%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : ALG210+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n017.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 : Thu Jul 14 12:09:57 EDT 2022
% Result : Theorem 0.42s 1.08s
% Output : Refutation 0.42s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : ALG210+1 : TPTP v8.1.0. Released v3.1.0.
% 0.10/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n017.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
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % DateTime : Wed Jun 8 16:33:03 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.42/1.08 *** allocated 10000 integers for termspace/termends
% 0.42/1.08 *** allocated 10000 integers for clauses
% 0.42/1.08 *** allocated 10000 integers for justifications
% 0.42/1.08 Bliksem 1.12
% 0.42/1.08
% 0.42/1.08
% 0.42/1.08 Automatic Strategy Selection
% 0.42/1.08
% 0.42/1.08
% 0.42/1.08 Clauses:
% 0.42/1.08
% 0.42/1.08 { times( times( X, Y ), Z ) = times( Y, times( Z, X ) ) }.
% 0.42/1.08 { ! element( X ), times( X, skol1( X ) ) = X }.
% 0.42/1.08 { ! element( X ), times( X, X ) = skol1( X ) }.
% 0.42/1.08 { ! times( X, Y ) = X, ! times( X, X ) = Y, element( X ) }.
% 0.42/1.08 { element( skol2 ) }.
% 0.42/1.08 { element( skol3 ) }.
% 0.42/1.08 { ! element( times( skol2, skol3 ) ) }.
% 0.42/1.08
% 0.42/1.08 percentage equality = 0.454545, percentage horn = 1.000000
% 0.42/1.08 This is a problem with some equality
% 0.42/1.08
% 0.42/1.08
% 0.42/1.08
% 0.42/1.08 Options Used:
% 0.42/1.08
% 0.42/1.08 useres = 1
% 0.42/1.08 useparamod = 1
% 0.42/1.08 useeqrefl = 1
% 0.42/1.08 useeqfact = 1
% 0.42/1.08 usefactor = 1
% 0.42/1.08 usesimpsplitting = 0
% 0.42/1.08 usesimpdemod = 5
% 0.42/1.08 usesimpres = 3
% 0.42/1.08
% 0.42/1.08 resimpinuse = 1000
% 0.42/1.08 resimpclauses = 20000
% 0.42/1.08 substype = eqrewr
% 0.42/1.08 backwardsubs = 1
% 0.42/1.08 selectoldest = 5
% 0.42/1.08
% 0.42/1.08 litorderings [0] = split
% 0.42/1.08 litorderings [1] = extend the termordering, first sorting on arguments
% 0.42/1.08
% 0.42/1.08 termordering = kbo
% 0.42/1.08
% 0.42/1.08 litapriori = 0
% 0.42/1.08 termapriori = 1
% 0.42/1.08 litaposteriori = 0
% 0.42/1.08 termaposteriori = 0
% 0.42/1.08 demodaposteriori = 0
% 0.42/1.08 ordereqreflfact = 0
% 0.42/1.08
% 0.42/1.08 litselect = negord
% 0.42/1.08
% 0.42/1.08 maxweight = 15
% 0.42/1.08 maxdepth = 30000
% 0.42/1.08 maxlength = 115
% 0.42/1.08 maxnrvars = 195
% 0.42/1.08 excuselevel = 1
% 0.42/1.08 increasemaxweight = 1
% 0.42/1.08
% 0.42/1.08 maxselected = 10000000
% 0.42/1.08 maxnrclauses = 10000000
% 0.42/1.08
% 0.42/1.08 showgenerated = 0
% 0.42/1.08 showkept = 0
% 0.42/1.08 showselected = 0
% 0.42/1.08 showdeleted = 0
% 0.42/1.08 showresimp = 1
% 0.42/1.08 showstatus = 2000
% 0.42/1.08
% 0.42/1.08 prologoutput = 0
% 0.42/1.08 nrgoals = 5000000
% 0.42/1.08 totalproof = 1
% 0.42/1.08
% 0.42/1.08 Symbols occurring in the translation:
% 0.42/1.08
% 0.42/1.08 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.42/1.08 . [1, 2] (w:1, o:18, a:1, s:1, b:0),
% 0.42/1.08 ! [4, 1] (w:0, o:11, a:1, s:1, b:0),
% 0.42/1.08 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.42/1.08 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.42/1.08 times [38, 2] (w:1, o:42, a:1, s:1, b:0),
% 0.42/1.08 element [39, 1] (w:1, o:16, a:1, s:1, b:0),
% 0.42/1.08 skol1 [40, 1] (w:1, o:17, a:1, s:1, b:1),
% 0.42/1.08 skol2 [41, 0] (w:1, o:9, a:1, s:1, b:1),
% 0.42/1.08 skol3 [42, 0] (w:1, o:10, a:1, s:1, b:1).
% 0.42/1.08
% 0.42/1.08
% 0.42/1.08 Starting Search:
% 0.42/1.08
% 0.42/1.08 *** allocated 15000 integers for clauses
% 0.42/1.08
% 0.42/1.08 Bliksems!, er is een bewijs:
% 0.42/1.08 % SZS status Theorem
% 0.42/1.08 % SZS output start Refutation
% 0.42/1.08
% 0.42/1.08 (0) {G0,W11,D4,L1,V3,M1} I { times( Y, times( Z, X ) ) ==> times( times( X
% 0.42/1.08 , Y ), Z ) }.
% 0.42/1.08 (1) {G0,W8,D4,L2,V1,M2} I { ! element( X ), times( X, skol1( X ) ) ==> X
% 0.42/1.08 }.
% 0.42/1.08 (2) {G0,W8,D3,L2,V1,M2} I { ! element( X ), times( X, X ) ==> skol1( X )
% 0.42/1.08 }.
% 0.42/1.08 (3) {G0,W12,D3,L3,V2,M3} I { ! times( X, Y ) ==> X, ! times( X, X ) = Y,
% 0.42/1.08 element( X ) }.
% 0.42/1.08 (4) {G0,W2,D2,L1,V0,M1} I { element( skol2 ) }.
% 0.42/1.08 (5) {G0,W2,D2,L1,V0,M1} I { element( skol3 ) }.
% 0.42/1.08 (6) {G0,W4,D3,L1,V0,M1} I { ! element( times( skol2, skol3 ) ) }.
% 0.42/1.08 (7) {G1,W9,D4,L2,V1,M2} Q(3);d(0) { element( X ), ! times( times( X, X ), X
% 0.42/1.08 ) ==> X }.
% 0.42/1.08 (8) {G1,W6,D3,L1,V0,M1} R(2,4) { times( skol2, skol2 ) ==> skol1( skol2 )
% 0.42/1.08 }.
% 0.42/1.08 (9) {G1,W6,D3,L1,V0,M1} R(2,5) { times( skol3, skol3 ) ==> skol1( skol3 )
% 0.42/1.08 }.
% 0.42/1.08 (10) {G1,W15,D5,L1,V4,M1} P(0,0);d(0);d(0);d(0) { times( times( times( T, X
% 0.42/1.08 ), Y ), Z ) = times( times( times( Y, Z ), T ), X ) }.
% 0.42/1.08 (11) {G2,W10,D4,L1,V1,M1} P(8,0) { times( times( skol2, X ), skol2 ) ==>
% 0.42/1.08 times( X, skol1( skol2 ) ) }.
% 0.42/1.08 (14) {G2,W10,D4,L1,V1,M1} P(9,0) { times( times( skol3, X ), skol3 ) ==>
% 0.42/1.08 times( X, skol1( skol3 ) ) }.
% 0.42/1.08 (15) {G1,W6,D4,L1,V0,M1} R(1,4) { times( skol2, skol1( skol2 ) ) ==> skol2
% 0.42/1.08 }.
% 0.42/1.08 (16) {G1,W6,D4,L1,V0,M1} R(1,5) { times( skol3, skol1( skol3 ) ) ==> skol3
% 0.42/1.08 }.
% 0.42/1.08 (18) {G2,W10,D5,L1,V1,M1} P(15,0) { times( times( skol1( skol2 ), X ),
% 0.42/1.08 skol2 ) ==> times( X, skol2 ) }.
% 0.42/1.08 (19) {G2,W10,D5,L1,V1,M1} P(16,0) { times( times( skol1( skol3 ), X ),
% 0.42/1.08 skol3 ) ==> times( X, skol3 ) }.
% 0.42/1.08 (29) {G3,W14,D5,L1,V2,M1} P(14,0);d(0);d(0);d(0) { times( times( times( Y,
% 0.42/1.08 X ), skol3 ), skol3 ) ==> times( times( skol1( skol3 ), Y ), X ) }.
% 0.42/1.08 (40) {G2,W14,D5,L1,V2,M1} P(8,10) { times( times( times( X, Y ), skol2 ),
% 0.42/1.08 skol2 ) ==> times( times( skol1( skol2 ), X ), Y ) }.
% 0.42/1.08 (50) {G3,W6,D4,L1,V0,M1} P(8,11);d(15) { times( skol1( skol2 ), skol2 ) ==>
% 0.42/1.08 skol2 }.
% 0.42/1.08 (53) {G4,W10,D4,L1,V1,M1} P(50,0) { times( times( skol2, X ), skol1( skol2
% 0.42/1.08 ) ) ==> times( X, skol2 ) }.
% 0.42/1.08 (63) {G5,W11,D4,L1,V2,M1} P(53,10);d(18) { times( times( X, skol2 ), Y ) =
% 0.42/1.08 times( times( Y, skol2 ), X ) }.
% 0.42/1.08 (89) {G3,W14,D6,L1,V2,M1} P(0,19) { times( times( times( Y, skol1( skol3 )
% 0.42/1.08 ), X ), skol3 ) ==> times( times( X, Y ), skol3 ) }.
% 0.42/1.08 (101) {G6,W10,D4,L1,V1,M1} P(8,63) { times( times( X, skol2 ), skol2 ) ==>
% 0.42/1.08 times( skol1( skol2 ), X ) }.
% 0.42/1.08 (106) {G7,W7,D3,L1,V1,M1} P(101,101);d(18);d(0);d(15) { times( X, skol2 ) =
% 0.42/1.08 times( skol2, X ) }.
% 0.42/1.08 (123) {G8,W4,D3,L1,V0,M1} P(106,6) { ! element( times( skol3, skol2 ) ) }.
% 0.42/1.08 (124) {G9,W7,D3,L1,V0,M1} R(123,7);d(0);d(0);d(0);d(29);d(0);d(0);d(0);d(40
% 0.42/1.08 );d(89);d(15) { ! times( skol2, skol3 ) ==> times( skol3, skol2 ) }.
% 0.42/1.08 (125) {G10,W0,D0,L0,V0,M0} P(106,124);q { }.
% 0.42/1.08
% 0.42/1.08
% 0.42/1.08 % SZS output end Refutation
% 0.42/1.08 found a proof!
% 0.42/1.08
% 0.42/1.08
% 0.42/1.08 Unprocessed initial clauses:
% 0.42/1.08
% 0.42/1.08 (127) {G0,W11,D4,L1,V3,M1} { times( times( X, Y ), Z ) = times( Y, times(
% 0.42/1.08 Z, X ) ) }.
% 0.42/1.08 (128) {G0,W8,D4,L2,V1,M2} { ! element( X ), times( X, skol1( X ) ) = X }.
% 0.42/1.08 (129) {G0,W8,D3,L2,V1,M2} { ! element( X ), times( X, X ) = skol1( X ) }.
% 0.42/1.08 (130) {G0,W12,D3,L3,V2,M3} { ! times( X, Y ) = X, ! times( X, X ) = Y,
% 0.42/1.08 element( X ) }.
% 0.42/1.08 (131) {G0,W2,D2,L1,V0,M1} { element( skol2 ) }.
% 0.42/1.08 (132) {G0,W2,D2,L1,V0,M1} { element( skol3 ) }.
% 0.42/1.08 (133) {G0,W4,D3,L1,V0,M1} { ! element( times( skol2, skol3 ) ) }.
% 0.42/1.08
% 0.42/1.08
% 0.42/1.08 Total Proof:
% 0.42/1.08
% 0.42/1.08 eqswap: (134) {G0,W11,D4,L1,V3,M1} { times( Y, times( Z, X ) ) = times(
% 0.42/1.08 times( X, Y ), Z ) }.
% 0.42/1.08 parent0[0]: (127) {G0,W11,D4,L1,V3,M1} { times( times( X, Y ), Z ) = times
% 0.42/1.08 ( Y, times( Z, X ) ) }.
% 0.42/1.08 substitution0:
% 0.42/1.08 X := X
% 0.42/1.08 Y := Y
% 0.42/1.08 Z := Z
% 0.42/1.08 end
% 0.42/1.08
% 0.42/1.08 subsumption: (0) {G0,W11,D4,L1,V3,M1} I { times( Y, times( Z, X ) ) ==>
% 0.42/1.08 times( times( X, Y ), Z ) }.
% 0.42/1.08 parent0: (134) {G0,W11,D4,L1,V3,M1} { times( Y, times( Z, X ) ) = times(
% 0.42/1.08 times( X, Y ), Z ) }.
% 0.42/1.08 substitution0:
% 0.42/1.08 X := X
% 0.42/1.08 Y := Y
% 0.42/1.08 Z := Z
% 0.42/1.08 end
% 0.42/1.08 permutation0:
% 0.42/1.08 0 ==> 0
% 0.42/1.08 end
% 0.42/1.08
% 0.42/1.08 subsumption: (1) {G0,W8,D4,L2,V1,M2} I { ! element( X ), times( X, skol1( X
% 0.42/1.08 ) ) ==> X }.
% 0.42/1.08 parent0: (128) {G0,W8,D4,L2,V1,M2} { ! element( X ), times( X, skol1( X )
% 0.42/1.08 ) = X }.
% 0.42/1.08 substitution0:
% 0.42/1.08 X := X
% 0.42/1.08 end
% 0.42/1.08 permutation0:
% 0.42/1.08 0 ==> 0
% 0.42/1.08 1 ==> 1
% 0.42/1.08 end
% 0.42/1.08
% 0.42/1.08 subsumption: (2) {G0,W8,D3,L2,V1,M2} I { ! element( X ), times( X, X ) ==>
% 0.42/1.08 skol1( X ) }.
% 0.42/1.08 parent0: (129) {G0,W8,D3,L2,V1,M2} { ! element( X ), times( X, X ) = skol1
% 0.42/1.08 ( X ) }.
% 0.42/1.08 substitution0:
% 0.42/1.08 X := X
% 0.42/1.08 end
% 0.42/1.08 permutation0:
% 0.42/1.08 0 ==> 0
% 0.42/1.08 1 ==> 1
% 0.42/1.08 end
% 0.42/1.08
% 0.42/1.08 subsumption: (3) {G0,W12,D3,L3,V2,M3} I { ! times( X, Y ) ==> X, ! times( X
% 0.42/1.08 , X ) = Y, element( X ) }.
% 0.42/1.08 parent0: (130) {G0,W12,D3,L3,V2,M3} { ! times( X, Y ) = X, ! times( X, X )
% 0.42/1.08 = Y, element( X ) }.
% 0.42/1.08 substitution0:
% 0.42/1.08 X := X
% 0.42/1.08 Y := Y
% 0.42/1.08 end
% 0.42/1.08 permutation0:
% 0.42/1.08 0 ==> 0
% 0.42/1.08 1 ==> 1
% 0.42/1.08 2 ==> 2
% 0.42/1.08 end
% 0.42/1.08
% 0.42/1.08 subsumption: (4) {G0,W2,D2,L1,V0,M1} I { element( skol2 ) }.
% 0.42/1.08 parent0: (131) {G0,W2,D2,L1,V0,M1} { element( skol2 ) }.
% 0.42/1.08 substitution0:
% 0.42/1.08 end
% 0.42/1.08 permutation0:
% 0.42/1.08 0 ==> 0
% 0.42/1.08 end
% 0.42/1.08
% 0.42/1.08 subsumption: (5) {G0,W2,D2,L1,V0,M1} I { element( skol3 ) }.
% 0.42/1.08 parent0: (132) {G0,W2,D2,L1,V0,M1} { element( skol3 ) }.
% 0.42/1.08 substitution0:
% 0.42/1.08 end
% 0.42/1.08 permutation0:
% 0.42/1.08 0 ==> 0
% 0.42/1.08 end
% 0.42/1.08
% 0.42/1.08 subsumption: (6) {G0,W4,D3,L1,V0,M1} I { ! element( times( skol2, skol3 ) )
% 0.42/1.08 }.
% 0.42/1.08 parent0: (133) {G0,W4,D3,L1,V0,M1} { ! element( times( skol2, skol3 ) )
% 0.42/1.08 }.
% 0.42/1.08 substitution0:
% 0.42/1.08 end
% 0.42/1.08 permutation0:
% 0.42/1.08 0 ==> 0
% 0.42/1.08 end
% 0.42/1.08
% 0.42/1.08 eqswap: (172) {G0,W12,D3,L3,V2,M3} { ! X ==> times( X, Y ), ! times( X, X
% 0.42/1.08 ) = Y, element( X ) }.
% 0.42/1.08 parent0[0]: (3) {G0,W12,D3,L3,V2,M3} I { ! times( X, Y ) ==> X, ! times( X
% 0.42/1.08 , X ) = Y, element( X ) }.
% 0.42/1.08 substitution0:
% 0.42/1.08 X := X
% 0.42/1.08 Y := Y
% 0.42/1.08 end
% 0.42/1.08
% 0.42/1.08 eqrefl: (176) {G0,W9,D4,L2,V1,M2} { ! X ==> times( X, times( X, X ) ),
% 0.42/1.08 element( X ) }.
% 0.42/1.08 parent0[1]: (172) {G0,W12,D3,L3,V2,M3} { ! X ==> times( X, Y ), ! times( X
% 0.42/1.08 , X ) = Y, element( X ) }.
% 0.42/1.08 substitution0:
% 0.42/1.08 X := X
% 0.42/1.08 Y := times( X, X )
% 0.42/1.08 end
% 0.42/1.08
% 0.42/1.08 paramod: (177) {G1,W9,D4,L2,V1,M2} { ! X ==> times( times( X, X ), X ),
% 0.42/1.08 element( X ) }.
% 0.42/1.08 parent0[0]: (0) {G0,W11,D4,L1,V3,M1} I { times( Y, times( Z, X ) ) ==>
% 0.42/1.08 times( times( X, Y ), Z ) }.
% 0.42/1.08 parent1[0; 3]: (176) {G0,W9,D4,L2,V1,M2} { ! X ==> times( X, times( X, X )
% 0.42/1.08 ), element( X ) }.
% 0.42/1.08 substitution0:
% 0.42/1.08 X := X
% 0.42/1.08 Y := X
% 0.42/1.08 Z := X
% 0.42/1.08 end
% 0.42/1.08 substitution1:
% 0.42/1.08 X := X
% 0.42/1.08 end
% 0.42/1.08
% 0.42/1.08 eqswap: (178) {G1,W9,D4,L2,V1,M2} { ! times( times( X, X ), X ) ==> X,
% 0.42/1.08 element( X ) }.
% 0.42/1.08 parent0[0]: (177) {G1,W9,D4,L2,V1,M2} { ! X ==> times( times( X, X ), X )
% 0.42/1.08 , element( X ) }.
% 0.42/1.08 substitution0:
% 0.42/1.08 X := X
% 0.42/1.08 end
% 0.42/1.08
% 0.42/1.08 subsumption: (7) {G1,W9,D4,L2,V1,M2} Q(3);d(0) { element( X ), ! times(
% 0.42/1.08 times( X, X ), X ) ==> X }.
% 0.42/1.08 parent0: (178) {G1,W9,D4,L2,V1,M2} { ! times( times( X, X ), X ) ==> X,
% 0.42/1.08 element( X ) }.
% 0.42/1.08 substitution0:
% 0.42/1.08 X := X
% 0.42/1.08 end
% 0.42/1.08 permutation0:
% 0.42/1.08 0 ==> 1
% 0.42/1.08 1 ==> 0
% 0.42/1.08 end
% 0.42/1.08
% 0.42/1.08 eqswap: (179) {G0,W8,D3,L2,V1,M2} { skol1( X ) ==> times( X, X ), !
% 0.42/1.08 element( X ) }.
% 0.42/1.08 parent0[1]: (2) {G0,W8,D3,L2,V1,M2} I { ! element( X ), times( X, X ) ==>
% 0.42/1.08 skol1( X ) }.
% 0.42/1.08 substitution0:
% 0.42/1.08 X := X
% 0.42/1.08 end
% 0.42/1.08
% 0.42/1.08 resolution: (180) {G1,W6,D3,L1,V0,M1} { skol1( skol2 ) ==> times( skol2,
% 0.42/1.08 skol2 ) }.
% 0.42/1.08 parent0[1]: (179) {G0,W8,D3,L2,V1,M2} { skol1( X ) ==> times( X, X ), !
% 0.42/1.08 element( X ) }.
% 0.42/1.08 parent1[0]: (4) {G0,W2,D2,L1,V0,M1} I { element( skol2 ) }.
% 0.42/1.08 substitution0:
% 0.42/1.08 X := skol2
% 0.42/1.08 end
% 0.42/1.08 substitution1:
% 0.42/1.08 end
% 0.42/1.08
% 0.42/1.08 eqswap: (181) {G1,W6,D3,L1,V0,M1} { times( skol2, skol2 ) ==> skol1( skol2
% 0.42/1.08 ) }.
% 0.42/1.08 parent0[0]: (180) {G1,W6,D3,L1,V0,M1} { skol1( skol2 ) ==> times( skol2,
% 0.42/1.08 skol2 ) }.
% 0.42/1.08 substitution0:
% 0.42/1.08 end
% 0.42/1.08
% 0.42/1.08 subsumption: (8) {G1,W6,D3,L1,V0,M1} R(2,4) { times( skol2, skol2 ) ==>
% 0.42/1.08 skol1( skol2 ) }.
% 0.42/1.08 parent0: (181) {G1,W6,D3,L1,V0,M1} { times( skol2, skol2 ) ==> skol1(
% 0.42/1.08 skol2 ) }.
% 0.42/1.08 substitution0:
% 0.42/1.08 end
% 0.42/1.08 permutation0:
% 0.42/1.08 0 ==> 0
% 0.42/1.08 end
% 0.42/1.08
% 0.42/1.08 eqswap: (182) {G0,W8,D3,L2,V1,M2} { skol1( X ) ==> times( X, X ), !
% 0.42/1.08 element( X ) }.
% 0.42/1.08 parent0[1]: (2) {G0,W8,D3,L2,V1,M2} I { ! element( X ), times( X, X ) ==>
% 0.42/1.08 skol1( X ) }.
% 0.42/1.08 substitution0:
% 0.42/1.08 X := X
% 0.42/1.08 end
% 0.42/1.08
% 0.42/1.08 resolution: (183) {G1,W6,D3,L1,V0,M1} { skol1( skol3 ) ==> times( skol3,
% 0.42/1.08 skol3 ) }.
% 0.42/1.08 parent0[1]: (182) {G0,W8,D3,L2,V1,M2} { skol1( X ) ==> times( X, X ), !
% 0.42/1.08 element( X ) }.
% 0.42/1.08 parent1[0]: (5) {G0,W2,D2,L1,V0,M1} I { element( skol3 ) }.
% 0.42/1.08 substitution0:
% 0.42/1.08 X := skol3
% 0.42/1.08 end
% 0.42/1.08 substitution1:
% 0.42/1.08 end
% 0.42/1.08
% 0.42/1.08 eqswap: (184) {G1,W6,D3,L1,V0,M1} { times( skol3, skol3 ) ==> skol1( skol3
% 0.42/1.08 ) }.
% 0.42/1.08 parent0[0]: (183) {G1,W6,D3,L1,V0,M1} { skol1( skol3 ) ==> times( skol3,
% 0.42/1.08 skol3 ) }.
% 0.42/1.08 substitution0:
% 0.42/1.08 end
% 0.42/1.08
% 0.42/1.08 subsumption: (9) {G1,W6,D3,L1,V0,M1} R(2,5) { times( skol3, skol3 ) ==>
% 0.42/1.08 skol1( skol3 ) }.
% 0.42/1.08 parent0: (184) {G1,W6,D3,L1,V0,M1} { times( skol3, skol3 ) ==> skol1(
% 0.42/1.08 skol3 ) }.
% 0.42/1.08 substitution0:
% 0.42/1.08 end
% 0.42/1.08 permutation0:
% 0.42/1.08 0 ==> 0
% 0.42/1.08 end
% 0.42/1.08
% 0.42/1.08 eqswap: (185) {G0,W11,D4,L1,V3,M1} { times( times( Z, X ), Y ) ==> times(
% 0.42/1.08 X, times( Y, Z ) ) }.
% 0.42/1.08 parent0[0]: (0) {G0,W11,D4,L1,V3,M1} I { times( Y, times( Z, X ) ) ==>
% 0.42/1.08 times( times( X, Y ), Z ) }.
% 0.42/1.08 substitution0:
% 0.42/1.08 X := Z
% 0.42/1.08 Y := X
% 0.42/1.08 Z := Y
% 0.42/1.08 end
% 0.42/1.08
% 0.42/1.08 paramod: (193) {G1,W15,D5,L1,V4,M1} { times( times( times( X, Y ), Z ), T
% 0.42/1.08 ) ==> times( Z, times( times( Y, T ), X ) ) }.
% 0.42/1.08 parent0[0]: (0) {G0,W11,D4,L1,V3,M1} I { times( Y, times( Z, X ) ) ==>
% 0.42/1.08 times( times( X, Y ), Z ) }.
% 0.42/1.08 parent1[0; 10]: (185) {G0,W11,D4,L1,V3,M1} { times( times( Z, X ), Y ) ==>
% 0.42/1.08 times( X, times( Y, Z ) ) }.
% 0.42/1.08 substitution0:
% 0.42/1.08 X := Y
% 0.42/1.08 Y := T
% 0.42/1.08 Z := X
% 0.42/1.08 end
% 0.42/1.08 substitution1:
% 0.42/1.08 X := Z
% 0.42/1.08 Y := T
% 0.42/1.08 Z := times( X, Y )
% 0.42/1.08 end
% 0.42/1.08
% 0.42/1.08 paramod: (200) {G1,W15,D5,L1,V4,M1} { times( times( times( X, Y ), Z ), T
% 0.42/1.08 ) ==> times( times( X, Z ), times( Y, T ) ) }.
% 0.42/1.08 parent0[0]: (0) {G0,W11,D4,L1,V3,M1} I { times( Y, times( Z, X ) ) ==>
% 0.42/1.08 times( times( X, Y ), Z ) }.
% 0.42/1.08 parent1[0; 8]: (193) {G1,W15,D5,L1,V4,M1} { times( times( times( X, Y ), Z
% 0.42/1.08 ), T ) ==> times( Z, times( times( Y, T ), X ) ) }.
% 0.42/1.08 substitution0:
% 0.42/1.08 X := X
% 0.42/1.08 Y := Z
% 0.42/1.08 Z := times( Y, T )
% 0.42/1.08 end
% 0.42/1.08 substitution1:
% 0.42/1.08 X := X
% 0.42/1.08 Y := Y
% 0.42/1.08 Z := Z
% 0.42/1.08 T := T
% 0.42/1.08 end
% 0.42/1.08
% 0.42/1.08 paramod: (203) {G1,W15,D5,L1,V4,M1} { times( times( times( X, Y ), Z ), T
% 0.42/1.08 ) ==> times( times( T, times( X, Z ) ), Y ) }.
% 0.42/1.08 parent0[0]: (0) {G0,W11,D4,L1,V3,M1} I { times( Y, times( Z, X ) ) ==>
% 0.42/1.08 times( times( X, Y ), Z ) }.
% 0.42/1.08 parent1[0; 8]: (200) {G1,W15,D5,L1,V4,M1} { times( times( times( X, Y ), Z
% 0.42/1.08 ), T ) ==> times( times( X, Z ), times( Y, T ) ) }.
% 0.42/1.08 substitution0:
% 0.42/1.08 X := T
% 0.42/1.08 Y := times( X, Z )
% 0.42/1.08 Z := Y
% 0.42/1.08 end
% 0.42/1.08 substitution1:
% 0.42/1.08 X := X
% 0.42/1.08 Y := Y
% 0.42/1.08 Z := Z
% 0.42/1.08 T := T
% 0.42/1.08 end
% 0.42/1.08
% 0.42/1.08 paramod: (205) {G1,W15,D5,L1,V4,M1} { times( times( times( X, Y ), Z ), T
% 0.42/1.08 ) ==> times( times( times( Z, T ), X ), Y ) }.
% 0.42/1.08 parent0[0]: (0) {G0,W11,D4,L1,V3,M1} I { times( Y, times( Z, X ) ) ==>
% 0.42/1.08 times( times( X, Y ), Z ) }.
% 0.42/1.08 parent1[0; 9]: (203) {G1,W15,D5,L1,V4,M1} { times( times( times( X, Y ), Z
% 0.42/1.08 ), T ) ==> times( times( T, times( X, Z ) ), Y ) }.
% 0.42/1.08 substitution0:
% 0.42/1.08 X := Z
% 0.42/1.08 Y := T
% 0.42/1.08 Z := X
% 0.42/1.08 end
% 0.42/1.08 substitution1:
% 0.42/1.08 X := X
% 0.42/1.08 Y := Y
% 0.42/1.08 Z := Z
% 0.42/1.08 T := T
% 0.42/1.08 end
% 0.42/1.08
% 0.42/1.08 subsumption: (10) {G1,W15,D5,L1,V4,M1} P(0,0);d(0);d(0);d(0) { times( times
% 0.42/1.08 ( times( T, X ), Y ), Z ) = times( times( times( Y, Z ), T ), X ) }.
% 0.42/1.08 parent0: (205) {G1,W15,D5,L1,V4,M1} { times( times( times( X, Y ), Z ), T
% 0.42/1.08 ) ==> times( times( times( Z, T ), X ), Y ) }.
% 0.42/1.08 substitution0:
% 0.42/1.08 X := T
% 0.42/1.08 Y := X
% 0.42/1.08 Z := Y
% 0.42/1.08 T := Z
% 0.42/1.08 end
% 0.42/1.08 permutation0:
% 0.42/1.08 0 ==> 0
% 0.42/1.08 end
% 0.42/1.08
% 0.42/1.08 eqswap: (207) {G0,W11,D4,L1,V3,M1} { times( times( Z, X ), Y ) ==> times(
% 0.42/1.08 X, times( Y, Z ) ) }.
% 0.42/1.08 parent0[0]: (0) {G0,W11,D4,L1,V3,M1} I { times( Y, times( Z, X ) ) ==>
% 0.42/1.08 times( times( X, Y ), Z ) }.
% 0.42/1.08 substitution0:
% 0.42/1.08 X := Z
% 0.42/1.08 Y := X
% 0.42/1.08 Z := Y
% 0.42/1.08 end
% 0.42/1.08
% 0.42/1.08 paramod: (209) {G1,W10,D4,L1,V1,M1} { times( times( skol2, X ), skol2 )
% 0.42/1.08 ==> times( X, skol1( skol2 ) ) }.
% 0.42/1.08 parent0[0]: (8) {G1,W6,D3,L1,V0,M1} R(2,4) { times( skol2, skol2 ) ==>
% 0.42/1.08 skol1( skol2 ) }.
% 0.42/1.08 parent1[0; 8]: (207) {G0,W11,D4,L1,V3,M1} { times( times( Z, X ), Y ) ==>
% 0.42/1.08 times( X, times( Y, Z ) ) }.
% 0.42/1.08 substitution0:
% 0.42/1.08 end
% 0.42/1.08 substitution1:
% 0.42/1.08 X := X
% 0.42/1.08 Y := skol2
% 0.42/1.08 Z := skol2
% 0.42/1.08 end
% 0.42/1.08
% 0.42/1.08 subsumption: (11) {G2,W10,D4,L1,V1,M1} P(8,0) { times( times( skol2, X ),
% 0.42/1.08 skol2 ) ==> times( X, skol1( skol2 ) ) }.
% 0.42/1.08 parent0: (209) {G1,W10,D4,L1,V1,M1} { times( times( skol2, X ), skol2 )
% 0.42/1.08 ==> times( X, skol1( skol2 ) ) }.
% 0.42/1.08 substitution0:
% 0.42/1.08 X := X
% 0.42/1.08 end
% 0.42/1.08 permutation0:
% 0.42/1.08 0 ==> 0
% 0.42/1.08 end
% 0.42/1.08
% 0.42/1.08 eqswap: (213) {G0,W11,D4,L1,V3,M1} { times( times( Z, X ), Y ) ==> times(
% 0.42/1.08 X, times( Y, Z ) ) }.
% 0.42/1.08 parent0[0]: (0) {G0,W11,D4,L1,V3,M1} I { times( Y, times( Z, X ) ) ==>
% 0.42/1.08 times( times( X, Y ), Z ) }.
% 0.42/1.08 substitution0:
% 0.42/1.08 X := Z
% 0.42/1.08 Y := X
% 0.42/1.08 Z := Y
% 0.42/1.08 end
% 0.42/1.08
% 0.42/1.08 paramod: (215) {G1,W10,D4,L1,V1,M1} { times( times( skol3, X ), skol3 )
% 0.42/1.08 ==> times( X, skol1( skol3 ) ) }.
% 0.42/1.08 parent0[0]: (9) {G1,W6,D3,L1,V0,M1} R(2,5) { times( skol3, skol3 ) ==>
% 0.42/1.08 skol1( skol3 ) }.
% 0.42/1.08 parent1[0; 8]: (213) {G0,W11,D4,L1,V3,M1} { times( times( Z, X ), Y ) ==>
% 0.42/1.08 times( X, times( Y, Z ) ) }.
% 0.42/1.08 substitution0:
% 0.42/1.08 end
% 0.42/1.08 substitution1:
% 0.42/1.08 X := X
% 0.42/1.08 Y := skol3
% 0.42/1.08 Z := skol3
% 0.42/1.08 end
% 0.42/1.08
% 0.42/1.08 subsumption: (14) {G2,W10,D4,L1,V1,M1} P(9,0) { times( times( skol3, X ),
% 0.42/1.08 skol3 ) ==> times( X, skol1( skol3 ) ) }.
% 0.42/1.08 parent0: (215) {G1,W10,D4,L1,V1,M1} { times( times( skol3, X ), skol3 )
% 0.42/1.08 ==> times( X, skol1( skol3 ) ) }.
% 0.42/1.08 substitution0:
% 0.42/1.08 X := X
% 0.42/1.08 end
% 0.42/1.08 permutation0:
% 0.42/1.08 0 ==> 0
% 0.42/1.08 end
% 0.42/1.08
% 0.42/1.08 eqswap: (218) {G0,W8,D4,L2,V1,M2} { X ==> times( X, skol1( X ) ), !
% 0.42/1.08 element( X ) }.
% 0.42/1.08 parent0[1]: (1) {G0,W8,D4,L2,V1,M2} I { ! element( X ), times( X, skol1( X
% 0.42/1.08 ) ) ==> X }.
% 0.42/1.08 substitution0:
% 0.42/1.08 X := X
% 0.42/1.08 end
% 0.42/1.08
% 0.42/1.08 resolution: (219) {G1,W6,D4,L1,V0,M1} { skol2 ==> times( skol2, skol1(
% 0.42/1.08 skol2 ) ) }.
% 0.42/1.08 parent0[1]: (218) {G0,W8,D4,L2,V1,M2} { X ==> times( X, skol1( X ) ), !
% 0.42/1.08 element( X ) }.
% 0.42/1.08 parent1[0]: (4) {G0,W2,D2,L1,V0,M1} I { element( skol2 ) }.
% 0.42/1.08 substitution0:
% 0.42/1.08 X := skol2
% 0.42/1.08 end
% 0.42/1.08 substitution1:
% 0.42/1.08 end
% 0.42/1.08
% 0.42/1.08 eqswap: (220) {G1,W6,D4,L1,V0,M1} { times( skol2, skol1( skol2 ) ) ==>
% 0.42/1.08 skol2 }.
% 0.42/1.08 parent0[0]: (219) {G1,W6,D4,L1,V0,M1} { skol2 ==> times( skol2, skol1(
% 0.42/1.08 skol2 ) ) }.
% 0.42/1.08 substitution0:
% 0.42/1.08 end
% 0.42/1.08
% 0.42/1.08 subsumption: (15) {G1,W6,D4,L1,V0,M1} R(1,4) { times( skol2, skol1( skol2 )
% 0.42/1.08 ) ==> skol2 }.
% 0.42/1.08 parent0: (220) {G1,W6,D4,L1,V0,M1} { times( skol2, skol1( skol2 ) ) ==>
% 0.42/1.08 skol2 }.
% 0.42/1.08 substitution0:
% 0.42/1.08 end
% 0.42/1.08 permutation0:
% 0.42/1.08 0 ==> 0
% 0.42/1.08 end
% 0.42/1.08
% 0.42/1.08 eqswap: (221) {G0,W8,D4,L2,V1,M2} { X ==> times( X, skol1( X ) ), !
% 0.42/1.08 element( X ) }.
% 0.42/1.08 parent0[1]: (1) {G0,W8,D4,L2,V1,M2} I { ! element( X ), times( X, skol1( X
% 0.42/1.08 ) ) ==> X }.
% 0.42/1.08 substitution0:
% 0.42/1.08 X := X
% 0.42/1.08 end
% 0.42/1.08
% 0.42/1.08 resolution: (222) {G1,W6,D4,L1,V0,M1} { skol3 ==> times( skol3, skol1(
% 0.42/1.08 skol3 ) ) }.
% 0.42/1.08 parent0[1]: (221) {G0,W8,D4,L2,V1,M2} { X ==> times( X, skol1( X ) ), !
% 0.42/1.08 element( X ) }.
% 0.42/1.08 parent1[0]: (5) {G0,W2,D2,L1,V0,M1} I { element( skol3 ) }.
% 0.42/1.08 substitution0:
% 0.42/1.08 X := skol3
% 0.42/1.08 end
% 0.42/1.08 substitution1:
% 0.42/1.08 end
% 0.42/1.08
% 0.42/1.08 eqswap: (223) {G1,W6,D4,L1,V0,M1} { times( skol3, skol1( skol3 ) ) ==>
% 0.42/1.08 skol3 }.
% 0.42/1.08 parent0[0]: (222) {G1,W6,D4,L1,V0,M1} { skol3 ==> times( skol3, skol1(
% 0.42/1.08 skol3 ) ) }.
% 0.42/1.08 substitution0:
% 0.42/1.08 end
% 0.42/1.08
% 0.42/1.08 subsumption: (16) {G1,W6,D4,L1,V0,M1} R(1,5) { times( skol3, skol1( skol3 )
% 0.42/1.08 ) ==> skol3 }.
% 0.42/1.08 parent0: (223) {G1,W6,D4,L1,V0,M1} { times( skol3, skol1( skol3 ) ) ==>
% 0.42/1.08 skol3 }.
% 0.42/1.08 substitution0:
% 0.42/1.08 end
% 0.42/1.08 permutation0:
% 0.42/1.08 0 ==> 0
% 0.42/1.08 end
% 0.42/1.08
% 0.42/1.08 eqswap: (225) {G0,W11,D4,L1,V3,M1} { times( times( Z, X ), Y ) ==> times(
% 0.42/1.08 X, times( Y, Z ) ) }.
% 0.42/1.08 parent0[0]: (0) {G0,W11,D4,L1,V3,M1} I { times( Y, times( Z, X ) ) ==>
% 0.42/1.08 times( times( X, Y ), Z ) }.
% 0.42/1.08 substitution0:
% 0.42/1.08 X := Z
% 0.42/1.08 Y := X
% 0.42/1.08 Z := Y
% 0.42/1.08 end
% 0.42/1.08
% 0.42/1.08 paramod: (227) {G1,W10,D5,L1,V1,M1} { times( times( skol1( skol2 ), X ),
% 0.42/1.08 skol2 ) ==> times( X, skol2 ) }.
% 0.42/1.08 parent0[0]: (15) {G1,W6,D4,L1,V0,M1} R(1,4) { times( skol2, skol1( skol2 )
% 0.42/1.08 ) ==> skol2 }.
% 0.42/1.08 parent1[0; 9]: (225) {G0,W11,D4,L1,V3,M1} { times( times( Z, X ), Y ) ==>
% 0.42/1.08 times( X, times( Y, Z ) ) }.
% 0.42/1.08 substitution0:
% 0.42/1.08 end
% 0.42/1.08 substitution1:
% 0.42/1.08 X := X
% 0.42/1.08 Y := skol2
% 0.42/1.08 Z := skol1( skol2 )
% 0.42/1.08 end
% 0.42/1.08
% 0.42/1.08 subsumption: (18) {G2,W10,D5,L1,V1,M1} P(15,0) { times( times( skol1( skol2
% 0.42/1.08 ), X ), skol2 ) ==> times( X, skol2 ) }.
% 0.42/1.08 parent0: (227) {G1,W10,D5,L1,V1,M1} { times( times( skol1( skol2 ), X ),
% 0.42/1.08 skol2 ) ==> times( X, skol2 ) }.
% 0.42/1.08 substitution0:
% 0.42/1.08 X := X
% 0.42/1.08 end
% 0.42/1.08 permutation0:
% 0.42/1.08 0 ==> 0
% 0.42/1.08 end
% 0.42/1.08
% 0.42/1.08 eqswap: (231) {G0,W11,D4,L1,V3,M1} { times( times( Z, X ), Y ) ==> times(
% 0.42/1.08 X, times( Y, Z ) ) }.
% 0.42/1.08 parent0[0]: (0) {G0,W11,D4,L1,V3,M1} I { times( Y, times( Z, X ) ) ==>
% 0.42/1.08 times( times( X, Y ), Z ) }.
% 0.42/1.08 substitution0:
% 0.42/1.08 X := Z
% 0.42/1.08 Y := X
% 0.42/1.08 Z := Y
% 0.42/1.08 end
% 0.42/1.08
% 0.42/1.08 paramod: (233) {G1,W10,D5,L1,V1,M1} { times( times( skol1( skol3 ), X ),
% 0.42/1.08 skol3 ) ==> times( X, skol3 ) }.
% 0.42/1.08 parent0[0]: (16) {G1,W6,D4,L1,V0,M1} R(1,5) { times( skol3, skol1( skol3 )
% 0.42/1.08 ) ==> skol3 }.
% 0.42/1.08 parent1[0; 9]: (231) {G0,W11,D4,L1,V3,M1} { times( times( Z, X ), Y ) ==>
% 0.42/1.08 times( X, times( Y, Z ) ) }.
% 0.42/1.08 substitution0:
% 0.42/1.08 end
% 0.42/1.08 substitution1:
% 0.42/1.08 X := X
% 0.42/1.08 Y := skol3
% 0.42/1.08 Z := skol1( skol3 )
% 0.42/1.08 end
% 0.42/1.08
% 0.42/1.08 subsumption: (19) {G2,W10,D5,L1,V1,M1} P(16,0) { times( times( skol1( skol3
% 0.42/1.08 ), X ), skol3 ) ==> times( X, skol3 ) }.
% 0.42/1.08 parent0: (233) {G1,W10,D5,L1,V1,M1} { times( times( skol1( skol3 ), X ),
% 0.42/1.08 skol3 ) ==> times( X, skol3 ) }.
% 0.42/1.08 substitution0:
% 0.42/1.08 X := X
% 0.42/1.08 end
% 0.42/1.08 permutation0:
% 0.42/1.08 0 ==> 0
% 0.42/1.08 end
% 0.42/1.08
% 0.42/1.08 eqswap: (237) {G0,W11,D4,L1,V3,M1} { times( times( Z, X ), Y ) ==> times(
% 0.42/1.08 X, times( Y, Z ) ) }.
% 0.42/1.08 parent0[0]: (0) {G0,W11,D4,L1,V3,M1} I { times( Y, times( Z, X ) ) ==>
% 0.42/1.08 times( times( X, Y ), Z ) }.
% 0.42/1.08 substitution0:
% 0.42/1.08 X := Z
% 0.42/1.08 Y := X
% 0.42/1.08 Z := Y
% 0.42/1.08 end
% 0.42/1.08
% 0.42/1.08 paramod: (244) {G1,W14,D5,L1,V2,M1} { times( times( skol3, X ), times(
% 0.42/1.08 skol3, Y ) ) ==> times( X, times( Y, skol1( skol3 ) ) ) }.
% 0.42/1.08 parent0[0]: (14) {G2,W10,D4,L1,V1,M1} P(9,0) { times( times( skol3, X ),
% 0.42/1.08 skol3 ) ==> times( X, skol1( skol3 ) ) }.
% 0.42/1.08 parent1[0; 10]: (237) {G0,W11,D4,L1,V3,M1} { times( times( Z, X ), Y ) ==>
% 0.42/1.08 times( X, times( Y, Z ) ) }.
% 0.42/1.08 substitution0:
% 0.42/1.08 X := Y
% 0.42/1.08 end
% 0.42/1.08 substitution1:
% 0.42/1.08 X := X
% 0.42/1.08 Y := times( skol3, Y )
% 0.42/1.08 Z := skol3
% 0.42/1.08 end
% 0.42/1.08
% 0.42/1.08 paramod: (246) {G1,W14,D5,L1,V2,M1} { times( times( skol3, X ), times(
% 0.42/1.08 skol3, Y ) ) ==> times( times( skol1( skol3 ), X ), Y ) }.
% 0.42/1.08 parent0[0]: (0) {G0,W11,D4,L1,V3,M1} I { times( Y, times( Z, X ) ) ==>
% 0.42/1.08 times( times( X, Y ), Z ) }.
% 0.42/1.08 parent1[0; 8]: (244) {G1,W14,D5,L1,V2,M1} { times( times( skol3, X ),
% 0.42/1.08 times( skol3, Y ) ) ==> times( X, times( Y, skol1( skol3 ) ) ) }.
% 0.42/1.08 substitution0:
% 0.42/1.08 X := skol1( skol3 )
% 0.42/1.08 Y := X
% 0.42/1.08 Z := Y
% 0.42/1.08 end
% 0.42/1.08 substitution1:
% 0.42/1.08 X := X
% 0.42/1.08 Y := Y
% 0.42/1.08 end
% 0.42/1.08
% 0.42/1.08 paramod: (250) {G1,W14,D5,L1,V2,M1} { times( times( Y, times( skol3, X ) )
% 0.42/1.08 , skol3 ) ==> times( times( skol1( skol3 ), X ), Y ) }.
% 0.42/1.08 parent0[0]: (0) {G0,W11,D4,L1,V3,M1} I { times( Y, times( Z, X ) ) ==>
% 0.42/1.08 times( times( X, Y ), Z ) }.
% 0.42/1.08 parent1[0; 1]: (246) {G1,W14,D5,L1,V2,M1} { times( times( skol3, X ),
% 0.42/1.08 times( skol3, Y ) ) ==> times( times( skol1( skol3 ), X ), Y ) }.
% 0.42/1.08 substitution0:
% 0.42/1.08 X := Y
% 0.42/1.08 Y := times( skol3, X )
% 0.42/1.08 Z := skol3
% 0.42/1.08 end
% 0.42/1.08 substitution1:
% 0.42/1.08 X := X
% 0.42/1.08 Y := Y
% 0.42/1.08 end
% 0.42/1.08
% 0.42/1.08 paramod: (252) {G1,W14,D5,L1,V2,M1} { times( times( times( Y, X ), skol3 )
% 0.42/1.08 , skol3 ) ==> times( times( skol1( skol3 ), Y ), X ) }.
% 0.42/1.08 parent0[0]: (0) {G0,W11,D4,L1,V3,M1} I { times( Y, times( Z, X ) ) ==>
% 0.42/1.08 times( times( X, Y ), Z ) }.
% 0.42/1.08 parent1[0; 2]: (250) {G1,W14,D5,L1,V2,M1} { times( times( Y, times( skol3
% 0.42/1.08 , X ) ), skol3 ) ==> times( times( skol1( skol3 ), X ), Y ) }.
% 0.42/1.08 substitution0:
% 0.42/1.08 X := Y
% 0.42/1.08 Y := X
% 0.42/1.08 Z := skol3
% 0.42/1.08 end
% 0.42/1.08 substitution1:
% 0.42/1.08 X := Y
% 0.42/1.08 Y := X
% 0.42/1.08 end
% 0.42/1.08
% 0.42/1.08 subsumption: (29) {G3,W14,D5,L1,V2,M1} P(14,0);d(0);d(0);d(0) { times(
% 0.42/1.08 times( times( Y, X ), skol3 ), skol3 ) ==> times( times( skol1( skol3 ),
% 0.42/1.08 Y ), X ) }.
% 0.42/1.08 parent0: (252) {G1,W14,D5,L1,V2,M1} { times( times( times( Y, X ), skol3 )
% 0.42/1.08 , skol3 ) ==> times( times( skol1( skol3 ), Y ), X ) }.
% 0.42/1.08 substitution0:
% 0.42/1.08 X := X
% 0.42/1.08 Y := Y
% 0.42/1.08 end
% 0.42/1.08 permutation0:
% 0.42/1.08 0 ==> 0
% 0.42/1.08 end
% 0.42/1.08
% 0.42/1.08 paramod: (256) {G2,W14,D5,L1,V2,M1} { times( times( times( X, Y ), skol2 )
% 0.42/1.08 , skol2 ) = times( times( skol1( skol2 ), X ), Y ) }.
% 0.42/1.08 parent0[0]: (8) {G1,W6,D3,L1,V0,M1} R(2,4) { times( skol2, skol2 ) ==>
% 0.42/1.08 skol1( skol2 ) }.
% 0.42/1.08 parent1[0; 10]: (10) {G1,W15,D5,L1,V4,M1} P(0,0);d(0);d(0);d(0) { times(
% 0.42/1.08 times( times( T, X ), Y ), Z ) = times( times( times( Y, Z ), T ), X )
% 0.42/1.08 }.
% 0.42/1.08 substitution0:
% 0.42/1.08 end
% 0.42/1.08 substitution1:
% 0.42/1.08 X := Y
% 0.42/1.08 Y := skol2
% 0.42/1.08 Z := skol2
% 0.42/1.08 T := X
% 0.42/1.08 end
% 0.42/1.08
% 0.42/1.08 subsumption: (40) {G2,W14,D5,L1,V2,M1} P(8,10) { times( times( times( X, Y
% 0.42/1.08 ), skol2 ), skol2 ) ==> times( times( skol1( skol2 ), X ), Y ) }.
% 0.42/1.08 parent0: (256) {G2,W14,D5,L1,V2,M1} { times( times( times( X, Y ), skol2 )
% 0.42/1.08 , skol2 ) = times( times( skol1( skol2 ), X ), Y ) }.
% 0.42/1.08 substitution0:
% 0.42/1.08 X := X
% 0.42/1.08 Y := Y
% 0.42/1.08 end
% 0.42/1.08 permutation0:
% 0.42/1.08 0 ==> 0
% 0.42/1.08 end
% 0.42/1.08
% 0.42/1.08 eqswap: (258) {G2,W10,D4,L1,V1,M1} { times( X, skol1( skol2 ) ) ==> times
% 0.42/1.08 ( times( skol2, X ), skol2 ) }.
% 0.42/1.08 parent0[0]: (11) {G2,W10,D4,L1,V1,M1} P(8,0) { times( times( skol2, X ),
% 0.42/1.08 skol2 ) ==> times( X, skol1( skol2 ) ) }.
% 0.42/1.08 substitution0:
% 0.42/1.08 X := X
% 0.42/1.08 end
% 0.42/1.08
% 0.42/1.08 paramod: (260) {G2,W9,D4,L1,V0,M1} { times( skol2, skol1( skol2 ) ) ==>
% 0.42/1.08 times( skol1( skol2 ), skol2 ) }.
% 0.42/1.08 parent0[0]: (8) {G1,W6,D3,L1,V0,M1} R(2,4) { times( skol2, skol2 ) ==>
% 0.42/1.08 skol1( skol2 ) }.
% 0.42/1.08 parent1[0; 6]: (258) {G2,W10,D4,L1,V1,M1} { times( X, skol1( skol2 ) ) ==>
% 0.42/1.08 times( times( skol2, X ), skol2 ) }.
% 0.42/1.08 substitution0:
% 0.42/1.08 end
% 0.42/1.08 substitution1:
% 0.42/1.08 X := skol2
% 0.42/1.08 end
% 0.42/1.08
% 0.42/1.08 paramod: (261) {G2,W6,D4,L1,V0,M1} { skol2 ==> times( skol1( skol2 ),
% 0.42/1.08 skol2 ) }.
% 0.42/1.08 parent0[0]: (15) {G1,W6,D4,L1,V0,M1} R(1,4) { times( skol2, skol1( skol2 )
% 0.42/1.08 ) ==> skol2 }.
% 0.42/1.08 parent1[0; 1]: (260) {G2,W9,D4,L1,V0,M1} { times( skol2, skol1( skol2 ) )
% 0.42/1.08 ==> times( skol1( skol2 ), skol2 ) }.
% 0.42/1.08 substitution0:
% 0.42/1.08 end
% 0.42/1.08 substitution1:
% 0.42/1.08 end
% 0.42/1.08
% 0.42/1.08 eqswap: (262) {G2,W6,D4,L1,V0,M1} { times( skol1( skol2 ), skol2 ) ==>
% 0.42/1.08 skol2 }.
% 0.42/1.08 parent0[0]: (261) {G2,W6,D4,L1,V0,M1} { skol2 ==> times( skol1( skol2 ),
% 0.42/1.08 skol2 ) }.
% 0.42/1.08 substitution0:
% 0.42/1.08 end
% 0.42/1.08
% 0.42/1.08 subsumption: (50) {G3,W6,D4,L1,V0,M1} P(8,11);d(15) { times( skol1( skol2 )
% 0.42/1.08 , skol2 ) ==> skol2 }.
% 0.42/1.08 parent0: (262) {G2,W6,D4,L1,V0,M1} { times( skol1( skol2 ), skol2 ) ==>
% 0.42/1.08 skol2 }.
% 0.42/1.08 substitution0:
% 0.42/1.08 end
% 0.42/1.08 permutation0:
% 0.42/1.08 0 ==> 0
% 0.42/1.08 end
% 0.42/1.08
% 0.42/1.08 eqswap: (264) {G0,W11,D4,L1,V3,M1} { times( times( Z, X ), Y ) ==> times(
% 0.42/1.08 X, times( Y, Z ) ) }.
% 0.42/1.08 parent0[0]: (0) {G0,W11,D4,L1,V3,M1} I { times( Y, times( Z, X ) ) ==>
% 0.42/1.08 times( times( X, Y ), Z ) }.
% 0.42/1.08 substitution0:
% 0.42/1.08 X := Z
% 0.42/1.08 Y := X
% 0.42/1.08 Z := Y
% 0.42/1.08 end
% 0.42/1.08
% 0.42/1.08 paramod: (266) {G1,W10,D4,L1,V1,M1} { times( times( skol2, X ), skol1(
% 0.42/1.08 skol2 ) ) ==> times( X, skol2 ) }.
% 0.42/1.08 parent0[0]: (50) {G3,W6,D4,L1,V0,M1} P(8,11);d(15) { times( skol1( skol2 )
% 0.42/1.08 , skol2 ) ==> skol2 }.
% 0.42/1.08 parent1[0; 9]: (264) {G0,W11,D4,L1,V3,M1} { times( times( Z, X ), Y ) ==>
% 0.42/1.08 times( X, times( Y, Z ) ) }.
% 0.42/1.08 substitution0:
% 0.42/1.08 end
% 0.42/1.08 substitution1:
% 0.42/1.08 X := X
% 0.42/1.08 Y := skol1( skol2 )
% 0.42/1.08 Z := skol2
% 0.42/1.08 end
% 0.42/1.08
% 0.42/1.08 subsumption: (53) {G4,W10,D4,L1,V1,M1} P(50,0) { times( times( skol2, X ),
% 0.42/1.08 skol1( skol2 ) ) ==> times( X, skol2 ) }.
% 0.42/1.08 parent0: (266) {G1,W10,D4,L1,V1,M1} { times( times( skol2, X ), skol1(
% 0.42/1.08 skol2 ) ) ==> times( X, skol2 ) }.
% 0.42/1.08 substitution0:
% 0.42/1.08 X := X
% 0.42/1.08 end
% 0.42/1.08 permutation0:
% 0.42/1.08 0 ==> 0
% 0.42/1.08 end
% 0.42/1.08
% 0.42/1.08 paramod: (275) {G2,W14,D6,L1,V2,M1} { times( times( times( skol1( skol2 )
% 0.42/1.08 , X ), skol2 ), Y ) = times( times( Y, skol2 ), X ) }.
% 0.42/1.08 parent0[0]: (53) {G4,W10,D4,L1,V1,M1} P(50,0) { times( times( skol2, X ),
% 0.42/1.08 skol1( skol2 ) ) ==> times( X, skol2 ) }.
% 0.42/1.08 parent1[0; 10]: (10) {G1,W15,D5,L1,V4,M1} P(0,0);d(0);d(0);d(0) { times(
% 0.42/1.08 times( times( T, X ), Y ), Z ) = times( times( times( Y, Z ), T ), X )
% 0.42/1.08 }.
% 0.42/1.08 substitution0:
% 0.42/1.08 X := Y
% 0.42/1.08 end
% 0.42/1.08 substitution1:
% 0.42/1.08 X := X
% 0.42/1.08 Y := skol2
% 0.42/1.08 Z := Y
% 0.42/1.08 T := skol1( skol2 )
% 0.42/1.08 end
% 0.42/1.08
% 0.42/1.08 paramod: (277) {G3,W11,D4,L1,V2,M1} { times( times( X, skol2 ), Y ) =
% 0.42/1.08 times( times( Y, skol2 ), X ) }.
% 0.42/1.08 parent0[0]: (18) {G2,W10,D5,L1,V1,M1} P(15,0) { times( times( skol1( skol2
% 0.42/1.08 ), X ), skol2 ) ==> times( X, skol2 ) }.
% 0.42/1.08 parent1[0; 2]: (275) {G2,W14,D6,L1,V2,M1} { times( times( times( skol1(
% 0.42/1.08 skol2 ), X ), skol2 ), Y ) = times( times( Y, skol2 ), X ) }.
% 0.42/1.08 substitution0:
% 0.42/1.08 X := X
% 0.42/1.08 end
% 0.42/1.08 substitution1:
% 0.42/1.08 X := X
% 0.42/1.08 Y := Y
% 0.42/1.08 end
% 0.42/1.08
% 0.42/1.08 subsumption: (63) {G5,W11,D4,L1,V2,M1} P(53,10);d(18) { times( times( X,
% 0.42/1.08 skol2 ), Y ) = times( times( Y, skol2 ), X ) }.
% 0.42/1.08 parent0: (277) {G3,W11,D4,L1,V2,M1} { times( times( X, skol2 ), Y ) =
% 0.42/1.08 times( times( Y, skol2 ), X ) }.
% 0.42/1.08 substitution0:
% 0.42/1.08 X := X
% 0.42/1.08 Y := Y
% 0.42/1.08 end
% 0.42/1.08 permutation0:
% 0.42/1.08 0 ==> 0
% 0.42/1.08 end
% 0.42/1.08
% 0.42/1.08 eqswap: (279) {G2,W10,D5,L1,V1,M1} { times( X, skol3 ) ==> times( times(
% 0.42/1.08 skol1( skol3 ), X ), skol3 ) }.
% 0.42/1.08 parent0[0]: (19) {G2,W10,D5,L1,V1,M1} P(16,0) { times( times( skol1( skol3
% 0.42/1.08 ), X ), skol3 ) ==> times( X, skol3 ) }.
% 0.42/1.08 substitution0:
% 0.42/1.08 X := X
% 0.42/1.08 end
% 0.42/1.08
% 0.42/1.08 paramod: (286) {G1,W14,D6,L1,V2,M1} { times( times( X, Y ), skol3 ) ==>
% 0.42/1.08 times( times( times( Y, skol1( skol3 ) ), X ), skol3 ) }.
% 0.42/1.08 parent0[0]: (0) {G0,W11,D4,L1,V3,M1} I { times( Y, times( Z, X ) ) ==>
% 0.42/1.08 times( times( X, Y ), Z ) }.
% 0.42/1.08 parent1[0; 7]: (279) {G2,W10,D5,L1,V1,M1} { times( X, skol3 ) ==> times(
% 0.42/1.08 times( skol1( skol3 ), X ), skol3 ) }.
% 0.42/1.08 substitution0:
% 0.42/1.08 X := Y
% 0.42/1.08 Y := skol1( skol3 )
% 0.42/1.08 Z := X
% 0.42/1.08 end
% 0.42/1.08 substitution1:
% 0.42/1.08 X := times( X, Y )
% 0.42/1.08 end
% 0.42/1.08
% 0.42/1.08 eqswap: (287) {G1,W14,D6,L1,V2,M1} { times( times( times( Y, skol1( skol3
% 0.42/1.08 ) ), X ), skol3 ) ==> times( times( X, Y ), skol3 ) }.
% 0.42/1.08 parent0[0]: (286) {G1,W14,D6,L1,V2,M1} { times( times( X, Y ), skol3 ) ==>
% 0.42/1.08 times( times( times( Y, skol1( skol3 ) ), X ), skol3 ) }.
% 0.42/1.08 substitution0:
% 0.42/1.08 X := X
% 0.42/1.08 Y := Y
% 0.42/1.08 end
% 0.42/1.08
% 0.42/1.08 subsumption: (89) {G3,W14,D6,L1,V2,M1} P(0,19) { times( times( times( Y,
% 0.42/1.08 skol1( skol3 ) ), X ), skol3 ) ==> times( times( X, Y ), skol3 ) }.
% 0.42/1.08 parent0: (287) {G1,W14,D6,L1,V2,M1} { times( times( times( Y, skol1( skol3
% 0.42/1.08 ) ), X ), skol3 ) ==> times( times( X, Y ), skol3 ) }.
% 0.42/1.08 substitution0:
% 0.42/1.08 X := X
% 0.42/1.08 Y := Y
% 0.42/1.08 end
% 0.42/1.08 permutation0:
% 0.42/1.08 0 ==> 0
% 0.42/1.08 end
% 0.42/1.08
% 0.42/1.08 paramod: (290) {G2,W10,D4,L1,V1,M1} { times( times( X, skol2 ), skol2 ) =
% 0.42/1.08 times( skol1( skol2 ), X ) }.
% 0.42/1.08 parent0[0]: (8) {G1,W6,D3,L1,V0,M1} R(2,4) { times( skol2, skol2 ) ==>
% 0.42/1.08 skol1( skol2 ) }.
% 0.42/1.08 parent1[0; 7]: (63) {G5,W11,D4,L1,V2,M1} P(53,10);d(18) { times( times( X,
% 0.42/1.08 skol2 ), Y ) = times( times( Y, skol2 ), X ) }.
% 0.42/1.08 substitution0:
% 0.42/1.08 end
% 0.42/1.08 substitution1:
% 0.42/1.08 X := X
% 0.42/1.08 Y := skol2
% 0.42/1.08 end
% 0.42/1.08
% 0.42/1.08 subsumption: (101) {G6,W10,D4,L1,V1,M1} P(8,63) { times( times( X, skol2 )
% 0.42/1.08 , skol2 ) ==> times( skol1( skol2 ), X ) }.
% 0.42/1.08 parent0: (290) {G2,W10,D4,L1,V1,M1} { times( times( X, skol2 ), skol2 ) =
% 0.42/1.08 times( skol1( skol2 ), X ) }.
% 0.42/1.08 substitution0:
% 0.42/1.08 X := X
% 0.42/1.08 end
% 0.42/1.08 permutation0:
% 0.42/1.08 0 ==> 0
% 0.42/1.08 end
% 0.42/1.08
% 0.42/1.08 eqswap: (291) {G6,W10,D4,L1,V1,M1} { times( skol1( skol2 ), X ) ==> times
% 0.42/1.08 ( times( X, skol2 ), skol2 ) }.
% 0.42/1.08 parent0[0]: (101) {G6,W10,D4,L1,V1,M1} P(8,63) { times( times( X, skol2 ),
% 0.42/1.08 skol2 ) ==> times( skol1( skol2 ), X ) }.
% 0.42/1.08 substitution0:
% 0.42/1.08 X := X
% 0.42/1.08 end
% 0.42/1.08
% 0.42/1.08 paramod: (297) {G7,W13,D5,L1,V1,M1} { times( skol1( skol2 ), times( X,
% 0.42/1.08 skol2 ) ) ==> times( times( skol1( skol2 ), X ), skol2 ) }.
% 0.42/1.08 parent0[0]: (101) {G6,W10,D4,L1,V1,M1} P(8,63) { times( times( X, skol2 ),
% 0.42/1.08 skol2 ) ==> times( skol1( skol2 ), X ) }.
% 0.42/1.08 parent1[0; 8]: (291) {G6,W10,D4,L1,V1,M1} { times( skol1( skol2 ), X ) ==>
% 0.42/1.08 times( times( X, skol2 ), skol2 ) }.
% 0.42/1.08 substitution0:
% 0.42/1.08 X := X
% 0.42/1.08 end
% 0.42/1.08 substitution1:
% 0.42/1.08 X := times( X, skol2 )
% 0.42/1.08 end
% 0.42/1.08
% 0.42/1.08 paramod: (298) {G3,W10,D4,L1,V1,M1} { times( skol1( skol2 ), times( X,
% 0.42/1.08 skol2 ) ) ==> times( X, skol2 ) }.
% 0.42/1.08 parent0[0]: (18) {G2,W10,D5,L1,V1,M1} P(15,0) { times( times( skol1( skol2
% 0.42/1.08 ), X ), skol2 ) ==> times( X, skol2 ) }.
% 0.42/1.08 parent1[0; 7]: (297) {G7,W13,D5,L1,V1,M1} { times( skol1( skol2 ), times(
% 0.42/1.08 X, skol2 ) ) ==> times( times( skol1( skol2 ), X ), skol2 ) }.
% 0.42/1.08 substitution0:
% 0.42/1.08 X := X
% 0.42/1.08 end
% 0.42/1.09 substitution1:
% 0.42/1.09 X := X
% 0.42/1.09 end
% 0.42/1.09
% 0.42/1.09 paramod: (299) {G1,W10,D5,L1,V1,M1} { times( times( skol2, skol1( skol2 )
% 0.42/1.09 ), X ) ==> times( X, skol2 ) }.
% 0.42/1.09 parent0[0]: (0) {G0,W11,D4,L1,V3,M1} I { times( Y, times( Z, X ) ) ==>
% 0.42/1.09 times( times( X, Y ), Z ) }.
% 0.42/1.09 parent1[0; 1]: (298) {G3,W10,D4,L1,V1,M1} { times( skol1( skol2 ), times(
% 0.42/1.09 X, skol2 ) ) ==> times( X, skol2 ) }.
% 0.42/1.09 substitution0:
% 0.42/1.09 X := skol2
% 0.42/1.09 Y := skol1( skol2 )
% 0.42/1.09 Z := X
% 0.42/1.09 end
% 0.42/1.09 substitution1:
% 0.42/1.09 X := X
% 0.42/1.09 end
% 0.42/1.09
% 0.42/1.09 paramod: (300) {G2,W7,D3,L1,V1,M1} { times( skol2, X ) ==> times( X, skol2
% 0.42/1.09 ) }.
% 0.42/1.09 parent0[0]: (15) {G1,W6,D4,L1,V0,M1} R(1,4) { times( skol2, skol1( skol2 )
% 0.42/1.09 ) ==> skol2 }.
% 0.42/1.09 parent1[0; 2]: (299) {G1,W10,D5,L1,V1,M1} { times( times( skol2, skol1(
% 0.42/1.09 skol2 ) ), X ) ==> times( X, skol2 ) }.
% 0.42/1.09 substitution0:
% 0.42/1.09 end
% 0.42/1.09 substitution1:
% 0.42/1.09 X := X
% 0.42/1.09 end
% 0.42/1.09
% 0.42/1.09 eqswap: (301) {G2,W7,D3,L1,V1,M1} { times( X, skol2 ) ==> times( skol2, X
% 0.42/1.09 ) }.
% 0.42/1.09 parent0[0]: (300) {G2,W7,D3,L1,V1,M1} { times( skol2, X ) ==> times( X,
% 0.42/1.09 skol2 ) }.
% 0.42/1.09 substitution0:
% 0.42/1.09 X := X
% 0.42/1.09 end
% 0.42/1.09
% 0.42/1.09 subsumption: (106) {G7,W7,D3,L1,V1,M1} P(101,101);d(18);d(0);d(15) { times
% 0.42/1.09 ( X, skol2 ) = times( skol2, X ) }.
% 0.42/1.09 parent0: (301) {G2,W7,D3,L1,V1,M1} { times( X, skol2 ) ==> times( skol2, X
% 0.42/1.09 ) }.
% 0.42/1.09 substitution0:
% 0.42/1.09 X := X
% 0.42/1.09 end
% 0.42/1.09 permutation0:
% 0.42/1.09 0 ==> 0
% 0.42/1.09 end
% 0.42/1.09
% 0.42/1.09 eqswap: (302) {G7,W7,D3,L1,V1,M1} { times( skol2, X ) = times( X, skol2 )
% 0.42/1.09 }.
% 0.42/1.09 parent0[0]: (106) {G7,W7,D3,L1,V1,M1} P(101,101);d(18);d(0);d(15) { times(
% 0.42/1.09 X, skol2 ) = times( skol2, X ) }.
% 0.42/1.09 substitution0:
% 0.42/1.09 X := X
% 0.42/1.09 end
% 0.42/1.09
% 0.42/1.09 paramod: (303) {G1,W4,D3,L1,V0,M1} { ! element( times( skol3, skol2 ) )
% 0.42/1.09 }.
% 0.42/1.09 parent0[0]: (302) {G7,W7,D3,L1,V1,M1} { times( skol2, X ) = times( X,
% 0.42/1.09 skol2 ) }.
% 0.42/1.09 parent1[0; 2]: (6) {G0,W4,D3,L1,V0,M1} I { ! element( times( skol2, skol3 )
% 0.42/1.09 ) }.
% 0.42/1.09 substitution0:
% 0.42/1.09 X := skol3
% 0.42/1.09 end
% 0.42/1.09 substitution1:
% 0.42/1.09 end
% 0.42/1.09
% 0.42/1.09 subsumption: (123) {G8,W4,D3,L1,V0,M1} P(106,6) { ! element( times( skol3,
% 0.42/1.09 skol2 ) ) }.
% 0.42/1.09 parent0: (303) {G1,W4,D3,L1,V0,M1} { ! element( times( skol3, skol2 ) )
% 0.42/1.09 }.
% 0.42/1.09 substitution0:
% 0.42/1.09 end
% 0.42/1.09 permutation0:
% 0.42/1.09 0 ==> 0
% 0.42/1.09 end
% 0.42/1.09
% 0.42/1.09 *** allocated 22500 integers for clauses
% 0.42/1.09 eqswap: (304) {G1,W9,D4,L2,V1,M2} { ! X ==> times( times( X, X ), X ),
% 0.42/1.09 element( X ) }.
% 0.42/1.09 parent0[1]: (7) {G1,W9,D4,L2,V1,M2} Q(3);d(0) { element( X ), ! times(
% 0.42/1.09 times( X, X ), X ) ==> X }.
% 0.42/1.09 substitution0:
% 0.42/1.09 X := X
% 0.42/1.09 end
% 0.42/1.09
% 0.42/1.09 resolution: (315) {G2,W15,D5,L1,V0,M1} { ! times( skol3, skol2 ) ==> times
% 0.42/1.09 ( times( times( skol3, skol2 ), times( skol3, skol2 ) ), times( skol3,
% 0.42/1.09 skol2 ) ) }.
% 0.42/1.09 parent0[0]: (123) {G8,W4,D3,L1,V0,M1} P(106,6) { ! element( times( skol3,
% 0.42/1.09 skol2 ) ) }.
% 0.42/1.09 parent1[1]: (304) {G1,W9,D4,L2,V1,M2} { ! X ==> times( times( X, X ), X )
% 0.42/1.09 , element( X ) }.
% 0.42/1.09 substitution0:
% 0.42/1.09 end
% 0.42/1.09 substitution1:
% 0.42/1.09 X := times( skol3, skol2 )
% 0.42/1.09 end
% 0.42/1.09
% 0.42/1.09 paramod: (316) {G1,W15,D6,L1,V0,M1} { ! times( skol3, skol2 ) ==> times(
% 0.42/1.09 times( skol2, times( times( skol3, skol2 ), times( skol3, skol2 ) ) ),
% 0.42/1.09 skol3 ) }.
% 0.42/1.09 parent0[0]: (0) {G0,W11,D4,L1,V3,M1} I { times( Y, times( Z, X ) ) ==>
% 0.42/1.09 times( times( X, Y ), Z ) }.
% 0.42/1.09 parent1[0; 5]: (315) {G2,W15,D5,L1,V0,M1} { ! times( skol3, skol2 ) ==>
% 0.42/1.09 times( times( times( skol3, skol2 ), times( skol3, skol2 ) ), times(
% 0.42/1.09 skol3, skol2 ) ) }.
% 0.42/1.09 substitution0:
% 0.42/1.09 X := skol2
% 0.42/1.09 Y := times( times( skol3, skol2 ), times( skol3, skol2 ) )
% 0.42/1.09 Z := skol3
% 0.42/1.09 end
% 0.42/1.09 substitution1:
% 0.42/1.09 end
% 0.42/1.09
% 0.42/1.09 paramod: (649) {G1,W15,D6,L1,V0,M1} { ! times( skol3, skol2 ) ==> times(
% 0.42/1.09 times( times( times( skol3, skol2 ), skol2 ), times( skol3, skol2 ) ),
% 0.42/1.09 skol3 ) }.
% 0.42/1.09 parent0[0]: (0) {G0,W11,D4,L1,V3,M1} I { times( Y, times( Z, X ) ) ==>
% 0.42/1.09 times( times( X, Y ), Z ) }.
% 0.42/1.09 parent1[0; 6]: (316) {G1,W15,D6,L1,V0,M1} { ! times( skol3, skol2 ) ==>
% 0.42/1.09 times( times( skol2, times( times( skol3, skol2 ), times( skol3, skol2 )
% 0.42/1.09 ) ), skol3 ) }.
% 0.42/1.09 substitution0:
% 0.42/1.09 X := times( skol3, skol2 )
% 0.42/1.09 Y := skol2
% 0.42/1.09 Z := times( skol3, skol2 )
% 0.42/1.09 end
% 0.42/1.09 substitution1:
% 0.42/1.09 end
% 0.42/1.09
% 0.42/1.09 paramod: (731) {G1,W15,D7,L1,V0,M1} { ! times( skol3, skol2 ) ==> times(
% 0.42/1.09 times( times( skol2, times( times( skol3, skol2 ), skol2 ) ), skol3 ),
% 0.42/1.09 skol3 ) }.
% 0.42/1.09 parent0[0]: (0) {G0,W11,D4,L1,V3,M1} I { times( Y, times( Z, X ) ) ==>
% 0.42/1.09 times( times( X, Y ), Z ) }.
% 0.42/1.09 parent1[0; 6]: (649) {G1,W15,D6,L1,V0,M1} { ! times( skol3, skol2 ) ==>
% 0.42/1.09 times( times( times( times( skol3, skol2 ), skol2 ), times( skol3, skol2
% 0.42/1.09 ) ), skol3 ) }.
% 0.42/1.09 substitution0:
% 0.42/1.09 X := skol2
% 0.42/1.09 Y := times( times( skol3, skol2 ), skol2 )
% 0.42/1.09 Z := skol3
% 0.42/1.09 end
% 0.42/1.09 substitution1:
% 0.42/1.09 end
% 0.42/1.09
% 0.42/1.09 paramod: (735) {G2,W14,D5,L1,V0,M1} { ! times( skol3, skol2 ) ==> times(
% 0.42/1.09 times( skol1( skol3 ), skol2 ), times( times( skol3, skol2 ), skol2 ) )
% 0.42/1.09 }.
% 0.42/1.09 parent0[0]: (29) {G3,W14,D5,L1,V2,M1} P(14,0);d(0);d(0);d(0) { times( times
% 0.42/1.09 ( times( Y, X ), skol3 ), skol3 ) ==> times( times( skol1( skol3 ), Y ),
% 0.42/1.09 X ) }.
% 0.42/1.09 parent1[0; 5]: (731) {G1,W15,D7,L1,V0,M1} { ! times( skol3, skol2 ) ==>
% 0.42/1.09 times( times( times( skol2, times( times( skol3, skol2 ), skol2 ) ),
% 0.42/1.09 skol3 ), skol3 ) }.
% 0.42/1.09 substitution0:
% 0.42/1.09 X := times( times( skol3, skol2 ), skol2 )
% 0.42/1.09 Y := skol2
% 0.42/1.09 end
% 0.42/1.09 substitution1:
% 0.42/1.09 end
% 0.42/1.09
% 0.42/1.09 paramod: (736) {G1,W14,D6,L1,V0,M1} { ! times( skol3, skol2 ) ==> times(
% 0.42/1.09 times( skol2, times( skol1( skol3 ), skol2 ) ), times( skol3, skol2 ) )
% 0.42/1.09 }.
% 0.42/1.09 parent0[0]: (0) {G0,W11,D4,L1,V3,M1} I { times( Y, times( Z, X ) ) ==>
% 0.42/1.09 times( times( X, Y ), Z ) }.
% 0.42/1.09 parent1[0; 5]: (735) {G2,W14,D5,L1,V0,M1} { ! times( skol3, skol2 ) ==>
% 0.42/1.09 times( times( skol1( skol3 ), skol2 ), times( times( skol3, skol2 ),
% 0.42/1.09 skol2 ) ) }.
% 0.42/1.09 substitution0:
% 0.42/1.09 X := skol2
% 0.42/1.09 Y := times( skol1( skol3 ), skol2 )
% 0.42/1.09 Z := times( skol3, skol2 )
% 0.42/1.09 end
% 0.42/1.09 substitution1:
% 0.42/1.09 end
% 0.42/1.09
% 0.42/1.09 paramod: (744) {G1,W14,D7,L1,V0,M1} { ! times( skol3, skol2 ) ==> times(
% 0.42/1.09 times( skol2, times( skol2, times( skol1( skol3 ), skol2 ) ) ), skol3 )
% 0.42/1.09 }.
% 0.42/1.09 parent0[0]: (0) {G0,W11,D4,L1,V3,M1} I { times( Y, times( Z, X ) ) ==>
% 0.42/1.09 times( times( X, Y ), Z ) }.
% 0.42/1.09 parent1[0; 5]: (736) {G1,W14,D6,L1,V0,M1} { ! times( skol3, skol2 ) ==>
% 0.42/1.09 times( times( skol2, times( skol1( skol3 ), skol2 ) ), times( skol3,
% 0.42/1.09 skol2 ) ) }.
% 0.42/1.09 substitution0:
% 0.42/1.09 X := skol2
% 0.42/1.09 Y := times( skol2, times( skol1( skol3 ), skol2 ) )
% 0.42/1.09 Z := skol3
% 0.42/1.09 end
% 0.42/1.09 substitution1:
% 0.42/1.09 end
% 0.42/1.09
% 0.42/1.09 paramod: (761) {G1,W14,D7,L1,V0,M1} { ! times( skol3, skol2 ) ==> times(
% 0.42/1.09 times( times( times( skol1( skol3 ), skol2 ), skol2 ), skol2 ), skol3 )
% 0.42/1.09 }.
% 0.42/1.09 parent0[0]: (0) {G0,W11,D4,L1,V3,M1} I { times( Y, times( Z, X ) ) ==>
% 0.42/1.09 times( times( X, Y ), Z ) }.
% 0.42/1.09 parent1[0; 6]: (744) {G1,W14,D7,L1,V0,M1} { ! times( skol3, skol2 ) ==>
% 0.42/1.09 times( times( skol2, times( skol2, times( skol1( skol3 ), skol2 ) ) ),
% 0.42/1.09 skol3 ) }.
% 0.42/1.09 substitution0:
% 0.42/1.09 X := times( skol1( skol3 ), skol2 )
% 0.42/1.09 Y := skol2
% 0.42/1.09 Z := skol2
% 0.42/1.09 end
% 0.42/1.09 substitution1:
% 0.42/1.09 end
% 0.42/1.09
% 0.42/1.09 paramod: (766) {G2,W13,D6,L1,V0,M1} { ! times( skol3, skol2 ) ==> times(
% 0.42/1.09 times( times( skol1( skol2 ), skol1( skol3 ) ), skol2 ), skol3 ) }.
% 0.42/1.09 parent0[0]: (40) {G2,W14,D5,L1,V2,M1} P(8,10) { times( times( times( X, Y )
% 0.42/1.09 , skol2 ), skol2 ) ==> times( times( skol1( skol2 ), X ), Y ) }.
% 0.42/1.09 parent1[0; 6]: (761) {G1,W14,D7,L1,V0,M1} { ! times( skol3, skol2 ) ==>
% 0.42/1.09 times( times( times( times( skol1( skol3 ), skol2 ), skol2 ), skol2 ),
% 0.42/1.09 skol3 ) }.
% 0.42/1.09 substitution0:
% 0.42/1.09 X := skol1( skol3 )
% 0.42/1.09 Y := skol2
% 0.42/1.09 end
% 0.42/1.09 substitution1:
% 0.42/1.09 end
% 0.42/1.09
% 0.42/1.09 paramod: (767) {G3,W10,D5,L1,V0,M1} { ! times( skol3, skol2 ) ==> times(
% 0.42/1.09 times( skol2, skol1( skol2 ) ), skol3 ) }.
% 0.42/1.09 parent0[0]: (89) {G3,W14,D6,L1,V2,M1} P(0,19) { times( times( times( Y,
% 0.42/1.09 skol1( skol3 ) ), X ), skol3 ) ==> times( times( X, Y ), skol3 ) }.
% 0.42/1.09 parent1[0; 5]: (766) {G2,W13,D6,L1,V0,M1} { ! times( skol3, skol2 ) ==>
% 0.42/1.09 times( times( times( skol1( skol2 ), skol1( skol3 ) ), skol2 ), skol3 )
% 0.42/1.09 }.
% 0.42/1.09 substitution0:
% 0.42/1.09 X := skol2
% 0.42/1.09 Y := skol1( skol2 )
% 0.42/1.09 end
% 0.42/1.09 substitution1:
% 0.42/1.09 end
% 0.42/1.09
% 0.42/1.09 paramod: (768) {G2,W7,D3,L1,V0,M1} { ! times( skol3, skol2 ) ==> times(
% 0.42/1.09 skol2, skol3 ) }.
% 0.42/1.09 parent0[0]: (15) {G1,W6,D4,L1,V0,M1} R(1,4) { times( skol2, skol1( skol2 )
% 0.42/1.09 ) ==> skol2 }.
% 0.42/1.09 parent1[0; 6]: (767) {G3,W10,D5,L1,V0,M1} { ! times( skol3, skol2 ) ==>
% 0.42/1.09 times( times( skol2, skol1( skol2 ) ), skol3 ) }.
% 0.42/1.09 substitution0:
% 0.42/1.09 end
% 0.42/1.09 substitution1:
% 0.42/1.09 end
% 0.42/1.09
% 0.42/1.09 eqswap: (769) {G2,W7,D3,L1,V0,M1} { ! times( skol2, skol3 ) ==> times(
% 0.42/1.09 skol3, skol2 ) }.
% 0.42/1.09 parent0[0]: (768) {G2,W7,D3,L1,V0,M1} { ! times( skol3, skol2 ) ==> times
% 0.42/1.09 ( skol2, skol3 ) }.
% 0.42/1.09 substitution0:
% 0.42/1.09 end
% 0.42/1.09
% 0.42/1.09 subsumption: (124) {G9,W7,D3,L1,V0,M1} R(123,7);d(0);d(0);d(0);d(29);d(0);d
% 0.42/1.09 (0);d(0);d(40);d(89);d(15) { ! times( skol2, skol3 ) ==> times( skol3,
% 0.42/1.09 skol2 ) }.
% 0.42/1.09 parent0: (769) {G2,W7,D3,L1,V0,M1} { ! times( skol2, skol3 ) ==> times(
% 0.42/1.09 skol3, skol2 ) }.
% 0.42/1.09 substitution0:
% 0.42/1.09 end
% 0.42/1.09 permutation0:
% 0.42/1.09 0 ==> 0
% 0.42/1.09 end
% 0.42/1.09
% 0.42/1.09 eqswap: (770) {G7,W7,D3,L1,V1,M1} { times( skol2, X ) = times( X, skol2 )
% 0.42/1.09 }.
% 0.42/1.09 parent0[0]: (106) {G7,W7,D3,L1,V1,M1} P(101,101);d(18);d(0);d(15) { times(
% 0.42/1.09 X, skol2 ) = times( skol2, X ) }.
% 0.42/1.09 substitution0:
% 0.42/1.09 X := X
% 0.42/1.09 end
% 0.42/1.09
% 0.42/1.09 eqswap: (771) {G9,W7,D3,L1,V0,M1} { ! times( skol3, skol2 ) ==> times(
% 0.42/1.09 skol2, skol3 ) }.
% 0.42/1.09 parent0[0]: (124) {G9,W7,D3,L1,V0,M1} R(123,7);d(0);d(0);d(0);d(29);d(0);d(
% 0.42/1.09 0);d(0);d(40);d(89);d(15) { ! times( skol2, skol3 ) ==> times( skol3,
% 0.42/1.09 skol2 ) }.
% 0.42/1.09 substitution0:
% 0.42/1.09 end
% 0.42/1.09
% 0.42/1.09 paramod: (772) {G8,W7,D3,L1,V0,M1} { ! times( skol3, skol2 ) ==> times(
% 0.42/1.09 skol3, skol2 ) }.
% 0.42/1.09 parent0[0]: (770) {G7,W7,D3,L1,V1,M1} { times( skol2, X ) = times( X,
% 0.42/1.09 skol2 ) }.
% 0.42/1.09 parent1[0; 5]: (771) {G9,W7,D3,L1,V0,M1} { ! times( skol3, skol2 ) ==>
% 0.42/1.09 times( skol2, skol3 ) }.
% 0.42/1.09 substitution0:
% 0.42/1.09 X := skol3
% 0.42/1.09 end
% 0.42/1.09 substitution1:
% 0.42/1.09 end
% 0.42/1.09
% 0.42/1.09 eqrefl: (773) {G0,W0,D0,L0,V0,M0} { }.
% 0.42/1.09 parent0[0]: (772) {G8,W7,D3,L1,V0,M1} { ! times( skol3, skol2 ) ==> times
% 0.42/1.09 ( skol3, skol2 ) }.
% 0.42/1.09 substitution0:
% 0.42/1.09 end
% 0.42/1.09
% 0.42/1.09 subsumption: (125) {G10,W0,D0,L0,V0,M0} P(106,124);q { }.
% 0.42/1.09 parent0: (773) {G0,W0,D0,L0,V0,M0} { }.
% 0.42/1.09 substitution0:
% 0.42/1.09 end
% 0.42/1.09 permutation0:
% 0.42/1.09 end
% 0.42/1.09
% 0.42/1.09 Proof check complete!
% 0.42/1.09
% 0.42/1.09 Memory use:
% 0.42/1.09
% 0.42/1.09 space for terms: 1625
% 0.42/1.09 space for clauses: 11019
% 0.42/1.09
% 0.42/1.09
% 0.42/1.09 clauses generated: 981
% 0.42/1.09 clauses kept: 126
% 0.42/1.09 clauses selected: 45
% 0.42/1.09 clauses deleted: 5
% 0.42/1.09 clauses inuse deleted: 0
% 0.42/1.09
% 0.42/1.09 subsentry: 2342
% 0.42/1.09 literals s-matched: 463
% 0.42/1.09 literals matched: 401
% 0.42/1.09 full subsumption: 0
% 0.42/1.09
% 0.42/1.09 checksum: 704837375
% 0.42/1.09
% 0.42/1.09
% 0.42/1.09 Bliksem ended
%------------------------------------------------------------------------------