skol5 ) ) ), multiplication( c( skol2 ), skol6 ) ), addition(
% 5.44/5.83 multiplication( skol2, skol4 ), multiplication( c( skol2 ), skol6 ) ) ),
% 5.44/5.83 ! leq( addition( multiplication( skol2, skol4 ), multiplication( c( skol2
% 5.44/5.83 ), skol6 ) ), addition( multiplication( skol2, addition( multiplication
% 5.44/5.83 ( skol2, skol4 ), multiplication( c( skol2 ), skol5 ) ) ), multiplication
% 5.44/5.83 ( c( skol2 ), skol6 ) ) ) }.
% 5.44/5.83 (30) {G1,W10,D4,L2,V1,M2} F(24);d(3) { ! test( X ), multiplication( c( X )
% 5.44/5.83 , c( X ) ) ==> c( X ) }.
% 5.44/5.83 (32) {G1,W5,D3,L1,V1,M1} P(2,0) { addition( zero, X ) ==> X }.
% 5.44/5.83 (48) {G1,W17,D5,L1,V4,M1} P(4,7) { addition( multiplication( multiplication
% 5.44/5.83 ( X, Y ), Z ), multiplication( X, T ) ) ==> multiplication( X, addition(
% 5.44/5.83 multiplication( Y, Z ), T ) ) }.
% 5.44/5.83 (149) {G1,W3,D2,L1,V1,M1} R(12,3) { leq( X, X ) }.
% 5.44/5.83 (182) {G1,W7,D3,L2,V2,M2} R(13,14) { complement( skol1( X ), X ), !
% 5.44/5.83 complement( Y, X ) }.
% 5.44/5.83 (183) {G1,W4,D3,L1,V0,M1} R(13,26) { complement( skol1( skol2 ), skol2 )
% 5.44/5.83 }.
% 5.44/5.83 (187) {G2,W4,D3,L1,V0,M1} R(183,16) { alpha1( skol2, skol1( skol2 ) ) }.
% 5.44/5.83 (195) {G2,W6,D4,L1,V0,M1} R(15,183) { multiplication( skol2, skol1( skol2 )
% 5.44/5.83 ) ==> zero }.
% 5.44/5.83 (237) {G3,W6,D4,L1,V0,M1} R(18,187) { multiplication( skol1( skol2 ), skol2
% 5.44/5.83 ) ==> zero }.
% 5.44/5.83 (240) {G1,W8,D3,L2,V2,M2} R(18,16) { multiplication( X, Y ) ==> zero, !
% 5.44/5.83 complement( X, Y ) }.
% 5.44/5.83 (263) {G3,W6,D4,L1,V0,M1} R(19,187) { addition( skol2, skol1( skol2 ) ) ==>
% 5.44/5.83 one }.
% 5.44/5.83 (267) {G1,W8,D3,L2,V2,M2} R(19,16) { addition( X, Y ) ==> one, ! complement
% 5.44/5.83 ( Y, X ) }.
% 5.44/5.83 (282) {G1,W18,D3,L4,V2,M4} R(20,17) { ! multiplication( X, Y ) ==> zero, !
% 5.44/5.83 addition( Y, X ) ==> one, ! multiplication( Y, X ) ==> zero, complement(
% 5.44/5.83 X, Y ) }.
% 5.44/5.83 (543) {G1,W48,D7,L2,V0,M2} P(0,28) { ! leq( addition( multiplication( skol2
% 5.44/5.83 , addition( multiplication( c( skol2 ), skol5 ), multiplication( skol2,
% 5.44/5.83 skol4 ) ) ), multiplication( c( skol2 ), skol6 ) ), addition(
% 5.44/5.83 multiplication( skol2, skol4 ), multiplication( c( skol2 ), skol6 ) ) ),
% 5.44/5.83 ! leq( addition( multiplication( skol2, skol4 ), multiplication( c( skol2
% 5.44/5.83 ), skol6 ) ), addition( multiplication( skol2, addition( multiplication
% 5.44/5.83 ( c( skol2 ), skol5 ), multiplication( skol2, skol4 ) ) ), multiplication
% 5.44/5.83 ( c( skol2 ), skol6 ) ) ) }.
% 5.44/5.83 (3708) {G4,W6,D4,L1,V0,M1} P(263,0) { addition( skol1( skol2 ), skol2 ) ==>
% 5.44/5.83 one }.
% 5.44/5.83 (5006) {G5,W4,D3,L1,V0,M1} R(195,20);d(3708);q { alpha1( skol1( skol2 ),
% 5.44/5.83 skol2 ) }.
% 5.44/5.83 (5015) {G3,W12,D6,L1,V2,M1} P(195,48);d(10);d(32) { multiplication( skol2,
% 5.44/5.83 addition( multiplication( skol1( skol2 ), X ), Y ) ) ==> multiplication(
% 5.44/5.83 skol2, Y ) }.
% 5.44/5.83 (5017) {G6,W4,D3,L1,V0,M1} R(5006,17);d(237);q { complement( skol2, skol1(
% 5.44/5.83 skol2 ) ) }.
% 5.44/5.83 (5018) {G7,W6,D4,L1,V0,M1} R(5017,182) { complement( skol1( skol1( skol2 )
% 5.44/5.83 ), skol1( skol2 ) ) }.
% 5.44/5.83 (5025) {G7,W5,D3,L1,V0,M1} R(5017,22);r(26) { c( skol2 ) ==> skol1( skol2 )
% 5.44/5.83 }.
% 5.44/5.83 (5027) {G7,W3,D3,L1,V0,M1} R(5017,14) { test( skol1( skol2 ) ) }.
% 5.44/5.83 (5038) {G8,W11,D5,L1,V0,M1} R(5027,30) { multiplication( c( skol1( skol2 )
% 5.44/5.83 ), c( skol1( skol2 ) ) ) ==> c( skol1( skol2 ) ) }.
% 5.44/5.83 (6665) {G2,W8,D3,L2,V2,M2} P(267,0) { addition( Y, X ) ==> one, !
% 5.44/5.83 complement( Y, X ) }.
% 5.44/5.83 (7375) {G3,W6,D2,L2,V2,M2} R(282,240);d(15);d(6665);q;q { complement( X, Y
% 5.44/5.83 ), ! complement( Y, X ) }.
% 5.44/5.83 (7395) {G8,W6,D4,L1,V0,M1} R(7375,5018) { complement( skol1( skol2 ), skol1
% 5.44/5.83 ( skol1( skol2 ) ) ) }.
% 5.44/5.83 (7420) {G4,W5,D2,L2,V2,M2} R(7375,14) { ! complement( X, Y ), test( X ) }.
% 5.44/5.83 (7449) {G5,W10,D3,L3,V3,M3} R(7420,22) { ! complement( X, Y ), ! complement
% 5.44/5.83 ( X, Z ), c( X ) = Z }.
% 5.44/5.83 (7453) {G6,W7,D3,L2,V2,M2} F(7449) { ! complement( X, Y ), c( X ) = Y }.
% 5.44/5.83 (9117) {G9,W7,D4,L1,V0,M1} R(7453,7395) { c( skol1( skol2 ) ) ==> skol1(
% 5.44/5.83 skol1( skol2 ) ) }.
% 5.44/5.83 (9142) {G10,W5,D4,L1,V0,M1} R(7453,183);d(9117) { skol1( skol1( skol2 ) )
% 5.44/5.83 ==> skol2 }.
% 5.44/5.83 (20034) {G11,W5,D4,L1,V0,M1} S(9117);d(9142) { c( skol1( skol2 ) ) ==>
% 5.44/5.83 skol2 }.
% 5.44/5.83 (20167) {G12,W5,D3,L1,V0,M1} S(5038);d(20034) { multiplication( skol2,
% 5.44/5.83 skol2 ) ==> skol2 }.
% 5.44/5.83 (20279) {G13,W0,D0,L0,V0,M0} S(543);d(5025);d(5025);d(5015);d(5015);d(4);d(
% 5.44/5.83 4);d(20167);d(20167);f;r(149) { }.
% 5.44/5.83
% 5.44/5.83
% 5.44/5.83 % SZS output end Refutation
% 5.44/5.83 found a proof!
% 5.44/5.83
% 5.44/5.83
% 5.44/5.83 Unprocessed initial clauses:
% 5.44/5.83
% 5.44/5.83 (20281) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X ) }.
% 5.44/5.83 (20282) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) = addition
% 5.44/5.83 ( addition( Z, Y ), X ) }.
% 5.44/5.83 (20283) {G0,W5,D3,L1,V1,M1} { addition( X, zero ) = X }.
% 5.44/5.83 (20284) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 5.44/5.83 (20285) {G0,W11,D4,L1,V3,M1} { multiplication( X, multiplication( Y, Z ) )
% 5.44/5.83 = multiplication( multiplication( X, Y ), Z ) }.
% 5.44/5.83 (20286) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 5.44/5.83 (20287) {G0,W5,D3,L1,V1,M1} { multiplication( one, X ) = X }.
% 5.44/5.83 (20288) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y, Z ) ) =
% 5.44/5.83 addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 5.44/5.83 (20289) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Y ), Z ) =
% 5.44/5.83 addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 5.44/5.83 (20290) {G0,W5,D3,L1,V1,M1} { multiplication( X, zero ) = zero }.
% 5.44/5.83 (20291) {G0,W5,D3,L1,V1,M1} { multiplication( zero, X ) = zero }.
% 5.44/5.83 (20292) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y }.
% 5.44/5.83 (20293) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 5.44/5.83 (20294) {G0,W6,D3,L2,V1,M2} { ! test( X ), complement( skol1( X ), X ) }.
% 5.44/5.83 (20295) {G0,W5,D2,L2,V2,M2} { ! complement( Y, X ), test( X ) }.
% 5.44/5.83 (20296) {G0,W8,D3,L2,V2,M2} { ! complement( Y, X ), multiplication( X, Y )
% 5.44/5.83 = zero }.
% 5.44/5.83 (20297) {G0,W6,D2,L2,V2,M2} { ! complement( Y, X ), alpha1( X, Y ) }.
% 5.44/5.83 (20298) {G0,W11,D3,L3,V2,M3} { ! multiplication( X, Y ) = zero, ! alpha1(
% 5.44/5.83 X, Y ), complement( Y, X ) }.
% 5.44/5.83 (20299) {G0,W8,D3,L2,V2,M2} { ! alpha1( X, Y ), multiplication( Y, X ) =
% 5.44/5.83 zero }.
% 5.44/5.83 (20300) {G0,W8,D3,L2,V2,M2} { ! alpha1( X, Y ), addition( X, Y ) = one }.
% 5.44/5.83 (20301) {G0,W13,D3,L3,V2,M3} { ! multiplication( Y, X ) = zero, ! addition
% 5.44/5.83 ( X, Y ) = one, alpha1( X, Y ) }.
% 5.44/5.83 (20302) {G0,W9,D3,L3,V2,M3} { ! test( X ), ! c( X ) = Y, complement( X, Y
% 5.44/5.83 ) }.
% 5.44/5.83 (20303) {G0,W9,D3,L3,V2,M3} { ! test( X ), ! complement( X, Y ), c( X ) =
% 5.44/5.83 Y }.
% 5.44/5.83 (20304) {G0,W6,D3,L2,V1,M2} { test( X ), c( X ) = zero }.
% 5.44/5.83 (20305) {G0,W14,D4,L3,V2,M3} { ! test( X ), ! test( Y ), c( addition( X, Y
% 5.44/5.83 ) ) = multiplication( c( X ), c( Y ) ) }.
% 5.44/5.83 (20306) {G0,W14,D4,L3,V2,M3} { ! test( X ), ! test( Y ), c( multiplication
% 5.44/5.83 ( X, Y ) ) = addition( c( X ), c( Y ) ) }.
% 5.44/5.83 (20307) {G0,W2,D2,L1,V0,M1} { test( skol2 ) }.
% 5.44/5.83 (20308) {G0,W2,D2,L1,V0,M1} { test( skol3 ) }.
% 5.44/5.83 (20309) {G0,W48,D7,L2,V0,M2} { ! leq( addition( multiplication( skol2,
% 5.44/5.83 addition( multiplication( skol2, skol4 ), multiplication( c( skol2 ),
% 5.44/5.83 skol5 ) ) ), multiplication( c( skol2 ), skol6 ) ), addition(
% 5.44/5.83 multiplication( skol2, skol4 ), multiplication( c( skol2 ), skol6 ) ) ),
% 5.44/5.83 ! leq( addition( multiplication( skol2, skol4 ), multiplication( c( skol2
% 5.44/5.83 ), skol6 ) ), addition( multiplication( skol2, addition( multiplication
% 5.44/5.83 ( skol2, skol4 ), multiplication( c( skol2 ), skol5 ) ) ), multiplication
% 5.44/5.83 ( c( skol2 ), skol6 ) ) ) }.
% 5.44/5.83
% 5.44/5.83
% 5.44/5.83 Total Proof:
% 5.44/5.83
% 5.44/5.83 subsumption: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X
% 5.44/5.83 ) }.
% 5.44/5.83 parent0: (20281) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X )
% 5.44/5.83 }.
% 5.44/5.83 substitution0:
% 5.44/5.83 X := X
% 5.44/5.83 Y := Y
% 5.44/5.83 end
% 5.44/5.83 permutation0:
% 5.44/5.83 0 ==> 0
% 5.44/5.83 end
% 5.44/5.83
% 5.44/5.83 subsumption: (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 5.44/5.83 parent0: (20283) {G0,W5,D3,L1,V1,M1} { addition( X, zero ) = X }.
% 5.44/5.83 substitution0:
% 5.44/5.83 X := X
% 5.44/5.83 end
% 5.44/5.83 permutation0:
% 5.44/5.83 0 ==> 0
% 5.44/5.83 end
% 5.44/5.83
% 5.44/5.83 subsumption: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 5.44/5.83 parent0: (20284) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 5.44/5.83 substitution0:
% 5.44/5.83 X := X
% 5.44/5.83 end
% 5.44/5.83 permutation0:
% 5.44/5.83 0 ==> 0
% 5.44/5.83 end
% 5.44/5.83
% 5.44/5.83 subsumption: (4) {G0,W11,D4,L1,V3,M1} I { multiplication( X, multiplication
% 5.44/5.83 ( Y, Z ) ) ==> multiplication( multiplication( X, Y ), Z ) }.
% 5.44/5.83 parent0: (20285) {G0,W11,D4,L1,V3,M1} { multiplication( X, multiplication
% 5.44/5.83 ( Y, Z ) ) = multiplication( multiplication( X, Y ), Z ) }.
% 5.44/5.83 substitution0:
% 5.44/5.83 X := X
% 5.44/5.83 Y := Y
% 5.44/5.83 Z := Z
% 5.44/5.83 end
% 5.44/5.83 permutation0:
% 5.44/5.83 0 ==> 0
% 5.44/5.83 end
% 5.44/5.83
% 5.44/5.83 eqswap: (20325) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Y ),
% 5.44/5.83 multiplication( X, Z ) ) = multiplication( X, addition( Y, Z ) ) }.
% 5.44/5.83 parent0[0]: (20288) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y
% 5.44/5.83 , Z ) ) = addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 5.44/5.83 substitution0:
% 5.44/5.83 X := X
% 5.44/5.83 Y := Y
% 5.44/5.83 Z := Z
% 5.44/5.83 end
% 5.44/5.83
% 5.44/5.83 subsumption: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y )
% 5.44/5.83 , multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 5.44/5.83 parent0: (20325) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Y ),
% 5.44/5.83 multiplication( X, Z ) ) = multiplication( X, addition( Y, Z ) ) }.
% 5.44/5.83 substitution0:
% 5.44/5.83 X := X
% 5.44/5.83 Y := Y
% 5.44/5.83 Z := Z
% 5.44/5.83 end
% 5.44/5.83 permutation0:
% 5.44/5.83 0 ==> 0
% 5.44/5.83 end
% 5.44/5.83
% 5.44/5.83 subsumption: (10) {G0,W5,D3,L1,V1,M1} I { multiplication( zero, X ) ==>
% 5.44/5.83 zero }.
% 5.44/5.83 parent0: (20291) {G0,W5,D3,L1,V1,M1} { multiplication( zero, X ) = zero
% 5.44/5.83 }.
% 5.44/5.83 substitution0:
% 5.44/5.83 X := X
% 5.44/5.83 end
% 5.44/5.83 permutation0:
% 5.44/5.83 0 ==> 0
% 5.44/5.83 end
% 5.44/5.83
% 5.44/5.83 subsumption: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X
% 5.44/5.83 , Y ) }.
% 5.44/5.83 parent0: (20293) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y )
% 5.44/5.83 }.
% 5.44/5.83 substitution0:
% 5.44/5.83 X := X
% 5.44/5.83 Y := Y
% 5.44/5.83 end
% 5.44/5.83 permutation0:
% 5.44/5.83 0 ==> 0
% 5.44/5.83 1 ==> 1
% 5.44/5.83 end
% 5.44/5.83
% 5.44/5.83 subsumption: (13) {G0,W6,D3,L2,V1,M2} I { ! test( X ), complement( skol1( X
% 5.44/5.83 ), X ) }.
% 5.44/5.83 parent0: (20294) {G0,W6,D3,L2,V1,M2} { ! test( X ), complement( skol1( X )
% 5.44/5.83 , X ) }.
% 5.44/5.83 substitution0:
% 5.44/5.83 X := X
% 5.44/5.83 end
% 5.44/5.83 permutation0:
% 5.44/5.83 0 ==> 0
% 5.44/5.83 1 ==> 1
% 5.44/5.83 end
% 5.44/5.83
% 5.44/5.83 subsumption: (14) {G0,W5,D2,L2,V2,M2} I { ! complement( Y, X ), test( X )
% 5.44/5.83 }.
% 5.44/5.83 parent0: (20295) {G0,W5,D2,L2,V2,M2} { ! complement( Y, X ), test( X ) }.
% 5.44/5.83 substitution0:
% 5.44/5.83 X := X
% 5.44/5.83 Y := Y
% 5.44/5.83 end
% 5.44/5.83 permutation0:
% 5.44/5.83 0 ==> 0
% 5.44/5.83 1 ==> 1
% 5.44/5.83 end
% 5.44/5.83
% 5.44/5.83 subsumption: (15) {G0,W8,D3,L2,V2,M2} I { ! complement( Y, X ),
% 5.44/5.83 multiplication( X, Y ) ==> zero }.
% 5.44/5.83 parent0: (20296) {G0,W8,D3,L2,V2,M2} { ! complement( Y, X ),
% 5.44/5.83 multiplication( X, Y ) = zero }.
% 5.44/5.83 substitution0:
% 5.44/5.83 X := X
% 5.44/5.83 Y := Y
% 5.44/5.83 end
% 5.44/5.83 permutation0:
% 5.44/5.83 0 ==> 0
% 5.44/5.83 1 ==> 1
% 5.44/5.83 end
% 5.44/5.83
% 5.44/5.83 subsumption: (16) {G0,W6,D2,L2,V2,M2} I { ! complement( Y, X ), alpha1( X,
% 5.44/5.83 Y ) }.
% 5.44/5.83 parent0: (20297) {G0,W6,D2,L2,V2,M2} { ! complement( Y, X ), alpha1( X, Y
% 5.44/5.83 ) }.
% 5.44/5.83 substitution0:
% 5.44/5.83 X := X
% 5.44/5.83 Y := Y
% 5.44/5.83 end
% 5.44/5.83 permutation0:
% 5.44/5.83 0 ==> 0
% 5.44/5.83 1 ==> 1
% 5.44/5.83 end
% 5.44/5.83
% 5.44/5.83 subsumption: (17) {G0,W11,D3,L3,V2,M3} I { ! multiplication( X, Y ) ==>
% 5.44/5.83 zero, ! alpha1( X, Y ), complement( Y, X ) }.
% 5.44/5.83 parent0: (20298) {G0,W11,D3,L3,V2,M3} { ! multiplication( X, Y ) = zero, !
% 5.44/5.83 alpha1( X, Y ), complement( Y, X ) }.
% 5.44/5.83 substitution0:
% 5.44/5.83 X := X
% 5.44/5.83 Y := Y
% 5.44/5.83 end
% 5.44/5.83 permutation0:
% 5.44/5.83 0 ==> 0
% 5.44/5.83 1 ==> 1
% 5.44/5.83 2 ==> 2
% 5.44/5.83 end
% 5.44/5.83
% 5.44/5.83 subsumption: (18) {G0,W8,D3,L2,V2,M2} I { ! alpha1( X, Y ), multiplication
% 5.44/5.83 ( Y, X ) ==> zero }.
% 5.44/5.83 parent0: (20299) {G0,W8,D3,L2,V2,M2} { ! alpha1( X, Y ), multiplication( Y
% 5.44/5.83 , X ) = zero }.
% 5.44/5.83 substitution0:
% 5.44/5.83 X := X
% 5.44/5.83 Y := Y
% 5.44/5.83 end
% 5.44/5.83 permutation0:
% 5.44/5.83 0 ==> 0
% 5.44/5.83 1 ==> 1
% 5.44/5.83 end
% 5.44/5.83
% 5.44/5.83 subsumption: (19) {G0,W8,D3,L2,V2,M2} I { ! alpha1( X, Y ), addition( X, Y
% 5.44/5.83 ) ==> one }.
% 5.44/5.83 parent0: (20300) {G0,W8,D3,L2,V2,M2} { ! alpha1( X, Y ), addition( X, Y )
% 5.44/5.83 = one }.
% 5.44/5.83 substitution0:
% 5.44/5.83 X := X
% 5.44/5.83 Y := Y
% 5.44/5.83 end
% 5.44/5.83 permutation0:
% 5.44/5.83 0 ==> 0
% 5.44/5.83 1 ==> 1
% 5.44/5.83 end
% 5.44/5.83
% 5.44/5.83 subsumption: (20) {G0,W13,D3,L3,V2,M3} I { ! multiplication( Y, X ) ==>
% 5.44/5.83 zero, ! addition( X, Y ) ==> one, alpha1( X, Y ) }.
% 5.44/5.83 parent0: (20301) {G0,W13,D3,L3,V2,M3} { ! multiplication( Y, X ) = zero, !
% 5.44/5.83 addition( X, Y ) = one, alpha1( X, Y ) }.
% 5.44/5.83 substitution0:
% 5.44/5.83 X := X
% 5.44/5.83 Y := Y
% 5.44/5.83 end
% 5.44/5.83 permutation0:
% 5.44/5.83 0 ==> 0
% 5.44/5.83 1 ==> 1
% 5.44/5.83 2 ==> 2
% 5.44/5.83 end
% 5.44/5.83
% 5.44/5.83 subsumption: (22) {G0,W9,D3,L3,V2,M3} I { ! test( X ), ! complement( X, Y )
% 5.44/5.83 , c( X ) = Y }.
% 5.44/5.83 parent0: (20303) {G0,W9,D3,L3,V2,M3} { ! test( X ), ! complement( X, Y ),
% 5.44/5.83 c( X ) = Y }.
% 5.44/5.83 substitution0:
% 5.44/5.83 X := X
% 5.44/5.83 Y := Y
% 5.44/5.83 end
% 5.44/5.83 permutation0:
% 5.44/5.83 0 ==> 0
% 5.44/5.83 1 ==> 1
% 5.44/5.83 2 ==> 2
% 5.44/5.83 end
% 5.44/5.83
% 5.44/5.83 eqswap: (20505) {G0,W14,D4,L3,V2,M3} { multiplication( c( X ), c( Y ) ) =
% 5.44/5.83 c( addition( X, Y ) ), ! test( X ), ! test( Y ) }.
% 5.44/5.83 parent0[2]: (20305) {G0,W14,D4,L3,V2,M3} { ! test( X ), ! test( Y ), c(
% 5.44/5.83 addition( X, Y ) ) = multiplication( c( X ), c( Y ) ) }.
% 5.44/5.83 substitution0:
% 5.44/5.83 X := X
% 5.44/5.83 Y := Y
% 5.44/5.83 end
% 5.44/5.83
% 5.44/5.83 subsumption: (24) {G0,W14,D4,L3,V2,M3} I { ! test( X ), ! test( Y ),
% 5.44/5.83 multiplication( c( X ), c( Y ) ) ==> c( addition( X, Y ) ) }.
% 5.44/5.83 parent0: (20505) {G0,W14,D4,L3,V2,M3} { multiplication( c( X ), c( Y ) ) =
% 5.44/5.83 c( addition( X, Y ) ), ! test( X ), ! test( Y ) }.
% 5.44/5.83 substitution0:
% 5.44/5.83 X := X
% 5.44/5.83 Y := Y
% 5.44/5.83 end
% 5.44/5.83 permutation0:
% 5.44/5.83 0 ==> 2
% 5.44/5.83 1 ==> 0
% 5.44/5.83 2 ==> 1
% 5.44/5.83 end
% 5.44/5.83
% 5.44/5.83 subsumption: (26) {G0,W2,D2,L1,V0,M1} I { test( skol2 ) }.
% 5.44/5.83 parent0: (20307) {G0,W2,D2,L1,V0,M1} { test( skol2 ) }.
% 5.44/5.83 substitution0:
% 5.44/5.83 end
% 5.44/5.83 permutation0:
% 5.44/5.83 0 ==> 0
% 5.44/5.83 end
% 5.44/5.83
% 5.44/5.83 subsumption: (28) {G0,W48,D7,L2,V0,M2} I { ! leq( addition( multiplication
% 5.44/5.83 ( skol2, addition( multiplication( skol2, skol4 ), multiplication( c(
% 5.44/5.83 skol2 ), skol5 ) ) ), multiplication( c( skol2 ), skol6 ) ), addition(
% 5.44/5.83 multiplication( skol2, skol4 ), multiplication( c( skol2 ), skol6 ) ) ),
% 5.44/5.83 ! leq( addition( multiplication( skol2, skol4 ), multiplication( c( skol2
% 5.44/5.83 ), skol6 ) ), addition( multiplication( skol2, addition( multiplication
% 5.44/5.83 ( skol2, skol4 ), multiplication( c( skol2 ), skol5 ) ) ), multiplication
% 5.44/5.84 ( c( skol2 ), skol6 ) ) ) }.
% 5.44/5.84 parent0: (20309) {G0,W48,D7,L2,V0,M2} { ! leq( addition( multiplication(
% 5.44/5.84 skol2, addition( multiplication( skol2, skol4 ), multiplication( c( skol2
% 5.44/5.84 ), skol5 ) ) ), multiplication( c( skol2 ), skol6 ) ), addition(
% 5.44/5.84 multiplication( skol2, skol4 ), multiplication( c( skol2 ), skol6 ) ) ),
% 5.44/5.84 ! leq( addition( multiplication( skol2, skol4 ), multiplication( c( skol2
% 5.44/5.84 ), skol6 ) ), addition( multiplication( skol2, addition( multiplication
% 5.44/5.84 ( skol2, skol4 ), multiplication( c( skol2 ), skol5 ) ) ), multiplication
% 5.44/5.84 ( c( skol2 ), skol6 ) ) ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 end
% 5.44/5.84 permutation0:
% 5.44/5.84 0 ==> 0
% 5.44/5.84 1 ==> 1
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 factor: (20567) {G0,W12,D4,L2,V1,M2} { ! test( X ), multiplication( c( X )
% 5.44/5.84 , c( X ) ) ==> c( addition( X, X ) ) }.
% 5.44/5.84 parent0[0, 1]: (24) {G0,W14,D4,L3,V2,M3} I { ! test( X ), ! test( Y ),
% 5.44/5.84 multiplication( c( X ), c( Y ) ) ==> c( addition( X, Y ) ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := X
% 5.44/5.84 Y := X
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 paramod: (20568) {G1,W10,D4,L2,V1,M2} { multiplication( c( X ), c( X ) )
% 5.44/5.84 ==> c( X ), ! test( X ) }.
% 5.44/5.84 parent0[0]: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 5.44/5.84 parent1[1; 7]: (20567) {G0,W12,D4,L2,V1,M2} { ! test( X ), multiplication
% 5.44/5.84 ( c( X ), c( X ) ) ==> c( addition( X, X ) ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := X
% 5.44/5.84 end
% 5.44/5.84 substitution1:
% 5.44/5.84 X := X
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 subsumption: (30) {G1,W10,D4,L2,V1,M2} F(24);d(3) { ! test( X ),
% 5.44/5.84 multiplication( c( X ), c( X ) ) ==> c( X ) }.
% 5.44/5.84 parent0: (20568) {G1,W10,D4,L2,V1,M2} { multiplication( c( X ), c( X ) )
% 5.44/5.84 ==> c( X ), ! test( X ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := X
% 5.44/5.84 end
% 5.44/5.84 permutation0:
% 5.44/5.84 0 ==> 1
% 5.44/5.84 1 ==> 0
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 eqswap: (20570) {G0,W5,D3,L1,V1,M1} { X ==> addition( X, zero ) }.
% 5.44/5.84 parent0[0]: (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := X
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 paramod: (20571) {G1,W5,D3,L1,V1,M1} { X ==> addition( zero, X ) }.
% 5.44/5.84 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 5.44/5.84 }.
% 5.44/5.84 parent1[0; 2]: (20570) {G0,W5,D3,L1,V1,M1} { X ==> addition( X, zero ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := X
% 5.44/5.84 Y := zero
% 5.44/5.84 end
% 5.44/5.84 substitution1:
% 5.44/5.84 X := X
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 eqswap: (20574) {G1,W5,D3,L1,V1,M1} { addition( zero, X ) ==> X }.
% 5.44/5.84 parent0[0]: (20571) {G1,W5,D3,L1,V1,M1} { X ==> addition( zero, X ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := X
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 subsumption: (32) {G1,W5,D3,L1,V1,M1} P(2,0) { addition( zero, X ) ==> X
% 5.44/5.84 }.
% 5.44/5.84 parent0: (20574) {G1,W5,D3,L1,V1,M1} { addition( zero, X ) ==> X }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := X
% 5.44/5.84 end
% 5.44/5.84 permutation0:
% 5.44/5.84 0 ==> 0
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 eqswap: (20576) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y, Z )
% 5.44/5.84 ) ==> addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 5.44/5.84 parent0[0]: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 5.44/5.84 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := X
% 5.44/5.84 Y := Y
% 5.44/5.84 Z := Z
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 paramod: (20577) {G1,W17,D5,L1,V4,M1} { multiplication( X, addition(
% 5.44/5.84 multiplication( Y, Z ), T ) ) ==> addition( multiplication(
% 5.44/5.84 multiplication( X, Y ), Z ), multiplication( X, T ) ) }.
% 5.44/5.84 parent0[0]: (4) {G0,W11,D4,L1,V3,M1} I { multiplication( X, multiplication
% 5.44/5.84 ( Y, Z ) ) ==> multiplication( multiplication( X, Y ), Z ) }.
% 5.44/5.84 parent1[0; 9]: (20576) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition
% 5.44/5.84 ( Y, Z ) ) ==> addition( multiplication( X, Y ), multiplication( X, Z ) )
% 5.44/5.84 }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := X
% 5.44/5.84 Y := Y
% 5.44/5.84 Z := Z
% 5.44/5.84 end
% 5.44/5.84 substitution1:
% 5.44/5.84 X := X
% 5.44/5.84 Y := multiplication( Y, Z )
% 5.44/5.84 Z := T
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 eqswap: (20579) {G1,W17,D5,L1,V4,M1} { addition( multiplication(
% 5.44/5.84 multiplication( X, Y ), Z ), multiplication( X, T ) ) ==> multiplication
% 5.44/5.84 ( X, addition( multiplication( Y, Z ), T ) ) }.
% 5.44/5.84 parent0[0]: (20577) {G1,W17,D5,L1,V4,M1} { multiplication( X, addition(
% 5.44/5.84 multiplication( Y, Z ), T ) ) ==> addition( multiplication(
% 5.44/5.84 multiplication( X, Y ), Z ), multiplication( X, T ) ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := X
% 5.44/5.84 Y := Y
% 5.44/5.84 Z := Z
% 5.44/5.84 T := T
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 subsumption: (48) {G1,W17,D5,L1,V4,M1} P(4,7) { addition( multiplication(
% 5.44/5.84 multiplication( X, Y ), Z ), multiplication( X, T ) ) ==> multiplication
% 5.44/5.84 ( X, addition( multiplication( Y, Z ), T ) ) }.
% 5.44/5.84 parent0: (20579) {G1,W17,D5,L1,V4,M1} { addition( multiplication(
% 5.44/5.84 multiplication( X, Y ), Z ), multiplication( X, T ) ) ==> multiplication
% 5.44/5.84 ( X, addition( multiplication( Y, Z ), T ) ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := X
% 5.44/5.84 Y := Y
% 5.44/5.84 Z := Z
% 5.44/5.84 T := T
% 5.44/5.84 end
% 5.44/5.84 permutation0:
% 5.44/5.84 0 ==> 0
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 eqswap: (20581) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y
% 5.44/5.84 ) }.
% 5.44/5.84 parent0[0]: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 5.44/5.84 Y ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := X
% 5.44/5.84 Y := Y
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 eqswap: (20582) {G0,W5,D3,L1,V1,M1} { X ==> addition( X, X ) }.
% 5.44/5.84 parent0[0]: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := X
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 resolution: (20583) {G1,W3,D2,L1,V1,M1} { leq( X, X ) }.
% 5.44/5.84 parent0[0]: (20581) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X
% 5.44/5.84 , Y ) }.
% 5.44/5.84 parent1[0]: (20582) {G0,W5,D3,L1,V1,M1} { X ==> addition( X, X ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := X
% 5.44/5.84 Y := X
% 5.44/5.84 end
% 5.44/5.84 substitution1:
% 5.44/5.84 X := X
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 subsumption: (149) {G1,W3,D2,L1,V1,M1} R(12,3) { leq( X, X ) }.
% 5.44/5.84 parent0: (20583) {G1,W3,D2,L1,V1,M1} { leq( X, X ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := X
% 5.44/5.84 end
% 5.44/5.84 permutation0:
% 5.44/5.84 0 ==> 0
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 resolution: (20584) {G1,W7,D3,L2,V2,M2} { complement( skol1( X ), X ), !
% 5.44/5.84 complement( Y, X ) }.
% 5.44/5.84 parent0[0]: (13) {G0,W6,D3,L2,V1,M2} I { ! test( X ), complement( skol1( X
% 5.44/5.84 ), X ) }.
% 5.44/5.84 parent1[1]: (14) {G0,W5,D2,L2,V2,M2} I { ! complement( Y, X ), test( X )
% 5.44/5.84 }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := X
% 5.44/5.84 end
% 5.44/5.84 substitution1:
% 5.44/5.84 X := X
% 5.44/5.84 Y := Y
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 subsumption: (182) {G1,W7,D3,L2,V2,M2} R(13,14) { complement( skol1( X ), X
% 5.44/5.84 ), ! complement( Y, X ) }.
% 5.44/5.84 parent0: (20584) {G1,W7,D3,L2,V2,M2} { complement( skol1( X ), X ), !
% 5.44/5.84 complement( Y, X ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := X
% 5.44/5.84 Y := Y
% 5.44/5.84 end
% 5.44/5.84 permutation0:
% 5.44/5.84 0 ==> 0
% 5.44/5.84 1 ==> 1
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 resolution: (20585) {G1,W4,D3,L1,V0,M1} { complement( skol1( skol2 ),
% 5.44/5.84 skol2 ) }.
% 5.44/5.84 parent0[0]: (13) {G0,W6,D3,L2,V1,M2} I { ! test( X ), complement( skol1( X
% 5.44/5.84 ), X ) }.
% 5.44/5.84 parent1[0]: (26) {G0,W2,D2,L1,V0,M1} I { test( skol2 ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := skol2
% 5.44/5.84 end
% 5.44/5.84 substitution1:
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 subsumption: (183) {G1,W4,D3,L1,V0,M1} R(13,26) { complement( skol1( skol2
% 5.44/5.84 ), skol2 ) }.
% 5.44/5.84 parent0: (20585) {G1,W4,D3,L1,V0,M1} { complement( skol1( skol2 ), skol2 )
% 5.44/5.84 }.
% 5.44/5.84 substitution0:
% 5.44/5.84 end
% 5.44/5.84 permutation0:
% 5.44/5.84 0 ==> 0
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 resolution: (20586) {G1,W4,D3,L1,V0,M1} { alpha1( skol2, skol1( skol2 ) )
% 5.44/5.84 }.
% 5.44/5.84 parent0[0]: (16) {G0,W6,D2,L2,V2,M2} I { ! complement( Y, X ), alpha1( X, Y
% 5.44/5.84 ) }.
% 5.44/5.84 parent1[0]: (183) {G1,W4,D3,L1,V0,M1} R(13,26) { complement( skol1( skol2 )
% 5.44/5.84 , skol2 ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := skol2
% 5.44/5.84 Y := skol1( skol2 )
% 5.44/5.84 end
% 5.44/5.84 substitution1:
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 subsumption: (187) {G2,W4,D3,L1,V0,M1} R(183,16) { alpha1( skol2, skol1(
% 5.44/5.84 skol2 ) ) }.
% 5.44/5.84 parent0: (20586) {G1,W4,D3,L1,V0,M1} { alpha1( skol2, skol1( skol2 ) ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 end
% 5.44/5.84 permutation0:
% 5.44/5.84 0 ==> 0
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 eqswap: (20587) {G0,W8,D3,L2,V2,M2} { zero ==> multiplication( X, Y ), !
% 5.44/5.84 complement( Y, X ) }.
% 5.44/5.84 parent0[1]: (15) {G0,W8,D3,L2,V2,M2} I { ! complement( Y, X ),
% 5.44/5.84 multiplication( X, Y ) ==> zero }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := X
% 5.44/5.84 Y := Y
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 resolution: (20588) {G1,W6,D4,L1,V0,M1} { zero ==> multiplication( skol2,
% 5.44/5.84 skol1( skol2 ) ) }.
% 5.44/5.84 parent0[1]: (20587) {G0,W8,D3,L2,V2,M2} { zero ==> multiplication( X, Y )
% 5.44/5.84 , ! complement( Y, X ) }.
% 5.44/5.84 parent1[0]: (183) {G1,W4,D3,L1,V0,M1} R(13,26) { complement( skol1( skol2 )
% 5.44/5.84 , skol2 ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := skol2
% 5.44/5.84 Y := skol1( skol2 )
% 5.44/5.84 end
% 5.44/5.84 substitution1:
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 eqswap: (20589) {G1,W6,D4,L1,V0,M1} { multiplication( skol2, skol1( skol2
% 5.44/5.84 ) ) ==> zero }.
% 5.44/5.84 parent0[0]: (20588) {G1,W6,D4,L1,V0,M1} { zero ==> multiplication( skol2,
% 5.44/5.84 skol1( skol2 ) ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 subsumption: (195) {G2,W6,D4,L1,V0,M1} R(15,183) { multiplication( skol2,
% 5.44/5.84 skol1( skol2 ) ) ==> zero }.
% 5.44/5.84 parent0: (20589) {G1,W6,D4,L1,V0,M1} { multiplication( skol2, skol1( skol2
% 5.44/5.84 ) ) ==> zero }.
% 5.44/5.84 substitution0:
% 5.44/5.84 end
% 5.44/5.84 permutation0:
% 5.44/5.84 0 ==> 0
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 eqswap: (20590) {G0,W8,D3,L2,V2,M2} { zero ==> multiplication( X, Y ), !
% 5.44/5.84 alpha1( Y, X ) }.
% 5.44/5.84 parent0[1]: (18) {G0,W8,D3,L2,V2,M2} I { ! alpha1( X, Y ), multiplication(
% 5.44/5.84 Y, X ) ==> zero }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := Y
% 5.44/5.84 Y := X
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 resolution: (20591) {G1,W6,D4,L1,V0,M1} { zero ==> multiplication( skol1(
% 5.44/5.84 skol2 ), skol2 ) }.
% 5.44/5.84 parent0[1]: (20590) {G0,W8,D3,L2,V2,M2} { zero ==> multiplication( X, Y )
% 5.44/5.84 , ! alpha1( Y, X ) }.
% 5.44/5.84 parent1[0]: (187) {G2,W4,D3,L1,V0,M1} R(183,16) { alpha1( skol2, skol1(
% 5.44/5.84 skol2 ) ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := skol1( skol2 )
% 5.44/5.84 Y := skol2
% 5.44/5.84 end
% 5.44/5.84 substitution1:
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 eqswap: (20592) {G1,W6,D4,L1,V0,M1} { multiplication( skol1( skol2 ),
% 5.44/5.84 skol2 ) ==> zero }.
% 5.44/5.84 parent0[0]: (20591) {G1,W6,D4,L1,V0,M1} { zero ==> multiplication( skol1(
% 5.44/5.84 skol2 ), skol2 ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 subsumption: (237) {G3,W6,D4,L1,V0,M1} R(18,187) { multiplication( skol1(
% 5.44/5.84 skol2 ), skol2 ) ==> zero }.
% 5.44/5.84 parent0: (20592) {G1,W6,D4,L1,V0,M1} { multiplication( skol1( skol2 ),
% 5.44/5.84 skol2 ) ==> zero }.
% 5.44/5.84 substitution0:
% 5.44/5.84 end
% 5.44/5.84 permutation0:
% 5.44/5.84 0 ==> 0
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 eqswap: (20593) {G0,W8,D3,L2,V2,M2} { zero ==> multiplication( X, Y ), !
% 5.44/5.84 alpha1( Y, X ) }.
% 5.44/5.84 parent0[1]: (18) {G0,W8,D3,L2,V2,M2} I { ! alpha1( X, Y ), multiplication(
% 5.44/5.84 Y, X ) ==> zero }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := Y
% 5.44/5.84 Y := X
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 resolution: (20594) {G1,W8,D3,L2,V2,M2} { zero ==> multiplication( X, Y )
% 5.44/5.84 , ! complement( X, Y ) }.
% 5.44/5.84 parent0[1]: (20593) {G0,W8,D3,L2,V2,M2} { zero ==> multiplication( X, Y )
% 5.44/5.84 , ! alpha1( Y, X ) }.
% 5.44/5.84 parent1[1]: (16) {G0,W6,D2,L2,V2,M2} I { ! complement( Y, X ), alpha1( X, Y
% 5.44/5.84 ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := X
% 5.44/5.84 Y := Y
% 5.44/5.84 end
% 5.44/5.84 substitution1:
% 5.44/5.84 X := Y
% 5.44/5.84 Y := X
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 eqswap: (20595) {G1,W8,D3,L2,V2,M2} { multiplication( X, Y ) ==> zero, !
% 5.44/5.84 complement( X, Y ) }.
% 5.44/5.84 parent0[0]: (20594) {G1,W8,D3,L2,V2,M2} { zero ==> multiplication( X, Y )
% 5.44/5.84 , ! complement( X, Y ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := X
% 5.44/5.84 Y := Y
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 subsumption: (240) {G1,W8,D3,L2,V2,M2} R(18,16) { multiplication( X, Y )
% 5.44/5.84 ==> zero, ! complement( X, Y ) }.
% 5.44/5.84 parent0: (20595) {G1,W8,D3,L2,V2,M2} { multiplication( X, Y ) ==> zero, !
% 5.44/5.84 complement( X, Y ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := X
% 5.44/5.84 Y := Y
% 5.44/5.84 end
% 5.44/5.84 permutation0:
% 5.44/5.84 0 ==> 0
% 5.44/5.84 1 ==> 1
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 eqswap: (20596) {G0,W8,D3,L2,V2,M2} { one ==> addition( X, Y ), ! alpha1(
% 5.44/5.84 X, Y ) }.
% 5.44/5.84 parent0[1]: (19) {G0,W8,D3,L2,V2,M2} I { ! alpha1( X, Y ), addition( X, Y )
% 5.44/5.84 ==> one }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := X
% 5.44/5.84 Y := Y
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 resolution: (20597) {G1,W6,D4,L1,V0,M1} { one ==> addition( skol2, skol1(
% 5.44/5.84 skol2 ) ) }.
% 5.44/5.84 parent0[1]: (20596) {G0,W8,D3,L2,V2,M2} { one ==> addition( X, Y ), !
% 5.44/5.84 alpha1( X, Y ) }.
% 5.44/5.84 parent1[0]: (187) {G2,W4,D3,L1,V0,M1} R(183,16) { alpha1( skol2, skol1(
% 5.44/5.84 skol2 ) ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := skol2
% 5.44/5.84 Y := skol1( skol2 )
% 5.44/5.84 end
% 5.44/5.84 substitution1:
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 eqswap: (20598) {G1,W6,D4,L1,V0,M1} { addition( skol2, skol1( skol2 ) )
% 5.44/5.84 ==> one }.
% 5.44/5.84 parent0[0]: (20597) {G1,W6,D4,L1,V0,M1} { one ==> addition( skol2, skol1(
% 5.44/5.84 skol2 ) ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 subsumption: (263) {G3,W6,D4,L1,V0,M1} R(19,187) { addition( skol2, skol1(
% 5.44/5.84 skol2 ) ) ==> one }.
% 5.44/5.84 parent0: (20598) {G1,W6,D4,L1,V0,M1} { addition( skol2, skol1( skol2 ) )
% 5.44/5.84 ==> one }.
% 5.44/5.84 substitution0:
% 5.44/5.84 end
% 5.44/5.84 permutation0:
% 5.44/5.84 0 ==> 0
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 eqswap: (20599) {G0,W8,D3,L2,V2,M2} { one ==> addition( X, Y ), ! alpha1(
% 5.44/5.84 X, Y ) }.
% 5.44/5.84 parent0[1]: (19) {G0,W8,D3,L2,V2,M2} I { ! alpha1( X, Y ), addition( X, Y )
% 5.44/5.84 ==> one }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := X
% 5.44/5.84 Y := Y
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 resolution: (20600) {G1,W8,D3,L2,V2,M2} { one ==> addition( X, Y ), !
% 5.44/5.84 complement( Y, X ) }.
% 5.44/5.84 parent0[1]: (20599) {G0,W8,D3,L2,V2,M2} { one ==> addition( X, Y ), !
% 5.44/5.84 alpha1( X, Y ) }.
% 5.44/5.84 parent1[1]: (16) {G0,W6,D2,L2,V2,M2} I { ! complement( Y, X ), alpha1( X, Y
% 5.44/5.84 ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := X
% 5.44/5.84 Y := Y
% 5.44/5.84 end
% 5.44/5.84 substitution1:
% 5.44/5.84 X := X
% 5.44/5.84 Y := Y
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 eqswap: (20601) {G1,W8,D3,L2,V2,M2} { addition( X, Y ) ==> one, !
% 5.44/5.84 complement( Y, X ) }.
% 5.44/5.84 parent0[0]: (20600) {G1,W8,D3,L2,V2,M2} { one ==> addition( X, Y ), !
% 5.44/5.84 complement( Y, X ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := X
% 5.44/5.84 Y := Y
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 subsumption: (267) {G1,W8,D3,L2,V2,M2} R(19,16) { addition( X, Y ) ==> one
% 5.44/5.84 , ! complement( Y, X ) }.
% 5.44/5.84 parent0: (20601) {G1,W8,D3,L2,V2,M2} { addition( X, Y ) ==> one, !
% 5.44/5.84 complement( Y, X ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := X
% 5.44/5.84 Y := Y
% 5.44/5.84 end
% 5.44/5.84 permutation0:
% 5.44/5.84 0 ==> 0
% 5.44/5.84 1 ==> 1
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 eqswap: (20602) {G0,W13,D3,L3,V2,M3} { ! zero ==> multiplication( X, Y ),
% 5.44/5.84 ! addition( Y, X ) ==> one, alpha1( Y, X ) }.
% 5.44/5.84 parent0[0]: (20) {G0,W13,D3,L3,V2,M3} I { ! multiplication( Y, X ) ==> zero
% 5.44/5.84 , ! addition( X, Y ) ==> one, alpha1( X, Y ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := Y
% 5.44/5.84 Y := X
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 eqswap: (20605) {G0,W11,D3,L3,V2,M3} { ! zero ==> multiplication( X, Y ),
% 5.44/5.84 ! alpha1( X, Y ), complement( Y, X ) }.
% 5.44/5.84 parent0[0]: (17) {G0,W11,D3,L3,V2,M3} I { ! multiplication( X, Y ) ==> zero
% 5.44/5.84 , ! alpha1( X, Y ), complement( Y, X ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := X
% 5.44/5.84 Y := Y
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 resolution: (20606) {G1,W18,D3,L4,V2,M4} { ! zero ==> multiplication( X, Y
% 5.44/5.84 ), complement( Y, X ), ! zero ==> multiplication( Y, X ), ! addition( X
% 5.44/5.84 , Y ) ==> one }.
% 5.44/5.84 parent0[1]: (20605) {G0,W11,D3,L3,V2,M3} { ! zero ==> multiplication( X, Y
% 5.44/5.84 ), ! alpha1( X, Y ), complement( Y, X ) }.
% 5.44/5.84 parent1[2]: (20602) {G0,W13,D3,L3,V2,M3} { ! zero ==> multiplication( X, Y
% 5.44/5.84 ), ! addition( Y, X ) ==> one, alpha1( Y, X ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := X
% 5.44/5.84 Y := Y
% 5.44/5.84 end
% 5.44/5.84 substitution1:
% 5.44/5.84 X := Y
% 5.44/5.84 Y := X
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 eqswap: (20609) {G1,W18,D3,L4,V2,M4} { ! one ==> addition( X, Y ), ! zero
% 5.44/5.84 ==> multiplication( X, Y ), complement( Y, X ), ! zero ==> multiplication
% 5.44/5.84 ( Y, X ) }.
% 5.44/5.84 parent0[3]: (20606) {G1,W18,D3,L4,V2,M4} { ! zero ==> multiplication( X, Y
% 5.44/5.84 ), complement( Y, X ), ! zero ==> multiplication( Y, X ), ! addition( X
% 5.44/5.84 , Y ) ==> one }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := X
% 5.44/5.84 Y := Y
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 eqswap: (20611) {G1,W18,D3,L4,V2,M4} { ! multiplication( X, Y ) ==> zero,
% 5.44/5.84 ! one ==> addition( Y, X ), ! zero ==> multiplication( Y, X ), complement
% 5.44/5.84 ( X, Y ) }.
% 5.44/5.84 parent0[3]: (20609) {G1,W18,D3,L4,V2,M4} { ! one ==> addition( X, Y ), !
% 5.44/5.84 zero ==> multiplication( X, Y ), complement( Y, X ), ! zero ==>
% 5.44/5.84 multiplication( Y, X ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := Y
% 5.44/5.84 Y := X
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 eqswap: (20612) {G1,W18,D3,L4,V2,M4} { ! multiplication( X, Y ) ==> zero,
% 5.44/5.84 ! multiplication( Y, X ) ==> zero, ! one ==> addition( X, Y ), complement
% 5.44/5.84 ( Y, X ) }.
% 5.44/5.84 parent0[2]: (20611) {G1,W18,D3,L4,V2,M4} { ! multiplication( X, Y ) ==>
% 5.44/5.84 zero, ! one ==> addition( Y, X ), ! zero ==> multiplication( Y, X ),
% 5.44/5.84 complement( X, Y ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := Y
% 5.44/5.84 Y := X
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 eqswap: (20613) {G1,W18,D3,L4,V2,M4} { ! addition( X, Y ) ==> one, !
% 5.44/5.84 multiplication( X, Y ) ==> zero, ! multiplication( Y, X ) ==> zero,
% 5.44/5.84 complement( Y, X ) }.
% 5.44/5.84 parent0[2]: (20612) {G1,W18,D3,L4,V2,M4} { ! multiplication( X, Y ) ==>
% 5.44/5.84 zero, ! multiplication( Y, X ) ==> zero, ! one ==> addition( X, Y ),
% 5.44/5.84 complement( Y, X ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := X
% 5.44/5.84 Y := Y
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 subsumption: (282) {G1,W18,D3,L4,V2,M4} R(20,17) { ! multiplication( X, Y )
% 5.44/5.84 ==> zero, ! addition( Y, X ) ==> one, ! multiplication( Y, X ) ==> zero
% 5.44/5.84 , complement( X, Y ) }.
% 5.44/5.84 parent0: (20613) {G1,W18,D3,L4,V2,M4} { ! addition( X, Y ) ==> one, !
% 5.44/5.84 multiplication( X, Y ) ==> zero, ! multiplication( Y, X ) ==> zero,
% 5.44/5.84 complement( Y, X ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := Y
% 5.44/5.84 Y := X
% 5.44/5.84 end
% 5.44/5.84 permutation0:
% 5.44/5.84 0 ==> 1
% 5.44/5.84 1 ==> 2
% 5.44/5.84 2 ==> 0
% 5.44/5.84 3 ==> 3
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 *** allocated 384427 integers for termspace/termends
% 5.44/5.84 paramod: (20623) {G1,W48,D7,L2,V0,M2} { ! leq( addition( multiplication(
% 5.44/5.84 skol2, skol4 ), multiplication( c( skol2 ), skol6 ) ), addition(
% 5.44/5.84 multiplication( skol2, addition( multiplication( c( skol2 ), skol5 ),
% 5.44/5.84 multiplication( skol2, skol4 ) ) ), multiplication( c( skol2 ), skol6 ) )
% 5.44/5.84 ), ! leq( addition( multiplication( skol2, addition( multiplication(
% 5.44/5.84 skol2, skol4 ), multiplication( c( skol2 ), skol5 ) ) ), multiplication(
% 5.44/5.84 c( skol2 ), skol6 ) ), addition( multiplication( skol2, skol4 ),
% 5.44/5.84 multiplication( c( skol2 ), skol6 ) ) ) }.
% 5.44/5.84 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 5.44/5.84 }.
% 5.44/5.84 parent1[1; 13]: (28) {G0,W48,D7,L2,V0,M2} I { ! leq( addition(
% 5.44/5.84 multiplication( skol2, addition( multiplication( skol2, skol4 ),
% 5.44/5.84 multiplication( c( skol2 ), skol5 ) ) ), multiplication( c( skol2 ),
% 5.44/5.84 skol6 ) ), addition( multiplication( skol2, skol4 ), multiplication( c(
% 5.44/5.84 skol2 ), skol6 ) ) ), ! leq( addition( multiplication( skol2, skol4 ),
% 5.44/5.84 multiplication( c( skol2 ), skol6 ) ), addition( multiplication( skol2,
% 5.44/5.84 addition( multiplication( skol2, skol4 ), multiplication( c( skol2 ),
% 5.44/5.84 skol5 ) ) ), multiplication( c( skol2 ), skol6 ) ) ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := multiplication( skol2, skol4 )
% 5.44/5.84 Y := multiplication( c( skol2 ), skol5 )
% 5.44/5.84 end
% 5.44/5.84 substitution1:
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 paramod: (20628) {G1,W48,D7,L2,V0,M2} { ! leq( addition( multiplication(
% 5.44/5.84 skol2, addition( multiplication( c( skol2 ), skol5 ), multiplication(
% 5.44/5.84 skol2, skol4 ) ) ), multiplication( c( skol2 ), skol6 ) ), addition(
% 5.44/5.84 multiplication( skol2, skol4 ), multiplication( c( skol2 ), skol6 ) ) ),
% 5.44/5.84 ! leq( addition( multiplication( skol2, skol4 ), multiplication( c( skol2
% 5.44/5.84 ), skol6 ) ), addition( multiplication( skol2, addition( multiplication
% 5.44/5.84 ( c( skol2 ), skol5 ), multiplication( skol2, skol4 ) ) ), multiplication
% 5.44/5.84 ( c( skol2 ), skol6 ) ) ) }.
% 5.44/5.84 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 5.44/5.84 }.
% 5.44/5.84 parent1[1; 5]: (20623) {G1,W48,D7,L2,V0,M2} { ! leq( addition(
% 5.44/5.84 multiplication( skol2, skol4 ), multiplication( c( skol2 ), skol6 ) ),
% 5.44/5.84 addition( multiplication( skol2, addition( multiplication( c( skol2 ),
% 5.44/5.84 skol5 ), multiplication( skol2, skol4 ) ) ), multiplication( c( skol2 ),
% 5.44/5.84 skol6 ) ) ), ! leq( addition( multiplication( skol2, addition(
% 5.44/5.84 multiplication( skol2, skol4 ), multiplication( c( skol2 ), skol5 ) ) ),
% 5.44/5.84 multiplication( c( skol2 ), skol6 ) ), addition( multiplication( skol2,
% 5.44/5.84 skol4 ), multiplication( c( skol2 ), skol6 ) ) ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := multiplication( skol2, skol4 )
% 5.44/5.84 Y := multiplication( c( skol2 ), skol5 )
% 5.44/5.84 end
% 5.44/5.84 substitution1:
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 subsumption: (543) {G1,W48,D7,L2,V0,M2} P(0,28) { ! leq( addition(
% 5.44/5.84 multiplication( skol2, addition( multiplication( c( skol2 ), skol5 ),
% 5.44/5.84 multiplication( skol2, skol4 ) ) ), multiplication( c( skol2 ), skol6 ) )
% 5.44/5.84 , addition( multiplication( skol2, skol4 ), multiplication( c( skol2 ),
% 5.44/5.84 skol6 ) ) ), ! leq( addition( multiplication( skol2, skol4 ),
% 5.44/5.84 multiplication( c( skol2 ), skol6 ) ), addition( multiplication( skol2,
% 5.44/5.84 addition( multiplication( c( skol2 ), skol5 ), multiplication( skol2,
% 5.44/5.84 skol4 ) ) ), multiplication( c( skol2 ), skol6 ) ) ) }.
% 5.44/5.84 parent0: (20628) {G1,W48,D7,L2,V0,M2} { ! leq( addition( multiplication(
% 5.44/5.84 skol2, addition( multiplication( c( skol2 ), skol5 ), multiplication(
% 5.44/5.84 skol2, skol4 ) ) ), multiplication( c( skol2 ), skol6 ) ), addition(
% 5.44/5.84 multiplication( skol2, skol4 ), multiplication( c( skol2 ), skol6 ) ) ),
% 5.44/5.84 ! leq( addition( multiplication( skol2, skol4 ), multiplication( c( skol2
% 5.44/5.84 ), skol6 ) ), addition( multiplication( skol2, addition( multiplication
% 5.44/5.84 ( c( skol2 ), skol5 ), multiplication( skol2, skol4 ) ) ), multiplication
% 5.44/5.84 ( c( skol2 ), skol6 ) ) ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 end
% 5.44/5.84 permutation0:
% 5.44/5.84 0 ==> 0
% 5.44/5.84 1 ==> 1
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 eqswap: (20660) {G3,W6,D4,L1,V0,M1} { one ==> addition( skol2, skol1(
% 5.44/5.84 skol2 ) ) }.
% 5.44/5.84 parent0[0]: (263) {G3,W6,D4,L1,V0,M1} R(19,187) { addition( skol2, skol1(
% 5.44/5.84 skol2 ) ) ==> one }.
% 5.44/5.84 substitution0:
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 paramod: (20661) {G1,W6,D4,L1,V0,M1} { one ==> addition( skol1( skol2 ),
% 5.44/5.84 skol2 ) }.
% 5.44/5.84 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 5.44/5.84 }.
% 5.44/5.84 parent1[0; 2]: (20660) {G3,W6,D4,L1,V0,M1} { one ==> addition( skol2,
% 5.44/5.84 skol1( skol2 ) ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := skol2
% 5.44/5.84 Y := skol1( skol2 )
% 5.44/5.84 end
% 5.44/5.84 substitution1:
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 eqswap: (20664) {G1,W6,D4,L1,V0,M1} { addition( skol1( skol2 ), skol2 )
% 5.44/5.84 ==> one }.
% 5.44/5.84 parent0[0]: (20661) {G1,W6,D4,L1,V0,M1} { one ==> addition( skol1( skol2 )
% 5.44/5.84 , skol2 ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 subsumption: (3708) {G4,W6,D4,L1,V0,M1} P(263,0) { addition( skol1( skol2 )
% 5.44/5.84 , skol2 ) ==> one }.
% 5.44/5.84 parent0: (20664) {G1,W6,D4,L1,V0,M1} { addition( skol1( skol2 ), skol2 )
% 5.44/5.84 ==> one }.
% 5.44/5.84 substitution0:
% 5.44/5.84 end
% 5.44/5.84 permutation0:
% 5.44/5.84 0 ==> 0
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 eqswap: (20665) {G2,W6,D4,L1,V0,M1} { zero ==> multiplication( skol2,
% 5.44/5.84 skol1( skol2 ) ) }.
% 5.44/5.84 parent0[0]: (195) {G2,W6,D4,L1,V0,M1} R(15,183) { multiplication( skol2,
% 5.44/5.84 skol1( skol2 ) ) ==> zero }.
% 5.44/5.84 substitution0:
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 eqswap: (20666) {G0,W13,D3,L3,V2,M3} { ! zero ==> multiplication( X, Y ),
% 5.44/5.84 ! addition( Y, X ) ==> one, alpha1( Y, X ) }.
% 5.44/5.84 parent0[0]: (20) {G0,W13,D3,L3,V2,M3} I { ! multiplication( Y, X ) ==> zero
% 5.44/5.84 , ! addition( X, Y ) ==> one, alpha1( X, Y ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := Y
% 5.44/5.84 Y := X
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 resolution: (20670) {G1,W10,D4,L2,V0,M2} { ! addition( skol1( skol2 ),
% 5.44/5.84 skol2 ) ==> one, alpha1( skol1( skol2 ), skol2 ) }.
% 5.44/5.84 parent0[0]: (20666) {G0,W13,D3,L3,V2,M3} { ! zero ==> multiplication( X, Y
% 5.44/5.84 ), ! addition( Y, X ) ==> one, alpha1( Y, X ) }.
% 5.44/5.84 parent1[0]: (20665) {G2,W6,D4,L1,V0,M1} { zero ==> multiplication( skol2,
% 5.44/5.84 skol1( skol2 ) ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := skol2
% 5.44/5.84 Y := skol1( skol2 )
% 5.44/5.84 end
% 5.44/5.84 substitution1:
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 paramod: (20671) {G2,W7,D3,L2,V0,M2} { ! one ==> one, alpha1( skol1( skol2
% 5.44/5.84 ), skol2 ) }.
% 5.44/5.84 parent0[0]: (3708) {G4,W6,D4,L1,V0,M1} P(263,0) { addition( skol1( skol2 )
% 5.44/5.84 , skol2 ) ==> one }.
% 5.44/5.84 parent1[0; 2]: (20670) {G1,W10,D4,L2,V0,M2} { ! addition( skol1( skol2 ),
% 5.44/5.84 skol2 ) ==> one, alpha1( skol1( skol2 ), skol2 ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 end
% 5.44/5.84 substitution1:
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 eqrefl: (20672) {G0,W4,D3,L1,V0,M1} { alpha1( skol1( skol2 ), skol2 ) }.
% 5.44/5.84 parent0[0]: (20671) {G2,W7,D3,L2,V0,M2} { ! one ==> one, alpha1( skol1(
% 5.44/5.84 skol2 ), skol2 ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 subsumption: (5006) {G5,W4,D3,L1,V0,M1} R(195,20);d(3708);q { alpha1( skol1
% 5.44/5.84 ( skol2 ), skol2 ) }.
% 5.44/5.84 parent0: (20672) {G0,W4,D3,L1,V0,M1} { alpha1( skol1( skol2 ), skol2 ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 end
% 5.44/5.84 permutation0:
% 5.44/5.84 0 ==> 0
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 eqswap: (20674) {G1,W17,D5,L1,V4,M1} { multiplication( X, addition(
% 5.44/5.84 multiplication( Y, Z ), T ) ) ==> addition( multiplication(
% 5.44/5.84 multiplication( X, Y ), Z ), multiplication( X, T ) ) }.
% 5.44/5.84 parent0[0]: (48) {G1,W17,D5,L1,V4,M1} P(4,7) { addition( multiplication(
% 5.44/5.84 multiplication( X, Y ), Z ), multiplication( X, T ) ) ==> multiplication
% 5.44/5.84 ( X, addition( multiplication( Y, Z ), T ) ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := X
% 5.44/5.84 Y := Y
% 5.44/5.84 Z := Z
% 5.44/5.84 T := T
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 paramod: (20678) {G2,W16,D6,L1,V2,M1} { multiplication( skol2, addition(
% 5.44/5.84 multiplication( skol1( skol2 ), X ), Y ) ) ==> addition( multiplication(
% 5.44/5.84 zero, X ), multiplication( skol2, Y ) ) }.
% 5.44/5.84 parent0[0]: (195) {G2,W6,D4,L1,V0,M1} R(15,183) { multiplication( skol2,
% 5.44/5.84 skol1( skol2 ) ) ==> zero }.
% 5.44/5.84 parent1[0; 11]: (20674) {G1,W17,D5,L1,V4,M1} { multiplication( X, addition
% 5.44/5.84 ( multiplication( Y, Z ), T ) ) ==> addition( multiplication(
% 5.44/5.84 multiplication( X, Y ), Z ), multiplication( X, T ) ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 end
% 5.44/5.84 substitution1:
% 5.44/5.84 X := skol2
% 5.44/5.84 Y := skol1( skol2 )
% 5.44/5.84 Z := X
% 5.44/5.84 T := Y
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 paramod: (20680) {G1,W14,D6,L1,V2,M1} { multiplication( skol2, addition(
% 5.44/5.84 multiplication( skol1( skol2 ), X ), Y ) ) ==> addition( zero,
% 5.44/5.84 multiplication( skol2, Y ) ) }.
% 5.44/5.84 parent0[0]: (10) {G0,W5,D3,L1,V1,M1} I { multiplication( zero, X ) ==> zero
% 5.44/5.84 }.
% 5.44/5.84 parent1[0; 10]: (20678) {G2,W16,D6,L1,V2,M1} { multiplication( skol2,
% 5.44/5.84 addition( multiplication( skol1( skol2 ), X ), Y ) ) ==> addition(
% 5.44/5.84 multiplication( zero, X ), multiplication( skol2, Y ) ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := X
% 5.44/5.84 end
% 5.44/5.84 substitution1:
% 5.44/5.84 X := X
% 5.44/5.84 Y := Y
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 paramod: (20681) {G2,W12,D6,L1,V2,M1} { multiplication( skol2, addition(
% 5.44/5.84 multiplication( skol1( skol2 ), X ), Y ) ) ==> multiplication( skol2, Y )
% 5.44/5.84 }.
% 5.44/5.84 parent0[0]: (32) {G1,W5,D3,L1,V1,M1} P(2,0) { addition( zero, X ) ==> X }.
% 5.44/5.84 parent1[0; 9]: (20680) {G1,W14,D6,L1,V2,M1} { multiplication( skol2,
% 5.44/5.84 addition( multiplication( skol1( skol2 ), X ), Y ) ) ==> addition( zero,
% 5.44/5.84 multiplication( skol2, Y ) ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := multiplication( skol2, Y )
% 5.44/5.84 end
% 5.44/5.84 substitution1:
% 5.44/5.84 X := X
% 5.44/5.84 Y := Y
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 subsumption: (5015) {G3,W12,D6,L1,V2,M1} P(195,48);d(10);d(32) {
% 5.44/5.84 multiplication( skol2, addition( multiplication( skol1( skol2 ), X ), Y )
% 5.44/5.84 ) ==> multiplication( skol2, Y ) }.
% 5.44/5.84 parent0: (20681) {G2,W12,D6,L1,V2,M1} { multiplication( skol2, addition(
% 5.44/5.84 multiplication( skol1( skol2 ), X ), Y ) ) ==> multiplication( skol2, Y )
% 5.44/5.84 }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := X
% 5.44/5.84 Y := Y
% 5.44/5.84 end
% 5.44/5.84 permutation0:
% 5.44/5.84 0 ==> 0
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 eqswap: (20683) {G0,W11,D3,L3,V2,M3} { ! zero ==> multiplication( X, Y ),
% 5.44/5.84 ! alpha1( X, Y ), complement( Y, X ) }.
% 5.44/5.84 parent0[0]: (17) {G0,W11,D3,L3,V2,M3} I { ! multiplication( X, Y ) ==> zero
% 5.44/5.84 , ! alpha1( X, Y ), complement( Y, X ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := X
% 5.44/5.84 Y := Y
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 resolution: (20685) {G1,W10,D4,L2,V0,M2} { ! zero ==> multiplication(
% 5.44/5.84 skol1( skol2 ), skol2 ), complement( skol2, skol1( skol2 ) ) }.
% 5.44/5.84 parent0[1]: (20683) {G0,W11,D3,L3,V2,M3} { ! zero ==> multiplication( X, Y
% 5.44/5.84 ), ! alpha1( X, Y ), complement( Y, X ) }.
% 5.44/5.84 parent1[0]: (5006) {G5,W4,D3,L1,V0,M1} R(195,20);d(3708);q { alpha1( skol1
% 5.44/5.84 ( skol2 ), skol2 ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := skol1( skol2 )
% 5.44/5.84 Y := skol2
% 5.44/5.84 end
% 5.44/5.84 substitution1:
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 paramod: (20686) {G2,W7,D3,L2,V0,M2} { ! zero ==> zero, complement( skol2
% 5.44/5.84 , skol1( skol2 ) ) }.
% 5.44/5.84 parent0[0]: (237) {G3,W6,D4,L1,V0,M1} R(18,187) { multiplication( skol1(
% 5.44/5.84 skol2 ), skol2 ) ==> zero }.
% 5.44/5.84 parent1[0; 3]: (20685) {G1,W10,D4,L2,V0,M2} { ! zero ==> multiplication(
% 5.44/5.84 skol1( skol2 ), skol2 ), complement( skol2, skol1( skol2 ) ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 end
% 5.44/5.84 substitution1:
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 eqrefl: (20687) {G0,W4,D3,L1,V0,M1} { complement( skol2, skol1( skol2 ) )
% 5.44/5.84 }.
% 5.44/5.84 parent0[0]: (20686) {G2,W7,D3,L2,V0,M2} { ! zero ==> zero, complement(
% 5.44/5.84 skol2, skol1( skol2 ) ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 subsumption: (5017) {G6,W4,D3,L1,V0,M1} R(5006,17);d(237);q { complement(
% 5.44/5.84 skol2, skol1( skol2 ) ) }.
% 5.44/5.84 parent0: (20687) {G0,W4,D3,L1,V0,M1} { complement( skol2, skol1( skol2 ) )
% 5.44/5.84 }.
% 5.44/5.84 substitution0:
% 5.44/5.84 end
% 5.44/5.84 permutation0:
% 5.44/5.84 0 ==> 0
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 resolution: (20688) {G2,W6,D4,L1,V0,M1} { complement( skol1( skol1( skol2
% 5.44/5.84 ) ), skol1( skol2 ) ) }.
% 5.44/5.84 parent0[1]: (182) {G1,W7,D3,L2,V2,M2} R(13,14) { complement( skol1( X ), X
% 5.44/5.84 ), ! complement( Y, X ) }.
% 5.44/5.84 parent1[0]: (5017) {G6,W4,D3,L1,V0,M1} R(5006,17);d(237);q { complement(
% 5.44/5.84 skol2, skol1( skol2 ) ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := skol1( skol2 )
% 5.44/5.84 Y := skol2
% 5.44/5.84 end
% 5.44/5.84 substitution1:
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 subsumption: (5018) {G7,W6,D4,L1,V0,M1} R(5017,182) { complement( skol1(
% 5.44/5.84 skol1( skol2 ) ), skol1( skol2 ) ) }.
% 5.44/5.84 parent0: (20688) {G2,W6,D4,L1,V0,M1} { complement( skol1( skol1( skol2 ) )
% 5.44/5.84 , skol1( skol2 ) ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 end
% 5.44/5.84 permutation0:
% 5.44/5.84 0 ==> 0
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 eqswap: (20689) {G0,W9,D3,L3,V2,M3} { Y = c( X ), ! test( X ), !
% 5.44/5.84 complement( X, Y ) }.
% 5.44/5.84 parent0[2]: (22) {G0,W9,D3,L3,V2,M3} I { ! test( X ), ! complement( X, Y )
% 5.44/5.84 , c( X ) = Y }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := X
% 5.44/5.84 Y := Y
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 resolution: (20690) {G1,W7,D3,L2,V0,M2} { skol1( skol2 ) = c( skol2 ), !
% 5.44/5.84 test( skol2 ) }.
% 5.44/5.84 parent0[2]: (20689) {G0,W9,D3,L3,V2,M3} { Y = c( X ), ! test( X ), !
% 5.44/5.84 complement( X, Y ) }.
% 5.44/5.84 parent1[0]: (5017) {G6,W4,D3,L1,V0,M1} R(5006,17);d(237);q { complement(
% 5.44/5.84 skol2, skol1( skol2 ) ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := skol2
% 5.44/5.84 Y := skol1( skol2 )
% 5.44/5.84 end
% 5.44/5.84 substitution1:
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 resolution: (20691) {G1,W5,D3,L1,V0,M1} { skol1( skol2 ) = c( skol2 ) }.
% 5.44/5.84 parent0[1]: (20690) {G1,W7,D3,L2,V0,M2} { skol1( skol2 ) = c( skol2 ), !
% 5.44/5.84 test( skol2 ) }.
% 5.44/5.84 parent1[0]: (26) {G0,W2,D2,L1,V0,M1} I { test( skol2 ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 end
% 5.44/5.84 substitution1:
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 eqswap: (20692) {G1,W5,D3,L1,V0,M1} { c( skol2 ) = skol1( skol2 ) }.
% 5.44/5.84 parent0[0]: (20691) {G1,W5,D3,L1,V0,M1} { skol1( skol2 ) = c( skol2 ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 subsumption: (5025) {G7,W5,D3,L1,V0,M1} R(5017,22);r(26) { c( skol2 ) ==>
% 5.44/5.84 skol1( skol2 ) }.
% 5.44/5.84 parent0: (20692) {G1,W5,D3,L1,V0,M1} { c( skol2 ) = skol1( skol2 ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 end
% 5.44/5.84 permutation0:
% 5.44/5.84 0 ==> 0
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 resolution: (20693) {G1,W3,D3,L1,V0,M1} { test( skol1( skol2 ) ) }.
% 5.44/5.84 parent0[0]: (14) {G0,W5,D2,L2,V2,M2} I { ! complement( Y, X ), test( X )
% 5.44/5.84 }.
% 5.44/5.84 parent1[0]: (5017) {G6,W4,D3,L1,V0,M1} R(5006,17);d(237);q { complement(
% 5.44/5.84 skol2, skol1( skol2 ) ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := skol1( skol2 )
% 5.44/5.84 Y := skol2
% 5.44/5.84 end
% 5.44/5.84 substitution1:
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 subsumption: (5027) {G7,W3,D3,L1,V0,M1} R(5017,14) { test( skol1( skol2 ) )
% 5.44/5.84 }.
% 5.44/5.84 parent0: (20693) {G1,W3,D3,L1,V0,M1} { test( skol1( skol2 ) ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 end
% 5.44/5.84 permutation0:
% 5.44/5.84 0 ==> 0
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 eqswap: (20694) {G1,W10,D4,L2,V1,M2} { c( X ) ==> multiplication( c( X ),
% 5.44/5.84 c( X ) ), ! test( X ) }.
% 5.44/5.84 parent0[1]: (30) {G1,W10,D4,L2,V1,M2} F(24);d(3) { ! test( X ),
% 5.44/5.84 multiplication( c( X ), c( X ) ) ==> c( X ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := X
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 resolution: (20695) {G2,W11,D5,L1,V0,M1} { c( skol1( skol2 ) ) ==>
% 5.44/5.84 multiplication( c( skol1( skol2 ) ), c( skol1( skol2 ) ) ) }.
% 5.44/5.84 parent0[1]: (20694) {G1,W10,D4,L2,V1,M2} { c( X ) ==> multiplication( c( X
% 5.44/5.84 ), c( X ) ), ! test( X ) }.
% 5.44/5.84 parent1[0]: (5027) {G7,W3,D3,L1,V0,M1} R(5017,14) { test( skol1( skol2 ) )
% 5.44/5.84 }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := skol1( skol2 )
% 5.44/5.84 end
% 5.44/5.84 substitution1:
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 eqswap: (20696) {G2,W11,D5,L1,V0,M1} { multiplication( c( skol1( skol2 ) )
% 5.44/5.84 , c( skol1( skol2 ) ) ) ==> c( skol1( skol2 ) ) }.
% 5.44/5.84 parent0[0]: (20695) {G2,W11,D5,L1,V0,M1} { c( skol1( skol2 ) ) ==>
% 5.44/5.84 multiplication( c( skol1( skol2 ) ), c( skol1( skol2 ) ) ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 subsumption: (5038) {G8,W11,D5,L1,V0,M1} R(5027,30) { multiplication( c(
% 5.44/5.84 skol1( skol2 ) ), c( skol1( skol2 ) ) ) ==> c( skol1( skol2 ) ) }.
% 5.44/5.84 parent0: (20696) {G2,W11,D5,L1,V0,M1} { multiplication( c( skol1( skol2 )
% 5.44/5.84 ), c( skol1( skol2 ) ) ) ==> c( skol1( skol2 ) ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 end
% 5.44/5.84 permutation0:
% 5.44/5.84 0 ==> 0
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 eqswap: (20697) {G1,W8,D3,L2,V2,M2} { one ==> addition( X, Y ), !
% 5.44/5.84 complement( Y, X ) }.
% 5.44/5.84 parent0[0]: (267) {G1,W8,D3,L2,V2,M2} R(19,16) { addition( X, Y ) ==> one,
% 5.44/5.84 ! complement( Y, X ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := X
% 5.44/5.84 Y := Y
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 paramod: (20698) {G1,W8,D3,L2,V2,M2} { one ==> addition( Y, X ), !
% 5.44/5.84 complement( Y, X ) }.
% 5.44/5.84 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 5.44/5.84 }.
% 5.44/5.84 parent1[0; 2]: (20697) {G1,W8,D3,L2,V2,M2} { one ==> addition( X, Y ), !
% 5.44/5.84 complement( Y, X ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := X
% 5.44/5.84 Y := Y
% 5.44/5.84 end
% 5.44/5.84 substitution1:
% 5.44/5.84 X := X
% 5.44/5.84 Y := Y
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 eqswap: (20701) {G1,W8,D3,L2,V2,M2} { addition( X, Y ) ==> one, !
% 5.44/5.84 complement( X, Y ) }.
% 5.44/5.84 parent0[0]: (20698) {G1,W8,D3,L2,V2,M2} { one ==> addition( Y, X ), !
% 5.44/5.84 complement( Y, X ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := Y
% 5.44/5.84 Y := X
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 subsumption: (6665) {G2,W8,D3,L2,V2,M2} P(267,0) { addition( Y, X ) ==> one
% 5.44/5.84 , ! complement( Y, X ) }.
% 5.44/5.84 parent0: (20701) {G1,W8,D3,L2,V2,M2} { addition( X, Y ) ==> one, !
% 5.44/5.84 complement( X, Y ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := Y
% 5.44/5.84 Y := X
% 5.44/5.84 end
% 5.44/5.84 permutation0:
% 5.44/5.84 0 ==> 0
% 5.44/5.84 1 ==> 1
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 eqswap: (20702) {G1,W18,D3,L4,V2,M4} { ! zero ==> multiplication( X, Y ),
% 5.44/5.84 ! addition( Y, X ) ==> one, ! multiplication( Y, X ) ==> zero, complement
% 5.44/5.84 ( X, Y ) }.
% 5.44/5.84 parent0[0]: (282) {G1,W18,D3,L4,V2,M4} R(20,17) { ! multiplication( X, Y )
% 5.44/5.84 ==> zero, ! addition( Y, X ) ==> one, ! multiplication( Y, X ) ==> zero,
% 5.44/5.84 complement( X, Y ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := X
% 5.44/5.84 Y := Y
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 resolution: (21378) {G2,W16,D3,L4,V2,M4} { ! zero ==> multiplication( X, Y
% 5.44/5.84 ), ! addition( Y, X ) ==> one, complement( X, Y ), ! complement( Y, X )
% 5.44/5.84 }.
% 5.44/5.84 parent0[2]: (20702) {G1,W18,D3,L4,V2,M4} { ! zero ==> multiplication( X, Y
% 5.44/5.84 ), ! addition( Y, X ) ==> one, ! multiplication( Y, X ) ==> zero,
% 5.44/5.84 complement( X, Y ) }.
% 5.44/5.84 parent1[0]: (240) {G1,W8,D3,L2,V2,M2} R(18,16) { multiplication( X, Y ) ==>
% 5.44/5.84 zero, ! complement( X, Y ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := X
% 5.44/5.84 Y := Y
% 5.44/5.84 end
% 5.44/5.84 substitution1:
% 5.44/5.84 X := Y
% 5.44/5.84 Y := X
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 paramod: (21379) {G1,W17,D3,L5,V2,M5} { ! zero ==> zero, ! complement( Y,
% 5.44/5.84 X ), ! addition( Y, X ) ==> one, complement( X, Y ), ! complement( Y, X )
% 5.44/5.84 }.
% 5.44/5.84 parent0[1]: (15) {G0,W8,D3,L2,V2,M2} I { ! complement( Y, X ),
% 5.44/5.84 multiplication( X, Y ) ==> zero }.
% 5.44/5.84 parent1[0; 3]: (21378) {G2,W16,D3,L4,V2,M4} { ! zero ==> multiplication( X
% 5.44/5.84 , Y ), ! addition( Y, X ) ==> one, complement( X, Y ), ! complement( Y, X
% 5.44/5.84 ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := X
% 5.44/5.84 Y := Y
% 5.44/5.84 end
% 5.44/5.84 substitution1:
% 5.44/5.84 X := X
% 5.44/5.84 Y := Y
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 factor: (21380) {G1,W14,D3,L4,V2,M4} { ! zero ==> zero, ! complement( X, Y
% 5.44/5.84 ), ! addition( X, Y ) ==> one, complement( Y, X ) }.
% 5.44/5.84 parent0[1, 4]: (21379) {G1,W17,D3,L5,V2,M5} { ! zero ==> zero, !
% 5.44/5.84 complement( Y, X ), ! addition( Y, X ) ==> one, complement( X, Y ), !
% 5.44/5.84 complement( Y, X ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := Y
% 5.44/5.84 Y := X
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 paramod: (21381) {G2,W15,D2,L5,V2,M5} { ! one ==> one, ! complement( X, Y
% 5.44/5.84 ), ! zero ==> zero, ! complement( X, Y ), complement( Y, X ) }.
% 5.44/5.84 parent0[0]: (6665) {G2,W8,D3,L2,V2,M2} P(267,0) { addition( Y, X ) ==> one
% 5.44/5.84 , ! complement( Y, X ) }.
% 5.44/5.84 parent1[2; 2]: (21380) {G1,W14,D3,L4,V2,M4} { ! zero ==> zero, !
% 5.44/5.84 complement( X, Y ), ! addition( X, Y ) ==> one, complement( Y, X ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := Y
% 5.44/5.84 Y := X
% 5.44/5.84 end
% 5.44/5.84 substitution1:
% 5.44/5.84 X := X
% 5.44/5.84 Y := Y
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 factor: (21382) {G2,W12,D2,L4,V2,M4} { ! one ==> one, ! complement( X, Y )
% 5.44/5.84 , ! zero ==> zero, complement( Y, X ) }.
% 5.44/5.84 parent0[1, 3]: (21381) {G2,W15,D2,L5,V2,M5} { ! one ==> one, ! complement
% 5.44/5.84 ( X, Y ), ! zero ==> zero, ! complement( X, Y ), complement( Y, X ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := X
% 5.44/5.84 Y := Y
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 eqrefl: (21383) {G0,W9,D2,L3,V2,M3} { ! complement( X, Y ), ! zero ==>
% 5.44/5.84 zero, complement( Y, X ) }.
% 5.44/5.84 parent0[0]: (21382) {G2,W12,D2,L4,V2,M4} { ! one ==> one, ! complement( X
% 5.44/5.84 , Y ), ! zero ==> zero, complement( Y, X ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := X
% 5.44/5.84 Y := Y
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 eqrefl: (21385) {G0,W6,D2,L2,V2,M2} { ! complement( X, Y ), complement( Y
% 5.44/5.84 , X ) }.
% 5.44/5.84 parent0[1]: (21383) {G0,W9,D2,L3,V2,M3} { ! complement( X, Y ), ! zero ==>
% 5.44/5.84 zero, complement( Y, X ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := X
% 5.44/5.84 Y := Y
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 subsumption: (7375) {G3,W6,D2,L2,V2,M2} R(282,240);d(15);d(6665);q;q {
% 5.44/5.84 complement( X, Y ), ! complement( Y, X ) }.
% 5.44/5.84 parent0: (21385) {G0,W6,D2,L2,V2,M2} { ! complement( X, Y ), complement( Y
% 5.44/5.84 , X ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := Y
% 5.44/5.84 Y := X
% 5.44/5.84 end
% 5.44/5.84 permutation0:
% 5.44/5.84 0 ==> 1
% 5.44/5.84 1 ==> 0
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 resolution: (21386) {G4,W6,D4,L1,V0,M1} { complement( skol1( skol2 ),
% 5.44/5.84 skol1( skol1( skol2 ) ) ) }.
% 5.44/5.84 parent0[1]: (7375) {G3,W6,D2,L2,V2,M2} R(282,240);d(15);d(6665);q;q {
% 5.44/5.84 complement( X, Y ), ! complement( Y, X ) }.
% 5.44/5.84 parent1[0]: (5018) {G7,W6,D4,L1,V0,M1} R(5017,182) { complement( skol1(
% 5.44/5.84 skol1( skol2 ) ), skol1( skol2 ) ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := skol1( skol2 )
% 5.44/5.84 Y := skol1( skol1( skol2 ) )
% 5.44/5.84 end
% 5.44/5.84 substitution1:
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 subsumption: (7395) {G8,W6,D4,L1,V0,M1} R(7375,5018) { complement( skol1(
% 5.44/5.84 skol2 ), skol1( skol1( skol2 ) ) ) }.
% 5.44/5.84 parent0: (21386) {G4,W6,D4,L1,V0,M1} { complement( skol1( skol2 ), skol1(
% 5.44/5.84 skol1( skol2 ) ) ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 end
% 5.44/5.84 permutation0:
% 5.44/5.84 0 ==> 0
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 resolution: (21387) {G1,W5,D2,L2,V2,M2} { test( Y ), ! complement( Y, X )
% 5.44/5.84 }.
% 5.44/5.84 parent0[0]: (14) {G0,W5,D2,L2,V2,M2} I { ! complement( Y, X ), test( X )
% 5.44/5.84 }.
% 5.44/5.84 parent1[0]: (7375) {G3,W6,D2,L2,V2,M2} R(282,240);d(15);d(6665);q;q {
% 5.44/5.84 complement( X, Y ), ! complement( Y, X ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := Y
% 5.44/5.84 Y := X
% 5.44/5.84 end
% 5.44/5.84 substitution1:
% 5.44/5.84 X := X
% 5.44/5.84 Y := Y
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 subsumption: (7420) {G4,W5,D2,L2,V2,M2} R(7375,14) { ! complement( X, Y ),
% 5.44/5.84 test( X ) }.
% 5.44/5.84 parent0: (21387) {G1,W5,D2,L2,V2,M2} { test( Y ), ! complement( Y, X ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := Y
% 5.44/5.84 Y := X
% 5.44/5.84 end
% 5.44/5.84 permutation0:
% 5.44/5.84 0 ==> 1
% 5.44/5.84 1 ==> 0
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 eqswap: (21388) {G0,W9,D3,L3,V2,M3} { Y = c( X ), ! test( X ), !
% 5.44/5.84 complement( X, Y ) }.
% 5.44/5.84 parent0[2]: (22) {G0,W9,D3,L3,V2,M3} I { ! test( X ), ! complement( X, Y )
% 5.44/5.84 , c( X ) = Y }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := X
% 5.44/5.84 Y := Y
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 resolution: (21389) {G1,W10,D3,L3,V3,M3} { X = c( Y ), ! complement( Y, X
% 5.44/5.84 ), ! complement( Y, Z ) }.
% 5.44/5.84 parent0[1]: (21388) {G0,W9,D3,L3,V2,M3} { Y = c( X ), ! test( X ), !
% 5.44/5.84 complement( X, Y ) }.
% 5.44/5.84 parent1[1]: (7420) {G4,W5,D2,L2,V2,M2} R(7375,14) { ! complement( X, Y ),
% 5.44/5.84 test( X ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := Y
% 5.44/5.84 Y := X
% 5.44/5.84 end
% 5.44/5.84 substitution1:
% 5.44/5.84 X := Y
% 5.44/5.84 Y := Z
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 eqswap: (21390) {G1,W10,D3,L3,V3,M3} { c( Y ) = X, ! complement( Y, X ), !
% 5.44/5.84 complement( Y, Z ) }.
% 5.44/5.84 parent0[0]: (21389) {G1,W10,D3,L3,V3,M3} { X = c( Y ), ! complement( Y, X
% 5.44/5.84 ), ! complement( Y, Z ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := X
% 5.44/5.84 Y := Y
% 5.44/5.84 Z := Z
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 subsumption: (7449) {G5,W10,D3,L3,V3,M3} R(7420,22) { ! complement( X, Y )
% 5.44/5.84 , ! complement( X, Z ), c( X ) = Z }.
% 5.44/5.84 parent0: (21390) {G1,W10,D3,L3,V3,M3} { c( Y ) = X, ! complement( Y, X ),
% 5.44/5.84 ! complement( Y, Z ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := Z
% 5.44/5.84 Y := X
% 5.44/5.84 Z := Y
% 5.44/5.84 end
% 5.44/5.84 permutation0:
% 5.44/5.84 0 ==> 2
% 5.44/5.84 1 ==> 1
% 5.44/5.84 2 ==> 0
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 factor: (21394) {G5,W7,D3,L2,V2,M2} { ! complement( X, Y ), c( X ) = Y }.
% 5.44/5.84 parent0[0, 1]: (7449) {G5,W10,D3,L3,V3,M3} R(7420,22) { ! complement( X, Y
% 5.44/5.84 ), ! complement( X, Z ), c( X ) = Z }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := X
% 5.44/5.84 Y := Y
% 5.44/5.84 Z := Y
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 subsumption: (7453) {G6,W7,D3,L2,V2,M2} F(7449) { ! complement( X, Y ), c(
% 5.44/5.84 X ) = Y }.
% 5.44/5.84 parent0: (21394) {G5,W7,D3,L2,V2,M2} { ! complement( X, Y ), c( X ) = Y
% 5.44/5.84 }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := X
% 5.44/5.84 Y := Y
% 5.44/5.84 end
% 5.44/5.84 permutation0:
% 5.44/5.84 0 ==> 0
% 5.44/5.84 1 ==> 1
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 eqswap: (21396) {G6,W7,D3,L2,V2,M2} { Y = c( X ), ! complement( X, Y ) }.
% 5.44/5.84 parent0[1]: (7453) {G6,W7,D3,L2,V2,M2} F(7449) { ! complement( X, Y ), c( X
% 5.44/5.84 ) = Y }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := X
% 5.44/5.84 Y := Y
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 resolution: (21397) {G7,W7,D4,L1,V0,M1} { skol1( skol1( skol2 ) ) = c(
% 5.44/5.84 skol1( skol2 ) ) }.
% 5.44/5.84 parent0[1]: (21396) {G6,W7,D3,L2,V2,M2} { Y = c( X ), ! complement( X, Y )
% 5.44/5.84 }.
% 5.44/5.84 parent1[0]: (7395) {G8,W6,D4,L1,V0,M1} R(7375,5018) { complement( skol1(
% 5.44/5.84 skol2 ), skol1( skol1( skol2 ) ) ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := skol1( skol2 )
% 5.44/5.84 Y := skol1( skol1( skol2 ) )
% 5.44/5.84 end
% 5.44/5.84 substitution1:
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 eqswap: (21398) {G7,W7,D4,L1,V0,M1} { c( skol1( skol2 ) ) = skol1( skol1(
% 5.44/5.84 skol2 ) ) }.
% 5.44/5.84 parent0[0]: (21397) {G7,W7,D4,L1,V0,M1} { skol1( skol1( skol2 ) ) = c(
% 5.44/5.84 skol1( skol2 ) ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 subsumption: (9117) {G9,W7,D4,L1,V0,M1} R(7453,7395) { c( skol1( skol2 ) )
% 5.44/5.84 ==> skol1( skol1( skol2 ) ) }.
% 5.44/5.84 parent0: (21398) {G7,W7,D4,L1,V0,M1} { c( skol1( skol2 ) ) = skol1( skol1
% 5.44/5.84 ( skol2 ) ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 end
% 5.44/5.84 permutation0:
% 5.44/5.84 0 ==> 0
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 eqswap: (21399) {G6,W7,D3,L2,V2,M2} { Y = c( X ), ! complement( X, Y ) }.
% 5.44/5.84 parent0[1]: (7453) {G6,W7,D3,L2,V2,M2} F(7449) { ! complement( X, Y ), c( X
% 5.44/5.84 ) = Y }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := X
% 5.44/5.84 Y := Y
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 resolution: (21401) {G2,W5,D4,L1,V0,M1} { skol2 = c( skol1( skol2 ) ) }.
% 5.44/5.84 parent0[1]: (21399) {G6,W7,D3,L2,V2,M2} { Y = c( X ), ! complement( X, Y )
% 5.44/5.84 }.
% 5.44/5.84 parent1[0]: (183) {G1,W4,D3,L1,V0,M1} R(13,26) { complement( skol1( skol2 )
% 5.44/5.84 , skol2 ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := skol1( skol2 )
% 5.44/5.84 Y := skol2
% 5.44/5.84 end
% 5.44/5.84 substitution1:
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 paramod: (21402) {G3,W5,D4,L1,V0,M1} { skol2 = skol1( skol1( skol2 ) ) }.
% 5.44/5.84 parent0[0]: (9117) {G9,W7,D4,L1,V0,M1} R(7453,7395) { c( skol1( skol2 ) )
% 5.44/5.84 ==> skol1( skol1( skol2 ) ) }.
% 5.44/5.84 parent1[0; 2]: (21401) {G2,W5,D4,L1,V0,M1} { skol2 = c( skol1( skol2 ) )
% 5.44/5.84 }.
% 5.44/5.84 substitution0:
% 5.44/5.84 end
% 5.44/5.84 substitution1:
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 eqswap: (21403) {G3,W5,D4,L1,V0,M1} { skol1( skol1( skol2 ) ) = skol2 }.
% 5.44/5.84 parent0[0]: (21402) {G3,W5,D4,L1,V0,M1} { skol2 = skol1( skol1( skol2 ) )
% 5.44/5.84 }.
% 5.44/5.84 substitution0:
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 subsumption: (9142) {G10,W5,D4,L1,V0,M1} R(7453,183);d(9117) { skol1( skol1
% 5.44/5.84 ( skol2 ) ) ==> skol2 }.
% 5.44/5.84 parent0: (21403) {G3,W5,D4,L1,V0,M1} { skol1( skol1( skol2 ) ) = skol2 }.
% 5.44/5.84 substitution0:
% 5.44/5.84 end
% 5.44/5.84 permutation0:
% 5.44/5.84 0 ==> 0
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 paramod: (21406) {G10,W5,D4,L1,V0,M1} { c( skol1( skol2 ) ) ==> skol2 }.
% 5.44/5.84 parent0[0]: (9142) {G10,W5,D4,L1,V0,M1} R(7453,183);d(9117) { skol1( skol1
% 5.44/5.84 ( skol2 ) ) ==> skol2 }.
% 5.44/5.84 parent1[0; 4]: (9117) {G9,W7,D4,L1,V0,M1} R(7453,7395) { c( skol1( skol2 )
% 5.44/5.84 ) ==> skol1( skol1( skol2 ) ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 end
% 5.44/5.84 substitution1:
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 subsumption: (20034) {G11,W5,D4,L1,V0,M1} S(9117);d(9142) { c( skol1( skol2
% 5.44/5.84 ) ) ==> skol2 }.
% 5.44/5.84 parent0: (21406) {G10,W5,D4,L1,V0,M1} { c( skol1( skol2 ) ) ==> skol2 }.
% 5.44/5.84 substitution0:
% 5.44/5.84 end
% 5.44/5.84 permutation0:
% 5.44/5.84 0 ==> 0
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 paramod: (21412) {G9,W9,D5,L1,V0,M1} { multiplication( c( skol1( skol2 ) )
% 5.44/5.84 , c( skol1( skol2 ) ) ) ==> skol2 }.
% 5.44/5.84 parent0[0]: (20034) {G11,W5,D4,L1,V0,M1} S(9117);d(9142) { c( skol1( skol2
% 5.44/5.84 ) ) ==> skol2 }.
% 5.44/5.84 parent1[0; 8]: (5038) {G8,W11,D5,L1,V0,M1} R(5027,30) { multiplication( c(
% 5.44/5.84 skol1( skol2 ) ), c( skol1( skol2 ) ) ) ==> c( skol1( skol2 ) ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 end
% 5.44/5.84 substitution1:
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 paramod: (21414) {G10,W7,D5,L1,V0,M1} { multiplication( c( skol1( skol2 )
% 5.44/5.84 ), skol2 ) ==> skol2 }.
% 5.44/5.84 parent0[0]: (20034) {G11,W5,D4,L1,V0,M1} S(9117);d(9142) { c( skol1( skol2
% 5.44/5.84 ) ) ==> skol2 }.
% 5.44/5.84 parent1[0; 5]: (21412) {G9,W9,D5,L1,V0,M1} { multiplication( c( skol1(
% 5.44/5.84 skol2 ) ), c( skol1( skol2 ) ) ) ==> skol2 }.
% 5.44/5.84 substitution0:
% 5.44/5.84 end
% 5.44/5.84 substitution1:
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 paramod: (21415) {G11,W5,D3,L1,V0,M1} { multiplication( skol2, skol2 ) ==>
% 5.44/5.84 skol2 }.
% 5.44/5.84 parent0[0]: (20034) {G11,W5,D4,L1,V0,M1} S(9117);d(9142) { c( skol1( skol2
% 5.44/5.84 ) ) ==> skol2 }.
% 5.44/5.84 parent1[0; 2]: (21414) {G10,W7,D5,L1,V0,M1} { multiplication( c( skol1(
% 5.44/5.84 skol2 ) ), skol2 ) ==> skol2 }.
% 5.44/5.84 substitution0:
% 5.44/5.84 end
% 5.44/5.84 substitution1:
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 subsumption: (20167) {G12,W5,D3,L1,V0,M1} S(5038);d(20034) { multiplication
% 5.44/5.84 ( skol2, skol2 ) ==> skol2 }.
% 5.44/5.84 parent0: (21415) {G11,W5,D3,L1,V0,M1} { multiplication( skol2, skol2 ) ==>
% 5.44/5.84 skol2 }.
% 5.44/5.84 substitution0:
% 5.44/5.84 end
% 5.44/5.84 permutation0:
% 5.44/5.84 0 ==> 0
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 paramod: (21437) {G2,W48,D7,L2,V0,M2} { ! leq( addition( multiplication(
% 5.44/5.84 skol2, skol4 ), multiplication( c( skol2 ), skol6 ) ), addition(
% 5.44/5.84 multiplication( skol2, addition( multiplication( c( skol2 ), skol5 ),
% 5.44/5.84 multiplication( skol2, skol4 ) ) ), multiplication( skol1( skol2 ), skol6
% 5.44/5.84 ) ) ), ! leq( addition( multiplication( skol2, addition( multiplication
% 5.44/5.84 ( c( skol2 ), skol5 ), multiplication( skol2, skol4 ) ) ), multiplication
% 5.44/5.84 ( c( skol2 ), skol6 ) ), addition( multiplication( skol2, skol4 ),
% 5.44/5.84 multiplication( c( skol2 ), skol6 ) ) ) }.
% 5.44/5.84 parent0[0]: (5025) {G7,W5,D3,L1,V0,M1} R(5017,22);r(26) { c( skol2 ) ==>
% 5.44/5.84 skol1( skol2 ) }.
% 5.44/5.84 parent1[1; 22]: (543) {G1,W48,D7,L2,V0,M2} P(0,28) { ! leq( addition(
% 5.44/5.84 multiplication( skol2, addition( multiplication( c( skol2 ), skol5 ),
% 5.44/5.84 multiplication( skol2, skol4 ) ) ), multiplication( c( skol2 ), skol6 ) )
% 5.44/5.84 , addition( multiplication( skol2, skol4 ), multiplication( c( skol2 ),
% 5.44/5.84 skol6 ) ) ), ! leq( addition( multiplication( skol2, skol4 ),
% 5.44/5.84 multiplication( c( skol2 ), skol6 ) ), addition( multiplication( skol2,
% 5.44/5.84 addition( multiplication( c( skol2 ), skol5 ), multiplication( skol2,
% 5.44/5.84 skol4 ) ) ), multiplication( c( skol2 ), skol6 ) ) ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 end
% 5.44/5.84 substitution1:
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 paramod: (21458) {G3,W48,D7,L2,V0,M2} { ! leq( addition( multiplication(
% 5.44/5.84 skol2, addition( multiplication( c( skol2 ), skol5 ), multiplication(
% 5.44/5.84 skol2, skol4 ) ) ), multiplication( c( skol2 ), skol6 ) ), addition(
% 5.44/5.84 multiplication( skol2, skol4 ), multiplication( skol1( skol2 ), skol6 ) )
% 5.44/5.84 ), ! leq( addition( multiplication( skol2, skol4 ), multiplication( c(
% 5.44/5.84 skol2 ), skol6 ) ), addition( multiplication( skol2, addition(
% 5.44/5.84 multiplication( c( skol2 ), skol5 ), multiplication( skol2, skol4 ) ) ),
% 5.44/5.84 multiplication( skol1( skol2 ), skol6 ) ) ) }.
% 5.44/5.84 parent0[0]: (5025) {G7,W5,D3,L1,V0,M1} R(5017,22);r(26) { c( skol2 ) ==>
% 5.44/5.84 skol1( skol2 ) }.
% 5.44/5.84 parent1[1; 22]: (21437) {G2,W48,D7,L2,V0,M2} { ! leq( addition(
% 5.44/5.84 multiplication( skol2, skol4 ), multiplication( c( skol2 ), skol6 ) ),
% 5.44/5.84 addition( multiplication( skol2, addition( multiplication( c( skol2 ),
% 5.44/5.84 skol5 ), multiplication( skol2, skol4 ) ) ), multiplication( skol1( skol2
% 5.44/5.84 ), skol6 ) ) ), ! leq( addition( multiplication( skol2, addition(
% 5.44/5.84 multiplication( c( skol2 ), skol5 ), multiplication( skol2, skol4 ) ) ),
% 5.44/5.84 multiplication( c( skol2 ), skol6 ) ), addition( multiplication( skol2,
% 5.44/5.84 skol4 ), multiplication( c( skol2 ), skol6 ) ) ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 end
% 5.44/5.84 substitution1:
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 paramod: (21462) {G4,W48,D7,L2,V0,M2} { ! leq( addition( multiplication(
% 5.44/5.84 skol2, skol4 ), multiplication( c( skol2 ), skol6 ) ), addition(
% 5.44/5.84 multiplication( skol2, addition( multiplication( skol1( skol2 ), skol5 )
% 5.44/5.84 , multiplication( skol2, skol4 ) ) ), multiplication( skol1( skol2 ),
% 5.44/5.84 skol6 ) ) ), ! leq( addition( multiplication( skol2, addition(
% 5.44/5.84 multiplication( c( skol2 ), skol5 ), multiplication( skol2, skol4 ) ) ),
% 5.44/5.84 multiplication( c( skol2 ), skol6 ) ), addition( multiplication( skol2,
% 5.44/5.84 skol4 ), multiplication( skol1( skol2 ), skol6 ) ) ) }.
% 5.44/5.84 parent0[0]: (5025) {G7,W5,D3,L1,V0,M1} R(5017,22);r(26) { c( skol2 ) ==>
% 5.44/5.84 skol1( skol2 ) }.
% 5.44/5.84 parent1[1; 15]: (21458) {G3,W48,D7,L2,V0,M2} { ! leq( addition(
% 5.44/5.84 multiplication( skol2, addition( multiplication( c( skol2 ), skol5 ),
% 5.44/5.84 multiplication( skol2, skol4 ) ) ), multiplication( c( skol2 ), skol6 ) )
% 5.44/5.84 , addition( multiplication( skol2, skol4 ), multiplication( skol1( skol2
% 5.44/5.84 ), skol6 ) ) ), ! leq( addition( multiplication( skol2, skol4 ),
% 5.44/5.84 multiplication( c( skol2 ), skol6 ) ), addition( multiplication( skol2,
% 5.44/5.84 addition( multiplication( c( skol2 ), skol5 ), multiplication( skol2,
% 5.44/5.84 skol4 ) ) ), multiplication( skol1( skol2 ), skol6 ) ) ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 end
% 5.44/5.84 substitution1:
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 paramod: (21465) {G5,W48,D7,L2,V0,M2} { ! leq( addition( multiplication(
% 5.44/5.84 skol2, addition( multiplication( c( skol2 ), skol5 ), multiplication(
% 5.44/5.84 skol2, skol4 ) ) ), multiplication( skol1( skol2 ), skol6 ) ), addition(
% 5.44/5.84 multiplication( skol2, skol4 ), multiplication( skol1( skol2 ), skol6 ) )
% 5.44/5.84 ), ! leq( addition( multiplication( skol2, skol4 ), multiplication( c(
% 5.44/5.84 skol2 ), skol6 ) ), addition( multiplication( skol2, addition(
% 5.44/5.84 multiplication( skol1( skol2 ), skol5 ), multiplication( skol2, skol4 ) )
% 5.44/5.84 ), multiplication( skol1( skol2 ), skol6 ) ) ) }.
% 5.44/5.84 parent0[0]: (5025) {G7,W5,D3,L1,V0,M1} R(5017,22);r(26) { c( skol2 ) ==>
% 5.44/5.84 skol1( skol2 ) }.
% 5.44/5.84 parent1[1; 14]: (21462) {G4,W48,D7,L2,V0,M2} { ! leq( addition(
% 5.44/5.84 multiplication( skol2, skol4 ), multiplication( c( skol2 ), skol6 ) ),
% 5.44/5.84 addition( multiplication( skol2, addition( multiplication( skol1( skol2 )
% 5.44/5.84 , skol5 ), multiplication( skol2, skol4 ) ) ), multiplication( skol1(
% 5.44/5.84 skol2 ), skol6 ) ) ), ! leq( addition( multiplication( skol2, addition(
% 5.44/5.84 multiplication( c( skol2 ), skol5 ), multiplication( skol2, skol4 ) ) ),
% 5.44/5.84 multiplication( c( skol2 ), skol6 ) ), addition( multiplication( skol2,
% 5.44/5.84 skol4 ), multiplication( skol1( skol2 ), skol6 ) ) ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 end
% 5.44/5.84 substitution1:
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 paramod: (21467) {G6,W48,D7,L2,V0,M2} { ! leq( addition( multiplication(
% 5.44/5.84 skol2, skol4 ), multiplication( skol1( skol2 ), skol6 ) ), addition(
% 5.44/5.84 multiplication( skol2, addition( multiplication( skol1( skol2 ), skol5 )
% 5.44/5.84 , multiplication( skol2, skol4 ) ) ), multiplication( skol1( skol2 ),
% 5.44/5.84 skol6 ) ) ), ! leq( addition( multiplication( skol2, addition(
% 5.44/5.84 multiplication( c( skol2 ), skol5 ), multiplication( skol2, skol4 ) ) ),
% 5.44/5.84 multiplication( skol1( skol2 ), skol6 ) ), addition( multiplication(
% 5.44/5.84 skol2, skol4 ), multiplication( skol1( skol2 ), skol6 ) ) ) }.
% 5.44/5.84 parent0[0]: (5025) {G7,W5,D3,L1,V0,M1} R(5017,22);r(26) { c( skol2 ) ==>
% 5.44/5.84 skol1( skol2 ) }.
% 5.44/5.84 parent1[1; 7]: (21465) {G5,W48,D7,L2,V0,M2} { ! leq( addition(
% 5.44/5.84 multiplication( skol2, addition( multiplication( c( skol2 ), skol5 ),
% 5.44/5.84 multiplication( skol2, skol4 ) ) ), multiplication( skol1( skol2 ), skol6
% 5.44/5.84 ) ), addition( multiplication( skol2, skol4 ), multiplication( skol1(
% 5.44/5.84 skol2 ), skol6 ) ) ), ! leq( addition( multiplication( skol2, skol4 ),
% 5.44/5.84 multiplication( c( skol2 ), skol6 ) ), addition( multiplication( skol2,
% 5.44/5.84 addition( multiplication( skol1( skol2 ), skol5 ), multiplication( skol2
% 5.44/5.84 , skol4 ) ) ), multiplication( skol1( skol2 ), skol6 ) ) ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 end
% 5.44/5.84 substitution1:
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 paramod: (21468) {G7,W48,D7,L2,V0,M2} { ! leq( addition( multiplication(
% 5.44/5.84 skol2, addition( multiplication( skol1( skol2 ), skol5 ), multiplication
% 5.44/5.84 ( skol2, skol4 ) ) ), multiplication( skol1( skol2 ), skol6 ) ), addition
% 5.44/5.84 ( multiplication( skol2, skol4 ), multiplication( skol1( skol2 ), skol6 )
% 5.44/5.84 ) ), ! leq( addition( multiplication( skol2, skol4 ), multiplication(
% 5.44/5.84 skol1( skol2 ), skol6 ) ), addition( multiplication( skol2, addition(
% 5.44/5.84 multiplication( skol1( skol2 ), skol5 ), multiplication( skol2, skol4 ) )
% 5.44/5.84 ), multiplication( skol1( skol2 ), skol6 ) ) ) }.
% 5.44/5.84 parent0[0]: (5025) {G7,W5,D3,L1,V0,M1} R(5017,22);r(26) { c( skol2 ) ==>
% 5.44/5.84 skol1( skol2 ) }.
% 5.44/5.84 parent1[1; 7]: (21467) {G6,W48,D7,L2,V0,M2} { ! leq( addition(
% 5.44/5.84 multiplication( skol2, skol4 ), multiplication( skol1( skol2 ), skol6 ) )
% 5.44/5.84 , addition( multiplication( skol2, addition( multiplication( skol1( skol2
% 5.44/5.84 ), skol5 ), multiplication( skol2, skol4 ) ) ), multiplication( skol1(
% 5.44/5.84 skol2 ), skol6 ) ) ), ! leq( addition( multiplication( skol2, addition(
% 5.44/5.84 multiplication( c( skol2 ), skol5 ), multiplication( skol2, skol4 ) ) ),
% 5.44/5.84 multiplication( skol1( skol2 ), skol6 ) ), addition( multiplication(
% 5.44/5.84 skol2, skol4 ), multiplication( skol1( skol2 ), skol6 ) ) ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 end
% 5.44/5.84 substitution1:
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 paramod: (21476) {G4,W43,D7,L2,V0,M2} { ! leq( addition( multiplication(
% 5.44/5.84 skol2, skol4 ), multiplication( skol1( skol2 ), skol6 ) ), addition(
% 5.44/5.84 multiplication( skol2, multiplication( skol2, skol4 ) ), multiplication(
% 5.44/5.84 skol1( skol2 ), skol6 ) ) ), ! leq( addition( multiplication( skol2,
% 5.44/5.84 addition( multiplication( skol1( skol2 ), skol5 ), multiplication( skol2
% 5.44/5.84 , skol4 ) ) ), multiplication( skol1( skol2 ), skol6 ) ), addition(
% 5.44/5.84 multiplication( skol2, skol4 ), multiplication( skol1( skol2 ), skol6 ) )
% 5.44/5.84 ) }.
% 5.44/5.84 parent0[0]: (5015) {G3,W12,D6,L1,V2,M1} P(195,48);d(10);d(32) {
% 5.44/5.84 multiplication( skol2, addition( multiplication( skol1( skol2 ), X ), Y )
% 5.44/5.84 ) ==> multiplication( skol2, Y ) }.
% 5.44/5.84 parent1[1; 11]: (21468) {G7,W48,D7,L2,V0,M2} { ! leq( addition(
% 5.44/5.84 multiplication( skol2, addition( multiplication( skol1( skol2 ), skol5 )
% 5.44/5.84 , multiplication( skol2, skol4 ) ) ), multiplication( skol1( skol2 ),
% 5.44/5.84 skol6 ) ), addition( multiplication( skol2, skol4 ), multiplication(
% 5.44/5.84 skol1( skol2 ), skol6 ) ) ), ! leq( addition( multiplication( skol2,
% 5.44/5.84 skol4 ), multiplication( skol1( skol2 ), skol6 ) ), addition(
% 5.44/5.84 multiplication( skol2, addition( multiplication( skol1( skol2 ), skol5 )
% 5.44/5.84 , multiplication( skol2, skol4 ) ) ), multiplication( skol1( skol2 ),
% 5.44/5.84 skol6 ) ) ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := skol5
% 5.44/5.84 Y := multiplication( skol2, skol4 )
% 5.44/5.84 end
% 5.44/5.84 substitution1:
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 paramod: (21478) {G4,W38,D5,L2,V0,M2} { ! leq( addition( multiplication(
% 5.44/5.84 skol2, multiplication( skol2, skol4 ) ), multiplication( skol1( skol2 ),
% 5.44/5.84 skol6 ) ), addition( multiplication( skol2, skol4 ), multiplication(
% 5.44/5.84 skol1( skol2 ), skol6 ) ) ), ! leq( addition( multiplication( skol2,
% 5.44/5.84 skol4 ), multiplication( skol1( skol2 ), skol6 ) ), addition(
% 5.44/5.84 multiplication( skol2, multiplication( skol2, skol4 ) ), multiplication(
% 5.44/5.84 skol1( skol2 ), skol6 ) ) ) }.
% 5.44/5.84 parent0[0]: (5015) {G3,W12,D6,L1,V2,M1} P(195,48);d(10);d(32) {
% 5.44/5.84 multiplication( skol2, addition( multiplication( skol1( skol2 ), X ), Y )
% 5.44/5.84 ) ==> multiplication( skol2, Y ) }.
% 5.44/5.84 parent1[1; 3]: (21476) {G4,W43,D7,L2,V0,M2} { ! leq( addition(
% 5.44/5.84 multiplication( skol2, skol4 ), multiplication( skol1( skol2 ), skol6 ) )
% 5.44/5.84 , addition( multiplication( skol2, multiplication( skol2, skol4 ) ),
% 5.44/5.84 multiplication( skol1( skol2 ), skol6 ) ) ), ! leq( addition(
% 5.44/5.84 multiplication( skol2, addition( multiplication( skol1( skol2 ), skol5 )
% 5.44/5.84 , multiplication( skol2, skol4 ) ) ), multiplication( skol1( skol2 ),
% 5.44/5.84 skol6 ) ), addition( multiplication( skol2, skol4 ), multiplication(
% 5.44/5.84 skol1( skol2 ), skol6 ) ) ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := skol5
% 5.44/5.84 Y := multiplication( skol2, skol4 )
% 5.44/5.84 end
% 5.44/5.84 substitution1:
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 paramod: (21480) {G1,W38,D5,L2,V0,M2} { ! leq( addition( multiplication(
% 5.44/5.84 skol2, skol4 ), multiplication( skol1( skol2 ), skol6 ) ), addition(
% 5.44/5.84 multiplication( multiplication( skol2, skol2 ), skol4 ), multiplication(
% 5.44/5.84 skol1( skol2 ), skol6 ) ) ), ! leq( addition( multiplication( skol2,
% 5.44/5.84 multiplication( skol2, skol4 ) ), multiplication( skol1( skol2 ), skol6 )
% 5.44/5.84 ), addition( multiplication( skol2, skol4 ), multiplication( skol1(
% 5.44/5.84 skol2 ), skol6 ) ) ) }.
% 5.44/5.84 parent0[0]: (4) {G0,W11,D4,L1,V3,M1} I { multiplication( X, multiplication
% 5.44/5.84 ( Y, Z ) ) ==> multiplication( multiplication( X, Y ), Z ) }.
% 5.44/5.84 parent1[1; 11]: (21478) {G4,W38,D5,L2,V0,M2} { ! leq( addition(
% 5.44/5.84 multiplication( skol2, multiplication( skol2, skol4 ) ), multiplication(
% 5.44/5.84 skol1( skol2 ), skol6 ) ), addition( multiplication( skol2, skol4 ),
% 5.44/5.84 multiplication( skol1( skol2 ), skol6 ) ) ), ! leq( addition(
% 5.44/5.84 multiplication( skol2, skol4 ), multiplication( skol1( skol2 ), skol6 ) )
% 5.44/5.84 , addition( multiplication( skol2, multiplication( skol2, skol4 ) ),
% 5.44/5.84 multiplication( skol1( skol2 ), skol6 ) ) ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := skol2
% 5.44/5.84 Y := skol2
% 5.44/5.84 Z := skol4
% 5.44/5.84 end
% 5.44/5.84 substitution1:
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 paramod: (21482) {G1,W38,D5,L2,V0,M2} { ! leq( addition( multiplication(
% 5.44/5.84 multiplication( skol2, skol2 ), skol4 ), multiplication( skol1( skol2 ),
% 5.44/5.84 skol6 ) ), addition( multiplication( skol2, skol4 ), multiplication(
% 5.44/5.84 skol1( skol2 ), skol6 ) ) ), ! leq( addition( multiplication( skol2,
% 5.44/5.84 skol4 ), multiplication( skol1( skol2 ), skol6 ) ), addition(
% 5.44/5.84 multiplication( multiplication( skol2, skol2 ), skol4 ), multiplication(
% 5.44/5.84 skol1( skol2 ), skol6 ) ) ) }.
% 5.44/5.84 parent0[0]: (4) {G0,W11,D4,L1,V3,M1} I { multiplication( X, multiplication
% 5.44/5.84 ( Y, Z ) ) ==> multiplication( multiplication( X, Y ), Z ) }.
% 5.44/5.84 parent1[1; 3]: (21480) {G1,W38,D5,L2,V0,M2} { ! leq( addition(
% 5.44/5.84 multiplication( skol2, skol4 ), multiplication( skol1( skol2 ), skol6 ) )
% 5.44/5.84 , addition( multiplication( multiplication( skol2, skol2 ), skol4 ),
% 5.44/5.84 multiplication( skol1( skol2 ), skol6 ) ) ), ! leq( addition(
% 5.44/5.84 multiplication( skol2, multiplication( skol2, skol4 ) ), multiplication(
% 5.44/5.84 skol1( skol2 ), skol6 ) ), addition( multiplication( skol2, skol4 ),
% 5.44/5.84 multiplication( skol1( skol2 ), skol6 ) ) ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 X := skol2
% 5.44/5.84 Y := skol2
% 5.44/5.84 Z := skol4
% 5.44/5.84 end
% 5.44/5.84 substitution1:
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 paramod: (21484) {G2,W36,D5,L2,V0,M2} { ! leq( addition( multiplication(
% 5.44/5.84 skol2, skol4 ), multiplication( skol1( skol2 ), skol6 ) ), addition(
% 5.44/5.84 multiplication( skol2, skol4 ), multiplication( skol1( skol2 ), skol6 ) )
% 5.44/5.84 ), ! leq( addition( multiplication( multiplication( skol2, skol2 ),
% 5.44/5.84 skol4 ), multiplication( skol1( skol2 ), skol6 ) ), addition(
% 5.44/5.84 multiplication( skol2, skol4 ), multiplication( skol1( skol2 ), skol6 ) )
% 5.44/5.84 ) }.
% 5.44/5.84 parent0[0]: (20167) {G12,W5,D3,L1,V0,M1} S(5038);d(20034) { multiplication
% 5.44/5.84 ( skol2, skol2 ) ==> skol2 }.
% 5.44/5.84 parent1[1; 12]: (21482) {G1,W38,D5,L2,V0,M2} { ! leq( addition(
% 5.44/5.84 multiplication( multiplication( skol2, skol2 ), skol4 ), multiplication(
% 5.44/5.84 skol1( skol2 ), skol6 ) ), addition( multiplication( skol2, skol4 ),
% 5.44/5.84 multiplication( skol1( skol2 ), skol6 ) ) ), ! leq( addition(
% 5.44/5.84 multiplication( skol2, skol4 ), multiplication( skol1( skol2 ), skol6 ) )
% 5.44/5.84 , addition( multiplication( multiplication( skol2, skol2 ), skol4 ),
% 5.44/5.84 multiplication( skol1( skol2 ), skol6 ) ) ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 end
% 5.44/5.84 substitution1:
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 paramod: (21487) {G3,W34,D5,L2,V0,M2} { ! leq( addition( multiplication(
% 5.44/5.84 skol2, skol4 ), multiplication( skol1( skol2 ), skol6 ) ), addition(
% 5.44/5.84 multiplication( skol2, skol4 ), multiplication( skol1( skol2 ), skol6 ) )
% 5.44/5.84 ), ! leq( addition( multiplication( skol2, skol4 ), multiplication(
% 5.44/5.84 skol1( skol2 ), skol6 ) ), addition( multiplication( skol2, skol4 ),
% 5.44/5.84 multiplication( skol1( skol2 ), skol6 ) ) ) }.
% 5.44/5.84 parent0[0]: (20167) {G12,W5,D3,L1,V0,M1} S(5038);d(20034) { multiplication
% 5.44/5.84 ( skol2, skol2 ) ==> skol2 }.
% 5.44/5.84 parent1[1; 4]: (21484) {G2,W36,D5,L2,V0,M2} { ! leq( addition(
% 5.44/5.84 multiplication( skol2, skol4 ), multiplication( skol1( skol2 ), skol6 ) )
% 5.44/5.84 , addition( multiplication( skol2, skol4 ), multiplication( skol1( skol2
% 5.44/5.84 ), skol6 ) ) ), ! leq( addition( multiplication( multiplication( skol2,
% 5.44/5.84 skol2 ), skol4 ), multiplication( skol1( skol2 ), skol6 ) ), addition(
% 5.44/5.84 multiplication( skol2, skol4 ), multiplication( skol1( skol2 ), skol6 ) )
% 5.44/5.84 ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 end
% 5.44/5.84 substitution1:
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 factor: (21488) {G3,W17,D5,L1,V0,M1} { ! leq( addition( multiplication(
% 5.44/5.84 skol2, skol4 ), multiplication( skol1( skol2 ), skol6 ) ), addition(
% 5.44/5.84 multiplication( skol2, skol4 ), multiplication( skol1( skol2 ), skol6 ) )
% 5.44/5.84 ) }.
% 5.44/5.84 parent0[0, 1]: (21487) {G3,W34,D5,L2,V0,M2} { ! leq( addition(
% 5.44/5.84 multiplication( skol2, skol4 ), multiplication( skol1( skol2 ), skol6 ) )
% 5.44/5.84 , addition( multiplication( skol2, skol4 ), multiplication( skol1( skol2
% 5.44/5.84 ), skol6 ) ) ), ! leq( addition( multiplication( skol2, skol4 ),
% 5.44/5.84 multiplication( skol1( skol2 ), skol6 ) ), addition( multiplication(
% 5.44/5.84 skol2, skol4 ), multiplication( skol1( skol2 ), skol6 ) ) ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 resolution: (21490) {G2,W0,D0,L0,V0,M0} { }.
% 5.44/5.84 parent0[0]: (21488) {G3,W17,D5,L1,V0,M1} { ! leq( addition( multiplication
% 5.44/5.84 ( skol2, skol4 ), multiplication( skol1( skol2 ), skol6 ) ), addition(
% 5.44/5.84 multiplication( skol2, skol4 ), multiplication( skol1( skol2 ), skol6 ) )
% 5.44/5.84 ) }.
% 5.44/5.84 parent1[0]: (149) {G1,W3,D2,L1,V1,M1} R(12,3) { leq( X, X ) }.
% 5.44/5.84 substitution0:
% 5.44/5.84 end
% 5.44/5.84 substitution1:
% 5.44/5.84 X := addition( multiplication( skol2, skol4 ), multiplication( skol1(
% 5.44/5.84 skol2 ), skol6 ) )
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 subsumption: (20279) {G13,W0,D0,L0,V0,M0} S(543);d(5025);d(5025);d(5015);d(
% 5.44/5.84 5015);d(4);d(4);d(20167);d(20167);f;r(149) { }.
% 5.44/5.84 parent0: (21490) {G2,W0,D0,L0,V0,M0} { }.
% 5.44/5.84 substitution0:
% 5.44/5.84 end
% 5.44/5.84 permutation0:
% 5.44/5.84 end
% 5.44/5.84
% 5.44/5.84 Proof check complete!
% 5.44/5.84
% 5.44/5.84 Memory use:
% 5.44/5.84
% 5.44/5.84 space for terms: 251506
% 5.44/5.84 space for clauses: 940995
% 5.44/5.84
% 5.44/5.84
% 5.44/5.84 clauses generated: 149620
% 5.44/5.84 clauses kept: 20280
% 5.44/5.84 clauses selected: 1396
% 5.44/5.84 clauses deleted: 5331
% 5.44/5.84 clauses inuse deleted: 348
% 5.44/5.84
% 5.44/5.84 subsentry: 1066053
% 5.44/5.84 literals s-matched: 604738
% 5.44/5.84 literals matched: 597229
% 5.44/5.84 full subsumption: 259051
% 5.44/5.84
% 5.44/5.84 checksum: 1123056283
% 5.44/5.84
% 5.44/5.84
% 5.44/5.84 Bliksem ended
%------------------------------------------------------------------------------