TSTP Solution File: KLE011+3 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : KLE011+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n020.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 01:36:36 EDT 2022
% Result : Theorem 5.39s 5.81s
% Output : Refutation 5.39s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE011+3 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n020.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 10:41:49 EDT 2022
% 0.12/0.34 % CPUTime :
% 5.39/5.81 *** allocated 10000 integers for termspace/termends
% 5.39/5.81 *** allocated 10000 integers for clauses
% 5.39/5.81 *** allocated 10000 integers for justifications
% 5.39/5.81 Bliksem 1.12
% 5.39/5.81
% 5.39/5.81
% 5.39/5.81 Automatic Strategy Selection
% 5.39/5.81
% 5.39/5.81
% 5.39/5.81 Clauses:
% 5.39/5.81
% 5.39/5.81 { addition( X, Y ) = addition( Y, X ) }.
% 5.39/5.81 { addition( Z, addition( Y, X ) ) = addition( addition( Z, Y ), X ) }.
% 5.39/5.81 { addition( X, zero ) = X }.
% 5.39/5.81 { addition( X, X ) = X }.
% 5.39/5.81 { multiplication( X, multiplication( Y, Z ) ) = multiplication(
% 5.39/5.81 multiplication( X, Y ), Z ) }.
% 5.39/5.81 { multiplication( X, one ) = X }.
% 5.39/5.81 { multiplication( one, X ) = X }.
% 5.39/5.81 { multiplication( X, addition( Y, Z ) ) = addition( multiplication( X, Y )
% 5.39/5.81 , multiplication( X, Z ) ) }.
% 5.39/5.81 { multiplication( addition( X, Y ), Z ) = addition( multiplication( X, Z )
% 5.39/5.81 , multiplication( Y, Z ) ) }.
% 5.39/5.81 { multiplication( X, zero ) = zero }.
% 5.39/5.81 { multiplication( zero, X ) = zero }.
% 5.39/5.81 { ! leq( X, Y ), addition( X, Y ) = Y }.
% 5.39/5.81 { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 5.39/5.81 { ! test( X ), complement( skol1( X ), X ) }.
% 5.39/5.81 { ! complement( Y, X ), test( X ) }.
% 5.39/5.81 { ! complement( Y, X ), multiplication( X, Y ) = zero }.
% 5.39/5.81 { ! complement( Y, X ), alpha1( X, Y ) }.
% 5.39/5.81 { ! multiplication( X, Y ) = zero, ! alpha1( X, Y ), complement( Y, X ) }.
% 5.39/5.81 { ! alpha1( X, Y ), multiplication( Y, X ) = zero }.
% 5.39/5.81 { ! alpha1( X, Y ), addition( X, Y ) = one }.
% 5.39/5.81 { ! multiplication( Y, X ) = zero, ! addition( X, Y ) = one, alpha1( X, Y )
% 5.39/5.81 }.
% 5.39/5.81 { ! test( X ), ! c( X ) = Y, complement( X, Y ) }.
% 5.39/5.81 { ! test( X ), ! complement( X, Y ), c( X ) = Y }.
% 5.39/5.81 { test( X ), c( X ) = zero }.
% 5.39/5.81 { ! test( X ), ! test( Y ), c( addition( X, Y ) ) = multiplication( c( X )
% 5.39/5.81 , c( Y ) ) }.
% 5.39/5.81 { ! test( X ), ! test( Y ), c( multiplication( X, Y ) ) = addition( c( X )
% 5.39/5.81 , c( Y ) ) }.
% 5.39/5.81 { test( skol3 ) }.
% 5.39/5.81 { test( skol2 ) }.
% 5.39/5.81 { ! one = addition( addition( multiplication( addition( skol3, c( skol3 ) )
% 5.39/5.81 , skol2 ), multiplication( addition( skol2, c( skol2 ) ), skol3 ) ),
% 5.39/5.81 multiplication( c( skol2 ), c( skol3 ) ) ) }.
% 5.39/5.81
% 5.39/5.81 percentage equality = 0.500000, percentage horn = 0.965517
% 5.39/5.81 This is a problem with some equality
% 5.39/5.81
% 5.39/5.81
% 5.39/5.81
% 5.39/5.81 Options Used:
% 5.39/5.81
% 5.39/5.81 useres = 1
% 5.39/5.81 useparamod = 1
% 5.39/5.81 useeqrefl = 1
% 5.39/5.81 useeqfact = 1
% 5.39/5.81 usefactor = 1
% 5.39/5.81 usesimpsplitting = 0
% 5.39/5.81 usesimpdemod = 5
% 5.39/5.81 usesimpres = 3
% 5.39/5.81
% 5.39/5.81 resimpinuse = 1000
% 5.39/5.81 resimpclauses = 20000
% 5.39/5.81 substype = eqrewr
% 5.39/5.81 backwardsubs = 1
% 5.39/5.81 selectoldest = 5
% 5.39/5.81
% 5.39/5.81 litorderings [0] = split
% 5.39/5.81 litorderings [1] = extend the termordering, first sorting on arguments
% 5.39/5.81
% 5.39/5.81 termordering = kbo
% 5.39/5.81
% 5.39/5.81 litapriori = 0
% 5.39/5.81 termapriori = 1
% 5.39/5.81 litaposteriori = 0
% 5.39/5.81 termaposteriori = 0
% 5.39/5.81 demodaposteriori = 0
% 5.39/5.81 ordereqreflfact = 0
% 5.39/5.81
% 5.39/5.81 litselect = negord
% 5.39/5.81
% 5.39/5.81 maxweight = 15
% 5.39/5.81 maxdepth = 30000
% 5.39/5.81 maxlength = 115
% 5.39/5.81 maxnrvars = 195
% 5.39/5.81 excuselevel = 1
% 5.39/5.81 increasemaxweight = 1
% 5.39/5.81
% 5.39/5.81 maxselected = 10000000
% 5.39/5.81 maxnrclauses = 10000000
% 5.39/5.81
% 5.39/5.81 showgenerated = 0
% 5.39/5.81 showkept = 0
% 5.39/5.81 showselected = 0
% 5.39/5.81 showdeleted = 0
% 5.39/5.81 showresimp = 1
% 5.39/5.81 showstatus = 2000
% 5.39/5.81
% 5.39/5.81 prologoutput = 0
% 5.39/5.81 nrgoals = 5000000
% 5.39/5.81 totalproof = 1
% 5.39/5.81
% 5.39/5.81 Symbols occurring in the translation:
% 5.39/5.81
% 5.39/5.81 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 5.39/5.81 . [1, 2] (w:1, o:23, a:1, s:1, b:0),
% 5.39/5.81 ! [4, 1] (w:0, o:15, a:1, s:1, b:0),
% 5.39/5.81 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 5.39/5.81 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 5.39/5.81 addition [37, 2] (w:1, o:47, a:1, s:1, b:0),
% 5.39/5.81 zero [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 5.39/5.81 multiplication [40, 2] (w:1, o:49, a:1, s:1, b:0),
% 5.39/5.81 one [41, 0] (w:1, o:10, a:1, s:1, b:0),
% 5.39/5.81 leq [42, 2] (w:1, o:48, a:1, s:1, b:0),
% 5.39/5.81 test [44, 1] (w:1, o:21, a:1, s:1, b:0),
% 5.39/5.81 complement [46, 2] (w:1, o:50, a:1, s:1, b:0),
% 5.39/5.81 c [47, 1] (w:1, o:22, a:1, s:1, b:0),
% 5.39/5.81 alpha1 [48, 2] (w:1, o:51, a:1, s:1, b:1),
% 5.39/5.81 skol1 [49, 1] (w:1, o:20, a:1, s:1, b:1),
% 5.39/5.81 skol2 [50, 0] (w:1, o:13, a:1, s:1, b:1),
% 5.39/5.81 skol3 [51, 0] (w:1, o:14, a:1, s:1, b:1).
% 5.39/5.81
% 5.39/5.81
% 5.39/5.81 Starting Search:
% 5.39/5.81
% 5.39/5.81 *** allocated 15000 integers for clauses
% 5.39/5.81 *** allocated 22500 integers for clauses
% 5.39/5.81 *** allocated 33750 integers for clauses
% 5.39/5.81 *** allocated 50625 integers for clauses
% 5.39/5.81 *** allocated 15000 integers for termspace/termends
% 5.39/5.81 *** allocated 75937 integers for clauses
% 5.39/5.81 Resimplifying inuse:
% 5.39/5.81 Done
% 5.39/5.81
% 5.39/5.81 *** allocated 22500 integers for termspace/termends
% 5.39/5.81 *** allocated 113905 integers for clauses
% 5.39/5.81 *** allocated 33750 integers for termspace/termends
% 5.39/5.81 *** allocated 170857 integers for clauses
% 5.39/5.81
% 5.39/5.81 Intermediate Status:
% 5.39/5.81 Generated: 12839
% 5.39/5.81 Kept: 2066
% 5.39/5.81 Inuse: 216
% 5.39/5.81 Deleted: 41
% 5.39/5.81 Deletedinuse: 22
% 5.39/5.81
% 5.39/5.81 Resimplifying inuse:
% 5.39/5.81 Done
% 5.39/5.81
% 5.39/5.81 *** allocated 50625 integers for termspace/termends
% 5.39/5.81 Resimplifying inuse:
% 5.39/5.81 Done
% 5.39/5.81
% 5.39/5.81 *** allocated 256285 integers for clauses
% 5.39/5.81
% 5.39/5.81 Intermediate Status:
% 5.39/5.81 Generated: 27976
% 5.39/5.81 Kept: 4070
% 5.39/5.81 Inuse: 451
% 5.39/5.81 Deleted: 163
% 5.39/5.81 Deletedinuse: 61
% 5.39/5.81
% 5.39/5.81 Resimplifying inuse:
% 5.39/5.81 Done
% 5.39/5.81
% 5.39/5.81 *** allocated 75937 integers for termspace/termends
% 5.39/5.81 *** allocated 384427 integers for clauses
% 5.39/5.81 Resimplifying inuse:
% 5.39/5.81 Done
% 5.39/5.81
% 5.39/5.81
% 5.39/5.81 Intermediate Status:
% 5.39/5.81 Generated: 44249
% 5.39/5.81 Kept: 6075
% 5.39/5.81 Inuse: 650
% 5.39/5.81 Deleted: 206
% 5.39/5.81 Deletedinuse: 71
% 5.39/5.81
% 5.39/5.81 Resimplifying inuse:
% 5.39/5.81 Done
% 5.39/5.81
% 5.39/5.81 *** allocated 113905 integers for termspace/termends
% 5.39/5.81 Resimplifying inuse:
% 5.39/5.81 Done
% 5.39/5.81
% 5.39/5.81 *** allocated 576640 integers for clauses
% 5.39/5.81
% 5.39/5.81 Intermediate Status:
% 5.39/5.81 Generated: 63456
% 5.39/5.81 Kept: 8093
% 5.39/5.81 Inuse: 764
% 5.39/5.81 Deleted: 236
% 5.39/5.81 Deletedinuse: 75
% 5.39/5.81
% 5.39/5.81 Resimplifying inuse:
% 5.39/5.81 Done
% 5.39/5.81
% 5.39/5.81 Resimplifying inuse:
% 5.39/5.81 Done
% 5.39/5.81
% 5.39/5.81 *** allocated 170857 integers for termspace/termends
% 5.39/5.81
% 5.39/5.81 Intermediate Status:
% 5.39/5.81 Generated: 74060
% 5.39/5.81 Kept: 10536
% 5.39/5.81 Inuse: 837
% 5.39/5.81 Deleted: 315
% 5.39/5.81 Deletedinuse: 145
% 5.39/5.81
% 5.39/5.81 Resimplifying inuse:
% 5.39/5.81 Done
% 5.39/5.81
% 5.39/5.81 Resimplifying inuse:
% 5.39/5.81 Done
% 5.39/5.81
% 5.39/5.81 *** allocated 864960 integers for clauses
% 5.39/5.81
% 5.39/5.81 Intermediate Status:
% 5.39/5.81 Generated: 87711
% 5.39/5.81 Kept: 12556
% 5.39/5.81 Inuse: 950
% 5.39/5.81 Deleted: 502
% 5.39/5.81 Deletedinuse: 288
% 5.39/5.81
% 5.39/5.81 Resimplifying inuse:
% 5.39/5.81 Done
% 5.39/5.81
% 5.39/5.81 Resimplifying inuse:
% 5.39/5.81 Done
% 5.39/5.81
% 5.39/5.81 *** allocated 256285 integers for termspace/termends
% 5.39/5.81
% 5.39/5.81 Intermediate Status:
% 5.39/5.81 Generated: 108217
% 5.39/5.81 Kept: 14690
% 5.39/5.81 Inuse: 1042
% 5.39/5.81 Deleted: 557
% 5.39/5.81 Deletedinuse: 304
% 5.39/5.81
% 5.39/5.81 Resimplifying inuse:
% 5.39/5.81 Done
% 5.39/5.81
% 5.39/5.81 Resimplifying inuse:
% 5.39/5.81 Done
% 5.39/5.81
% 5.39/5.81
% 5.39/5.81 Intermediate Status:
% 5.39/5.81 Generated: 126928
% 5.39/5.81 Kept: 16701
% 5.39/5.81 Inuse: 1168
% 5.39/5.81 Deleted: 699
% 5.39/5.81 Deletedinuse: 304
% 5.39/5.81
% 5.39/5.81 Resimplifying inuse:
% 5.39/5.81 Done
% 5.39/5.81
% 5.39/5.81 Resimplifying inuse:
% 5.39/5.81 Done
% 5.39/5.81
% 5.39/5.81 *** allocated 1297440 integers for clauses
% 5.39/5.81
% 5.39/5.81 Intermediate Status:
% 5.39/5.81 Generated: 142778
% 5.39/5.81 Kept: 18731
% 5.39/5.81 Inuse: 1270
% 5.39/5.81 Deleted: 728
% 5.39/5.81 Deletedinuse: 305
% 5.39/5.81
% 5.39/5.81 Resimplifying inuse:
% 5.39/5.81 Done
% 5.39/5.81
% 5.39/5.81 Resimplifying inuse:
% 5.39/5.81 Done
% 5.39/5.81
% 5.39/5.81 Resimplifying clauses:
% 5.39/5.81
% 5.39/5.81 Bliksems!, er is een bewijs:
% 5.39/5.81 % SZS status Theorem
% 5.39/5.81 % SZS output start Refutation
% 5.39/5.81
% 5.39/5.81 (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X ) }.
% 5.39/5.81 (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) ) ==> addition(
% 5.39/5.81 addition( Z, Y ), X ) }.
% 5.39/5.81 (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 5.39/5.81 (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 5.39/5.81 (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 5.39/5.81 (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 5.39/5.81 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 5.39/5.81 (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ),
% 5.39/5.81 multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 5.39/5.81 (13) {G0,W6,D3,L2,V1,M2} I { ! test( X ), complement( skol1( X ), X ) }.
% 5.39/5.81 (15) {G0,W8,D3,L2,V2,M2} I { ! complement( Y, X ), multiplication( X, Y )
% 5.39/5.81 ==> zero }.
% 5.39/5.81 (16) {G0,W6,D2,L2,V2,M2} I { ! complement( Y, X ), alpha1( X, Y ) }.
% 5.39/5.81 (17) {G0,W11,D3,L3,V2,M3} I { ! multiplication( X, Y ) ==> zero, ! alpha1(
% 5.39/5.81 X, Y ), complement( Y, X ) }.
% 5.39/5.81 (18) {G0,W8,D3,L2,V2,M2} I { ! alpha1( X, Y ), multiplication( Y, X ) ==>
% 5.39/5.81 zero }.
% 5.39/5.81 (19) {G0,W8,D3,L2,V2,M2} I { ! alpha1( X, Y ), addition( X, Y ) ==> one }.
% 5.39/5.81 (20) {G0,W13,D3,L3,V2,M3} I { ! multiplication( Y, X ) ==> zero, ! addition
% 5.39/5.81 ( X, Y ) ==> one, alpha1( X, Y ) }.
% 5.39/5.81 (22) {G0,W9,D3,L3,V2,M3} I { ! test( X ), ! complement( X, Y ), c( X ) = Y
% 5.39/5.81 }.
% 5.39/5.81 (26) {G0,W2,D2,L1,V0,M1} I { test( skol3 ) }.
% 5.39/5.81 (27) {G0,W2,D2,L1,V0,M1} I { test( skol2 ) }.
% 5.39/5.81 (28) {G0,W21,D7,L1,V0,M1} I { ! addition( addition( multiplication(
% 5.39/5.81 addition( skol3, c( skol3 ) ), skol2 ), multiplication( addition( skol2,
% 5.39/5.81 c( skol2 ) ), skol3 ) ), multiplication( c( skol2 ), c( skol3 ) ) ) ==>
% 5.39/5.81 one }.
% 5.39/5.81 (34) {G1,W9,D4,L1,V2,M1} P(3,1) { addition( addition( Y, X ), X ) ==>
% 5.39/5.81 addition( Y, X ) }.
% 5.39/5.81 (50) {G1,W17,D5,L1,V4,M1} P(7,1) { addition( addition( T, multiplication( X
% 5.39/5.81 , Y ) ), multiplication( X, Z ) ) ==> addition( T, multiplication( X,
% 5.39/5.81 addition( Y, Z ) ) ) }.
% 5.39/5.81 (51) {G1,W11,D4,L1,V2,M1} P(5,7) { addition( X, multiplication( X, Y ) ) =
% 5.39/5.81 multiplication( X, addition( one, Y ) ) }.
% 5.39/5.81 (63) {G1,W17,D5,L1,V4,M1} P(8,1) { addition( addition( T, multiplication( X
% 5.39/5.81 , Y ) ), multiplication( Z, Y ) ) ==> addition( T, multiplication(
% 5.39/5.81 addition( X, Z ), Y ) ) }.
% 5.39/5.81 (183) {G1,W4,D3,L1,V0,M1} R(13,26) { complement( skol1( skol3 ), skol3 )
% 5.39/5.81 }.
% 5.39/5.81 (184) {G1,W4,D3,L1,V0,M1} R(13,27) { complement( skol1( skol2 ), skol2 )
% 5.39/5.81 }.
% 5.39/5.81 (187) {G2,W4,D3,L1,V0,M1} R(183,16) { alpha1( skol3, skol1( skol3 ) ) }.
% 5.39/5.81 (191) {G2,W4,D3,L1,V0,M1} R(184,16) { alpha1( skol2, skol1( skol2 ) ) }.
% 5.39/5.81 (194) {G2,W6,D4,L1,V0,M1} R(15,184) { multiplication( skol2, skol1( skol2 )
% 5.39/5.81 ) ==> zero }.
% 5.39/5.81 (195) {G2,W6,D4,L1,V0,M1} R(15,183) { multiplication( skol3, skol1( skol3 )
% 5.39/5.81 ) ==> zero }.
% 5.39/5.81 (236) {G3,W6,D4,L1,V0,M1} R(18,191) { multiplication( skol1( skol2 ), skol2
% 5.39/5.81 ) ==> zero }.
% 5.39/5.81 (237) {G3,W6,D4,L1,V0,M1} R(18,187) { multiplication( skol1( skol3 ), skol3
% 5.39/5.81 ) ==> zero }.
% 5.39/5.81 (262) {G3,W6,D4,L1,V0,M1} R(19,191) { addition( skol2, skol1( skol2 ) ) ==>
% 5.39/5.81 one }.
% 5.39/5.81 (263) {G3,W6,D4,L1,V0,M1} R(19,187) { addition( skol3, skol1( skol3 ) ) ==>
% 5.39/5.81 one }.
% 5.39/5.81 (527) {G1,W20,D7,L2,V0,M2} P(19,28);d(6) { ! alpha1( skol3, c( skol3 ) ), !
% 5.39/5.81 addition( addition( skol2, multiplication( addition( skol2, c( skol2 ) )
% 5.39/5.81 , skol3 ) ), multiplication( c( skol2 ), c( skol3 ) ) ) ==> one }.
% 5.39/5.81 (2396) {G4,W6,D4,L1,V0,M1} P(262,0) { addition( skol1( skol2 ), skol2 ) ==>
% 5.39/5.81 one }.
% 5.39/5.81 (2431) {G5,W4,D3,L1,V0,M1} R(2396,20);d(194);q { alpha1( skol1( skol2 ),
% 5.39/5.81 skol2 ) }.
% 5.39/5.81 (2446) {G6,W4,D3,L1,V0,M1} R(2431,17);d(236);q { complement( skol2, skol1(
% 5.39/5.81 skol2 ) ) }.
% 5.39/5.81 (2451) {G7,W5,D3,L1,V0,M1} R(2446,22);r(27) { c( skol2 ) ==> skol1( skol2 )
% 5.39/5.81 }.
% 5.39/5.81 (2752) {G4,W6,D4,L1,V0,M1} P(263,0) { addition( skol1( skol3 ), skol3 ) ==>
% 5.39/5.81 one }.
% 5.39/5.81 (2787) {G5,W4,D3,L1,V0,M1} R(2752,20);d(195);q { alpha1( skol1( skol3 ),
% 5.39/5.81 skol3 ) }.
% 5.39/5.81 (2799) {G5,W5,D3,L1,V0,M1} P(2752,34) { addition( one, skol3 ) ==> one }.
% 5.39/5.81 (2802) {G6,W4,D3,L1,V0,M1} R(2787,17);d(237);q { complement( skol3, skol1(
% 5.39/5.81 skol3 ) ) }.
% 5.39/5.81 (2807) {G7,W5,D3,L1,V0,M1} R(2802,22);r(26) { c( skol3 ) ==> skol1( skol3 )
% 5.39/5.81 }.
% 5.39/5.81 (2865) {G6,W7,D4,L1,V1,M1} P(2799,51);d(5) { addition( X, multiplication( X
% 5.39/5.81 , skol3 ) ) ==> X }.
% 5.39/5.81 (18520) {G7,W13,D5,L1,V2,M1} P(2865,63) { addition( X, multiplication(
% 5.39/5.81 addition( X, Y ), skol3 ) ) ==> addition( X, multiplication( Y, skol3 ) )
% 5.39/5.81 }.
% 5.39/5.81 (20585) {G8,W0,D0,L0,V0,M0} S(527);d(2807);d(18520);d(50);d(2451);d(2807);d
% 5.39/5.81 (19);d(5);d(262);q;r(187) { }.
% 5.39/5.81
% 5.39/5.81
% 5.39/5.81 % SZS output end Refutation
% 5.39/5.81 found a proof!
% 5.39/5.81
% 5.39/5.81
% 5.39/5.81 Unprocessed initial clauses:
% 5.39/5.81
% 5.39/5.81 (20587) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X ) }.
% 5.39/5.81 (20588) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) = addition
% 5.39/5.81 ( addition( Z, Y ), X ) }.
% 5.39/5.81 (20589) {G0,W5,D3,L1,V1,M1} { addition( X, zero ) = X }.
% 5.39/5.81 (20590) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 5.39/5.81 (20591) {G0,W11,D4,L1,V3,M1} { multiplication( X, multiplication( Y, Z ) )
% 5.39/5.81 = multiplication( multiplication( X, Y ), Z ) }.
% 5.39/5.81 (20592) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 5.39/5.81 (20593) {G0,W5,D3,L1,V1,M1} { multiplication( one, X ) = X }.
% 5.39/5.81 (20594) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y, Z ) ) =
% 5.39/5.81 addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 5.39/5.81 (20595) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Y ), Z ) =
% 5.39/5.81 addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 5.39/5.81 (20596) {G0,W5,D3,L1,V1,M1} { multiplication( X, zero ) = zero }.
% 5.39/5.81 (20597) {G0,W5,D3,L1,V1,M1} { multiplication( zero, X ) = zero }.
% 5.39/5.81 (20598) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y }.
% 5.39/5.81 (20599) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 5.39/5.81 (20600) {G0,W6,D3,L2,V1,M2} { ! test( X ), complement( skol1( X ), X ) }.
% 5.39/5.81 (20601) {G0,W5,D2,L2,V2,M2} { ! complement( Y, X ), test( X ) }.
% 5.39/5.81 (20602) {G0,W8,D3,L2,V2,M2} { ! complement( Y, X ), multiplication( X, Y )
% 5.39/5.81 = zero }.
% 5.39/5.81 (20603) {G0,W6,D2,L2,V2,M2} { ! complement( Y, X ), alpha1( X, Y ) }.
% 5.39/5.81 (20604) {G0,W11,D3,L3,V2,M3} { ! multiplication( X, Y ) = zero, ! alpha1(
% 5.39/5.81 X, Y ), complement( Y, X ) }.
% 5.39/5.81 (20605) {G0,W8,D3,L2,V2,M2} { ! alpha1( X, Y ), multiplication( Y, X ) =
% 5.39/5.81 zero }.
% 5.39/5.81 (20606) {G0,W8,D3,L2,V2,M2} { ! alpha1( X, Y ), addition( X, Y ) = one }.
% 5.39/5.81 (20607) {G0,W13,D3,L3,V2,M3} { ! multiplication( Y, X ) = zero, ! addition
% 5.39/5.81 ( X, Y ) = one, alpha1( X, Y ) }.
% 5.39/5.81 (20608) {G0,W9,D3,L3,V2,M3} { ! test( X ), ! c( X ) = Y, complement( X, Y
% 5.39/5.81 ) }.
% 5.39/5.81 (20609) {G0,W9,D3,L3,V2,M3} { ! test( X ), ! complement( X, Y ), c( X ) =
% 5.39/5.81 Y }.
% 5.39/5.81 (20610) {G0,W6,D3,L2,V1,M2} { test( X ), c( X ) = zero }.
% 5.39/5.81 (20611) {G0,W14,D4,L3,V2,M3} { ! test( X ), ! test( Y ), c( addition( X, Y
% 5.39/5.81 ) ) = multiplication( c( X ), c( Y ) ) }.
% 5.39/5.81 (20612) {G0,W14,D4,L3,V2,M3} { ! test( X ), ! test( Y ), c( multiplication
% 5.39/5.81 ( X, Y ) ) = addition( c( X ), c( Y ) ) }.
% 5.39/5.81 (20613) {G0,W2,D2,L1,V0,M1} { test( skol3 ) }.
% 5.39/5.81 (20614) {G0,W2,D2,L1,V0,M1} { test( skol2 ) }.
% 5.39/5.81 (20615) {G0,W21,D7,L1,V0,M1} { ! one = addition( addition( multiplication
% 5.39/5.81 ( addition( skol3, c( skol3 ) ), skol2 ), multiplication( addition( skol2
% 5.39/5.81 , c( skol2 ) ), skol3 ) ), multiplication( c( skol2 ), c( skol3 ) ) ) }.
% 5.39/5.81
% 5.39/5.81
% 5.39/5.81 Total Proof:
% 5.39/5.81
% 5.39/5.81 subsumption: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X
% 5.39/5.81 ) }.
% 5.39/5.81 parent0: (20587) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X )
% 5.39/5.81 }.
% 5.39/5.81 substitution0:
% 5.39/5.81 X := X
% 5.39/5.81 Y := Y
% 5.39/5.81 end
% 5.39/5.81 permutation0:
% 5.39/5.81 0 ==> 0
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 subsumption: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 5.39/5.81 ==> addition( addition( Z, Y ), X ) }.
% 5.39/5.81 parent0: (20588) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) =
% 5.39/5.81 addition( addition( Z, Y ), X ) }.
% 5.39/5.81 substitution0:
% 5.39/5.81 X := X
% 5.39/5.81 Y := Y
% 5.39/5.81 Z := Z
% 5.39/5.81 end
% 5.39/5.81 permutation0:
% 5.39/5.81 0 ==> 0
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 subsumption: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 5.39/5.81 parent0: (20590) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 5.39/5.81 substitution0:
% 5.39/5.81 X := X
% 5.39/5.81 end
% 5.39/5.81 permutation0:
% 5.39/5.81 0 ==> 0
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 subsumption: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 5.39/5.81 parent0: (20592) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 5.39/5.81 substitution0:
% 5.39/5.81 X := X
% 5.39/5.81 end
% 5.39/5.81 permutation0:
% 5.39/5.81 0 ==> 0
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 subsumption: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 5.39/5.81 parent0: (20593) {G0,W5,D3,L1,V1,M1} { multiplication( one, X ) = X }.
% 5.39/5.81 substitution0:
% 5.39/5.81 X := X
% 5.39/5.81 end
% 5.39/5.81 permutation0:
% 5.39/5.81 0 ==> 0
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 eqswap: (20637) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Y ),
% 5.39/5.81 multiplication( X, Z ) ) = multiplication( X, addition( Y, Z ) ) }.
% 5.39/5.81 parent0[0]: (20594) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y
% 5.39/5.81 , Z ) ) = addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 5.39/5.81 substitution0:
% 5.39/5.81 X := X
% 5.39/5.81 Y := Y
% 5.39/5.81 Z := Z
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 subsumption: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y )
% 5.39/5.81 , multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 5.39/5.81 parent0: (20637) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Y ),
% 5.39/5.81 multiplication( X, Z ) ) = multiplication( X, addition( Y, Z ) ) }.
% 5.39/5.81 substitution0:
% 5.39/5.81 X := X
% 5.39/5.81 Y := Y
% 5.39/5.81 Z := Z
% 5.39/5.81 end
% 5.39/5.81 permutation0:
% 5.39/5.81 0 ==> 0
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 eqswap: (20645) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Z ),
% 5.39/5.81 multiplication( Y, Z ) ) = multiplication( addition( X, Y ), Z ) }.
% 5.39/5.81 parent0[0]: (20595) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Y
% 5.39/5.81 ), Z ) = addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 5.39/5.81 substitution0:
% 5.39/5.81 X := X
% 5.39/5.81 Y := Y
% 5.39/5.81 Z := Z
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 subsumption: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z )
% 5.39/5.81 , multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 5.39/5.81 parent0: (20645) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Z ),
% 5.39/5.81 multiplication( Y, Z ) ) = multiplication( addition( X, Y ), Z ) }.
% 5.39/5.81 substitution0:
% 5.39/5.81 X := X
% 5.39/5.81 Y := Y
% 5.39/5.81 Z := Z
% 5.39/5.81 end
% 5.39/5.81 permutation0:
% 5.39/5.81 0 ==> 0
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 subsumption: (13) {G0,W6,D3,L2,V1,M2} I { ! test( X ), complement( skol1( X
% 5.39/5.81 ), X ) }.
% 5.39/5.81 parent0: (20600) {G0,W6,D3,L2,V1,M2} { ! test( X ), complement( skol1( X )
% 5.39/5.81 , X ) }.
% 5.39/5.81 substitution0:
% 5.39/5.81 X := X
% 5.39/5.81 end
% 5.39/5.81 permutation0:
% 5.39/5.81 0 ==> 0
% 5.39/5.81 1 ==> 1
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 subsumption: (15) {G0,W8,D3,L2,V2,M2} I { ! complement( Y, X ),
% 5.39/5.81 multiplication( X, Y ) ==> zero }.
% 5.39/5.81 parent0: (20602) {G0,W8,D3,L2,V2,M2} { ! complement( Y, X ),
% 5.39/5.81 multiplication( X, Y ) = zero }.
% 5.39/5.81 substitution0:
% 5.39/5.81 X := X
% 5.39/5.81 Y := Y
% 5.39/5.81 end
% 5.39/5.81 permutation0:
% 5.39/5.81 0 ==> 0
% 5.39/5.81 1 ==> 1
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 subsumption: (16) {G0,W6,D2,L2,V2,M2} I { ! complement( Y, X ), alpha1( X,
% 5.39/5.81 Y ) }.
% 5.39/5.81 parent0: (20603) {G0,W6,D2,L2,V2,M2} { ! complement( Y, X ), alpha1( X, Y
% 5.39/5.81 ) }.
% 5.39/5.81 substitution0:
% 5.39/5.81 X := X
% 5.39/5.81 Y := Y
% 5.39/5.81 end
% 5.39/5.81 permutation0:
% 5.39/5.81 0 ==> 0
% 5.39/5.81 1 ==> 1
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 subsumption: (17) {G0,W11,D3,L3,V2,M3} I { ! multiplication( X, Y ) ==>
% 5.39/5.81 zero, ! alpha1( X, Y ), complement( Y, X ) }.
% 5.39/5.81 parent0: (20604) {G0,W11,D3,L3,V2,M3} { ! multiplication( X, Y ) = zero, !
% 5.39/5.81 alpha1( X, Y ), complement( Y, X ) }.
% 5.39/5.81 substitution0:
% 5.39/5.81 X := X
% 5.39/5.81 Y := Y
% 5.39/5.81 end
% 5.39/5.81 permutation0:
% 5.39/5.81 0 ==> 0
% 5.39/5.81 1 ==> 1
% 5.39/5.81 2 ==> 2
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 subsumption: (18) {G0,W8,D3,L2,V2,M2} I { ! alpha1( X, Y ), multiplication
% 5.39/5.81 ( Y, X ) ==> zero }.
% 5.39/5.81 parent0: (20605) {G0,W8,D3,L2,V2,M2} { ! alpha1( X, Y ), multiplication( Y
% 5.39/5.81 , X ) = zero }.
% 5.39/5.81 substitution0:
% 5.39/5.81 X := X
% 5.39/5.81 Y := Y
% 5.39/5.81 end
% 5.39/5.81 permutation0:
% 5.39/5.81 0 ==> 0
% 5.39/5.81 1 ==> 1
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 subsumption: (19) {G0,W8,D3,L2,V2,M2} I { ! alpha1( X, Y ), addition( X, Y
% 5.39/5.81 ) ==> one }.
% 5.39/5.81 parent0: (20606) {G0,W8,D3,L2,V2,M2} { ! alpha1( X, Y ), addition( X, Y )
% 5.39/5.81 = one }.
% 5.39/5.81 substitution0:
% 5.39/5.81 X := X
% 5.39/5.81 Y := Y
% 5.39/5.81 end
% 5.39/5.81 permutation0:
% 5.39/5.81 0 ==> 0
% 5.39/5.81 1 ==> 1
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 subsumption: (20) {G0,W13,D3,L3,V2,M3} I { ! multiplication( Y, X ) ==>
% 5.39/5.81 zero, ! addition( X, Y ) ==> one, alpha1( X, Y ) }.
% 5.39/5.81 parent0: (20607) {G0,W13,D3,L3,V2,M3} { ! multiplication( Y, X ) = zero, !
% 5.39/5.81 addition( X, Y ) = one, alpha1( X, Y ) }.
% 5.39/5.81 substitution0:
% 5.39/5.81 X := X
% 5.39/5.81 Y := Y
% 5.39/5.81 end
% 5.39/5.81 permutation0:
% 5.39/5.81 0 ==> 0
% 5.39/5.81 1 ==> 1
% 5.39/5.81 2 ==> 2
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 subsumption: (22) {G0,W9,D3,L3,V2,M3} I { ! test( X ), ! complement( X, Y )
% 5.39/5.81 , c( X ) = Y }.
% 5.39/5.81 parent0: (20609) {G0,W9,D3,L3,V2,M3} { ! test( X ), ! complement( X, Y ),
% 5.39/5.81 c( X ) = Y }.
% 5.39/5.81 substitution0:
% 5.39/5.81 X := X
% 5.39/5.81 Y := Y
% 5.39/5.81 end
% 5.39/5.81 permutation0:
% 5.39/5.81 0 ==> 0
% 5.39/5.81 1 ==> 1
% 5.39/5.81 2 ==> 2
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 subsumption: (26) {G0,W2,D2,L1,V0,M1} I { test( skol3 ) }.
% 5.39/5.81 parent0: (20613) {G0,W2,D2,L1,V0,M1} { test( skol3 ) }.
% 5.39/5.81 substitution0:
% 5.39/5.81 end
% 5.39/5.81 permutation0:
% 5.39/5.81 0 ==> 0
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 subsumption: (27) {G0,W2,D2,L1,V0,M1} I { test( skol2 ) }.
% 5.39/5.81 parent0: (20614) {G0,W2,D2,L1,V0,M1} { test( skol2 ) }.
% 5.39/5.81 substitution0:
% 5.39/5.81 end
% 5.39/5.81 permutation0:
% 5.39/5.81 0 ==> 0
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 eqswap: (20853) {G0,W21,D7,L1,V0,M1} { ! addition( addition(
% 5.39/5.81 multiplication( addition( skol3, c( skol3 ) ), skol2 ), multiplication(
% 5.39/5.81 addition( skol2, c( skol2 ) ), skol3 ) ), multiplication( c( skol2 ), c(
% 5.39/5.81 skol3 ) ) ) = one }.
% 5.39/5.81 parent0[0]: (20615) {G0,W21,D7,L1,V0,M1} { ! one = addition( addition(
% 5.39/5.81 multiplication( addition( skol3, c( skol3 ) ), skol2 ), multiplication(
% 5.39/5.81 addition( skol2, c( skol2 ) ), skol3 ) ), multiplication( c( skol2 ), c(
% 5.39/5.81 skol3 ) ) ) }.
% 5.39/5.81 substitution0:
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 subsumption: (28) {G0,W21,D7,L1,V0,M1} I { ! addition( addition(
% 5.39/5.81 multiplication( addition( skol3, c( skol3 ) ), skol2 ), multiplication(
% 5.39/5.81 addition( skol2, c( skol2 ) ), skol3 ) ), multiplication( c( skol2 ), c(
% 5.39/5.81 skol3 ) ) ) ==> one }.
% 5.39/5.81 parent0: (20853) {G0,W21,D7,L1,V0,M1} { ! addition( addition(
% 5.39/5.81 multiplication( addition( skol3, c( skol3 ) ), skol2 ), multiplication(
% 5.39/5.81 addition( skol2, c( skol2 ) ), skol3 ) ), multiplication( c( skol2 ), c(
% 5.39/5.81 skol3 ) ) ) = one }.
% 5.39/5.81 substitution0:
% 5.39/5.81 end
% 5.39/5.81 permutation0:
% 5.39/5.81 0 ==> 0
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 eqswap: (20855) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z ) ==>
% 5.39/5.81 addition( X, addition( Y, Z ) ) }.
% 5.39/5.81 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 5.39/5.81 ==> addition( addition( Z, Y ), X ) }.
% 5.39/5.81 substitution0:
% 5.39/5.81 X := Z
% 5.39/5.81 Y := Y
% 5.39/5.81 Z := X
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 paramod: (20861) {G1,W9,D4,L1,V2,M1} { addition( addition( X, Y ), Y ) ==>
% 5.39/5.81 addition( X, Y ) }.
% 5.39/5.81 parent0[0]: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 5.39/5.81 parent1[0; 8]: (20855) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y ),
% 5.39/5.81 Z ) ==> addition( X, addition( Y, Z ) ) }.
% 5.39/5.81 substitution0:
% 5.39/5.81 X := Y
% 5.39/5.81 end
% 5.39/5.81 substitution1:
% 5.39/5.81 X := X
% 5.39/5.81 Y := Y
% 5.39/5.81 Z := Y
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 subsumption: (34) {G1,W9,D4,L1,V2,M1} P(3,1) { addition( addition( Y, X ),
% 5.39/5.81 X ) ==> addition( Y, X ) }.
% 5.39/5.81 parent0: (20861) {G1,W9,D4,L1,V2,M1} { addition( addition( X, Y ), Y ) ==>
% 5.39/5.81 addition( X, Y ) }.
% 5.39/5.81 substitution0:
% 5.39/5.81 X := Y
% 5.39/5.81 Y := X
% 5.39/5.81 end
% 5.39/5.81 permutation0:
% 5.39/5.81 0 ==> 0
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 eqswap: (20867) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z ) ==>
% 5.39/5.81 addition( X, addition( Y, Z ) ) }.
% 5.39/5.81 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 5.39/5.81 ==> addition( addition( Z, Y ), X ) }.
% 5.39/5.81 substitution0:
% 5.39/5.81 X := Z
% 5.39/5.81 Y := Y
% 5.39/5.81 Z := X
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 paramod: (20871) {G1,W17,D5,L1,V4,M1} { addition( addition( X,
% 5.39/5.81 multiplication( Y, Z ) ), multiplication( Y, T ) ) ==> addition( X,
% 5.39/5.81 multiplication( Y, addition( Z, T ) ) ) }.
% 5.39/5.81 parent0[0]: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 5.39/5.81 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 5.39/5.81 parent1[0; 12]: (20867) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y )
% 5.39/5.81 , Z ) ==> addition( X, addition( Y, Z ) ) }.
% 5.39/5.81 substitution0:
% 5.39/5.81 X := Y
% 5.39/5.81 Y := Z
% 5.39/5.81 Z := T
% 5.39/5.81 end
% 5.39/5.81 substitution1:
% 5.39/5.81 X := X
% 5.39/5.81 Y := multiplication( Y, Z )
% 5.39/5.81 Z := multiplication( Y, T )
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 subsumption: (50) {G1,W17,D5,L1,V4,M1} P(7,1) { addition( addition( T,
% 5.39/5.81 multiplication( X, Y ) ), multiplication( X, Z ) ) ==> addition( T,
% 5.39/5.81 multiplication( X, addition( Y, Z ) ) ) }.
% 5.39/5.81 parent0: (20871) {G1,W17,D5,L1,V4,M1} { addition( addition( X,
% 5.39/5.81 multiplication( Y, Z ) ), multiplication( Y, T ) ) ==> addition( X,
% 5.39/5.81 multiplication( Y, addition( Z, T ) ) ) }.
% 5.39/5.81 substitution0:
% 5.39/5.81 X := T
% 5.39/5.81 Y := X
% 5.39/5.81 Z := Y
% 5.39/5.81 T := Z
% 5.39/5.81 end
% 5.39/5.81 permutation0:
% 5.39/5.81 0 ==> 0
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 eqswap: (20875) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y, Z )
% 5.39/5.81 ) ==> addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 5.39/5.81 parent0[0]: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 5.39/5.81 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 5.39/5.81 substitution0:
% 5.39/5.81 X := X
% 5.39/5.81 Y := Y
% 5.39/5.81 Z := Z
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 paramod: (20876) {G1,W11,D4,L1,V2,M1} { multiplication( X, addition( one,
% 5.39/5.81 Y ) ) ==> addition( X, multiplication( X, Y ) ) }.
% 5.39/5.81 parent0[0]: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 5.39/5.81 parent1[0; 7]: (20875) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition
% 5.39/5.81 ( Y, Z ) ) ==> addition( multiplication( X, Y ), multiplication( X, Z ) )
% 5.39/5.81 }.
% 5.39/5.81 substitution0:
% 5.39/5.81 X := X
% 5.39/5.81 end
% 5.39/5.81 substitution1:
% 5.39/5.81 X := X
% 5.39/5.81 Y := one
% 5.39/5.81 Z := Y
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 eqswap: (20878) {G1,W11,D4,L1,V2,M1} { addition( X, multiplication( X, Y )
% 5.39/5.81 ) ==> multiplication( X, addition( one, Y ) ) }.
% 5.39/5.81 parent0[0]: (20876) {G1,W11,D4,L1,V2,M1} { multiplication( X, addition(
% 5.39/5.81 one, Y ) ) ==> addition( X, multiplication( X, Y ) ) }.
% 5.39/5.81 substitution0:
% 5.39/5.81 X := X
% 5.39/5.81 Y := Y
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 subsumption: (51) {G1,W11,D4,L1,V2,M1} P(5,7) { addition( X, multiplication
% 5.39/5.81 ( X, Y ) ) = multiplication( X, addition( one, Y ) ) }.
% 5.39/5.81 parent0: (20878) {G1,W11,D4,L1,V2,M1} { addition( X, multiplication( X, Y
% 5.39/5.81 ) ) ==> multiplication( X, addition( one, Y ) ) }.
% 5.39/5.81 substitution0:
% 5.39/5.81 X := X
% 5.39/5.81 Y := Y
% 5.39/5.81 end
% 5.39/5.81 permutation0:
% 5.39/5.81 0 ==> 0
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 eqswap: (20881) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z ) ==>
% 5.39/5.81 addition( X, addition( Y, Z ) ) }.
% 5.39/5.81 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 5.39/5.81 ==> addition( addition( Z, Y ), X ) }.
% 5.39/5.81 substitution0:
% 5.39/5.81 X := Z
% 5.39/5.81 Y := Y
% 5.39/5.81 Z := X
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 paramod: (20885) {G1,W17,D5,L1,V4,M1} { addition( addition( X,
% 5.39/5.81 multiplication( Y, Z ) ), multiplication( T, Z ) ) ==> addition( X,
% 5.39/5.81 multiplication( addition( Y, T ), Z ) ) }.
% 5.39/5.81 parent0[0]: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ),
% 5.39/5.81 multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 5.39/5.81 parent1[0; 12]: (20881) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y )
% 5.39/5.81 , Z ) ==> addition( X, addition( Y, Z ) ) }.
% 5.39/5.81 substitution0:
% 5.39/5.81 X := Y
% 5.39/5.81 Y := T
% 5.39/5.81 Z := Z
% 5.39/5.81 end
% 5.39/5.81 substitution1:
% 5.39/5.81 X := X
% 5.39/5.81 Y := multiplication( Y, Z )
% 5.39/5.81 Z := multiplication( T, Z )
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 subsumption: (63) {G1,W17,D5,L1,V4,M1} P(8,1) { addition( addition( T,
% 5.39/5.81 multiplication( X, Y ) ), multiplication( Z, Y ) ) ==> addition( T,
% 5.39/5.81 multiplication( addition( X, Z ), Y ) ) }.
% 5.39/5.81 parent0: (20885) {G1,W17,D5,L1,V4,M1} { addition( addition( X,
% 5.39/5.81 multiplication( Y, Z ) ), multiplication( T, Z ) ) ==> addition( X,
% 5.39/5.81 multiplication( addition( Y, T ), Z ) ) }.
% 5.39/5.81 substitution0:
% 5.39/5.81 X := T
% 5.39/5.81 Y := X
% 5.39/5.81 Z := Y
% 5.39/5.81 T := Z
% 5.39/5.81 end
% 5.39/5.81 permutation0:
% 5.39/5.81 0 ==> 0
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 resolution: (20888) {G1,W4,D3,L1,V0,M1} { complement( skol1( skol3 ),
% 5.39/5.81 skol3 ) }.
% 5.39/5.81 parent0[0]: (13) {G0,W6,D3,L2,V1,M2} I { ! test( X ), complement( skol1( X
% 5.39/5.81 ), X ) }.
% 5.39/5.81 parent1[0]: (26) {G0,W2,D2,L1,V0,M1} I { test( skol3 ) }.
% 5.39/5.81 substitution0:
% 5.39/5.81 X := skol3
% 5.39/5.81 end
% 5.39/5.81 substitution1:
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 subsumption: (183) {G1,W4,D3,L1,V0,M1} R(13,26) { complement( skol1( skol3
% 5.39/5.81 ), skol3 ) }.
% 5.39/5.81 parent0: (20888) {G1,W4,D3,L1,V0,M1} { complement( skol1( skol3 ), skol3 )
% 5.39/5.81 }.
% 5.39/5.81 substitution0:
% 5.39/5.81 end
% 5.39/5.81 permutation0:
% 5.39/5.81 0 ==> 0
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 resolution: (20889) {G1,W4,D3,L1,V0,M1} { complement( skol1( skol2 ),
% 5.39/5.81 skol2 ) }.
% 5.39/5.81 parent0[0]: (13) {G0,W6,D3,L2,V1,M2} I { ! test( X ), complement( skol1( X
% 5.39/5.81 ), X ) }.
% 5.39/5.81 parent1[0]: (27) {G0,W2,D2,L1,V0,M1} I { test( skol2 ) }.
% 5.39/5.81 substitution0:
% 5.39/5.81 X := skol2
% 5.39/5.81 end
% 5.39/5.81 substitution1:
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 subsumption: (184) {G1,W4,D3,L1,V0,M1} R(13,27) { complement( skol1( skol2
% 5.39/5.81 ), skol2 ) }.
% 5.39/5.81 parent0: (20889) {G1,W4,D3,L1,V0,M1} { complement( skol1( skol2 ), skol2 )
% 5.39/5.81 }.
% 5.39/5.81 substitution0:
% 5.39/5.81 end
% 5.39/5.81 permutation0:
% 5.39/5.81 0 ==> 0
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 resolution: (20890) {G1,W4,D3,L1,V0,M1} { alpha1( skol3, skol1( skol3 ) )
% 5.39/5.81 }.
% 5.39/5.81 parent0[0]: (16) {G0,W6,D2,L2,V2,M2} I { ! complement( Y, X ), alpha1( X, Y
% 5.39/5.81 ) }.
% 5.39/5.81 parent1[0]: (183) {G1,W4,D3,L1,V0,M1} R(13,26) { complement( skol1( skol3 )
% 5.39/5.81 , skol3 ) }.
% 5.39/5.81 substitution0:
% 5.39/5.81 X := skol3
% 5.39/5.81 Y := skol1( skol3 )
% 5.39/5.81 end
% 5.39/5.81 substitution1:
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 subsumption: (187) {G2,W4,D3,L1,V0,M1} R(183,16) { alpha1( skol3, skol1(
% 5.39/5.81 skol3 ) ) }.
% 5.39/5.81 parent0: (20890) {G1,W4,D3,L1,V0,M1} { alpha1( skol3, skol1( skol3 ) ) }.
% 5.39/5.81 substitution0:
% 5.39/5.81 end
% 5.39/5.81 permutation0:
% 5.39/5.81 0 ==> 0
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 resolution: (20891) {G1,W4,D3,L1,V0,M1} { alpha1( skol2, skol1( skol2 ) )
% 5.39/5.81 }.
% 5.39/5.81 parent0[0]: (16) {G0,W6,D2,L2,V2,M2} I { ! complement( Y, X ), alpha1( X, Y
% 5.39/5.81 ) }.
% 5.39/5.81 parent1[0]: (184) {G1,W4,D3,L1,V0,M1} R(13,27) { complement( skol1( skol2 )
% 5.39/5.81 , skol2 ) }.
% 5.39/5.81 substitution0:
% 5.39/5.81 X := skol2
% 5.39/5.81 Y := skol1( skol2 )
% 5.39/5.81 end
% 5.39/5.81 substitution1:
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 subsumption: (191) {G2,W4,D3,L1,V0,M1} R(184,16) { alpha1( skol2, skol1(
% 5.39/5.81 skol2 ) ) }.
% 5.39/5.81 parent0: (20891) {G1,W4,D3,L1,V0,M1} { alpha1( skol2, skol1( skol2 ) ) }.
% 5.39/5.81 substitution0:
% 5.39/5.81 end
% 5.39/5.81 permutation0:
% 5.39/5.81 0 ==> 0
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 eqswap: (20892) {G0,W8,D3,L2,V2,M2} { zero ==> multiplication( X, Y ), !
% 5.39/5.81 complement( Y, X ) }.
% 5.39/5.81 parent0[1]: (15) {G0,W8,D3,L2,V2,M2} I { ! complement( Y, X ),
% 5.39/5.81 multiplication( X, Y ) ==> zero }.
% 5.39/5.81 substitution0:
% 5.39/5.81 X := X
% 5.39/5.81 Y := Y
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 resolution: (20893) {G1,W6,D4,L1,V0,M1} { zero ==> multiplication( skol2,
% 5.39/5.81 skol1( skol2 ) ) }.
% 5.39/5.81 parent0[1]: (20892) {G0,W8,D3,L2,V2,M2} { zero ==> multiplication( X, Y )
% 5.39/5.81 , ! complement( Y, X ) }.
% 5.39/5.81 parent1[0]: (184) {G1,W4,D3,L1,V0,M1} R(13,27) { complement( skol1( skol2 )
% 5.39/5.81 , skol2 ) }.
% 5.39/5.81 substitution0:
% 5.39/5.81 X := skol2
% 5.39/5.81 Y := skol1( skol2 )
% 5.39/5.81 end
% 5.39/5.81 substitution1:
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 eqswap: (20894) {G1,W6,D4,L1,V0,M1} { multiplication( skol2, skol1( skol2
% 5.39/5.81 ) ) ==> zero }.
% 5.39/5.81 parent0[0]: (20893) {G1,W6,D4,L1,V0,M1} { zero ==> multiplication( skol2,
% 5.39/5.81 skol1( skol2 ) ) }.
% 5.39/5.81 substitution0:
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 subsumption: (194) {G2,W6,D4,L1,V0,M1} R(15,184) { multiplication( skol2,
% 5.39/5.81 skol1( skol2 ) ) ==> zero }.
% 5.39/5.81 parent0: (20894) {G1,W6,D4,L1,V0,M1} { multiplication( skol2, skol1( skol2
% 5.39/5.81 ) ) ==> zero }.
% 5.39/5.81 substitution0:
% 5.39/5.81 end
% 5.39/5.81 permutation0:
% 5.39/5.81 0 ==> 0
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 eqswap: (20895) {G0,W8,D3,L2,V2,M2} { zero ==> multiplication( X, Y ), !
% 5.39/5.81 complement( Y, X ) }.
% 5.39/5.81 parent0[1]: (15) {G0,W8,D3,L2,V2,M2} I { ! complement( Y, X ),
% 5.39/5.81 multiplication( X, Y ) ==> zero }.
% 5.39/5.81 substitution0:
% 5.39/5.81 X := X
% 5.39/5.81 Y := Y
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 resolution: (20896) {G1,W6,D4,L1,V0,M1} { zero ==> multiplication( skol3,
% 5.39/5.81 skol1( skol3 ) ) }.
% 5.39/5.81 parent0[1]: (20895) {G0,W8,D3,L2,V2,M2} { zero ==> multiplication( X, Y )
% 5.39/5.81 , ! complement( Y, X ) }.
% 5.39/5.81 parent1[0]: (183) {G1,W4,D3,L1,V0,M1} R(13,26) { complement( skol1( skol3 )
% 5.39/5.81 , skol3 ) }.
% 5.39/5.81 substitution0:
% 5.39/5.81 X := skol3
% 5.39/5.81 Y := skol1( skol3 )
% 5.39/5.81 end
% 5.39/5.81 substitution1:
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 eqswap: (20897) {G1,W6,D4,L1,V0,M1} { multiplication( skol3, skol1( skol3
% 5.39/5.81 ) ) ==> zero }.
% 5.39/5.81 parent0[0]: (20896) {G1,W6,D4,L1,V0,M1} { zero ==> multiplication( skol3,
% 5.39/5.81 skol1( skol3 ) ) }.
% 5.39/5.81 substitution0:
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 subsumption: (195) {G2,W6,D4,L1,V0,M1} R(15,183) { multiplication( skol3,
% 5.39/5.81 skol1( skol3 ) ) ==> zero }.
% 5.39/5.81 parent0: (20897) {G1,W6,D4,L1,V0,M1} { multiplication( skol3, skol1( skol3
% 5.39/5.81 ) ) ==> zero }.
% 5.39/5.81 substitution0:
% 5.39/5.81 end
% 5.39/5.81 permutation0:
% 5.39/5.81 0 ==> 0
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 eqswap: (20898) {G0,W8,D3,L2,V2,M2} { zero ==> multiplication( X, Y ), !
% 5.39/5.81 alpha1( Y, X ) }.
% 5.39/5.81 parent0[1]: (18) {G0,W8,D3,L2,V2,M2} I { ! alpha1( X, Y ), multiplication(
% 5.39/5.81 Y, X ) ==> zero }.
% 5.39/5.81 substitution0:
% 5.39/5.81 X := Y
% 5.39/5.81 Y := X
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 resolution: (20899) {G1,W6,D4,L1,V0,M1} { zero ==> multiplication( skol1(
% 5.39/5.81 skol2 ), skol2 ) }.
% 5.39/5.81 parent0[1]: (20898) {G0,W8,D3,L2,V2,M2} { zero ==> multiplication( X, Y )
% 5.39/5.81 , ! alpha1( Y, X ) }.
% 5.39/5.81 parent1[0]: (191) {G2,W4,D3,L1,V0,M1} R(184,16) { alpha1( skol2, skol1(
% 5.39/5.81 skol2 ) ) }.
% 5.39/5.81 substitution0:
% 5.39/5.81 X := skol1( skol2 )
% 5.39/5.81 Y := skol2
% 5.39/5.81 end
% 5.39/5.81 substitution1:
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 eqswap: (20900) {G1,W6,D4,L1,V0,M1} { multiplication( skol1( skol2 ),
% 5.39/5.81 skol2 ) ==> zero }.
% 5.39/5.81 parent0[0]: (20899) {G1,W6,D4,L1,V0,M1} { zero ==> multiplication( skol1(
% 5.39/5.81 skol2 ), skol2 ) }.
% 5.39/5.81 substitution0:
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 subsumption: (236) {G3,W6,D4,L1,V0,M1} R(18,191) { multiplication( skol1(
% 5.39/5.81 skol2 ), skol2 ) ==> zero }.
% 5.39/5.81 parent0: (20900) {G1,W6,D4,L1,V0,M1} { multiplication( skol1( skol2 ),
% 5.39/5.81 skol2 ) ==> zero }.
% 5.39/5.81 substitution0:
% 5.39/5.81 end
% 5.39/5.81 permutation0:
% 5.39/5.81 0 ==> 0
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 eqswap: (20901) {G0,W8,D3,L2,V2,M2} { zero ==> multiplication( X, Y ), !
% 5.39/5.81 alpha1( Y, X ) }.
% 5.39/5.81 parent0[1]: (18) {G0,W8,D3,L2,V2,M2} I { ! alpha1( X, Y ), multiplication(
% 5.39/5.81 Y, X ) ==> zero }.
% 5.39/5.81 substitution0:
% 5.39/5.81 X := Y
% 5.39/5.81 Y := X
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 resolution: (20902) {G1,W6,D4,L1,V0,M1} { zero ==> multiplication( skol1(
% 5.39/5.81 skol3 ), skol3 ) }.
% 5.39/5.81 parent0[1]: (20901) {G0,W8,D3,L2,V2,M2} { zero ==> multiplication( X, Y )
% 5.39/5.81 , ! alpha1( Y, X ) }.
% 5.39/5.81 parent1[0]: (187) {G2,W4,D3,L1,V0,M1} R(183,16) { alpha1( skol3, skol1(
% 5.39/5.81 skol3 ) ) }.
% 5.39/5.81 substitution0:
% 5.39/5.81 X := skol1( skol3 )
% 5.39/5.81 Y := skol3
% 5.39/5.81 end
% 5.39/5.81 substitution1:
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 eqswap: (20903) {G1,W6,D4,L1,V0,M1} { multiplication( skol1( skol3 ),
% 5.39/5.81 skol3 ) ==> zero }.
% 5.39/5.81 parent0[0]: (20902) {G1,W6,D4,L1,V0,M1} { zero ==> multiplication( skol1(
% 5.39/5.81 skol3 ), skol3 ) }.
% 5.39/5.81 substitution0:
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 subsumption: (237) {G3,W6,D4,L1,V0,M1} R(18,187) { multiplication( skol1(
% 5.39/5.81 skol3 ), skol3 ) ==> zero }.
% 5.39/5.81 parent0: (20903) {G1,W6,D4,L1,V0,M1} { multiplication( skol1( skol3 ),
% 5.39/5.81 skol3 ) ==> zero }.
% 5.39/5.81 substitution0:
% 5.39/5.81 end
% 5.39/5.81 permutation0:
% 5.39/5.81 0 ==> 0
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 eqswap: (20904) {G0,W8,D3,L2,V2,M2} { one ==> addition( X, Y ), ! alpha1(
% 5.39/5.81 X, Y ) }.
% 5.39/5.81 parent0[1]: (19) {G0,W8,D3,L2,V2,M2} I { ! alpha1( X, Y ), addition( X, Y )
% 5.39/5.81 ==> one }.
% 5.39/5.81 substitution0:
% 5.39/5.81 X := X
% 5.39/5.81 Y := Y
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 resolution: (20905) {G1,W6,D4,L1,V0,M1} { one ==> addition( skol2, skol1(
% 5.39/5.81 skol2 ) ) }.
% 5.39/5.81 parent0[1]: (20904) {G0,W8,D3,L2,V2,M2} { one ==> addition( X, Y ), !
% 5.39/5.81 alpha1( X, Y ) }.
% 5.39/5.81 parent1[0]: (191) {G2,W4,D3,L1,V0,M1} R(184,16) { alpha1( skol2, skol1(
% 5.39/5.81 skol2 ) ) }.
% 5.39/5.81 substitution0:
% 5.39/5.81 X := skol2
% 5.39/5.81 Y := skol1( skol2 )
% 5.39/5.81 end
% 5.39/5.81 substitution1:
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 eqswap: (20906) {G1,W6,D4,L1,V0,M1} { addition( skol2, skol1( skol2 ) )
% 5.39/5.81 ==> one }.
% 5.39/5.81 parent0[0]: (20905) {G1,W6,D4,L1,V0,M1} { one ==> addition( skol2, skol1(
% 5.39/5.81 skol2 ) ) }.
% 5.39/5.81 substitution0:
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 subsumption: (262) {G3,W6,D4,L1,V0,M1} R(19,191) { addition( skol2, skol1(
% 5.39/5.81 skol2 ) ) ==> one }.
% 5.39/5.81 parent0: (20906) {G1,W6,D4,L1,V0,M1} { addition( skol2, skol1( skol2 ) )
% 5.39/5.81 ==> one }.
% 5.39/5.81 substitution0:
% 5.39/5.81 end
% 5.39/5.81 permutation0:
% 5.39/5.81 0 ==> 0
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 eqswap: (20907) {G0,W8,D3,L2,V2,M2} { one ==> addition( X, Y ), ! alpha1(
% 5.39/5.81 X, Y ) }.
% 5.39/5.81 parent0[1]: (19) {G0,W8,D3,L2,V2,M2} I { ! alpha1( X, Y ), addition( X, Y )
% 5.39/5.81 ==> one }.
% 5.39/5.81 substitution0:
% 5.39/5.81 X := X
% 5.39/5.81 Y := Y
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 resolution: (20908) {G1,W6,D4,L1,V0,M1} { one ==> addition( skol3, skol1(
% 5.39/5.81 skol3 ) ) }.
% 5.39/5.81 parent0[1]: (20907) {G0,W8,D3,L2,V2,M2} { one ==> addition( X, Y ), !
% 5.39/5.81 alpha1( X, Y ) }.
% 5.39/5.81 parent1[0]: (187) {G2,W4,D3,L1,V0,M1} R(183,16) { alpha1( skol3, skol1(
% 5.39/5.81 skol3 ) ) }.
% 5.39/5.81 substitution0:
% 5.39/5.81 X := skol3
% 5.39/5.81 Y := skol1( skol3 )
% 5.39/5.81 end
% 5.39/5.81 substitution1:
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 eqswap: (20909) {G1,W6,D4,L1,V0,M1} { addition( skol3, skol1( skol3 ) )
% 5.39/5.81 ==> one }.
% 5.39/5.81 parent0[0]: (20908) {G1,W6,D4,L1,V0,M1} { one ==> addition( skol3, skol1(
% 5.39/5.81 skol3 ) ) }.
% 5.39/5.81 substitution0:
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 subsumption: (263) {G3,W6,D4,L1,V0,M1} R(19,187) { addition( skol3, skol1(
% 5.39/5.81 skol3 ) ) ==> one }.
% 5.39/5.81 parent0: (20909) {G1,W6,D4,L1,V0,M1} { addition( skol3, skol1( skol3 ) )
% 5.39/5.81 ==> one }.
% 5.39/5.81 substitution0:
% 5.39/5.81 end
% 5.39/5.81 permutation0:
% 5.39/5.81 0 ==> 0
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 eqswap: (20911) {G0,W21,D7,L1,V0,M1} { ! one ==> addition( addition(
% 5.39/5.81 multiplication( addition( skol3, c( skol3 ) ), skol2 ), multiplication(
% 5.39/5.81 addition( skol2, c( skol2 ) ), skol3 ) ), multiplication( c( skol2 ), c(
% 5.39/5.81 skol3 ) ) ) }.
% 5.39/5.81 parent0[0]: (28) {G0,W21,D7,L1,V0,M1} I { ! addition( addition(
% 5.39/5.81 multiplication( addition( skol3, c( skol3 ) ), skol2 ), multiplication(
% 5.39/5.81 addition( skol2, c( skol2 ) ), skol3 ) ), multiplication( c( skol2 ), c(
% 5.39/5.81 skol3 ) ) ) ==> one }.
% 5.39/5.81 substitution0:
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 paramod: (20915) {G1,W22,D7,L2,V0,M2} { ! one ==> addition( addition(
% 5.39/5.81 multiplication( one, skol2 ), multiplication( addition( skol2, c( skol2 )
% 5.39/5.81 ), skol3 ) ), multiplication( c( skol2 ), c( skol3 ) ) ), ! alpha1(
% 5.39/5.81 skol3, c( skol3 ) ) }.
% 5.39/5.81 parent0[1]: (19) {G0,W8,D3,L2,V2,M2} I { ! alpha1( X, Y ), addition( X, Y )
% 5.39/5.81 ==> one }.
% 5.39/5.81 parent1[0; 6]: (20911) {G0,W21,D7,L1,V0,M1} { ! one ==> addition( addition
% 5.39/5.81 ( multiplication( addition( skol3, c( skol3 ) ), skol2 ), multiplication
% 5.39/5.81 ( addition( skol2, c( skol2 ) ), skol3 ) ), multiplication( c( skol2 ), c
% 5.39/5.81 ( skol3 ) ) ) }.
% 5.39/5.81 substitution0:
% 5.39/5.81 X := skol3
% 5.39/5.81 Y := c( skol3 )
% 5.39/5.81 end
% 5.39/5.81 substitution1:
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 paramod: (20951) {G1,W20,D7,L2,V0,M2} { ! one ==> addition( addition(
% 5.39/5.81 skol2, multiplication( addition( skol2, c( skol2 ) ), skol3 ) ),
% 5.39/5.81 multiplication( c( skol2 ), c( skol3 ) ) ), ! alpha1( skol3, c( skol3 ) )
% 5.39/5.81 }.
% 5.39/5.81 parent0[0]: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 5.39/5.81 parent1[0; 5]: (20915) {G1,W22,D7,L2,V0,M2} { ! one ==> addition( addition
% 5.39/5.81 ( multiplication( one, skol2 ), multiplication( addition( skol2, c( skol2
% 5.39/5.81 ) ), skol3 ) ), multiplication( c( skol2 ), c( skol3 ) ) ), ! alpha1(
% 5.39/5.81 skol3, c( skol3 ) ) }.
% 5.39/5.81 substitution0:
% 5.39/5.81 X := skol2
% 5.39/5.81 end
% 5.39/5.81 substitution1:
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 eqswap: (20952) {G1,W20,D7,L2,V0,M2} { ! addition( addition( skol2,
% 5.39/5.81 multiplication( addition( skol2, c( skol2 ) ), skol3 ) ), multiplication
% 5.39/5.81 ( c( skol2 ), c( skol3 ) ) ) ==> one, ! alpha1( skol3, c( skol3 ) ) }.
% 5.39/5.81 parent0[0]: (20951) {G1,W20,D7,L2,V0,M2} { ! one ==> addition( addition(
% 5.39/5.81 skol2, multiplication( addition( skol2, c( skol2 ) ), skol3 ) ),
% 5.39/5.81 multiplication( c( skol2 ), c( skol3 ) ) ), ! alpha1( skol3, c( skol3 ) )
% 5.39/5.81 }.
% 5.39/5.81 substitution0:
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 subsumption: (527) {G1,W20,D7,L2,V0,M2} P(19,28);d(6) { ! alpha1( skol3, c
% 5.39/5.81 ( skol3 ) ), ! addition( addition( skol2, multiplication( addition( skol2
% 5.39/5.81 , c( skol2 ) ), skol3 ) ), multiplication( c( skol2 ), c( skol3 ) ) ) ==>
% 5.39/5.81 one }.
% 5.39/5.81 parent0: (20952) {G1,W20,D7,L2,V0,M2} { ! addition( addition( skol2,
% 5.39/5.81 multiplication( addition( skol2, c( skol2 ) ), skol3 ) ), multiplication
% 5.39/5.81 ( c( skol2 ), c( skol3 ) ) ) ==> one, ! alpha1( skol3, c( skol3 ) ) }.
% 5.39/5.81 substitution0:
% 5.39/5.81 end
% 5.39/5.81 permutation0:
% 5.39/5.81 0 ==> 1
% 5.39/5.81 1 ==> 0
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 eqswap: (20953) {G3,W6,D4,L1,V0,M1} { one ==> addition( skol2, skol1(
% 5.39/5.81 skol2 ) ) }.
% 5.39/5.81 parent0[0]: (262) {G3,W6,D4,L1,V0,M1} R(19,191) { addition( skol2, skol1(
% 5.39/5.81 skol2 ) ) ==> one }.
% 5.39/5.81 substitution0:
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 paramod: (20954) {G1,W6,D4,L1,V0,M1} { one ==> addition( skol1( skol2 ),
% 5.39/5.81 skol2 ) }.
% 5.39/5.81 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 5.39/5.81 }.
% 5.39/5.81 parent1[0; 2]: (20953) {G3,W6,D4,L1,V0,M1} { one ==> addition( skol2,
% 5.39/5.81 skol1( skol2 ) ) }.
% 5.39/5.81 substitution0:
% 5.39/5.81 X := skol2
% 5.39/5.81 Y := skol1( skol2 )
% 5.39/5.81 end
% 5.39/5.81 substitution1:
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 eqswap: (20957) {G1,W6,D4,L1,V0,M1} { addition( skol1( skol2 ), skol2 )
% 5.39/5.81 ==> one }.
% 5.39/5.81 parent0[0]: (20954) {G1,W6,D4,L1,V0,M1} { one ==> addition( skol1( skol2 )
% 5.39/5.81 , skol2 ) }.
% 5.39/5.81 substitution0:
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 subsumption: (2396) {G4,W6,D4,L1,V0,M1} P(262,0) { addition( skol1( skol2 )
% 5.39/5.81 , skol2 ) ==> one }.
% 5.39/5.81 parent0: (20957) {G1,W6,D4,L1,V0,M1} { addition( skol1( skol2 ), skol2 )
% 5.39/5.81 ==> one }.
% 5.39/5.81 substitution0:
% 5.39/5.81 end
% 5.39/5.81 permutation0:
% 5.39/5.81 0 ==> 0
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 eqswap: (20958) {G4,W6,D4,L1,V0,M1} { one ==> addition( skol1( skol2 ),
% 5.39/5.81 skol2 ) }.
% 5.39/5.81 parent0[0]: (2396) {G4,W6,D4,L1,V0,M1} P(262,0) { addition( skol1( skol2 )
% 5.39/5.81 , skol2 ) ==> one }.
% 5.39/5.81 substitution0:
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 eqswap: (20960) {G0,W13,D3,L3,V2,M3} { ! one ==> addition( X, Y ), !
% 5.39/5.81 multiplication( Y, X ) ==> zero, alpha1( X, Y ) }.
% 5.39/5.81 parent0[1]: (20) {G0,W13,D3,L3,V2,M3} I { ! multiplication( Y, X ) ==> zero
% 5.39/5.81 , ! addition( X, Y ) ==> one, alpha1( X, Y ) }.
% 5.39/5.81 substitution0:
% 5.39/5.81 X := X
% 5.39/5.81 Y := Y
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 eqswap: (20961) {G0,W13,D3,L3,V2,M3} { ! zero ==> multiplication( X, Y ),
% 5.39/5.81 ! one ==> addition( Y, X ), alpha1( Y, X ) }.
% 5.39/5.81 parent0[1]: (20960) {G0,W13,D3,L3,V2,M3} { ! one ==> addition( X, Y ), !
% 5.39/5.81 multiplication( Y, X ) ==> zero, alpha1( X, Y ) }.
% 5.39/5.81 substitution0:
% 5.39/5.81 X := Y
% 5.39/5.81 Y := X
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 resolution: (20963) {G1,W10,D4,L2,V0,M2} { ! zero ==> multiplication(
% 5.39/5.81 skol2, skol1( skol2 ) ), alpha1( skol1( skol2 ), skol2 ) }.
% 5.39/5.81 parent0[1]: (20961) {G0,W13,D3,L3,V2,M3} { ! zero ==> multiplication( X, Y
% 5.39/5.81 ), ! one ==> addition( Y, X ), alpha1( Y, X ) }.
% 5.39/5.81 parent1[0]: (20958) {G4,W6,D4,L1,V0,M1} { one ==> addition( skol1( skol2 )
% 5.39/5.81 , skol2 ) }.
% 5.39/5.81 substitution0:
% 5.39/5.81 X := skol2
% 5.39/5.81 Y := skol1( skol2 )
% 5.39/5.81 end
% 5.39/5.81 substitution1:
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 paramod: (20964) {G2,W7,D3,L2,V0,M2} { ! zero ==> zero, alpha1( skol1(
% 5.39/5.81 skol2 ), skol2 ) }.
% 5.39/5.81 parent0[0]: (194) {G2,W6,D4,L1,V0,M1} R(15,184) { multiplication( skol2,
% 5.39/5.81 skol1( skol2 ) ) ==> zero }.
% 5.39/5.81 parent1[0; 3]: (20963) {G1,W10,D4,L2,V0,M2} { ! zero ==> multiplication(
% 5.39/5.81 skol2, skol1( skol2 ) ), alpha1( skol1( skol2 ), skol2 ) }.
% 5.39/5.81 substitution0:
% 5.39/5.81 end
% 5.39/5.81 substitution1:
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 eqrefl: (20965) {G0,W4,D3,L1,V0,M1} { alpha1( skol1( skol2 ), skol2 ) }.
% 5.39/5.81 parent0[0]: (20964) {G2,W7,D3,L2,V0,M2} { ! zero ==> zero, alpha1( skol1(
% 5.39/5.81 skol2 ), skol2 ) }.
% 5.39/5.81 substitution0:
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 subsumption: (2431) {G5,W4,D3,L1,V0,M1} R(2396,20);d(194);q { alpha1( skol1
% 5.39/5.81 ( skol2 ), skol2 ) }.
% 5.39/5.81 parent0: (20965) {G0,W4,D3,L1,V0,M1} { alpha1( skol1( skol2 ), skol2 ) }.
% 5.39/5.81 substitution0:
% 5.39/5.81 end
% 5.39/5.81 permutation0:
% 5.39/5.81 0 ==> 0
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 eqswap: (20966) {G0,W11,D3,L3,V2,M3} { ! zero ==> multiplication( X, Y ),
% 5.39/5.81 ! alpha1( X, Y ), complement( Y, X ) }.
% 5.39/5.81 parent0[0]: (17) {G0,W11,D3,L3,V2,M3} I { ! multiplication( X, Y ) ==> zero
% 5.39/5.81 , ! alpha1( X, Y ), complement( Y, X ) }.
% 5.39/5.81 substitution0:
% 5.39/5.81 X := X
% 5.39/5.81 Y := Y
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 resolution: (20968) {G1,W10,D4,L2,V0,M2} { ! zero ==> multiplication(
% 5.39/5.81 skol1( skol2 ), skol2 ), complement( skol2, skol1( skol2 ) ) }.
% 5.39/5.81 parent0[1]: (20966) {G0,W11,D3,L3,V2,M3} { ! zero ==> multiplication( X, Y
% 5.39/5.81 ), ! alpha1( X, Y ), complement( Y, X ) }.
% 5.39/5.81 parent1[0]: (2431) {G5,W4,D3,L1,V0,M1} R(2396,20);d(194);q { alpha1( skol1
% 5.39/5.81 ( skol2 ), skol2 ) }.
% 5.39/5.81 substitution0:
% 5.39/5.81 X := skol1( skol2 )
% 5.39/5.81 Y := skol2
% 5.39/5.81 end
% 5.39/5.81 substitution1:
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 paramod: (20969) {G2,W7,D3,L2,V0,M2} { ! zero ==> zero, complement( skol2
% 5.39/5.81 , skol1( skol2 ) ) }.
% 5.39/5.81 parent0[0]: (236) {G3,W6,D4,L1,V0,M1} R(18,191) { multiplication( skol1(
% 5.39/5.81 skol2 ), skol2 ) ==> zero }.
% 5.39/5.81 parent1[0; 3]: (20968) {G1,W10,D4,L2,V0,M2} { ! zero ==> multiplication(
% 5.39/5.81 skol1( skol2 ), skol2 ), complement( skol2, skol1( skol2 ) ) }.
% 5.39/5.81 substitution0:
% 5.39/5.81 end
% 5.39/5.81 substitution1:
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 eqrefl: (20970) {G0,W4,D3,L1,V0,M1} { complement( skol2, skol1( skol2 ) )
% 5.39/5.81 }.
% 5.39/5.81 parent0[0]: (20969) {G2,W7,D3,L2,V0,M2} { ! zero ==> zero, complement(
% 5.39/5.81 skol2, skol1( skol2 ) ) }.
% 5.39/5.81 substitution0:
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 subsumption: (2446) {G6,W4,D3,L1,V0,M1} R(2431,17);d(236);q { complement(
% 5.39/5.81 skol2, skol1( skol2 ) ) }.
% 5.39/5.81 parent0: (20970) {G0,W4,D3,L1,V0,M1} { complement( skol2, skol1( skol2 ) )
% 5.39/5.81 }.
% 5.39/5.81 substitution0:
% 5.39/5.81 end
% 5.39/5.81 permutation0:
% 5.39/5.81 0 ==> 0
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 eqswap: (20971) {G0,W9,D3,L3,V2,M3} { Y = c( X ), ! test( X ), !
% 5.39/5.81 complement( X, Y ) }.
% 5.39/5.81 parent0[2]: (22) {G0,W9,D3,L3,V2,M3} I { ! test( X ), ! complement( X, Y )
% 5.39/5.81 , c( X ) = Y }.
% 5.39/5.81 substitution0:
% 5.39/5.81 X := X
% 5.39/5.81 Y := Y
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 resolution: (20972) {G1,W7,D3,L2,V0,M2} { skol1( skol2 ) = c( skol2 ), !
% 5.39/5.81 test( skol2 ) }.
% 5.39/5.81 parent0[2]: (20971) {G0,W9,D3,L3,V2,M3} { Y = c( X ), ! test( X ), !
% 5.39/5.81 complement( X, Y ) }.
% 5.39/5.81 parent1[0]: (2446) {G6,W4,D3,L1,V0,M1} R(2431,17);d(236);q { complement(
% 5.39/5.81 skol2, skol1( skol2 ) ) }.
% 5.39/5.81 substitution0:
% 5.39/5.81 X := skol2
% 5.39/5.81 Y := skol1( skol2 )
% 5.39/5.81 end
% 5.39/5.81 substitution1:
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 resolution: (20973) {G1,W5,D3,L1,V0,M1} { skol1( skol2 ) = c( skol2 ) }.
% 5.39/5.81 parent0[1]: (20972) {G1,W7,D3,L2,V0,M2} { skol1( skol2 ) = c( skol2 ), !
% 5.39/5.81 test( skol2 ) }.
% 5.39/5.81 parent1[0]: (27) {G0,W2,D2,L1,V0,M1} I { test( skol2 ) }.
% 5.39/5.81 substitution0:
% 5.39/5.81 end
% 5.39/5.81 substitution1:
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 eqswap: (20974) {G1,W5,D3,L1,V0,M1} { c( skol2 ) = skol1( skol2 ) }.
% 5.39/5.81 parent0[0]: (20973) {G1,W5,D3,L1,V0,M1} { skol1( skol2 ) = c( skol2 ) }.
% 5.39/5.81 substitution0:
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 subsumption: (2451) {G7,W5,D3,L1,V0,M1} R(2446,22);r(27) { c( skol2 ) ==>
% 5.39/5.81 skol1( skol2 ) }.
% 5.39/5.81 parent0: (20974) {G1,W5,D3,L1,V0,M1} { c( skol2 ) = skol1( skol2 ) }.
% 5.39/5.81 substitution0:
% 5.39/5.81 end
% 5.39/5.81 permutation0:
% 5.39/5.81 0 ==> 0
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 eqswap: (20975) {G3,W6,D4,L1,V0,M1} { one ==> addition( skol3, skol1(
% 5.39/5.81 skol3 ) ) }.
% 5.39/5.81 parent0[0]: (263) {G3,W6,D4,L1,V0,M1} R(19,187) { addition( skol3, skol1(
% 5.39/5.81 skol3 ) ) ==> one }.
% 5.39/5.81 substitution0:
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 paramod: (20976) {G1,W6,D4,L1,V0,M1} { one ==> addition( skol1( skol3 ),
% 5.39/5.81 skol3 ) }.
% 5.39/5.81 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 5.39/5.81 }.
% 5.39/5.81 parent1[0; 2]: (20975) {G3,W6,D4,L1,V0,M1} { one ==> addition( skol3,
% 5.39/5.81 skol1( skol3 ) ) }.
% 5.39/5.81 substitution0:
% 5.39/5.81 X := skol3
% 5.39/5.81 Y := skol1( skol3 )
% 5.39/5.81 end
% 5.39/5.81 substitution1:
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 eqswap: (20979) {G1,W6,D4,L1,V0,M1} { addition( skol1( skol3 ), skol3 )
% 5.39/5.81 ==> one }.
% 5.39/5.81 parent0[0]: (20976) {G1,W6,D4,L1,V0,M1} { one ==> addition( skol1( skol3 )
% 5.39/5.81 , skol3 ) }.
% 5.39/5.81 substitution0:
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 subsumption: (2752) {G4,W6,D4,L1,V0,M1} P(263,0) { addition( skol1( skol3 )
% 5.39/5.81 , skol3 ) ==> one }.
% 5.39/5.81 parent0: (20979) {G1,W6,D4,L1,V0,M1} { addition( skol1( skol3 ), skol3 )
% 5.39/5.81 ==> one }.
% 5.39/5.81 substitution0:
% 5.39/5.81 end
% 5.39/5.81 permutation0:
% 5.39/5.81 0 ==> 0
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 eqswap: (20980) {G4,W6,D4,L1,V0,M1} { one ==> addition( skol1( skol3 ),
% 5.39/5.81 skol3 ) }.
% 5.39/5.81 parent0[0]: (2752) {G4,W6,D4,L1,V0,M1} P(263,0) { addition( skol1( skol3 )
% 5.39/5.81 , skol3 ) ==> one }.
% 5.39/5.81 substitution0:
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 eqswap: (20982) {G0,W13,D3,L3,V2,M3} { ! one ==> addition( X, Y ), !
% 5.39/5.81 multiplication( Y, X ) ==> zero, alpha1( X, Y ) }.
% 5.39/5.81 parent0[1]: (20) {G0,W13,D3,L3,V2,M3} I { ! multiplication( Y, X ) ==> zero
% 5.39/5.81 , ! addition( X, Y ) ==> one, alpha1( X, Y ) }.
% 5.39/5.81 substitution0:
% 5.39/5.81 X := X
% 5.39/5.81 Y := Y
% 5.39/5.81 end
% 5.39/5.81
% 5.39/5.81 eqswap: (20983) {G0,W13,D3,L3,V2,M3} { ! zero ==> multiplication( X, Y ),
% 5.39/5.82 ! one ==> addition( Y, X ), alpha1( Y, X ) }.
% 5.39/5.82 parent0[1]: (20982) {G0,W13,D3,L3,V2,M3} { ! one ==> addition( X, Y ), !
% 5.39/5.82 multiplication( Y, X ) ==> zero, alpha1( X, Y ) }.
% 5.39/5.82 substitution0:
% 5.39/5.82 X := Y
% 5.39/5.82 Y := X
% 5.39/5.82 end
% 5.39/5.82
% 5.39/5.82 resolution: (20985) {G1,W10,D4,L2,V0,M2} { ! zero ==> multiplication(
% 5.39/5.82 skol3, skol1( skol3 ) ), alpha1( skol1( skol3 ), skol3 ) }.
% 5.39/5.82 parent0[1]: (20983) {G0,W13,D3,L3,V2,M3} { ! zero ==> multiplication( X, Y
% 5.39/5.82 ), ! one ==> addition( Y, X ), alpha1( Y, X ) }.
% 5.39/5.82 parent1[0]: (20980) {G4,W6,D4,L1,V0,M1} { one ==> addition( skol1( skol3 )
% 5.39/5.82 , skol3 ) }.
% 5.39/5.82 substitution0:
% 5.39/5.82 X := skol3
% 5.39/5.82 Y := skol1( skol3 )
% 5.39/5.82 end
% 5.39/5.82 substitution1:
% 5.39/5.82 end
% 5.39/5.82
% 5.39/5.82 paramod: (20986) {G2,W7,D3,L2,V0,M2} { ! zero ==> zero, alpha1( skol1(
% 5.39/5.82 skol3 ), skol3 ) }.
% 5.39/5.82 parent0[0]: (195) {G2,W6,D4,L1,V0,M1} R(15,183) { multiplication( skol3,
% 5.39/5.82 skol1( skol3 ) ) ==> zero }.
% 5.39/5.82 parent1[0; 3]: (20985) {G1,W10,D4,L2,V0,M2} { ! zero ==> multiplication(
% 5.39/5.82 skol3, skol1( skol3 ) ), alpha1( skol1( skol3 ), skol3 ) }.
% 5.39/5.82 substitution0:
% 5.39/5.82 end
% 5.39/5.82 substitution1:
% 5.39/5.82 end
% 5.39/5.82
% 5.39/5.82 eqrefl: (20987) {G0,W4,D3,L1,V0,M1} { alpha1( skol1( skol3 ), skol3 ) }.
% 5.39/5.82 parent0[0]: (20986) {G2,W7,D3,L2,V0,M2} { ! zero ==> zero, alpha1( skol1(
% 5.39/5.82 skol3 ), skol3 ) }.
% 5.39/5.82 substitution0:
% 5.39/5.82 end
% 5.39/5.82
% 5.39/5.82 subsumption: (2787) {G5,W4,D3,L1,V0,M1} R(2752,20);d(195);q { alpha1( skol1
% 5.39/5.82 ( skol3 ), skol3 ) }.
% 5.39/5.82 parent0: (20987) {G0,W4,D3,L1,V0,M1} { alpha1( skol1( skol3 ), skol3 ) }.
% 5.39/5.82 substitution0:
% 5.39/5.82 end
% 5.39/5.82 permutation0:
% 5.39/5.82 0 ==> 0
% 5.39/5.82 end
% 5.39/5.82
% 5.39/5.82 eqswap: (20989) {G1,W9,D4,L1,V2,M1} { addition( X, Y ) ==> addition(
% 5.39/5.82 addition( X, Y ), Y ) }.
% 5.39/5.82 parent0[0]: (34) {G1,W9,D4,L1,V2,M1} P(3,1) { addition( addition( Y, X ), X
% 5.39/5.82 ) ==> addition( Y, X ) }.
% 5.39/5.82 substitution0:
% 5.39/5.82 X := Y
% 5.39/5.82 Y := X
% 5.39/5.82 end
% 5.39/5.82
% 5.39/5.82 paramod: (20991) {G2,W8,D4,L1,V0,M1} { addition( skol1( skol3 ), skol3 )
% 5.39/5.82 ==> addition( one, skol3 ) }.
% 5.39/5.82 parent0[0]: (2752) {G4,W6,D4,L1,V0,M1} P(263,0) { addition( skol1( skol3 )
% 5.39/5.82 , skol3 ) ==> one }.
% 5.39/5.82 parent1[0; 6]: (20989) {G1,W9,D4,L1,V2,M1} { addition( X, Y ) ==> addition
% 5.39/5.82 ( addition( X, Y ), Y ) }.
% 5.39/5.82 substitution0:
% 5.39/5.82 end
% 5.39/5.82 substitution1:
% 5.39/5.82 X := skol1( skol3 )
% 5.39/5.82 Y := skol3
% 5.39/5.82 end
% 5.39/5.82
% 5.39/5.82 paramod: (20992) {G3,W5,D3,L1,V0,M1} { one ==> addition( one, skol3 ) }.
% 5.39/5.82 parent0[0]: (2752) {G4,W6,D4,L1,V0,M1} P(263,0) { addition( skol1( skol3 )
% 5.39/5.82 , skol3 ) ==> one }.
% 5.39/5.82 parent1[0; 1]: (20991) {G2,W8,D4,L1,V0,M1} { addition( skol1( skol3 ),
% 5.39/5.82 skol3 ) ==> addition( one, skol3 ) }.
% 5.39/5.82 substitution0:
% 5.39/5.82 end
% 5.39/5.82 substitution1:
% 5.39/5.82 end
% 5.39/5.82
% 5.39/5.82 eqswap: (20994) {G3,W5,D3,L1,V0,M1} { addition( one, skol3 ) ==> one }.
% 5.39/5.82 parent0[0]: (20992) {G3,W5,D3,L1,V0,M1} { one ==> addition( one, skol3 )
% 5.39/5.82 }.
% 5.39/5.82 substitution0:
% 5.39/5.82 end
% 5.39/5.82
% 5.39/5.82 subsumption: (2799) {G5,W5,D3,L1,V0,M1} P(2752,34) { addition( one, skol3 )
% 5.39/5.82 ==> one }.
% 5.39/5.82 parent0: (20994) {G3,W5,D3,L1,V0,M1} { addition( one, skol3 ) ==> one }.
% 5.39/5.82 substitution0:
% 5.39/5.82 end
% 5.39/5.82 permutation0:
% 5.39/5.82 0 ==> 0
% 5.39/5.82 end
% 5.39/5.82
% 5.39/5.82 eqswap: (20996) {G0,W11,D3,L3,V2,M3} { ! zero ==> multiplication( X, Y ),
% 5.39/5.82 ! alpha1( X, Y ), complement( Y, X ) }.
% 5.39/5.82 parent0[0]: (17) {G0,W11,D3,L3,V2,M3} I { ! multiplication( X, Y ) ==> zero
% 5.39/5.82 , ! alpha1( X, Y ), complement( Y, X ) }.
% 5.39/5.82 substitution0:
% 5.39/5.82 X := X
% 5.39/5.82 Y := Y
% 5.39/5.82 end
% 5.39/5.82
% 5.39/5.82 resolution: (20998) {G1,W10,D4,L2,V0,M2} { ! zero ==> multiplication(
% 5.39/5.82 skol1( skol3 ), skol3 ), complement( skol3, skol1( skol3 ) ) }.
% 5.39/5.82 parent0[1]: (20996) {G0,W11,D3,L3,V2,M3} { ! zero ==> multiplication( X, Y
% 5.39/5.82 ), ! alpha1( X, Y ), complement( Y, X ) }.
% 5.39/5.82 parent1[0]: (2787) {G5,W4,D3,L1,V0,M1} R(2752,20);d(195);q { alpha1( skol1
% 5.39/5.82 ( skol3 ), skol3 ) }.
% 5.39/5.82 substitution0:
% 5.39/5.82 X := skol1( skol3 )
% 5.39/5.82 Y := skol3
% 5.39/5.82 end
% 5.39/5.82 substitution1:
% 5.39/5.82 end
% 5.39/5.82
% 5.39/5.82 paramod: (20999) {G2,W7,D3,L2,V0,M2} { ! zero ==> zero, complement( skol3
% 5.39/5.82 , skol1( skol3 ) ) }.
% 5.39/5.82 parent0[0]: (237) {G3,W6,D4,L1,V0,M1} R(18,187) { multiplication( skol1(
% 5.39/5.82 skol3 ), skol3 ) ==> zero }.
% 5.39/5.82 parent1[0; 3]: (20998) {G1,W10,D4,L2,V0,M2} { ! zero ==> multiplication(
% 5.39/5.82 skol1( skol3 ), skol3 ), complement( skol3, skol1( skol3 ) ) }.
% 5.39/5.82 substitution0:
% 5.39/5.82 end
% 5.39/5.82 substitution1:
% 5.39/5.82 end
% 5.39/5.82
% 5.39/5.82 eqrefl: (21000) {G0,W4,D3,L1,V0,M1} { complement( skol3, skol1( skol3 ) )
% 5.39/5.82 }.
% 5.39/5.82 parent0[0]: (20999) {G2,W7,D3,L2,V0,M2} { ! zero ==> zero, complement(
% 5.39/5.82 skol3, skol1( skol3 ) ) }.
% 5.39/5.82 substitution0:
% 5.39/5.82 end
% 5.39/5.82
% 5.39/5.82 subsumption: (2802) {G6,W4,D3,L1,V0,M1} R(2787,17);d(237);q { complement(
% 5.39/5.82 skol3, skol1( skol3 ) ) }.
% 5.39/5.82 parent0: (21000) {G0,W4,D3,L1,V0,M1} { complement( skol3, skol1( skol3 ) )
% 5.39/5.82 }.
% 5.39/5.82 substitution0:
% 5.39/5.82 end
% 5.39/5.82 permutation0:
% 5.39/5.82 0 ==> 0
% 5.39/5.82 end
% 5.39/5.82
% 5.39/5.82 eqswap: (21001) {G0,W9,D3,L3,V2,M3} { Y = c( X ), ! test( X ), !
% 5.39/5.82 complement( X, Y ) }.
% 5.39/5.82 parent0[2]: (22) {G0,W9,D3,L3,V2,M3} I { ! test( X ), ! complement( X, Y )
% 5.39/5.82 , c( X ) = Y }.
% 5.39/5.82 substitution0:
% 5.39/5.82 X := X
% 5.39/5.82 Y := Y
% 5.39/5.82 end
% 5.39/5.82
% 5.39/5.82 resolution: (21002) {G1,W7,D3,L2,V0,M2} { skol1( skol3 ) = c( skol3 ), !
% 5.39/5.82 test( skol3 ) }.
% 5.39/5.82 parent0[2]: (21001) {G0,W9,D3,L3,V2,M3} { Y = c( X ), ! test( X ), !
% 5.39/5.82 complement( X, Y ) }.
% 5.39/5.82 parent1[0]: (2802) {G6,W4,D3,L1,V0,M1} R(2787,17);d(237);q { complement(
% 5.39/5.82 skol3, skol1( skol3 ) ) }.
% 5.39/5.82 substitution0:
% 5.39/5.82 X := skol3
% 5.39/5.82 Y := skol1( skol3 )
% 5.39/5.82 end
% 5.39/5.82 substitution1:
% 5.39/5.82 end
% 5.39/5.82
% 5.39/5.82 resolution: (21003) {G1,W5,D3,L1,V0,M1} { skol1( skol3 ) = c( skol3 ) }.
% 5.39/5.82 parent0[1]: (21002) {G1,W7,D3,L2,V0,M2} { skol1( skol3 ) = c( skol3 ), !
% 5.39/5.82 test( skol3 ) }.
% 5.39/5.82 parent1[0]: (26) {G0,W2,D2,L1,V0,M1} I { test( skol3 ) }.
% 5.39/5.82 substitution0:
% 5.39/5.82 end
% 5.39/5.82 substitution1:
% 5.39/5.82 end
% 5.39/5.82
% 5.39/5.82 eqswap: (21004) {G1,W5,D3,L1,V0,M1} { c( skol3 ) = skol1( skol3 ) }.
% 5.39/5.82 parent0[0]: (21003) {G1,W5,D3,L1,V0,M1} { skol1( skol3 ) = c( skol3 ) }.
% 5.39/5.82 substitution0:
% 5.39/5.82 end
% 5.39/5.82
% 5.39/5.82 subsumption: (2807) {G7,W5,D3,L1,V0,M1} R(2802,22);r(26) { c( skol3 ) ==>
% 5.39/5.82 skol1( skol3 ) }.
% 5.39/5.82 parent0: (21004) {G1,W5,D3,L1,V0,M1} { c( skol3 ) = skol1( skol3 ) }.
% 5.39/5.82 substitution0:
% 5.39/5.82 end
% 5.39/5.82 permutation0:
% 5.39/5.82 0 ==> 0
% 5.39/5.82 end
% 5.39/5.82
% 5.39/5.82 eqswap: (21006) {G1,W11,D4,L1,V2,M1} { multiplication( X, addition( one, Y
% 5.39/5.82 ) ) = addition( X, multiplication( X, Y ) ) }.
% 5.39/5.82 parent0[0]: (51) {G1,W11,D4,L1,V2,M1} P(5,7) { addition( X, multiplication
% 5.39/5.82 ( X, Y ) ) = multiplication( X, addition( one, Y ) ) }.
% 5.39/5.82 substitution0:
% 5.39/5.82 X := X
% 5.39/5.82 Y := Y
% 5.39/5.82 end
% 5.39/5.82
% 5.39/5.82 paramod: (21008) {G2,W9,D4,L1,V1,M1} { multiplication( X, one ) = addition
% 5.39/5.82 ( X, multiplication( X, skol3 ) ) }.
% 5.39/5.82 parent0[0]: (2799) {G5,W5,D3,L1,V0,M1} P(2752,34) { addition( one, skol3 )
% 5.39/5.82 ==> one }.
% 5.39/5.82 parent1[0; 3]: (21006) {G1,W11,D4,L1,V2,M1} { multiplication( X, addition
% 5.39/5.82 ( one, Y ) ) = addition( X, multiplication( X, Y ) ) }.
% 5.39/5.82 substitution0:
% 5.39/5.82 end
% 5.39/5.82 substitution1:
% 5.39/5.82 X := X
% 5.39/5.82 Y := skol3
% 5.39/5.82 end
% 5.39/5.82
% 5.39/5.82 paramod: (21009) {G1,W7,D4,L1,V1,M1} { X = addition( X, multiplication( X
% 5.39/5.82 , skol3 ) ) }.
% 5.39/5.82 parent0[0]: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 5.39/5.82 parent1[0; 1]: (21008) {G2,W9,D4,L1,V1,M1} { multiplication( X, one ) =
% 5.39/5.82 addition( X, multiplication( X, skol3 ) ) }.
% 5.39/5.82 substitution0:
% 5.39/5.82 X := X
% 5.39/5.82 end
% 5.39/5.82 substitution1:
% 5.39/5.82 X := X
% 5.39/5.82 end
% 5.39/5.82
% 5.39/5.82 eqswap: (21010) {G1,W7,D4,L1,V1,M1} { addition( X, multiplication( X,
% 5.39/5.82 skol3 ) ) = X }.
% 5.39/5.82 parent0[0]: (21009) {G1,W7,D4,L1,V1,M1} { X = addition( X, multiplication
% 5.39/5.82 ( X, skol3 ) ) }.
% 5.39/5.82 substitution0:
% 5.39/5.82 X := X
% 5.39/5.82 end
% 5.39/5.82
% 5.39/5.82 subsumption: (2865) {G6,W7,D4,L1,V1,M1} P(2799,51);d(5) { addition( X,
% 5.39/5.82 multiplication( X, skol3 ) ) ==> X }.
% 5.39/5.82 parent0: (21010) {G1,W7,D4,L1,V1,M1} { addition( X, multiplication( X,
% 5.39/5.82 skol3 ) ) = X }.
% 5.39/5.82 substitution0:
% 5.39/5.82 X := X
% 5.39/5.82 end
% 5.39/5.82 permutation0:
% 5.39/5.82 0 ==> 0
% 5.39/5.82 end
% 5.39/5.82
% 5.39/5.82 eqswap: (21012) {G1,W17,D5,L1,V4,M1} { addition( X, multiplication(
% 5.39/5.82 addition( Y, T ), Z ) ) ==> addition( addition( X, multiplication( Y, Z )
% 5.39/5.82 ), multiplication( T, Z ) ) }.
% 5.39/5.82 parent0[0]: (63) {G1,W17,D5,L1,V4,M1} P(8,1) { addition( addition( T,
% 5.39/5.82 multiplication( X, Y ) ), multiplication( Z, Y ) ) ==> addition( T,
% 5.39/5.82 multiplication( addition( X, Z ), Y ) ) }.
% 5.39/5.82 substitution0:
% 5.39/5.82 X := Y
% 5.39/5.82 Y := Z
% 5.39/5.82 Z := T
% 5.39/5.82 T := X
% 5.39/5.82 end
% 5.39/5.82
% 5.39/5.82 paramod: (21018) {G2,W13,D5,L1,V2,M1} { addition( X, multiplication(
% 5.39/5.82 addition( X, Y ), skol3 ) ) ==> addition( X, multiplication( Y, skol3 ) )
% 5.39/5.82 }.
% 5.39/5.82 parent0[0]: (2865) {G6,W7,D4,L1,V1,M1} P(2799,51);d(5) { addition( X,
% 5.39/5.82 multiplication( X, skol3 ) ) ==> X }.
% 5.39/5.82 parent1[0; 9]: (21012) {G1,W17,D5,L1,V4,M1} { addition( X, multiplication
% 5.39/5.82 ( addition( Y, T ), Z ) ) ==> addition( addition( X, multiplication( Y, Z
% 5.39/5.82 ) ), multiplication( T, Z ) ) }.
% 5.39/5.82 substitution0:
% 5.39/5.82 X := X
% 5.39/5.82 end
% 5.39/5.82 substitution1:
% 5.39/5.82 X := X
% 5.39/5.82 Y := X
% 5.39/5.82 Z := skol3
% 5.39/5.82 T := Y
% 5.39/5.82 end
% 5.39/5.82
% 5.39/5.82 subsumption: (18520) {G7,W13,D5,L1,V2,M1} P(2865,63) { addition( X,
% 5.39/5.82 multiplication( addition( X, Y ), skol3 ) ) ==> addition( X,
% 5.39/5.82 multiplication( Y, skol3 ) ) }.
% 5.39/5.82 parent0: (21018) {G2,W13,D5,L1,V2,M1} { addition( X, multiplication(
% 5.39/5.82 addition( X, Y ), skol3 ) ) ==> addition( X, multiplication( Y, skol3 ) )
% 5.39/5.82 }.
% 5.39/5.82 substitution0:
% 5.39/5.82 X := X
% 5.39/5.82 Y := Y
% 5.39/5.82 end
% 5.39/5.82 permutation0:
% 5.39/5.82 0 ==> 0
% 5.39/5.82 end
% 5.39/5.82
% 5.39/5.82 paramod: (21033) {G2,W20,D7,L2,V0,M2} { ! addition( addition( skol2,
% 5.39/5.82 multiplication( addition( skol2, c( skol2 ) ), skol3 ) ), multiplication
% 5.39/5.82 ( c( skol2 ), skol1( skol3 ) ) ) ==> one, ! alpha1( skol3, c( skol3 ) )
% 5.39/5.82 }.
% 5.39/5.82 parent0[0]: (2807) {G7,W5,D3,L1,V0,M1} R(2802,22);r(26) { c( skol3 ) ==>
% 5.39/5.82 skol1( skol3 ) }.
% 5.39/5.82 parent1[1; 14]: (527) {G1,W20,D7,L2,V0,M2} P(19,28);d(6) { ! alpha1( skol3
% 5.39/5.82 , c( skol3 ) ), ! addition( addition( skol2, multiplication( addition(
% 5.39/5.82 skol2, c( skol2 ) ), skol3 ) ), multiplication( c( skol2 ), c( skol3 ) )
% 5.39/5.82 ) ==> one }.
% 5.39/5.82 substitution0:
% 5.39/5.82 end
% 5.39/5.82 substitution1:
% 5.39/5.82 end
% 5.39/5.82
% 5.39/5.82 paramod: (21035) {G3,W18,D6,L2,V0,M2} { ! addition( addition( skol2,
% 5.39/5.82 multiplication( c( skol2 ), skol3 ) ), multiplication( c( skol2 ), skol1
% 5.39/5.82 ( skol3 ) ) ) ==> one, ! alpha1( skol3, c( skol3 ) ) }.
% 5.39/5.82 parent0[0]: (18520) {G7,W13,D5,L1,V2,M1} P(2865,63) { addition( X,
% 5.39/5.82 multiplication( addition( X, Y ), skol3 ) ) ==> addition( X,
% 5.39/5.82 multiplication( Y, skol3 ) ) }.
% 5.39/5.82 parent1[0; 3]: (21033) {G2,W20,D7,L2,V0,M2} { ! addition( addition( skol2
% 5.39/5.82 , multiplication( addition( skol2, c( skol2 ) ), skol3 ) ),
% 5.39/5.82 multiplication( c( skol2 ), skol1( skol3 ) ) ) ==> one, ! alpha1( skol3,
% 5.39/5.82 c( skol3 ) ) }.
% 5.39/5.82 substitution0:
% 5.39/5.82 X := skol2
% 5.39/5.82 Y := c( skol2 )
% 5.39/5.82 end
% 5.39/5.82 substitution1:
% 5.39/5.82 end
% 5.39/5.82
% 5.39/5.82 paramod: (21036) {G2,W15,D6,L2,V0,M2} { ! addition( skol2, multiplication
% 5.39/5.82 ( c( skol2 ), addition( skol3, skol1( skol3 ) ) ) ) ==> one, ! alpha1(
% 5.39/5.82 skol3, c( skol3 ) ) }.
% 5.39/5.82 parent0[0]: (50) {G1,W17,D5,L1,V4,M1} P(7,1) { addition( addition( T,
% 5.39/5.82 multiplication( X, Y ) ), multiplication( X, Z ) ) ==> addition( T,
% 5.39/5.82 multiplication( X, addition( Y, Z ) ) ) }.
% 5.39/5.82 parent1[0; 2]: (21035) {G3,W18,D6,L2,V0,M2} { ! addition( addition( skol2
% 5.39/5.82 , multiplication( c( skol2 ), skol3 ) ), multiplication( c( skol2 ),
% 5.39/5.82 skol1( skol3 ) ) ) ==> one, ! alpha1( skol3, c( skol3 ) ) }.
% 5.39/5.82 substitution0:
% 5.39/5.82 X := c( skol2 )
% 5.39/5.82 Y := skol3
% 5.39/5.82 Z := skol1( skol3 )
% 5.39/5.82 T := skol2
% 5.39/5.82 end
% 5.39/5.82 substitution1:
% 5.39/5.82 end
% 5.39/5.82
% 5.39/5.82 paramod: (21037) {G3,W15,D6,L2,V0,M2} { ! addition( skol2, multiplication
% 5.39/5.82 ( skol1( skol2 ), addition( skol3, skol1( skol3 ) ) ) ) ==> one, ! alpha1
% 5.39/5.82 ( skol3, c( skol3 ) ) }.
% 5.39/5.82 parent0[0]: (2451) {G7,W5,D3,L1,V0,M1} R(2446,22);r(27) { c( skol2 ) ==>
% 5.39/5.82 skol1( skol2 ) }.
% 5.39/5.82 parent1[0; 5]: (21036) {G2,W15,D6,L2,V0,M2} { ! addition( skol2,
% 5.39/5.82 multiplication( c( skol2 ), addition( skol3, skol1( skol3 ) ) ) ) ==> one
% 5.39/5.82 , ! alpha1( skol3, c( skol3 ) ) }.
% 5.39/5.82 substitution0:
% 5.39/5.82 end
% 5.39/5.82 substitution1:
% 5.39/5.82 end
% 5.39/5.82
% 5.39/5.82 paramod: (21038) {G4,W15,D6,L2,V0,M2} { ! alpha1( skol3, skol1( skol3 ) )
% 5.39/5.82 , ! addition( skol2, multiplication( skol1( skol2 ), addition( skol3,
% 5.39/5.82 skol1( skol3 ) ) ) ) ==> one }.
% 5.39/5.82 parent0[0]: (2807) {G7,W5,D3,L1,V0,M1} R(2802,22);r(26) { c( skol3 ) ==>
% 5.39/5.82 skol1( skol3 ) }.
% 5.39/5.82 parent1[1; 3]: (21037) {G3,W15,D6,L2,V0,M2} { ! addition( skol2,
% 5.39/5.82 multiplication( skol1( skol2 ), addition( skol3, skol1( skol3 ) ) ) ) ==>
% 5.39/5.82 one, ! alpha1( skol3, c( skol3 ) ) }.
% 5.39/5.82 substitution0:
% 5.39/5.82 end
% 5.39/5.82 substitution1:
% 5.39/5.82 end
% 5.39/5.82
% 5.39/5.82 paramod: (21040) {G1,W16,D5,L3,V0,M3} { ! addition( skol2, multiplication
% 5.39/5.82 ( skol1( skol2 ), one ) ) ==> one, ! alpha1( skol3, skol1( skol3 ) ), !
% 5.39/5.82 alpha1( skol3, skol1( skol3 ) ) }.
% 5.39/5.82 parent0[1]: (19) {G0,W8,D3,L2,V2,M2} I { ! alpha1( X, Y ), addition( X, Y )
% 5.39/5.82 ==> one }.
% 5.39/5.82 parent1[1; 7]: (21038) {G4,W15,D6,L2,V0,M2} { ! alpha1( skol3, skol1(
% 5.39/5.82 skol3 ) ), ! addition( skol2, multiplication( skol1( skol2 ), addition(
% 5.39/5.82 skol3, skol1( skol3 ) ) ) ) ==> one }.
% 5.39/5.82 substitution0:
% 5.39/5.82 X := skol3
% 5.39/5.82 Y := skol1( skol3 )
% 5.39/5.82 end
% 5.39/5.82 substitution1:
% 5.39/5.82 end
% 5.39/5.82
% 5.39/5.82 factor: (21043) {G1,W12,D5,L2,V0,M2} { ! addition( skol2, multiplication(
% 5.39/5.82 skol1( skol2 ), one ) ) ==> one, ! alpha1( skol3, skol1( skol3 ) ) }.
% 5.39/5.82 parent0[1, 2]: (21040) {G1,W16,D5,L3,V0,M3} { ! addition( skol2,
% 5.39/5.82 multiplication( skol1( skol2 ), one ) ) ==> one, ! alpha1( skol3, skol1(
% 5.39/5.82 skol3 ) ), ! alpha1( skol3, skol1( skol3 ) ) }.
% 5.39/5.82 substitution0:
% 5.39/5.82 end
% 5.39/5.82
% 5.39/5.82 paramod: (21044) {G1,W10,D4,L2,V0,M2} { ! addition( skol2, skol1( skol2 )
% 5.39/5.82 ) ==> one, ! alpha1( skol3, skol1( skol3 ) ) }.
% 5.39/5.82 parent0[0]: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 5.39/5.82 parent1[0; 4]: (21043) {G1,W12,D5,L2,V0,M2} { ! addition( skol2,
% 5.39/5.82 multiplication( skol1( skol2 ), one ) ) ==> one, ! alpha1( skol3, skol1(
% 5.39/5.82 skol3 ) ) }.
% 5.39/5.82 substitution0:
% 5.39/5.82 X := skol1( skol2 )
% 5.39/5.82 end
% 5.39/5.82 substitution1:
% 5.39/5.82 end
% 5.39/5.82
% 5.39/5.82 paramod: (21045) {G2,W7,D3,L2,V0,M2} { ! one ==> one, ! alpha1( skol3,
% 5.39/5.82 skol1( skol3 ) ) }.
% 5.39/5.82 parent0[0]: (262) {G3,W6,D4,L1,V0,M1} R(19,191) { addition( skol2, skol1(
% 5.39/5.82 skol2 ) ) ==> one }.
% 5.39/5.82 parent1[0; 2]: (21044) {G1,W10,D4,L2,V0,M2} { ! addition( skol2, skol1(
% 5.39/5.82 skol2 ) ) ==> one, ! alpha1( skol3, skol1( skol3 ) ) }.
% 5.39/5.82 substitution0:
% 5.39/5.82 end
% 5.39/5.82 substitution1:
% 5.39/5.82 end
% 5.39/5.82
% 5.39/5.82 eqrefl: (21046) {G0,W4,D3,L1,V0,M1} { ! alpha1( skol3, skol1( skol3 ) )
% 5.39/5.82 }.
% 5.39/5.82 parent0[0]: (21045) {G2,W7,D3,L2,V0,M2} { ! one ==> one, ! alpha1( skol3,
% 5.39/5.82 skol1( skol3 ) ) }.
% 5.39/5.82 substitution0:
% 5.39/5.82 end
% 5.39/5.82
% 5.39/5.82 resolution: (21047) {G1,W0,D0,L0,V0,M0} { }.
% 5.39/5.82 parent0[0]: (21046) {G0,W4,D3,L1,V0,M1} { ! alpha1( skol3, skol1( skol3 )
% 5.39/5.82 ) }.
% 5.39/5.82 parent1[0]: (187) {G2,W4,D3,L1,V0,M1} R(183,16) { alpha1( skol3, skol1(
% 5.39/5.82 skol3 ) ) }.
% 5.39/5.82 substitution0:
% 5.39/5.82 end
% 5.39/5.82 substitution1:
% 5.39/5.82 end
% 5.39/5.82
% 5.39/5.82 subsumption: (20585) {G8,W0,D0,L0,V0,M0} S(527);d(2807);d(18520);d(50);d(
% 5.39/5.82 2451);d(2807);d(19);d(5);d(262);q;r(187) { }.
% 5.39/5.82 parent0: (21047) {G1,W0,D0,L0,V0,M0} { }.
% 5.39/5.82 substitution0:
% 5.39/5.82 end
% 5.39/5.82 permutation0:
% 5.39/5.82 end
% 5.39/5.82
% 5.39/5.82 Proof check complete!
% 5.39/5.82
% 5.39/5.82 Memory use:
% 5.39/5.82
% 5.39/5.82 space for terms: 251901
% 5.39/5.82 space for clauses: 978634
% 5.39/5.82
% 5.39/5.82
% 5.39/5.82 clauses generated: 158248
% 5.39/5.82 clauses kept: 20586
% 5.39/5.82 clauses selected: 1323
% 5.39/5.82 clauses deleted: 5278
% 5.39/5.82 clauses inuse deleted: 305
% 5.39/5.82
% 5.39/5.82 subsentry: 991907
% 5.39/5.82 literals s-matched: 546591
% 5.39/5.82 literals matched: 538562
% 5.39/5.82 full subsumption: 204750
% 5.39/5.82
% 5.39/5.82 checksum: -324707272
% 5.39/5.82
% 5.39/5.82
% 5.39/5.82 Bliksem ended
%------------------------------------------------------------------------------