TSTP Solution File: KLE027+3 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : KLE027+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Sun Jul 17 01:36:44 EDT 2022
% Result : Theorem 5.45s 5.84s
% Output : Refutation 5.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE027+3 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n022.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % DateTime : Thu Jun 16 09:29:47 EDT 2022
% 0.12/0.33 % CPUTime :
% 5.45/5.84 *** allocated 10000 integers for termspace/termends
% 5.45/5.84 *** allocated 10000 integers for clauses
% 5.45/5.84 *** allocated 10000 integers for justifications
% 5.45/5.84 Bliksem 1.12
% 5.45/5.84
% 5.45/5.84
% 5.45/5.84 Automatic Strategy Selection
% 5.45/5.84
% 5.45/5.84
% 5.45/5.84 Clauses:
% 5.45/5.84
% 5.45/5.84 { addition( X, Y ) = addition( Y, X ) }.
% 5.45/5.84 { addition( Z, addition( Y, X ) ) = addition( addition( Z, Y ), X ) }.
% 5.45/5.84 { addition( X, zero ) = X }.
% 5.45/5.84 { addition( X, X ) = X }.
% 5.45/5.84 { multiplication( X, multiplication( Y, Z ) ) = multiplication(
% 5.45/5.84 multiplication( X, Y ), Z ) }.
% 5.45/5.84 { multiplication( X, one ) = X }.
% 5.45/5.84 { multiplication( one, X ) = X }.
% 5.45/5.84 { multiplication( X, addition( Y, Z ) ) = addition( multiplication( X, Y )
% 5.45/5.84 , multiplication( X, Z ) ) }.
% 5.45/5.84 { multiplication( addition( X, Y ), Z ) = addition( multiplication( X, Z )
% 5.45/5.84 , multiplication( Y, Z ) ) }.
% 5.45/5.84 { multiplication( X, zero ) = zero }.
% 5.45/5.84 { multiplication( zero, X ) = zero }.
% 5.45/5.84 { ! leq( X, Y ), addition( X, Y ) = Y }.
% 5.45/5.84 { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 5.45/5.84 { ! test( X ), complement( skol1( X ), X ) }.
% 5.45/5.84 { ! complement( Y, X ), test( X ) }.
% 5.45/5.84 { ! complement( Y, X ), multiplication( X, Y ) = zero }.
% 5.45/5.84 { ! complement( Y, X ), alpha1( X, Y ) }.
% 5.45/5.84 { ! multiplication( X, Y ) = zero, ! alpha1( X, Y ), complement( Y, X ) }.
% 5.45/5.84 { ! alpha1( X, Y ), multiplication( Y, X ) = zero }.
% 5.45/5.84 { ! alpha1( X, Y ), addition( X, Y ) = one }.
% 5.45/5.84 { ! multiplication( Y, X ) = zero, ! addition( X, Y ) = one, alpha1( X, Y )
% 5.45/5.84 }.
% 5.45/5.84 { ! test( X ), ! c( X ) = Y, complement( X, Y ) }.
% 5.45/5.84 { ! test( X ), ! complement( X, Y ), c( X ) = Y }.
% 5.45/5.84 { test( X ), c( X ) = zero }.
% 5.45/5.84 { ! test( X ), ! test( Y ), c( addition( X, Y ) ) = multiplication( c( X )
% 5.45/5.84 , c( Y ) ) }.
% 5.45/5.84 { ! test( X ), ! test( Y ), c( multiplication( X, Y ) ) = addition( c( X )
% 5.45/5.84 , c( Y ) ) }.
% 5.45/5.84 { test( skol2 ) }.
% 5.45/5.84 { test( skol3 ) }.
% 5.45/5.84 { ! addition( multiplication( skol2, addition( multiplication( skol2, skol4
% 5.45/5.84 ), multiplication( c( skol2 ), skol5 ) ) ), multiplication( c( skol2 ),
% 5.45/5.84 skol6 ) ) = addition( multiplication( skol2, skol4 ), multiplication( c(
% 5.45/5.84 skol2 ), skol6 ) ) }.
% 5.45/5.84
% 5.45/5.84 percentage equality = 0.500000, percentage horn = 0.965517
% 5.45/5.84 This is a problem with some equality
% 5.45/5.84
% 5.45/5.84
% 5.45/5.84
% 5.45/5.84 Options Used:
% 5.45/5.84
% 5.45/5.84 useres = 1
% 5.45/5.84 useparamod = 1
% 5.45/5.84 useeqrefl = 1
% 5.45/5.84 useeqfact = 1
% 5.45/5.84 usefactor = 1
% 5.45/5.84 usesimpsplitting = 0
% 5.45/5.84 usesimpdemod = 5
% 5.45/5.84 usesimpres = 3
% 5.45/5.84
% 5.45/5.84 resimpinuse = 1000
% 5.45/5.84 resimpclauses = 20000
% 5.45/5.84 substype = eqrewr
% 5.45/5.84 backwardsubs = 1
% 5.45/5.84 selectoldest = 5
% 5.45/5.84
% 5.45/5.84 litorderings [0] = split
% 5.45/5.84 litorderings [1] = extend the termordering, first sorting on arguments
% 5.45/5.84
% 5.45/5.84 termordering = kbo
% 5.45/5.84
% 5.45/5.84 litapriori = 0
% 5.45/5.84 termapriori = 1
% 5.45/5.84 litaposteriori = 0
% 5.45/5.84 termaposteriori = 0
% 5.45/5.84 demodaposteriori = 0
% 5.45/5.84 ordereqreflfact = 0
% 5.45/5.84
% 5.45/5.84 litselect = negord
% 5.45/5.84
% 5.45/5.84 maxweight = 15
% 5.45/5.84 maxdepth = 30000
% 5.45/5.84 maxlength = 115
% 5.45/5.84 maxnrvars = 195
% 5.45/5.84 excuselevel = 1
% 5.45/5.84 increasemaxweight = 1
% 5.45/5.84
% 5.45/5.84 maxselected = 10000000
% 5.45/5.84 maxnrclauses = 10000000
% 5.45/5.84
% 5.45/5.84 showgenerated = 0
% 5.45/5.84 showkept = 0
% 5.45/5.84 showselected = 0
% 5.45/5.84 showdeleted = 0
% 5.45/5.84 showresimp = 1
% 5.45/5.84 showstatus = 2000
% 5.45/5.84
% 5.45/5.84 prologoutput = 0
% 5.45/5.84 nrgoals = 5000000
% 5.45/5.84 totalproof = 1
% 5.45/5.84
% 5.45/5.84 Symbols occurring in the translation:
% 5.45/5.84
% 5.45/5.84 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 5.45/5.84 . [1, 2] (w:1, o:29, a:1, s:1, b:0),
% 5.45/5.84 ! [4, 1] (w:0, o:21, a:1, s:1, b:0),
% 5.45/5.84 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 5.45/5.84 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 5.45/5.84 addition [37, 2] (w:1, o:53, a:1, s:1, b:0),
% 5.45/5.84 zero [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 5.45/5.84 multiplication [40, 2] (w:1, o:55, a:1, s:1, b:0),
% 5.45/5.84 one [41, 0] (w:1, o:10, a:1, s:1, b:0),
% 5.45/5.84 leq [42, 2] (w:1, o:54, a:1, s:1, b:0),
% 5.45/5.84 test [44, 1] (w:1, o:27, a:1, s:1, b:0),
% 5.45/5.84 complement [46, 2] (w:1, o:56, a:1, s:1, b:0),
% 5.45/5.84 c [47, 1] (w:1, o:28, a:1, s:1, b:0),
% 5.45/5.84 alpha1 [51, 2] (w:1, o:57, a:1, s:1, b:1),
% 5.45/5.84 skol1 [52, 1] (w:1, o:26, a:1, s:1, b:1),
% 5.45/5.84 skol2 [53, 0] (w:1, o:16, a:1, s:1, b:1),
% 5.45/5.84 skol3 [54, 0] (w:1, o:17, a:1, s:1, b:1),
% 5.45/5.84 skol4 [55, 0] (w:1, o:18, a:1, s:1, b:1),
% 5.45/5.84 skol5 [56, 0] (w:1, o:19, a:1, s:1, b:1),
% 5.45/5.84 skol6 [57, 0] (w:1, o:20, a:1, s:1, b:1).
% 5.45/5.84
% 5.45/5.84
% 5.45/5.84 Starting Search:
% 5.45/5.84
% 5.45/5.84 *** allocated 15000 integers for clauses
% 5.45/5.84 *** allocated 22500 integers for clauses
% 5.45/5.84 *** allocated 33750 integers for clauses
% 5.45/5.84 *** allocated 50625 integers for clauses
% 5.45/5.84 *** allocated 15000 integers for termspace/termends
% 5.45/5.84 *** allocated 75937 integers for clauses
% 5.45/5.84 Resimplifying inuse:
% 5.45/5.84 Done
% 5.45/5.84
% 5.45/5.84 *** allocated 22500 integers for termspace/termends
% 5.45/5.84 *** allocated 113905 integers for clauses
% 5.45/5.84 *** allocated 33750 integers for termspace/termends
% 5.45/5.84
% 5.45/5.84 Intermediate Status:
% 5.45/5.84 Generated: 13330
% 5.45/5.84 Kept: 2026
% 5.45/5.84 Inuse: 261
% 5.45/5.84 Deleted: 42
% 5.45/5.84 Deletedinuse: 22
% 5.45/5.84
% 5.45/5.84 Resimplifying inuse:
% 5.45/5.84 Done
% 5.45/5.84
% 5.45/5.84 *** allocated 170857 integers for clauses
% 5.45/5.84 *** allocated 50625 integers for termspace/termends
% 5.45/5.84 Resimplifying inuse:
% 5.45/5.84 Done
% 5.45/5.84
% 5.45/5.84 *** allocated 256285 integers for clauses
% 5.45/5.84
% 5.45/5.84 Intermediate Status:
% 5.45/5.84 Generated: 27887
% 5.45/5.84 Kept: 4056
% 5.45/5.84 Inuse: 453
% 5.45/5.84 Deleted: 161
% 5.45/5.84 Deletedinuse: 35
% 5.45/5.84
% 5.45/5.84 Resimplifying inuse:
% 5.45/5.84 Done
% 5.45/5.84
% 5.45/5.84 *** allocated 75937 integers for termspace/termends
% 5.45/5.84 *** allocated 384427 integers for clauses
% 5.45/5.84 Resimplifying inuse:
% 5.45/5.84 Done
% 5.45/5.84
% 5.45/5.84
% 5.45/5.84 Intermediate Status:
% 5.45/5.84 Generated: 43291
% 5.45/5.84 Kept: 6062
% 5.45/5.84 Inuse: 684
% 5.45/5.84 Deleted: 288
% 5.45/5.84 Deletedinuse: 104
% 5.45/5.84
% 5.45/5.84 Resimplifying inuse:
% 5.45/5.84 Done
% 5.45/5.84
% 5.45/5.84 *** allocated 113905 integers for termspace/termends
% 5.45/5.84 Resimplifying inuse:
% 5.45/5.84 Done
% 5.45/5.84
% 5.45/5.84 *** allocated 576640 integers for clauses
% 5.45/5.84
% 5.45/5.84 Intermediate Status:
% 5.45/5.84 Generated: 59965
% 5.45/5.84 Kept: 8069
% 5.45/5.84 Inuse: 810
% 5.45/5.84 Deleted: 308
% 5.45/5.84 Deletedinuse: 110
% 5.45/5.84
% 5.45/5.84 Resimplifying inuse:
% 5.45/5.84 Done
% 5.45/5.84
% 5.45/5.84 *** allocated 170857 integers for termspace/termends
% 5.45/5.84 Resimplifying inuse:
% 5.45/5.84 Done
% 5.45/5.84
% 5.45/5.84
% 5.45/5.84 Intermediate Status:
% 5.45/5.84 Generated: 69061
% 5.45/5.84 Kept: 10130
% 5.45/5.84 Inuse: 887
% 5.45/5.84 Deleted: 495
% 5.45/5.84 Deletedinuse: 277
% 5.45/5.84
% 5.45/5.84 Resimplifying inuse:
% 5.45/5.84 Done
% 5.45/5.84
% 5.45/5.84 Resimplifying inuse:
% 5.45/5.84 Done
% 5.45/5.84
% 5.45/5.84 *** allocated 864960 integers for clauses
% 5.45/5.84
% 5.45/5.84 Intermediate Status:
% 5.45/5.84 Generated: 82225
% 5.45/5.84 Kept: 12132
% 5.45/5.84 Inuse: 990
% 5.45/5.84 Deleted: 567
% 5.45/5.84 Deletedinuse: 294
% 5.45/5.84
% 5.45/5.84 Resimplifying inuse:
% 5.45/5.84 Done
% 5.45/5.84
% 5.45/5.84 Resimplifying inuse:
% 5.45/5.84 Done
% 5.45/5.84
% 5.45/5.84 *** allocated 256285 integers for termspace/termends
% 5.45/5.84
% 5.45/5.84 Intermediate Status:
% 5.45/5.84 Generated: 95592
% 5.45/5.84 Kept: 14141
% 5.45/5.84 Inuse: 1084
% 5.45/5.84 Deleted: 700
% 5.45/5.84 Deletedinuse: 335
% 5.45/5.84
% 5.45/5.84 Resimplifying inuse:
% 5.45/5.84 Done
% 5.45/5.84
% 5.45/5.84 Resimplifying inuse:
% 5.45/5.84 Done
% 5.45/5.84
% 5.45/5.84
% 5.45/5.84 Intermediate Status:
% 5.45/5.84 Generated: 115192
% 5.45/5.84 Kept: 16272
% 5.45/5.84 Inuse: 1211
% 5.45/5.84 Deleted: 793
% 5.45/5.84 Deletedinuse: 345
% 5.45/5.84
% 5.45/5.84 Resimplifying inuse:
% 5.45/5.84 Done
% 5.45/5.84
% 5.45/5.84
% 5.45/5.84 Intermediate Status:
% 5.45/5.84 Generated: 136235
% 5.45/5.84 Kept: 18305
% 5.45/5.84 Inuse: 1315
% 5.45/5.84 Deleted: 956
% 5.45/5.84 Deletedinuse: 345
% 5.45/5.84
% 5.45/5.84 Resimplifying inuse:
% 5.45/5.84 Done
% 5.45/5.84
% 5.45/5.84 *** allocated 1297440 integers for clauses
% 5.45/5.84 Resimplifying inuse:
% 5.45/5.84 Done
% 5.45/5.84
% 5.45/5.84 Resimplifying clauses:
% 5.45/5.84
% 5.45/5.84 Bliksems!, er is een bewijs:
% 5.45/5.84 % SZS status Theorem
% 5.45/5.84 % SZS output start Refutation
% 5.45/5.84
% 5.45/5.84 (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X ) }.
% 5.45/5.84 (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 5.45/5.84 (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 5.45/5.84 (4) {G0,W11,D4,L1,V3,M1} I { multiplication( X, multiplication( Y, Z ) )
% 5.45/5.84 ==> multiplication( multiplication( X, Y ), Z ) }.
% 5.45/5.84 (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 5.45/5.84 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 5.45/5.84 (10) {G0,W5,D3,L1,V1,M1} I { multiplication( zero, X ) ==> zero }.
% 5.45/5.84 (13) {G0,W6,D3,L2,V1,M2} I { ! test( X ), complement( skol1( X ), X ) }.
% 5.45/5.84 (14) {G0,W5,D2,L2,V2,M2} I { ! complement( Y, X ), test( X ) }.
% 5.45/5.84 (15) {G0,W8,D3,L2,V2,M2} I { ! complement( Y, X ), multiplication( X, Y )
% 5.45/5.84 ==> zero }.
% 5.45/5.84 (16) {G0,W6,D2,L2,V2,M2} I { ! complement( Y, X ), alpha1( X, Y ) }.
% 5.45/5.84 (17) {G0,W11,D3,L3,V2,M3} I { ! multiplication( X, Y ) ==> zero, ! alpha1(
% 5.45/5.84 X, Y ), complement( Y, X ) }.
% 5.45/5.84 (18) {G0,W8,D3,L2,V2,M2} I { ! alpha1( X, Y ), multiplication( Y, X ) ==>
% 5.45/5.84 zero }.
% 5.45/5.84 (19) {G0,W8,D3,L2,V2,M2} I { ! alpha1( X, Y ), addition( X, Y ) ==> one }.
% 5.45/5.84 (20) {G0,W13,D3,L3,V2,M3} I { ! multiplication( Y, X ) ==> zero, ! addition
% 5.45/5.84 ( X, Y ) ==> one, alpha1( X, Y ) }.
% 5.45/5.84 (22) {G0,W9,D3,L3,V2,M3} I { ! test( X ), ! complement( X, Y ), c( X ) = Y
% 5.45/5.84 }.
% 5.45/5.84 (24) {G0,W14,D4,L3,V2,M3} I { ! test( X ), ! test( Y ), multiplication( c(
% 5.45/5.84 X ), c( Y ) ) ==> c( addition( X, Y ) ) }.
% 5.45/5.84 (26) {G0,W2,D2,L1,V0,M1} I { test( skol2 ) }.
% 5.45/5.84 (28) {G0,W24,D7,L1,V0,M1} I { ! addition( multiplication( skol2, addition(
% 5.45/5.84 multiplication( skol2, skol4 ), multiplication( c( skol2 ), skol5 ) ) ),
% 5.45/5.84 multiplication( c( skol2 ), skol6 ) ) ==> addition( multiplication( skol2
% 5.45/5.84 , skol4 ), multiplication( c( skol2 ), skol6 ) ) }.
% 5.45/5.84 (30) {G1,W10,D4,L2,V1,M2} F(24);d(3) { ! test( X ), multiplication( c( X )
% 5.45/5.84 , c( X ) ) ==> c( X ) }.
% 5.45/5.84 (32) {G1,W5,D3,L1,V1,M1} P(2,0) { addition( zero, X ) ==> X }.
% 5.45/5.84 (48) {G1,W17,D5,L1,V4,M1} P(4,7) { addition( multiplication( multiplication
% 5.45/5.84 ( X, Y ), Z ), multiplication( X, T ) ) ==> multiplication( X, addition(
% 5.45/5.84 multiplication( Y, Z ), T ) ) }.
% 5.45/5.84 (182) {G1,W7,D3,L2,V2,M2} R(13,14) { complement( skol1( X ), X ), !
% 5.45/5.84 complement( Y, X ) }.
% 5.45/5.84 (183) {G1,W4,D3,L1,V0,M1} R(13,26) { complement( skol1( skol2 ), skol2 )
% 5.45/5.84 }.
% 5.45/5.84 (187) {G2,W4,D3,L1,V0,M1} R(183,16) { alpha1( skol2, skol1( skol2 ) ) }.
% 5.45/5.84 (195) {G2,W6,D4,L1,V0,M1} R(15,183) { multiplication( skol2, skol1( skol2 )
% 5.45/5.84 ) ==> zero }.
% 5.45/5.84 (237) {G3,W6,D4,L1,V0,M1} R(18,187) { multiplication( skol1( skol2 ), skol2
% 5.45/5.84 ) ==> zero }.
% 5.45/5.84 (240) {G1,W8,D3,L2,V2,M2} R(18,16) { multiplication( X, Y ) ==> zero, !
% 5.45/5.84 complement( X, Y ) }.
% 5.45/5.84 (263) {G3,W6,D4,L1,V0,M1} R(19,187) { addition( skol2, skol1( skol2 ) ) ==>
% 5.45/5.84 one }.
% 5.45/5.84 (267) {G1,W8,D3,L2,V2,M2} R(19,16) { addition( X, Y ) ==> one, ! complement
% 5.45/5.84 ( Y, X ) }.
% 5.45/5.84 (282) {G1,W18,D3,L4,V2,M4} R(20,17) { ! multiplication( X, Y ) ==> zero, !
% 5.45/5.84 addition( Y, X ) ==> one, ! multiplication( Y, X ) ==> zero, complement(
% 5.45/5.84 X, Y ) }.
% 5.45/5.84 (541) {G1,W24,D7,L1,V0,M1} P(0,28) { ! addition( multiplication( skol2,
% 5.45/5.84 addition( multiplication( c( skol2 ), skol5 ), multiplication( skol2,
% 5.45/5.84 skol4 ) ) ), multiplication( c( skol2 ), skol6 ) ) ==> addition(
% 5.45/5.84 multiplication( skol2, skol4 ), multiplication( c( skol2 ), skol6 ) ) }.
% 5.45/5.84 (3705) {G4,W6,D4,L1,V0,M1} P(263,0) { addition( skol1( skol2 ), skol2 ) ==>
% 5.45/5.84 one }.
% 5.45/5.84 (5003) {G5,W4,D3,L1,V0,M1} R(195,20);d(3705);q { alpha1( skol1( skol2 ),
% 5.45/5.84 skol2 ) }.
% 5.45/5.84 (5012) {G3,W12,D6,L1,V2,M1} P(195,48);d(10);d(32) { multiplication( skol2,
% 5.45/5.84 addition( multiplication( skol1( skol2 ), X ), Y ) ) ==> multiplication(
% 5.45/5.84 skol2, Y ) }.
% 5.45/5.84 (5014) {G6,W4,D3,L1,V0,M1} R(5003,17);d(237);q { complement( skol2, skol1(
% 5.45/5.84 skol2 ) ) }.
% 5.45/5.84 (5015) {G7,W6,D4,L1,V0,M1} R(5014,182) { complement( skol1( skol1( skol2 )
% 5.45/5.84 ), skol1( skol2 ) ) }.
% 5.45/5.84 (5022) {G7,W5,D3,L1,V0,M1} R(5014,22);r(26) { c( skol2 ) ==> skol1( skol2 )
% 5.45/5.84 }.
% 5.45/5.84 (5024) {G7,W3,D3,L1,V0,M1} R(5014,14) { test( skol1( skol2 ) ) }.
% 5.45/5.84 (5035) {G8,W11,D5,L1,V0,M1} R(5024,30) { multiplication( c( skol1( skol2 )
% 5.45/5.84 ), c( skol1( skol2 ) ) ) ==> c( skol1( skol2 ) ) }.
% 5.45/5.84 (6662) {G2,W8,D3,L2,V2,M2} P(267,0) { addition( Y, X ) ==> one, !
% 5.45/5.84 complement( Y, X ) }.
% 5.45/5.84 (7372) {G3,W6,D2,L2,V2,M2} R(282,240);d(15);d(6662);q;q { complement( X, Y
% 5.45/5.84 ), ! complement( Y, X ) }.
% 5.45/5.84 (7392) {G8,W6,D4,L1,V0,M1} R(7372,5015) { complement( skol1( skol2 ), skol1
% 5.45/5.84 ( skol1( skol2 ) ) ) }.
% 5.45/5.84 (7417) {G4,W5,D2,L2,V2,M2} R(7372,14) { ! complement( X, Y ), test( X ) }.
% 5.45/5.84 (7446) {G5,W10,D3,L3,V3,M3} R(7417,22) { ! complement( X, Y ), ! complement
% 5.45/5.84 ( X, Z ), c( X ) = Z }.
% 5.45/5.84 (7450) {G6,W7,D3,L2,V2,M2} F(7446) { ! complement( X, Y ), c( X ) = Y }.
% 5.45/5.84 (9114) {G9,W7,D4,L1,V0,M1} R(7450,7392) { c( skol1( skol2 ) ) ==> skol1(
% 5.45/5.84 skol1( skol2 ) ) }.
% 5.45/5.84 (9139) {G10,W5,D4,L1,V0,M1} R(7450,183);d(9114) { skol1( skol1( skol2 ) )
% 5.45/5.84 ==> skol2 }.
% 5.45/5.84 (20032) {G11,W5,D4,L1,V0,M1} S(9114);d(9139) { c( skol1( skol2 ) ) ==>
% 5.45/5.84 skol2 }.
% 5.45/5.84 (20165) {G12,W5,D3,L1,V0,M1} S(5035);d(20032) { multiplication( skol2,
% 5.45/5.84 skol2 ) ==> skol2 }.
% 5.45/5.84 (20275) {G13,W0,D0,L0,V0,M0} S(541);d(5022);d(5012);d(4);d(20165);q { }.
% 5.45/5.84
% 5.45/5.84
% 5.45/5.84 % SZS output end Refutation
% 5.45/5.84 found a proof!
% 5.45/5.84
% 5.45/5.84
% 5.45/5.84 Unprocessed initial clauses:
% 5.45/5.84
% 5.45/5.84 (20277) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X ) }.
% 5.45/5.84 (20278) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) = addition
% 5.45/5.84 ( addition( Z, Y ), X ) }.
% 5.45/5.84 (20279) {G0,W5,D3,L1,V1,M1} { addition( X, zero ) = X }.
% 5.45/5.84 (20280) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 5.45/5.84 (20281) {G0,W11,D4,L1,V3,M1} { multiplication( X, multiplication( Y, Z ) )
% 5.45/5.84 = multiplication( multiplication( X, Y ), Z ) }.
% 5.45/5.84 (20282) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 5.45/5.84 (20283) {G0,W5,D3,L1,V1,M1} { multiplication( one, X ) = X }.
% 5.45/5.84 (20284) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y, Z ) ) =
% 5.45/5.84 addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 5.45/5.84 (20285) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Y ), Z ) =
% 5.45/5.84 addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 5.45/5.84 (20286) {G0,W5,D3,L1,V1,M1} { multiplication( X, zero ) = zero }.
% 5.45/5.84 (20287) {G0,W5,D3,L1,V1,M1} { multiplication( zero, X ) = zero }.
% 5.45/5.84 (20288) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y }.
% 5.45/5.84 (20289) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 5.45/5.84 (20290) {G0,W6,D3,L2,V1,M2} { ! test( X ), complement( skol1( X ), X ) }.
% 5.45/5.84 (20291) {G0,W5,D2,L2,V2,M2} { ! complement( Y, X ), test( X ) }.
% 5.45/5.84 (20292) {G0,W8,D3,L2,V2,M2} { ! complement( Y, X ), multiplication( X, Y )
% 5.45/5.84 = zero }.
% 5.45/5.84 (20293) {G0,W6,D2,L2,V2,M2} { ! complement( Y, X ), alpha1( X, Y ) }.
% 5.45/5.84 (20294) {G0,W11,D3,L3,V2,M3} { ! multiplication( X, Y ) = zero, ! alpha1(
% 5.45/5.84 X, Y ), complement( Y, X ) }.
% 5.45/5.84 (20295) {G0,W8,D3,L2,V2,M2} { ! alpha1( X, Y ), multiplication( Y, X ) =
% 5.45/5.84 zero }.
% 5.45/5.84 (20296) {G0,W8,D3,L2,V2,M2} { ! alpha1( X, Y ), addition( X, Y ) = one }.
% 5.45/5.84 (20297) {G0,W13,D3,L3,V2,M3} { ! multiplication( Y, X ) = zero, ! addition
% 5.45/5.84 ( X, Y ) = one, alpha1( X, Y ) }.
% 5.45/5.84 (20298) {G0,W9,D3,L3,V2,M3} { ! test( X ), ! c( X ) = Y, complement( X, Y
% 5.45/5.84 ) }.
% 5.45/5.84 (20299) {G0,W9,D3,L3,V2,M3} { ! test( X ), ! complement( X, Y ), c( X ) =
% 5.45/5.84 Y }.
% 5.45/5.84 (20300) {G0,W6,D3,L2,V1,M2} { test( X ), c( X ) = zero }.
% 5.45/5.84 (20301) {G0,W14,D4,L3,V2,M3} { ! test( X ), ! test( Y ), c( addition( X, Y
% 5.45/5.84 ) ) = multiplication( c( X ), c( Y ) ) }.
% 5.45/5.84 (20302) {G0,W14,D4,L3,V2,M3} { ! test( X ), ! test( Y ), c( multiplication
% 5.45/5.84 ( X, Y ) ) = addition( c( X ), c( Y ) ) }.
% 5.45/5.84 (20303) {G0,W2,D2,L1,V0,M1} { test( skol2 ) }.
% 5.45/5.84 (20304) {G0,W2,D2,L1,V0,M1} { test( skol3 ) }.
% 5.45/5.84 (20305) {G0,W24,D7,L1,V0,M1} { ! addition( multiplication( skol2, addition
% 5.45/5.84 ( multiplication( skol2, skol4 ), multiplication( c( skol2 ), skol5 ) ) )
% 5.45/5.84 , multiplication( c( skol2 ), skol6 ) ) = addition( multiplication( skol2
% 5.45/5.84 , skol4 ), multiplication( c( skol2 ), skol6 ) ) }.
% 5.45/5.84
% 5.45/5.84
% 5.45/5.84 Total Proof:
% 5.45/5.84
% 5.45/5.84 subsumption: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X
% 5.45/5.84 ) }.
% 5.45/5.84 parent0: (20277) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X )
% 5.45/5.84 }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := X
% 5.45/5.84 Y := Y
% 5.45/5.84 end
% 5.45/5.84 permutation0:
% 5.45/5.84 0 ==> 0
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 subsumption: (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 5.45/5.84 parent0: (20279) {G0,W5,D3,L1,V1,M1} { addition( X, zero ) = X }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := X
% 5.45/5.84 end
% 5.45/5.84 permutation0:
% 5.45/5.84 0 ==> 0
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 subsumption: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 5.45/5.84 parent0: (20280) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := X
% 5.45/5.84 end
% 5.45/5.84 permutation0:
% 5.45/5.84 0 ==> 0
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 subsumption: (4) {G0,W11,D4,L1,V3,M1} I { multiplication( X, multiplication
% 5.45/5.84 ( Y, Z ) ) ==> multiplication( multiplication( X, Y ), Z ) }.
% 5.45/5.84 parent0: (20281) {G0,W11,D4,L1,V3,M1} { multiplication( X, multiplication
% 5.45/5.84 ( Y, Z ) ) = multiplication( multiplication( X, Y ), Z ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := X
% 5.45/5.84 Y := Y
% 5.45/5.84 Z := Z
% 5.45/5.84 end
% 5.45/5.84 permutation0:
% 5.45/5.84 0 ==> 0
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 eqswap: (20321) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Y ),
% 5.45/5.84 multiplication( X, Z ) ) = multiplication( X, addition( Y, Z ) ) }.
% 5.45/5.84 parent0[0]: (20284) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y
% 5.45/5.84 , Z ) ) = addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := X
% 5.45/5.84 Y := Y
% 5.45/5.84 Z := Z
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 subsumption: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y )
% 5.45/5.84 , multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 5.45/5.84 parent0: (20321) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Y ),
% 5.45/5.84 multiplication( X, Z ) ) = multiplication( X, addition( Y, Z ) ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := X
% 5.45/5.84 Y := Y
% 5.45/5.84 Z := Z
% 5.45/5.84 end
% 5.45/5.84 permutation0:
% 5.45/5.84 0 ==> 0
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 subsumption: (10) {G0,W5,D3,L1,V1,M1} I { multiplication( zero, X ) ==>
% 5.45/5.84 zero }.
% 5.45/5.84 parent0: (20287) {G0,W5,D3,L1,V1,M1} { multiplication( zero, X ) = zero
% 5.45/5.84 }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := X
% 5.45/5.84 end
% 5.45/5.84 permutation0:
% 5.45/5.84 0 ==> 0
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 subsumption: (13) {G0,W6,D3,L2,V1,M2} I { ! test( X ), complement( skol1( X
% 5.45/5.84 ), X ) }.
% 5.45/5.84 parent0: (20290) {G0,W6,D3,L2,V1,M2} { ! test( X ), complement( skol1( X )
% 5.45/5.84 , X ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := X
% 5.45/5.84 end
% 5.45/5.84 permutation0:
% 5.45/5.84 0 ==> 0
% 5.45/5.84 1 ==> 1
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 subsumption: (14) {G0,W5,D2,L2,V2,M2} I { ! complement( Y, X ), test( X )
% 5.45/5.84 }.
% 5.45/5.84 parent0: (20291) {G0,W5,D2,L2,V2,M2} { ! complement( Y, X ), test( X ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := X
% 5.45/5.84 Y := Y
% 5.45/5.84 end
% 5.45/5.84 permutation0:
% 5.45/5.84 0 ==> 0
% 5.45/5.84 1 ==> 1
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 subsumption: (15) {G0,W8,D3,L2,V2,M2} I { ! complement( Y, X ),
% 5.45/5.84 multiplication( X, Y ) ==> zero }.
% 5.45/5.84 parent0: (20292) {G0,W8,D3,L2,V2,M2} { ! complement( Y, X ),
% 5.45/5.84 multiplication( X, Y ) = zero }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := X
% 5.45/5.84 Y := Y
% 5.45/5.84 end
% 5.45/5.84 permutation0:
% 5.45/5.84 0 ==> 0
% 5.45/5.84 1 ==> 1
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 subsumption: (16) {G0,W6,D2,L2,V2,M2} I { ! complement( Y, X ), alpha1( X,
% 5.45/5.84 Y ) }.
% 5.45/5.84 parent0: (20293) {G0,W6,D2,L2,V2,M2} { ! complement( Y, X ), alpha1( X, Y
% 5.45/5.84 ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := X
% 5.45/5.84 Y := Y
% 5.45/5.84 end
% 5.45/5.84 permutation0:
% 5.45/5.84 0 ==> 0
% 5.45/5.84 1 ==> 1
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 subsumption: (17) {G0,W11,D3,L3,V2,M3} I { ! multiplication( X, Y ) ==>
% 5.45/5.84 zero, ! alpha1( X, Y ), complement( Y, X ) }.
% 5.45/5.84 parent0: (20294) {G0,W11,D3,L3,V2,M3} { ! multiplication( X, Y ) = zero, !
% 5.45/5.84 alpha1( X, Y ), complement( Y, X ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := X
% 5.45/5.84 Y := Y
% 5.45/5.84 end
% 5.45/5.84 permutation0:
% 5.45/5.84 0 ==> 0
% 5.45/5.84 1 ==> 1
% 5.45/5.84 2 ==> 2
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 subsumption: (18) {G0,W8,D3,L2,V2,M2} I { ! alpha1( X, Y ), multiplication
% 5.45/5.84 ( Y, X ) ==> zero }.
% 5.45/5.84 parent0: (20295) {G0,W8,D3,L2,V2,M2} { ! alpha1( X, Y ), multiplication( Y
% 5.45/5.84 , X ) = zero }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := X
% 5.45/5.84 Y := Y
% 5.45/5.84 end
% 5.45/5.84 permutation0:
% 5.45/5.84 0 ==> 0
% 5.45/5.84 1 ==> 1
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 subsumption: (19) {G0,W8,D3,L2,V2,M2} I { ! alpha1( X, Y ), addition( X, Y
% 5.45/5.84 ) ==> one }.
% 5.45/5.84 parent0: (20296) {G0,W8,D3,L2,V2,M2} { ! alpha1( X, Y ), addition( X, Y )
% 5.45/5.84 = one }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := X
% 5.45/5.84 Y := Y
% 5.45/5.84 end
% 5.45/5.84 permutation0:
% 5.45/5.84 0 ==> 0
% 5.45/5.84 1 ==> 1
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 subsumption: (20) {G0,W13,D3,L3,V2,M3} I { ! multiplication( Y, X ) ==>
% 5.45/5.84 zero, ! addition( X, Y ) ==> one, alpha1( X, Y ) }.
% 5.45/5.84 parent0: (20297) {G0,W13,D3,L3,V2,M3} { ! multiplication( Y, X ) = zero, !
% 5.45/5.84 addition( X, Y ) = one, alpha1( X, Y ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := X
% 5.45/5.84 Y := Y
% 5.45/5.84 end
% 5.45/5.84 permutation0:
% 5.45/5.84 0 ==> 0
% 5.45/5.84 1 ==> 1
% 5.45/5.84 2 ==> 2
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 subsumption: (22) {G0,W9,D3,L3,V2,M3} I { ! test( X ), ! complement( X, Y )
% 5.45/5.84 , c( X ) = Y }.
% 5.45/5.84 parent0: (20299) {G0,W9,D3,L3,V2,M3} { ! test( X ), ! complement( X, Y ),
% 5.45/5.84 c( X ) = Y }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := X
% 5.45/5.84 Y := Y
% 5.45/5.84 end
% 5.45/5.84 permutation0:
% 5.45/5.84 0 ==> 0
% 5.45/5.84 1 ==> 1
% 5.45/5.84 2 ==> 2
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 eqswap: (20489) {G0,W14,D4,L3,V2,M3} { multiplication( c( X ), c( Y ) ) =
% 5.45/5.84 c( addition( X, Y ) ), ! test( X ), ! test( Y ) }.
% 5.45/5.84 parent0[2]: (20301) {G0,W14,D4,L3,V2,M3} { ! test( X ), ! test( Y ), c(
% 5.45/5.84 addition( X, Y ) ) = multiplication( c( X ), c( Y ) ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := X
% 5.45/5.84 Y := Y
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 subsumption: (24) {G0,W14,D4,L3,V2,M3} I { ! test( X ), ! test( Y ),
% 5.45/5.84 multiplication( c( X ), c( Y ) ) ==> c( addition( X, Y ) ) }.
% 5.45/5.84 parent0: (20489) {G0,W14,D4,L3,V2,M3} { multiplication( c( X ), c( Y ) ) =
% 5.45/5.84 c( addition( X, Y ) ), ! test( X ), ! test( Y ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := X
% 5.45/5.84 Y := Y
% 5.45/5.84 end
% 5.45/5.84 permutation0:
% 5.45/5.84 0 ==> 2
% 5.45/5.84 1 ==> 0
% 5.45/5.84 2 ==> 1
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 subsumption: (26) {G0,W2,D2,L1,V0,M1} I { test( skol2 ) }.
% 5.45/5.84 parent0: (20303) {G0,W2,D2,L1,V0,M1} { test( skol2 ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 end
% 5.45/5.84 permutation0:
% 5.45/5.84 0 ==> 0
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 subsumption: (28) {G0,W24,D7,L1,V0,M1} I { ! addition( multiplication(
% 5.45/5.84 skol2, addition( multiplication( skol2, skol4 ), multiplication( c( skol2
% 5.45/5.84 ), skol5 ) ) ), multiplication( c( skol2 ), skol6 ) ) ==> addition(
% 5.45/5.84 multiplication( skol2, skol4 ), multiplication( c( skol2 ), skol6 ) ) }.
% 5.45/5.84 parent0: (20305) {G0,W24,D7,L1,V0,M1} { ! addition( multiplication( skol2
% 5.45/5.84 , addition( multiplication( skol2, skol4 ), multiplication( c( skol2 ),
% 5.45/5.84 skol5 ) ) ), multiplication( c( skol2 ), skol6 ) ) = addition(
% 5.45/5.84 multiplication( skol2, skol4 ), multiplication( c( skol2 ), skol6 ) ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 end
% 5.45/5.84 permutation0:
% 5.45/5.84 0 ==> 0
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 factor: (20552) {G0,W12,D4,L2,V1,M2} { ! test( X ), multiplication( c( X )
% 5.45/5.84 , c( X ) ) ==> c( addition( X, X ) ) }.
% 5.45/5.84 parent0[0, 1]: (24) {G0,W14,D4,L3,V2,M3} I { ! test( X ), ! test( Y ),
% 5.45/5.84 multiplication( c( X ), c( Y ) ) ==> c( addition( X, Y ) ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := X
% 5.45/5.84 Y := X
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 paramod: (20553) {G1,W10,D4,L2,V1,M2} { multiplication( c( X ), c( X ) )
% 5.45/5.84 ==> c( X ), ! test( X ) }.
% 5.45/5.84 parent0[0]: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 5.45/5.84 parent1[1; 7]: (20552) {G0,W12,D4,L2,V1,M2} { ! test( X ), multiplication
% 5.45/5.84 ( c( X ), c( X ) ) ==> c( addition( X, X ) ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := X
% 5.45/5.84 end
% 5.45/5.84 substitution1:
% 5.45/5.84 X := X
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 subsumption: (30) {G1,W10,D4,L2,V1,M2} F(24);d(3) { ! test( X ),
% 5.45/5.84 multiplication( c( X ), c( X ) ) ==> c( X ) }.
% 5.45/5.84 parent0: (20553) {G1,W10,D4,L2,V1,M2} { multiplication( c( X ), c( X ) )
% 5.45/5.84 ==> c( X ), ! test( X ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := X
% 5.45/5.84 end
% 5.45/5.84 permutation0:
% 5.45/5.84 0 ==> 1
% 5.45/5.84 1 ==> 0
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 eqswap: (20555) {G0,W5,D3,L1,V1,M1} { X ==> addition( X, zero ) }.
% 5.45/5.84 parent0[0]: (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := X
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 paramod: (20556) {G1,W5,D3,L1,V1,M1} { X ==> addition( zero, X ) }.
% 5.45/5.84 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 5.45/5.84 }.
% 5.45/5.84 parent1[0; 2]: (20555) {G0,W5,D3,L1,V1,M1} { X ==> addition( X, zero ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := X
% 5.45/5.84 Y := zero
% 5.45/5.84 end
% 5.45/5.84 substitution1:
% 5.45/5.84 X := X
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 eqswap: (20559) {G1,W5,D3,L1,V1,M1} { addition( zero, X ) ==> X }.
% 5.45/5.84 parent0[0]: (20556) {G1,W5,D3,L1,V1,M1} { X ==> addition( zero, X ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := X
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 subsumption: (32) {G1,W5,D3,L1,V1,M1} P(2,0) { addition( zero, X ) ==> X
% 5.45/5.84 }.
% 5.45/5.84 parent0: (20559) {G1,W5,D3,L1,V1,M1} { addition( zero, X ) ==> X }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := X
% 5.45/5.84 end
% 5.45/5.84 permutation0:
% 5.45/5.84 0 ==> 0
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 eqswap: (20561) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y, Z )
% 5.45/5.84 ) ==> addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 5.45/5.84 parent0[0]: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 5.45/5.84 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := X
% 5.45/5.84 Y := Y
% 5.45/5.84 Z := Z
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 paramod: (20562) {G1,W17,D5,L1,V4,M1} { multiplication( X, addition(
% 5.45/5.84 multiplication( Y, Z ), T ) ) ==> addition( multiplication(
% 5.45/5.84 multiplication( X, Y ), Z ), multiplication( X, T ) ) }.
% 5.45/5.84 parent0[0]: (4) {G0,W11,D4,L1,V3,M1} I { multiplication( X, multiplication
% 5.45/5.84 ( Y, Z ) ) ==> multiplication( multiplication( X, Y ), Z ) }.
% 5.45/5.84 parent1[0; 9]: (20561) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition
% 5.45/5.84 ( Y, Z ) ) ==> addition( multiplication( X, Y ), multiplication( X, Z ) )
% 5.45/5.84 }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := X
% 5.45/5.84 Y := Y
% 5.45/5.84 Z := Z
% 5.45/5.84 end
% 5.45/5.84 substitution1:
% 5.45/5.84 X := X
% 5.45/5.84 Y := multiplication( Y, Z )
% 5.45/5.84 Z := T
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 eqswap: (20564) {G1,W17,D5,L1,V4,M1} { addition( multiplication(
% 5.45/5.84 multiplication( X, Y ), Z ), multiplication( X, T ) ) ==> multiplication
% 5.45/5.84 ( X, addition( multiplication( Y, Z ), T ) ) }.
% 5.45/5.84 parent0[0]: (20562) {G1,W17,D5,L1,V4,M1} { multiplication( X, addition(
% 5.45/5.84 multiplication( Y, Z ), T ) ) ==> addition( multiplication(
% 5.45/5.84 multiplication( X, Y ), Z ), multiplication( X, T ) ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := X
% 5.45/5.84 Y := Y
% 5.45/5.84 Z := Z
% 5.45/5.84 T := T
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 subsumption: (48) {G1,W17,D5,L1,V4,M1} P(4,7) { addition( multiplication(
% 5.45/5.84 multiplication( X, Y ), Z ), multiplication( X, T ) ) ==> multiplication
% 5.45/5.84 ( X, addition( multiplication( Y, Z ), T ) ) }.
% 5.45/5.84 parent0: (20564) {G1,W17,D5,L1,V4,M1} { addition( multiplication(
% 5.45/5.84 multiplication( X, Y ), Z ), multiplication( X, T ) ) ==> multiplication
% 5.45/5.84 ( X, addition( multiplication( Y, Z ), T ) ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := X
% 5.45/5.84 Y := Y
% 5.45/5.84 Z := Z
% 5.45/5.84 T := T
% 5.45/5.84 end
% 5.45/5.84 permutation0:
% 5.45/5.84 0 ==> 0
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 resolution: (20566) {G1,W7,D3,L2,V2,M2} { complement( skol1( X ), X ), !
% 5.45/5.84 complement( Y, X ) }.
% 5.45/5.84 parent0[0]: (13) {G0,W6,D3,L2,V1,M2} I { ! test( X ), complement( skol1( X
% 5.45/5.84 ), X ) }.
% 5.45/5.84 parent1[1]: (14) {G0,W5,D2,L2,V2,M2} I { ! complement( Y, X ), test( X )
% 5.45/5.84 }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := X
% 5.45/5.84 end
% 5.45/5.84 substitution1:
% 5.45/5.84 X := X
% 5.45/5.84 Y := Y
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 subsumption: (182) {G1,W7,D3,L2,V2,M2} R(13,14) { complement( skol1( X ), X
% 5.45/5.84 ), ! complement( Y, X ) }.
% 5.45/5.84 parent0: (20566) {G1,W7,D3,L2,V2,M2} { complement( skol1( X ), X ), !
% 5.45/5.84 complement( Y, X ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := X
% 5.45/5.84 Y := Y
% 5.45/5.84 end
% 5.45/5.84 permutation0:
% 5.45/5.84 0 ==> 0
% 5.45/5.84 1 ==> 1
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 resolution: (20567) {G1,W4,D3,L1,V0,M1} { complement( skol1( skol2 ),
% 5.45/5.84 skol2 ) }.
% 5.45/5.84 parent0[0]: (13) {G0,W6,D3,L2,V1,M2} I { ! test( X ), complement( skol1( X
% 5.45/5.84 ), X ) }.
% 5.45/5.84 parent1[0]: (26) {G0,W2,D2,L1,V0,M1} I { test( skol2 ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := skol2
% 5.45/5.84 end
% 5.45/5.84 substitution1:
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 subsumption: (183) {G1,W4,D3,L1,V0,M1} R(13,26) { complement( skol1( skol2
% 5.45/5.84 ), skol2 ) }.
% 5.45/5.84 parent0: (20567) {G1,W4,D3,L1,V0,M1} { complement( skol1( skol2 ), skol2 )
% 5.45/5.84 }.
% 5.45/5.84 substitution0:
% 5.45/5.84 end
% 5.45/5.84 permutation0:
% 5.45/5.84 0 ==> 0
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 resolution: (20568) {G1,W4,D3,L1,V0,M1} { alpha1( skol2, skol1( skol2 ) )
% 5.45/5.84 }.
% 5.45/5.84 parent0[0]: (16) {G0,W6,D2,L2,V2,M2} I { ! complement( Y, X ), alpha1( X, Y
% 5.45/5.84 ) }.
% 5.45/5.84 parent1[0]: (183) {G1,W4,D3,L1,V0,M1} R(13,26) { complement( skol1( skol2 )
% 5.45/5.84 , skol2 ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := skol2
% 5.45/5.84 Y := skol1( skol2 )
% 5.45/5.84 end
% 5.45/5.84 substitution1:
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 subsumption: (187) {G2,W4,D3,L1,V0,M1} R(183,16) { alpha1( skol2, skol1(
% 5.45/5.84 skol2 ) ) }.
% 5.45/5.84 parent0: (20568) {G1,W4,D3,L1,V0,M1} { alpha1( skol2, skol1( skol2 ) ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 end
% 5.45/5.84 permutation0:
% 5.45/5.84 0 ==> 0
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 eqswap: (20569) {G0,W8,D3,L2,V2,M2} { zero ==> multiplication( X, Y ), !
% 5.45/5.84 complement( Y, X ) }.
% 5.45/5.84 parent0[1]: (15) {G0,W8,D3,L2,V2,M2} I { ! complement( Y, X ),
% 5.45/5.84 multiplication( X, Y ) ==> zero }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := X
% 5.45/5.84 Y := Y
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 resolution: (20570) {G1,W6,D4,L1,V0,M1} { zero ==> multiplication( skol2,
% 5.45/5.84 skol1( skol2 ) ) }.
% 5.45/5.84 parent0[1]: (20569) {G0,W8,D3,L2,V2,M2} { zero ==> multiplication( X, Y )
% 5.45/5.84 , ! complement( Y, X ) }.
% 5.45/5.84 parent1[0]: (183) {G1,W4,D3,L1,V0,M1} R(13,26) { complement( skol1( skol2 )
% 5.45/5.84 , skol2 ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := skol2
% 5.45/5.84 Y := skol1( skol2 )
% 5.45/5.84 end
% 5.45/5.84 substitution1:
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 eqswap: (20571) {G1,W6,D4,L1,V0,M1} { multiplication( skol2, skol1( skol2
% 5.45/5.84 ) ) ==> zero }.
% 5.45/5.84 parent0[0]: (20570) {G1,W6,D4,L1,V0,M1} { zero ==> multiplication( skol2,
% 5.45/5.84 skol1( skol2 ) ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 subsumption: (195) {G2,W6,D4,L1,V0,M1} R(15,183) { multiplication( skol2,
% 5.45/5.84 skol1( skol2 ) ) ==> zero }.
% 5.45/5.84 parent0: (20571) {G1,W6,D4,L1,V0,M1} { multiplication( skol2, skol1( skol2
% 5.45/5.84 ) ) ==> zero }.
% 5.45/5.84 substitution0:
% 5.45/5.84 end
% 5.45/5.84 permutation0:
% 5.45/5.84 0 ==> 0
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 eqswap: (20572) {G0,W8,D3,L2,V2,M2} { zero ==> multiplication( X, Y ), !
% 5.45/5.84 alpha1( Y, X ) }.
% 5.45/5.84 parent0[1]: (18) {G0,W8,D3,L2,V2,M2} I { ! alpha1( X, Y ), multiplication(
% 5.45/5.84 Y, X ) ==> zero }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := Y
% 5.45/5.84 Y := X
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 resolution: (20573) {G1,W6,D4,L1,V0,M1} { zero ==> multiplication( skol1(
% 5.45/5.84 skol2 ), skol2 ) }.
% 5.45/5.84 parent0[1]: (20572) {G0,W8,D3,L2,V2,M2} { zero ==> multiplication( X, Y )
% 5.45/5.84 , ! alpha1( Y, X ) }.
% 5.45/5.84 parent1[0]: (187) {G2,W4,D3,L1,V0,M1} R(183,16) { alpha1( skol2, skol1(
% 5.45/5.84 skol2 ) ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := skol1( skol2 )
% 5.45/5.84 Y := skol2
% 5.45/5.84 end
% 5.45/5.84 substitution1:
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 eqswap: (20574) {G1,W6,D4,L1,V0,M1} { multiplication( skol1( skol2 ),
% 5.45/5.84 skol2 ) ==> zero }.
% 5.45/5.84 parent0[0]: (20573) {G1,W6,D4,L1,V0,M1} { zero ==> multiplication( skol1(
% 5.45/5.84 skol2 ), skol2 ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 subsumption: (237) {G3,W6,D4,L1,V0,M1} R(18,187) { multiplication( skol1(
% 5.45/5.84 skol2 ), skol2 ) ==> zero }.
% 5.45/5.84 parent0: (20574) {G1,W6,D4,L1,V0,M1} { multiplication( skol1( skol2 ),
% 5.45/5.84 skol2 ) ==> zero }.
% 5.45/5.84 substitution0:
% 5.45/5.84 end
% 5.45/5.84 permutation0:
% 5.45/5.84 0 ==> 0
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 eqswap: (20575) {G0,W8,D3,L2,V2,M2} { zero ==> multiplication( X, Y ), !
% 5.45/5.84 alpha1( Y, X ) }.
% 5.45/5.84 parent0[1]: (18) {G0,W8,D3,L2,V2,M2} I { ! alpha1( X, Y ), multiplication(
% 5.45/5.84 Y, X ) ==> zero }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := Y
% 5.45/5.84 Y := X
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 resolution: (20576) {G1,W8,D3,L2,V2,M2} { zero ==> multiplication( X, Y )
% 5.45/5.84 , ! complement( X, Y ) }.
% 5.45/5.84 parent0[1]: (20575) {G0,W8,D3,L2,V2,M2} { zero ==> multiplication( X, Y )
% 5.45/5.84 , ! alpha1( Y, X ) }.
% 5.45/5.84 parent1[1]: (16) {G0,W6,D2,L2,V2,M2} I { ! complement( Y, X ), alpha1( X, Y
% 5.45/5.84 ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := X
% 5.45/5.84 Y := Y
% 5.45/5.84 end
% 5.45/5.84 substitution1:
% 5.45/5.84 X := Y
% 5.45/5.84 Y := X
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 eqswap: (20577) {G1,W8,D3,L2,V2,M2} { multiplication( X, Y ) ==> zero, !
% 5.45/5.84 complement( X, Y ) }.
% 5.45/5.84 parent0[0]: (20576) {G1,W8,D3,L2,V2,M2} { zero ==> multiplication( X, Y )
% 5.45/5.84 , ! complement( X, Y ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := X
% 5.45/5.84 Y := Y
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 subsumption: (240) {G1,W8,D3,L2,V2,M2} R(18,16) { multiplication( X, Y )
% 5.45/5.84 ==> zero, ! complement( X, Y ) }.
% 5.45/5.84 parent0: (20577) {G1,W8,D3,L2,V2,M2} { multiplication( X, Y ) ==> zero, !
% 5.45/5.84 complement( X, Y ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := X
% 5.45/5.84 Y := Y
% 5.45/5.84 end
% 5.45/5.84 permutation0:
% 5.45/5.84 0 ==> 0
% 5.45/5.84 1 ==> 1
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 eqswap: (20578) {G0,W8,D3,L2,V2,M2} { one ==> addition( X, Y ), ! alpha1(
% 5.45/5.84 X, Y ) }.
% 5.45/5.84 parent0[1]: (19) {G0,W8,D3,L2,V2,M2} I { ! alpha1( X, Y ), addition( X, Y )
% 5.45/5.84 ==> one }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := X
% 5.45/5.84 Y := Y
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 resolution: (20579) {G1,W6,D4,L1,V0,M1} { one ==> addition( skol2, skol1(
% 5.45/5.84 skol2 ) ) }.
% 5.45/5.84 parent0[1]: (20578) {G0,W8,D3,L2,V2,M2} { one ==> addition( X, Y ), !
% 5.45/5.84 alpha1( X, Y ) }.
% 5.45/5.84 parent1[0]: (187) {G2,W4,D3,L1,V0,M1} R(183,16) { alpha1( skol2, skol1(
% 5.45/5.84 skol2 ) ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := skol2
% 5.45/5.84 Y := skol1( skol2 )
% 5.45/5.84 end
% 5.45/5.84 substitution1:
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 eqswap: (20580) {G1,W6,D4,L1,V0,M1} { addition( skol2, skol1( skol2 ) )
% 5.45/5.84 ==> one }.
% 5.45/5.84 parent0[0]: (20579) {G1,W6,D4,L1,V0,M1} { one ==> addition( skol2, skol1(
% 5.45/5.84 skol2 ) ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 subsumption: (263) {G3,W6,D4,L1,V0,M1} R(19,187) { addition( skol2, skol1(
% 5.45/5.84 skol2 ) ) ==> one }.
% 5.45/5.84 parent0: (20580) {G1,W6,D4,L1,V0,M1} { addition( skol2, skol1( skol2 ) )
% 5.45/5.84 ==> one }.
% 5.45/5.84 substitution0:
% 5.45/5.84 end
% 5.45/5.84 permutation0:
% 5.45/5.84 0 ==> 0
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 eqswap: (20581) {G0,W8,D3,L2,V2,M2} { one ==> addition( X, Y ), ! alpha1(
% 5.45/5.84 X, Y ) }.
% 5.45/5.84 parent0[1]: (19) {G0,W8,D3,L2,V2,M2} I { ! alpha1( X, Y ), addition( X, Y )
% 5.45/5.84 ==> one }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := X
% 5.45/5.84 Y := Y
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 resolution: (20582) {G1,W8,D3,L2,V2,M2} { one ==> addition( X, Y ), !
% 5.45/5.84 complement( Y, X ) }.
% 5.45/5.84 parent0[1]: (20581) {G0,W8,D3,L2,V2,M2} { one ==> addition( X, Y ), !
% 5.45/5.84 alpha1( X, Y ) }.
% 5.45/5.84 parent1[1]: (16) {G0,W6,D2,L2,V2,M2} I { ! complement( Y, X ), alpha1( X, Y
% 5.45/5.84 ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := X
% 5.45/5.84 Y := Y
% 5.45/5.84 end
% 5.45/5.84 substitution1:
% 5.45/5.84 X := X
% 5.45/5.84 Y := Y
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 eqswap: (20583) {G1,W8,D3,L2,V2,M2} { addition( X, Y ) ==> one, !
% 5.45/5.84 complement( Y, X ) }.
% 5.45/5.84 parent0[0]: (20582) {G1,W8,D3,L2,V2,M2} { one ==> addition( X, Y ), !
% 5.45/5.84 complement( Y, X ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := X
% 5.45/5.84 Y := Y
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 subsumption: (267) {G1,W8,D3,L2,V2,M2} R(19,16) { addition( X, Y ) ==> one
% 5.45/5.84 , ! complement( Y, X ) }.
% 5.45/5.84 parent0: (20583) {G1,W8,D3,L2,V2,M2} { addition( X, Y ) ==> one, !
% 5.45/5.84 complement( Y, X ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := X
% 5.45/5.84 Y := Y
% 5.45/5.84 end
% 5.45/5.84 permutation0:
% 5.45/5.84 0 ==> 0
% 5.45/5.84 1 ==> 1
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 eqswap: (20584) {G0,W13,D3,L3,V2,M3} { ! zero ==> multiplication( X, Y ),
% 5.45/5.84 ! addition( Y, X ) ==> one, alpha1( Y, X ) }.
% 5.45/5.84 parent0[0]: (20) {G0,W13,D3,L3,V2,M3} I { ! multiplication( Y, X ) ==> zero
% 5.45/5.84 , ! addition( X, Y ) ==> one, alpha1( X, Y ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := Y
% 5.45/5.84 Y := X
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 eqswap: (20587) {G0,W11,D3,L3,V2,M3} { ! zero ==> multiplication( X, Y ),
% 5.45/5.84 ! alpha1( X, Y ), complement( Y, X ) }.
% 5.45/5.84 parent0[0]: (17) {G0,W11,D3,L3,V2,M3} I { ! multiplication( X, Y ) ==> zero
% 5.45/5.84 , ! alpha1( X, Y ), complement( Y, X ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := X
% 5.45/5.84 Y := Y
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 resolution: (20588) {G1,W18,D3,L4,V2,M4} { ! zero ==> multiplication( X, Y
% 5.45/5.84 ), complement( Y, X ), ! zero ==> multiplication( Y, X ), ! addition( X
% 5.45/5.84 , Y ) ==> one }.
% 5.45/5.84 parent0[1]: (20587) {G0,W11,D3,L3,V2,M3} { ! zero ==> multiplication( X, Y
% 5.45/5.84 ), ! alpha1( X, Y ), complement( Y, X ) }.
% 5.45/5.84 parent1[2]: (20584) {G0,W13,D3,L3,V2,M3} { ! zero ==> multiplication( X, Y
% 5.45/5.84 ), ! addition( Y, X ) ==> one, alpha1( Y, X ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := X
% 5.45/5.84 Y := Y
% 5.45/5.84 end
% 5.45/5.84 substitution1:
% 5.45/5.84 X := Y
% 5.45/5.84 Y := X
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 eqswap: (20591) {G1,W18,D3,L4,V2,M4} { ! one ==> addition( X, Y ), ! zero
% 5.45/5.84 ==> multiplication( X, Y ), complement( Y, X ), ! zero ==> multiplication
% 5.45/5.84 ( Y, X ) }.
% 5.45/5.84 parent0[3]: (20588) {G1,W18,D3,L4,V2,M4} { ! zero ==> multiplication( X, Y
% 5.45/5.84 ), complement( Y, X ), ! zero ==> multiplication( Y, X ), ! addition( X
% 5.45/5.84 , Y ) ==> one }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := X
% 5.45/5.84 Y := Y
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 eqswap: (20593) {G1,W18,D3,L4,V2,M4} { ! multiplication( X, Y ) ==> zero,
% 5.45/5.84 ! one ==> addition( Y, X ), ! zero ==> multiplication( Y, X ), complement
% 5.45/5.84 ( X, Y ) }.
% 5.45/5.84 parent0[3]: (20591) {G1,W18,D3,L4,V2,M4} { ! one ==> addition( X, Y ), !
% 5.45/5.84 zero ==> multiplication( X, Y ), complement( Y, X ), ! zero ==>
% 5.45/5.84 multiplication( Y, X ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := Y
% 5.45/5.84 Y := X
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 eqswap: (20594) {G1,W18,D3,L4,V2,M4} { ! multiplication( X, Y ) ==> zero,
% 5.45/5.84 ! multiplication( Y, X ) ==> zero, ! one ==> addition( X, Y ), complement
% 5.45/5.84 ( Y, X ) }.
% 5.45/5.84 parent0[2]: (20593) {G1,W18,D3,L4,V2,M4} { ! multiplication( X, Y ) ==>
% 5.45/5.84 zero, ! one ==> addition( Y, X ), ! zero ==> multiplication( Y, X ),
% 5.45/5.84 complement( X, Y ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := Y
% 5.45/5.84 Y := X
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 eqswap: (20595) {G1,W18,D3,L4,V2,M4} { ! addition( X, Y ) ==> one, !
% 5.45/5.84 multiplication( X, Y ) ==> zero, ! multiplication( Y, X ) ==> zero,
% 5.45/5.84 complement( Y, X ) }.
% 5.45/5.84 parent0[2]: (20594) {G1,W18,D3,L4,V2,M4} { ! multiplication( X, Y ) ==>
% 5.45/5.84 zero, ! multiplication( Y, X ) ==> zero, ! one ==> addition( X, Y ),
% 5.45/5.84 complement( Y, X ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := X
% 5.45/5.84 Y := Y
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 subsumption: (282) {G1,W18,D3,L4,V2,M4} R(20,17) { ! multiplication( X, Y )
% 5.45/5.84 ==> zero, ! addition( Y, X ) ==> one, ! multiplication( Y, X ) ==> zero
% 5.45/5.84 , complement( X, Y ) }.
% 5.45/5.84 parent0: (20595) {G1,W18,D3,L4,V2,M4} { ! addition( X, Y ) ==> one, !
% 5.45/5.84 multiplication( X, Y ) ==> zero, ! multiplication( Y, X ) ==> zero,
% 5.45/5.84 complement( Y, X ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := Y
% 5.45/5.84 Y := X
% 5.45/5.84 end
% 5.45/5.84 permutation0:
% 5.45/5.84 0 ==> 1
% 5.45/5.84 1 ==> 2
% 5.45/5.84 2 ==> 0
% 5.45/5.84 3 ==> 3
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 eqswap: (20600) {G0,W24,D7,L1,V0,M1} { ! addition( multiplication( skol2,
% 5.45/5.84 skol4 ), multiplication( c( skol2 ), skol6 ) ) ==> addition(
% 5.45/5.84 multiplication( skol2, addition( multiplication( skol2, skol4 ),
% 5.45/5.84 multiplication( c( skol2 ), skol5 ) ) ), multiplication( c( skol2 ),
% 5.45/5.84 skol6 ) ) }.
% 5.45/5.84 parent0[0]: (28) {G0,W24,D7,L1,V0,M1} I { ! addition( multiplication( skol2
% 5.45/5.84 , addition( multiplication( skol2, skol4 ), multiplication( c( skol2 ),
% 5.45/5.84 skol5 ) ) ), multiplication( c( skol2 ), skol6 ) ) ==> addition(
% 5.45/5.84 multiplication( skol2, skol4 ), multiplication( c( skol2 ), skol6 ) ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 paramod: (20603) {G1,W24,D7,L1,V0,M1} { ! addition( multiplication( skol2
% 5.45/5.84 , skol4 ), multiplication( c( skol2 ), skol6 ) ) ==> addition(
% 5.45/5.84 multiplication( skol2, addition( multiplication( c( skol2 ), skol5 ),
% 5.45/5.84 multiplication( skol2, skol4 ) ) ), multiplication( c( skol2 ), skol6 ) )
% 5.45/5.84 }.
% 5.45/5.84 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 5.45/5.84 }.
% 5.45/5.84 parent1[0; 13]: (20600) {G0,W24,D7,L1,V0,M1} { ! addition( multiplication
% 5.45/5.84 ( skol2, skol4 ), multiplication( c( skol2 ), skol6 ) ) ==> addition(
% 5.45/5.84 multiplication( skol2, addition( multiplication( skol2, skol4 ),
% 5.45/5.84 multiplication( c( skol2 ), skol5 ) ) ), multiplication( c( skol2 ),
% 5.45/5.84 skol6 ) ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := multiplication( skol2, skol4 )
% 5.45/5.84 Y := multiplication( c( skol2 ), skol5 )
% 5.45/5.84 end
% 5.45/5.84 substitution1:
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 eqswap: (20616) {G1,W24,D7,L1,V0,M1} { ! addition( multiplication( skol2,
% 5.45/5.84 addition( multiplication( c( skol2 ), skol5 ), multiplication( skol2,
% 5.45/5.84 skol4 ) ) ), multiplication( c( skol2 ), skol6 ) ) ==> addition(
% 5.45/5.84 multiplication( skol2, skol4 ), multiplication( c( skol2 ), skol6 ) ) }.
% 5.45/5.84 parent0[0]: (20603) {G1,W24,D7,L1,V0,M1} { ! addition( multiplication(
% 5.45/5.84 skol2, skol4 ), multiplication( c( skol2 ), skol6 ) ) ==> addition(
% 5.45/5.84 multiplication( skol2, addition( multiplication( c( skol2 ), skol5 ),
% 5.45/5.84 multiplication( skol2, skol4 ) ) ), multiplication( c( skol2 ), skol6 ) )
% 5.45/5.84 }.
% 5.45/5.84 substitution0:
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 subsumption: (541) {G1,W24,D7,L1,V0,M1} P(0,28) { ! addition(
% 5.45/5.84 multiplication( skol2, addition( multiplication( c( skol2 ), skol5 ),
% 5.45/5.84 multiplication( skol2, skol4 ) ) ), multiplication( c( skol2 ), skol6 ) )
% 5.45/5.84 ==> addition( multiplication( skol2, skol4 ), multiplication( c( skol2 )
% 5.45/5.84 , skol6 ) ) }.
% 5.45/5.84 parent0: (20616) {G1,W24,D7,L1,V0,M1} { ! addition( multiplication( skol2
% 5.45/5.84 , addition( multiplication( c( skol2 ), skol5 ), multiplication( skol2,
% 5.45/5.84 skol4 ) ) ), multiplication( c( skol2 ), skol6 ) ) ==> addition(
% 5.45/5.84 multiplication( skol2, skol4 ), multiplication( c( skol2 ), skol6 ) ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 end
% 5.45/5.84 permutation0:
% 5.45/5.84 0 ==> 0
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 eqswap: (20617) {G3,W6,D4,L1,V0,M1} { one ==> addition( skol2, skol1(
% 5.45/5.84 skol2 ) ) }.
% 5.45/5.84 parent0[0]: (263) {G3,W6,D4,L1,V0,M1} R(19,187) { addition( skol2, skol1(
% 5.45/5.84 skol2 ) ) ==> one }.
% 5.45/5.84 substitution0:
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 paramod: (20618) {G1,W6,D4,L1,V0,M1} { one ==> addition( skol1( skol2 ),
% 5.45/5.84 skol2 ) }.
% 5.45/5.84 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 5.45/5.84 }.
% 5.45/5.84 parent1[0; 2]: (20617) {G3,W6,D4,L1,V0,M1} { one ==> addition( skol2,
% 5.45/5.84 skol1( skol2 ) ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := skol2
% 5.45/5.84 Y := skol1( skol2 )
% 5.45/5.84 end
% 5.45/5.84 substitution1:
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 eqswap: (20621) {G1,W6,D4,L1,V0,M1} { addition( skol1( skol2 ), skol2 )
% 5.45/5.84 ==> one }.
% 5.45/5.84 parent0[0]: (20618) {G1,W6,D4,L1,V0,M1} { one ==> addition( skol1( skol2 )
% 5.45/5.84 , skol2 ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 subsumption: (3705) {G4,W6,D4,L1,V0,M1} P(263,0) { addition( skol1( skol2 )
% 5.45/5.84 , skol2 ) ==> one }.
% 5.45/5.84 parent0: (20621) {G1,W6,D4,L1,V0,M1} { addition( skol1( skol2 ), skol2 )
% 5.45/5.84 ==> one }.
% 5.45/5.84 substitution0:
% 5.45/5.84 end
% 5.45/5.84 permutation0:
% 5.45/5.84 0 ==> 0
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 eqswap: (20622) {G2,W6,D4,L1,V0,M1} { zero ==> multiplication( skol2,
% 5.45/5.84 skol1( skol2 ) ) }.
% 5.45/5.84 parent0[0]: (195) {G2,W6,D4,L1,V0,M1} R(15,183) { multiplication( skol2,
% 5.45/5.84 skol1( skol2 ) ) ==> zero }.
% 5.45/5.84 substitution0:
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 eqswap: (20623) {G0,W13,D3,L3,V2,M3} { ! zero ==> multiplication( X, Y ),
% 5.45/5.84 ! addition( Y, X ) ==> one, alpha1( Y, X ) }.
% 5.45/5.84 parent0[0]: (20) {G0,W13,D3,L3,V2,M3} I { ! multiplication( Y, X ) ==> zero
% 5.45/5.84 , ! addition( X, Y ) ==> one, alpha1( X, Y ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := Y
% 5.45/5.84 Y := X
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 resolution: (20627) {G1,W10,D4,L2,V0,M2} { ! addition( skol1( skol2 ),
% 5.45/5.84 skol2 ) ==> one, alpha1( skol1( skol2 ), skol2 ) }.
% 5.45/5.84 parent0[0]: (20623) {G0,W13,D3,L3,V2,M3} { ! zero ==> multiplication( X, Y
% 5.45/5.84 ), ! addition( Y, X ) ==> one, alpha1( Y, X ) }.
% 5.45/5.84 parent1[0]: (20622) {G2,W6,D4,L1,V0,M1} { zero ==> multiplication( skol2,
% 5.45/5.84 skol1( skol2 ) ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := skol2
% 5.45/5.84 Y := skol1( skol2 )
% 5.45/5.84 end
% 5.45/5.84 substitution1:
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 paramod: (20628) {G2,W7,D3,L2,V0,M2} { ! one ==> one, alpha1( skol1( skol2
% 5.45/5.84 ), skol2 ) }.
% 5.45/5.84 parent0[0]: (3705) {G4,W6,D4,L1,V0,M1} P(263,0) { addition( skol1( skol2 )
% 5.45/5.84 , skol2 ) ==> one }.
% 5.45/5.84 parent1[0; 2]: (20627) {G1,W10,D4,L2,V0,M2} { ! addition( skol1( skol2 ),
% 5.45/5.84 skol2 ) ==> one, alpha1( skol1( skol2 ), skol2 ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 end
% 5.45/5.84 substitution1:
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 eqrefl: (20629) {G0,W4,D3,L1,V0,M1} { alpha1( skol1( skol2 ), skol2 ) }.
% 5.45/5.84 parent0[0]: (20628) {G2,W7,D3,L2,V0,M2} { ! one ==> one, alpha1( skol1(
% 5.45/5.84 skol2 ), skol2 ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 subsumption: (5003) {G5,W4,D3,L1,V0,M1} R(195,20);d(3705);q { alpha1( skol1
% 5.45/5.84 ( skol2 ), skol2 ) }.
% 5.45/5.84 parent0: (20629) {G0,W4,D3,L1,V0,M1} { alpha1( skol1( skol2 ), skol2 ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 end
% 5.45/5.84 permutation0:
% 5.45/5.84 0 ==> 0
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 eqswap: (20631) {G1,W17,D5,L1,V4,M1} { multiplication( X, addition(
% 5.45/5.84 multiplication( Y, Z ), T ) ) ==> addition( multiplication(
% 5.45/5.84 multiplication( X, Y ), Z ), multiplication( X, T ) ) }.
% 5.45/5.84 parent0[0]: (48) {G1,W17,D5,L1,V4,M1} P(4,7) { addition( multiplication(
% 5.45/5.84 multiplication( X, Y ), Z ), multiplication( X, T ) ) ==> multiplication
% 5.45/5.84 ( X, addition( multiplication( Y, Z ), T ) ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := X
% 5.45/5.84 Y := Y
% 5.45/5.84 Z := Z
% 5.45/5.84 T := T
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 paramod: (20635) {G2,W16,D6,L1,V2,M1} { multiplication( skol2, addition(
% 5.45/5.84 multiplication( skol1( skol2 ), X ), Y ) ) ==> addition( multiplication(
% 5.45/5.84 zero, X ), multiplication( skol2, Y ) ) }.
% 5.45/5.84 parent0[0]: (195) {G2,W6,D4,L1,V0,M1} R(15,183) { multiplication( skol2,
% 5.45/5.84 skol1( skol2 ) ) ==> zero }.
% 5.45/5.84 parent1[0; 11]: (20631) {G1,W17,D5,L1,V4,M1} { multiplication( X, addition
% 5.45/5.84 ( multiplication( Y, Z ), T ) ) ==> addition( multiplication(
% 5.45/5.84 multiplication( X, Y ), Z ), multiplication( X, T ) ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 end
% 5.45/5.84 substitution1:
% 5.45/5.84 X := skol2
% 5.45/5.84 Y := skol1( skol2 )
% 5.45/5.84 Z := X
% 5.45/5.84 T := Y
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 paramod: (20637) {G1,W14,D6,L1,V2,M1} { multiplication( skol2, addition(
% 5.45/5.84 multiplication( skol1( skol2 ), X ), Y ) ) ==> addition( zero,
% 5.45/5.84 multiplication( skol2, Y ) ) }.
% 5.45/5.84 parent0[0]: (10) {G0,W5,D3,L1,V1,M1} I { multiplication( zero, X ) ==> zero
% 5.45/5.84 }.
% 5.45/5.84 parent1[0; 10]: (20635) {G2,W16,D6,L1,V2,M1} { multiplication( skol2,
% 5.45/5.84 addition( multiplication( skol1( skol2 ), X ), Y ) ) ==> addition(
% 5.45/5.84 multiplication( zero, X ), multiplication( skol2, Y ) ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := X
% 5.45/5.84 end
% 5.45/5.84 substitution1:
% 5.45/5.84 X := X
% 5.45/5.84 Y := Y
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 paramod: (20638) {G2,W12,D6,L1,V2,M1} { multiplication( skol2, addition(
% 5.45/5.84 multiplication( skol1( skol2 ), X ), Y ) ) ==> multiplication( skol2, Y )
% 5.45/5.84 }.
% 5.45/5.84 parent0[0]: (32) {G1,W5,D3,L1,V1,M1} P(2,0) { addition( zero, X ) ==> X }.
% 5.45/5.84 parent1[0; 9]: (20637) {G1,W14,D6,L1,V2,M1} { multiplication( skol2,
% 5.45/5.84 addition( multiplication( skol1( skol2 ), X ), Y ) ) ==> addition( zero,
% 5.45/5.84 multiplication( skol2, Y ) ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := multiplication( skol2, Y )
% 5.45/5.84 end
% 5.45/5.84 substitution1:
% 5.45/5.84 X := X
% 5.45/5.84 Y := Y
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 subsumption: (5012) {G3,W12,D6,L1,V2,M1} P(195,48);d(10);d(32) {
% 5.45/5.84 multiplication( skol2, addition( multiplication( skol1( skol2 ), X ), Y )
% 5.45/5.84 ) ==> multiplication( skol2, Y ) }.
% 5.45/5.84 parent0: (20638) {G2,W12,D6,L1,V2,M1} { multiplication( skol2, addition(
% 5.45/5.84 multiplication( skol1( skol2 ), X ), Y ) ) ==> multiplication( skol2, Y )
% 5.45/5.84 }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := X
% 5.45/5.84 Y := Y
% 5.45/5.84 end
% 5.45/5.84 permutation0:
% 5.45/5.84 0 ==> 0
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 eqswap: (20640) {G0,W11,D3,L3,V2,M3} { ! zero ==> multiplication( X, Y ),
% 5.45/5.84 ! alpha1( X, Y ), complement( Y, X ) }.
% 5.45/5.84 parent0[0]: (17) {G0,W11,D3,L3,V2,M3} I { ! multiplication( X, Y ) ==> zero
% 5.45/5.84 , ! alpha1( X, Y ), complement( Y, X ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := X
% 5.45/5.84 Y := Y
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 resolution: (20642) {G1,W10,D4,L2,V0,M2} { ! zero ==> multiplication(
% 5.45/5.84 skol1( skol2 ), skol2 ), complement( skol2, skol1( skol2 ) ) }.
% 5.45/5.84 parent0[1]: (20640) {G0,W11,D3,L3,V2,M3} { ! zero ==> multiplication( X, Y
% 5.45/5.84 ), ! alpha1( X, Y ), complement( Y, X ) }.
% 5.45/5.84 parent1[0]: (5003) {G5,W4,D3,L1,V0,M1} R(195,20);d(3705);q { alpha1( skol1
% 5.45/5.84 ( skol2 ), skol2 ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := skol1( skol2 )
% 5.45/5.84 Y := skol2
% 5.45/5.84 end
% 5.45/5.84 substitution1:
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 paramod: (20643) {G2,W7,D3,L2,V0,M2} { ! zero ==> zero, complement( skol2
% 5.45/5.84 , skol1( skol2 ) ) }.
% 5.45/5.84 parent0[0]: (237) {G3,W6,D4,L1,V0,M1} R(18,187) { multiplication( skol1(
% 5.45/5.84 skol2 ), skol2 ) ==> zero }.
% 5.45/5.84 parent1[0; 3]: (20642) {G1,W10,D4,L2,V0,M2} { ! zero ==> multiplication(
% 5.45/5.84 skol1( skol2 ), skol2 ), complement( skol2, skol1( skol2 ) ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 end
% 5.45/5.84 substitution1:
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 eqrefl: (20644) {G0,W4,D3,L1,V0,M1} { complement( skol2, skol1( skol2 ) )
% 5.45/5.84 }.
% 5.45/5.84 parent0[0]: (20643) {G2,W7,D3,L2,V0,M2} { ! zero ==> zero, complement(
% 5.45/5.84 skol2, skol1( skol2 ) ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 subsumption: (5014) {G6,W4,D3,L1,V0,M1} R(5003,17);d(237);q { complement(
% 5.45/5.84 skol2, skol1( skol2 ) ) }.
% 5.45/5.84 parent0: (20644) {G0,W4,D3,L1,V0,M1} { complement( skol2, skol1( skol2 ) )
% 5.45/5.84 }.
% 5.45/5.84 substitution0:
% 5.45/5.84 end
% 5.45/5.84 permutation0:
% 5.45/5.84 0 ==> 0
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 resolution: (20645) {G2,W6,D4,L1,V0,M1} { complement( skol1( skol1( skol2
% 5.45/5.84 ) ), skol1( skol2 ) ) }.
% 5.45/5.84 parent0[1]: (182) {G1,W7,D3,L2,V2,M2} R(13,14) { complement( skol1( X ), X
% 5.45/5.84 ), ! complement( Y, X ) }.
% 5.45/5.84 parent1[0]: (5014) {G6,W4,D3,L1,V0,M1} R(5003,17);d(237);q { complement(
% 5.45/5.84 skol2, skol1( skol2 ) ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := skol1( skol2 )
% 5.45/5.84 Y := skol2
% 5.45/5.84 end
% 5.45/5.84 substitution1:
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 subsumption: (5015) {G7,W6,D4,L1,V0,M1} R(5014,182) { complement( skol1(
% 5.45/5.84 skol1( skol2 ) ), skol1( skol2 ) ) }.
% 5.45/5.84 parent0: (20645) {G2,W6,D4,L1,V0,M1} { complement( skol1( skol1( skol2 ) )
% 5.45/5.84 , skol1( skol2 ) ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 end
% 5.45/5.84 permutation0:
% 5.45/5.84 0 ==> 0
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 eqswap: (20646) {G0,W9,D3,L3,V2,M3} { Y = c( X ), ! test( X ), !
% 5.45/5.84 complement( X, Y ) }.
% 5.45/5.84 parent0[2]: (22) {G0,W9,D3,L3,V2,M3} I { ! test( X ), ! complement( X, Y )
% 5.45/5.84 , c( X ) = Y }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := X
% 5.45/5.84 Y := Y
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 resolution: (20647) {G1,W7,D3,L2,V0,M2} { skol1( skol2 ) = c( skol2 ), !
% 5.45/5.84 test( skol2 ) }.
% 5.45/5.84 parent0[2]: (20646) {G0,W9,D3,L3,V2,M3} { Y = c( X ), ! test( X ), !
% 5.45/5.84 complement( X, Y ) }.
% 5.45/5.84 parent1[0]: (5014) {G6,W4,D3,L1,V0,M1} R(5003,17);d(237);q { complement(
% 5.45/5.84 skol2, skol1( skol2 ) ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := skol2
% 5.45/5.84 Y := skol1( skol2 )
% 5.45/5.84 end
% 5.45/5.84 substitution1:
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 resolution: (20648) {G1,W5,D3,L1,V0,M1} { skol1( skol2 ) = c( skol2 ) }.
% 5.45/5.84 parent0[1]: (20647) {G1,W7,D3,L2,V0,M2} { skol1( skol2 ) = c( skol2 ), !
% 5.45/5.84 test( skol2 ) }.
% 5.45/5.84 parent1[0]: (26) {G0,W2,D2,L1,V0,M1} I { test( skol2 ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 end
% 5.45/5.84 substitution1:
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 eqswap: (20649) {G1,W5,D3,L1,V0,M1} { c( skol2 ) = skol1( skol2 ) }.
% 5.45/5.84 parent0[0]: (20648) {G1,W5,D3,L1,V0,M1} { skol1( skol2 ) = c( skol2 ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 subsumption: (5022) {G7,W5,D3,L1,V0,M1} R(5014,22);r(26) { c( skol2 ) ==>
% 5.45/5.84 skol1( skol2 ) }.
% 5.45/5.84 parent0: (20649) {G1,W5,D3,L1,V0,M1} { c( skol2 ) = skol1( skol2 ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 end
% 5.45/5.84 permutation0:
% 5.45/5.84 0 ==> 0
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 resolution: (20650) {G1,W3,D3,L1,V0,M1} { test( skol1( skol2 ) ) }.
% 5.45/5.84 parent0[0]: (14) {G0,W5,D2,L2,V2,M2} I { ! complement( Y, X ), test( X )
% 5.45/5.84 }.
% 5.45/5.84 parent1[0]: (5014) {G6,W4,D3,L1,V0,M1} R(5003,17);d(237);q { complement(
% 5.45/5.84 skol2, skol1( skol2 ) ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := skol1( skol2 )
% 5.45/5.84 Y := skol2
% 5.45/5.84 end
% 5.45/5.84 substitution1:
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 subsumption: (5024) {G7,W3,D3,L1,V0,M1} R(5014,14) { test( skol1( skol2 ) )
% 5.45/5.84 }.
% 5.45/5.84 parent0: (20650) {G1,W3,D3,L1,V0,M1} { test( skol1( skol2 ) ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 end
% 5.45/5.84 permutation0:
% 5.45/5.84 0 ==> 0
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 eqswap: (20651) {G1,W10,D4,L2,V1,M2} { c( X ) ==> multiplication( c( X ),
% 5.45/5.84 c( X ) ), ! test( X ) }.
% 5.45/5.84 parent0[1]: (30) {G1,W10,D4,L2,V1,M2} F(24);d(3) { ! test( X ),
% 5.45/5.84 multiplication( c( X ), c( X ) ) ==> c( X ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := X
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 resolution: (20652) {G2,W11,D5,L1,V0,M1} { c( skol1( skol2 ) ) ==>
% 5.45/5.84 multiplication( c( skol1( skol2 ) ), c( skol1( skol2 ) ) ) }.
% 5.45/5.84 parent0[1]: (20651) {G1,W10,D4,L2,V1,M2} { c( X ) ==> multiplication( c( X
% 5.45/5.84 ), c( X ) ), ! test( X ) }.
% 5.45/5.84 parent1[0]: (5024) {G7,W3,D3,L1,V0,M1} R(5014,14) { test( skol1( skol2 ) )
% 5.45/5.84 }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := skol1( skol2 )
% 5.45/5.84 end
% 5.45/5.84 substitution1:
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 eqswap: (20653) {G2,W11,D5,L1,V0,M1} { multiplication( c( skol1( skol2 ) )
% 5.45/5.84 , c( skol1( skol2 ) ) ) ==> c( skol1( skol2 ) ) }.
% 5.45/5.84 parent0[0]: (20652) {G2,W11,D5,L1,V0,M1} { c( skol1( skol2 ) ) ==>
% 5.45/5.84 multiplication( c( skol1( skol2 ) ), c( skol1( skol2 ) ) ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 subsumption: (5035) {G8,W11,D5,L1,V0,M1} R(5024,30) { multiplication( c(
% 5.45/5.84 skol1( skol2 ) ), c( skol1( skol2 ) ) ) ==> c( skol1( skol2 ) ) }.
% 5.45/5.84 parent0: (20653) {G2,W11,D5,L1,V0,M1} { multiplication( c( skol1( skol2 )
% 5.45/5.84 ), c( skol1( skol2 ) ) ) ==> c( skol1( skol2 ) ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 end
% 5.45/5.84 permutation0:
% 5.45/5.84 0 ==> 0
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 eqswap: (20654) {G1,W8,D3,L2,V2,M2} { one ==> addition( X, Y ), !
% 5.45/5.84 complement( Y, X ) }.
% 5.45/5.84 parent0[0]: (267) {G1,W8,D3,L2,V2,M2} R(19,16) { addition( X, Y ) ==> one,
% 5.45/5.84 ! complement( Y, X ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := X
% 5.45/5.84 Y := Y
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 paramod: (20655) {G1,W8,D3,L2,V2,M2} { one ==> addition( Y, X ), !
% 5.45/5.84 complement( Y, X ) }.
% 5.45/5.84 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 5.45/5.84 }.
% 5.45/5.84 parent1[0; 2]: (20654) {G1,W8,D3,L2,V2,M2} { one ==> addition( X, Y ), !
% 5.45/5.84 complement( Y, X ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := X
% 5.45/5.84 Y := Y
% 5.45/5.84 end
% 5.45/5.84 substitution1:
% 5.45/5.84 X := X
% 5.45/5.84 Y := Y
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 eqswap: (20658) {G1,W8,D3,L2,V2,M2} { addition( X, Y ) ==> one, !
% 5.45/5.84 complement( X, Y ) }.
% 5.45/5.84 parent0[0]: (20655) {G1,W8,D3,L2,V2,M2} { one ==> addition( Y, X ), !
% 5.45/5.84 complement( Y, X ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := Y
% 5.45/5.84 Y := X
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 subsumption: (6662) {G2,W8,D3,L2,V2,M2} P(267,0) { addition( Y, X ) ==> one
% 5.45/5.84 , ! complement( Y, X ) }.
% 5.45/5.84 parent0: (20658) {G1,W8,D3,L2,V2,M2} { addition( X, Y ) ==> one, !
% 5.45/5.84 complement( X, Y ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := Y
% 5.45/5.84 Y := X
% 5.45/5.84 end
% 5.45/5.84 permutation0:
% 5.45/5.84 0 ==> 0
% 5.45/5.84 1 ==> 1
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 eqswap: (20659) {G1,W18,D3,L4,V2,M4} { ! zero ==> multiplication( X, Y ),
% 5.45/5.84 ! addition( Y, X ) ==> one, ! multiplication( Y, X ) ==> zero, complement
% 5.45/5.84 ( X, Y ) }.
% 5.45/5.84 parent0[0]: (282) {G1,W18,D3,L4,V2,M4} R(20,17) { ! multiplication( X, Y )
% 5.45/5.84 ==> zero, ! addition( Y, X ) ==> one, ! multiplication( Y, X ) ==> zero,
% 5.45/5.84 complement( X, Y ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := X
% 5.45/5.84 Y := Y
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 resolution: (21335) {G2,W16,D3,L4,V2,M4} { ! zero ==> multiplication( X, Y
% 5.45/5.84 ), ! addition( Y, X ) ==> one, complement( X, Y ), ! complement( Y, X )
% 5.45/5.84 }.
% 5.45/5.84 parent0[2]: (20659) {G1,W18,D3,L4,V2,M4} { ! zero ==> multiplication( X, Y
% 5.45/5.84 ), ! addition( Y, X ) ==> one, ! multiplication( Y, X ) ==> zero,
% 5.45/5.84 complement( X, Y ) }.
% 5.45/5.84 parent1[0]: (240) {G1,W8,D3,L2,V2,M2} R(18,16) { multiplication( X, Y ) ==>
% 5.45/5.84 zero, ! complement( X, Y ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := X
% 5.45/5.84 Y := Y
% 5.45/5.84 end
% 5.45/5.84 substitution1:
% 5.45/5.84 X := Y
% 5.45/5.84 Y := X
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 paramod: (21336) {G1,W17,D3,L5,V2,M5} { ! zero ==> zero, ! complement( Y,
% 5.45/5.84 X ), ! addition( Y, X ) ==> one, complement( X, Y ), ! complement( Y, X )
% 5.45/5.84 }.
% 5.45/5.84 parent0[1]: (15) {G0,W8,D3,L2,V2,M2} I { ! complement( Y, X ),
% 5.45/5.84 multiplication( X, Y ) ==> zero }.
% 5.45/5.84 parent1[0; 3]: (21335) {G2,W16,D3,L4,V2,M4} { ! zero ==> multiplication( X
% 5.45/5.84 , Y ), ! addition( Y, X ) ==> one, complement( X, Y ), ! complement( Y, X
% 5.45/5.84 ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := X
% 5.45/5.84 Y := Y
% 5.45/5.84 end
% 5.45/5.84 substitution1:
% 5.45/5.84 X := X
% 5.45/5.84 Y := Y
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 factor: (21337) {G1,W14,D3,L4,V2,M4} { ! zero ==> zero, ! complement( X, Y
% 5.45/5.84 ), ! addition( X, Y ) ==> one, complement( Y, X ) }.
% 5.45/5.84 parent0[1, 4]: (21336) {G1,W17,D3,L5,V2,M5} { ! zero ==> zero, !
% 5.45/5.84 complement( Y, X ), ! addition( Y, X ) ==> one, complement( X, Y ), !
% 5.45/5.84 complement( Y, X ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := Y
% 5.45/5.84 Y := X
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 paramod: (21338) {G2,W15,D2,L5,V2,M5} { ! one ==> one, ! complement( X, Y
% 5.45/5.84 ), ! zero ==> zero, ! complement( X, Y ), complement( Y, X ) }.
% 5.45/5.84 parent0[0]: (6662) {G2,W8,D3,L2,V2,M2} P(267,0) { addition( Y, X ) ==> one
% 5.45/5.84 , ! complement( Y, X ) }.
% 5.45/5.84 parent1[2; 2]: (21337) {G1,W14,D3,L4,V2,M4} { ! zero ==> zero, !
% 5.45/5.84 complement( X, Y ), ! addition( X, Y ) ==> one, complement( Y, X ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := Y
% 5.45/5.84 Y := X
% 5.45/5.84 end
% 5.45/5.84 substitution1:
% 5.45/5.84 X := X
% 5.45/5.84 Y := Y
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 factor: (21339) {G2,W12,D2,L4,V2,M4} { ! one ==> one, ! complement( X, Y )
% 5.45/5.84 , ! zero ==> zero, complement( Y, X ) }.
% 5.45/5.84 parent0[1, 3]: (21338) {G2,W15,D2,L5,V2,M5} { ! one ==> one, ! complement
% 5.45/5.84 ( X, Y ), ! zero ==> zero, ! complement( X, Y ), complement( Y, X ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := X
% 5.45/5.84 Y := Y
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 eqrefl: (21340) {G0,W9,D2,L3,V2,M3} { ! complement( X, Y ), ! zero ==>
% 5.45/5.84 zero, complement( Y, X ) }.
% 5.45/5.84 parent0[0]: (21339) {G2,W12,D2,L4,V2,M4} { ! one ==> one, ! complement( X
% 5.45/5.84 , Y ), ! zero ==> zero, complement( Y, X ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := X
% 5.45/5.84 Y := Y
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 eqrefl: (21342) {G0,W6,D2,L2,V2,M2} { ! complement( X, Y ), complement( Y
% 5.45/5.84 , X ) }.
% 5.45/5.84 parent0[1]: (21340) {G0,W9,D2,L3,V2,M3} { ! complement( X, Y ), ! zero ==>
% 5.45/5.84 zero, complement( Y, X ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := X
% 5.45/5.84 Y := Y
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 subsumption: (7372) {G3,W6,D2,L2,V2,M2} R(282,240);d(15);d(6662);q;q {
% 5.45/5.84 complement( X, Y ), ! complement( Y, X ) }.
% 5.45/5.84 parent0: (21342) {G0,W6,D2,L2,V2,M2} { ! complement( X, Y ), complement( Y
% 5.45/5.84 , X ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := Y
% 5.45/5.84 Y := X
% 5.45/5.84 end
% 5.45/5.84 permutation0:
% 5.45/5.84 0 ==> 1
% 5.45/5.84 1 ==> 0
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 resolution: (21343) {G4,W6,D4,L1,V0,M1} { complement( skol1( skol2 ),
% 5.45/5.84 skol1( skol1( skol2 ) ) ) }.
% 5.45/5.84 parent0[1]: (7372) {G3,W6,D2,L2,V2,M2} R(282,240);d(15);d(6662);q;q {
% 5.45/5.84 complement( X, Y ), ! complement( Y, X ) }.
% 5.45/5.84 parent1[0]: (5015) {G7,W6,D4,L1,V0,M1} R(5014,182) { complement( skol1(
% 5.45/5.84 skol1( skol2 ) ), skol1( skol2 ) ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := skol1( skol2 )
% 5.45/5.84 Y := skol1( skol1( skol2 ) )
% 5.45/5.84 end
% 5.45/5.84 substitution1:
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 subsumption: (7392) {G8,W6,D4,L1,V0,M1} R(7372,5015) { complement( skol1(
% 5.45/5.84 skol2 ), skol1( skol1( skol2 ) ) ) }.
% 5.45/5.84 parent0: (21343) {G4,W6,D4,L1,V0,M1} { complement( skol1( skol2 ), skol1(
% 5.45/5.84 skol1( skol2 ) ) ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 end
% 5.45/5.84 permutation0:
% 5.45/5.84 0 ==> 0
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 resolution: (21344) {G1,W5,D2,L2,V2,M2} { test( Y ), ! complement( Y, X )
% 5.45/5.84 }.
% 5.45/5.84 parent0[0]: (14) {G0,W5,D2,L2,V2,M2} I { ! complement( Y, X ), test( X )
% 5.45/5.84 }.
% 5.45/5.84 parent1[0]: (7372) {G3,W6,D2,L2,V2,M2} R(282,240);d(15);d(6662);q;q {
% 5.45/5.84 complement( X, Y ), ! complement( Y, X ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := Y
% 5.45/5.84 Y := X
% 5.45/5.84 end
% 5.45/5.84 substitution1:
% 5.45/5.84 X := X
% 5.45/5.84 Y := Y
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 subsumption: (7417) {G4,W5,D2,L2,V2,M2} R(7372,14) { ! complement( X, Y ),
% 5.45/5.84 test( X ) }.
% 5.45/5.84 parent0: (21344) {G1,W5,D2,L2,V2,M2} { test( Y ), ! complement( Y, X ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := Y
% 5.45/5.84 Y := X
% 5.45/5.84 end
% 5.45/5.84 permutation0:
% 5.45/5.84 0 ==> 1
% 5.45/5.84 1 ==> 0
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 eqswap: (21345) {G0,W9,D3,L3,V2,M3} { Y = c( X ), ! test( X ), !
% 5.45/5.84 complement( X, Y ) }.
% 5.45/5.84 parent0[2]: (22) {G0,W9,D3,L3,V2,M3} I { ! test( X ), ! complement( X, Y )
% 5.45/5.84 , c( X ) = Y }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := X
% 5.45/5.84 Y := Y
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 resolution: (21346) {G1,W10,D3,L3,V3,M3} { X = c( Y ), ! complement( Y, X
% 5.45/5.84 ), ! complement( Y, Z ) }.
% 5.45/5.84 parent0[1]: (21345) {G0,W9,D3,L3,V2,M3} { Y = c( X ), ! test( X ), !
% 5.45/5.84 complement( X, Y ) }.
% 5.45/5.84 parent1[1]: (7417) {G4,W5,D2,L2,V2,M2} R(7372,14) { ! complement( X, Y ),
% 5.45/5.84 test( X ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := Y
% 5.45/5.84 Y := X
% 5.45/5.84 end
% 5.45/5.84 substitution1:
% 5.45/5.84 X := Y
% 5.45/5.84 Y := Z
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 eqswap: (21347) {G1,W10,D3,L3,V3,M3} { c( Y ) = X, ! complement( Y, X ), !
% 5.45/5.84 complement( Y, Z ) }.
% 5.45/5.84 parent0[0]: (21346) {G1,W10,D3,L3,V3,M3} { X = c( Y ), ! complement( Y, X
% 5.45/5.84 ), ! complement( Y, Z ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := X
% 5.45/5.84 Y := Y
% 5.45/5.84 Z := Z
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 subsumption: (7446) {G5,W10,D3,L3,V3,M3} R(7417,22) { ! complement( X, Y )
% 5.45/5.84 , ! complement( X, Z ), c( X ) = Z }.
% 5.45/5.84 parent0: (21347) {G1,W10,D3,L3,V3,M3} { c( Y ) = X, ! complement( Y, X ),
% 5.45/5.84 ! complement( Y, Z ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := Z
% 5.45/5.84 Y := X
% 5.45/5.84 Z := Y
% 5.45/5.84 end
% 5.45/5.84 permutation0:
% 5.45/5.84 0 ==> 2
% 5.45/5.84 1 ==> 1
% 5.45/5.84 2 ==> 0
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 factor: (21351) {G5,W7,D3,L2,V2,M2} { ! complement( X, Y ), c( X ) = Y }.
% 5.45/5.84 parent0[0, 1]: (7446) {G5,W10,D3,L3,V3,M3} R(7417,22) { ! complement( X, Y
% 5.45/5.84 ), ! complement( X, Z ), c( X ) = Z }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := X
% 5.45/5.84 Y := Y
% 5.45/5.84 Z := Y
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 subsumption: (7450) {G6,W7,D3,L2,V2,M2} F(7446) { ! complement( X, Y ), c(
% 5.45/5.84 X ) = Y }.
% 5.45/5.84 parent0: (21351) {G5,W7,D3,L2,V2,M2} { ! complement( X, Y ), c( X ) = Y
% 5.45/5.84 }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := X
% 5.45/5.84 Y := Y
% 5.45/5.84 end
% 5.45/5.84 permutation0:
% 5.45/5.84 0 ==> 0
% 5.45/5.84 1 ==> 1
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 eqswap: (21353) {G6,W7,D3,L2,V2,M2} { Y = c( X ), ! complement( X, Y ) }.
% 5.45/5.84 parent0[1]: (7450) {G6,W7,D3,L2,V2,M2} F(7446) { ! complement( X, Y ), c( X
% 5.45/5.84 ) = Y }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := X
% 5.45/5.84 Y := Y
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 resolution: (21354) {G7,W7,D4,L1,V0,M1} { skol1( skol1( skol2 ) ) = c(
% 5.45/5.84 skol1( skol2 ) ) }.
% 5.45/5.84 parent0[1]: (21353) {G6,W7,D3,L2,V2,M2} { Y = c( X ), ! complement( X, Y )
% 5.45/5.84 }.
% 5.45/5.84 parent1[0]: (7392) {G8,W6,D4,L1,V0,M1} R(7372,5015) { complement( skol1(
% 5.45/5.84 skol2 ), skol1( skol1( skol2 ) ) ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := skol1( skol2 )
% 5.45/5.84 Y := skol1( skol1( skol2 ) )
% 5.45/5.84 end
% 5.45/5.84 substitution1:
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 eqswap: (21355) {G7,W7,D4,L1,V0,M1} { c( skol1( skol2 ) ) = skol1( skol1(
% 5.45/5.84 skol2 ) ) }.
% 5.45/5.84 parent0[0]: (21354) {G7,W7,D4,L1,V0,M1} { skol1( skol1( skol2 ) ) = c(
% 5.45/5.84 skol1( skol2 ) ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 subsumption: (9114) {G9,W7,D4,L1,V0,M1} R(7450,7392) { c( skol1( skol2 ) )
% 5.45/5.84 ==> skol1( skol1( skol2 ) ) }.
% 5.45/5.84 parent0: (21355) {G7,W7,D4,L1,V0,M1} { c( skol1( skol2 ) ) = skol1( skol1
% 5.45/5.84 ( skol2 ) ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 end
% 5.45/5.84 permutation0:
% 5.45/5.84 0 ==> 0
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 eqswap: (21356) {G6,W7,D3,L2,V2,M2} { Y = c( X ), ! complement( X, Y ) }.
% 5.45/5.84 parent0[1]: (7450) {G6,W7,D3,L2,V2,M2} F(7446) { ! complement( X, Y ), c( X
% 5.45/5.84 ) = Y }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := X
% 5.45/5.84 Y := Y
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 resolution: (21358) {G2,W5,D4,L1,V0,M1} { skol2 = c( skol1( skol2 ) ) }.
% 5.45/5.84 parent0[1]: (21356) {G6,W7,D3,L2,V2,M2} { Y = c( X ), ! complement( X, Y )
% 5.45/5.84 }.
% 5.45/5.84 parent1[0]: (183) {G1,W4,D3,L1,V0,M1} R(13,26) { complement( skol1( skol2 )
% 5.45/5.84 , skol2 ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := skol1( skol2 )
% 5.45/5.84 Y := skol2
% 5.45/5.84 end
% 5.45/5.84 substitution1:
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 paramod: (21359) {G3,W5,D4,L1,V0,M1} { skol2 = skol1( skol1( skol2 ) ) }.
% 5.45/5.84 parent0[0]: (9114) {G9,W7,D4,L1,V0,M1} R(7450,7392) { c( skol1( skol2 ) )
% 5.45/5.84 ==> skol1( skol1( skol2 ) ) }.
% 5.45/5.84 parent1[0; 2]: (21358) {G2,W5,D4,L1,V0,M1} { skol2 = c( skol1( skol2 ) )
% 5.45/5.84 }.
% 5.45/5.84 substitution0:
% 5.45/5.84 end
% 5.45/5.84 substitution1:
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 eqswap: (21360) {G3,W5,D4,L1,V0,M1} { skol1( skol1( skol2 ) ) = skol2 }.
% 5.45/5.84 parent0[0]: (21359) {G3,W5,D4,L1,V0,M1} { skol2 = skol1( skol1( skol2 ) )
% 5.45/5.84 }.
% 5.45/5.84 substitution0:
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 subsumption: (9139) {G10,W5,D4,L1,V0,M1} R(7450,183);d(9114) { skol1( skol1
% 5.45/5.84 ( skol2 ) ) ==> skol2 }.
% 5.45/5.84 parent0: (21360) {G3,W5,D4,L1,V0,M1} { skol1( skol1( skol2 ) ) = skol2 }.
% 5.45/5.84 substitution0:
% 5.45/5.84 end
% 5.45/5.84 permutation0:
% 5.45/5.84 0 ==> 0
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 paramod: (21363) {G10,W5,D4,L1,V0,M1} { c( skol1( skol2 ) ) ==> skol2 }.
% 5.45/5.84 parent0[0]: (9139) {G10,W5,D4,L1,V0,M1} R(7450,183);d(9114) { skol1( skol1
% 5.45/5.84 ( skol2 ) ) ==> skol2 }.
% 5.45/5.84 parent1[0; 4]: (9114) {G9,W7,D4,L1,V0,M1} R(7450,7392) { c( skol1( skol2 )
% 5.45/5.84 ) ==> skol1( skol1( skol2 ) ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 end
% 5.45/5.84 substitution1:
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 subsumption: (20032) {G11,W5,D4,L1,V0,M1} S(9114);d(9139) { c( skol1( skol2
% 5.45/5.84 ) ) ==> skol2 }.
% 5.45/5.84 parent0: (21363) {G10,W5,D4,L1,V0,M1} { c( skol1( skol2 ) ) ==> skol2 }.
% 5.45/5.84 substitution0:
% 5.45/5.84 end
% 5.45/5.84 permutation0:
% 5.45/5.84 0 ==> 0
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 paramod: (21369) {G9,W9,D5,L1,V0,M1} { multiplication( c( skol1( skol2 ) )
% 5.45/5.84 , c( skol1( skol2 ) ) ) ==> skol2 }.
% 5.45/5.84 parent0[0]: (20032) {G11,W5,D4,L1,V0,M1} S(9114);d(9139) { c( skol1( skol2
% 5.45/5.84 ) ) ==> skol2 }.
% 5.45/5.84 parent1[0; 8]: (5035) {G8,W11,D5,L1,V0,M1} R(5024,30) { multiplication( c(
% 5.45/5.84 skol1( skol2 ) ), c( skol1( skol2 ) ) ) ==> c( skol1( skol2 ) ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 end
% 5.45/5.84 substitution1:
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 paramod: (21371) {G10,W7,D5,L1,V0,M1} { multiplication( c( skol1( skol2 )
% 5.45/5.84 ), skol2 ) ==> skol2 }.
% 5.45/5.84 parent0[0]: (20032) {G11,W5,D4,L1,V0,M1} S(9114);d(9139) { c( skol1( skol2
% 5.45/5.84 ) ) ==> skol2 }.
% 5.45/5.84 parent1[0; 5]: (21369) {G9,W9,D5,L1,V0,M1} { multiplication( c( skol1(
% 5.45/5.84 skol2 ) ), c( skol1( skol2 ) ) ) ==> skol2 }.
% 5.45/5.84 substitution0:
% 5.45/5.84 end
% 5.45/5.84 substitution1:
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 paramod: (21372) {G11,W5,D3,L1,V0,M1} { multiplication( skol2, skol2 ) ==>
% 5.45/5.84 skol2 }.
% 5.45/5.84 parent0[0]: (20032) {G11,W5,D4,L1,V0,M1} S(9114);d(9139) { c( skol1( skol2
% 5.45/5.84 ) ) ==> skol2 }.
% 5.45/5.84 parent1[0; 2]: (21371) {G10,W7,D5,L1,V0,M1} { multiplication( c( skol1(
% 5.45/5.84 skol2 ) ), skol2 ) ==> skol2 }.
% 5.45/5.84 substitution0:
% 5.45/5.84 end
% 5.45/5.84 substitution1:
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 subsumption: (20165) {G12,W5,D3,L1,V0,M1} S(5035);d(20032) { multiplication
% 5.45/5.84 ( skol2, skol2 ) ==> skol2 }.
% 5.45/5.84 parent0: (21372) {G11,W5,D3,L1,V0,M1} { multiplication( skol2, skol2 ) ==>
% 5.45/5.84 skol2 }.
% 5.45/5.84 substitution0:
% 5.45/5.84 end
% 5.45/5.84 permutation0:
% 5.45/5.84 0 ==> 0
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 paramod: (21388) {G2,W24,D7,L1,V0,M1} { ! addition( multiplication( skol2
% 5.45/5.84 , addition( multiplication( c( skol2 ), skol5 ), multiplication( skol2,
% 5.45/5.84 skol4 ) ) ), multiplication( c( skol2 ), skol6 ) ) ==> addition(
% 5.45/5.84 multiplication( skol2, skol4 ), multiplication( skol1( skol2 ), skol6 ) )
% 5.45/5.84 }.
% 5.45/5.84 parent0[0]: (5022) {G7,W5,D3,L1,V0,M1} R(5014,22);r(26) { c( skol2 ) ==>
% 5.45/5.84 skol1( skol2 ) }.
% 5.45/5.84 parent1[0; 22]: (541) {G1,W24,D7,L1,V0,M1} P(0,28) { ! addition(
% 5.45/5.84 multiplication( skol2, addition( multiplication( c( skol2 ), skol5 ),
% 5.45/5.84 multiplication( skol2, skol4 ) ) ), multiplication( c( skol2 ), skol6 ) )
% 5.45/5.84 ==> addition( multiplication( skol2, skol4 ), multiplication( c( skol2 )
% 5.45/5.84 , skol6 ) ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 end
% 5.45/5.84 substitution1:
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 paramod: (21390) {G3,W24,D7,L1,V0,M1} { ! addition( multiplication( skol2
% 5.45/5.84 , addition( multiplication( c( skol2 ), skol5 ), multiplication( skol2,
% 5.45/5.84 skol4 ) ) ), multiplication( skol1( skol2 ), skol6 ) ) ==> addition(
% 5.45/5.84 multiplication( skol2, skol4 ), multiplication( skol1( skol2 ), skol6 ) )
% 5.45/5.84 }.
% 5.45/5.84 parent0[0]: (5022) {G7,W5,D3,L1,V0,M1} R(5014,22);r(26) { c( skol2 ) ==>
% 5.45/5.84 skol1( skol2 ) }.
% 5.45/5.84 parent1[0; 14]: (21388) {G2,W24,D7,L1,V0,M1} { ! addition( multiplication
% 5.45/5.84 ( skol2, addition( multiplication( c( skol2 ), skol5 ), multiplication(
% 5.45/5.84 skol2, skol4 ) ) ), multiplication( c( skol2 ), skol6 ) ) ==> addition(
% 5.45/5.84 multiplication( skol2, skol4 ), multiplication( skol1( skol2 ), skol6 ) )
% 5.45/5.84 }.
% 5.45/5.84 substitution0:
% 5.45/5.84 end
% 5.45/5.84 substitution1:
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 paramod: (21391) {G4,W24,D7,L1,V0,M1} { ! addition( multiplication( skol2
% 5.45/5.84 , addition( multiplication( skol1( skol2 ), skol5 ), multiplication(
% 5.45/5.84 skol2, skol4 ) ) ), multiplication( skol1( skol2 ), skol6 ) ) ==>
% 5.45/5.84 addition( multiplication( skol2, skol4 ), multiplication( skol1( skol2 )
% 5.45/5.84 , skol6 ) ) }.
% 5.45/5.84 parent0[0]: (5022) {G7,W5,D3,L1,V0,M1} R(5014,22);r(26) { c( skol2 ) ==>
% 5.45/5.84 skol1( skol2 ) }.
% 5.45/5.84 parent1[0; 7]: (21390) {G3,W24,D7,L1,V0,M1} { ! addition( multiplication(
% 5.45/5.84 skol2, addition( multiplication( c( skol2 ), skol5 ), multiplication(
% 5.45/5.84 skol2, skol4 ) ) ), multiplication( skol1( skol2 ), skol6 ) ) ==>
% 5.45/5.84 addition( multiplication( skol2, skol4 ), multiplication( skol1( skol2 )
% 5.45/5.84 , skol6 ) ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 end
% 5.45/5.84 substitution1:
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 paramod: (21393) {G4,W19,D5,L1,V0,M1} { ! addition( multiplication( skol2
% 5.45/5.84 , multiplication( skol2, skol4 ) ), multiplication( skol1( skol2 ), skol6
% 5.45/5.84 ) ) ==> addition( multiplication( skol2, skol4 ), multiplication( skol1
% 5.45/5.84 ( skol2 ), skol6 ) ) }.
% 5.45/5.84 parent0[0]: (5012) {G3,W12,D6,L1,V2,M1} P(195,48);d(10);d(32) {
% 5.45/5.84 multiplication( skol2, addition( multiplication( skol1( skol2 ), X ), Y )
% 5.45/5.84 ) ==> multiplication( skol2, Y ) }.
% 5.45/5.84 parent1[0; 3]: (21391) {G4,W24,D7,L1,V0,M1} { ! addition( multiplication(
% 5.45/5.84 skol2, addition( multiplication( skol1( skol2 ), skol5 ), multiplication
% 5.45/5.84 ( skol2, skol4 ) ) ), multiplication( skol1( skol2 ), skol6 ) ) ==>
% 5.45/5.84 addition( multiplication( skol2, skol4 ), multiplication( skol1( skol2 )
% 5.45/5.84 , skol6 ) ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := skol5
% 5.45/5.84 Y := multiplication( skol2, skol4 )
% 5.45/5.84 end
% 5.45/5.84 substitution1:
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 paramod: (21394) {G1,W19,D5,L1,V0,M1} { ! addition( multiplication(
% 5.45/5.84 multiplication( skol2, skol2 ), skol4 ), multiplication( skol1( skol2 ),
% 5.45/5.84 skol6 ) ) ==> addition( multiplication( skol2, skol4 ), multiplication(
% 5.45/5.84 skol1( skol2 ), skol6 ) ) }.
% 5.45/5.84 parent0[0]: (4) {G0,W11,D4,L1,V3,M1} I { multiplication( X, multiplication
% 5.45/5.84 ( Y, Z ) ) ==> multiplication( multiplication( X, Y ), Z ) }.
% 5.45/5.84 parent1[0; 3]: (21393) {G4,W19,D5,L1,V0,M1} { ! addition( multiplication(
% 5.45/5.84 skol2, multiplication( skol2, skol4 ) ), multiplication( skol1( skol2 ),
% 5.45/5.84 skol6 ) ) ==> addition( multiplication( skol2, skol4 ), multiplication(
% 5.45/5.84 skol1( skol2 ), skol6 ) ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 X := skol2
% 5.45/5.84 Y := skol2
% 5.45/5.84 Z := skol4
% 5.45/5.84 end
% 5.45/5.84 substitution1:
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 paramod: (21395) {G2,W17,D5,L1,V0,M1} { ! addition( multiplication( skol2
% 5.45/5.84 , skol4 ), multiplication( skol1( skol2 ), skol6 ) ) ==> addition(
% 5.45/5.84 multiplication( skol2, skol4 ), multiplication( skol1( skol2 ), skol6 ) )
% 5.45/5.84 }.
% 5.45/5.84 parent0[0]: (20165) {G12,W5,D3,L1,V0,M1} S(5035);d(20032) { multiplication
% 5.45/5.84 ( skol2, skol2 ) ==> skol2 }.
% 5.45/5.84 parent1[0; 4]: (21394) {G1,W19,D5,L1,V0,M1} { ! addition( multiplication(
% 5.45/5.84 multiplication( skol2, skol2 ), skol4 ), multiplication( skol1( skol2 ),
% 5.45/5.84 skol6 ) ) ==> addition( multiplication( skol2, skol4 ), multiplication(
% 5.45/5.84 skol1( skol2 ), skol6 ) ) }.
% 5.45/5.84 substitution0:
% 5.45/5.84 end
% 5.45/5.84 substitution1:
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 eqrefl: (21396) {G0,W0,D0,L0,V0,M0} { }.
% 5.45/5.84 parent0[0]: (21395) {G2,W17,D5,L1,V0,M1} { ! addition( multiplication(
% 5.45/5.84 skol2, skol4 ), multiplication( skol1( skol2 ), skol6 ) ) ==> addition(
% 5.45/5.84 multiplication( skol2, skol4 ), multiplication( skol1( skol2 ), skol6 ) )
% 5.45/5.84 }.
% 5.45/5.84 substitution0:
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 subsumption: (20275) {G13,W0,D0,L0,V0,M0} S(541);d(5022);d(5012);d(4);d(
% 5.45/5.84 20165);q { }.
% 5.45/5.84 parent0: (21396) {G0,W0,D0,L0,V0,M0} { }.
% 5.45/5.84 substitution0:
% 5.45/5.84 end
% 5.45/5.84 permutation0:
% 5.45/5.84 end
% 5.45/5.84
% 5.45/5.84 Proof check complete!
% 5.45/5.84
% 5.45/5.84 Memory use:
% 5.45/5.84
% 5.45/5.84 space for terms: 250768
% 5.45/5.84 space for clauses: 940345
% 5.45/5.84
% 5.45/5.84
% 5.45/5.84 clauses generated: 148887
% 5.45/5.84 clauses kept: 20276
% 5.45/5.84 clauses selected: 1396
% 5.45/5.84 clauses deleted: 5329
% 5.45/5.84 clauses inuse deleted: 348
% 5.45/5.84
% 5.45/5.84 subsentry: 1067928
% 5.45/5.84 literals s-matched: 605339
% 5.45/5.84 literals matched: 597835
% 5.45/5.84 full subsumption: 259488
% 5.45/5.84
% 5.45/5.84 checksum: -119425590
% 5.45/5.84
% 5.45/5.84
% 5.45/5.84 Bliksem ended
%------------------------------------------------------------------------------