TSTP Solution File: NUM846+1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : NUM846+1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n009.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 06:27:00 EDT 2022
% Result : Theorem 0.43s 1.06s
% Output : Refutation 0.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : NUM846+1 : TPTP v8.1.0. Released v4.1.0.
% 0.12/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n009.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 : Wed Jul 6 19:44:52 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.43/1.06 *** allocated 10000 integers for termspace/termends
% 0.43/1.06 *** allocated 10000 integers for clauses
% 0.43/1.06 *** allocated 10000 integers for justifications
% 0.43/1.06 Bliksem 1.12
% 0.43/1.06
% 0.43/1.06
% 0.43/1.06 Automatic Strategy Selection
% 0.43/1.06
% 0.43/1.06
% 0.43/1.06 Clauses:
% 0.43/1.06
% 0.43/1.06 { ! vplus( vmul( vd436, vplus( vd437, vd439 ) ), vd436 ) = vplus( vplus(
% 0.43/1.06 vmul( vd436, vd437 ), vmul( vd436, vd439 ) ), vd436 ) }.
% 0.43/1.06 { vmul( vd436, vsucc( vplus( vd437, vd439 ) ) ) = vplus( vmul( vd436, vplus
% 0.43/1.06 ( vd437, vd439 ) ), vd436 ) }.
% 0.43/1.06 { vmul( vd436, vplus( vd437, vsucc( vd439 ) ) ) = vmul( vd436, vsucc( vplus
% 0.43/1.06 ( vd437, vd439 ) ) ) }.
% 0.43/1.06 { vmul( vd436, vplus( vd437, vd439 ) ) = vplus( vmul( vd436, vd437 ), vmul
% 0.43/1.06 ( vd436, vd439 ) ) }.
% 0.43/1.06 { vplus( vmul( vd436, vd437 ), vd436 ) = vplus( vmul( vd436, vd437 ), vmul
% 0.43/1.06 ( vd436, v1 ) ) }.
% 0.43/1.06 { vmul( vd436, vsucc( vd437 ) ) = vplus( vmul( vd436, vd437 ), vd436 ) }.
% 0.43/1.06 { vmul( vd436, vplus( vd437, v1 ) ) = vmul( vd436, vsucc( vd437 ) ) }.
% 0.43/1.06 { vmul( X, Y ) = vmul( Y, X ) }.
% 0.43/1.06 { vmul( vsucc( X ), Y ) = vplus( vmul( X, Y ), Y ) }.
% 0.43/1.06 { vmul( v1, X ) = X }.
% 0.43/1.06 { vmul( X, vsucc( Y ) ) = vplus( vmul( X, Y ), X ) }.
% 0.43/1.06 { vmul( X, v1 ) = X }.
% 0.43/1.06 { ! less( X, vplus( Y, v1 ) ), leq( X, Y ) }.
% 0.43/1.06 { ! greater( X, Y ), geq( X, vplus( Y, v1 ) ) }.
% 0.43/1.06 { geq( X, v1 ) }.
% 0.43/1.06 { ! geq( Z, T ), ! geq( X, Y ), geq( vplus( X, Z ), vplus( Y, T ) ) }.
% 0.43/1.06 { ! greater( Z, T ), ! geq( X, Y ), greater( vplus( X, Z ), vplus( Y, T ) )
% 0.43/1.06 }.
% 0.43/1.06 { ! geq( Z, T ), ! greater( X, Y ), greater( vplus( X, Z ), vplus( Y, T ) )
% 0.43/1.06 }.
% 0.43/1.06 { ! greater( Z, T ), ! greater( X, Y ), greater( vplus( X, Z ), vplus( Y, T
% 0.43/1.06 ) ) }.
% 0.43/1.06 { ! less( vplus( X, Z ), vplus( Y, Z ) ), less( X, Y ) }.
% 0.43/1.06 { ! vplus( X, Z ) = vplus( Y, Z ), X = Y }.
% 0.43/1.06 { ! greater( vplus( X, Z ), vplus( Y, Z ) ), greater( X, Y ) }.
% 0.43/1.06 { ! less( X, Y ), less( vplus( X, Z ), vplus( Y, Z ) ) }.
% 0.43/1.06 { ! X = Y, vplus( X, Z ) = vplus( Y, Z ) }.
% 0.43/1.06 { ! greater( X, Y ), greater( vplus( X, Z ), vplus( Y, Z ) ) }.
% 0.43/1.06 { greater( vplus( X, Y ), X ) }.
% 0.43/1.06 { ! leq( Z, Y ), ! leq( X, Z ), leq( X, Y ) }.
% 0.43/1.06 { ! less( Z, Y ), ! leq( X, Z ), less( X, Y ) }.
% 0.43/1.06 { ! leq( Z, Y ), ! less( X, Z ), less( X, Y ) }.
% 0.43/1.06 { ! less( Z, Y ), ! less( X, Z ), less( X, Y ) }.
% 0.43/1.06 { ! leq( X, Y ), geq( Y, X ) }.
% 0.43/1.06 { ! geq( X, Y ), leq( Y, X ) }.
% 0.43/1.06 { ! leq( Y, X ), less( Y, X ), Y = X }.
% 0.43/1.06 { ! less( Y, X ), leq( Y, X ) }.
% 0.43/1.06 { ! Y = X, leq( Y, X ) }.
% 0.43/1.06 { ! geq( Y, X ), greater( Y, X ), Y = X }.
% 0.43/1.06 { ! greater( Y, X ), geq( Y, X ) }.
% 0.43/1.06 { ! Y = X, geq( Y, X ) }.
% 0.43/1.06 { ! less( X, Y ), greater( Y, X ) }.
% 0.43/1.06 { ! greater( X, Y ), less( Y, X ) }.
% 0.43/1.06 { X = Y, greater( X, Y ), less( X, Y ) }.
% 0.43/1.06 { ! X = Y, ! less( X, Y ) }.
% 0.43/1.06 { ! greater( X, Y ), ! less( X, Y ) }.
% 0.43/1.06 { ! X = Y, ! greater( X, Y ) }.
% 0.43/1.06 { ! less( Y, X ), X = vplus( Y, skol1( X, Y ) ) }.
% 0.43/1.06 { ! X = vplus( Y, Z ), less( Y, X ) }.
% 0.43/1.06 { ! greater( Y, X ), Y = vplus( X, skol2( X, Y ) ) }.
% 0.43/1.06 { ! Y = vplus( X, Z ), greater( Y, X ) }.
% 0.43/1.06 { X = Y, X = vplus( Y, skol3( X, Y ) ), Y = vplus( X, skol4( X, Y ) ) }.
% 0.43/1.06 { ! X = Y, ! Y = vplus( X, Z ) }.
% 0.43/1.06 { ! X = vplus( Y, Z ), ! Y = vplus( X, T ) }.
% 0.43/1.06 { ! X = Y, ! X = vplus( Y, Z ) }.
% 0.43/1.06 { X = Y, ! vplus( Z, X ) = vplus( Z, Y ) }.
% 0.43/1.06 { ! Y = vplus( X, Y ) }.
% 0.43/1.06 { vplus( Y, X ) = vplus( X, Y ) }.
% 0.43/1.06 { vplus( vsucc( X ), Y ) = vsucc( vplus( X, Y ) ) }.
% 0.43/1.06 { vplus( v1, X ) = vsucc( X ) }.
% 0.43/1.06 { vplus( vplus( X, Y ), Z ) = vplus( X, vplus( Y, Z ) ) }.
% 0.43/1.06 { vplus( X, vsucc( Y ) ) = vsucc( vplus( X, Y ) ) }.
% 0.43/1.06 { vplus( X, v1 ) = vsucc( X ) }.
% 0.43/1.06 { X = v1, X = vsucc( vskolem2( X ) ) }.
% 0.43/1.06 { ! vsucc( X ) = X }.
% 0.43/1.06 { X = Y, ! vsucc( X ) = vsucc( Y ) }.
% 0.43/1.06 { ! vsucc( X ) = vsucc( Y ), X = Y }.
% 0.43/1.06 { ! vsucc( X ) = v1 }.
% 0.43/1.06
% 0.43/1.06 percentage equality = 0.435897, percentage horn = 0.921875
% 0.43/1.06 This is a problem with some equality
% 0.43/1.06
% 0.43/1.06
% 0.43/1.06
% 0.43/1.06 Options Used:
% 0.43/1.06
% 0.43/1.06 useres = 1
% 0.43/1.06 useparamod = 1
% 0.43/1.06 useeqrefl = 1
% 0.43/1.06 useeqfact = 1
% 0.43/1.06 usefactor = 1
% 0.43/1.06 usesimpsplitting = 0
% 0.43/1.06 usesimpdemod = 5
% 0.43/1.06 usesimpres = 3
% 0.43/1.06
% 0.43/1.06 resimpinuse = 1000
% 0.43/1.06 resimpclauses = 20000
% 0.43/1.06 substype = eqrewr
% 0.43/1.06 backwardsubs = 1
% 0.43/1.06 selectoldest = 5
% 0.43/1.06
% 0.43/1.06 litorderings [0] = split
% 0.43/1.06 litorderings [1] = extend the termordering, first sorting on arguments
% 0.43/1.06
% 0.43/1.06 termordering = kbo
% 0.43/1.06
% 0.43/1.06 litapriori = 0
% 0.43/1.06 termapriori = 1
% 0.43/1.06 litaposteriori = 0
% 0.43/1.06 termaposteriori = 0
% 0.43/1.06 demodaposteriori = 0
% 0.43/1.06 ordereqreflfact = 0
% 0.43/1.06
% 0.43/1.06 litselect = negord
% 0.43/1.06
% 0.43/1.06 maxweight = 15
% 0.43/1.06 maxdepth = 30000
% 0.43/1.06 maxlength = 115
% 0.43/1.06 maxnrvars = 195
% 0.43/1.06 excuselevel = 1
% 0.43/1.06 increasemaxweight = 1
% 0.43/1.06
% 0.43/1.06 maxselected = 10000000
% 0.43/1.06 maxnrclauses = 10000000
% 0.43/1.06
% 0.43/1.06 showgenerated = 0
% 0.43/1.06 showkept = 0
% 0.43/1.06 showselected = 0
% 0.43/1.06 showdeleted = 0
% 0.43/1.06 showresimp = 1
% 0.43/1.06 showstatus = 2000
% 0.43/1.06
% 0.43/1.06 prologoutput = 0
% 0.43/1.06 nrgoals = 5000000
% 0.43/1.06 totalproof = 1
% 0.43/1.06
% 0.43/1.06 Symbols occurring in the translation:
% 0.43/1.06
% 0.43/1.06 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.43/1.06 . [1, 2] (w:1, o:104, a:1, s:1, b:0),
% 0.43/1.06 ! [4, 1] (w:0, o:97, a:1, s:1, b:0),
% 0.43/1.06 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.43/1.06 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.43/1.06 vd436 [35, 0] (w:1, o:6, a:1, s:1, b:0),
% 0.43/1.06 vd437 [36, 0] (w:1, o:7, a:1, s:1, b:0),
% 0.43/1.06 vd439 [37, 0] (w:1, o:8, a:1, s:1, b:0),
% 0.43/1.06 vplus [38, 2] (w:1, o:128, a:1, s:1, b:0),
% 0.43/1.06 vmul [39, 2] (w:1, o:129, a:1, s:1, b:0),
% 0.43/1.06 vsucc [40, 1] (w:1, o:102, a:1, s:1, b:0),
% 0.43/1.06 v1 [41, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.43/1.06 less [51, 2] (w:1, o:130, a:1, s:1, b:0),
% 0.43/1.06 leq [52, 2] (w:1, o:131, a:1, s:1, b:0),
% 0.43/1.06 greater [55, 2] (w:1, o:132, a:1, s:1, b:0),
% 0.43/1.06 geq [56, 2] (w:1, o:133, a:1, s:1, b:0),
% 0.43/1.06 vskolem2 [127, 1] (w:1, o:103, a:1, s:1, b:0),
% 0.43/1.06 skol1 [134, 2] (w:1, o:134, a:1, s:1, b:1),
% 0.43/1.06 skol2 [135, 2] (w:1, o:135, a:1, s:1, b:1),
% 0.43/1.06 skol3 [136, 2] (w:1, o:136, a:1, s:1, b:1),
% 0.43/1.06 skol4 [137, 2] (w:1, o:137, a:1, s:1, b:1).
% 0.43/1.06
% 0.43/1.06
% 0.43/1.06 Starting Search:
% 0.43/1.06
% 0.43/1.06
% 0.43/1.06 Bliksems!, er is een bewijs:
% 0.43/1.06 % SZS status Theorem
% 0.43/1.06 % SZS output start Refutation
% 0.43/1.06
% 0.43/1.06 (0) {G0,W17,D5,L1,V0,M1} I { ! vplus( vplus( vmul( vd436, vd437 ), vmul(
% 0.43/1.06 vd436, vd439 ) ), vd436 ) ==> vplus( vmul( vd436, vplus( vd437, vd439 ) )
% 0.43/1.06 , vd436 ) }.
% 0.43/1.06 (3) {G0,W13,D4,L1,V0,M1} I { vplus( vmul( vd436, vd437 ), vmul( vd436,
% 0.43/1.06 vd439 ) ) ==> vmul( vd436, vplus( vd437, vd439 ) ) }.
% 0.43/1.06 (72) {G1,W0,D0,L0,V0,M0} S(0);d(3);q { }.
% 0.43/1.06
% 0.43/1.06
% 0.43/1.06 % SZS output end Refutation
% 0.43/1.06 found a proof!
% 0.43/1.06
% 0.43/1.06
% 0.43/1.06 Unprocessed initial clauses:
% 0.43/1.06
% 0.43/1.06 (74) {G0,W17,D5,L1,V0,M1} { ! vplus( vmul( vd436, vplus( vd437, vd439 ) )
% 0.43/1.06 , vd436 ) = vplus( vplus( vmul( vd436, vd437 ), vmul( vd436, vd439 ) ),
% 0.43/1.06 vd436 ) }.
% 0.43/1.06 (75) {G0,W14,D5,L1,V0,M1} { vmul( vd436, vsucc( vplus( vd437, vd439 ) ) )
% 0.43/1.06 = vplus( vmul( vd436, vplus( vd437, vd439 ) ), vd436 ) }.
% 0.43/1.06 (76) {G0,W13,D5,L1,V0,M1} { vmul( vd436, vplus( vd437, vsucc( vd439 ) ) )
% 0.43/1.06 = vmul( vd436, vsucc( vplus( vd437, vd439 ) ) ) }.
% 0.43/1.06 (77) {G0,W13,D4,L1,V0,M1} { vmul( vd436, vplus( vd437, vd439 ) ) = vplus(
% 0.43/1.06 vmul( vd436, vd437 ), vmul( vd436, vd439 ) ) }.
% 0.43/1.06 (78) {G0,W13,D4,L1,V0,M1} { vplus( vmul( vd436, vd437 ), vd436 ) = vplus(
% 0.43/1.06 vmul( vd436, vd437 ), vmul( vd436, v1 ) ) }.
% 0.43/1.06 (79) {G0,W10,D4,L1,V0,M1} { vmul( vd436, vsucc( vd437 ) ) = vplus( vmul(
% 0.43/1.06 vd436, vd437 ), vd436 ) }.
% 0.43/1.06 (80) {G0,W10,D4,L1,V0,M1} { vmul( vd436, vplus( vd437, v1 ) ) = vmul(
% 0.43/1.06 vd436, vsucc( vd437 ) ) }.
% 0.43/1.06 (81) {G0,W7,D3,L1,V2,M1} { vmul( X, Y ) = vmul( Y, X ) }.
% 0.43/1.06 (82) {G0,W10,D4,L1,V2,M1} { vmul( vsucc( X ), Y ) = vplus( vmul( X, Y ), Y
% 0.43/1.06 ) }.
% 0.43/1.06 (83) {G0,W5,D3,L1,V1,M1} { vmul( v1, X ) = X }.
% 0.43/1.06 (84) {G0,W10,D4,L1,V2,M1} { vmul( X, vsucc( Y ) ) = vplus( vmul( X, Y ), X
% 0.43/1.06 ) }.
% 0.43/1.06 (85) {G0,W5,D3,L1,V1,M1} { vmul( X, v1 ) = X }.
% 0.43/1.06 (86) {G0,W8,D3,L2,V2,M2} { ! less( X, vplus( Y, v1 ) ), leq( X, Y ) }.
% 0.43/1.06 (87) {G0,W8,D3,L2,V2,M2} { ! greater( X, Y ), geq( X, vplus( Y, v1 ) ) }.
% 0.43/1.06 (88) {G0,W3,D2,L1,V1,M1} { geq( X, v1 ) }.
% 0.43/1.06 (89) {G0,W13,D3,L3,V4,M3} { ! geq( Z, T ), ! geq( X, Y ), geq( vplus( X, Z
% 0.43/1.06 ), vplus( Y, T ) ) }.
% 0.43/1.06 (90) {G0,W13,D3,L3,V4,M3} { ! greater( Z, T ), ! geq( X, Y ), greater(
% 0.43/1.06 vplus( X, Z ), vplus( Y, T ) ) }.
% 0.43/1.06 (91) {G0,W13,D3,L3,V4,M3} { ! geq( Z, T ), ! greater( X, Y ), greater(
% 0.43/1.06 vplus( X, Z ), vplus( Y, T ) ) }.
% 0.43/1.06 (92) {G0,W13,D3,L3,V4,M3} { ! greater( Z, T ), ! greater( X, Y ), greater
% 0.43/1.06 ( vplus( X, Z ), vplus( Y, T ) ) }.
% 0.43/1.06 (93) {G0,W10,D3,L2,V3,M2} { ! less( vplus( X, Z ), vplus( Y, Z ) ), less(
% 0.43/1.06 X, Y ) }.
% 0.43/1.06 (94) {G0,W10,D3,L2,V3,M2} { ! vplus( X, Z ) = vplus( Y, Z ), X = Y }.
% 0.43/1.06 (95) {G0,W10,D3,L2,V3,M2} { ! greater( vplus( X, Z ), vplus( Y, Z ) ),
% 0.43/1.06 greater( X, Y ) }.
% 0.43/1.06 (96) {G0,W10,D3,L2,V3,M2} { ! less( X, Y ), less( vplus( X, Z ), vplus( Y
% 0.43/1.06 , Z ) ) }.
% 0.43/1.06 (97) {G0,W10,D3,L2,V3,M2} { ! X = Y, vplus( X, Z ) = vplus( Y, Z ) }.
% 0.43/1.06 (98) {G0,W10,D3,L2,V3,M2} { ! greater( X, Y ), greater( vplus( X, Z ),
% 0.43/1.06 vplus( Y, Z ) ) }.
% 0.43/1.06 (99) {G0,W5,D3,L1,V2,M1} { greater( vplus( X, Y ), X ) }.
% 0.43/1.06 (100) {G0,W9,D2,L3,V3,M3} { ! leq( Z, Y ), ! leq( X, Z ), leq( X, Y ) }.
% 0.43/1.06 (101) {G0,W9,D2,L3,V3,M3} { ! less( Z, Y ), ! leq( X, Z ), less( X, Y )
% 0.43/1.06 }.
% 0.43/1.06 (102) {G0,W9,D2,L3,V3,M3} { ! leq( Z, Y ), ! less( X, Z ), less( X, Y )
% 0.43/1.06 }.
% 0.43/1.06 (103) {G0,W9,D2,L3,V3,M3} { ! less( Z, Y ), ! less( X, Z ), less( X, Y )
% 0.43/1.06 }.
% 0.43/1.06 (104) {G0,W6,D2,L2,V2,M2} { ! leq( X, Y ), geq( Y, X ) }.
% 0.43/1.06 (105) {G0,W6,D2,L2,V2,M2} { ! geq( X, Y ), leq( Y, X ) }.
% 0.43/1.06 (106) {G0,W9,D2,L3,V2,M3} { ! leq( Y, X ), less( Y, X ), Y = X }.
% 0.43/1.06 (107) {G0,W6,D2,L2,V2,M2} { ! less( Y, X ), leq( Y, X ) }.
% 0.43/1.06 (108) {G0,W6,D2,L2,V2,M2} { ! Y = X, leq( Y, X ) }.
% 0.43/1.06 (109) {G0,W9,D2,L3,V2,M3} { ! geq( Y, X ), greater( Y, X ), Y = X }.
% 0.43/1.06 (110) {G0,W6,D2,L2,V2,M2} { ! greater( Y, X ), geq( Y, X ) }.
% 0.43/1.06 (111) {G0,W6,D2,L2,V2,M2} { ! Y = X, geq( Y, X ) }.
% 0.43/1.06 (112) {G0,W6,D2,L2,V2,M2} { ! less( X, Y ), greater( Y, X ) }.
% 0.43/1.06 (113) {G0,W6,D2,L2,V2,M2} { ! greater( X, Y ), less( Y, X ) }.
% 0.43/1.06 (114) {G0,W9,D2,L3,V2,M3} { X = Y, greater( X, Y ), less( X, Y ) }.
% 0.43/1.06 (115) {G0,W6,D2,L2,V2,M2} { ! X = Y, ! less( X, Y ) }.
% 0.43/1.06 (116) {G0,W6,D2,L2,V2,M2} { ! greater( X, Y ), ! less( X, Y ) }.
% 0.43/1.06 (117) {G0,W6,D2,L2,V2,M2} { ! X = Y, ! greater( X, Y ) }.
% 0.43/1.06 (118) {G0,W10,D4,L2,V2,M2} { ! less( Y, X ), X = vplus( Y, skol1( X, Y ) )
% 0.43/1.06 }.
% 0.43/1.06 (119) {G0,W8,D3,L2,V3,M2} { ! X = vplus( Y, Z ), less( Y, X ) }.
% 0.43/1.06 (120) {G0,W10,D4,L2,V2,M2} { ! greater( Y, X ), Y = vplus( X, skol2( X, Y
% 0.43/1.06 ) ) }.
% 0.43/1.06 (121) {G0,W8,D3,L2,V3,M2} { ! Y = vplus( X, Z ), greater( Y, X ) }.
% 0.43/1.06 (122) {G0,W17,D4,L3,V2,M3} { X = Y, X = vplus( Y, skol3( X, Y ) ), Y =
% 0.43/1.06 vplus( X, skol4( X, Y ) ) }.
% 0.43/1.06 (123) {G0,W8,D3,L2,V3,M2} { ! X = Y, ! Y = vplus( X, Z ) }.
% 0.43/1.06 (124) {G0,W10,D3,L2,V4,M2} { ! X = vplus( Y, Z ), ! Y = vplus( X, T ) }.
% 0.43/1.06 (125) {G0,W8,D3,L2,V3,M2} { ! X = Y, ! X = vplus( Y, Z ) }.
% 0.43/1.06 (126) {G0,W10,D3,L2,V3,M2} { X = Y, ! vplus( Z, X ) = vplus( Z, Y ) }.
% 0.43/1.06 (127) {G0,W5,D3,L1,V2,M1} { ! Y = vplus( X, Y ) }.
% 0.43/1.06 (128) {G0,W7,D3,L1,V2,M1} { vplus( Y, X ) = vplus( X, Y ) }.
% 0.43/1.06 (129) {G0,W9,D4,L1,V2,M1} { vplus( vsucc( X ), Y ) = vsucc( vplus( X, Y )
% 0.43/1.06 ) }.
% 0.43/1.06 (130) {G0,W6,D3,L1,V1,M1} { vplus( v1, X ) = vsucc( X ) }.
% 0.43/1.06 (131) {G0,W11,D4,L1,V3,M1} { vplus( vplus( X, Y ), Z ) = vplus( X, vplus(
% 0.43/1.06 Y, Z ) ) }.
% 0.43/1.06 (132) {G0,W9,D4,L1,V2,M1} { vplus( X, vsucc( Y ) ) = vsucc( vplus( X, Y )
% 0.43/1.06 ) }.
% 0.43/1.06 (133) {G0,W6,D3,L1,V1,M1} { vplus( X, v1 ) = vsucc( X ) }.
% 0.43/1.06 (134) {G0,W8,D4,L2,V1,M2} { X = v1, X = vsucc( vskolem2( X ) ) }.
% 0.43/1.06 (135) {G0,W4,D3,L1,V1,M1} { ! vsucc( X ) = X }.
% 0.43/1.06 (136) {G0,W8,D3,L2,V2,M2} { X = Y, ! vsucc( X ) = vsucc( Y ) }.
% 0.43/1.06 (137) {G0,W8,D3,L2,V2,M2} { ! vsucc( X ) = vsucc( Y ), X = Y }.
% 0.43/1.06 (138) {G0,W4,D3,L1,V1,M1} { ! vsucc( X ) = v1 }.
% 0.43/1.06
% 0.43/1.06
% 0.43/1.06 Total Proof:
% 0.43/1.06
% 0.43/1.06 eqswap: (139) {G0,W17,D5,L1,V0,M1} { ! vplus( vplus( vmul( vd436, vd437 )
% 0.43/1.06 , vmul( vd436, vd439 ) ), vd436 ) = vplus( vmul( vd436, vplus( vd437,
% 0.43/1.07 vd439 ) ), vd436 ) }.
% 0.43/1.07 parent0[0]: (74) {G0,W17,D5,L1,V0,M1} { ! vplus( vmul( vd436, vplus( vd437
% 0.43/1.07 , vd439 ) ), vd436 ) = vplus( vplus( vmul( vd436, vd437 ), vmul( vd436,
% 0.43/1.07 vd439 ) ), vd436 ) }.
% 0.43/1.07 substitution0:
% 0.43/1.07 end
% 0.43/1.07
% 0.43/1.07 subsumption: (0) {G0,W17,D5,L1,V0,M1} I { ! vplus( vplus( vmul( vd436,
% 0.43/1.07 vd437 ), vmul( vd436, vd439 ) ), vd436 ) ==> vplus( vmul( vd436, vplus(
% 0.43/1.07 vd437, vd439 ) ), vd436 ) }.
% 0.43/1.07 parent0: (139) {G0,W17,D5,L1,V0,M1} { ! vplus( vplus( vmul( vd436, vd437 )
% 0.43/1.07 , vmul( vd436, vd439 ) ), vd436 ) = vplus( vmul( vd436, vplus( vd437,
% 0.43/1.07 vd439 ) ), vd436 ) }.
% 0.43/1.07 substitution0:
% 0.43/1.07 end
% 0.43/1.07 permutation0:
% 0.43/1.07 0 ==> 0
% 0.43/1.07 end
% 0.43/1.07
% 0.43/1.07 eqswap: (143) {G0,W13,D4,L1,V0,M1} { vplus( vmul( vd436, vd437 ), vmul(
% 0.43/1.07 vd436, vd439 ) ) = vmul( vd436, vplus( vd437, vd439 ) ) }.
% 0.43/1.07 parent0[0]: (77) {G0,W13,D4,L1,V0,M1} { vmul( vd436, vplus( vd437, vd439 )
% 0.43/1.07 ) = vplus( vmul( vd436, vd437 ), vmul( vd436, vd439 ) ) }.
% 0.43/1.07 substitution0:
% 0.43/1.07 end
% 0.43/1.07
% 0.43/1.07 subsumption: (3) {G0,W13,D4,L1,V0,M1} I { vplus( vmul( vd436, vd437 ), vmul
% 0.43/1.07 ( vd436, vd439 ) ) ==> vmul( vd436, vplus( vd437, vd439 ) ) }.
% 0.43/1.07 parent0: (143) {G0,W13,D4,L1,V0,M1} { vplus( vmul( vd436, vd437 ), vmul(
% 0.43/1.07 vd436, vd439 ) ) = vmul( vd436, vplus( vd437, vd439 ) ) }.
% 0.43/1.07 substitution0:
% 0.43/1.07 end
% 0.43/1.07 permutation0:
% 0.43/1.07 0 ==> 0
% 0.43/1.07 end
% 0.43/1.07
% 0.43/1.07 paramod: (146) {G1,W15,D5,L1,V0,M1} { ! vplus( vmul( vd436, vplus( vd437,
% 0.43/1.07 vd439 ) ), vd436 ) ==> vplus( vmul( vd436, vplus( vd437, vd439 ) ), vd436
% 0.43/1.07 ) }.
% 0.43/1.07 parent0[0]: (3) {G0,W13,D4,L1,V0,M1} I { vplus( vmul( vd436, vd437 ), vmul
% 0.43/1.07 ( vd436, vd439 ) ) ==> vmul( vd436, vplus( vd437, vd439 ) ) }.
% 0.43/1.07 parent1[0; 3]: (0) {G0,W17,D5,L1,V0,M1} I { ! vplus( vplus( vmul( vd436,
% 0.43/1.07 vd437 ), vmul( vd436, vd439 ) ), vd436 ) ==> vplus( vmul( vd436, vplus(
% 0.43/1.07 vd437, vd439 ) ), vd436 ) }.
% 0.43/1.07 substitution0:
% 0.43/1.07 end
% 0.43/1.07 substitution1:
% 0.43/1.07 end
% 0.43/1.07
% 0.43/1.07 eqrefl: (147) {G0,W0,D0,L0,V0,M0} { }.
% 0.43/1.07 parent0[0]: (146) {G1,W15,D5,L1,V0,M1} { ! vplus( vmul( vd436, vplus(
% 0.43/1.07 vd437, vd439 ) ), vd436 ) ==> vplus( vmul( vd436, vplus( vd437, vd439 ) )
% 0.43/1.07 , vd436 ) }.
% 0.43/1.07 substitution0:
% 0.43/1.07 end
% 0.43/1.07
% 0.43/1.07 subsumption: (72) {G1,W0,D0,L0,V0,M0} S(0);d(3);q { }.
% 0.43/1.07 parent0: (147) {G0,W0,D0,L0,V0,M0} { }.
% 0.43/1.07 substitution0:
% 0.43/1.07 end
% 0.43/1.07 permutation0:
% 0.43/1.07 end
% 0.43/1.07
% 0.43/1.07 Proof check complete!
% 0.43/1.07
% 0.43/1.07 Memory use:
% 0.43/1.07
% 0.43/1.07 space for terms: 2276
% 0.43/1.07 space for clauses: 5145
% 0.43/1.07
% 0.43/1.07
% 0.43/1.07 clauses generated: 85
% 0.43/1.07 clauses kept: 73
% 0.43/1.07 clauses selected: 5
% 0.43/1.07 clauses deleted: 1
% 0.43/1.07 clauses inuse deleted: 0
% 0.43/1.07
% 0.43/1.07 subsentry: 63
% 0.43/1.07 literals s-matched: 31
% 0.43/1.07 literals matched: 31
% 0.43/1.07 full subsumption: 7
% 0.43/1.07
% 0.43/1.07 checksum: 1233484093
% 0.43/1.07
% 0.43/1.07
% 0.43/1.07 Bliksem ended
%------------------------------------------------------------------------------