TSTP Solution File: GRP715+1 by Bliksem---1.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : GRP715+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n007.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 07:39:13 EDT 2022
% Result : Theorem 0.74s 1.13s
% Output : Refutation 0.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP715+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n007.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 : Mon Jun 13 10:45:39 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.74/1.13 *** allocated 10000 integers for termspace/termends
% 0.74/1.13 *** allocated 10000 integers for clauses
% 0.74/1.13 *** allocated 10000 integers for justifications
% 0.74/1.13 Bliksem 1.12
% 0.74/1.13
% 0.74/1.13
% 0.74/1.13 Automatic Strategy Selection
% 0.74/1.13
% 0.74/1.13
% 0.74/1.13 Clauses:
% 0.74/1.13
% 0.74/1.13 { plus( plus( Z, Y ), X ) = plus( Z, plus( Y, X ) ) }.
% 0.74/1.13 { plus( Y, X ) = plus( X, Y ) }.
% 0.74/1.13 { plus( X, op_0 ) = X }.
% 0.74/1.13 { plus( X, minus( X ) ) = op_0 }.
% 0.74/1.13 { mult( Z, plus( Y, X ) ) = plus( mult( Z, Y ), mult( Z, X ) ) }.
% 0.74/1.13 { mult( mult( mult( Z, Y ), X ), Y ) = mult( Z, mult( mult( Y, X ), Y ) ) }
% 0.74/1.13 .
% 0.74/1.13 { mult( Y, mult( X, X ) ) = mult( mult( Y, X ), X ) }.
% 0.74/1.13 { mult( X, unit ) = X }.
% 0.74/1.13 { mult( unit, X ) = X }.
% 0.74/1.13 { mult( op_a, op_b ) = unit }.
% 0.74/1.13 { mult( op_b, op_a ) = unit }.
% 0.74/1.13 { ! mult( mult( skol1, op_a ), op_b ) = skol1, ! mult( mult( skol1, op_b )
% 0.74/1.13 , op_a ) = skol1 }.
% 0.74/1.13
% 0.74/1.13 percentage equality = 1.000000, percentage horn = 1.000000
% 0.74/1.13 This is a pure equality problem
% 0.74/1.13
% 0.74/1.13
% 0.74/1.13
% 0.74/1.13 Options Used:
% 0.74/1.13
% 0.74/1.13 useres = 1
% 0.74/1.13 useparamod = 1
% 0.74/1.13 useeqrefl = 1
% 0.74/1.13 useeqfact = 1
% 0.74/1.13 usefactor = 1
% 0.74/1.13 usesimpsplitting = 0
% 0.74/1.13 usesimpdemod = 5
% 0.74/1.13 usesimpres = 3
% 0.74/1.13
% 0.74/1.13 resimpinuse = 1000
% 0.74/1.13 resimpclauses = 20000
% 0.74/1.13 substype = eqrewr
% 0.74/1.13 backwardsubs = 1
% 0.74/1.13 selectoldest = 5
% 0.74/1.13
% 0.74/1.13 litorderings [0] = split
% 0.74/1.13 litorderings [1] = extend the termordering, first sorting on arguments
% 0.74/1.13
% 0.74/1.13 termordering = kbo
% 0.74/1.13
% 0.74/1.13 litapriori = 0
% 0.74/1.13 termapriori = 1
% 0.74/1.13 litaposteriori = 0
% 0.74/1.13 termaposteriori = 0
% 0.74/1.13 demodaposteriori = 0
% 0.74/1.13 ordereqreflfact = 0
% 0.74/1.13
% 0.74/1.13 litselect = negord
% 0.74/1.13
% 0.74/1.13 maxweight = 15
% 0.74/1.13 maxdepth = 30000
% 0.74/1.13 maxlength = 115
% 0.74/1.13 maxnrvars = 195
% 0.74/1.13 excuselevel = 1
% 0.74/1.13 increasemaxweight = 1
% 0.74/1.13
% 0.74/1.13 maxselected = 10000000
% 0.74/1.13 maxnrclauses = 10000000
% 0.74/1.13
% 0.74/1.13 showgenerated = 0
% 0.74/1.13 showkept = 0
% 0.74/1.13 showselected = 0
% 0.74/1.13 showdeleted = 0
% 0.74/1.13 showresimp = 1
% 0.74/1.13 showstatus = 2000
% 0.74/1.13
% 0.74/1.13 prologoutput = 0
% 0.74/1.13 nrgoals = 5000000
% 0.74/1.13 totalproof = 1
% 0.74/1.13
% 0.74/1.13 Symbols occurring in the translation:
% 0.74/1.13
% 0.74/1.13 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.74/1.13 . [1, 2] (w:1, o:21, a:1, s:1, b:0),
% 0.74/1.13 ! [4, 1] (w:0, o:15, a:1, s:1, b:0),
% 0.74/1.13 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.74/1.13 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.74/1.13 plus [38, 2] (w:1, o:45, a:1, s:1, b:0),
% 0.74/1.13 op_0 [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.74/1.13 minus [40, 1] (w:1, o:20, a:1, s:1, b:0),
% 0.74/1.13 mult [41, 2] (w:1, o:46, a:1, s:1, b:0),
% 0.74/1.13 unit [42, 0] (w:1, o:10, a:1, s:1, b:0),
% 0.74/1.13 op_a [43, 0] (w:1, o:11, a:1, s:1, b:0),
% 0.74/1.13 op_b [44, 0] (w:1, o:12, a:1, s:1, b:0),
% 0.74/1.13 skol1 [46, 0] (w:1, o:14, a:1, s:1, b:1).
% 0.74/1.13
% 0.74/1.13
% 0.74/1.13 Starting Search:
% 0.74/1.13
% 0.74/1.13 *** allocated 15000 integers for clauses
% 0.74/1.13 *** allocated 22500 integers for clauses
% 0.74/1.13 *** allocated 33750 integers for clauses
% 0.74/1.13 *** allocated 50625 integers for clauses
% 0.74/1.13
% 0.74/1.13 Bliksems!, er is een bewijs:
% 0.74/1.13 % SZS status Theorem
% 0.74/1.13 % SZS output start Refutation
% 0.74/1.13
% 0.74/1.13 (5) {G0,W15,D5,L1,V3,M1} I { mult( Z, mult( mult( Y, X ), Y ) ) ==> mult(
% 0.74/1.13 mult( mult( Z, Y ), X ), Y ) }.
% 0.74/1.13 (6) {G0,W11,D4,L1,V2,M1} I { mult( Y, mult( X, X ) ) ==> mult( mult( Y, X )
% 0.74/1.13 , X ) }.
% 0.74/1.13 (7) {G0,W5,D3,L1,V1,M1} I { mult( X, unit ) ==> X }.
% 0.74/1.13 (8) {G0,W5,D3,L1,V1,M1} I { mult( unit, X ) ==> X }.
% 0.74/1.13 (9) {G0,W5,D3,L1,V0,M1} I { mult( op_a, op_b ) ==> unit }.
% 0.74/1.13 (10) {G0,W5,D3,L1,V0,M1} I { mult( op_b, op_a ) ==> unit }.
% 0.74/1.13 (11) {G0,W14,D4,L2,V0,M2} I { ! mult( mult( skol1, op_a ), op_b ) ==> skol1
% 0.74/1.13 , ! mult( mult( skol1, op_b ), op_a ) ==> skol1 }.
% 0.74/1.13 (46) {G1,W11,D5,L1,V1,M1} P(9,5);d(8) { mult( mult( mult( X, op_a ), op_b )
% 0.74/1.13 , op_a ) ==> mult( X, op_a ) }.
% 0.74/1.13 (65) {G1,W19,D6,L1,V3,M1} P(6,5);d(6) { mult( Z, mult( mult( mult( X, Y ),
% 0.74/1.13 Y ), X ) ) ==> mult( mult( mult( mult( Z, X ), Y ), Y ), X ) }.
% 0.74/1.13 (394) {G2,W11,D6,L1,V1,M1} P(9,65);d(8);d(10);d(7) { mult( mult( mult( mult
% 0.74/1.13 ( X, op_a ), op_b ), op_b ), op_a ) ==> X }.
% 0.74/1.13 (398) {G3,W7,D4,L1,V1,M1} P(394,46) { mult( mult( X, op_b ), op_a ) ==> X
% 0.74/1.13 }.
% 0.74/1.13 (406) {G4,W7,D4,L1,V1,M1} P(398,394) { mult( mult( X, op_a ), op_b ) ==> X
% 0.74/1.13 }.
% 0.74/1.13 (408) {G5,W0,D0,L0,V0,M0} P(398,11);q;d(406);q { }.
% 0.74/1.13
% 0.74/1.13
% 0.74/1.13 % SZS output end Refutation
% 0.74/1.13 found a proof!
% 0.74/1.13
% 0.74/1.13
% 0.74/1.13 Unprocessed initial clauses:
% 0.74/1.13
% 0.74/1.13 (410) {G0,W11,D4,L1,V3,M1} { plus( plus( Z, Y ), X ) = plus( Z, plus( Y, X
% 0.74/1.13 ) ) }.
% 0.74/1.13 (411) {G0,W7,D3,L1,V2,M1} { plus( Y, X ) = plus( X, Y ) }.
% 0.74/1.13 (412) {G0,W5,D3,L1,V1,M1} { plus( X, op_0 ) = X }.
% 0.74/1.13 (413) {G0,W6,D4,L1,V1,M1} { plus( X, minus( X ) ) = op_0 }.
% 0.74/1.13 (414) {G0,W13,D4,L1,V3,M1} { mult( Z, plus( Y, X ) ) = plus( mult( Z, Y )
% 0.74/1.13 , mult( Z, X ) ) }.
% 0.74/1.13 (415) {G0,W15,D5,L1,V3,M1} { mult( mult( mult( Z, Y ), X ), Y ) = mult( Z
% 0.74/1.13 , mult( mult( Y, X ), Y ) ) }.
% 0.74/1.13 (416) {G0,W11,D4,L1,V2,M1} { mult( Y, mult( X, X ) ) = mult( mult( Y, X )
% 0.74/1.13 , X ) }.
% 0.74/1.13 (417) {G0,W5,D3,L1,V1,M1} { mult( X, unit ) = X }.
% 0.74/1.13 (418) {G0,W5,D3,L1,V1,M1} { mult( unit, X ) = X }.
% 0.74/1.13 (419) {G0,W5,D3,L1,V0,M1} { mult( op_a, op_b ) = unit }.
% 0.74/1.13 (420) {G0,W5,D3,L1,V0,M1} { mult( op_b, op_a ) = unit }.
% 0.74/1.13 (421) {G0,W14,D4,L2,V0,M2} { ! mult( mult( skol1, op_a ), op_b ) = skol1,
% 0.74/1.13 ! mult( mult( skol1, op_b ), op_a ) = skol1 }.
% 0.74/1.13
% 0.74/1.13
% 0.74/1.13 Total Proof:
% 0.74/1.13
% 0.74/1.13 eqswap: (426) {G0,W15,D5,L1,V3,M1} { mult( X, mult( mult( Y, Z ), Y ) ) =
% 0.74/1.13 mult( mult( mult( X, Y ), Z ), Y ) }.
% 0.74/1.13 parent0[0]: (415) {G0,W15,D5,L1,V3,M1} { mult( mult( mult( Z, Y ), X ), Y
% 0.74/1.13 ) = mult( Z, mult( mult( Y, X ), Y ) ) }.
% 0.74/1.13 substitution0:
% 0.74/1.13 X := Z
% 0.74/1.13 Y := Y
% 0.74/1.13 Z := X
% 0.74/1.13 end
% 0.74/1.13
% 0.74/1.13 subsumption: (5) {G0,W15,D5,L1,V3,M1} I { mult( Z, mult( mult( Y, X ), Y )
% 0.74/1.13 ) ==> mult( mult( mult( Z, Y ), X ), Y ) }.
% 0.74/1.13 parent0: (426) {G0,W15,D5,L1,V3,M1} { mult( X, mult( mult( Y, Z ), Y ) ) =
% 0.74/1.13 mult( mult( mult( X, Y ), Z ), Y ) }.
% 0.74/1.13 substitution0:
% 0.74/1.13 X := Z
% 0.74/1.13 Y := Y
% 0.74/1.13 Z := X
% 0.74/1.13 end
% 0.74/1.13 permutation0:
% 0.74/1.13 0 ==> 0
% 0.74/1.13 end
% 0.74/1.13
% 0.74/1.13 subsumption: (6) {G0,W11,D4,L1,V2,M1} I { mult( Y, mult( X, X ) ) ==> mult
% 0.74/1.13 ( mult( Y, X ), X ) }.
% 0.74/1.13 parent0: (416) {G0,W11,D4,L1,V2,M1} { mult( Y, mult( X, X ) ) = mult( mult
% 0.74/1.13 ( Y, X ), X ) }.
% 0.74/1.13 substitution0:
% 0.74/1.13 X := X
% 0.74/1.13 Y := Y
% 0.74/1.13 end
% 0.74/1.13 permutation0:
% 0.74/1.13 0 ==> 0
% 0.74/1.13 end
% 0.74/1.13
% 0.74/1.13 subsumption: (7) {G0,W5,D3,L1,V1,M1} I { mult( X, unit ) ==> X }.
% 0.74/1.13 parent0: (417) {G0,W5,D3,L1,V1,M1} { mult( X, unit ) = X }.
% 0.74/1.13 substitution0:
% 0.74/1.13 X := X
% 0.74/1.13 end
% 0.74/1.13 permutation0:
% 0.74/1.13 0 ==> 0
% 0.74/1.13 end
% 0.74/1.13
% 0.74/1.13 subsumption: (8) {G0,W5,D3,L1,V1,M1} I { mult( unit, X ) ==> X }.
% 0.74/1.13 parent0: (418) {G0,W5,D3,L1,V1,M1} { mult( unit, X ) = X }.
% 0.74/1.13 substitution0:
% 0.74/1.13 X := X
% 0.74/1.13 end
% 0.74/1.13 permutation0:
% 0.74/1.13 0 ==> 0
% 0.74/1.13 end
% 0.74/1.13
% 0.74/1.13 subsumption: (9) {G0,W5,D3,L1,V0,M1} I { mult( op_a, op_b ) ==> unit }.
% 0.74/1.13 parent0: (419) {G0,W5,D3,L1,V0,M1} { mult( op_a, op_b ) = unit }.
% 0.74/1.13 substitution0:
% 0.74/1.13 end
% 0.74/1.13 permutation0:
% 0.74/1.13 0 ==> 0
% 0.74/1.13 end
% 0.74/1.13
% 0.74/1.13 subsumption: (10) {G0,W5,D3,L1,V0,M1} I { mult( op_b, op_a ) ==> unit }.
% 0.74/1.13 parent0: (420) {G0,W5,D3,L1,V0,M1} { mult( op_b, op_a ) = unit }.
% 0.74/1.13 substitution0:
% 0.74/1.13 end
% 0.74/1.13 permutation0:
% 0.74/1.13 0 ==> 0
% 0.74/1.13 end
% 0.74/1.13
% 0.74/1.13 subsumption: (11) {G0,W14,D4,L2,V0,M2} I { ! mult( mult( skol1, op_a ),
% 0.74/1.13 op_b ) ==> skol1, ! mult( mult( skol1, op_b ), op_a ) ==> skol1 }.
% 0.74/1.13 parent0: (421) {G0,W14,D4,L2,V0,M2} { ! mult( mult( skol1, op_a ), op_b )
% 0.74/1.13 = skol1, ! mult( mult( skol1, op_b ), op_a ) = skol1 }.
% 0.74/1.13 substitution0:
% 0.74/1.13 end
% 0.74/1.13 permutation0:
% 0.74/1.13 0 ==> 0
% 0.74/1.13 1 ==> 1
% 0.74/1.13 end
% 0.74/1.13
% 0.74/1.13 eqswap: (481) {G0,W15,D5,L1,V3,M1} { mult( mult( mult( X, Y ), Z ), Y )
% 0.74/1.13 ==> mult( X, mult( mult( Y, Z ), Y ) ) }.
% 0.74/1.13 parent0[0]: (5) {G0,W15,D5,L1,V3,M1} I { mult( Z, mult( mult( Y, X ), Y ) )
% 0.74/1.13 ==> mult( mult( mult( Z, Y ), X ), Y ) }.
% 0.74/1.13 substitution0:
% 0.74/1.13 X := Z
% 0.74/1.13 Y := Y
% 0.74/1.13 Z := X
% 0.74/1.13 end
% 0.74/1.13
% 0.74/1.13 paramod: (484) {G1,W13,D5,L1,V1,M1} { mult( mult( mult( X, op_a ), op_b )
% 0.74/1.13 , op_a ) ==> mult( X, mult( unit, op_a ) ) }.
% 0.74/1.13 parent0[0]: (9) {G0,W5,D3,L1,V0,M1} I { mult( op_a, op_b ) ==> unit }.
% 0.74/1.13 parent1[0; 11]: (481) {G0,W15,D5,L1,V3,M1} { mult( mult( mult( X, Y ), Z )
% 0.74/1.13 , Y ) ==> mult( X, mult( mult( Y, Z ), Y ) ) }.
% 0.74/1.13 substitution0:
% 0.74/1.13 end
% 0.74/1.13 substitution1:
% 0.74/1.13 X := X
% 0.74/1.13 Y := op_a
% 0.74/1.13 Z := op_b
% 0.74/1.13 end
% 0.74/1.13
% 0.74/1.13 paramod: (485) {G1,W11,D5,L1,V1,M1} { mult( mult( mult( X, op_a ), op_b )
% 0.74/1.13 , op_a ) ==> mult( X, op_a ) }.
% 0.74/1.13 parent0[0]: (8) {G0,W5,D3,L1,V1,M1} I { mult( unit, X ) ==> X }.
% 0.74/1.13 parent1[0; 10]: (484) {G1,W13,D5,L1,V1,M1} { mult( mult( mult( X, op_a ),
% 0.74/1.13 op_b ), op_a ) ==> mult( X, mult( unit, op_a ) ) }.
% 0.74/1.13 substitution0:
% 0.74/1.13 X := op_a
% 0.74/1.13 end
% 0.74/1.13 substitution1:
% 0.74/1.13 X := X
% 0.74/1.13 end
% 0.74/1.13
% 0.74/1.13 subsumption: (46) {G1,W11,D5,L1,V1,M1} P(9,5);d(8) { mult( mult( mult( X,
% 0.74/1.13 op_a ), op_b ), op_a ) ==> mult( X, op_a ) }.
% 0.74/1.13 parent0: (485) {G1,W11,D5,L1,V1,M1} { mult( mult( mult( X, op_a ), op_b )
% 0.74/1.13 , op_a ) ==> mult( X, op_a ) }.
% 0.74/1.13 substitution0:
% 0.74/1.13 X := X
% 0.74/1.13 end
% 0.74/1.13 permutation0:
% 0.74/1.13 0 ==> 0
% 0.74/1.13 end
% 0.74/1.13
% 0.74/1.13 eqswap: (488) {G0,W15,D5,L1,V3,M1} { mult( mult( mult( X, Y ), Z ), Y )
% 0.74/1.13 ==> mult( X, mult( mult( Y, Z ), Y ) ) }.
% 0.74/1.13 parent0[0]: (5) {G0,W15,D5,L1,V3,M1} I { mult( Z, mult( mult( Y, X ), Y ) )
% 0.74/1.13 ==> mult( mult( mult( Z, Y ), X ), Y ) }.
% 0.74/1.13 substitution0:
% 0.74/1.13 X := Z
% 0.74/1.13 Y := Y
% 0.74/1.13 Z := X
% 0.74/1.13 end
% 0.74/1.13
% 0.74/1.13 paramod: (507) {G1,W19,D6,L1,V3,M1} { mult( mult( mult( X, Y ), mult( Z, Z
% 0.74/1.13 ) ), Y ) ==> mult( X, mult( mult( mult( Y, Z ), Z ), Y ) ) }.
% 0.74/1.13 parent0[0]: (6) {G0,W11,D4,L1,V2,M1} I { mult( Y, mult( X, X ) ) ==> mult(
% 0.74/1.13 mult( Y, X ), X ) }.
% 0.74/1.13 parent1[0; 13]: (488) {G0,W15,D5,L1,V3,M1} { mult( mult( mult( X, Y ), Z )
% 0.74/1.13 , Y ) ==> mult( X, mult( mult( Y, Z ), Y ) ) }.
% 0.74/1.13 substitution0:
% 0.74/1.13 X := Z
% 0.74/1.13 Y := Y
% 0.74/1.13 end
% 0.74/1.13 substitution1:
% 0.74/1.13 X := X
% 0.74/1.13 Y := Y
% 0.74/1.13 Z := mult( Z, Z )
% 0.74/1.13 end
% 0.74/1.13
% 0.74/1.13 paramod: (513) {G1,W19,D6,L1,V3,M1} { mult( mult( mult( mult( X, Y ), Z )
% 0.74/1.13 , Z ), Y ) ==> mult( X, mult( mult( mult( Y, Z ), Z ), Y ) ) }.
% 0.74/1.13 parent0[0]: (6) {G0,W11,D4,L1,V2,M1} I { mult( Y, mult( X, X ) ) ==> mult(
% 0.74/1.13 mult( Y, X ), X ) }.
% 0.74/1.13 parent1[0; 2]: (507) {G1,W19,D6,L1,V3,M1} { mult( mult( mult( X, Y ), mult
% 0.74/1.13 ( Z, Z ) ), Y ) ==> mult( X, mult( mult( mult( Y, Z ), Z ), Y ) ) }.
% 0.74/1.13 substitution0:
% 0.74/1.13 X := Z
% 0.74/1.13 Y := mult( X, Y )
% 0.74/1.13 end
% 0.74/1.13 substitution1:
% 0.74/1.13 X := X
% 0.74/1.13 Y := Y
% 0.74/1.13 Z := Z
% 0.74/1.13 end
% 0.74/1.13
% 0.74/1.13 eqswap: (514) {G1,W19,D6,L1,V3,M1} { mult( X, mult( mult( mult( Y, Z ), Z
% 0.74/1.13 ), Y ) ) ==> mult( mult( mult( mult( X, Y ), Z ), Z ), Y ) }.
% 0.74/1.13 parent0[0]: (513) {G1,W19,D6,L1,V3,M1} { mult( mult( mult( mult( X, Y ), Z
% 0.74/1.13 ), Z ), Y ) ==> mult( X, mult( mult( mult( Y, Z ), Z ), Y ) ) }.
% 0.74/1.13 substitution0:
% 0.74/1.13 X := X
% 0.74/1.13 Y := Y
% 0.74/1.13 Z := Z
% 0.74/1.13 end
% 0.74/1.13
% 0.74/1.13 subsumption: (65) {G1,W19,D6,L1,V3,M1} P(6,5);d(6) { mult( Z, mult( mult(
% 0.74/1.13 mult( X, Y ), Y ), X ) ) ==> mult( mult( mult( mult( Z, X ), Y ), Y ), X
% 0.74/1.13 ) }.
% 0.74/1.13 parent0: (514) {G1,W19,D6,L1,V3,M1} { mult( X, mult( mult( mult( Y, Z ), Z
% 0.74/1.13 ), Y ) ) ==> mult( mult( mult( mult( X, Y ), Z ), Z ), Y ) }.
% 0.74/1.13 substitution0:
% 0.74/1.13 X := Z
% 0.74/1.13 Y := X
% 0.74/1.13 Z := Y
% 0.74/1.13 end
% 0.74/1.13 permutation0:
% 0.74/1.13 0 ==> 0
% 0.74/1.13 end
% 0.74/1.13
% 0.74/1.13 eqswap: (516) {G1,W19,D6,L1,V3,M1} { mult( mult( mult( mult( X, Y ), Z ),
% 0.74/1.13 Z ), Y ) ==> mult( X, mult( mult( mult( Y, Z ), Z ), Y ) ) }.
% 0.74/1.13 parent0[0]: (65) {G1,W19,D6,L1,V3,M1} P(6,5);d(6) { mult( Z, mult( mult(
% 0.74/1.13 mult( X, Y ), Y ), X ) ) ==> mult( mult( mult( mult( Z, X ), Y ), Y ), X
% 0.74/1.13 ) }.
% 0.74/1.13 substitution0:
% 0.74/1.13 X := Y
% 0.74/1.13 Y := Z
% 0.74/1.13 Z := X
% 0.74/1.13 end
% 0.74/1.13
% 0.74/1.13 paramod: (521) {G1,W17,D6,L1,V1,M1} { mult( mult( mult( mult( X, op_a ),
% 0.74/1.13 op_b ), op_b ), op_a ) ==> mult( X, mult( mult( unit, op_b ), op_a ) )
% 0.74/1.13 }.
% 0.74/1.13 parent0[0]: (9) {G0,W5,D3,L1,V0,M1} I { mult( op_a, op_b ) ==> unit }.
% 0.74/1.13 parent1[0; 14]: (516) {G1,W19,D6,L1,V3,M1} { mult( mult( mult( mult( X, Y
% 0.74/1.13 ), Z ), Z ), Y ) ==> mult( X, mult( mult( mult( Y, Z ), Z ), Y ) ) }.
% 0.74/1.13 substitution0:
% 0.74/1.13 end
% 0.74/1.13 substitution1:
% 0.74/1.13 X := X
% 0.74/1.13 Y := op_a
% 0.74/1.13 Z := op_b
% 0.74/1.13 end
% 0.74/1.13
% 0.74/1.13 paramod: (522) {G1,W15,D6,L1,V1,M1} { mult( mult( mult( mult( X, op_a ),
% 0.74/1.13 op_b ), op_b ), op_a ) ==> mult( X, mult( op_b, op_a ) ) }.
% 0.74/1.13 parent0[0]: (8) {G0,W5,D3,L1,V1,M1} I { mult( unit, X ) ==> X }.
% 0.74/1.13 parent1[0; 13]: (521) {G1,W17,D6,L1,V1,M1} { mult( mult( mult( mult( X,
% 0.74/1.13 op_a ), op_b ), op_b ), op_a ) ==> mult( X, mult( mult( unit, op_b ),
% 0.74/1.13 op_a ) ) }.
% 0.74/1.13 substitution0:
% 0.74/1.13 X := op_b
% 0.74/1.13 end
% 0.74/1.13 substitution1:
% 0.74/1.13 X := X
% 0.74/1.13 end
% 0.74/1.13
% 0.74/1.13 paramod: (523) {G1,W13,D6,L1,V1,M1} { mult( mult( mult( mult( X, op_a ),
% 0.74/1.13 op_b ), op_b ), op_a ) ==> mult( X, unit ) }.
% 0.74/1.13 parent0[0]: (10) {G0,W5,D3,L1,V0,M1} I { mult( op_b, op_a ) ==> unit }.
% 0.74/1.13 parent1[0; 12]: (522) {G1,W15,D6,L1,V1,M1} { mult( mult( mult( mult( X,
% 0.74/1.13 op_a ), op_b ), op_b ), op_a ) ==> mult( X, mult( op_b, op_a ) ) }.
% 0.74/1.13 substitution0:
% 0.74/1.13 end
% 0.74/1.13 substitution1:
% 0.74/1.13 X := X
% 0.74/1.13 end
% 0.74/1.13
% 0.74/1.13 paramod: (524) {G1,W11,D6,L1,V1,M1} { mult( mult( mult( mult( X, op_a ),
% 0.74/1.13 op_b ), op_b ), op_a ) ==> X }.
% 0.74/1.13 parent0[0]: (7) {G0,W5,D3,L1,V1,M1} I { mult( X, unit ) ==> X }.
% 0.74/1.13 parent1[0; 10]: (523) {G1,W13,D6,L1,V1,M1} { mult( mult( mult( mult( X,
% 0.74/1.13 op_a ), op_b ), op_b ), op_a ) ==> mult( X, unit ) }.
% 0.74/1.13 substitution0:
% 0.74/1.13 X := X
% 0.74/1.13 end
% 0.74/1.13 substitution1:
% 0.74/1.13 X := X
% 0.74/1.13 end
% 0.74/1.13
% 0.74/1.13 subsumption: (394) {G2,W11,D6,L1,V1,M1} P(9,65);d(8);d(10);d(7) { mult(
% 0.74/1.13 mult( mult( mult( X, op_a ), op_b ), op_b ), op_a ) ==> X }.
% 0.74/1.13 parent0: (524) {G1,W11,D6,L1,V1,M1} { mult( mult( mult( mult( X, op_a ),
% 0.74/1.13 op_b ), op_b ), op_a ) ==> X }.
% 0.74/1.13 substitution0:
% 0.74/1.13 X := X
% 0.74/1.13 end
% 0.74/1.13 permutation0:
% 0.74/1.13 0 ==> 0
% 0.74/1.13 end
% 0.74/1.13
% 0.74/1.13 eqswap: (527) {G1,W11,D5,L1,V1,M1} { mult( X, op_a ) ==> mult( mult( mult
% 0.74/1.13 ( X, op_a ), op_b ), op_a ) }.
% 0.74/1.13 parent0[0]: (46) {G1,W11,D5,L1,V1,M1} P(9,5);d(8) { mult( mult( mult( X,
% 0.74/1.13 op_a ), op_b ), op_a ) ==> mult( X, op_a ) }.
% 0.74/1.13 substitution0:
% 0.74/1.13 X := X
% 0.74/1.13 end
% 0.74/1.13
% 0.74/1.13 paramod: (531) {G2,W15,D6,L1,V1,M1} { mult( mult( mult( mult( X, op_a ),
% 0.74/1.13 op_b ), op_b ), op_a ) ==> mult( mult( X, op_b ), op_a ) }.
% 0.74/1.13 parent0[0]: (394) {G2,W11,D6,L1,V1,M1} P(9,65);d(8);d(10);d(7) { mult( mult
% 0.74/1.13 ( mult( mult( X, op_a ), op_b ), op_b ), op_a ) ==> X }.
% 0.74/1.13 parent1[0; 12]: (527) {G1,W11,D5,L1,V1,M1} { mult( X, op_a ) ==> mult(
% 0.74/1.13 mult( mult( X, op_a ), op_b ), op_a ) }.
% 0.74/1.13 substitution0:
% 0.74/1.13 X := X
% 0.74/1.13 end
% 0.74/1.13 substitution1:
% 0.74/1.13 X := mult( mult( mult( X, op_a ), op_b ), op_b )
% 0.74/1.13 end
% 0.74/1.13
% 0.74/1.13 paramod: (532) {G3,W7,D4,L1,V1,M1} { X ==> mult( mult( X, op_b ), op_a )
% 0.74/1.13 }.
% 0.74/1.13 parent0[0]: (394) {G2,W11,D6,L1,V1,M1} P(9,65);d(8);d(10);d(7) { mult( mult
% 0.74/1.13 ( mult( mult( X, op_a ), op_b ), op_b ), op_a ) ==> X }.
% 0.74/1.13 parent1[0; 1]: (531) {G2,W15,D6,L1,V1,M1} { mult( mult( mult( mult( X,
% 0.74/1.13 op_a ), op_b ), op_b ), op_a ) ==> mult( mult( X, op_b ), op_a ) }.
% 0.74/1.13 substitution0:
% 0.74/1.13 X := X
% 0.74/1.13 end
% 0.74/1.13 substitution1:
% 0.74/1.13 X := X
% 0.74/1.13 end
% 0.74/1.13
% 0.74/1.13 eqswap: (534) {G3,W7,D4,L1,V1,M1} { mult( mult( X, op_b ), op_a ) ==> X
% 0.74/1.13 }.
% 0.74/1.13 parent0[0]: (532) {G3,W7,D4,L1,V1,M1} { X ==> mult( mult( X, op_b ), op_a
% 0.74/1.13 ) }.
% 0.74/1.13 substitution0:
% 0.74/1.13 X := X
% 0.74/1.13 end
% 0.74/1.13
% 0.74/1.13 subsumption: (398) {G3,W7,D4,L1,V1,M1} P(394,46) { mult( mult( X, op_b ),
% 0.74/1.13 op_a ) ==> X }.
% 0.74/1.13 parent0: (534) {G3,W7,D4,L1,V1,M1} { mult( mult( X, op_b ), op_a ) ==> X
% 0.74/1.13 }.
% 0.74/1.13 substitution0:
% 0.74/1.13 X := X
% 0.74/1.13 end
% 0.74/1.13 permutation0:
% 0.74/1.13 0 ==> 0
% 0.74/1.13 end
% 0.74/1.13
% 0.74/1.13 eqswap: (536) {G3,W7,D4,L1,V1,M1} { X ==> mult( mult( X, op_b ), op_a )
% 0.74/1.13 }.
% 0.74/1.13 parent0[0]: (398) {G3,W7,D4,L1,V1,M1} P(394,46) { mult( mult( X, op_b ),
% 0.74/1.13 op_a ) ==> X }.
% 0.74/1.13 substitution0:
% 0.74/1.13 X := X
% 0.74/1.13 end
% 0.74/1.13
% 0.74/1.13 paramod: (538) {G3,W7,D4,L1,V1,M1} { mult( mult( X, op_a ), op_b ) ==> X
% 0.74/1.13 }.
% 0.74/1.13 parent0[0]: (394) {G2,W11,D6,L1,V1,M1} P(9,65);d(8);d(10);d(7) { mult( mult
% 0.74/1.13 ( mult( mult( X, op_a ), op_b ), op_b ), op_a ) ==> X }.
% 0.74/1.13 parent1[0; 6]: (536) {G3,W7,D4,L1,V1,M1} { X ==> mult( mult( X, op_b ),
% 0.74/1.13 op_a ) }.
% 0.74/1.13 substitution0:
% 0.74/1.13 X := X
% 0.74/1.13 end
% 0.74/1.13 substitution1:
% 0.74/1.13 X := mult( mult( X, op_a ), op_b )
% 0.74/1.13 end
% 0.74/1.13
% 0.74/1.13 subsumption: (406) {G4,W7,D4,L1,V1,M1} P(398,394) { mult( mult( X, op_a ),
% 0.74/1.13 op_b ) ==> X }.
% 0.74/1.13 parent0: (538) {G3,W7,D4,L1,V1,M1} { mult( mult( X, op_a ), op_b ) ==> X
% 0.74/1.13 }.
% 0.74/1.13 substitution0:
% 0.74/1.13 X := X
% 0.74/1.13 end
% 0.74/1.13 permutation0:
% 0.74/1.13 0 ==> 0
% 0.74/1.13 end
% 0.74/1.13
% 0.74/1.13 eqswap: (541) {G0,W14,D4,L2,V0,M2} { ! skol1 ==> mult( mult( skol1, op_a )
% 0.74/1.13 , op_b ), ! mult( mult( skol1, op_b ), op_a ) ==> skol1 }.
% 0.74/1.13 parent0[0]: (11) {G0,W14,D4,L2,V0,M2} I { ! mult( mult( skol1, op_a ), op_b
% 0.74/1.13 ) ==> skol1, ! mult( mult( skol1, op_b ), op_a ) ==> skol1 }.
% 0.74/1.13 substitution0:
% 0.74/1.13 end
% 0.74/1.13
% 0.74/1.13 paramod: (545) {G1,W10,D4,L2,V0,M2} { ! skol1 ==> skol1, ! skol1 ==> mult
% 0.74/1.13 ( mult( skol1, op_a ), op_b ) }.
% 0.74/1.13 parent0[0]: (398) {G3,W7,D4,L1,V1,M1} P(394,46) { mult( mult( X, op_b ),
% 0.74/1.13 op_a ) ==> X }.
% 0.74/1.13 parent1[1; 2]: (541) {G0,W14,D4,L2,V0,M2} { ! skol1 ==> mult( mult( skol1
% 0.74/1.13 , op_a ), op_b ), ! mult( mult( skol1, op_b ), op_a ) ==> skol1 }.
% 0.74/1.13 substitution0:
% 0.74/1.13 X := skol1
% 0.74/1.13 end
% 0.74/1.13 substitution1:
% 0.74/1.13 end
% 0.74/1.13
% 0.74/1.13 eqrefl: (546) {G0,W7,D4,L1,V0,M1} { ! skol1 ==> mult( mult( skol1, op_a )
% 0.74/1.13 , op_b ) }.
% 0.74/1.13 parent0[0]: (545) {G1,W10,D4,L2,V0,M2} { ! skol1 ==> skol1, ! skol1 ==>
% 0.74/1.13 mult( mult( skol1, op_a ), op_b ) }.
% 0.74/1.13 substitution0:
% 0.74/1.13 end
% 0.74/1.13
% 0.74/1.13 paramod: (547) {G1,W3,D2,L1,V0,M1} { ! skol1 ==> skol1 }.
% 0.74/1.13 parent0[0]: (406) {G4,W7,D4,L1,V1,M1} P(398,394) { mult( mult( X, op_a ),
% 0.74/1.13 op_b ) ==> X }.
% 0.74/1.13 parent1[0; 3]: (546) {G0,W7,D4,L1,V0,M1} { ! skol1 ==> mult( mult( skol1,
% 0.74/1.13 op_a ), op_b ) }.
% 0.74/1.13 substitution0:
% 0.74/1.13 X := skol1
% 0.74/1.13 end
% 0.74/1.13 substitution1:
% 0.74/1.13 end
% 0.74/1.13
% 0.74/1.13 eqrefl: (548) {G0,W0,D0,L0,V0,M0} { }.
% 0.74/1.13 parent0[0]: (547) {G1,W3,D2,L1,V0,M1} { ! skol1 ==> skol1 }.
% 0.74/1.13 substitution0:
% 0.74/1.13 end
% 0.74/1.13
% 0.74/1.13 subsumption: (408) {G5,W0,D0,L0,V0,M0} P(398,11);q;d(406);q { }.
% 0.74/1.13 parent0: (548) {G0,W0,D0,L0,V0,M0} { }.
% 0.74/1.13 substitution0:
% 0.74/1.13 end
% 0.74/1.13 permutation0:
% 0.74/1.13 end
% 0.74/1.13
% 0.74/1.13 Proof check complete!
% 0.74/1.13
% 0.74/1.13 Memory use:
% 0.74/1.13
% 0.74/1.13 space for terms: 5519
% 0.74/1.13 space for clauses: 43380
% 0.74/1.14
% 0.74/1.14
% 0.74/1.14 clauses generated: 9742
% 0.74/1.14 clauses kept: 409
% 0.74/1.14 clauses selected: 103
% 0.74/1.14 clauses deleted: 60
% 0.74/1.14 clauses inuse deleted: 0
% 0.74/1.14
% 0.74/1.14 subsentry: 2756
% 0.74/1.14 literals s-matched: 2387
% 0.74/1.14 literals matched: 2380
% 0.74/1.14 full subsumption: 0
% 0.74/1.14
% 0.74/1.14 checksum: -71685102
% 0.74/1.14
% 0.74/1.14
% 0.74/1.14 Bliksem ended
%------------------------------------------------------------------------------