%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : GRP656+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n014.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 07:38:25 EDT 2022
% Result : Theorem 0.70s 1.09s
% Output : Refutation 0.70s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP656+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : bliksem %s
% 0.13/0.33 % Computer : n014.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % DateTime : Tue Jun 14 08:50:51 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.70/1.09 *** allocated 10000 integers for termspace/termends
% 0.70/1.09 *** allocated 10000 integers for clauses
% 0.70/1.09 *** allocated 10000 integers for justifications
% 0.70/1.09 Bliksem 1.12
% 0.70/1.09
% 0.70/1.09
% 0.70/1.09 Automatic Strategy Selection
% 0.70/1.09
% 0.70/1.09
% 0.70/1.09 Clauses:
% 0.70/1.09
% 0.70/1.09 { mult( Y, ld( Y, X ) ) = X }.
% 0.70/1.09 { ld( Y, mult( Y, X ) ) = X }.
% 0.70/1.09 { mult( rd( Y, X ), X ) = Y }.
% 0.70/1.09 { rd( mult( Y, X ), X ) = Y }.
% 0.70/1.09 { mult( mult( Z, Y ), mult( X, Z ) ) = mult( mult( Z, mult( Y, X ) ), Z ) }
% 0.70/1.09 .
% 0.70/1.09 { ! mult( skol1( X ), X ) = skol1( X ), ! mult( X, skol1( X ) ) = skol1( X
% 0.70/1.09 ) }.
% 0.70/1.09
% 0.70/1.09 percentage equality = 1.000000, percentage horn = 1.000000
% 0.70/1.09 This is a pure equality problem
% 0.70/1.09
% 0.70/1.09
% 0.70/1.09
% 0.70/1.09 Options Used:
% 0.70/1.09
% 0.70/1.09 useres = 1
% 0.70/1.09 useparamod = 1
% 0.70/1.09 useeqrefl = 1
% 0.70/1.09 useeqfact = 1
% 0.70/1.09 usefactor = 1
% 0.70/1.09 usesimpsplitting = 0
% 0.70/1.09 usesimpdemod = 5
% 0.70/1.09 usesimpres = 3
% 0.70/1.09
% 0.70/1.09 resimpinuse = 1000
% 0.70/1.09 resimpclauses = 20000
% 0.70/1.09 substype = eqrewr
% 0.70/1.09 backwardsubs = 1
% 0.70/1.09 selectoldest = 5
% 0.70/1.09
% 0.70/1.09 litorderings [0] = split
% 0.70/1.09 litorderings [1] = extend the termordering, first sorting on arguments
% 0.70/1.09
% 0.70/1.09 termordering = kbo
% 0.70/1.09
% 0.70/1.09 litapriori = 0
% 0.70/1.09 termapriori = 1
% 0.70/1.09 litaposteriori = 0
% 0.70/1.09 termaposteriori = 0
% 0.70/1.09 demodaposteriori = 0
% 0.70/1.09 ordereqreflfact = 0
% 0.70/1.09
% 0.70/1.09 litselect = negord
% 0.70/1.09
% 0.70/1.09 maxweight = 15
% 0.70/1.09 maxdepth = 30000
% 0.70/1.09 maxlength = 115
% 0.70/1.09 maxnrvars = 195
% 0.70/1.09 excuselevel = 1
% 0.70/1.09 increasemaxweight = 1
% 0.70/1.09
% 0.70/1.09 maxselected = 10000000
% 0.70/1.09 maxnrclauses = 10000000
% 0.70/1.09
% 0.70/1.09 showgenerated = 0
% 0.70/1.09 showkept = 0
% 0.70/1.09 showselected = 0
% 0.70/1.09 showdeleted = 0
% 0.70/1.09 showresimp = 1
% 0.70/1.09 showstatus = 2000
% 0.70/1.09
% 0.70/1.09 prologoutput = 0
% 0.70/1.09 nrgoals = 5000000
% 0.70/1.09 totalproof = 1
% 0.70/1.09
% 0.70/1.09 Symbols occurring in the translation:
% 0.70/1.09
% 0.70/1.09 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.70/1.09 . [1, 2] (w:1, o:17, a:1, s:1, b:0),
% 0.70/1.09 ! [4, 1] (w:0, o:11, a:1, s:1, b:0),
% 0.70/1.09 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.70/1.09 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.70/1.09 ld [37, 2] (w:1, o:41, a:1, s:1, b:0),
% 0.70/1.09 mult [38, 2] (w:1, o:42, a:1, s:1, b:0),
% 0.70/1.09 rd [39, 2] (w:1, o:43, a:1, s:1, b:0),
% 0.70/1.09 skol1 [43, 1] (w:1, o:16, a:1, s:1, b:1).
% 0.70/1.09
% 0.70/1.09
% 0.70/1.09 Starting Search:
% 0.70/1.09
% 0.70/1.09
% 0.70/1.09 Bliksems!, er is een bewijs:
% 0.70/1.09 % SZS status Theorem
% 0.70/1.09 % SZS output start Refutation
% 0.70/1.09
% 0.70/1.09 (0) {G0,W7,D4,L1,V2,M1} I { mult( Y, ld( Y, X ) ) ==> X }.
% 0.70/1.09 (1) {G0,W7,D4,L1,V2,M1} I { ld( Y, mult( Y, X ) ) ==> X }.
% 0.70/1.09 (2) {G0,W7,D4,L1,V2,M1} I { mult( rd( Y, X ), X ) ==> Y }.
% 0.70/1.09 (3) {G0,W7,D4,L1,V2,M1} I { rd( mult( Y, X ), X ) ==> Y }.
% 0.70/1.09 (4) {G0,W15,D5,L1,V3,M1} I { mult( mult( Z, Y ), mult( X, Z ) ) ==> mult(
% 0.70/1.09 mult( Z, mult( Y, X ) ), Z ) }.
% 0.70/1.09 (5) {G0,W14,D4,L2,V1,M2} I { ! mult( skol1( X ), X ) ==> skol1( X ), ! mult
% 0.70/1.09 ( X, skol1( X ) ) ==> skol1( X ) }.
% 0.70/1.09 (10) {G1,W15,D6,L1,V3,M1} P(0,4) { mult( mult( X, mult( ld( X, Y ), Z ) ),
% 0.70/1.09 X ) ==> mult( Y, mult( Z, X ) ) }.
% 0.70/1.09 (18) {G2,W15,D5,L1,V3,M1} P(10,3) { rd( mult( Y, mult( Z, X ) ), X ) ==>
% 0.70/1.09 mult( X, mult( ld( X, Y ), Z ) ) }.
% 0.70/1.09 (20) {G3,W15,D5,L1,V3,M1} P(2,18) { mult( Y, mult( ld( Y, Z ), rd( X, Y ) )
% 0.70/1.09 ) ==> rd( mult( Z, X ), Y ) }.
% 0.70/1.09 (22) {G4,W15,D5,L1,V3,M1} P(1,20) { rd( mult( mult( X, Y ), Z ), X ) ==>
% 0.70/1.09 mult( X, mult( Y, rd( Z, X ) ) ) }.
% 0.70/1.09 (27) {G5,W11,D5,L1,V2,M1} P(22,3) { mult( X, mult( Y, rd( X, X ) ) ) ==>
% 0.70/1.09 mult( X, Y ) }.
% 0.70/1.09 (29) {G6,W7,D4,L1,V2,M1} P(27,1);d(1) { mult( Y, rd( X, X ) ) ==> Y }.
% 0.70/1.09 (38) {G7,W7,D3,L1,V2,M1} P(29,1) { ld( X, X ) = rd( Y, Y ) }.
% 0.70/1.09 (40) {G8,W7,D3,L1,V2,M1} P(38,38) { rd( Y, Y ) = rd( Z, Z ) }.
% 0.70/1.09 (47) {G9,W7,D4,L1,V2,M1} P(40,2) { mult( rd( Y, Y ), X ) ==> X }.
% 0.70/1.09 (51) {G10,W0,D0,L0,V0,M0} R(47,5);d(29);q { }.
% 0.70/1.09
% 0.70/1.09
% 0.70/1.09 % SZS output end Refutation
% 0.70/1.09 found a proof!
% 0.70/1.09
% 0.70/1.09
% 0.70/1.09 Unprocessed initial clauses:
% 0.70/1.09
% 0.70/1.09 (53) {G0,W7,D4,L1,V2,M1} { mult( Y, ld( Y, X ) ) = X }.
% 0.70/1.09 (54) {G0,W7,D4,L1,V2,M1} { ld( Y, mult( Y, X ) ) = X }.
% 0.70/1.09 (55) {G0,W7,D4,L1,V2,M1} { mult( rd( Y, X ), X ) = Y }.
% 0.70/1.09 (56) {G0,W7,D4,L1,V2,M1} { rd( mult( Y, X ), X ) = Y }.
% 0.70/1.09 (57) {G0,W15,D5,L1,V3,M1} { mult( mult( Z, Y ), mult( X, Z ) ) = mult(
% 0.70/1.09 mult( Z, mult( Y, X ) ), Z ) }.
% 0.70/1.09 (58) {G0,W14,D4,L2,V1,M2} { ! mult( skol1( X ), X ) = skol1( X ), ! mult(
% 0.70/1.09 X, skol1( X ) ) = skol1( X ) }.
% 0.70/1.09
% 0.70/1.09
% 0.70/1.09 Total Proof:
% 0.70/1.09
% 0.70/1.09 subsumption: (0) {G0,W7,D4,L1,V2,M1} I { mult( Y, ld( Y, X ) ) ==> X }.
% 0.70/1.09 parent0: (53) {G0,W7,D4,L1,V2,M1} { mult( Y, ld( Y, X ) ) = X }.
% 0.70/1.09 substitution0:
% 0.70/1.09 X := X
% 0.70/1.09 Y := Y
% 0.70/1.09 end
% 0.70/1.09 permutation0:
% 0.70/1.09 0 ==> 0
% 0.70/1.09 end
% 0.70/1.09
% 0.70/1.09 subsumption: (1) {G0,W7,D4,L1,V2,M1} I { ld( Y, mult( Y, X ) ) ==> X }.
% 0.70/1.09 parent0: (54) {G0,W7,D4,L1,V2,M1} { ld( Y, mult( Y, X ) ) = X }.
% 0.70/1.09 substitution0:
% 0.70/1.09 X := X
% 0.70/1.09 Y := Y
% 0.70/1.09 end
% 0.70/1.09 permutation0:
% 0.70/1.09 0 ==> 0
% 0.70/1.09 end
% 0.70/1.09
% 0.70/1.09 subsumption: (2) {G0,W7,D4,L1,V2,M1} I { mult( rd( Y, X ), X ) ==> Y }.
% 0.70/1.09 parent0: (55) {G0,W7,D4,L1,V2,M1} { mult( rd( Y, X ), X ) = Y }.
% 0.70/1.09 substitution0:
% 0.70/1.09 X := X
% 0.70/1.09 Y := Y
% 0.70/1.09 end
% 0.70/1.09 permutation0:
% 0.70/1.09 0 ==> 0
% 0.70/1.09 end
% 0.70/1.09
% 0.70/1.09 subsumption: (3) {G0,W7,D4,L1,V2,M1} I { rd( mult( Y, X ), X ) ==> Y }.
% 0.70/1.09 parent0: (56) {G0,W7,D4,L1,V2,M1} { rd( mult( Y, X ), X ) = Y }.
% 0.70/1.09 substitution0:
% 0.70/1.09 X := X
% 0.70/1.09 Y := Y
% 0.70/1.09 end
% 0.70/1.09 permutation0:
% 0.70/1.09 0 ==> 0
% 0.70/1.09 end
% 0.70/1.09
% 0.70/1.09 subsumption: (4) {G0,W15,D5,L1,V3,M1} I { mult( mult( Z, Y ), mult( X, Z )
% 0.70/1.09 ) ==> mult( mult( Z, mult( Y, X ) ), Z ) }.
% 0.70/1.09 parent0: (57) {G0,W15,D5,L1,V3,M1} { mult( mult( Z, Y ), mult( X, Z ) ) =
% 0.70/1.09 mult( mult( Z, mult( Y, X ) ), Z ) }.
% 0.70/1.09 substitution0:
% 0.70/1.09 X := X
% 0.70/1.09 Y := Y
% 0.70/1.09 Z := Z
% 0.70/1.09 end
% 0.70/1.09 permutation0:
% 0.70/1.09 0 ==> 0
% 0.70/1.09 end
% 0.70/1.09
% 0.70/1.09 subsumption: (5) {G0,W14,D4,L2,V1,M2} I { ! mult( skol1( X ), X ) ==> skol1
% 0.70/1.09 ( X ), ! mult( X, skol1( X ) ) ==> skol1( X ) }.
% 0.70/1.09 parent0: (58) {G0,W14,D4,L2,V1,M2} { ! mult( skol1( X ), X ) = skol1( X )
% 0.70/1.09 , ! mult( X, skol1( X ) ) = skol1( X ) }.
% 0.70/1.09 substitution0:
% 0.70/1.09 X := X
% 0.70/1.09 end
% 0.70/1.09 permutation0:
% 0.70/1.09 0 ==> 0
% 0.70/1.09 1 ==> 1
% 0.70/1.09 end
% 0.70/1.09
% 0.70/1.09 eqswap: (83) {G0,W15,D5,L1,V3,M1} { mult( mult( X, mult( Y, Z ) ), X ) ==>
% 0.70/1.09 mult( mult( X, Y ), mult( Z, X ) ) }.
% 0.70/1.09 parent0[0]: (4) {G0,W15,D5,L1,V3,M1} I { mult( mult( Z, Y ), mult( X, Z ) )
% 0.70/1.09 ==> mult( mult( Z, mult( Y, X ) ), Z ) }.
% 0.70/1.09 substitution0:
% 0.70/1.09 X := Z
% 0.70/1.09 Y := Y
% 0.70/1.09 Z := X
% 0.70/1.09 end
% 0.70/1.09
% 0.70/1.09 paramod: (85) {G1,W15,D6,L1,V3,M1} { mult( mult( X, mult( ld( X, Y ), Z )
% 0.70/1.09 ), X ) ==> mult( Y, mult( Z, X ) ) }.
% 0.70/1.09 parent0[0]: (0) {G0,W7,D4,L1,V2,M1} I { mult( Y, ld( Y, X ) ) ==> X }.
% 0.70/1.09 parent1[0; 11]: (83) {G0,W15,D5,L1,V3,M1} { mult( mult( X, mult( Y, Z ) )
% 0.70/1.09 , X ) ==> mult( mult( X, Y ), mult( Z, X ) ) }.
% 0.70/1.09 substitution0:
% 0.70/1.09 X := Y
% 0.70/1.09 Y := X
% 0.70/1.09 end
% 0.70/1.09 substitution1:
% 0.70/1.09 X := X
% 0.70/1.09 Y := ld( X, Y )
% 0.70/1.09 Z := Z
% 0.70/1.09 end
% 0.70/1.09
% 0.70/1.09 subsumption: (10) {G1,W15,D6,L1,V3,M1} P(0,4) { mult( mult( X, mult( ld( X
% 0.70/1.09 , Y ), Z ) ), X ) ==> mult( Y, mult( Z, X ) ) }.
% 0.70/1.09 parent0: (85) {G1,W15,D6,L1,V3,M1} { mult( mult( X, mult( ld( X, Y ), Z )
% 0.70/1.09 ), X ) ==> mult( Y, mult( Z, X ) ) }.
% 0.70/1.09 substitution0:
% 0.70/1.09 X := X
% 0.70/1.09 Y := Y
% 0.70/1.09 Z := Z
% 0.70/1.09 end
% 0.70/1.09 permutation0:
% 0.70/1.09 0 ==> 0
% 0.70/1.09 end
% 0.70/1.09
% 0.70/1.09 eqswap: (91) {G0,W7,D4,L1,V2,M1} { X ==> rd( mult( X, Y ), Y ) }.
% 0.70/1.09 parent0[0]: (3) {G0,W7,D4,L1,V2,M1} I { rd( mult( Y, X ), X ) ==> Y }.
% 0.70/1.09 substitution0:
% 0.70/1.09 X := Y
% 0.70/1.09 Y := X
% 0.70/1.09 end
% 0.70/1.09
% 0.70/1.09 paramod: (92) {G1,W15,D5,L1,V3,M1} { mult( X, mult( ld( X, Y ), Z ) ) ==>
% 0.70/1.09 rd( mult( Y, mult( Z, X ) ), X ) }.
% 0.70/1.09 parent0[0]: (10) {G1,W15,D6,L1,V3,M1} P(0,4) { mult( mult( X, mult( ld( X,
% 0.70/1.09 Y ), Z ) ), X ) ==> mult( Y, mult( Z, X ) ) }.
% 0.70/1.09 parent1[0; 9]: (91) {G0,W7,D4,L1,V2,M1} { X ==> rd( mult( X, Y ), Y ) }.
% 0.70/1.09 substitution0:
% 0.70/1.09 X := X
% 0.70/1.09 Y := Y
% 0.70/1.09 Z := Z
% 0.70/1.09 end
% 0.70/1.09 substitution1:
% 0.70/1.09 X := mult( X, mult( ld( X, Y ), Z ) )
% 0.70/1.09 Y := X
% 0.70/1.09 end
% 0.70/1.09
% 0.70/1.09 eqswap: (93) {G1,W15,D5,L1,V3,M1} { rd( mult( Y, mult( Z, X ) ), X ) ==>
% 0.70/1.09 mult( X, mult( ld( X, Y ), Z ) ) }.
% 0.70/1.09 parent0[0]: (92) {G1,W15,D5,L1,V3,M1} { mult( X, mult( ld( X, Y ), Z ) )
% 0.70/1.09 ==> rd( mult( Y, mult( Z, X ) ), X ) }.
% 0.70/1.09 substitution0:
% 0.70/1.09 X := X
% 0.70/1.09 Y := Y
% 0.70/1.09 Z := Z
% 0.70/1.09 end
% 0.70/1.09
% 0.70/1.09 subsumption: (18) {G2,W15,D5,L1,V3,M1} P(10,3) { rd( mult( Y, mult( Z, X )
% 0.70/1.09 ), X ) ==> mult( X, mult( ld( X, Y ), Z ) ) }.
% 0.70/1.09 parent0: (93) {G1,W15,D5,L1,V3,M1} { rd( mult( Y, mult( Z, X ) ), X ) ==>
% 0.70/1.09 mult( X, mult( ld( X, Y ), Z ) ) }.
% 0.70/1.09 substitution0:
% 0.70/1.09 X := X
% 0.70/1.09 Y := Y
% 0.70/1.09 Z := Z
% 0.70/1.09 end
% 0.70/1.09 permutation0:
% 0.70/1.09 0 ==> 0
% 0.70/1.09 end
% 0.70/1.09
% 0.70/1.09 eqswap: (95) {G2,W15,D5,L1,V3,M1} { mult( Z, mult( ld( Z, X ), Y ) ) ==>
% 0.70/1.09 rd( mult( X, mult( Y, Z ) ), Z ) }.
% 0.70/1.09 parent0[0]: (18) {G2,W15,D5,L1,V3,M1} P(10,3) { rd( mult( Y, mult( Z, X ) )
% 0.70/1.09 , X ) ==> mult( X, mult( ld( X, Y ), Z ) ) }.
% 0.70/1.09 substitution0:
% 0.70/1.09 X := Z
% 0.70/1.09 Y := X
% 0.70/1.09 Z := Y
% 0.70/1.09 end
% 0.70/1.09
% 0.70/1.09 paramod: (99) {G1,W15,D5,L1,V3,M1} { mult( X, mult( ld( X, Y ), rd( Z, X )
% 0.70/1.09 ) ) ==> rd( mult( Y, Z ), X ) }.
% 0.70/1.09 parent0[0]: (2) {G0,W7,D4,L1,V2,M1} I { mult( rd( Y, X ), X ) ==> Y }.
% 0.70/1.09 parent1[0; 13]: (95) {G2,W15,D5,L1,V3,M1} { mult( Z, mult( ld( Z, X ), Y )
% 0.70/1.09 ) ==> rd( mult( X, mult( Y, Z ) ), Z ) }.
% 0.70/1.09 substitution0:
% 0.70/1.09 X := X
% 0.70/1.09 Y := Z
% 0.70/1.09 end
% 0.70/1.09 substitution1:
% 0.70/1.09 X := Y
% 0.70/1.09 Y := rd( Z, X )
% 0.70/1.09 Z := X
% 0.70/1.09 end
% 0.70/1.09
% 0.70/1.09 subsumption: (20) {G3,W15,D5,L1,V3,M1} P(2,18) { mult( Y, mult( ld( Y, Z )
% 0.70/1.09 , rd( X, Y ) ) ) ==> rd( mult( Z, X ), Y ) }.
% 0.70/1.09 parent0: (99) {G1,W15,D5,L1,V3,M1} { mult( X, mult( ld( X, Y ), rd( Z, X )
% 0.70/1.09 ) ) ==> rd( mult( Y, Z ), X ) }.
% 0.70/1.09 substitution0:
% 0.70/1.09 X := Y
% 0.70/1.09 Y := Z
% 0.70/1.09 Z := X
% 0.70/1.09 end
% 0.70/1.09 permutation0:
% 0.70/1.09 0 ==> 0
% 0.70/1.09 end
% 0.70/1.09
% 0.70/1.09 eqswap: (103) {G3,W15,D5,L1,V3,M1} { rd( mult( Y, Z ), X ) ==> mult( X,
% 0.70/1.09 mult( ld( X, Y ), rd( Z, X ) ) ) }.
% 0.70/1.09 parent0[0]: (20) {G3,W15,D5,L1,V3,M1} P(2,18) { mult( Y, mult( ld( Y, Z ),
% 0.70/1.09 rd( X, Y ) ) ) ==> rd( mult( Z, X ), Y ) }.
% 0.70/1.09 substitution0:
% 0.70/1.09 X := Z
% 0.70/1.09 Y := X
% 0.70/1.09 Z := Y
% 0.70/1.09 end
% 0.70/1.09
% 0.70/1.09 paramod: (106) {G1,W15,D5,L1,V3,M1} { rd( mult( mult( X, Y ), Z ), X ) ==>
% 0.70/1.09 mult( X, mult( Y, rd( Z, X ) ) ) }.
% 0.70/1.09 parent0[0]: (1) {G0,W7,D4,L1,V2,M1} I { ld( Y, mult( Y, X ) ) ==> X }.
% 0.70/1.09 parent1[0; 11]: (103) {G3,W15,D5,L1,V3,M1} { rd( mult( Y, Z ), X ) ==>
% 0.70/1.09 mult( X, mult( ld( X, Y ), rd( Z, X ) ) ) }.
% 0.70/1.09 substitution0:
% 0.70/1.09 X := Y
% 0.70/1.09 Y := X
% 0.70/1.09 end
% 0.70/1.09 substitution1:
% 0.70/1.09 X := X
% 0.70/1.09 Y := mult( X, Y )
% 0.70/1.09 Z := Z
% 0.70/1.09 end
% 0.70/1.09
% 0.70/1.09 subsumption: (22) {G4,W15,D5,L1,V3,M1} P(1,20) { rd( mult( mult( X, Y ), Z
% 0.70/1.09 ), X ) ==> mult( X, mult( Y, rd( Z, X ) ) ) }.
% 0.70/1.09 parent0: (106) {G1,W15,D5,L1,V3,M1} { rd( mult( mult( X, Y ), Z ), X ) ==>
% 0.70/1.09 mult( X, mult( Y, rd( Z, X ) ) ) }.
% 0.70/1.09 substitution0:
% 0.70/1.09 X := X
% 0.70/1.09 Y := Y
% 0.70/1.09 Z := Z
% 0.70/1.09 end
% 0.70/1.09 permutation0:
% 0.70/1.09 0 ==> 0
% 0.70/1.09 end
% 0.70/1.09
% 0.70/1.09 eqswap: (108) {G4,W15,D5,L1,V3,M1} { mult( X, mult( Y, rd( Z, X ) ) ) ==>
% 0.70/1.09 rd( mult( mult( X, Y ), Z ), X ) }.
% 0.70/1.09 parent0[0]: (22) {G4,W15,D5,L1,V3,M1} P(1,20) { rd( mult( mult( X, Y ), Z )
% 0.70/1.09 , X ) ==> mult( X, mult( Y, rd( Z, X ) ) ) }.
% 0.70/1.09 substitution0:
% 0.70/1.09 X := X
% 0.70/1.09 Y := Y
% 0.70/1.09 Z := Z
% 0.70/1.09 end
% 0.70/1.09
% 0.70/1.09 paramod: (111) {G1,W11,D5,L1,V2,M1} { mult( X, mult( Y, rd( X, X ) ) ) ==>
% 0.70/1.09 mult( X, Y ) }.
% 0.70/1.09 parent0[0]: (3) {G0,W7,D4,L1,V2,M1} I { rd( mult( Y, X ), X ) ==> Y }.
% 0.70/1.09 parent1[0; 8]: (108) {G4,W15,D5,L1,V3,M1} { mult( X, mult( Y, rd( Z, X ) )
% 0.70/1.09 ) ==> rd( mult( mult( X, Y ), Z ), X ) }.
% 0.70/1.09 substitution0:
% 0.70/1.09 X := X
% 0.70/1.09 Y := mult( X, Y )
% 0.70/1.09 end
% 0.70/1.09 substitution1:
% 0.70/1.09 X := X
% 0.70/1.09 Y := Y
% 0.70/1.09 Z := X
% 0.70/1.09 end
% 0.70/1.09
% 0.70/1.09 subsumption: (27) {G5,W11,D5,L1,V2,M1} P(22,3) { mult( X, mult( Y, rd( X, X
% 0.70/1.09 ) ) ) ==> mult( X, Y ) }.
% 0.70/1.09 parent0: (111) {G1,W11,D5,L1,V2,M1} { mult( X, mult( Y, rd( X, X ) ) ) ==>
% 0.70/1.09 mult( X, Y ) }.
% 0.70/1.09 substitution0:
% 0.70/1.09 X := X
% 0.70/1.09 Y := Y
% 0.70/1.09 end
% 0.70/1.09 permutation0:
% 0.70/1.09 0 ==> 0
% 0.70/1.09 end
% 0.70/1.09
% 0.70/1.09 eqswap: (115) {G0,W7,D4,L1,V2,M1} { Y ==> ld( X, mult( X, Y ) ) }.
% 0.70/1.09 parent0[0]: (1) {G0,W7,D4,L1,V2,M1} I { ld( Y, mult( Y, X ) ) ==> X }.
% 0.70/1.09 substitution0:
% 0.70/1.09 X := Y
% 0.70/1.09 Y := X
% 0.70/1.09 end
% 0.70/1.09
% 0.70/1.09 paramod: (117) {G1,W11,D4,L1,V2,M1} { mult( X, rd( Y, Y ) ) ==> ld( Y,
% 0.70/1.09 mult( Y, X ) ) }.
% 0.70/1.09 parent0[0]: (27) {G5,W11,D5,L1,V2,M1} P(22,3) { mult( X, mult( Y, rd( X, X
% 0.70/1.09 ) ) ) ==> mult( X, Y ) }.
% 0.70/1.09 parent1[0; 8]: (115) {G0,W7,D4,L1,V2,M1} { Y ==> ld( X, mult( X, Y ) ) }.
% 0.70/1.09 substitution0:
% 0.70/1.09 X := Y
% 0.70/1.09 Y := X
% 0.70/1.09 end
% 0.70/1.09 substitution1:
% 0.70/1.09 X := Y
% 0.70/1.09 Y := mult( X, rd( Y, Y ) )
% 0.70/1.09 end
% 0.70/1.09
% 0.70/1.09 paramod: (118) {G1,W7,D4,L1,V2,M1} { mult( X, rd( Y, Y ) ) ==> X }.
% 0.70/1.09 parent0[0]: (1) {G0,W7,D4,L1,V2,M1} I { ld( Y, mult( Y, X ) ) ==> X }.
% 0.70/1.09 parent1[0; 6]: (117) {G1,W11,D4,L1,V2,M1} { mult( X, rd( Y, Y ) ) ==> ld(
% 0.70/1.09 Y, mult( Y, X ) ) }.
% 0.70/1.09 substitution0:
% 0.70/1.09 X := X
% 0.70/1.09 Y := Y
% 0.70/1.09 end
% 0.70/1.09 substitution1:
% 0.70/1.09 X := X
% 0.70/1.09 Y := Y
% 0.70/1.09 end
% 0.70/1.09
% 0.70/1.09 subsumption: (29) {G6,W7,D4,L1,V2,M1} P(27,1);d(1) { mult( Y, rd( X, X ) )
% 0.70/1.09 ==> Y }.
% 0.70/1.09 parent0: (118) {G1,W7,D4,L1,V2,M1} { mult( X, rd( Y, Y ) ) ==> X }.
% 0.70/1.09 substitution0:
% 0.70/1.09 X := Y
% 0.70/1.09 Y := X
% 0.70/1.09 end
% 0.70/1.09 permutation0:
% 0.70/1.09 0 ==> 0
% 0.70/1.09 end
% 0.70/1.09
% 0.70/1.09 eqswap: (121) {G0,W7,D4,L1,V2,M1} { Y ==> ld( X, mult( X, Y ) ) }.
% 0.70/1.09 parent0[0]: (1) {G0,W7,D4,L1,V2,M1} I { ld( Y, mult( Y, X ) ) ==> X }.
% 0.70/1.09 substitution0:
% 0.70/1.09 X := Y
% 0.70/1.09 Y := X
% 0.70/1.09 end
% 0.70/1.09
% 0.70/1.09 paramod: (122) {G1,W7,D3,L1,V2,M1} { rd( X, X ) ==> ld( Y, Y ) }.
% 0.70/1.09 parent0[0]: (29) {G6,W7,D4,L1,V2,M1} P(27,1);d(1) { mult( Y, rd( X, X ) )
% 0.70/1.09 ==> Y }.
% 0.70/1.09 parent1[0; 6]: (121) {G0,W7,D4,L1,V2,M1} { Y ==> ld( X, mult( X, Y ) ) }.
% 0.70/1.09 substitution0:
% 0.70/1.09 X := X
% 0.70/1.09 Y := Y
% 0.70/1.09 end
% 0.70/1.09 substitution1:
% 0.70/1.09 X := Y
% 0.70/1.09 Y := rd( X, X )
% 0.70/1.09 end
% 0.70/1.09
% 0.70/1.09 eqswap: (123) {G1,W7,D3,L1,V2,M1} { ld( Y, Y ) ==> rd( X, X ) }.
% 0.70/1.09 parent0[0]: (122) {G1,W7,D3,L1,V2,M1} { rd( X, X ) ==> ld( Y, Y ) }.
% 0.70/1.09 substitution0:
% 0.70/1.09 X := X
% 0.70/1.09 Y := Y
% 0.70/1.09 end
% 0.70/1.09
% 0.70/1.09 subsumption: (38) {G7,W7,D3,L1,V2,M1} P(29,1) { ld( X, X ) = rd( Y, Y ) }.
% 0.70/1.09 parent0: (123) {G1,W7,D3,L1,V2,M1} { ld( Y, Y ) ==> rd( X, X ) }.
% 0.70/1.09 substitution0:
% 0.70/1.09 X := Y
% 0.70/1.09 Y := X
% 0.70/1.09 end
% 0.70/1.09 permutation0:
% 0.70/1.09 0 ==> 0
% 0.70/1.09 end
% 0.70/1.09
% 0.70/1.09 eqswap: (124) {G7,W7,D3,L1,V2,M1} { rd( Y, Y ) = ld( X, X ) }.
% 0.70/1.09 parent0[0]: (38) {G7,W7,D3,L1,V2,M1} P(29,1) { ld( X, X ) = rd( Y, Y ) }.
% 0.70/1.09 substitution0:
% 0.70/1.09 X := X
% 0.70/1.09 Y := Y
% 0.70/1.09 end
% 0.70/1.09
% 0.70/1.09 paramod: (129) {G8,W7,D3,L1,V2,M1} { rd( X, X ) = rd( Z, Z ) }.
% 0.70/1.09 parent0[0]: (38) {G7,W7,D3,L1,V2,M1} P(29,1) { ld( X, X ) = rd( Y, Y ) }.
% 0.70/1.09 parent1[0; 4]: (124) {G7,W7,D3,L1,V2,M1} { rd( Y, Y ) = ld( X, X ) }.
% 0.70/1.09 substitution0:
% 0.70/1.09 X := Y
% 0.70/1.09 Y := Z
% 0.70/1.09 end
% 0.70/1.09 substitution1:
% 0.70/1.09 X := Y
% 0.70/1.09 Y := X
% 0.70/1.09 end
% 0.70/1.09
% 0.70/1.09 subsumption: (40) {G8,W7,D3,L1,V2,M1} P(38,38) { rd( Y, Y ) = rd( Z, Z )
% 0.70/1.09 }.
% 0.70/1.09 parent0: (129) {G8,W7,D3,L1,V2,M1} { rd( X, X ) = rd( Z, Z ) }.
% 0.70/1.09 substitution0:
% 0.70/1.09 X := Y
% 0.70/1.09 Y := T
% 0.70/1.09 Z := Z
% 0.70/1.09 end
% 0.70/1.09 permutation0:
% 0.70/1.09 0 ==> 0
% 0.70/1.09 end
% 0.70/1.09
% 0.70/1.09 eqswap: (130) {G0,W7,D4,L1,V2,M1} { X ==> mult( rd( X, Y ), Y ) }.
% 0.70/1.09 parent0[0]: (2) {G0,W7,D4,L1,V2,M1} I { mult( rd( Y, X ), X ) ==> Y }.
% 0.70/1.09 substitution0:
% 0.70/1.09 X := Y
% 0.70/1.09 Y := X
% 0.70/1.09 end
% 0.70/1.09
% 0.70/1.09 paramod: (131) {G1,W7,D4,L1,V2,M1} { X ==> mult( rd( Y, Y ), X ) }.
% 0.70/1.09 parent0[0]: (40) {G8,W7,D3,L1,V2,M1} P(38,38) { rd( Y, Y ) = rd( Z, Z ) }.
% 0.70/1.09 parent1[0; 3]: (130) {G0,W7,D4,L1,V2,M1} { X ==> mult( rd( X, Y ), Y ) }.
% 0.70/1.09 substitution0:
% 0.70/1.09 X := Z
% 0.70/1.09 Y := X
% 0.70/1.09 Z := Y
% 0.70/1.09 end
% 0.70/1.09 substitution1:
% 0.70/1.09 X := X
% 0.70/1.09 Y := X
% 0.70/1.09 end
% 0.70/1.09
% 0.70/1.09 eqswap: (132) {G1,W7,D4,L1,V2,M1} { mult( rd( Y, Y ), X ) ==> X }.
% 0.70/1.09 parent0[0]: (131) {G1,W7,D4,L1,V2,M1} { X ==> mult( rd( Y, Y ), X ) }.
% 0.70/1.09 substitution0:
% 0.70/1.09 X := X
% 0.70/1.09 Y := Y
% 0.70/1.09 end
% 0.70/1.09
% 0.70/1.09 subsumption: (47) {G9,W7,D4,L1,V2,M1} P(40,2) { mult( rd( Y, Y ), X ) ==> X
% 0.70/1.09 }.
% 0.70/1.09 parent0: (132) {G1,W7,D4,L1,V2,M1} { mult( rd( Y, Y ), X ) ==> X }.
% 0.70/1.09 substitution0:
% 0.70/1.09 X := X
% 0.70/1.09 Y := Y
% 0.70/1.09 end
% 0.70/1.09 permutation0:
% 0.70/1.09 0 ==> 0
% 0.70/1.09 end
% 0.70/1.09
% 0.70/1.09 eqswap: (133) {G9,W7,D4,L1,V2,M1} { Y ==> mult( rd( X, X ), Y ) }.
% 0.70/1.09 parent0[0]: (47) {G9,W7,D4,L1,V2,M1} P(40,2) { mult( rd( Y, Y ), X ) ==> X
% 0.70/1.09 }.
% 0.70/1.09 substitution0:
% 0.70/1.09 X := Y
% 0.70/1.09 Y := X
% 0.70/1.09 end
% 0.70/1.09
% 0.70/1.09 eqswap: (135) {G0,W14,D4,L2,V1,M2} { ! skol1( X ) ==> mult( X, skol1( X )
% 0.70/1.09 ), ! mult( skol1( X ), X ) ==> skol1( X ) }.
% 0.70/1.09 parent0[1]: (5) {G0,W14,D4,L2,V1,M2} I { ! mult( skol1( X ), X ) ==> skol1
% 0.70/1.09 ( X ), ! mult( X, skol1( X ) ) ==> skol1( X ) }.
% 0.70/1.09 substitution0:
% 0.70/1.09 X := X
% 0.70/1.09 end
% 0.70/1.09
% 0.70/1.09 eqswap: (136) {G0,W14,D4,L2,V1,M2} { ! skol1( X ) ==> mult( skol1( X ), X
% 0.70/1.09 ), ! skol1( X ) ==> mult( X, skol1( X ) ) }.
% 0.70/1.09 parent0[1]: (135) {G0,W14,D4,L2,V1,M2} { ! skol1( X ) ==> mult( X, skol1(
% 0.70/1.09 X ) ), ! mult( skol1( X ), X ) ==> skol1( X ) }.
% 0.70/1.09 substitution0:
% 0.70/1.09 X := X
% 0.70/1.09 end
% 0.70/1.09
% 0.70/1.09 resolution: (138) {G1,W13,D5,L1,V1,M1} { ! skol1( rd( X, X ) ) ==> mult(
% 0.70/1.09 skol1( rd( X, X ) ), rd( X, X ) ) }.
% 0.70/1.09 parent0[1]: (136) {G0,W14,D4,L2,V1,M2} { ! skol1( X ) ==> mult( skol1( X )
% 0.70/1.09 , X ), ! skol1( X ) ==> mult( X, skol1( X ) ) }.
% 0.70/1.09 parent1[0]: (133) {G9,W7,D4,L1,V2,M1} { Y ==> mult( rd( X, X ), Y ) }.
% 0.70/1.09 substitution0:
% 0.70/1.09 X := rd( X, X )
% 0.70/1.09 end
% 0.70/1.09 substitution1:
% 0.70/1.09 X := X
% 0.70/1.09 Y := skol1( rd( X, X ) )
% 0.70/1.09 end
% 0.70/1.09
% 0.70/1.09 paramod: (139) {G2,W9,D4,L1,V1,M1} { ! skol1( rd( X, X ) ) ==> skol1( rd(
% 0.70/1.09 X, X ) ) }.
% 0.70/1.09 parent0[0]: (29) {G6,W7,D4,L1,V2,M1} P(27,1);d(1) { mult( Y, rd( X, X ) )
% 0.70/1.09 ==> Y }.
% 0.70/1.09 parent1[0; 6]: (138) {G1,W13,D5,L1,V1,M1} { ! skol1( rd( X, X ) ) ==> mult
% 0.70/1.09 ( skol1( rd( X, X ) ), rd( X, X ) ) }.
% 0.70/1.09 substitution0:
% 0.70/1.09 X := X
% 0.70/1.09 Y := skol1( rd( X, X ) )
% 0.70/1.09 end
% 0.70/1.09 substitution1:
% 0.70/1.09 X := X
% 0.70/1.09 end
% 0.70/1.09
% 0.70/1.09 eqrefl: (140) {G0,W0,D0,L0,V0,M0} { }.
% 0.70/1.09 parent0[0]: (139) {G2,W9,D4,L1,V1,M1} { ! skol1( rd( X, X ) ) ==> skol1(
% 0.70/1.09 rd( X, X ) ) }.
% 0.70/1.09 substitution0:
% 0.70/1.09 X := X
% 0.70/1.09 end
% 0.70/1.09
% 0.70/1.09 subsumption: (51) {G10,W0,D0,L0,V0,M0} R(47,5);d(29);q { }.
% 0.70/1.09 parent0: (140) {G0,W0,D0,L0,V0,M0} { }.
% 0.70/1.09 substitution0:
% 0.70/1.09 end
% 0.70/1.09 permutation0:
% 0.70/1.09 end
% 0.70/1.09
% 0.70/1.09 Proof check complete!
% 0.70/1.09
% 0.70/1.09 Memory use:
% 0.70/1.09
% 0.70/1.09 space for terms: 791
% 0.70/1.09 space for clauses: 6873
% 0.70/1.09
% 0.70/1.09
% 0.70/1.09 clauses generated: 407
% 0.70/1.09 clauses kept: 52
% 0.70/1.09 clauses selected: 24
% 0.70/1.09 clauses deleted: 0
% 0.70/1.09 clauses inuse deleted: 0
% 0.70/1.09
% 0.70/1.09 subsentry: 351
% 0.70/1.09 literals s-matched: 159
% 0.70/1.09 literals matched: 159
% 0.70/1.09 full subsumption: 0
% 0.70/1.09
% 0.70/1.09 checksum: 825269633
% 0.70/1.09
% 0.70/1.09
% 0.70/1.09 Bliksem ended
%------------------------------------------------------------------------------