TSTP Solution File: NUM852+1 by Bliksem---1.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Bliksem---1.12
% Problem  : NUM852+1 : TPTP v8.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : bliksem %s

% Computer : n013.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 06:27:05 EDT 2022

% Result   : Theorem 0.75s 1.61s
% Output   : Refutation 0.75s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : NUM852+1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.13  % Command  : bliksem %s
% 0.12/0.34  % Computer : n013.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 : Thu Jul  7 21:44:44 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.75/1.61  *** allocated 10000 integers for termspace/termends
% 0.75/1.61  *** allocated 10000 integers for clauses
% 0.75/1.61  *** allocated 10000 integers for justifications
% 0.75/1.61  Bliksem 1.12
% 0.75/1.61  
% 0.75/1.61  
% 0.75/1.61  Automatic Strategy Selection
% 0.75/1.61  
% 0.75/1.61  
% 0.75/1.61  Clauses:
% 0.75/1.61  
% 0.75/1.61  { ! greater( vmul( vd481, vd469 ), vmul( vd480, vd469 ) ) }.
% 0.75/1.61  { greater( vd481, vd480 ) }.
% 0.75/1.61  { less( vd480, vd481 ) }.
% 0.75/1.61  { ! X = Y, vmul( X, vd469 ) = vmul( Y, vd469 ) }.
% 0.75/1.61  { ! greater( X, Y ), greater( vplus( vmul( Y, vd469 ), vmul( vskolem9( X, Y
% 0.75/1.61     ), vd469 ) ), vmul( Y, vd469 ) ) }.
% 0.75/1.61  { ! greater( X, Y ), vmul( vplus( Y, vskolem9( X, Y ) ), vd469 ) = vplus( 
% 0.75/1.61    vmul( Y, vd469 ), vmul( vskolem9( X, Y ), vd469 ) ) }.
% 0.75/1.61  { ! greater( X, Y ), vmul( X, vd469 ) = vmul( vplus( Y, vskolem9( X, Y ) )
% 0.75/1.61    , vd469 ) }.
% 0.75/1.61  { ! greater( X, Y ), X = vplus( Y, vskolem9( X, Y ) ) }.
% 0.75/1.61  { vmul( vmul( X, Y ), Z ) = vmul( X, vmul( Y, Z ) ) }.
% 0.75/1.61  { vmul( X, vplus( Y, Z ) ) = vplus( vmul( X, Y ), vmul( X, Z ) ) }.
% 0.75/1.61  { vmul( X, Y ) = vmul( Y, X ) }.
% 0.75/1.61  { vmul( vsucc( X ), Y ) = vplus( vmul( X, Y ), Y ) }.
% 0.75/1.61  { vmul( v1, X ) = X }.
% 0.75/1.61  { vmul( X, vsucc( Y ) ) = vplus( vmul( X, Y ), X ) }.
% 0.75/1.61  { vmul( X, v1 ) = X }.
% 0.75/1.61  { ! less( X, vplus( Y, v1 ) ), leq( X, Y ) }.
% 0.75/1.61  { ! greater( X, Y ), geq( X, vplus( Y, v1 ) ) }.
% 0.75/1.61  { geq( X, v1 ) }.
% 0.75/1.61  { ! geq( Z, T ), ! geq( X, Y ), geq( vplus( X, Z ), vplus( Y, T ) ) }.
% 0.75/1.61  { ! greater( Z, T ), ! geq( X, Y ), greater( vplus( X, Z ), vplus( Y, T ) )
% 0.75/1.61     }.
% 0.75/1.61  { ! geq( Z, T ), ! greater( X, Y ), greater( vplus( X, Z ), vplus( Y, T ) )
% 0.75/1.61     }.
% 0.75/1.61  { ! greater( Z, T ), ! greater( X, Y ), greater( vplus( X, Z ), vplus( Y, T
% 0.75/1.61     ) ) }.
% 0.75/1.61  { ! less( vplus( X, Z ), vplus( Y, Z ) ), less( X, Y ) }.
% 0.75/1.61  { ! vplus( X, Z ) = vplus( Y, Z ), X = Y }.
% 0.75/1.61  { ! greater( vplus( X, Z ), vplus( Y, Z ) ), greater( X, Y ) }.
% 0.75/1.61  { ! less( X, Y ), less( vplus( X, Z ), vplus( Y, Z ) ) }.
% 0.75/1.61  { ! X = Y, vplus( X, Z ) = vplus( Y, Z ) }.
% 0.75/1.61  { ! greater( X, Y ), greater( vplus( X, Z ), vplus( Y, Z ) ) }.
% 0.75/1.61  { greater( vplus( X, Y ), X ) }.
% 0.75/1.61  { ! leq( Z, Y ), ! leq( X, Z ), leq( X, Y ) }.
% 0.75/1.61  { ! less( Z, Y ), ! leq( X, Z ), less( X, Y ) }.
% 0.75/1.61  { ! leq( Z, Y ), ! less( X, Z ), less( X, Y ) }.
% 0.75/1.61  { ! less( Z, Y ), ! less( X, Z ), less( X, Y ) }.
% 0.75/1.61  { ! leq( X, Y ), geq( Y, X ) }.
% 0.75/1.61  { ! geq( X, Y ), leq( Y, X ) }.
% 0.75/1.61  { ! leq( Y, X ), less( Y, X ), Y = X }.
% 0.75/1.61  { ! less( Y, X ), leq( Y, X ) }.
% 0.75/1.61  { ! Y = X, leq( Y, X ) }.
% 0.75/1.61  { ! geq( Y, X ), greater( Y, X ), Y = X }.
% 0.75/1.61  { ! greater( Y, X ), geq( Y, X ) }.
% 0.75/1.61  { ! Y = X, geq( Y, X ) }.
% 0.75/1.61  { ! less( X, Y ), greater( Y, X ) }.
% 0.75/1.61  { ! greater( X, Y ), less( Y, X ) }.
% 0.75/1.61  { X = Y, greater( X, Y ), less( X, Y ) }.
% 0.75/1.61  { ! X = Y, ! less( X, Y ) }.
% 0.75/1.61  { ! greater( X, Y ), ! less( X, Y ) }.
% 0.75/1.61  { ! X = Y, ! greater( X, Y ) }.
% 0.75/1.61  { ! less( Y, X ), X = vplus( Y, skol1( X, Y ) ) }.
% 0.75/1.61  { ! X = vplus( Y, Z ), less( Y, X ) }.
% 0.75/1.61  { ! greater( Y, X ), Y = vplus( X, skol2( X, Y ) ) }.
% 0.75/1.61  { ! Y = vplus( X, Z ), greater( Y, X ) }.
% 0.75/1.61  { X = Y, X = vplus( Y, skol3( X, Y ) ), Y = vplus( X, skol4( X, Y ) ) }.
% 0.75/1.61  { ! X = Y, ! Y = vplus( X, Z ) }.
% 0.75/1.61  { ! X = vplus( Y, Z ), ! Y = vplus( X, T ) }.
% 0.75/1.61  { ! X = Y, ! X = vplus( Y, Z ) }.
% 0.75/1.61  { X = Y, ! vplus( Z, X ) = vplus( Z, Y ) }.
% 0.75/1.61  { ! Y = vplus( X, Y ) }.
% 0.75/1.61  { vplus( Y, X ) = vplus( X, Y ) }.
% 0.75/1.61  { vplus( vsucc( X ), Y ) = vsucc( vplus( X, Y ) ) }.
% 0.75/1.61  { vplus( v1, X ) = vsucc( X ) }.
% 0.75/1.61  { vplus( vplus( X, Y ), Z ) = vplus( X, vplus( Y, Z ) ) }.
% 0.75/1.61  { vplus( X, vsucc( Y ) ) = vsucc( vplus( X, Y ) ) }.
% 0.75/1.61  { vplus( X, v1 ) = vsucc( X ) }.
% 0.75/1.61  { X = v1, X = vsucc( vskolem2( X ) ) }.
% 0.75/1.61  { ! vsucc( X ) = X }.
% 0.75/1.61  { X = Y, ! vsucc( X ) = vsucc( Y ) }.
% 0.75/1.61  { ! vsucc( X ) = vsucc( Y ), X = Y }.
% 0.75/1.61  { ! vsucc( X ) = v1 }.
% 0.75/1.61  
% 0.75/1.61  percentage equality = 0.408000, percentage horn = 0.925373
% 0.75/1.61  This is a problem with some equality
% 0.75/1.61  
% 0.75/1.61  
% 0.75/1.61  
% 0.75/1.61  Options Used:
% 0.75/1.61  
% 0.75/1.61  useres =            1
% 0.75/1.61  useparamod =        1
% 0.75/1.61  useeqrefl =         1
% 0.75/1.61  useeqfact =         1
% 0.75/1.61  usefactor =         1
% 0.75/1.61  usesimpsplitting =  0
% 0.75/1.61  usesimpdemod =      5
% 0.75/1.61  usesimpres =        3
% 0.75/1.61  
% 0.75/1.61  resimpinuse      =  1000
% 0.75/1.61  resimpclauses =     20000
% 0.75/1.61  substype =          eqrewr
% 0.75/1.61  backwardsubs =      1
% 0.75/1.61  selectoldest =      5
% 0.75/1.61  
% 0.75/1.61  litorderings [0] =  split
% 0.75/1.61  litorderings [1] =  extend the termordering, first sorting on arguments
% 0.75/1.61  
% 0.75/1.61  termordering =      kbo
% 0.75/1.61  
% 0.75/1.61  litapriori =        0
% 0.75/1.61  termapriori =       1
% 0.75/1.61  litaposteriori =    0
% 0.75/1.61  termaposteriori =   0
% 0.75/1.61  demodaposteriori =  0
% 0.75/1.61  ordereqreflfact =   0
% 0.75/1.61  
% 0.75/1.61  litselect =         negord
% 0.75/1.61  
% 0.75/1.61  maxweight =         15
% 0.75/1.61  maxdepth =          30000
% 0.75/1.61  maxlength =         115
% 0.75/1.61  maxnrvars =         195
% 0.75/1.61  excuselevel =       1
% 0.75/1.61  increasemaxweight = 1
% 0.75/1.61  
% 0.75/1.61  maxselected =       10000000
% 0.75/1.61  maxnrclauses =      10000000
% 0.75/1.61  
% 0.75/1.61  showgenerated =    0
% 0.75/1.61  showkept =         0
% 0.75/1.61  showselected =     0
% 0.75/1.61  showdeleted =      0
% 0.75/1.61  showresimp =       1
% 0.75/1.61  showstatus =       2000
% 0.75/1.61  
% 0.75/1.61  prologoutput =     0
% 0.75/1.61  nrgoals =          5000000
% 0.75/1.61  totalproof =       1
% 0.75/1.61  
% 0.75/1.61  Symbols occurring in the translation:
% 0.75/1.61  
% 0.75/1.61  {}  [0, 0]      (w:1, o:2, a:1, s:1, b:0), 
% 0.75/1.61  .  [1, 2]      (w:1, o:114, a:1, s:1, b:0), 
% 0.75/1.61  !  [4, 1]      (w:0, o:107, a:1, s:1, b:0), 
% 0.75/1.61  =  [13, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 0.75/1.61  ==>  [14, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 0.75/1.61  vd481  [35, 0]      (w:1, o:7, a:1, s:1, b:0), 
% 0.75/1.61  vd469  [36, 0]      (w:1, o:8, a:1, s:1, b:0), 
% 0.75/1.61  vmul  [37, 2]      (w:1, o:138, a:1, s:1, b:0), 
% 0.75/1.61  vd480  [38, 0]      (w:1, o:6, a:1, s:1, b:0), 
% 0.75/1.61  greater  [39, 2]      (w:1, o:139, a:1, s:1, b:0), 
% 0.75/1.61  less  [40, 2]      (w:1, o:140, a:1, s:1, b:0), 
% 0.75/1.61  vskolem9  [45, 2]      (w:1, o:141, a:1, s:1, b:0), 
% 0.75/1.61  vplus  [46, 2]      (w:1, o:142, a:1, s:1, b:0), 
% 0.75/1.61  vsucc  [57, 1]      (w:1, o:112, a:1, s:1, b:0), 
% 0.75/1.61  v1  [59, 0]      (w:1, o:94, a:1, s:1, b:0), 
% 0.75/1.61  leq  [64, 2]      (w:1, o:143, a:1, s:1, b:0), 
% 0.75/1.61  geq  [67, 2]      (w:1, o:144, a:1, s:1, b:0), 
% 0.75/1.61  vskolem2  [138, 1]      (w:1, o:113, a:1, s:1, b:0), 
% 0.75/1.61  skol1  [145, 2]      (w:1, o:145, a:1, s:1, b:1), 
% 0.75/1.61  skol2  [146, 2]      (w:1, o:146, a:1, s:1, b:1), 
% 0.75/1.61  skol3  [147, 2]      (w:1, o:147, a:1, s:1, b:1), 
% 0.75/1.61  skol4  [148, 2]      (w:1, o:148, a:1, s:1, b:1).
% 0.75/1.61  
% 0.75/1.61  
% 0.75/1.61  Starting Search:
% 0.75/1.61  
% 0.75/1.61  *** allocated 15000 integers for clauses
% 0.75/1.61  *** allocated 22500 integers for clauses
% 0.75/1.61  *** allocated 33750 integers for clauses
% 0.75/1.61  *** allocated 50625 integers for clauses
% 0.75/1.61  *** allocated 15000 integers for termspace/termends
% 0.75/1.61  *** allocated 75937 integers for clauses
% 0.75/1.61  Resimplifying inuse:
% 0.75/1.61  Done
% 0.75/1.61  
% 0.75/1.61  *** allocated 22500 integers for termspace/termends
% 0.75/1.61  *** allocated 113905 integers for clauses
% 0.75/1.61  *** allocated 33750 integers for termspace/termends
% 0.75/1.61  
% 0.75/1.61  Intermediate Status:
% 0.75/1.61  Generated:    4659
% 0.75/1.61  Kept:         2002
% 0.75/1.61  Inuse:        152
% 0.75/1.61  Deleted:      7
% 0.75/1.61  Deletedinuse: 2
% 0.75/1.61  
% 0.75/1.61  Resimplifying inuse:
% 0.75/1.61  Done
% 0.75/1.61  
% 0.75/1.61  *** allocated 170857 integers for clauses
% 0.75/1.61  *** allocated 50625 integers for termspace/termends
% 0.75/1.61  Resimplifying inuse:
% 0.75/1.61  Done
% 0.75/1.61  
% 0.75/1.61  *** allocated 256285 integers for clauses
% 0.75/1.61  *** allocated 75937 integers for termspace/termends
% 0.75/1.61  
% 0.75/1.61  Intermediate Status:
% 0.75/1.61  Generated:    10081
% 0.75/1.61  Kept:         4065
% 0.75/1.61  Inuse:        206
% 0.75/1.61  Deleted:      7
% 0.75/1.61  Deletedinuse: 2
% 0.75/1.61  
% 0.75/1.61  Resimplifying inuse:
% 0.75/1.61  Done
% 0.75/1.61  
% 0.75/1.61  *** allocated 384427 integers for clauses
% 0.75/1.61  Resimplifying inuse:
% 0.75/1.61  Done
% 0.75/1.61  
% 0.75/1.61  *** allocated 113905 integers for termspace/termends
% 0.75/1.61  
% 0.75/1.61  Intermediate Status:
% 0.75/1.61  Generated:    16812
% 0.75/1.61  Kept:         6092
% 0.75/1.61  Inuse:        279
% 0.75/1.61  Deleted:      8
% 0.75/1.61  Deletedinuse: 2
% 0.75/1.61  
% 0.75/1.61  Resimplifying inuse:
% 0.75/1.61  Done
% 0.75/1.61  
% 0.75/1.61  Resimplifying inuse:
% 0.75/1.61  Done
% 0.75/1.61  
% 0.75/1.61  *** allocated 576640 integers for clauses
% 0.75/1.61  
% 0.75/1.61  Intermediate Status:
% 0.75/1.61  Generated:    23626
% 0.75/1.61  Kept:         8097
% 0.75/1.61  Inuse:        366
% 0.75/1.61  Deleted:      9
% 0.75/1.61  Deletedinuse: 3
% 0.75/1.61  
% 0.75/1.61  Resimplifying inuse:
% 0.75/1.61  Done
% 0.75/1.61  
% 0.75/1.61  *** allocated 170857 integers for termspace/termends
% 0.75/1.61  
% 0.75/1.61  Bliksems!, er is een bewijs:
% 0.75/1.61  % SZS status Theorem
% 0.75/1.61  % SZS output start Refutation
% 0.75/1.61  
% 0.75/1.61  (0) {G0,W7,D3,L1,V0,M1} I { ! greater( vmul( vd481, vd469 ), vmul( vd480, 
% 0.75/1.61    vd469 ) ) }.
% 0.75/1.61  (1) {G0,W3,D2,L1,V0,M1} I { greater( vd481, vd480 ) }.
% 0.75/1.61  (7) {G0,W10,D4,L2,V2,M2} I { ! greater( X, Y ), vplus( Y, vskolem9( X, Y )
% 0.75/1.61     ) ==> X }.
% 0.75/1.61  (9) {G0,W13,D4,L1,V3,M1} I { vplus( vmul( X, Y ), vmul( X, Z ) ) ==> vmul( 
% 0.75/1.61    X, vplus( Y, Z ) ) }.
% 0.75/1.61  (10) {G0,W7,D3,L1,V2,M1} I { vmul( X, Y ) = vmul( Y, X ) }.
% 0.75/1.61  (28) {G0,W5,D3,L1,V2,M1} I { greater( vplus( X, Y ), X ) }.
% 0.75/1.61  (90) {G1,W7,D4,L1,V0,M1} R(7,1) { vplus( vd480, vskolem9( vd481, vd480 ) ) 
% 0.75/1.61    ==> vd481 }.
% 0.75/1.61  (107) {G1,W9,D4,L1,V3,M1} P(9,28) { greater( vmul( X, vplus( Y, Z ) ), vmul
% 0.75/1.61    ( X, Y ) ) }.
% 0.75/1.61  (127) {G1,W7,D3,L1,V0,M1} P(10,0) { ! greater( vmul( vd469, vd481 ), vmul( 
% 0.75/1.61    vd480, vd469 ) ) }.
% 0.75/1.61  (7549) {G2,W7,D3,L1,V1,M1} P(90,107) { greater( vmul( X, vd481 ), vmul( X, 
% 0.75/1.61    vd480 ) ) }.
% 0.75/1.61  (9376) {G3,W0,D0,L0,V0,M0} P(10,127);r(7549) {  }.
% 0.75/1.61  
% 0.75/1.61  
% 0.75/1.61  % SZS output end Refutation
% 0.75/1.61  found a proof!
% 0.75/1.61  
% 0.75/1.61  
% 0.75/1.61  Unprocessed initial clauses:
% 0.75/1.61  
% 0.75/1.61  (9378) {G0,W7,D3,L1,V0,M1}  { ! greater( vmul( vd481, vd469 ), vmul( vd480
% 0.75/1.61    , vd469 ) ) }.
% 0.75/1.61  (9379) {G0,W3,D2,L1,V0,M1}  { greater( vd481, vd480 ) }.
% 0.75/1.61  (9380) {G0,W3,D2,L1,V0,M1}  { less( vd480, vd481 ) }.
% 0.75/1.61  (9381) {G0,W10,D3,L2,V2,M2}  { ! X = Y, vmul( X, vd469 ) = vmul( Y, vd469 )
% 0.75/1.61     }.
% 0.75/1.61  (9382) {G0,W16,D5,L2,V2,M2}  { ! greater( X, Y ), greater( vplus( vmul( Y, 
% 0.75/1.61    vd469 ), vmul( vskolem9( X, Y ), vd469 ) ), vmul( Y, vd469 ) ) }.
% 0.75/1.61  (9383) {G0,W20,D5,L2,V2,M2}  { ! greater( X, Y ), vmul( vplus( Y, vskolem9
% 0.75/1.61    ( X, Y ) ), vd469 ) = vplus( vmul( Y, vd469 ), vmul( vskolem9( X, Y ), 
% 0.75/1.61    vd469 ) ) }.
% 0.75/1.61  (9384) {G0,W14,D5,L2,V2,M2}  { ! greater( X, Y ), vmul( X, vd469 ) = vmul( 
% 0.75/1.61    vplus( Y, vskolem9( X, Y ) ), vd469 ) }.
% 0.75/1.61  (9385) {G0,W10,D4,L2,V2,M2}  { ! greater( X, Y ), X = vplus( Y, vskolem9( X
% 0.75/1.61    , Y ) ) }.
% 0.75/1.61  (9386) {G0,W11,D4,L1,V3,M1}  { vmul( vmul( X, Y ), Z ) = vmul( X, vmul( Y, 
% 0.75/1.61    Z ) ) }.
% 0.75/1.61  (9387) {G0,W13,D4,L1,V3,M1}  { vmul( X, vplus( Y, Z ) ) = vplus( vmul( X, Y
% 0.75/1.61     ), vmul( X, Z ) ) }.
% 0.75/1.61  (9388) {G0,W7,D3,L1,V2,M1}  { vmul( X, Y ) = vmul( Y, X ) }.
% 0.75/1.61  (9389) {G0,W10,D4,L1,V2,M1}  { vmul( vsucc( X ), Y ) = vplus( vmul( X, Y )
% 0.75/1.61    , Y ) }.
% 0.75/1.61  (9390) {G0,W5,D3,L1,V1,M1}  { vmul( v1, X ) = X }.
% 0.75/1.61  (9391) {G0,W10,D4,L1,V2,M1}  { vmul( X, vsucc( Y ) ) = vplus( vmul( X, Y )
% 0.75/1.61    , X ) }.
% 0.75/1.61  (9392) {G0,W5,D3,L1,V1,M1}  { vmul( X, v1 ) = X }.
% 0.75/1.61  (9393) {G0,W8,D3,L2,V2,M2}  { ! less( X, vplus( Y, v1 ) ), leq( X, Y ) }.
% 0.75/1.61  (9394) {G0,W8,D3,L2,V2,M2}  { ! greater( X, Y ), geq( X, vplus( Y, v1 ) )
% 0.75/1.61     }.
% 0.75/1.61  (9395) {G0,W3,D2,L1,V1,M1}  { geq( X, v1 ) }.
% 0.75/1.61  (9396) {G0,W13,D3,L3,V4,M3}  { ! geq( Z, T ), ! geq( X, Y ), geq( vplus( X
% 0.75/1.61    , Z ), vplus( Y, T ) ) }.
% 0.75/1.61  (9397) {G0,W13,D3,L3,V4,M3}  { ! greater( Z, T ), ! geq( X, Y ), greater( 
% 0.75/1.61    vplus( X, Z ), vplus( Y, T ) ) }.
% 0.75/1.61  (9398) {G0,W13,D3,L3,V4,M3}  { ! geq( Z, T ), ! greater( X, Y ), greater( 
% 0.75/1.61    vplus( X, Z ), vplus( Y, T ) ) }.
% 0.75/1.61  (9399) {G0,W13,D3,L3,V4,M3}  { ! greater( Z, T ), ! greater( X, Y ), 
% 0.75/1.61    greater( vplus( X, Z ), vplus( Y, T ) ) }.
% 0.75/1.61  (9400) {G0,W10,D3,L2,V3,M2}  { ! less( vplus( X, Z ), vplus( Y, Z ) ), less
% 0.75/1.61    ( X, Y ) }.
% 0.75/1.61  (9401) {G0,W10,D3,L2,V3,M2}  { ! vplus( X, Z ) = vplus( Y, Z ), X = Y }.
% 0.75/1.61  (9402) {G0,W10,D3,L2,V3,M2}  { ! greater( vplus( X, Z ), vplus( Y, Z ) ), 
% 0.75/1.61    greater( X, Y ) }.
% 0.75/1.61  (9403) {G0,W10,D3,L2,V3,M2}  { ! less( X, Y ), less( vplus( X, Z ), vplus( 
% 0.75/1.61    Y, Z ) ) }.
% 0.75/1.61  (9404) {G0,W10,D3,L2,V3,M2}  { ! X = Y, vplus( X, Z ) = vplus( Y, Z ) }.
% 0.75/1.61  (9405) {G0,W10,D3,L2,V3,M2}  { ! greater( X, Y ), greater( vplus( X, Z ), 
% 0.75/1.61    vplus( Y, Z ) ) }.
% 0.75/1.61  (9406) {G0,W5,D3,L1,V2,M1}  { greater( vplus( X, Y ), X ) }.
% 0.75/1.61  (9407) {G0,W9,D2,L3,V3,M3}  { ! leq( Z, Y ), ! leq( X, Z ), leq( X, Y ) }.
% 0.75/1.61  (9408) {G0,W9,D2,L3,V3,M3}  { ! less( Z, Y ), ! leq( X, Z ), less( X, Y )
% 0.75/1.61     }.
% 0.75/1.61  (9409) {G0,W9,D2,L3,V3,M3}  { ! leq( Z, Y ), ! less( X, Z ), less( X, Y )
% 0.75/1.61     }.
% 0.75/1.61  (9410) {G0,W9,D2,L3,V3,M3}  { ! less( Z, Y ), ! less( X, Z ), less( X, Y )
% 0.75/1.61     }.
% 0.75/1.61  (9411) {G0,W6,D2,L2,V2,M2}  { ! leq( X, Y ), geq( Y, X ) }.
% 0.75/1.61  (9412) {G0,W6,D2,L2,V2,M2}  { ! geq( X, Y ), leq( Y, X ) }.
% 0.75/1.61  (9413) {G0,W9,D2,L3,V2,M3}  { ! leq( Y, X ), less( Y, X ), Y = X }.
% 0.75/1.61  (9414) {G0,W6,D2,L2,V2,M2}  { ! less( Y, X ), leq( Y, X ) }.
% 0.75/1.61  (9415) {G0,W6,D2,L2,V2,M2}  { ! Y = X, leq( Y, X ) }.
% 0.75/1.61  (9416) {G0,W9,D2,L3,V2,M3}  { ! geq( Y, X ), greater( Y, X ), Y = X }.
% 0.75/1.61  (9417) {G0,W6,D2,L2,V2,M2}  { ! greater( Y, X ), geq( Y, X ) }.
% 0.75/1.61  (9418) {G0,W6,D2,L2,V2,M2}  { ! Y = X, geq( Y, X ) }.
% 0.75/1.61  (9419) {G0,W6,D2,L2,V2,M2}  { ! less( X, Y ), greater( Y, X ) }.
% 0.75/1.61  (9420) {G0,W6,D2,L2,V2,M2}  { ! greater( X, Y ), less( Y, X ) }.
% 0.75/1.61  (9421) {G0,W9,D2,L3,V2,M3}  { X = Y, greater( X, Y ), less( X, Y ) }.
% 0.75/1.61  (9422) {G0,W6,D2,L2,V2,M2}  { ! X = Y, ! less( X, Y ) }.
% 0.75/1.61  (9423) {G0,W6,D2,L2,V2,M2}  { ! greater( X, Y ), ! less( X, Y ) }.
% 0.75/1.61  (9424) {G0,W6,D2,L2,V2,M2}  { ! X = Y, ! greater( X, Y ) }.
% 0.75/1.61  (9425) {G0,W10,D4,L2,V2,M2}  { ! less( Y, X ), X = vplus( Y, skol1( X, Y )
% 0.75/1.61     ) }.
% 0.75/1.61  (9426) {G0,W8,D3,L2,V3,M2}  { ! X = vplus( Y, Z ), less( Y, X ) }.
% 0.75/1.61  (9427) {G0,W10,D4,L2,V2,M2}  { ! greater( Y, X ), Y = vplus( X, skol2( X, Y
% 0.75/1.61     ) ) }.
% 0.75/1.61  (9428) {G0,W8,D3,L2,V3,M2}  { ! Y = vplus( X, Z ), greater( Y, X ) }.
% 0.75/1.61  (9429) {G0,W17,D4,L3,V2,M3}  { X = Y, X = vplus( Y, skol3( X, Y ) ), Y = 
% 0.75/1.61    vplus( X, skol4( X, Y ) ) }.
% 0.75/1.61  (9430) {G0,W8,D3,L2,V3,M2}  { ! X = Y, ! Y = vplus( X, Z ) }.
% 0.75/1.61  (9431) {G0,W10,D3,L2,V4,M2}  { ! X = vplus( Y, Z ), ! Y = vplus( X, T ) }.
% 0.75/1.61  (9432) {G0,W8,D3,L2,V3,M2}  { ! X = Y, ! X = vplus( Y, Z ) }.
% 0.75/1.61  (9433) {G0,W10,D3,L2,V3,M2}  { X = Y, ! vplus( Z, X ) = vplus( Z, Y ) }.
% 0.75/1.61  (9434) {G0,W5,D3,L1,V2,M1}  { ! Y = vplus( X, Y ) }.
% 0.75/1.61  (9435) {G0,W7,D3,L1,V2,M1}  { vplus( Y, X ) = vplus( X, Y ) }.
% 0.75/1.61  (9436) {G0,W9,D4,L1,V2,M1}  { vplus( vsucc( X ), Y ) = vsucc( vplus( X, Y )
% 0.75/1.61     ) }.
% 0.75/1.61  (9437) {G0,W6,D3,L1,V1,M1}  { vplus( v1, X ) = vsucc( X ) }.
% 0.75/1.61  (9438) {G0,W11,D4,L1,V3,M1}  { vplus( vplus( X, Y ), Z ) = vplus( X, vplus
% 0.75/1.61    ( Y, Z ) ) }.
% 0.75/1.61  (9439) {G0,W9,D4,L1,V2,M1}  { vplus( X, vsucc( Y ) ) = vsucc( vplus( X, Y )
% 0.75/1.61     ) }.
% 0.75/1.61  (9440) {G0,W6,D3,L1,V1,M1}  { vplus( X, v1 ) = vsucc( X ) }.
% 0.75/1.61  (9441) {G0,W8,D4,L2,V1,M2}  { X = v1, X = vsucc( vskolem2( X ) ) }.
% 0.75/1.61  (9442) {G0,W4,D3,L1,V1,M1}  { ! vsucc( X ) = X }.
% 0.75/1.61  (9443) {G0,W8,D3,L2,V2,M2}  { X = Y, ! vsucc( X ) = vsucc( Y ) }.
% 0.75/1.61  (9444) {G0,W8,D3,L2,V2,M2}  { ! vsucc( X ) = vsucc( Y ), X = Y }.
% 0.75/1.61  (9445) {G0,W4,D3,L1,V1,M1}  { ! vsucc( X ) = v1 }.
% 0.75/1.61  
% 0.75/1.61  
% 0.75/1.61  Total Proof:
% 0.75/1.61  
% 0.75/1.61  subsumption: (0) {G0,W7,D3,L1,V0,M1} I { ! greater( vmul( vd481, vd469 ), 
% 0.75/1.61    vmul( vd480, vd469 ) ) }.
% 0.75/1.61  parent0: (9378) {G0,W7,D3,L1,V0,M1}  { ! greater( vmul( vd481, vd469 ), 
% 0.75/1.61    vmul( vd480, vd469 ) ) }.
% 0.75/1.61  substitution0:
% 0.75/1.61  end
% 0.75/1.61  permutation0:
% 0.75/1.61     0 ==> 0
% 0.75/1.61  end
% 0.75/1.61  
% 0.75/1.61  subsumption: (1) {G0,W3,D2,L1,V0,M1} I { greater( vd481, vd480 ) }.
% 0.75/1.61  parent0: (9379) {G0,W3,D2,L1,V0,M1}  { greater( vd481, vd480 ) }.
% 0.75/1.61  substitution0:
% 0.75/1.61  end
% 0.75/1.61  permutation0:
% 0.75/1.61     0 ==> 0
% 0.75/1.61  end
% 0.75/1.61  
% 0.75/1.61  eqswap: (9449) {G0,W10,D4,L2,V2,M2}  { vplus( Y, vskolem9( X, Y ) ) = X, ! 
% 0.75/1.61    greater( X, Y ) }.
% 0.75/1.61  parent0[1]: (9385) {G0,W10,D4,L2,V2,M2}  { ! greater( X, Y ), X = vplus( Y
% 0.75/1.61    , vskolem9( X, Y ) ) }.
% 0.75/1.61  substitution0:
% 0.75/1.61     X := X
% 0.75/1.61     Y := Y
% 0.75/1.61  end
% 0.75/1.61  
% 0.75/1.61  subsumption: (7) {G0,W10,D4,L2,V2,M2} I { ! greater( X, Y ), vplus( Y, 
% 0.75/1.61    vskolem9( X, Y ) ) ==> X }.
% 0.75/1.61  parent0: (9449) {G0,W10,D4,L2,V2,M2}  { vplus( Y, vskolem9( X, Y ) ) = X, !
% 0.75/1.61     greater( X, Y ) }.
% 0.75/1.61  substitution0:
% 0.75/1.61     X := X
% 0.75/1.61     Y := Y
% 0.75/1.61  end
% 0.75/1.61  permutation0:
% 0.75/1.61     0 ==> 1
% 0.75/1.61     1 ==> 0
% 0.75/1.61  end
% 0.75/1.61  
% 0.75/1.61  eqswap: (9455) {G0,W13,D4,L1,V3,M1}  { vplus( vmul( X, Y ), vmul( X, Z ) ) 
% 0.75/1.61    = vmul( X, vplus( Y, Z ) ) }.
% 0.75/1.61  parent0[0]: (9387) {G0,W13,D4,L1,V3,M1}  { vmul( X, vplus( Y, Z ) ) = vplus
% 0.75/1.61    ( vmul( X, Y ), vmul( X, Z ) ) }.
% 0.75/1.61  substitution0:
% 0.75/1.61     X := X
% 0.75/1.61     Y := Y
% 0.75/1.61     Z := Z
% 0.75/1.61  end
% 0.75/1.61  
% 0.75/1.61  subsumption: (9) {G0,W13,D4,L1,V3,M1} I { vplus( vmul( X, Y ), vmul( X, Z )
% 0.75/1.61     ) ==> vmul( X, vplus( Y, Z ) ) }.
% 0.75/1.61  parent0: (9455) {G0,W13,D4,L1,V3,M1}  { vplus( vmul( X, Y ), vmul( X, Z ) )
% 0.75/1.61     = vmul( X, vplus( Y, Z ) ) }.
% 0.75/1.61  substitution0:
% 0.75/1.61     X := X
% 0.75/1.61     Y := Y
% 0.75/1.61     Z := Z
% 0.75/1.61  end
% 0.75/1.61  permutation0:
% 0.75/1.61     0 ==> 0
% 0.75/1.61  end
% 0.75/1.61  
% 0.75/1.61  subsumption: (10) {G0,W7,D3,L1,V2,M1} I { vmul( X, Y ) = vmul( Y, X ) }.
% 0.75/1.61  parent0: (9388) {G0,W7,D3,L1,V2,M1}  { vmul( X, Y ) = vmul( Y, X ) }.
% 0.75/1.61  substitution0:
% 0.75/1.61     X := X
% 0.75/1.61     Y := Y
% 0.75/1.61  end
% 0.75/1.61  permutation0:
% 0.75/1.61     0 ==> 0
% 0.75/1.61  end
% 0.75/1.61  
% 0.75/1.61  subsumption: (28) {G0,W5,D3,L1,V2,M1} I { greater( vplus( X, Y ), X ) }.
% 0.75/1.61  parent0: (9406) {G0,W5,D3,L1,V2,M1}  { greater( vplus( X, Y ), X ) }.
% 0.75/1.61  substitution0:
% 0.75/1.61     X := X
% 0.75/1.61     Y := Y
% 0.75/1.61  end
% 0.75/1.61  permutation0:
% 0.75/1.61     0 ==> 0
% 0.75/1.61  end
% 0.75/1.61  
% 0.75/1.61  eqswap: (9476) {G0,W10,D4,L2,V2,M2}  { Y ==> vplus( X, vskolem9( Y, X ) ), 
% 0.75/1.61    ! greater( Y, X ) }.
% 0.75/1.61  parent0[1]: (7) {G0,W10,D4,L2,V2,M2} I { ! greater( X, Y ), vplus( Y, 
% 0.75/1.61    vskolem9( X, Y ) ) ==> X }.
% 0.75/1.61  substitution0:
% 0.75/1.61     X := Y
% 0.75/1.61     Y := X
% 0.75/1.61  end
% 0.75/1.61  
% 0.75/1.61  resolution: (9477) {G1,W7,D4,L1,V0,M1}  { vd481 ==> vplus( vd480, vskolem9
% 0.75/1.61    ( vd481, vd480 ) ) }.
% 0.75/1.61  parent0[1]: (9476) {G0,W10,D4,L2,V2,M2}  { Y ==> vplus( X, vskolem9( Y, X )
% 0.75/1.61     ), ! greater( Y, X ) }.
% 0.75/1.61  parent1[0]: (1) {G0,W3,D2,L1,V0,M1} I { greater( vd481, vd480 ) }.
% 0.75/1.61  substitution0:
% 0.75/1.61     X := vd480
% 0.75/1.61     Y := vd481
% 0.75/1.61  end
% 0.75/1.61  substitution1:
% 0.75/1.61  end
% 0.75/1.61  
% 0.75/1.61  eqswap: (9478) {G1,W7,D4,L1,V0,M1}  { vplus( vd480, vskolem9( vd481, vd480
% 0.75/1.61     ) ) ==> vd481 }.
% 0.75/1.61  parent0[0]: (9477) {G1,W7,D4,L1,V0,M1}  { vd481 ==> vplus( vd480, vskolem9
% 0.75/1.61    ( vd481, vd480 ) ) }.
% 0.75/1.61  substitution0:
% 0.75/1.61  end
% 0.75/1.61  
% 0.75/1.61  subsumption: (90) {G1,W7,D4,L1,V0,M1} R(7,1) { vplus( vd480, vskolem9( 
% 0.75/1.61    vd481, vd480 ) ) ==> vd481 }.
% 0.75/1.61  parent0: (9478) {G1,W7,D4,L1,V0,M1}  { vplus( vd480, vskolem9( vd481, vd480
% 0.75/1.61     ) ) ==> vd481 }.
% 0.75/1.61  substitution0:
% 0.75/1.61  end
% 0.75/1.61  permutation0:
% 0.75/1.61     0 ==> 0
% 0.75/1.61  end
% 0.75/1.61  
% 0.75/1.61  paramod: (9480) {G1,W9,D4,L1,V3,M1}  { greater( vmul( X, vplus( Y, Z ) ), 
% 0.75/1.61    vmul( X, Y ) ) }.
% 0.75/1.61  parent0[0]: (9) {G0,W13,D4,L1,V3,M1} I { vplus( vmul( X, Y ), vmul( X, Z )
% 0.75/1.61     ) ==> vmul( X, vplus( Y, Z ) ) }.
% 0.75/1.61  parent1[0; 1]: (28) {G0,W5,D3,L1,V2,M1} I { greater( vplus( X, Y ), X ) }.
% 0.75/1.61  substitution0:
% 0.75/1.61     X := X
% 0.75/1.61     Y := Y
% 0.75/1.61     Z := Z
% 0.75/1.61  end
% 0.75/1.61  substitution1:
% 0.75/1.61     X := vmul( X, Y )
% 0.75/1.61     Y := vmul( X, Z )
% 0.75/1.61  end
% 0.75/1.61  
% 0.75/1.61  subsumption: (107) {G1,W9,D4,L1,V3,M1} P(9,28) { greater( vmul( X, vplus( Y
% 0.75/1.61    , Z ) ), vmul( X, Y ) ) }.
% 0.75/1.61  parent0: (9480) {G1,W9,D4,L1,V3,M1}  { greater( vmul( X, vplus( Y, Z ) ), 
% 0.75/1.61    vmul( X, Y ) ) }.
% 0.75/1.61  substitution0:
% 0.75/1.61     X := X
% 0.75/1.61     Y := Y
% 0.75/1.61     Z := Z
% 0.75/1.61  end
% 0.75/1.61  permutation0:
% 0.75/1.61     0 ==> 0
% 0.75/1.61  end
% 0.75/1.61  
% 0.75/1.61  paramod: (9481) {G1,W7,D3,L1,V0,M1}  { ! greater( vmul( vd469, vd481 ), 
% 0.75/1.61    vmul( vd480, vd469 ) ) }.
% 0.75/1.61  parent0[0]: (10) {G0,W7,D3,L1,V2,M1} I { vmul( X, Y ) = vmul( Y, X ) }.
% 0.75/1.61  parent1[0; 2]: (0) {G0,W7,D3,L1,V0,M1} I { ! greater( vmul( vd481, vd469 )
% 0.75/1.61    , vmul( vd480, vd469 ) ) }.
% 0.75/1.61  substitution0:
% 0.75/1.61     X := vd481
% 0.75/1.61     Y := vd469
% 0.75/1.61  end
% 0.75/1.61  substitution1:
% 0.75/1.61  end
% 0.75/1.61  
% 0.75/1.61  subsumption: (127) {G1,W7,D3,L1,V0,M1} P(10,0) { ! greater( vmul( vd469, 
% 0.75/1.61    vd481 ), vmul( vd480, vd469 ) ) }.
% 0.75/1.61  parent0: (9481) {G1,W7,D3,L1,V0,M1}  { ! greater( vmul( vd469, vd481 ), 
% 0.75/1.61    vmul( vd480, vd469 ) ) }.
% 0.75/1.61  substitution0:
% 0.75/1.61  end
% 0.75/1.61  permutation0:
% 0.75/1.61     0 ==> 0
% 0.75/1.61  end
% 0.75/1.61  
% 0.75/1.61  paramod: (9486) {G2,W7,D3,L1,V1,M1}  { greater( vmul( X, vd481 ), vmul( X, 
% 0.75/1.61    vd480 ) ) }.
% 0.75/1.61  parent0[0]: (90) {G1,W7,D4,L1,V0,M1} R(7,1) { vplus( vd480, vskolem9( vd481
% 0.75/1.61    , vd480 ) ) ==> vd481 }.
% 0.75/1.61  parent1[0; 3]: (107) {G1,W9,D4,L1,V3,M1} P(9,28) { greater( vmul( X, vplus
% 0.75/1.61    ( Y, Z ) ), vmul( X, Y ) ) }.
% 0.75/1.61  substitution0:
% 0.75/1.61  end
% 0.75/1.61  substitution1:
% 0.75/1.61     X := X
% 0.75/1.61     Y := vd480
% 0.75/1.61     Z := vskolem9( vd481, vd480 )
% 0.75/1.61  end
% 0.75/1.61  
% 0.75/1.61  subsumption: (7549) {G2,W7,D3,L1,V1,M1} P(90,107) { greater( vmul( X, vd481
% 0.75/1.61     ), vmul( X, vd480 ) ) }.
% 0.75/1.61  parent0: (9486) {G2,W7,D3,L1,V1,M1}  { greater( vmul( X, vd481 ), vmul( X, 
% 0.75/1.61    vd480 ) ) }.
% 0.75/1.61  substitution0:
% 0.75/1.61     X := X
% 0.75/1.61  end
% 0.75/1.61  permutation0:
% 0.75/1.61     0 ==> 0
% 0.75/1.61  end
% 0.75/1.61  
% 0.75/1.61  paramod: (9488) {G1,W7,D3,L1,V0,M1}  { ! greater( vmul( vd469, vd481 ), 
% 0.75/1.61    vmul( vd469, vd480 ) ) }.
% 0.75/1.61  parent0[0]: (10) {G0,W7,D3,L1,V2,M1} I { vmul( X, Y ) = vmul( Y, X ) }.
% 0.75/1.61  parent1[0; 5]: (127) {G1,W7,D3,L1,V0,M1} P(10,0) { ! greater( vmul( vd469, 
% 0.75/1.61    vd481 ), vmul( vd480, vd469 ) ) }.
% 0.75/1.61  substitution0:
% 0.75/1.61     X := vd480
% 0.75/1.61     Y := vd469
% 0.75/1.61  end
% 0.75/1.61  substitution1:
% 0.75/1.61  end
% 0.75/1.61  
% 0.75/1.61  resolution: (9491) {G2,W0,D0,L0,V0,M0}  {  }.
% 0.75/1.61  parent0[0]: (9488) {G1,W7,D3,L1,V0,M1}  { ! greater( vmul( vd469, vd481 ), 
% 0.75/1.61    vmul( vd469, vd480 ) ) }.
% 0.75/1.61  parent1[0]: (7549) {G2,W7,D3,L1,V1,M1} P(90,107) { greater( vmul( X, vd481
% 0.75/1.61     ), vmul( X, vd480 ) ) }.
% 0.75/1.61  substitution0:
% 0.75/1.61  end
% 0.75/1.61  substitution1:
% 0.75/1.61     X := vd469
% 0.75/1.61  end
% 0.75/1.61  
% 0.75/1.61  subsumption: (9376) {G3,W0,D0,L0,V0,M0} P(10,127);r(7549) {  }.
% 0.75/1.61  parent0: (9491) {G2,W0,D0,L0,V0,M0}  {  }.
% 0.75/1.61  substitution0:
% 0.75/1.61  end
% 0.75/1.61  permutation0:
% 0.75/1.61  end
% 0.75/1.61  
% 0.75/1.61  Proof check complete!
% 0.75/1.61  
% 0.75/1.61  Memory use:
% 0.75/1.61  
% 0.75/1.61  space for terms:        118818
% 0.75/1.61  space for clauses:      467423
% 0.75/1.61  
% 0.75/1.61  
% 0.75/1.61  clauses generated:      28056
% 0.75/1.61  clauses kept:           9377
% 0.75/1.61  clauses selected:       405
% 0.75/1.61  clauses deleted:        9
% 0.75/1.61  clauses inuse deleted:  3
% 0.75/1.61  
% 0.75/1.61  subsentry:          128729
% 0.75/1.61  literals s-matched: 84683
% 0.75/1.61  literals matched:   83842
% 0.75/1.61  full subsumption:   45426
% 0.75/1.61  
% 0.75/1.61  checksum:           -1980169804
% 0.75/1.61  
% 0.75/1.61  
% 0.75/1.61  Bliksem ended
%------------------------------------------------------------------------------