TSTP Solution File: NUM846+2 by Bliksem---1.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Bliksem---1.12
% Problem  : NUM846+2 : TPTP v8.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : bliksem %s

% Computer : n010.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 0.68s 1.06s
% Output   : Refutation 0.68s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem  : NUM846+2 : TPTP v8.1.0. Released v4.1.0.
% 0.10/0.12  % Command  : bliksem %s
% 0.13/0.33  % Computer : n010.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % DateTime : Tue Jul  5 14:25:32 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 0.68/1.06  *** allocated 10000 integers for termspace/termends
% 0.68/1.06  *** allocated 10000 integers for clauses
% 0.68/1.06  *** allocated 10000 integers for justifications
% 0.68/1.06  Bliksem 1.12
% 0.68/1.06  
% 0.68/1.06  
% 0.68/1.06  Automatic Strategy Selection
% 0.68/1.06  
% 0.68/1.06  
% 0.68/1.06  Clauses:
% 0.68/1.06  
% 0.68/1.06  { ! vplus( vmul( vd436, vplus( vd437, vd439 ) ), vd436 ) = vplus( vplus( 
% 0.68/1.06    vmul( vd436, vd437 ), vmul( vd436, vd439 ) ), vd436 ) }.
% 0.68/1.06  { vmul( vd436, vsucc( vplus( vd437, vd439 ) ) ) = vplus( vmul( vd436, vplus
% 0.68/1.06    ( vd437, vd439 ) ), vd436 ) }.
% 0.68/1.06  { vmul( vd436, vplus( vd437, vsucc( vd439 ) ) ) = vmul( vd436, vsucc( vplus
% 0.68/1.06    ( vd437, vd439 ) ) ) }.
% 0.68/1.06  { vmul( vd436, vplus( vd437, vd439 ) ) = vplus( vmul( vd436, vd437 ), vmul
% 0.68/1.06    ( vd436, vd439 ) ) }.
% 0.68/1.06  { vplus( vmul( vd436, vd437 ), vd436 ) = vplus( vmul( vd436, vd437 ), vmul
% 0.68/1.06    ( vd436, v1 ) ) }.
% 0.68/1.06  { vmul( vd436, vsucc( vd437 ) ) = vplus( vmul( vd436, vd437 ), vd436 ) }.
% 0.68/1.06  { vmul( vd436, vplus( vd437, v1 ) ) = vmul( vd436, vsucc( vd437 ) ) }.
% 0.68/1.06  { vmul( X, Y ) = vmul( Y, X ) }.
% 0.68/1.06  { vmul( v1, X ) = X }.
% 0.68/1.06  { vmul( X, vsucc( Y ) ) = vplus( vmul( X, Y ), X ) }.
% 0.68/1.06  { vmul( X, v1 ) = X }.
% 0.68/1.06  { ! less( X, vplus( Y, v1 ) ), leq( X, Y ) }.
% 0.68/1.06  { ! greater( X, Y ), geq( X, vplus( Y, v1 ) ) }.
% 0.68/1.06  { geq( X, v1 ) }.
% 0.68/1.06  { vplus( Y, X ) = vplus( X, Y ) }.
% 0.68/1.06  { vplus( vsucc( X ), Y ) = vsucc( vplus( X, Y ) ) }.
% 0.68/1.06  { vplus( v1, X ) = vsucc( X ) }.
% 0.68/1.06  { vplus( vplus( X, Y ), Z ) = vplus( X, vplus( Y, Z ) ) }.
% 0.68/1.06  { vplus( X, vsucc( Y ) ) = vsucc( vplus( X, Y ) ) }.
% 0.68/1.06  { vplus( X, v1 ) = vsucc( X ) }.
% 0.68/1.06  { X = v1, X = vsucc( vskolem2( X ) ) }.
% 0.68/1.06  { ! vsucc( X ) = X }.
% 0.68/1.06  { X = Y, ! vsucc( X ) = vsucc( Y ) }.
% 0.68/1.06  
% 0.68/1.06  percentage equality = 0.814815, percentage horn = 0.956522
% 0.68/1.06  This is a pure equality problem
% 0.68/1.06  
% 0.68/1.06  
% 0.68/1.06  
% 0.68/1.06  Options Used:
% 0.68/1.06  
% 0.68/1.06  useres =            1
% 0.68/1.06  useparamod =        1
% 0.68/1.06  useeqrefl =         1
% 0.68/1.06  useeqfact =         1
% 0.68/1.06  usefactor =         1
% 0.68/1.06  usesimpsplitting =  0
% 0.68/1.06  usesimpdemod =      5
% 0.68/1.06  usesimpres =        3
% 0.68/1.06  
% 0.68/1.06  resimpinuse      =  1000
% 0.68/1.06  resimpclauses =     20000
% 0.68/1.06  substype =          eqrewr
% 0.68/1.06  backwardsubs =      1
% 0.68/1.06  selectoldest =      5
% 0.68/1.06  
% 0.68/1.06  litorderings [0] =  split
% 0.68/1.06  litorderings [1] =  extend the termordering, first sorting on arguments
% 0.68/1.06  
% 0.68/1.06  termordering =      kbo
% 0.68/1.06  
% 0.68/1.06  litapriori =        0
% 0.68/1.06  termapriori =       1
% 0.68/1.06  litaposteriori =    0
% 0.68/1.06  termaposteriori =   0
% 0.68/1.06  demodaposteriori =  0
% 0.68/1.06  ordereqreflfact =   0
% 0.68/1.06  
% 0.68/1.06  litselect =         negord
% 0.68/1.06  
% 0.68/1.06  maxweight =         15
% 0.68/1.06  maxdepth =          30000
% 0.68/1.06  maxlength =         115
% 0.68/1.06  maxnrvars =         195
% 0.68/1.06  excuselevel =       1
% 0.68/1.06  increasemaxweight = 1
% 0.68/1.06  
% 0.68/1.06  maxselected =       10000000
% 0.68/1.06  maxnrclauses =      10000000
% 0.68/1.06  
% 0.68/1.06  showgenerated =    0
% 0.68/1.06  showkept =         0
% 0.68/1.06  showselected =     0
% 0.68/1.06  showdeleted =      0
% 0.68/1.06  showresimp =       1
% 0.68/1.06  showstatus =       2000
% 0.68/1.06  
% 0.68/1.06  prologoutput =     0
% 0.68/1.06  nrgoals =          5000000
% 0.68/1.06  totalproof =       1
% 0.68/1.06  
% 0.68/1.06  Symbols occurring in the translation:
% 0.68/1.06  
% 0.68/1.06  {}  [0, 0]      (w:1, o:2, a:1, s:1, b:0), 
% 0.68/1.06  .  [1, 2]      (w:1, o:41, a:1, s:1, b:0), 
% 0.68/1.06  !  [4, 1]      (w:0, o:34, a:1, s:1, b:0), 
% 0.68/1.06  =  [13, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 0.68/1.06  ==>  [14, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 0.68/1.06  vd436  [35, 0]      (w:1, o:6, a:1, s:1, b:0), 
% 0.68/1.06  vd437  [36, 0]      (w:1, o:7, a:1, s:1, b:0), 
% 0.68/1.06  vd439  [37, 0]      (w:1, o:8, a:1, s:1, b:0), 
% 0.68/1.06  vplus  [38, 2]      (w:1, o:65, a:1, s:1, b:0), 
% 0.68/1.06  vmul  [39, 2]      (w:1, o:66, a:1, s:1, b:0), 
% 0.68/1.06  vsucc  [40, 1]      (w:1, o:39, a:1, s:1, b:0), 
% 0.68/1.06  v1  [41, 0]      (w:1, o:9, a:1, s:1, b:0), 
% 0.68/1.06  less  [49, 2]      (w:1, o:67, a:1, s:1, b:0), 
% 0.68/1.06  leq  [50, 2]      (w:1, o:68, a:1, s:1, b:0), 
% 0.68/1.06  greater  [53, 2]      (w:1, o:69, a:1, s:1, b:0), 
% 0.68/1.06  geq  [54, 2]      (w:1, o:70, a:1, s:1, b:0), 
% 0.68/1.06  vskolem2  [67, 1]      (w:1, o:40, a:1, s:1, b:0).
% 0.68/1.06  
% 0.68/1.06  
% 0.68/1.06  Starting Search:
% 0.68/1.06  
% 0.68/1.06  
% 0.68/1.06  Bliksems!, er is een bewijs:
% 0.68/1.06  % SZS status Theorem
% 0.68/1.06  % SZS output start Refutation
% 0.68/1.06  
% 0.68/1.06  (0) {G0,W17,D5,L1,V0,M1} I { ! vplus( vplus( vmul( vd436, vd437 ), vmul( 
% 0.68/1.06    vd436, vd439 ) ), vd436 ) ==> vplus( vmul( vd436, vplus( vd437, vd439 ) )
% 0.68/1.06    , vd436 ) }.
% 0.68/1.06  (3) {G0,W13,D4,L1,V0,M1} I { vplus( vmul( vd436, vd437 ), vmul( vd436, 
% 0.68/1.06    vd439 ) ) ==> vmul( vd436, vplus( vd437, vd439 ) ) }.
% 0.68/1.06  (23) {G1,W0,D0,L0,V0,M0} S(0);d(3);q {  }.
% 0.68/1.06  
% 0.68/1.06  
% 0.68/1.06  % SZS output end Refutation
% 0.68/1.06  found a proof!
% 0.68/1.06  
% 0.68/1.06  
% 0.68/1.06  Unprocessed initial clauses:
% 0.68/1.06  
% 0.68/1.06  (25) {G0,W17,D5,L1,V0,M1}  { ! vplus( vmul( vd436, vplus( vd437, vd439 ) )
% 0.68/1.06    , vd436 ) = vplus( vplus( vmul( vd436, vd437 ), vmul( vd436, vd439 ) ), 
% 0.68/1.06    vd436 ) }.
% 0.68/1.06  (26) {G0,W14,D5,L1,V0,M1}  { vmul( vd436, vsucc( vplus( vd437, vd439 ) ) ) 
% 0.68/1.06    = vplus( vmul( vd436, vplus( vd437, vd439 ) ), vd436 ) }.
% 0.68/1.06  (27) {G0,W13,D5,L1,V0,M1}  { vmul( vd436, vplus( vd437, vsucc( vd439 ) ) ) 
% 0.68/1.06    = vmul( vd436, vsucc( vplus( vd437, vd439 ) ) ) }.
% 0.68/1.06  (28) {G0,W13,D4,L1,V0,M1}  { vmul( vd436, vplus( vd437, vd439 ) ) = vplus( 
% 0.68/1.06    vmul( vd436, vd437 ), vmul( vd436, vd439 ) ) }.
% 0.68/1.06  (29) {G0,W13,D4,L1,V0,M1}  { vplus( vmul( vd436, vd437 ), vd436 ) = vplus( 
% 0.68/1.06    vmul( vd436, vd437 ), vmul( vd436, v1 ) ) }.
% 0.68/1.06  (30) {G0,W10,D4,L1,V0,M1}  { vmul( vd436, vsucc( vd437 ) ) = vplus( vmul( 
% 0.68/1.06    vd436, vd437 ), vd436 ) }.
% 0.68/1.06  (31) {G0,W10,D4,L1,V0,M1}  { vmul( vd436, vplus( vd437, v1 ) ) = vmul( 
% 0.68/1.06    vd436, vsucc( vd437 ) ) }.
% 0.68/1.06  (32) {G0,W7,D3,L1,V2,M1}  { vmul( X, Y ) = vmul( Y, X ) }.
% 0.68/1.06  (33) {G0,W5,D3,L1,V1,M1}  { vmul( v1, X ) = X }.
% 0.68/1.06  (34) {G0,W10,D4,L1,V2,M1}  { vmul( X, vsucc( Y ) ) = vplus( vmul( X, Y ), X
% 0.68/1.06     ) }.
% 0.68/1.06  (35) {G0,W5,D3,L1,V1,M1}  { vmul( X, v1 ) = X }.
% 0.68/1.06  (36) {G0,W8,D3,L2,V2,M2}  { ! less( X, vplus( Y, v1 ) ), leq( X, Y ) }.
% 0.68/1.06  (37) {G0,W8,D3,L2,V2,M2}  { ! greater( X, Y ), geq( X, vplus( Y, v1 ) ) }.
% 0.68/1.06  (38) {G0,W3,D2,L1,V1,M1}  { geq( X, v1 ) }.
% 0.68/1.06  (39) {G0,W7,D3,L1,V2,M1}  { vplus( Y, X ) = vplus( X, Y ) }.
% 0.68/1.06  (40) {G0,W9,D4,L1,V2,M1}  { vplus( vsucc( X ), Y ) = vsucc( vplus( X, Y ) )
% 0.68/1.06     }.
% 0.68/1.06  (41) {G0,W6,D3,L1,V1,M1}  { vplus( v1, X ) = vsucc( X ) }.
% 0.68/1.06  (42) {G0,W11,D4,L1,V3,M1}  { vplus( vplus( X, Y ), Z ) = vplus( X, vplus( Y
% 0.68/1.06    , Z ) ) }.
% 0.68/1.06  (43) {G0,W9,D4,L1,V2,M1}  { vplus( X, vsucc( Y ) ) = vsucc( vplus( X, Y ) )
% 0.68/1.06     }.
% 0.68/1.06  (44) {G0,W6,D3,L1,V1,M1}  { vplus( X, v1 ) = vsucc( X ) }.
% 0.68/1.06  (45) {G0,W8,D4,L2,V1,M2}  { X = v1, X = vsucc( vskolem2( X ) ) }.
% 0.68/1.06  (46) {G0,W4,D3,L1,V1,M1}  { ! vsucc( X ) = X }.
% 0.68/1.06  (47) {G0,W8,D3,L2,V2,M2}  { X = Y, ! vsucc( X ) = vsucc( Y ) }.
% 0.68/1.06  
% 0.68/1.06  
% 0.68/1.06  Total Proof:
% 0.68/1.06  
% 0.68/1.06  eqswap: (48) {G0,W17,D5,L1,V0,M1}  { ! vplus( vplus( vmul( vd436, vd437 ), 
% 0.68/1.06    vmul( vd436, vd439 ) ), vd436 ) = vplus( vmul( vd436, vplus( vd437, vd439
% 0.68/1.06     ) ), vd436 ) }.
% 0.68/1.06  parent0[0]: (25) {G0,W17,D5,L1,V0,M1}  { ! vplus( vmul( vd436, vplus( vd437
% 0.68/1.06    , vd439 ) ), vd436 ) = vplus( vplus( vmul( vd436, vd437 ), vmul( vd436, 
% 0.68/1.06    vd439 ) ), vd436 ) }.
% 0.68/1.06  substitution0:
% 0.68/1.06  end
% 0.68/1.06  
% 0.68/1.06  subsumption: (0) {G0,W17,D5,L1,V0,M1} I { ! vplus( vplus( vmul( vd436, 
% 0.68/1.06    vd437 ), vmul( vd436, vd439 ) ), vd436 ) ==> vplus( vmul( vd436, vplus( 
% 0.68/1.06    vd437, vd439 ) ), vd436 ) }.
% 0.68/1.06  parent0: (48) {G0,W17,D5,L1,V0,M1}  { ! vplus( vplus( vmul( vd436, vd437 )
% 0.68/1.06    , vmul( vd436, vd439 ) ), vd436 ) = vplus( vmul( vd436, vplus( vd437, 
% 0.68/1.06    vd439 ) ), vd436 ) }.
% 0.68/1.06  substitution0:
% 0.68/1.06  end
% 0.68/1.06  permutation0:
% 0.68/1.06     0 ==> 0
% 0.68/1.06  end
% 0.68/1.06  
% 0.68/1.06  eqswap: (52) {G0,W13,D4,L1,V0,M1}  { vplus( vmul( vd436, vd437 ), vmul( 
% 0.68/1.06    vd436, vd439 ) ) = vmul( vd436, vplus( vd437, vd439 ) ) }.
% 0.68/1.06  parent0[0]: (28) {G0,W13,D4,L1,V0,M1}  { vmul( vd436, vplus( vd437, vd439 )
% 0.68/1.06     ) = vplus( vmul( vd436, vd437 ), vmul( vd436, vd439 ) ) }.
% 0.68/1.06  substitution0:
% 0.68/1.06  end
% 0.68/1.06  
% 0.68/1.06  subsumption: (3) {G0,W13,D4,L1,V0,M1} I { vplus( vmul( vd436, vd437 ), vmul
% 0.68/1.06    ( vd436, vd439 ) ) ==> vmul( vd436, vplus( vd437, vd439 ) ) }.
% 0.68/1.06  parent0: (52) {G0,W13,D4,L1,V0,M1}  { vplus( vmul( vd436, vd437 ), vmul( 
% 0.68/1.06    vd436, vd439 ) ) = vmul( vd436, vplus( vd437, vd439 ) ) }.
% 0.68/1.06  substitution0:
% 0.68/1.06  end
% 0.68/1.06  permutation0:
% 0.68/1.06     0 ==> 0
% 0.68/1.06  end
% 0.68/1.06  
% 0.68/1.06  paramod: (55) {G1,W15,D5,L1,V0,M1}  { ! vplus( vmul( vd436, vplus( vd437, 
% 0.68/1.06    vd439 ) ), vd436 ) ==> vplus( vmul( vd436, vplus( vd437, vd439 ) ), vd436
% 0.68/1.06     ) }.
% 0.68/1.06  parent0[0]: (3) {G0,W13,D4,L1,V0,M1} I { vplus( vmul( vd436, vd437 ), vmul
% 0.68/1.06    ( vd436, vd439 ) ) ==> vmul( vd436, vplus( vd437, vd439 ) ) }.
% 0.68/1.06  parent1[0; 3]: (0) {G0,W17,D5,L1,V0,M1} I { ! vplus( vplus( vmul( vd436, 
% 0.68/1.06    vd437 ), vmul( vd436, vd439 ) ), vd436 ) ==> vplus( vmul( vd436, vplus( 
% 0.68/1.06    vd437, vd439 ) ), vd436 ) }.
% 0.68/1.06  substitution0:
% 0.68/1.06  end
% 0.68/1.06  substitution1:
% 0.68/1.06  end
% 0.68/1.06  
% 0.68/1.06  eqrefl: (56) {G0,W0,D0,L0,V0,M0}  {  }.
% 0.68/1.06  parent0[0]: (55) {G1,W15,D5,L1,V0,M1}  { ! vplus( vmul( vd436, vplus( vd437
% 0.68/1.06    , vd439 ) ), vd436 ) ==> vplus( vmul( vd436, vplus( vd437, vd439 ) ), 
% 0.68/1.06    vd436 ) }.
% 0.68/1.06  substitution0:
% 0.68/1.06  end
% 0.68/1.06  
% 0.68/1.06  subsumption: (23) {G1,W0,D0,L0,V0,M0} S(0);d(3);q {  }.
% 0.68/1.06  parent0: (56) {G0,W0,D0,L0,V0,M0}  {  }.
% 0.68/1.06  substitution0:
% 0.68/1.06  end
% 0.68/1.06  permutation0:
% 0.68/1.06  end
% 0.68/1.06  
% 0.68/1.06  Proof check complete!
% 0.68/1.06  
% 0.68/1.06  Memory use:
% 0.68/1.06  
% 0.68/1.06  space for terms:        732
% 0.68/1.06  space for clauses:      2285
% 0.68/1.06  
% 0.68/1.06  
% 0.68/1.06  clauses generated:      33
% 0.68/1.06  clauses kept:           24
% 0.68/1.06  clauses selected:       5
% 0.68/1.06  clauses deleted:        1
% 0.68/1.06  clauses inuse deleted:  0
% 0.68/1.06  
% 0.68/1.06  subsentry:          36
% 0.68/1.06  literals s-matched: 17
% 0.68/1.06  literals matched:   17
% 0.68/1.06  full subsumption:   0
% 0.68/1.06  
% 0.68/1.06  checksum:           -1630649171
% 0.68/1.06  
% 0.68/1.06  
% 0.68/1.06  Bliksem ended
%------------------------------------------------------------------------------