TSTP Solution File: NUM847+1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : NUM847+1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n023.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 : Mon Jul 18 06:27:01 EDT 2022
% Result : Theorem 0.72s 1.12s
% Output : Refutation 0.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : NUM847+1 : TPTP v8.1.0. Released v4.1.0.
% 0.04/0.13 % Command : bliksem %s
% 0.12/0.34 % Computer : n023.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % DateTime : Tue Jul 5 06:19:12 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.72/1.12 *** allocated 10000 integers for termspace/termends
% 0.72/1.12 *** allocated 10000 integers for clauses
% 0.72/1.12 *** allocated 10000 integers for justifications
% 0.72/1.12 Bliksem 1.12
% 0.72/1.12
% 0.72/1.12
% 0.72/1.12 Automatic Strategy Selection
% 0.72/1.12
% 0.72/1.12
% 0.72/1.12 Clauses:
% 0.72/1.12
% 0.72/1.12 { ! vplus( vplus( vmul( vd436, vd437 ), vmul( vd436, vd439 ) ), vd436 ) =
% 0.72/1.12 vplus( vmul( vd436, vd437 ), vplus( vmul( vd436, vd439 ), vd436 ) ) }.
% 0.72/1.12 { vplus( vmul( vd436, vplus( vd437, vd439 ) ), vd436 ) = vplus( vplus( vmul
% 0.72/1.12 ( vd436, vd437 ), vmul( vd436, vd439 ) ), vd436 ) }.
% 0.72/1.12 { vmul( vd436, vsucc( vplus( vd437, vd439 ) ) ) = vplus( vmul( vd436, vplus
% 0.72/1.12 ( vd437, vd439 ) ), vd436 ) }.
% 0.72/1.12 { vmul( vd436, vplus( vd437, vsucc( vd439 ) ) ) = vmul( vd436, vsucc( vplus
% 0.72/1.12 ( vd437, vd439 ) ) ) }.
% 0.72/1.12 { vmul( vd436, vplus( vd437, vd439 ) ) = vplus( vmul( vd436, vd437 ), vmul
% 0.72/1.12 ( vd436, vd439 ) ) }.
% 0.72/1.12 { vplus( vmul( vd436, vd437 ), vd436 ) = vplus( vmul( vd436, vd437 ), vmul
% 0.72/1.12 ( vd436, v1 ) ) }.
% 0.72/1.12 { vmul( vd436, vsucc( vd437 ) ) = vplus( vmul( vd436, vd437 ), vd436 ) }.
% 0.72/1.12 { vmul( vd436, vplus( vd437, v1 ) ) = vmul( vd436, vsucc( vd437 ) ) }.
% 0.72/1.12 { vmul( X, Y ) = vmul( Y, X ) }.
% 0.72/1.12 { vmul( vsucc( X ), Y ) = vplus( vmul( X, Y ), Y ) }.
% 0.72/1.12 { vmul( v1, X ) = X }.
% 0.72/1.12 { vmul( X, vsucc( Y ) ) = vplus( vmul( X, Y ), X ) }.
% 0.72/1.12 { vmul( X, v1 ) = X }.
% 0.72/1.12 { ! less( X, vplus( Y, v1 ) ), leq( X, Y ) }.
% 0.72/1.12 { ! greater( X, Y ), geq( X, vplus( Y, v1 ) ) }.
% 0.72/1.12 { geq( X, v1 ) }.
% 0.72/1.12 { ! geq( Z, T ), ! geq( X, Y ), geq( vplus( X, Z ), vplus( Y, T ) ) }.
% 0.72/1.12 { ! greater( Z, T ), ! geq( X, Y ), greater( vplus( X, Z ), vplus( Y, T ) )
% 0.72/1.12 }.
% 0.72/1.12 { ! geq( Z, T ), ! greater( X, Y ), greater( vplus( X, Z ), vplus( Y, T ) )
% 0.72/1.12 }.
% 0.72/1.12 { ! greater( Z, T ), ! greater( X, Y ), greater( vplus( X, Z ), vplus( Y, T
% 0.72/1.12 ) ) }.
% 0.72/1.12 { ! less( vplus( X, Z ), vplus( Y, Z ) ), less( X, Y ) }.
% 0.72/1.12 { ! vplus( X, Z ) = vplus( Y, Z ), X = Y }.
% 0.72/1.12 { ! greater( vplus( X, Z ), vplus( Y, Z ) ), greater( X, Y ) }.
% 0.72/1.12 { ! less( X, Y ), less( vplus( X, Z ), vplus( Y, Z ) ) }.
% 0.72/1.12 { ! X = Y, vplus( X, Z ) = vplus( Y, Z ) }.
% 0.72/1.12 { ! greater( X, Y ), greater( vplus( X, Z ), vplus( Y, Z ) ) }.
% 0.72/1.12 { greater( vplus( X, Y ), X ) }.
% 0.72/1.12 { ! leq( Z, Y ), ! leq( X, Z ), leq( X, Y ) }.
% 0.72/1.12 { ! less( Z, Y ), ! leq( X, Z ), less( X, Y ) }.
% 0.72/1.12 { ! leq( Z, Y ), ! less( X, Z ), less( X, Y ) }.
% 0.72/1.12 { ! less( Z, Y ), ! less( X, Z ), less( X, Y ) }.
% 0.72/1.12 { ! leq( X, Y ), geq( Y, X ) }.
% 0.72/1.12 { ! geq( X, Y ), leq( Y, X ) }.
% 0.72/1.12 { ! leq( Y, X ), less( Y, X ), Y = X }.
% 0.72/1.12 { ! less( Y, X ), leq( Y, X ) }.
% 0.72/1.12 { ! Y = X, leq( Y, X ) }.
% 0.72/1.12 { ! geq( Y, X ), greater( Y, X ), Y = X }.
% 0.72/1.12 { ! greater( Y, X ), geq( Y, X ) }.
% 0.72/1.12 { ! Y = X, geq( Y, X ) }.
% 0.72/1.12 { ! less( X, Y ), greater( Y, X ) }.
% 0.72/1.12 { ! greater( X, Y ), less( Y, X ) }.
% 0.72/1.12 { X = Y, greater( X, Y ), less( X, Y ) }.
% 0.72/1.12 { ! X = Y, ! less( X, Y ) }.
% 0.72/1.12 { ! greater( X, Y ), ! less( X, Y ) }.
% 0.72/1.12 { ! X = Y, ! greater( X, Y ) }.
% 0.72/1.12 { ! less( Y, X ), X = vplus( Y, skol1( X, Y ) ) }.
% 0.72/1.12 { ! X = vplus( Y, Z ), less( Y, X ) }.
% 0.72/1.12 { ! greater( Y, X ), Y = vplus( X, skol2( X, Y ) ) }.
% 0.72/1.12 { ! Y = vplus( X, Z ), greater( Y, X ) }.
% 0.72/1.12 { X = Y, X = vplus( Y, skol3( X, Y ) ), Y = vplus( X, skol4( X, Y ) ) }.
% 0.72/1.12 { ! X = Y, ! Y = vplus( X, Z ) }.
% 0.72/1.12 { ! X = vplus( Y, Z ), ! Y = vplus( X, T ) }.
% 0.72/1.12 { ! X = Y, ! X = vplus( Y, Z ) }.
% 0.72/1.12 { X = Y, ! vplus( Z, X ) = vplus( Z, Y ) }.
% 0.72/1.12 { ! Y = vplus( X, Y ) }.
% 0.72/1.12 { vplus( Y, X ) = vplus( X, Y ) }.
% 0.72/1.12 { vplus( vsucc( X ), Y ) = vsucc( vplus( X, Y ) ) }.
% 0.72/1.12 { vplus( v1, X ) = vsucc( X ) }.
% 0.72/1.12 { vplus( vplus( X, Y ), Z ) = vplus( X, vplus( Y, Z ) ) }.
% 0.72/1.12 { vplus( X, vsucc( Y ) ) = vsucc( vplus( X, Y ) ) }.
% 0.72/1.12 { vplus( X, v1 ) = vsucc( X ) }.
% 0.72/1.12 { X = v1, X = vsucc( vskolem2( X ) ) }.
% 0.72/1.12 { ! vsucc( X ) = X }.
% 0.72/1.12 { X = Y, ! vsucc( X ) = vsucc( Y ) }.
% 0.72/1.12 { ! vsucc( X ) = vsucc( Y ), X = Y }.
% 0.72/1.12 { ! vsucc( X ) = v1 }.
% 0.72/1.12
% 0.72/1.12 percentage equality = 0.440678, percentage horn = 0.923077
% 0.72/1.12 This is a problem with some equality
% 0.72/1.12
% 0.72/1.12
% 0.72/1.12
% 0.72/1.12 Options Used:
% 0.72/1.12
% 0.72/1.12 useres = 1
% 0.72/1.12 useparamod = 1
% 0.72/1.12 useeqrefl = 1
% 0.72/1.12 useeqfact = 1
% 0.72/1.12 usefactor = 1
% 0.72/1.12 usesimpsplitting = 0
% 0.72/1.12 usesimpdemod = 5
% 0.72/1.12 usesimpres = 3
% 0.72/1.12
% 0.72/1.12 resimpinuse = 1000
% 0.72/1.12 resimpclauses = 20000
% 0.72/1.12 substype = eqrewr
% 0.72/1.12 backwardsubs = 1
% 0.72/1.12 selectoldest = 5
% 0.72/1.12
% 0.72/1.12 litorderings [0] = split
% 0.72/1.12 litorderings [1] = extend the termordering, first sorting on arguments
% 0.72/1.12
% 0.72/1.12 termordering = kbo
% 0.72/1.12
% 0.72/1.12 litapriori = 0
% 0.72/1.12 termapriori = 1
% 0.72/1.12 litaposteriori = 0
% 0.72/1.12 termaposteriori = 0
% 0.72/1.12 demodaposteriori = 0
% 0.72/1.12 ordereqreflfact = 0
% 0.72/1.12
% 0.72/1.12 litselect = negord
% 0.72/1.12
% 0.72/1.12 maxweight = 15
% 0.72/1.12 maxdepth = 30000
% 0.72/1.12 maxlength = 115
% 0.72/1.12 maxnrvars = 195
% 0.72/1.12 excuselevel = 1
% 0.72/1.12 increasemaxweight = 1
% 0.72/1.12
% 0.72/1.12 maxselected = 10000000
% 0.72/1.12 maxnrclauses = 10000000
% 0.72/1.12
% 0.72/1.12 showgenerated = 0
% 0.72/1.12 showkept = 0
% 0.72/1.12 showselected = 0
% 0.72/1.12 showdeleted = 0
% 0.72/1.12 showresimp = 1
% 0.72/1.12 showstatus = 2000
% 0.72/1.12
% 0.72/1.12 prologoutput = 0
% 0.72/1.12 nrgoals = 5000000
% 0.72/1.12 totalproof = 1
% 0.72/1.12
% 0.72/1.12 Symbols occurring in the translation:
% 0.72/1.12
% 0.72/1.12 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.72/1.12 . [1, 2] (w:1, o:104, a:1, s:1, b:0),
% 0.72/1.12 ! [4, 1] (w:0, o:97, a:1, s:1, b:0),
% 0.72/1.12 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.72/1.12 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.72/1.12 vd436 [35, 0] (w:1, o:6, a:1, s:1, b:0),
% 0.72/1.12 vd437 [36, 0] (w:1, o:7, a:1, s:1, b:0),
% 0.72/1.12 vmul [37, 2] (w:1, o:128, a:1, s:1, b:0),
% 0.72/1.12 vd439 [38, 0] (w:1, o:8, a:1, s:1, b:0),
% 0.72/1.12 vplus [39, 2] (w:1, o:129, a:1, s:1, b:0),
% 0.72/1.12 vsucc [40, 1] (w:1, o:102, a:1, s:1, b:0),
% 0.72/1.12 v1 [41, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.72/1.12 less [51, 2] (w:1, o:130, a:1, s:1, b:0),
% 0.72/1.12 leq [52, 2] (w:1, o:131, a:1, s:1, b:0),
% 0.72/1.12 greater [55, 2] (w:1, o:132, a:1, s:1, b:0),
% 0.72/1.12 geq [56, 2] (w:1, o:133, a:1, s:1, b:0),
% 0.72/1.12 vskolem2 [127, 1] (w:1, o:103, a:1, s:1, b:0),
% 0.72/1.12 skol1 [134, 2] (w:1, o:134, a:1, s:1, b:1),
% 0.72/1.12 skol2 [135, 2] (w:1, o:135, a:1, s:1, b:1),
% 0.72/1.12 skol3 [136, 2] (w:1, o:136, a:1, s:1, b:1),
% 0.72/1.12 skol4 [137, 2] (w:1, o:137, a:1, s:1, b:1).
% 0.72/1.12
% 0.72/1.12
% 0.72/1.12 Starting Search:
% 0.72/1.12
% 0.72/1.12
% 0.72/1.12 Bliksems!, er is een bewijs:
% 0.72/1.12 % SZS status Theorem
% 0.72/1.12 % SZS output start Refutation
% 0.72/1.12
% 0.72/1.12 (0) {G0,W19,D5,L1,V0,M1} I { ! vplus( vmul( vd436, vd437 ), vplus( vmul(
% 0.72/1.12 vd436, vd439 ), vd436 ) ) ==> vplus( vplus( vmul( vd436, vd437 ), vmul(
% 0.72/1.12 vd436, vd439 ) ), vd436 ) }.
% 0.72/1.12 (57) {G0,W11,D4,L1,V3,M1} I { vplus( X, vplus( Y, Z ) ) ==> vplus( vplus( X
% 0.72/1.12 , Y ), Z ) }.
% 0.72/1.12 (73) {G1,W0,D0,L0,V0,M0} S(0);d(57);q { }.
% 0.72/1.12
% 0.72/1.12
% 0.72/1.12 % SZS output end Refutation
% 0.72/1.12 found a proof!
% 0.72/1.12
% 0.72/1.12
% 0.72/1.12 Unprocessed initial clauses:
% 0.72/1.12
% 0.72/1.12 (75) {G0,W19,D5,L1,V0,M1} { ! vplus( vplus( vmul( vd436, vd437 ), vmul(
% 0.72/1.12 vd436, vd439 ) ), vd436 ) = vplus( vmul( vd436, vd437 ), vplus( vmul(
% 0.72/1.12 vd436, vd439 ), vd436 ) ) }.
% 0.72/1.12 (76) {G0,W17,D5,L1,V0,M1} { vplus( vmul( vd436, vplus( vd437, vd439 ) ),
% 0.72/1.12 vd436 ) = vplus( vplus( vmul( vd436, vd437 ), vmul( vd436, vd439 ) ),
% 0.72/1.12 vd436 ) }.
% 0.72/1.12 (77) {G0,W14,D5,L1,V0,M1} { vmul( vd436, vsucc( vplus( vd437, vd439 ) ) )
% 0.72/1.12 = vplus( vmul( vd436, vplus( vd437, vd439 ) ), vd436 ) }.
% 0.72/1.12 (78) {G0,W13,D5,L1,V0,M1} { vmul( vd436, vplus( vd437, vsucc( vd439 ) ) )
% 0.72/1.12 = vmul( vd436, vsucc( vplus( vd437, vd439 ) ) ) }.
% 0.72/1.12 (79) {G0,W13,D4,L1,V0,M1} { vmul( vd436, vplus( vd437, vd439 ) ) = vplus(
% 0.72/1.12 vmul( vd436, vd437 ), vmul( vd436, vd439 ) ) }.
% 0.72/1.12 (80) {G0,W13,D4,L1,V0,M1} { vplus( vmul( vd436, vd437 ), vd436 ) = vplus(
% 0.72/1.12 vmul( vd436, vd437 ), vmul( vd436, v1 ) ) }.
% 0.72/1.12 (81) {G0,W10,D4,L1,V0,M1} { vmul( vd436, vsucc( vd437 ) ) = vplus( vmul(
% 0.72/1.12 vd436, vd437 ), vd436 ) }.
% 0.72/1.12 (82) {G0,W10,D4,L1,V0,M1} { vmul( vd436, vplus( vd437, v1 ) ) = vmul(
% 0.72/1.12 vd436, vsucc( vd437 ) ) }.
% 0.72/1.12 (83) {G0,W7,D3,L1,V2,M1} { vmul( X, Y ) = vmul( Y, X ) }.
% 0.72/1.12 (84) {G0,W10,D4,L1,V2,M1} { vmul( vsucc( X ), Y ) = vplus( vmul( X, Y ), Y
% 0.72/1.12 ) }.
% 0.72/1.12 (85) {G0,W5,D3,L1,V1,M1} { vmul( v1, X ) = X }.
% 0.72/1.12 (86) {G0,W10,D4,L1,V2,M1} { vmul( X, vsucc( Y ) ) = vplus( vmul( X, Y ), X
% 0.72/1.12 ) }.
% 0.72/1.12 (87) {G0,W5,D3,L1,V1,M1} { vmul( X, v1 ) = X }.
% 0.72/1.12 (88) {G0,W8,D3,L2,V2,M2} { ! less( X, vplus( Y, v1 ) ), leq( X, Y ) }.
% 0.72/1.12 (89) {G0,W8,D3,L2,V2,M2} { ! greater( X, Y ), geq( X, vplus( Y, v1 ) ) }.
% 0.72/1.12 (90) {G0,W3,D2,L1,V1,M1} { geq( X, v1 ) }.
% 0.72/1.12 (91) {G0,W13,D3,L3,V4,M3} { ! geq( Z, T ), ! geq( X, Y ), geq( vplus( X, Z
% 0.72/1.12 ), vplus( Y, T ) ) }.
% 0.72/1.12 (92) {G0,W13,D3,L3,V4,M3} { ! greater( Z, T ), ! geq( X, Y ), greater(
% 0.72/1.12 vplus( X, Z ), vplus( Y, T ) ) }.
% 0.72/1.12 (93) {G0,W13,D3,L3,V4,M3} { ! geq( Z, T ), ! greater( X, Y ), greater(
% 0.72/1.12 vplus( X, Z ), vplus( Y, T ) ) }.
% 0.72/1.12 (94) {G0,W13,D3,L3,V4,M3} { ! greater( Z, T ), ! greater( X, Y ), greater
% 0.72/1.12 ( vplus( X, Z ), vplus( Y, T ) ) }.
% 0.72/1.12 (95) {G0,W10,D3,L2,V3,M2} { ! less( vplus( X, Z ), vplus( Y, Z ) ), less(
% 0.72/1.12 X, Y ) }.
% 0.72/1.12 (96) {G0,W10,D3,L2,V3,M2} { ! vplus( X, Z ) = vplus( Y, Z ), X = Y }.
% 0.72/1.12 (97) {G0,W10,D3,L2,V3,M2} { ! greater( vplus( X, Z ), vplus( Y, Z ) ),
% 0.72/1.12 greater( X, Y ) }.
% 0.72/1.12 (98) {G0,W10,D3,L2,V3,M2} { ! less( X, Y ), less( vplus( X, Z ), vplus( Y
% 0.72/1.12 , Z ) ) }.
% 0.72/1.12 (99) {G0,W10,D3,L2,V3,M2} { ! X = Y, vplus( X, Z ) = vplus( Y, Z ) }.
% 0.72/1.12 (100) {G0,W10,D3,L2,V3,M2} { ! greater( X, Y ), greater( vplus( X, Z ),
% 0.72/1.12 vplus( Y, Z ) ) }.
% 0.72/1.12 (101) {G0,W5,D3,L1,V2,M1} { greater( vplus( X, Y ), X ) }.
% 0.72/1.12 (102) {G0,W9,D2,L3,V3,M3} { ! leq( Z, Y ), ! leq( X, Z ), leq( X, Y ) }.
% 0.72/1.12 (103) {G0,W9,D2,L3,V3,M3} { ! less( Z, Y ), ! leq( X, Z ), less( X, Y )
% 0.72/1.12 }.
% 0.72/1.12 (104) {G0,W9,D2,L3,V3,M3} { ! leq( Z, Y ), ! less( X, Z ), less( X, Y )
% 0.72/1.12 }.
% 0.72/1.12 (105) {G0,W9,D2,L3,V3,M3} { ! less( Z, Y ), ! less( X, Z ), less( X, Y )
% 0.72/1.12 }.
% 0.72/1.12 (106) {G0,W6,D2,L2,V2,M2} { ! leq( X, Y ), geq( Y, X ) }.
% 0.72/1.12 (107) {G0,W6,D2,L2,V2,M2} { ! geq( X, Y ), leq( Y, X ) }.
% 0.72/1.12 (108) {G0,W9,D2,L3,V2,M3} { ! leq( Y, X ), less( Y, X ), Y = X }.
% 0.72/1.12 (109) {G0,W6,D2,L2,V2,M2} { ! less( Y, X ), leq( Y, X ) }.
% 0.72/1.12 (110) {G0,W6,D2,L2,V2,M2} { ! Y = X, leq( Y, X ) }.
% 0.72/1.12 (111) {G0,W9,D2,L3,V2,M3} { ! geq( Y, X ), greater( Y, X ), Y = X }.
% 0.72/1.12 (112) {G0,W6,D2,L2,V2,M2} { ! greater( Y, X ), geq( Y, X ) }.
% 0.72/1.12 (113) {G0,W6,D2,L2,V2,M2} { ! Y = X, geq( Y, X ) }.
% 0.72/1.12 (114) {G0,W6,D2,L2,V2,M2} { ! less( X, Y ), greater( Y, X ) }.
% 0.72/1.12 (115) {G0,W6,D2,L2,V2,M2} { ! greater( X, Y ), less( Y, X ) }.
% 0.72/1.12 (116) {G0,W9,D2,L3,V2,M3} { X = Y, greater( X, Y ), less( X, Y ) }.
% 0.72/1.12 (117) {G0,W6,D2,L2,V2,M2} { ! X = Y, ! less( X, Y ) }.
% 0.72/1.12 (118) {G0,W6,D2,L2,V2,M2} { ! greater( X, Y ), ! less( X, Y ) }.
% 0.72/1.12 (119) {G0,W6,D2,L2,V2,M2} { ! X = Y, ! greater( X, Y ) }.
% 0.72/1.12 (120) {G0,W10,D4,L2,V2,M2} { ! less( Y, X ), X = vplus( Y, skol1( X, Y ) )
% 0.72/1.12 }.
% 0.72/1.12 (121) {G0,W8,D3,L2,V3,M2} { ! X = vplus( Y, Z ), less( Y, X ) }.
% 0.72/1.12 (122) {G0,W10,D4,L2,V2,M2} { ! greater( Y, X ), Y = vplus( X, skol2( X, Y
% 0.72/1.12 ) ) }.
% 0.72/1.12 (123) {G0,W8,D3,L2,V3,M2} { ! Y = vplus( X, Z ), greater( Y, X ) }.
% 0.72/1.12 (124) {G0,W17,D4,L3,V2,M3} { X = Y, X = vplus( Y, skol3( X, Y ) ), Y =
% 0.72/1.12 vplus( X, skol4( X, Y ) ) }.
% 0.72/1.12 (125) {G0,W8,D3,L2,V3,M2} { ! X = Y, ! Y = vplus( X, Z ) }.
% 0.72/1.12 (126) {G0,W10,D3,L2,V4,M2} { ! X = vplus( Y, Z ), ! Y = vplus( X, T ) }.
% 0.72/1.12 (127) {G0,W8,D3,L2,V3,M2} { ! X = Y, ! X = vplus( Y, Z ) }.
% 0.72/1.12 (128) {G0,W10,D3,L2,V3,M2} { X = Y, ! vplus( Z, X ) = vplus( Z, Y ) }.
% 0.72/1.12 (129) {G0,W5,D3,L1,V2,M1} { ! Y = vplus( X, Y ) }.
% 0.72/1.12 (130) {G0,W7,D3,L1,V2,M1} { vplus( Y, X ) = vplus( X, Y ) }.
% 0.72/1.12 (131) {G0,W9,D4,L1,V2,M1} { vplus( vsucc( X ), Y ) = vsucc( vplus( X, Y )
% 0.72/1.12 ) }.
% 0.72/1.12 (132) {G0,W6,D3,L1,V1,M1} { vplus( v1, X ) = vsucc( X ) }.
% 0.72/1.12 (133) {G0,W11,D4,L1,V3,M1} { vplus( vplus( X, Y ), Z ) = vplus( X, vplus(
% 0.72/1.12 Y, Z ) ) }.
% 0.72/1.12 (134) {G0,W9,D4,L1,V2,M1} { vplus( X, vsucc( Y ) ) = vsucc( vplus( X, Y )
% 0.72/1.12 ) }.
% 0.72/1.12 (135) {G0,W6,D3,L1,V1,M1} { vplus( X, v1 ) = vsucc( X ) }.
% 0.72/1.12 (136) {G0,W8,D4,L2,V1,M2} { X = v1, X = vsucc( vskolem2( X ) ) }.
% 0.72/1.12 (137) {G0,W4,D3,L1,V1,M1} { ! vsucc( X ) = X }.
% 0.72/1.12 (138) {G0,W8,D3,L2,V2,M2} { X = Y, ! vsucc( X ) = vsucc( Y ) }.
% 0.72/1.12 (139) {G0,W8,D3,L2,V2,M2} { ! vsucc( X ) = vsucc( Y ), X = Y }.
% 0.72/1.12 (140) {G0,W4,D3,L1,V1,M1} { ! vsucc( X ) = v1 }.
% 0.72/1.12
% 0.72/1.12
% 0.72/1.12 Total Proof:
% 0.72/1.12
% 0.72/1.12 eqswap: (141) {G0,W19,D5,L1,V0,M1} { ! vplus( vmul( vd436, vd437 ), vplus
% 0.72/1.12 ( vmul( vd436, vd439 ), vd436 ) ) = vplus( vplus( vmul( vd436, vd437 ),
% 0.72/1.12 vmul( vd436, vd439 ) ), vd436 ) }.
% 0.72/1.12 parent0[0]: (75) {G0,W19,D5,L1,V0,M1} { ! vplus( vplus( vmul( vd436, vd437
% 0.72/1.12 ), vmul( vd436, vd439 ) ), vd436 ) = vplus( vmul( vd436, vd437 ), vplus
% 0.72/1.12 ( vmul( vd436, vd439 ), vd436 ) ) }.
% 0.72/1.12 substitution0:
% 0.72/1.12 end
% 0.72/1.12
% 0.72/1.12 subsumption: (0) {G0,W19,D5,L1,V0,M1} I { ! vplus( vmul( vd436, vd437 ),
% 0.72/1.12 vplus( vmul( vd436, vd439 ), vd436 ) ) ==> vplus( vplus( vmul( vd436,
% 0.72/1.12 vd437 ), vmul( vd436, vd439 ) ), vd436 ) }.
% 0.72/1.12 parent0: (141) {G0,W19,D5,L1,V0,M1} { ! vplus( vmul( vd436, vd437 ), vplus
% 0.72/1.12 ( vmul( vd436, vd439 ), vd436 ) ) = vplus( vplus( vmul( vd436, vd437 ),
% 0.72/1.12 vmul( vd436, vd439 ) ), vd436 ) }.
% 0.72/1.12 substitution0:
% 0.72/1.12 end
% 0.72/1.12 permutation0:
% 0.72/1.12 0 ==> 0
% 0.72/1.12 end
% 0.72/1.12
% 0.72/1.12 eqswap: (192) {G0,W11,D4,L1,V3,M1} { vplus( X, vplus( Y, Z ) ) = vplus(
% 0.72/1.12 vplus( X, Y ), Z ) }.
% 0.72/1.12 parent0[0]: (133) {G0,W11,D4,L1,V3,M1} { vplus( vplus( X, Y ), Z ) = vplus
% 0.72/1.12 ( X, vplus( Y, Z ) ) }.
% 0.72/1.12 substitution0:
% 0.72/1.12 X := X
% 0.72/1.12 Y := Y
% 0.72/1.12 Z := Z
% 0.72/1.12 end
% 0.72/1.12
% 0.72/1.12 subsumption: (57) {G0,W11,D4,L1,V3,M1} I { vplus( X, vplus( Y, Z ) ) ==>
% 0.72/1.12 vplus( vplus( X, Y ), Z ) }.
% 0.72/1.12 parent0: (192) {G0,W11,D4,L1,V3,M1} { vplus( X, vplus( Y, Z ) ) = vplus(
% 0.72/1.12 vplus( X, Y ), Z ) }.
% 0.72/1.12 substitution0:
% 0.72/1.12 X := X
% 0.72/1.12 Y := Y
% 0.72/1.12 Z := Z
% 0.72/1.12 end
% 0.72/1.12 permutation0:
% 0.72/1.12 0 ==> 0
% 0.72/1.12 end
% 0.72/1.12
% 0.72/1.12 paramod: (195) {G1,W19,D5,L1,V0,M1} { ! vplus( vplus( vmul( vd436, vd437 )
% 0.72/1.12 , vmul( vd436, vd439 ) ), vd436 ) ==> vplus( vplus( vmul( vd436, vd437 )
% 0.72/1.12 , vmul( vd436, vd439 ) ), vd436 ) }.
% 0.72/1.12 parent0[0]: (57) {G0,W11,D4,L1,V3,M1} I { vplus( X, vplus( Y, Z ) ) ==>
% 0.72/1.12 vplus( vplus( X, Y ), Z ) }.
% 0.72/1.12 parent1[0; 2]: (0) {G0,W19,D5,L1,V0,M1} I { ! vplus( vmul( vd436, vd437 ),
% 0.72/1.12 vplus( vmul( vd436, vd439 ), vd436 ) ) ==> vplus( vplus( vmul( vd436,
% 0.72/1.12 vd437 ), vmul( vd436, vd439 ) ), vd436 ) }.
% 0.72/1.12 substitution0:
% 0.72/1.12 X := vmul( vd436, vd437 )
% 0.72/1.12 Y := vmul( vd436, vd439 )
% 0.72/1.12 Z := vd436
% 0.72/1.12 end
% 0.72/1.12 substitution1:
% 0.72/1.12 end
% 0.72/1.12
% 0.72/1.12 eqrefl: (196) {G0,W0,D0,L0,V0,M0} { }.
% 0.72/1.12 parent0[0]: (195) {G1,W19,D5,L1,V0,M1} { ! vplus( vplus( vmul( vd436,
% 0.72/1.12 vd437 ), vmul( vd436, vd439 ) ), vd436 ) ==> vplus( vplus( vmul( vd436,
% 0.72/1.12 vd437 ), vmul( vd436, vd439 ) ), vd436 ) }.
% 0.72/1.12 substitution0:
% 0.72/1.12 end
% 0.72/1.12
% 0.72/1.12 subsumption: (73) {G1,W0,D0,L0,V0,M0} S(0);d(57);q { }.
% 0.72/1.12 parent0: (196) {G0,W0,D0,L0,V0,M0} { }.
% 0.72/1.12 substitution0:
% 0.72/1.12 end
% 0.72/1.12 permutation0:
% 0.72/1.12 end
% 0.72/1.12
% 0.72/1.12 Proof check complete!
% 0.72/1.12
% 0.72/1.12 Memory use:
% 0.72/1.12
% 0.72/1.12 space for terms: 2335
% 0.72/1.12 space for clauses: 5357
% 0.72/1.12
% 0.72/1.12
% 0.72/1.12 clauses generated: 86
% 0.72/1.12 clauses kept: 74
% 0.72/1.12 clauses selected: 5
% 0.72/1.12 clauses deleted: 1
% 0.72/1.12 clauses inuse deleted: 0
% 0.72/1.12
% 0.72/1.12 subsentry: 549
% 0.72/1.12 literals s-matched: 283
% 0.72/1.12 literals matched: 283
% 0.72/1.12 full subsumption: 92
% 0.72/1.12
% 0.72/1.12 checksum: -372041449
% 0.72/1.12
% 0.72/1.12
% 0.72/1.12 Bliksem ended
%------------------------------------------------------------------------------