TSTP Solution File: GRP747+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : GRP747+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n008.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 : Sat Jul 16 07:39:21 EDT 2022
% Result : Theorem 0.71s 1.12s
% Output : Refutation 0.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GRP747+1 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.13 % Command : bliksem %s
% 0.12/0.34 % Computer : n008.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % DateTime : Tue Jun 14 07:15:52 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.71/1.11 *** allocated 10000 integers for termspace/termends
% 0.71/1.11 *** allocated 10000 integers for clauses
% 0.71/1.11 *** allocated 10000 integers for justifications
% 0.71/1.11 Bliksem 1.12
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 Automatic Strategy Selection
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 Clauses:
% 0.71/1.11
% 0.71/1.11 { mult( Y, ld( Y, X ) ) = X }.
% 0.71/1.11 { ld( Y, mult( Y, X ) ) = X }.
% 0.71/1.11 { mult( rd( Y, X ), X ) = Y }.
% 0.71/1.11 { rd( mult( Y, X ), X ) = Y }.
% 0.71/1.11 { mult( X, unit ) = X }.
% 0.71/1.11 { mult( unit, X ) = X }.
% 0.71/1.11 { mult( mult( mult( Z, Y ), X ), Y ) = mult( Z, mult( mult( Y, X ), Y ) ) }
% 0.71/1.11 .
% 0.71/1.11 { alpha1( X, Y, Z ), mult( mult( X, Y ), Z ) = mult( mult( X, Z ), Y ) }.
% 0.71/1.11 { alpha1( X, Y, Z ), mult( X, mult( Y, Z ) ) = mult( X, mult( Z, Y ) ) }.
% 0.71/1.11 { ! alpha1( X, Y, Z ), mult( mult( X, Y ), Z ) = mult( X, mult( Z, Y ) ) }
% 0.71/1.11 .
% 0.71/1.11 { ! alpha1( X, Y, Z ), mult( mult( X, Z ), Y ) = mult( X, mult( Y, Z ) ) }
% 0.71/1.11 .
% 0.71/1.11 { ! mult( mult( X, Y ), Z ) = mult( X, mult( Z, Y ) ), ! mult( mult( X, Z )
% 0.71/1.11 , Y ) = mult( X, mult( Y, Z ) ), alpha1( X, Y, Z ) }.
% 0.71/1.11 { ! mult( mult( a, b ), c ) = mult( a, mult( b, c ) ) }.
% 0.71/1.11
% 0.71/1.11 percentage equality = 0.736842, percentage horn = 0.846154
% 0.71/1.11 This is a problem with some equality
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 Options Used:
% 0.71/1.11
% 0.71/1.11 useres = 1
% 0.71/1.11 useparamod = 1
% 0.71/1.11 useeqrefl = 1
% 0.71/1.11 useeqfact = 1
% 0.71/1.11 usefactor = 1
% 0.71/1.11 usesimpsplitting = 0
% 0.71/1.11 usesimpdemod = 5
% 0.71/1.11 usesimpres = 3
% 0.71/1.11
% 0.71/1.11 resimpinuse = 1000
% 0.71/1.11 resimpclauses = 20000
% 0.71/1.11 substype = eqrewr
% 0.71/1.11 backwardsubs = 1
% 0.71/1.11 selectoldest = 5
% 0.71/1.11
% 0.71/1.11 litorderings [0] = split
% 0.71/1.11 litorderings [1] = extend the termordering, first sorting on arguments
% 0.71/1.11
% 0.71/1.11 termordering = kbo
% 0.71/1.11
% 0.71/1.11 litapriori = 0
% 0.71/1.11 termapriori = 1
% 0.71/1.11 litaposteriori = 0
% 0.71/1.11 termaposteriori = 0
% 0.71/1.11 demodaposteriori = 0
% 0.71/1.11 ordereqreflfact = 0
% 0.71/1.11
% 0.71/1.11 litselect = negord
% 0.71/1.11
% 0.71/1.11 maxweight = 15
% 0.71/1.11 maxdepth = 30000
% 0.71/1.11 maxlength = 115
% 0.71/1.11 maxnrvars = 195
% 0.71/1.11 excuselevel = 1
% 0.71/1.11 increasemaxweight = 1
% 0.71/1.11
% 0.71/1.11 maxselected = 10000000
% 0.71/1.11 maxnrclauses = 10000000
% 0.71/1.11
% 0.71/1.11 showgenerated = 0
% 0.71/1.11 showkept = 0
% 0.71/1.11 showselected = 0
% 0.71/1.11 showdeleted = 0
% 0.71/1.11 showresimp = 1
% 0.71/1.11 showstatus = 2000
% 0.71/1.11
% 0.71/1.11 prologoutput = 0
% 0.71/1.11 nrgoals = 5000000
% 0.71/1.11 totalproof = 1
% 0.71/1.11
% 0.71/1.11 Symbols occurring in the translation:
% 0.71/1.12
% 0.71/1.12 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.71/1.12 . [1, 2] (w:1, o:21, a:1, s:1, b:0),
% 0.71/1.12 ! [4, 1] (w:0, o:16, a:1, s:1, b:0),
% 0.71/1.12 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.71/1.12 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.71/1.12 ld [37, 2] (w:1, o:45, a:1, s:1, b:0),
% 0.71/1.12 mult [38, 2] (w:1, o:46, a:1, s:1, b:0),
% 0.71/1.12 rd [39, 2] (w:1, o:47, a:1, s:1, b:0),
% 0.71/1.12 unit [40, 0] (w:1, o:8, a:1, s:1, b:0),
% 0.71/1.12 a [45, 0] (w:1, o:13, a:1, s:1, b:0),
% 0.71/1.12 b [46, 0] (w:1, o:14, a:1, s:1, b:0),
% 0.71/1.12 c [47, 0] (w:1, o:15, a:1, s:1, b:0),
% 0.71/1.12 alpha1 [48, 3] (w:1, o:48, a:1, s:1, b:1).
% 0.71/1.12
% 0.71/1.12
% 0.71/1.12 Starting Search:
% 0.71/1.12
% 0.71/1.12 *** allocated 15000 integers for clauses
% 0.71/1.12 *** allocated 22500 integers for clauses
% 0.71/1.12 *** allocated 33750 integers for clauses
% 0.71/1.12
% 0.71/1.12 Bliksems!, er is een bewijs:
% 0.71/1.12 % SZS status Theorem
% 0.71/1.12 % SZS output start Refutation
% 0.71/1.12
% 0.71/1.12 (0) {G0,W7,D4,L1,V2,M1} I { mult( Y, ld( Y, X ) ) ==> X }.
% 0.71/1.12 (1) {G0,W7,D4,L1,V2,M1} I { ld( Y, mult( Y, X ) ) ==> X }.
% 0.71/1.12 (4) {G0,W5,D3,L1,V1,M1} I { mult( X, unit ) ==> X }.
% 0.71/1.12 (5) {G0,W5,D3,L1,V1,M1} I { mult( unit, X ) ==> X }.
% 0.71/1.12 (7) {G0,W15,D4,L2,V3,M2} I { alpha1( X, Y, Z ), mult( mult( X, Y ), Z ) =
% 0.71/1.12 mult( mult( X, Z ), Y ) }.
% 0.71/1.12 (8) {G0,W15,D4,L2,V3,M2} I { alpha1( X, Y, Z ), mult( X, mult( Y, Z ) ) =
% 0.71/1.12 mult( X, mult( Z, Y ) ) }.
% 0.71/1.12 (9) {G0,W15,D4,L2,V3,M2} I { ! alpha1( X, Y, Z ), mult( X, mult( Z, Y ) )
% 0.71/1.12 ==> mult( mult( X, Y ), Z ) }.
% 0.71/1.12 (10) {G0,W15,D4,L2,V3,M2} I { ! alpha1( X, Y, Z ), mult( X, mult( Y, Z ) )
% 0.71/1.12 ==> mult( mult( X, Z ), Y ) }.
% 0.71/1.12 (12) {G0,W11,D4,L1,V0,M1} I { ! mult( a, mult( b, c ) ) ==> mult( mult( a,
% 0.71/1.12 b ), c ) }.
% 0.71/1.12 (92) {G1,W11,D3,L2,V3,M2} P(8,1);d(1) { alpha1( X, Y, Z ), mult( Z, Y ) =
% 0.71/1.12 mult( Y, Z ) }.
% 0.71/1.12 (143) {G2,W7,D3,L1,V2,M1} P(9,5);d(5);r(92) { mult( Y, X ) = mult( X, Y )
% 0.71/1.12 }.
% 0.71/1.12 (145) {G3,W11,D4,L1,V3,M1} P(143,9);d(10);r(7) { mult( mult( Z, X ), Y ) =
% 0.71/1.12 mult( mult( Z, Y ), X ) }.
% 0.71/1.12 (158) {G3,W7,D4,L1,V2,M1} P(143,1) { ld( X, mult( Y, X ) ) ==> Y }.
% 0.71/1.12 (160) {G3,W7,D4,L1,V2,M1} P(143,0) { mult( ld( X, Y ), X ) ==> Y }.
% 0.71/1.12 (170) {G4,W7,D4,L1,V2,M1} P(0,158) { ld( ld( X, Y ), Y ) ==> X }.
% 0.71/1.12 (197) {G4,W11,D4,L1,V3,M1} P(145,143) { mult( Z, mult( X, Y ) ) ==> mult(
% 0.71/1.12 mult( X, Z ), Y ) }.
% 0.71/1.12 (207) {G5,W11,D4,L1,V3,M1} P(143,197);d(197) { mult( mult( Y, Z ), X ) =
% 0.71/1.12 mult( mult( X, Z ), Y ) }.
% 0.71/1.12 (208) {G5,W11,D4,L1,V0,M1} P(197,12) { ! mult( mult( a, b ), c ) ==> mult(
% 0.71/1.12 mult( b, a ), c ) }.
% 0.71/1.12 (216) {G6,W11,D4,L1,V3,M1} P(160,207) { mult( mult( Z, X ), ld( X, Y ) )
% 0.71/1.12 ==> mult( Y, Z ) }.
% 0.71/1.12 (225) {G7,W11,D4,L1,V3,M1} P(160,216) { mult( Y, ld( X, Z ) ) = mult( Z, ld
% 0.71/1.12 ( X, Y ) ) }.
% 0.71/1.12 (236) {G8,W11,D4,L1,V3,M1} P(225,143) { mult( Z, ld( Y, X ) ) ==> mult( ld
% 0.71/1.12 ( Y, Z ), X ) }.
% 0.71/1.12 (249) {G9,W9,D4,L1,V2,M1} P(236,5) { mult( ld( X, unit ), Y ) ==> ld( X, Y
% 0.71/1.12 ) }.
% 0.71/1.12 (252) {G10,W11,D4,L1,V3,M1} P(249,207);d(236);d(4) { mult( ld( X, Y ), Z )
% 0.71/1.12 ==> ld( X, mult( Z, Y ) ) }.
% 0.71/1.12 (254) {G10,W9,D4,L1,V2,M1} P(170,249) { ld( ld( X, unit ), Y ) ==> mult( X
% 0.71/1.12 , Y ) }.
% 0.71/1.12 (257) {G11,W11,D4,L1,V3,M1} P(254,225);d(197);d(236);d(252);d(254);d(197)
% 0.71/1.12 { mult( mult( X, Z ), Y ) = mult( mult( Z, X ), Y ) }.
% 0.71/1.12 (299) {G12,W0,D0,L0,V0,M0} P(257,208);q { }.
% 0.71/1.12
% 0.71/1.12
% 0.71/1.12 % SZS output end Refutation
% 0.71/1.12 found a proof!
% 0.71/1.12
% 0.71/1.12
% 0.71/1.12 Unprocessed initial clauses:
% 0.71/1.12
% 0.71/1.12 (301) {G0,W7,D4,L1,V2,M1} { mult( Y, ld( Y, X ) ) = X }.
% 0.71/1.12 (302) {G0,W7,D4,L1,V2,M1} { ld( Y, mult( Y, X ) ) = X }.
% 0.71/1.12 (303) {G0,W7,D4,L1,V2,M1} { mult( rd( Y, X ), X ) = Y }.
% 0.71/1.12 (304) {G0,W7,D4,L1,V2,M1} { rd( mult( Y, X ), X ) = Y }.
% 0.71/1.12 (305) {G0,W5,D3,L1,V1,M1} { mult( X, unit ) = X }.
% 0.71/1.12 (306) {G0,W5,D3,L1,V1,M1} { mult( unit, X ) = X }.
% 0.71/1.12 (307) {G0,W15,D5,L1,V3,M1} { mult( mult( mult( Z, Y ), X ), Y ) = mult( Z
% 0.71/1.12 , mult( mult( Y, X ), Y ) ) }.
% 0.71/1.12 (308) {G0,W15,D4,L2,V3,M2} { alpha1( X, Y, Z ), mult( mult( X, Y ), Z ) =
% 0.71/1.12 mult( mult( X, Z ), Y ) }.
% 0.71/1.12 (309) {G0,W15,D4,L2,V3,M2} { alpha1( X, Y, Z ), mult( X, mult( Y, Z ) ) =
% 0.71/1.12 mult( X, mult( Z, Y ) ) }.
% 0.71/1.12 (310) {G0,W15,D4,L2,V3,M2} { ! alpha1( X, Y, Z ), mult( mult( X, Y ), Z )
% 0.71/1.12 = mult( X, mult( Z, Y ) ) }.
% 0.71/1.12 (311) {G0,W15,D4,L2,V3,M2} { ! alpha1( X, Y, Z ), mult( mult( X, Z ), Y )
% 0.71/1.12 = mult( X, mult( Y, Z ) ) }.
% 0.71/1.12 (312) {G0,W26,D4,L3,V3,M3} { ! mult( mult( X, Y ), Z ) = mult( X, mult( Z
% 0.71/1.12 , Y ) ), ! mult( mult( X, Z ), Y ) = mult( X, mult( Y, Z ) ), alpha1( X,
% 0.71/1.12 Y, Z ) }.
% 0.71/1.12 (313) {G0,W11,D4,L1,V0,M1} { ! mult( mult( a, b ), c ) = mult( a, mult( b
% 0.71/1.12 , c ) ) }.
% 0.71/1.12
% 0.71/1.12
% 0.71/1.12 Total Proof:
% 0.71/1.12
% 0.71/1.12 subsumption: (0) {G0,W7,D4,L1,V2,M1} I { mult( Y, ld( Y, X ) ) ==> X }.
% 0.71/1.12 parent0: (301) {G0,W7,D4,L1,V2,M1} { mult( Y, ld( Y, X ) ) = X }.
% 0.71/1.12 substitution0:
% 0.71/1.12 X := X
% 0.71/1.12 Y := Y
% 0.71/1.12 end
% 0.71/1.12 permutation0:
% 0.71/1.12 0 ==> 0
% 0.71/1.12 end
% 0.71/1.12
% 0.71/1.12 subsumption: (1) {G0,W7,D4,L1,V2,M1} I { ld( Y, mult( Y, X ) ) ==> X }.
% 0.71/1.12 parent0: (302) {G0,W7,D4,L1,V2,M1} { ld( Y, mult( Y, X ) ) = X }.
% 0.71/1.12 substitution0:
% 0.71/1.12 X := X
% 0.71/1.12 Y := Y
% 0.71/1.12 end
% 0.71/1.12 permutation0:
% 0.71/1.12 0 ==> 0
% 0.71/1.12 end
% 0.71/1.12
% 0.71/1.12 subsumption: (4) {G0,W5,D3,L1,V1,M1} I { mult( X, unit ) ==> X }.
% 0.71/1.12 parent0: (305) {G0,W5,D3,L1,V1,M1} { mult( X, unit ) = X }.
% 0.71/1.12 substitution0:
% 0.71/1.12 X := X
% 0.71/1.12 end
% 0.71/1.12 permutation0:
% 0.71/1.12 0 ==> 0
% 0.71/1.12 end
% 0.71/1.12
% 0.71/1.12 subsumption: (5) {G0,W5,D3,L1,V1,M1} I { mult( unit, X ) ==> X }.
% 0.71/1.12 parent0: (306) {G0,W5,D3,L1,V1,M1} { mult( unit, X ) = X }.
% 0.71/1.12 substitution0:
% 0.71/1.12 X := X
% 0.71/1.12 end
% 0.71/1.12 permutation0:
% 0.71/1.12 0 ==> 0
% 0.71/1.12 end
% 0.71/1.12
% 0.71/1.12 subsumption: (7) {G0,W15,D4,L2,V3,M2} I { alpha1( X, Y, Z ), mult( mult( X
% 0.71/1.12 , Y ), Z ) = mult( mult( X, Z ), Y ) }.
% 0.71/1.12 parent0: (308) {G0,W15,D4,L2,V3,M2} { alpha1( X, Y, Z ), mult( mult( X, Y
% 0.71/1.12 ), Z ) = mult( mult( X, Z ), Y ) }.
% 0.71/1.12 substitution0:
% 0.71/1.12 X := X
% 0.71/1.12 Y := Y
% 0.71/1.12 Z := Z
% 0.71/1.12 end
% 0.71/1.12 permutation0:
% 0.71/1.12 0 ==> 0
% 0.71/1.12 1 ==> 1
% 0.71/1.12 end
% 0.71/1.12
% 0.71/1.12 subsumption: (8) {G0,W15,D4,L2,V3,M2} I { alpha1( X, Y, Z ), mult( X, mult
% 0.71/1.12 ( Y, Z ) ) = mult( X, mult( Z, Y ) ) }.
% 0.71/1.12 parent0: (309) {G0,W15,D4,L2,V3,M2} { alpha1( X, Y, Z ), mult( X, mult( Y
% 0.71/1.12 , Z ) ) = mult( X, mult( Z, Y ) ) }.
% 0.71/1.12 substitution0:
% 0.71/1.12 X := X
% 0.71/1.12 Y := Y
% 0.71/1.12 Z := Z
% 0.71/1.12 end
% 0.71/1.12 permutation0:
% 0.71/1.12 0 ==> 0
% 0.71/1.12 1 ==> 1
% 0.71/1.12 end
% 0.71/1.12
% 0.71/1.12 eqswap: (354) {G0,W15,D4,L2,V3,M2} { mult( X, mult( Z, Y ) ) = mult( mult
% 0.71/1.12 ( X, Y ), Z ), ! alpha1( X, Y, Z ) }.
% 0.71/1.12 parent0[1]: (310) {G0,W15,D4,L2,V3,M2} { ! alpha1( X, Y, Z ), mult( mult(
% 0.71/1.12 X, Y ), Z ) = mult( X, mult( Z, Y ) ) }.
% 0.71/1.12 substitution0:
% 0.71/1.12 X := X
% 0.71/1.12 Y := Y
% 0.71/1.12 Z := Z
% 0.71/1.12 end
% 0.71/1.12
% 0.71/1.12 subsumption: (9) {G0,W15,D4,L2,V3,M2} I { ! alpha1( X, Y, Z ), mult( X,
% 0.71/1.12 mult( Z, Y ) ) ==> mult( mult( X, Y ), Z ) }.
% 0.71/1.12 parent0: (354) {G0,W15,D4,L2,V3,M2} { mult( X, mult( Z, Y ) ) = mult( mult
% 0.71/1.12 ( X, Y ), Z ), ! alpha1( X, Y, Z ) }.
% 0.71/1.12 substitution0:
% 0.71/1.12 X := X
% 0.71/1.12 Y := Y
% 0.71/1.12 Z := Z
% 0.71/1.12 end
% 0.71/1.12 permutation0:
% 0.71/1.12 0 ==> 1
% 0.71/1.12 1 ==> 0
% 0.71/1.12 end
% 0.71/1.12
% 0.71/1.12 eqswap: (365) {G0,W15,D4,L2,V3,M2} { mult( X, mult( Z, Y ) ) = mult( mult
% 0.71/1.12 ( X, Y ), Z ), ! alpha1( X, Z, Y ) }.
% 0.71/1.12 parent0[1]: (311) {G0,W15,D4,L2,V3,M2} { ! alpha1( X, Y, Z ), mult( mult(
% 0.71/1.12 X, Z ), Y ) = mult( X, mult( Y, Z ) ) }.
% 0.71/1.12 substitution0:
% 0.71/1.12 X := X
% 0.71/1.12 Y := Z
% 0.71/1.12 Z := Y
% 0.71/1.12 end
% 0.71/1.12
% 0.71/1.12 subsumption: (10) {G0,W15,D4,L2,V3,M2} I { ! alpha1( X, Y, Z ), mult( X,
% 0.71/1.12 mult( Y, Z ) ) ==> mult( mult( X, Z ), Y ) }.
% 0.71/1.12 parent0: (365) {G0,W15,D4,L2,V3,M2} { mult( X, mult( Z, Y ) ) = mult( mult
% 0.71/1.12 ( X, Y ), Z ), ! alpha1( X, Z, Y ) }.
% 0.71/1.12 substitution0:
% 0.71/1.12 X := X
% 0.71/1.12 Y := Z
% 0.71/1.12 Z := Y
% 0.71/1.12 end
% 0.71/1.12 permutation0:
% 0.71/1.12 0 ==> 1
% 0.71/1.12 1 ==> 0
% 0.71/1.12 end
% 0.71/1.12
% 0.71/1.12 eqswap: (382) {G0,W11,D4,L1,V0,M1} { ! mult( a, mult( b, c ) ) = mult(
% 0.71/1.12 mult( a, b ), c ) }.
% 0.71/1.12 parent0[0]: (313) {G0,W11,D4,L1,V0,M1} { ! mult( mult( a, b ), c ) = mult
% 0.71/1.12 ( a, mult( b, c ) ) }.
% 0.71/1.12 substitution0:
% 0.71/1.12 end
% 0.71/1.12
% 0.71/1.12 subsumption: (12) {G0,W11,D4,L1,V0,M1} I { ! mult( a, mult( b, c ) ) ==>
% 0.71/1.12 mult( mult( a, b ), c ) }.
% 0.71/1.12 parent0: (382) {G0,W11,D4,L1,V0,M1} { ! mult( a, mult( b, c ) ) = mult(
% 0.71/1.12 mult( a, b ), c ) }.
% 0.71/1.12 substitution0:
% 0.71/1.12 end
% 0.71/1.12 permutation0:
% 0.71/1.12 0 ==> 0
% 0.71/1.12 end
% 0.71/1.12
% 0.71/1.12 eqswap: (383) {G0,W15,D4,L2,V3,M2} { mult( X, mult( Z, Y ) ) = mult( X,
% 0.71/1.12 mult( Y, Z ) ), alpha1( X, Y, Z ) }.
% 0.71/1.12 parent0[1]: (8) {G0,W15,D4,L2,V3,M2} I { alpha1( X, Y, Z ), mult( X, mult(
% 0.71/1.12 Y, Z ) ) = mult( X, mult( Z, Y ) ) }.
% 0.71/1.12 substitution0:
% 0.71/1.12 X := X
% 0.71/1.12 Y := Y
% 0.71/1.12 Z := Z
% 0.71/1.12 end
% 0.71/1.12
% 0.71/1.12 eqswap: (384) {G0,W7,D4,L1,V2,M1} { Y ==> ld( X, mult( X, Y ) ) }.
% 0.71/1.12 parent0[0]: (1) {G0,W7,D4,L1,V2,M1} I { ld( Y, mult( Y, X ) ) ==> X }.
% 0.71/1.12 substitution0:
% 0.71/1.12 X := Y
% 0.71/1.12 Y := X
% 0.71/1.12 end
% 0.71/1.12
% 0.71/1.12 paramod: (386) {G1,W15,D5,L2,V3,M2} { mult( X, Y ) ==> ld( Z, mult( Z,
% 0.71/1.12 mult( Y, X ) ) ), alpha1( Z, Y, X ) }.
% 0.71/1.12 parent0[0]: (383) {G0,W15,D4,L2,V3,M2} { mult( X, mult( Z, Y ) ) = mult( X
% 0.71/1.12 , mult( Y, Z ) ), alpha1( X, Y, Z ) }.
% 0.71/1.12 parent1[0; 6]: (384) {G0,W7,D4,L1,V2,M1} { Y ==> ld( X, mult( X, Y ) ) }.
% 0.71/1.12 substitution0:
% 0.71/1.12 X := Z
% 0.71/1.12 Y := Y
% 0.71/1.12 Z := X
% 0.71/1.12 end
% 0.71/1.12 substitution1:
% 0.71/1.12 X := Z
% 0.71/1.12 Y := mult( X, Y )
% 0.71/1.12 end
% 0.71/1.12
% 0.71/1.12 paramod: (406) {G1,W11,D3,L2,V3,M2} { mult( X, Y ) ==> mult( Y, X ),
% 0.71/1.12 alpha1( Z, Y, X ) }.
% 0.71/1.12 parent0[0]: (1) {G0,W7,D4,L1,V2,M1} I { ld( Y, mult( Y, X ) ) ==> X }.
% 0.71/1.12 parent1[0; 4]: (386) {G1,W15,D5,L2,V3,M2} { mult( X, Y ) ==> ld( Z, mult(
% 0.71/1.12 Z, mult( Y, X ) ) ), alpha1( Z, Y, X ) }.
% 0.71/1.12 substitution0:
% 0.71/1.12 X := mult( Y, X )
% 0.71/1.12 Y := Z
% 0.71/1.12 end
% 0.71/1.12 substitution1:
% 0.71/1.12 X := X
% 0.71/1.12 Y := Y
% 0.71/1.12 Z := Z
% 0.71/1.12 end
% 0.71/1.12
% 0.71/1.12 subsumption: (92) {G1,W11,D3,L2,V3,M2} P(8,1);d(1) { alpha1( X, Y, Z ),
% 0.71/1.12 mult( Z, Y ) = mult( Y, Z ) }.
% 0.71/1.12 parent0: (406) {G1,W11,D3,L2,V3,M2} { mult( X, Y ) ==> mult( Y, X ),
% 0.71/1.12 alpha1( Z, Y, X ) }.
% 0.71/1.12 substitution0:
% 0.71/1.12 X := Z
% 0.71/1.12 Y := Y
% 0.71/1.12 Z := X
% 0.71/1.12 end
% 0.71/1.12 permutation0:
% 0.71/1.12 0 ==> 1
% 0.71/1.12 1 ==> 0
% 0.71/1.12 end
% 0.71/1.12
% 0.71/1.12 eqswap: (408) {G0,W15,D4,L2,V3,M2} { mult( mult( X, Z ), Y ) ==> mult( X,
% 0.71/1.12 mult( Y, Z ) ), ! alpha1( X, Z, Y ) }.
% 0.71/1.12 parent0[1]: (9) {G0,W15,D4,L2,V3,M2} I { ! alpha1( X, Y, Z ), mult( X, mult
% 0.71/1.12 ( Z, Y ) ) ==> mult( mult( X, Y ), Z ) }.
% 0.71/1.12 substitution0:
% 0.71/1.12 X := X
% 0.71/1.12 Y := Z
% 0.71/1.12 Z := Y
% 0.71/1.12 end
% 0.71/1.12
% 0.71/1.12 eqswap: (411) {G1,W11,D3,L2,V3,M2} { mult( Y, X ) = mult( X, Y ), alpha1(
% 0.71/1.12 Z, Y, X ) }.
% 0.71/1.12 parent0[1]: (92) {G1,W11,D3,L2,V3,M2} P(8,1);d(1) { alpha1( X, Y, Z ), mult
% 0.71/1.12 ( Z, Y ) = mult( Y, Z ) }.
% 0.71/1.12 substitution0:
% 0.71/1.12 X := Z
% 0.71/1.12 Y := Y
% 0.71/1.12 Z := X
% 0.71/1.12 end
% 0.71/1.12
% 0.71/1.12 paramod: (413) {G1,W13,D4,L2,V2,M2} { mult( mult( unit, X ), Y ) ==> mult
% 0.71/1.12 ( Y, X ), ! alpha1( unit, X, Y ) }.
% 0.71/1.12 parent0[0]: (5) {G0,W5,D3,L1,V1,M1} I { mult( unit, X ) ==> X }.
% 0.71/1.12 parent1[0; 6]: (408) {G0,W15,D4,L2,V3,M2} { mult( mult( X, Z ), Y ) ==>
% 0.71/1.12 mult( X, mult( Y, Z ) ), ! alpha1( X, Z, Y ) }.
% 0.71/1.12 substitution0:
% 0.71/1.12 X := mult( Y, X )
% 0.71/1.12 end
% 0.71/1.12 substitution1:
% 0.71/1.12 X := unit
% 0.71/1.12 Y := Y
% 0.71/1.12 Z := X
% 0.71/1.12 end
% 0.71/1.12
% 0.71/1.12 paramod: (416) {G1,W11,D3,L2,V2,M2} { mult( X, Y ) ==> mult( Y, X ), !
% 0.71/1.12 alpha1( unit, X, Y ) }.
% 0.71/1.12 parent0[0]: (5) {G0,W5,D3,L1,V1,M1} I { mult( unit, X ) ==> X }.
% 0.71/1.12 parent1[0; 2]: (413) {G1,W13,D4,L2,V2,M2} { mult( mult( unit, X ), Y ) ==>
% 0.71/1.12 mult( Y, X ), ! alpha1( unit, X, Y ) }.
% 0.71/1.12 substitution0:
% 0.71/1.12 X := X
% 0.71/1.12 end
% 0.71/1.12 substitution1:
% 0.71/1.12 X := X
% 0.71/1.12 Y := Y
% 0.71/1.12 end
% 0.71/1.12
% 0.71/1.12 resolution: (417) {G2,W14,D3,L2,V2,M2} { mult( X, Y ) ==> mult( Y, X ),
% 0.71/1.12 mult( X, Y ) = mult( Y, X ) }.
% 0.71/1.12 parent0[1]: (416) {G1,W11,D3,L2,V2,M2} { mult( X, Y ) ==> mult( Y, X ), !
% 0.71/1.12 alpha1( unit, X, Y ) }.
% 0.71/1.12 parent1[1]: (411) {G1,W11,D3,L2,V3,M2} { mult( Y, X ) = mult( X, Y ),
% 0.71/1.12 alpha1( Z, Y, X ) }.
% 0.71/1.12 substitution0:
% 0.71/1.12 X := X
% 0.71/1.12 Y := Y
% 0.71/1.12 end
% 0.71/1.12 substitution1:
% 0.71/1.12 X := Y
% 0.71/1.12 Y := X
% 0.71/1.12 Z := unit
% 0.71/1.12 end
% 0.71/1.12
% 0.71/1.12 factor: (420) {G2,W7,D3,L1,V2,M1} { mult( X, Y ) ==> mult( Y, X ) }.
% 0.71/1.12 parent0[0, 1]: (417) {G2,W14,D3,L2,V2,M2} { mult( X, Y ) ==> mult( Y, X )
% 0.71/1.12 , mult( X, Y ) = mult( Y, X ) }.
% 0.71/1.12 substitution0:
% 0.71/1.12 X := X
% 0.71/1.12 Y := Y
% 0.71/1.12 end
% 0.71/1.12
% 0.71/1.12 subsumption: (143) {G2,W7,D3,L1,V2,M1} P(9,5);d(5);r(92) { mult( Y, X ) =
% 0.71/1.12 mult( X, Y ) }.
% 0.71/1.12 parent0: (420) {G2,W7,D3,L1,V2,M1} { mult( X, Y ) ==> mult( Y, X ) }.
% 0.71/1.12 substitution0:
% 0.71/1.12 X := Y
% 0.71/1.12 Y := X
% 0.71/1.12 end
% 0.71/1.12 permutation0:
% 0.71/1.12 0 ==> 0
% 0.71/1.12 end
% 0.71/1.12
% 0.71/1.12 eqswap: (421) {G0,W15,D4,L2,V3,M2} { mult( mult( X, Z ), Y ) ==> mult( X,
% 0.71/1.12 mult( Y, Z ) ), ! alpha1( X, Z, Y ) }.
% 0.71/1.12 parent0[1]: (9) {G0,W15,D4,L2,V3,M2} I { ! alpha1( X, Y, Z ), mult( X, mult
% 0.71/1.12 ( Z, Y ) ) ==> mult( mult( X, Y ), Z ) }.
% 0.71/1.12 substitution0:
% 0.71/1.12 X := X
% 0.71/1.12 Y := Z
% 0.71/1.12 Z := Y
% 0.71/1.12 end
% 0.71/1.12
% 0.71/1.12 eqswap: (423) {G0,W15,D4,L2,V3,M2} { mult( mult( X, Z ), Y ) = mult( mult
% 0.71/1.12 ( X, Y ), Z ), alpha1( X, Y, Z ) }.
% 0.71/1.12 parent0[1]: (7) {G0,W15,D4,L2,V3,M2} I { alpha1( X, Y, Z ), mult( mult( X,
% 0.71/1.12 Y ), Z ) = mult( mult( X, Z ), Y ) }.
% 0.71/1.12 substitution0:
% 0.71/1.12 X := X
% 0.71/1.12 Y := Y
% 0.71/1.12 Z := Z
% 0.71/1.12 end
% 0.71/1.12
% 0.71/1.12 paramod: (427) {G1,W15,D4,L2,V3,M2} { mult( mult( X, Y ), Z ) ==> mult( X
% 0.71/1.12 , mult( Y, Z ) ), ! alpha1( X, Y, Z ) }.
% 0.71/1.12 parent0[0]: (143) {G2,W7,D3,L1,V2,M1} P(9,5);d(5);r(92) { mult( Y, X ) =
% 0.71/1.12 mult( X, Y ) }.
% 0.71/1.12 parent1[0; 8]: (421) {G0,W15,D4,L2,V3,M2} { mult( mult( X, Z ), Y ) ==>
% 0.71/1.12 mult( X, mult( Y, Z ) ), ! alpha1( X, Z, Y ) }.
% 0.71/1.12 substitution0:
% 0.71/1.12 X := Y
% 0.71/1.12 Y := Z
% 0.71/1.12 end
% 0.71/1.12 substitution1:
% 0.71/1.12 X := X
% 0.71/1.12 Y := Z
% 0.71/1.12 Z := Y
% 0.71/1.12 end
% 0.71/1.12
% 0.71/1.12 paramod: (440) {G1,W19,D4,L3,V3,M3} { mult( mult( X, Y ), Z ) ==> mult(
% 0.71/1.12 mult( X, Z ), Y ), ! alpha1( X, Y, Z ), ! alpha1( X, Y, Z ) }.
% 0.71/1.12 parent0[1]: (10) {G0,W15,D4,L2,V3,M2} I { ! alpha1( X, Y, Z ), mult( X,
% 0.71/1.12 mult( Y, Z ) ) ==> mult( mult( X, Z ), Y ) }.
% 0.71/1.12 parent1[0; 6]: (427) {G1,W15,D4,L2,V3,M2} { mult( mult( X, Y ), Z ) ==>
% 0.71/1.12 mult( X, mult( Y, Z ) ), ! alpha1( X, Y, Z ) }.
% 0.71/1.12 substitution0:
% 0.71/1.12 X := X
% 0.71/1.12 Y := Y
% 0.71/1.12 Z := Z
% 0.71/1.12 end
% 0.71/1.12 substitution1:
% 0.71/1.12 X := X
% 0.71/1.12 Y := Y
% 0.71/1.12 Z := Z
% 0.71/1.12 end
% 0.71/1.12
% 0.71/1.12 factor: (441) {G1,W15,D4,L2,V3,M2} { mult( mult( X, Y ), Z ) ==> mult(
% 0.71/1.12 mult( X, Z ), Y ), ! alpha1( X, Y, Z ) }.
% 0.71/1.12 parent0[1, 2]: (440) {G1,W19,D4,L3,V3,M3} { mult( mult( X, Y ), Z ) ==>
% 0.71/1.12 mult( mult( X, Z ), Y ), ! alpha1( X, Y, Z ), ! alpha1( X, Y, Z ) }.
% 0.71/1.12 substitution0:
% 0.71/1.12 X := X
% 0.71/1.12 Y := Y
% 0.71/1.12 Z := Z
% 0.71/1.12 end
% 0.71/1.12
% 0.71/1.12 resolution: (442) {G1,W22,D4,L2,V3,M2} { mult( mult( X, Y ), Z ) ==> mult
% 0.71/1.12 ( mult( X, Z ), Y ), mult( mult( X, Z ), Y ) = mult( mult( X, Y ), Z )
% 0.71/1.12 }.
% 0.71/1.12 parent0[1]: (441) {G1,W15,D4,L2,V3,M2} { mult( mult( X, Y ), Z ) ==> mult
% 0.71/1.12 ( mult( X, Z ), Y ), ! alpha1( X, Y, Z ) }.
% 0.71/1.12 parent1[1]: (423) {G0,W15,D4,L2,V3,M2} { mult( mult( X, Z ), Y ) = mult(
% 0.71/1.12 mult( X, Y ), Z ), alpha1( X, Y, Z ) }.
% 0.71/1.12 substitution0:
% 0.71/1.12 X := X
% 0.71/1.12 Y := Y
% 0.71/1.12 Z := Z
% 0.71/1.12 end
% 0.71/1.12 substitution1:
% 0.71/1.12 X := X
% 0.71/1.12 Y := Y
% 0.71/1.12 Z := Z
% 0.71/1.12 end
% 0.71/1.12
% 0.71/1.12 eqswap: (443) {G1,W22,D4,L2,V3,M2} { mult( mult( X, Z ), Y ) ==> mult(
% 0.71/1.12 mult( X, Y ), Z ), mult( mult( X, Z ), Y ) = mult( mult( X, Y ), Z ) }.
% 0.71/1.12 parent0[0]: (442) {G1,W22,D4,L2,V3,M2} { mult( mult( X, Y ), Z ) ==> mult
% 0.71/1.12 ( mult( X, Z ), Y ), mult( mult( X, Z ), Y ) = mult( mult( X, Y ), Z )
% 0.71/1.12 }.
% 0.71/1.12 substitution0:
% 0.71/1.12 X := X
% 0.71/1.12 Y := Y
% 0.71/1.12 Z := Z
% 0.71/1.12 end
% 0.71/1.12
% 0.71/1.12 factor: (444) {G1,W11,D4,L1,V3,M1} { mult( mult( X, Y ), Z ) ==> mult(
% 0.71/1.12 mult( X, Z ), Y ) }.
% 0.71/1.12 parent0[0, 1]: (443) {G1,W22,D4,L2,V3,M2} { mult( mult( X, Z ), Y ) ==>
% 0.71/1.12 mult( mult( X, Y ), Z ), mult( mult( X, Z ), Y ) = mult( mult( X, Y ), Z
% 0.71/1.12 ) }.
% 0.71/1.12 substitution0:
% 0.71/1.12 X := X
% 0.71/1.12 Y := Z
% 0.71/1.12 Z := Y
% 0.71/1.12 end
% 0.71/1.12
% 0.71/1.12 subsumption: (145) {G3,W11,D4,L1,V3,M1} P(143,9);d(10);r(7) { mult( mult( Z
% 0.71/1.12 , X ), Y ) = mult( mult( Z, Y ), X ) }.
% 0.71/1.12 parent0: (444) {G1,W11,D4,L1,V3,M1} { mult( mult( X, Y ), Z ) ==> mult(
% 0.71/1.12 mult( X, Z ), Y ) }.
% 0.71/1.12 substitution0:
% 0.71/1.12 X := Z
% 0.71/1.12 Y := X
% 0.71/1.12 Z := Y
% 0.71/1.12 end
% 0.71/1.12 permutation0:
% 0.71/1.12 0 ==> 0
% 0.71/1.12 end
% 0.71/1.12
% 0.71/1.12 eqswap: (445) {G0,W7,D4,L1,V2,M1} { Y ==> ld( X, mult( X, Y ) ) }.
% 0.71/1.12 parent0[0]: (1) {G0,W7,D4,L1,V2,M1} I { ld( Y, mult( Y, X ) ) ==> X }.
% 0.71/1.12 substitution0:
% 0.71/1.12 X := Y
% 0.71/1.12 Y := X
% 0.71/1.12 end
% 0.71/1.12
% 0.71/1.12 paramod: (446) {G1,W7,D4,L1,V2,M1} { X ==> ld( Y, mult( X, Y ) ) }.
% 0.71/1.12 parent0[0]: (143) {G2,W7,D3,L1,V2,M1} P(9,5);d(5);r(92) { mult( Y, X ) =
% 0.71/1.12 mult( X, Y ) }.
% 0.71/1.12 parent1[0; 4]: (445) {G0,W7,D4,L1,V2,M1} { Y ==> ld( X, mult( X, Y ) ) }.
% 0.71/1.12 substitution0:
% 0.71/1.12 X := X
% 0.71/1.12 Y := Y
% 0.71/1.12 end
% 0.71/1.12 substitution1:
% 0.71/1.12 X := Y
% 0.71/1.12 Y := X
% 0.71/1.12 end
% 0.71/1.12
% 0.71/1.12 eqswap: (449) {G1,W7,D4,L1,V2,M1} { ld( Y, mult( X, Y ) ) ==> X }.
% 0.71/1.12 parent0[0]: (446) {G1,W7,D4,L1,V2,M1} { X ==> ld( Y, mult( X, Y ) ) }.
% 0.71/1.12 substitution0:
% 0.71/1.12 X := X
% 0.71/1.12 Y := Y
% 0.71/1.12 end
% 0.71/1.12
% 0.71/1.12 subsumption: (158) {G3,W7,D4,L1,V2,M1} P(143,1) { ld( X, mult( Y, X ) ) ==>
% 0.71/1.12 Y }.
% 0.71/1.12 parent0: (449) {G1,W7,D4,L1,V2,M1} { ld( Y, mult( X, Y ) ) ==> X }.
% 0.71/1.12 substitution0:
% 0.71/1.12 X := Y
% 0.71/1.12 Y := X
% 0.71/1.12 end
% 0.71/1.12 permutation0:
% 0.71/1.12 0 ==> 0
% 0.71/1.12 end
% 0.71/1.12
% 0.71/1.12 eqswap: (450) {G0,W7,D4,L1,V2,M1} { Y ==> mult( X, ld( X, Y ) ) }.
% 0.71/1.12 parent0[0]: (0) {G0,W7,D4,L1,V2,M1} I { mult( Y, ld( Y, X ) ) ==> X }.
% 0.71/1.12 substitution0:
% 0.71/1.12 X := Y
% 0.71/1.12 Y := X
% 0.71/1.12 end
% 0.71/1.12
% 0.71/1.12 paramod: (451) {G1,W7,D4,L1,V2,M1} { X ==> mult( ld( Y, X ), Y ) }.
% 0.71/1.12 parent0[0]: (143) {G2,W7,D3,L1,V2,M1} P(9,5);d(5);r(92) { mult( Y, X ) =
% 0.71/1.12 mult( X, Y ) }.
% 0.71/1.12 parent1[0; 2]: (450) {G0,W7,D4,L1,V2,M1} { Y ==> mult( X, ld( X, Y ) ) }.
% 0.71/1.12 substitution0:
% 0.71/1.12 X := ld( Y, X )
% 0.71/1.12 Y := Y
% 0.71/1.12 end
% 0.71/1.12 substitution1:
% 0.71/1.12 X := Y
% 0.71/1.12 Y := X
% 0.71/1.12 end
% 0.71/1.12
% 0.71/1.12 eqswap: (454) {G1,W7,D4,L1,V2,M1} { mult( ld( Y, X ), Y ) ==> X }.
% 0.71/1.12 parent0[0]: (451) {G1,W7,D4,L1,V2,M1} { X ==> mult( ld( Y, X ), Y ) }.
% 0.71/1.12 substitution0:
% 0.71/1.12 X := X
% 0.71/1.12 Y := Y
% 0.71/1.12 end
% 0.71/1.12
% 0.71/1.12 subsumption: (160) {G3,W7,D4,L1,V2,M1} P(143,0) { mult( ld( X, Y ), X ) ==>
% 0.71/1.12 Y }.
% 0.71/1.12 parent0: (454) {G1,W7,D4,L1,V2,M1} { mult( ld( Y, X ), Y ) ==> X }.
% 0.71/1.12 substitution0:
% 0.71/1.12 X := Y
% 0.71/1.12 Y := X
% 0.71/1.12 end
% 0.71/1.12 permutation0:
% 0.71/1.12 0 ==> 0
% 0.71/1.12 end
% 0.71/1.12
% 0.71/1.12 eqswap: (456) {G3,W7,D4,L1,V2,M1} { Y ==> ld( X, mult( Y, X ) ) }.
% 0.71/1.12 parent0[0]: (158) {G3,W7,D4,L1,V2,M1} P(143,1) { ld( X, mult( Y, X ) ) ==>
% 0.71/1.12 Y }.
% 0.71/1.12 substitution0:
% 0.71/1.12 X := X
% 0.71/1.12 Y := Y
% 0.71/1.12 end
% 0.71/1.12
% 0.71/1.12 paramod: (458) {G1,W7,D4,L1,V2,M1} { X ==> ld( ld( X, Y ), Y ) }.
% 0.71/1.12 parent0[0]: (0) {G0,W7,D4,L1,V2,M1} I { mult( Y, ld( Y, X ) ) ==> X }.
% 0.71/1.12 parent1[0; 6]: (456) {G3,W7,D4,L1,V2,M1} { Y ==> ld( X, mult( Y, X ) ) }.
% 0.71/1.12 substitution0:
% 0.71/1.12 X := Y
% 0.71/1.12 Y := X
% 0.71/1.12 end
% 0.71/1.12 substitution1:
% 0.71/1.12 X := ld( X, Y )
% 0.71/1.12 Y := X
% 0.71/1.12 end
% 0.71/1.12
% 0.71/1.12 eqswap: (459) {G1,W7,D4,L1,V2,M1} { ld( ld( X, Y ), Y ) ==> X }.
% 0.71/1.12 parent0[0]: (458) {G1,W7,D4,L1,V2,M1} { X ==> ld( ld( X, Y ), Y ) }.
% 0.71/1.12 substitution0:
% 0.71/1.12 X := X
% 0.71/1.12 Y := Y
% 0.71/1.12 end
% 0.71/1.12
% 0.71/1.12 subsumption: (170) {G4,W7,D4,L1,V2,M1} P(0,158) { ld( ld( X, Y ), Y ) ==> X
% 0.71/1.12 }.
% 0.71/1.12 parent0: (459) {G1,W7,D4,L1,V2,M1} { ld( ld( X, Y ), Y ) ==> X }.
% 0.71/1.12 substitution0:
% 0.71/1.12 X := X
% 0.71/1.12 Y := Y
% 0.71/1.12 end
% 0.71/1.12 permutation0:
% 0.71/1.12 0 ==> 0
% 0.71/1.12 end
% 0.71/1.12
% 0.71/1.12 paramod: (461) {G3,W11,D4,L1,V3,M1} { mult( X, mult( Y, Z ) ) = mult( mult
% 0.71/1.12 ( Y, X ), Z ) }.
% 0.71/1.12 parent0[0]: (145) {G3,W11,D4,L1,V3,M1} P(143,9);d(10);r(7) { mult( mult( Z
% 0.71/1.12 , X ), Y ) = mult( mult( Z, Y ), X ) }.
% 0.71/1.12 parent1[0; 6]: (143) {G2,W7,D3,L1,V2,M1} P(9,5);d(5);r(92) { mult( Y, X ) =
% 0.71/1.12 mult( X, Y ) }.
% 0.71/1.12 substitution0:
% 0.71/1.12 X := Z
% 0.71/1.12 Y := X
% 0.71/1.12 Z := Y
% 0.71/1.12 end
% 0.71/1.12 substitution1:
% 0.71/1.12 X := mult( Y, Z )
% 0.71/1.12 Y := X
% 0.71/1.12 end
% 0.71/1.12
% 0.71/1.12 subsumption: (197) {G4,W11,D4,L1,V3,M1} P(145,143) { mult( Z, mult( X, Y )
% 0.71/1.12 ) ==> mult( mult( X, Z ), Y ) }.
% 0.71/1.12 parent0: (461) {G3,W11,D4,L1,V3,M1} { mult( X, mult( Y, Z ) ) = mult( mult
% 0.71/1.12 ( Y, X ), Z ) }.
% 0.71/1.12 substitution0:
% 0.71/1.12 X := Z
% 0.71/1.12 Y := X
% 0.71/1.12 Z := Y
% 0.71/1.12 end
% 0.71/1.12 permutation0:
% 0.71/1.12 0 ==> 0
% 0.71/1.12 end
% 0.71/1.12
% 0.71/1.12 eqswap: (464) {G4,W11,D4,L1,V3,M1} { mult( mult( Y, X ), Z ) ==> mult( X,
% 0.71/1.12 mult( Y, Z ) ) }.
% 0.71/1.12 parent0[0]: (197) {G4,W11,D4,L1,V3,M1} P(145,143) { mult( Z, mult( X, Y ) )
% 0.71/1.12 ==> mult( mult( X, Z ), Y ) }.
% 0.71/1.12 substitution0:
% 0.71/1.12 X := Y
% 0.71/1.12 Y := Z
% 0.71/1.12 Z := X
% 0.71/1.12 end
% 0.71/1.12
% 0.71/1.12 paramod: (469) {G3,W11,D4,L1,V3,M1} { mult( mult( X, Y ), Z ) ==> mult( Y
% 0.71/1.12 , mult( Z, X ) ) }.
% 0.71/1.12 parent0[0]: (143) {G2,W7,D3,L1,V2,M1} P(9,5);d(5);r(92) { mult( Y, X ) =
% 0.71/1.12 mult( X, Y ) }.
% 0.71/1.12 parent1[0; 8]: (464) {G4,W11,D4,L1,V3,M1} { mult( mult( Y, X ), Z ) ==>
% 0.71/1.12 mult( X, mult( Y, Z ) ) }.
% 0.71/1.12 substitution0:
% 0.71/1.12 X := Z
% 0.71/1.12 Y := X
% 0.71/1.12 end
% 0.71/1.12 substitution1:
% 0.71/1.12 X := Y
% 0.71/1.12 Y := X
% 0.71/1.12 Z := Z
% 0.71/1.12 end
% 0.71/1.12
% 0.71/1.12 paramod: (482) {G4,W11,D4,L1,V3,M1} { mult( mult( X, Y ), Z ) ==> mult(
% 0.71/1.12 mult( Z, Y ), X ) }.
% 0.71/1.12 parent0[0]: (197) {G4,W11,D4,L1,V3,M1} P(145,143) { mult( Z, mult( X, Y ) )
% 0.71/1.12 ==> mult( mult( X, Z ), Y ) }.
% 0.71/1.12 parent1[0; 6]: (469) {G3,W11,D4,L1,V3,M1} { mult( mult( X, Y ), Z ) ==>
% 0.71/1.12 mult( Y, mult( Z, X ) ) }.
% 0.71/1.12 substitution0:
% 0.71/1.12 X := Z
% 0.71/1.12 Y := X
% 0.71/1.12 Z := Y
% 0.71/1.12 end
% 0.71/1.12 substitution1:
% 0.71/1.12 X := X
% 0.71/1.12 Y := Y
% 0.71/1.12 Z := Z
% 0.71/1.12 end
% 0.71/1.12
% 0.71/1.12 subsumption: (207) {G5,W11,D4,L1,V3,M1} P(143,197);d(197) { mult( mult( Y,
% 0.71/1.12 Z ), X ) = mult( mult( X, Z ), Y ) }.
% 0.71/1.12 parent0: (482) {G4,W11,D4,L1,V3,M1} { mult( mult( X, Y ), Z ) ==> mult(
% 0.71/1.12 mult( Z, Y ), X ) }.
% 0.71/1.12 substitution0:
% 0.71/1.12 X := Y
% 0.71/1.12 Y := Z
% 0.71/1.12 Z := X
% 0.71/1.12 end
% 0.71/1.12 permutation0:
% 0.71/1.12 0 ==> 0
% 0.71/1.12 end
% 0.71/1.12
% 0.71/1.12 eqswap: (484) {G0,W11,D4,L1,V0,M1} { ! mult( mult( a, b ), c ) ==> mult( a
% 0.71/1.12 , mult( b, c ) ) }.
% 0.71/1.12 parent0[0]: (12) {G0,W11,D4,L1,V0,M1} I { ! mult( a, mult( b, c ) ) ==>
% 0.71/1.12 mult( mult( a, b ), c ) }.
% 0.71/1.12 substitution0:
% 0.71/1.12 end
% 0.71/1.12
% 0.71/1.12 paramod: (485) {G1,W11,D4,L1,V0,M1} { ! mult( mult( a, b ), c ) ==> mult(
% 0.71/1.12 mult( b, a ), c ) }.
% 0.71/1.12 parent0[0]: (197) {G4,W11,D4,L1,V3,M1} P(145,143) { mult( Z, mult( X, Y ) )
% 0.71/1.12 ==> mult( mult( X, Z ), Y ) }.
% 0.71/1.12 parent1[0; 7]: (484) {G0,W11,D4,L1,V0,M1} { ! mult( mult( a, b ), c ) ==>
% 0.71/1.12 mult( a, mult( b, c ) ) }.
% 0.71/1.12 substitution0:
% 0.71/1.12 X := b
% 0.71/1.12 Y := c
% 0.71/1.12 Z := a
% 0.71/1.12 end
% 0.71/1.12 substitution1:
% 0.71/1.12 end
% 0.71/1.12
% 0.71/1.12 subsumption: (208) {G5,W11,D4,L1,V0,M1} P(197,12) { ! mult( mult( a, b ), c
% 0.71/1.12 ) ==> mult( mult( b, a ), c ) }.
% 0.71/1.12 parent0: (485) {G1,W11,D4,L1,V0,M1} { ! mult( mult( a, b ), c ) ==> mult(
% 0.71/1.12 mult( b, a ), c ) }.
% 0.71/1.12 substitution0:
% 0.71/1.12 end
% 0.71/1.12 permutation0:
% 0.71/1.12 0 ==> 0
% 0.71/1.12 end
% 0.71/1.12
% 0.71/1.12 paramod: (489) {G4,W11,D4,L1,V3,M1} { mult( mult( X, Y ), ld( Y, Z ) ) =
% 0.71/1.12 mult( Z, X ) }.
% 0.71/1.12 parent0[0]: (160) {G3,W7,D4,L1,V2,M1} P(143,0) { mult( ld( X, Y ), X ) ==>
% 0.71/1.12 Y }.
% 0.71/1.12 parent1[0; 9]: (207) {G5,W11,D4,L1,V3,M1} P(143,197);d(197) { mult( mult( Y
% 0.71/1.12 , Z ), X ) = mult( mult( X, Z ), Y ) }.
% 0.71/1.12 substitution0:
% 0.71/1.12 X := Y
% 0.71/1.12 Y := Z
% 0.71/1.12 end
% 0.71/1.12 substitution1:
% 0.71/1.12 X := ld( Y, Z )
% 0.71/1.12 Y := X
% 0.71/1.12 Z := Y
% 0.71/1.12 end
% 0.71/1.12
% 0.71/1.12 subsumption: (216) {G6,W11,D4,L1,V3,M1} P(160,207) { mult( mult( Z, X ), ld
% 0.71/1.12 ( X, Y ) ) ==> mult( Y, Z ) }.
% 0.71/1.12 parent0: (489) {G4,W11,D4,L1,V3,M1} { mult( mult( X, Y ), ld( Y, Z ) ) =
% 0.71/1.12 mult( Z, X ) }.
% 0.71/1.12 substitution0:
% 0.71/1.12 X := Z
% 0.71/1.12 Y := X
% 0.71/1.12 Z := Y
% 0.71/1.12 end
% 0.71/1.12 permutation0:
% 0.71/1.12 0 ==> 0
% 0.71/1.12 end
% 0.71/1.12
% 0.71/1.12 eqswap: (491) {G6,W11,D4,L1,V3,M1} { mult( Z, X ) ==> mult( mult( X, Y ),
% 0.71/1.12 ld( Y, Z ) ) }.
% 0.71/1.12 parent0[0]: (216) {G6,W11,D4,L1,V3,M1} P(160,207) { mult( mult( Z, X ), ld
% 0.71/1.12 ( X, Y ) ) ==> mult( Y, Z ) }.
% 0.71/1.12 substitution0:
% 0.71/1.12 X := Y
% 0.71/1.12 Y := Z
% 0.71/1.12 Z := X
% 0.71/1.12 end
% 0.71/1.12
% 0.71/1.12 paramod: (493) {G4,W11,D4,L1,V3,M1} { mult( X, ld( Y, Z ) ) ==> mult( Z,
% 0.71/1.12 ld( Y, X ) ) }.
% 0.71/1.12 parent0[0]: (160) {G3,W7,D4,L1,V2,M1} P(143,0) { mult( ld( X, Y ), X ) ==>
% 0.71/1.12 Y }.
% 0.71/1.12 parent1[0; 7]: (491) {G6,W11,D4,L1,V3,M1} { mult( Z, X ) ==> mult( mult( X
% 0.71/1.12 , Y ), ld( Y, Z ) ) }.
% 0.71/1.12 substitution0:
% 0.71/1.12 X := Y
% 0.71/1.12 Y := Z
% 0.71/1.12 end
% 0.71/1.12 substitution1:
% 0.71/1.12 X := ld( Y, Z )
% 0.71/1.12 Y := Y
% 0.71/1.12 Z := X
% 0.71/1.12 end
% 0.71/1.12
% 0.71/1.12 subsumption: (225) {G7,W11,D4,L1,V3,M1} P(160,216) { mult( Y, ld( X, Z ) )
% 0.71/1.12 = mult( Z, ld( X, Y ) ) }.
% 0.71/1.12 parent0: (493) {G4,W11,D4,L1,V3,M1} { mult( X, ld( Y, Z ) ) ==> mult( Z,
% 0.71/1.12 ld( Y, X ) ) }.
% 0.71/1.12 substitution0:
% 0.71/1.12 X := Y
% 0.71/1.12 Y := X
% 0.71/1.12 Z := Z
% 0.71/1.12 end
% 0.71/1.12 permutation0:
% 0.71/1.12 0 ==> 0
% 0.71/1.12 end
% 0.71/1.12
% 0.71/1.12 paramod: (495) {G3,W11,D4,L1,V3,M1} { mult( Z, ld( Y, X ) ) = mult( ld( Y
% 0.71/1.12 , Z ), X ) }.
% 0.71/1.12 parent0[0]: (225) {G7,W11,D4,L1,V3,M1} P(160,216) { mult( Y, ld( X, Z ) ) =
% 0.71/1.12 mult( Z, ld( X, Y ) ) }.
% 0.71/1.12 parent1[0; 1]: (143) {G2,W7,D3,L1,V2,M1} P(9,5);d(5);r(92) { mult( Y, X ) =
% 0.71/1.12 mult( X, Y ) }.
% 0.71/1.12 substitution0:
% 0.71/1.12 X := Y
% 0.71/1.12 Y := X
% 0.71/1.12 Z := Z
% 0.71/1.12 end
% 0.71/1.12 substitution1:
% 0.71/1.12 X := ld( Y, Z )
% 0.71/1.12 Y := X
% 0.71/1.12 end
% 0.71/1.12
% 0.71/1.12 subsumption: (236) {G8,W11,D4,L1,V3,M1} P(225,143) { mult( Z, ld( Y, X ) )
% 0.71/1.12 ==> mult( ld( Y, Z ), X ) }.
% 0.71/1.12 parent0: (495) {G3,W11,D4,L1,V3,M1} { mult( Z, ld( Y, X ) ) = mult( ld( Y
% 0.71/1.12 , Z ), X ) }.
% 0.71/1.12 substitution0:
% 0.71/1.12 X := X
% 0.71/1.12 Y := Y
% 0.71/1.12 Z := Z
% 0.71/1.12 end
% 0.71/1.12 permutation0:
% 0.71/1.12 0 ==> 0
% 0.71/1.12 end
% 0.71/1.12
% 0.71/1.12 eqswap: (499) {G8,W11,D4,L1,V3,M1} { mult( ld( Y, X ), Z ) ==> mult( X, ld
% 0.71/1.12 ( Y, Z ) ) }.
% 0.71/1.12 parent0[0]: (236) {G8,W11,D4,L1,V3,M1} P(225,143) { mult( Z, ld( Y, X ) )
% 0.71/1.12 ==> mult( ld( Y, Z ), X ) }.
% 0.71/1.12 substitution0:
% 0.71/1.12 X := Z
% 0.71/1.12 Y := Y
% 0.71/1.12 Z := X
% 0.71/1.12 end
% 0.71/1.12
% 0.71/1.12 paramod: (501) {G1,W9,D4,L1,V2,M1} { mult( ld( X, unit ), Y ) ==> ld( X, Y
% 0.71/1.12 ) }.
% 0.71/1.12 parent0[0]: (5) {G0,W5,D3,L1,V1,M1} I { mult( unit, X ) ==> X }.
% 0.71/1.12 parent1[0; 6]: (499) {G8,W11,D4,L1,V3,M1} { mult( ld( Y, X ), Z ) ==> mult
% 0.71/1.12 ( X, ld( Y, Z ) ) }.
% 0.71/1.12 substitution0:
% 0.71/1.12 X := ld( X, Y )
% 0.71/1.12 end
% 0.71/1.12 substitution1:
% 0.71/1.12 X := unit
% 0.71/1.12 Y := X
% 0.71/1.12 Z := Y
% 0.71/1.12 end
% 0.71/1.12
% 0.71/1.12 subsumption: (249) {G9,W9,D4,L1,V2,M1} P(236,5) { mult( ld( X, unit ), Y )
% 0.71/1.12 ==> ld( X, Y ) }.
% 0.71/1.12 parent0: (501) {G1,W9,D4,L1,V2,M1} { mult( ld( X, unit ), Y ) ==> ld( X, Y
% 0.71/1.12 ) }.
% 0.71/1.12 substitution0:
% 0.71/1.12 X := X
% 0.71/1.12 Y := Y
% 0.71/1.12 end
% 0.71/1.12 permutation0:
% 0.71/1.12 0 ==> 0
% 0.71/1.12 end
% 0.71/1.12
% 0.71/1.12 paramod: (507) {G6,W13,D4,L1,V3,M1} { mult( mult( X, Y ), ld( Z, unit ) )
% 0.71/1.12 = mult( ld( Z, Y ), X ) }.
% 0.71/1.12 parent0[0]: (249) {G9,W9,D4,L1,V2,M1} P(236,5) { mult( ld( X, unit ), Y )
% 0.71/1.12 ==> ld( X, Y ) }.
% 0.71/1.12 parent1[0; 9]: (207) {G5,W11,D4,L1,V3,M1} P(143,197);d(197) { mult( mult( Y
% 0.71/1.12 , Z ), X ) = mult( mult( X, Z ), Y ) }.
% 0.71/1.12 substitution0:
% 0.71/1.12 X := Z
% 0.71/1.12 Y := Y
% 0.71/1.12 end
% 0.71/1.12 substitution1:
% 0.71/1.12 X := ld( Z, unit )
% 0.71/1.12 Y := X
% 0.71/1.12 Z := Y
% 0.71/1.12 end
% 0.71/1.12
% 0.71/1.12 paramod: (508) {G7,W13,D5,L1,V3,M1} { mult( ld( Z, mult( X, Y ) ), unit )
% 0.71/1.12 = mult( ld( Z, Y ), X ) }.
% 0.71/1.12 parent0[0]: (236) {G8,W11,D4,L1,V3,M1} P(225,143) { mult( Z, ld( Y, X ) )
% 0.71/1.12 ==> mult( ld( Y, Z ), X ) }.
% 0.71/1.12 parent1[0; 1]: (507) {G6,W13,D4,L1,V3,M1} { mult( mult( X, Y ), ld( Z,
% 0.71/1.12 unit ) ) = mult( ld( Z, Y ), X ) }.
% 0.71/1.12 substitution0:
% 0.71/1.12 X := unit
% 0.71/1.12 Y := Z
% 0.71/1.12 Z := mult( X, Y )
% 0.71/1.12 end
% 0.71/1.12 substitution1:
% 0.71/1.12 X := X
% 0.71/1.12 Y := Y
% 0.71/1.12 Z := Z
% 0.71/1.12 end
% 0.71/1.12
% 0.71/1.12 paramod: (509) {G1,W11,D4,L1,V3,M1} { ld( X, mult( Y, Z ) ) = mult( ld( X
% 0.71/1.12 , Z ), Y ) }.
% 0.71/1.12 parent0[0]: (4) {G0,W5,D3,L1,V1,M1} I { mult( X, unit ) ==> X }.
% 0.71/1.12 parent1[0; 1]: (508) {G7,W13,D5,L1,V3,M1} { mult( ld( Z, mult( X, Y ) ),
% 0.71/1.12 unit ) = mult( ld( Z, Y ), X ) }.
% 0.71/1.12 substitution0:
% 0.71/1.12 X := ld( X, mult( Y, Z ) )
% 0.71/1.12 end
% 0.71/1.12 substitution1:
% 0.71/1.12 X := Y
% 0.71/1.12 Y := Z
% 0.71/1.12 Z := X
% 0.71/1.12 end
% 0.71/1.12
% 0.71/1.12 eqswap: (510) {G1,W11,D4,L1,V3,M1} { mult( ld( X, Z ), Y ) = ld( X, mult(
% 0.71/1.12 Y, Z ) ) }.
% 0.71/1.12 parent0[0]: (509) {G1,W11,D4,L1,V3,M1} { ld( X, mult( Y, Z ) ) = mult( ld
% 0.71/1.12 ( X, Z ), Y ) }.
% 0.71/1.12 substitution0:
% 0.71/1.12 X := X
% 0.71/1.12 Y := Y
% 0.71/1.12 Z := Z
% 0.71/1.12 end
% 0.71/1.12
% 0.71/1.12 subsumption: (252) {G10,W11,D4,L1,V3,M1} P(249,207);d(236);d(4) { mult( ld
% 0.71/1.12 ( X, Y ), Z ) ==> ld( X, mult( Z, Y ) ) }.
% 0.71/1.12 parent0: (510) {G1,W11,D4,L1,V3,M1} { mult( ld( X, Z ), Y ) = ld( X, mult
% 0.71/1.12 ( Y, Z ) ) }.
% 0.71/1.12 substitution0:
% 0.71/1.12 X := X
% 0.71/1.12 Y := Z
% 0.71/1.12 Z := Y
% 0.71/1.12 end
% 0.71/1.12 permutation0:
% 0.71/1.12 0 ==> 0
% 0.71/1.12 end
% 0.71/1.12
% 0.71/1.12 eqswap: (512) {G9,W9,D4,L1,V2,M1} { ld( X, Y ) ==> mult( ld( X, unit ), Y
% 0.71/1.12 ) }.
% 0.71/1.12 parent0[0]: (249) {G9,W9,D4,L1,V2,M1} P(236,5) { mult( ld( X, unit ), Y )
% 0.71/1.12 ==> ld( X, Y ) }.
% 0.71/1.12 substitution0:
% 0.71/1.12 X := X
% 0.71/1.12 Y := Y
% 0.71/1.12 end
% 0.71/1.12
% 0.71/1.12 paramod: (514) {G5,W9,D4,L1,V2,M1} { ld( ld( X, unit ), Y ) ==> mult( X, Y
% 0.71/1.12 ) }.
% 0.71/1.12 parent0[0]: (170) {G4,W7,D4,L1,V2,M1} P(0,158) { ld( ld( X, Y ), Y ) ==> X
% 0.71/1.12 }.
% 0.71/1.12 parent1[0; 7]: (512) {G9,W9,D4,L1,V2,M1} { ld( X, Y ) ==> mult( ld( X,
% 0.71/1.12 unit ), Y ) }.
% 0.71/1.12 substitution0:
% 0.71/1.12 X := X
% 0.71/1.12 Y := unit
% 0.71/1.12 end
% 0.71/1.12 substitution1:
% 0.71/1.12 X := ld( X, unit )
% 0.71/1.12 Y := Y
% 0.71/1.12 end
% 0.71/1.12
% 0.71/1.12 subsumption: (254) {G10,W9,D4,L1,V2,M1} P(170,249) { ld( ld( X, unit ), Y )
% 0.71/1.12 ==> mult( X, Y ) }.
% 0.71/1.12 parent0: (514) {G5,W9,D4,L1,V2,M1} { ld( ld( X, unit ), Y ) ==> mult( X, Y
% 0.71/1.12 ) }.
% 0.71/1.12 substitution0:
% 0.71/1.12 X := X
% 0.71/1.12 Y := Y
% 0.71/1.12 end
% 0.71/1.12 permutation0:
% 0.71/1.12 0 ==> 0
% 0.71/1.12 end
% 0.71/1.12
% 0.71/1.12 paramod: (526) {G8,W13,D5,L1,V3,M1} { mult( X, ld( ld( Y, unit ), Z ) ) =
% 0.71/1.12 mult( Z, mult( Y, X ) ) }.
% 0.71/1.12 parent0[0]: (254) {G10,W9,D4,L1,V2,M1} P(170,249) { ld( ld( X, unit ), Y )
% 0.71/1.12 ==> mult( X, Y ) }.
% 0.71/1.12 parent1[0; 10]: (225) {G7,W11,D4,L1,V3,M1} P(160,216) { mult( Y, ld( X, Z )
% 0.71/1.12 ) = mult( Z, ld( X, Y ) ) }.
% 0.71/1.12 substitution0:
% 0.71/1.12 X := Y
% 0.71/1.12 Y := X
% 0.71/1.12 end
% 0.71/1.12 substitution1:
% 0.71/1.12 X := ld( Y, unit )
% 0.71/1.12 Y := X
% 0.71/1.12 Z := Z
% 0.71/1.12 end
% 0.71/1.12
% 0.71/1.12 paramod: (528) {G5,W13,D5,L1,V3,M1} { mult( X, ld( ld( Y, unit ), Z ) ) =
% 0.71/1.12 mult( mult( Y, Z ), X ) }.
% 0.71/1.12 parent0[0]: (197) {G4,W11,D4,L1,V3,M1} P(145,143) { mult( Z, mult( X, Y ) )
% 0.71/1.12 ==> mult( mult( X, Z ), Y ) }.
% 0.71/1.12 parent1[0; 8]: (526) {G8,W13,D5,L1,V3,M1} { mult( X, ld( ld( Y, unit ), Z
% 0.71/1.12 ) ) = mult( Z, mult( Y, X ) ) }.
% 0.71/1.12 substitution0:
% 0.71/1.12 X := Y
% 0.71/1.12 Y := X
% 0.71/1.12 Z := Z
% 0.71/1.12 end
% 0.71/1.12 substitution1:
% 0.71/1.12 X := X
% 0.71/1.12 Y := Y
% 0.71/1.12 Z := Z
% 0.71/1.12 end
% 0.71/1.12
% 0.71/1.12 paramod: (529) {G6,W13,D5,L1,V3,M1} { mult( ld( ld( Y, unit ), X ), Z ) =
% 0.71/1.12 mult( mult( Y, Z ), X ) }.
% 0.71/1.12 parent0[0]: (236) {G8,W11,D4,L1,V3,M1} P(225,143) { mult( Z, ld( Y, X ) )
% 0.71/1.12 ==> mult( ld( Y, Z ), X ) }.
% 0.71/1.12 parent1[0; 1]: (528) {G5,W13,D5,L1,V3,M1} { mult( X, ld( ld( Y, unit ), Z
% 0.71/1.12 ) ) = mult( mult( Y, Z ), X ) }.
% 0.71/1.12 substitution0:
% 0.71/1.12 X := Z
% 0.71/1.12 Y := ld( Y, unit )
% 0.71/1.12 Z := X
% 0.71/1.12 end
% 0.71/1.12 substitution1:
% 0.71/1.12 X := X
% 0.71/1.12 Y := Y
% 0.71/1.12 Z := Z
% 0.71/1.12 end
% 0.71/1.12
% 0.71/1.12 paramod: (530) {G7,W13,D4,L1,V3,M1} { ld( ld( X, unit ), mult( Z, Y ) ) =
% 0.71/1.12 mult( mult( X, Z ), Y ) }.
% 0.71/1.12 parent0[0]: (252) {G10,W11,D4,L1,V3,M1} P(249,207);d(236);d(4) { mult( ld(
% 0.71/1.12 X, Y ), Z ) ==> ld( X, mult( Z, Y ) ) }.
% 0.71/1.12 parent1[0; 1]: (529) {G6,W13,D5,L1,V3,M1} { mult( ld( ld( Y, unit ), X ),
% 0.71/1.12 Z ) = mult( mult( Y, Z ), X ) }.
% 0.71/1.12 substitution0:
% 0.71/1.12 X := ld( X, unit )
% 0.71/1.12 Y := Y
% 0.71/1.12 Z := Z
% 0.71/1.12 end
% 0.71/1.12 substitution1:
% 0.71/1.12 X := Y
% 0.71/1.12 Y := X
% 0.71/1.12 Z := Z
% 0.71/1.12 end
% 0.71/1.12
% 0.71/1.12 paramod: (531) {G8,W11,D4,L1,V3,M1} { mult( X, mult( Y, Z ) ) = mult( mult
% 0.71/1.12 ( X, Y ), Z ) }.
% 0.71/1.12 parent0[0]: (254) {G10,W9,D4,L1,V2,M1} P(170,249) { ld( ld( X, unit ), Y )
% 0.71/1.12 ==> mult( X, Y ) }.
% 0.71/1.12 parent1[0; 1]: (530) {G7,W13,D4,L1,V3,M1} { ld( ld( X, unit ), mult( Z, Y
% 0.71/1.12 ) ) = mult( mult( X, Z ), Y ) }.
% 0.71/1.12 substitution0:
% 0.71/1.12 X := X
% 0.71/1.12 Y := mult( Y, Z )
% 0.71/1.12 end
% 0.71/1.12 substitution1:
% 0.71/1.12 X := X
% 0.71/1.12 Y := Z
% 0.71/1.12 Z := Y
% 0.71/1.12 end
% 0.71/1.12
% 0.71/1.12 paramod: (532) {G5,W11,D4,L1,V3,M1} { mult( mult( Y, X ), Z ) = mult( mult
% 0.71/1.12 ( X, Y ), Z ) }.
% 0.71/1.12 parent0[0]: (197) {G4,W11,D4,L1,V3,M1} P(145,143) { mult( Z, mult( X, Y ) )
% 0.71/1.12 ==> mult( mult( X, Z ), Y ) }.
% 0.71/1.12 parent1[0; 1]: (531) {G8,W11,D4,L1,V3,M1} { mult( X, mult( Y, Z ) ) = mult
% 0.71/1.12 ( mult( X, Y ), Z ) }.
% 0.71/1.12 substitution0:
% 0.71/1.12 X := Y
% 0.71/1.12 Y := Z
% 0.71/1.12 Z := X
% 0.71/1.12 end
% 0.71/1.12 substitution1:
% 0.71/1.12 X := X
% 0.71/1.12 Y := Y
% 0.71/1.12 Z := Z
% 0.71/1.12 end
% 0.71/1.12
% 0.71/1.12 subsumption: (257) {G11,W11,D4,L1,V3,M1} P(254,225);d(197);d(236);d(252);d(
% 0.71/1.12 254);d(197) { mult( mult( X, Z ), Y ) = mult( mult( Z, X ), Y ) }.
% 0.71/1.12 parent0: (532) {G5,W11,D4,L1,V3,M1} { mult( mult( Y, X ), Z ) = mult( mult
% 0.71/1.12 ( X, Y ), Z ) }.
% 0.71/1.12 substitution0:
% 0.71/1.12 X := Z
% 0.71/1.12 Y := X
% 0.71/1.12 Z := Y
% 0.71/1.12 end
% 0.71/1.12 permutation0:
% 0.71/1.12 0 ==> 0
% 0.71/1.12 end
% 0.71/1.12
% 0.71/1.12 eqswap: (533) {G5,W11,D4,L1,V0,M1} { ! mult( mult( b, a ), c ) ==> mult(
% 0.71/1.12 mult( a, b ), c ) }.
% 0.71/1.12 parent0[0]: (208) {G5,W11,D4,L1,V0,M1} P(197,12) { ! mult( mult( a, b ), c
% 0.71/1.12 ) ==> mult( mult( b, a ), c ) }.
% 0.71/1.12 substitution0:
% 0.71/1.12 end
% 0.71/1.12
% 0.71/1.12 paramod: (535) {G6,W11,D4,L1,V0,M1} { ! mult( mult( b, a ), c ) ==> mult(
% 0.71/1.12 mult( b, a ), c ) }.
% 0.71/1.12 parent0[0]: (257) {G11,W11,D4,L1,V3,M1} P(254,225);d(197);d(236);d(252);d(
% 0.71/1.12 254);d(197) { mult( mult( X, Z ), Y ) = mult( mult( Z, X ), Y ) }.
% 0.71/1.12 parent1[0; 7]: (533) {G5,W11,D4,L1,V0,M1} { ! mult( mult( b, a ), c ) ==>
% 0.71/1.12 mult( mult( a, b ), c ) }.
% 0.71/1.12 substitution0:
% 0.71/1.12 X := a
% 0.71/1.12 Y := c
% 0.71/1.12 Z := b
% 0.71/1.12 end
% 0.71/1.12 substitution1:
% 0.71/1.12 end
% 0.71/1.12
% 0.71/1.12 eqrefl: (538) {G0,W0,D0,L0,V0,M0} { }.
% 0.71/1.12 parent0[0]: (535) {G6,W11,D4,L1,V0,M1} { ! mult( mult( b, a ), c ) ==>
% 0.71/1.12 mult( mult( b, a ), c ) }.
% 0.71/1.12 substitution0:
% 0.71/1.12 end
% 0.71/1.12
% 0.71/1.12 subsumption: (299) {G12,W0,D0,L0,V0,M0} P(257,208);q { }.
% 0.71/1.12 parent0: (538) {G0,W0,D0,L0,V0,M0} { }.
% 0.71/1.12 substitution0:
% 0.71/1.12 end
% 0.71/1.12 permutation0:
% 0.71/1.12 end
% 0.71/1.12
% 0.71/1.12 Proof check complete!
% 0.71/1.12
% 0.71/1.12 Memory use:
% 0.71/1.12
% 0.71/1.12 space for terms: 5095
% 0.71/1.12 space for clauses: 26939
% 0.71/1.12
% 0.71/1.12
% 0.71/1.12 clauses generated: 2862
% 0.71/1.12 clauses kept: 300
% 0.71/1.12 clauses selected: 53
% 0.71/1.12 clauses deleted: 24
% 0.71/1.12 clauses inuse deleted: 0
% 0.71/1.12
% 0.71/1.12 subsentry: 2769
% 0.71/1.12 literals s-matched: 1834
% 0.71/1.12 literals matched: 1656
% 0.71/1.12 full subsumption: 277
% 0.71/1.12
% 0.71/1.12 checksum: -882408601
% 0.71/1.12
% 0.71/1.12
% 0.71/1.12 Bliksem ended
%------------------------------------------------------------------------------