TSTP Solution File: KLE052+1 by Bliksem---1.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Bliksem---1.12
% Problem  : KLE052+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : bliksem %s

% Computer : n032.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 : Sun Jul 17 01:36:55 EDT 2022

% Result   : Theorem 0.49s 1.01s
% Output   : Refutation 0.49s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09  % Problem  : KLE052+1 : TPTP v8.1.0. Released v4.0.0.
% 0.02/0.09  % Command  : bliksem %s
% 0.09/0.29  % Computer : n032.cluster.edu
% 0.09/0.29  % Model    : x86_64 x86_64
% 0.09/0.29  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29  % Memory   : 8042.1875MB
% 0.09/0.29  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29  % CPULimit : 300
% 0.09/0.29  % DateTime : Thu Jun 16 13:41:45 EDT 2022
% 0.09/0.29  % CPUTime  : 
% 0.49/1.01  *** allocated 10000 integers for termspace/termends
% 0.49/1.01  *** allocated 10000 integers for clauses
% 0.49/1.01  *** allocated 10000 integers for justifications
% 0.49/1.01  Bliksem 1.12
% 0.49/1.01  
% 0.49/1.01  
% 0.49/1.01  Automatic Strategy Selection
% 0.49/1.01  
% 0.49/1.01  
% 0.49/1.01  Clauses:
% 0.49/1.01  
% 0.49/1.01  { addition( X, Y ) = addition( Y, X ) }.
% 0.49/1.01  { addition( Z, addition( Y, X ) ) = addition( addition( Z, Y ), X ) }.
% 0.49/1.01  { addition( X, zero ) = X }.
% 0.49/1.01  { addition( X, X ) = X }.
% 0.49/1.01  { multiplication( X, multiplication( Y, Z ) ) = multiplication( 
% 0.49/1.01    multiplication( X, Y ), Z ) }.
% 0.49/1.01  { multiplication( X, one ) = X }.
% 0.49/1.01  { multiplication( one, X ) = X }.
% 0.49/1.01  { multiplication( X, addition( Y, Z ) ) = addition( multiplication( X, Y )
% 0.49/1.01    , multiplication( X, Z ) ) }.
% 0.49/1.01  { multiplication( addition( X, Y ), Z ) = addition( multiplication( X, Z )
% 0.49/1.01    , multiplication( Y, Z ) ) }.
% 0.49/1.01  { multiplication( X, zero ) = zero }.
% 0.49/1.01  { multiplication( zero, X ) = zero }.
% 0.49/1.01  { ! leq( X, Y ), addition( X, Y ) = Y }.
% 0.49/1.01  { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 0.49/1.01  { addition( X, multiplication( domain( X ), X ) ) = multiplication( domain
% 0.49/1.01    ( X ), X ) }.
% 0.49/1.01  { domain( multiplication( X, Y ) ) = domain( multiplication( X, domain( Y )
% 0.49/1.01     ) ) }.
% 0.49/1.01  { addition( domain( X ), one ) = one }.
% 0.49/1.01  { domain( zero ) = zero }.
% 0.49/1.01  { domain( addition( X, Y ) ) = addition( domain( X ), domain( Y ) ) }.
% 0.49/1.01  { ! multiplication( domain( skol1 ), skol1 ) = skol1 }.
% 0.49/1.01  
% 0.49/1.01  percentage equality = 0.904762, percentage horn = 1.000000
% 0.49/1.01  This is a pure equality problem
% 0.49/1.01  
% 0.49/1.01  
% 0.49/1.01  
% 0.49/1.01  Options Used:
% 0.49/1.01  
% 0.49/1.01  useres =            1
% 0.49/1.01  useparamod =        1
% 0.49/1.01  useeqrefl =         1
% 0.49/1.01  useeqfact =         1
% 0.49/1.01  usefactor =         1
% 0.49/1.01  usesimpsplitting =  0
% 0.49/1.01  usesimpdemod =      5
% 0.49/1.01  usesimpres =        3
% 0.49/1.01  
% 0.49/1.01  resimpinuse      =  1000
% 0.49/1.01  resimpclauses =     20000
% 0.49/1.01  substype =          eqrewr
% 0.49/1.01  backwardsubs =      1
% 0.49/1.01  selectoldest =      5
% 0.49/1.01  
% 0.49/1.01  litorderings [0] =  split
% 0.49/1.01  litorderings [1] =  extend the termordering, first sorting on arguments
% 0.49/1.01  
% 0.49/1.01  termordering =      kbo
% 0.49/1.01  
% 0.49/1.01  litapriori =        0
% 0.49/1.01  termapriori =       1
% 0.49/1.01  litaposteriori =    0
% 0.49/1.01  termaposteriori =   0
% 0.49/1.01  demodaposteriori =  0
% 0.49/1.01  ordereqreflfact =   0
% 0.49/1.01  
% 0.49/1.01  litselect =         negord
% 0.49/1.01  
% 0.49/1.01  maxweight =         15
% 0.49/1.01  maxdepth =          30000
% 0.49/1.01  maxlength =         115
% 0.49/1.01  maxnrvars =         195
% 0.49/1.01  excuselevel =       1
% 0.49/1.01  increasemaxweight = 1
% 0.49/1.01  
% 0.49/1.01  maxselected =       10000000
% 0.49/1.01  maxnrclauses =      10000000
% 0.49/1.01  
% 0.49/1.01  showgenerated =    0
% 0.49/1.01  showkept =         0
% 0.49/1.01  showselected =     0
% 0.49/1.01  showdeleted =      0
% 0.49/1.01  showresimp =       1
% 0.49/1.01  showstatus =       2000
% 0.49/1.01  
% 0.49/1.01  prologoutput =     0
% 0.49/1.01  nrgoals =          5000000
% 0.49/1.01  totalproof =       1
% 0.49/1.01  
% 0.49/1.01  Symbols occurring in the translation:
% 0.49/1.01  
% 0.49/1.01  {}  [0, 0]      (w:1, o:2, a:1, s:1, b:0), 
% 0.49/1.01  .  [1, 2]      (w:1, o:20, a:1, s:1, b:0), 
% 0.49/1.01  !  [4, 1]      (w:0, o:14, a:1, s:1, b:0), 
% 0.49/1.01  =  [13, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 0.49/1.01  ==>  [14, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 0.49/1.01  addition  [37, 2]      (w:1, o:44, a:1, s:1, b:0), 
% 0.49/1.01  zero  [39, 0]      (w:1, o:9, a:1, s:1, b:0), 
% 0.49/1.01  multiplication  [40, 2]      (w:1, o:46, a:1, s:1, b:0), 
% 0.49/1.01  one  [41, 0]      (w:1, o:10, a:1, s:1, b:0), 
% 0.49/1.01  leq  [42, 2]      (w:1, o:45, a:1, s:1, b:0), 
% 0.49/1.01  domain  [44, 1]      (w:1, o:19, a:1, s:1, b:0), 
% 0.49/1.01  skol1  [46, 0]      (w:1, o:13, a:1, s:1, b:1).
% 0.49/1.01  
% 0.49/1.01  
% 0.49/1.01  Starting Search:
% 0.49/1.01  
% 0.49/1.01  *** allocated 15000 integers for clauses
% 0.49/1.01  *** allocated 22500 integers for clauses
% 0.49/1.01  *** allocated 33750 integers for clauses
% 0.49/1.01  *** allocated 50625 integers for clauses
% 0.49/1.01  *** allocated 75937 integers for clauses
% 0.49/1.01  *** allocated 15000 integers for termspace/termends
% 0.49/1.01  Resimplifying inuse:
% 0.49/1.01  Done
% 0.49/1.01  
% 0.49/1.01  *** allocated 22500 integers for termspace/termends
% 0.49/1.01  *** allocated 113905 integers for clauses
% 0.49/1.01  *** allocated 33750 integers for termspace/termends
% 0.49/1.01  
% 0.49/1.01  Intermediate Status:
% 0.49/1.01  Generated:    14368
% 0.49/1.01  Kept:         2005
% 0.49/1.01  Inuse:        224
% 0.49/1.01  Deleted:      13
% 0.49/1.01  Deletedinuse: 5
% 0.49/1.01  
% 0.49/1.01  Resimplifying inuse:
% 0.49/1.01  Done
% 0.49/1.01  
% 0.49/1.01  *** allocated 170857 integers for clauses
% 0.49/1.01  
% 0.49/1.01  Bliksems!, er is een bewijs:
% 0.49/1.01  % SZS status Theorem
% 0.49/1.01  % SZS output start Refutation
% 0.49/1.01  
% 0.49/1.01  (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X ) }.
% 0.49/1.01  (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 0.49/1.01  (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ), 
% 0.49/1.01    multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 0.49/1.01  (13) {G0,W11,D5,L1,V1,M1} I { addition( X, multiplication( domain( X ), X )
% 0.49/1.01     ) ==> multiplication( domain( X ), X ) }.
% 0.49/1.01  (15) {G0,W6,D4,L1,V1,M1} I { addition( domain( X ), one ) ==> one }.
% 0.49/1.01  (18) {G0,W6,D4,L1,V0,M1} I { ! multiplication( domain( skol1 ), skol1 ) ==>
% 0.49/1.01     skol1 }.
% 0.49/1.01  (20) {G1,W6,D4,L1,V1,M1} P(15,0) { addition( one, domain( X ) ) ==> one }.
% 0.49/1.01  (78) {G1,W11,D4,L1,V2,M1} P(6,8) { addition( X, multiplication( Y, X ) ) = 
% 0.49/1.01    multiplication( addition( one, Y ), X ) }.
% 0.49/1.01  (2400) {G2,W6,D4,L1,V1,M1} P(78,13);d(20);d(6) { multiplication( domain( X
% 0.49/1.01     ), X ) ==> X }.
% 0.49/1.01  (2411) {G3,W0,D0,L0,V0,M0} R(2400,18) {  }.
% 0.49/1.01  
% 0.49/1.01  
% 0.49/1.01  % SZS output end Refutation
% 0.49/1.01  found a proof!
% 0.49/1.01  
% 0.49/1.01  
% 0.49/1.01  Unprocessed initial clauses:
% 0.49/1.01  
% 0.49/1.01  (2413) {G0,W7,D3,L1,V2,M1}  { addition( X, Y ) = addition( Y, X ) }.
% 0.49/1.01  (2414) {G0,W11,D4,L1,V3,M1}  { addition( Z, addition( Y, X ) ) = addition( 
% 0.49/1.01    addition( Z, Y ), X ) }.
% 0.49/1.01  (2415) {G0,W5,D3,L1,V1,M1}  { addition( X, zero ) = X }.
% 0.49/1.01  (2416) {G0,W5,D3,L1,V1,M1}  { addition( X, X ) = X }.
% 0.49/1.01  (2417) {G0,W11,D4,L1,V3,M1}  { multiplication( X, multiplication( Y, Z ) ) 
% 0.49/1.01    = multiplication( multiplication( X, Y ), Z ) }.
% 0.49/1.01  (2418) {G0,W5,D3,L1,V1,M1}  { multiplication( X, one ) = X }.
% 0.49/1.01  (2419) {G0,W5,D3,L1,V1,M1}  { multiplication( one, X ) = X }.
% 0.49/1.01  (2420) {G0,W13,D4,L1,V3,M1}  { multiplication( X, addition( Y, Z ) ) = 
% 0.49/1.01    addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 0.49/1.01  (2421) {G0,W13,D4,L1,V3,M1}  { multiplication( addition( X, Y ), Z ) = 
% 0.49/1.01    addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 0.49/1.01  (2422) {G0,W5,D3,L1,V1,M1}  { multiplication( X, zero ) = zero }.
% 0.49/1.01  (2423) {G0,W5,D3,L1,V1,M1}  { multiplication( zero, X ) = zero }.
% 0.49/1.01  (2424) {G0,W8,D3,L2,V2,M2}  { ! leq( X, Y ), addition( X, Y ) = Y }.
% 0.49/1.01  (2425) {G0,W8,D3,L2,V2,M2}  { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 0.49/1.01  (2426) {G0,W11,D5,L1,V1,M1}  { addition( X, multiplication( domain( X ), X
% 0.49/1.01     ) ) = multiplication( domain( X ), X ) }.
% 0.49/1.01  (2427) {G0,W10,D5,L1,V2,M1}  { domain( multiplication( X, Y ) ) = domain( 
% 0.49/1.01    multiplication( X, domain( Y ) ) ) }.
% 0.49/1.01  (2428) {G0,W6,D4,L1,V1,M1}  { addition( domain( X ), one ) = one }.
% 0.49/1.01  (2429) {G0,W4,D3,L1,V0,M1}  { domain( zero ) = zero }.
% 0.49/1.01  (2430) {G0,W10,D4,L1,V2,M1}  { domain( addition( X, Y ) ) = addition( 
% 0.49/1.01    domain( X ), domain( Y ) ) }.
% 0.49/1.01  (2431) {G0,W6,D4,L1,V0,M1}  { ! multiplication( domain( skol1 ), skol1 ) = 
% 0.49/1.01    skol1 }.
% 0.49/1.01  
% 0.49/1.01  
% 0.49/1.01  Total Proof:
% 0.49/1.01  
% 0.49/1.01  subsumption: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X
% 0.49/1.01     ) }.
% 0.49/1.01  parent0: (2413) {G0,W7,D3,L1,V2,M1}  { addition( X, Y ) = addition( Y, X )
% 0.49/1.01     }.
% 0.49/1.01  substitution0:
% 0.49/1.01     X := X
% 0.49/1.01     Y := Y
% 0.49/1.01  end
% 0.49/1.01  permutation0:
% 0.49/1.01     0 ==> 0
% 0.49/1.01  end
% 0.49/1.01  
% 0.49/1.01  subsumption: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 0.49/1.01  parent0: (2419) {G0,W5,D3,L1,V1,M1}  { multiplication( one, X ) = X }.
% 0.49/1.01  substitution0:
% 0.49/1.01     X := X
% 0.49/1.01  end
% 0.49/1.01  permutation0:
% 0.49/1.01     0 ==> 0
% 0.49/1.01  end
% 0.49/1.01  
% 0.49/1.01  eqswap: (2445) {G0,W13,D4,L1,V3,M1}  { addition( multiplication( X, Z ), 
% 0.49/1.01    multiplication( Y, Z ) ) = multiplication( addition( X, Y ), Z ) }.
% 0.49/1.01  parent0[0]: (2421) {G0,W13,D4,L1,V3,M1}  { multiplication( addition( X, Y )
% 0.49/1.01    , Z ) = addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 0.49/1.01  substitution0:
% 0.49/1.01     X := X
% 0.49/1.01     Y := Y
% 0.49/1.01     Z := Z
% 0.49/1.01  end
% 0.49/1.01  
% 0.49/1.01  subsumption: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z )
% 0.49/1.01    , multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 0.49/1.01  parent0: (2445) {G0,W13,D4,L1,V3,M1}  { addition( multiplication( X, Z ), 
% 0.49/1.01    multiplication( Y, Z ) ) = multiplication( addition( X, Y ), Z ) }.
% 0.49/1.01  substitution0:
% 0.49/1.01     X := X
% 0.49/1.01     Y := Y
% 0.49/1.01     Z := Z
% 0.49/1.01  end
% 0.49/1.01  permutation0:
% 0.49/1.01     0 ==> 0
% 0.49/1.01  end
% 0.49/1.01  
% 0.49/1.01  subsumption: (13) {G0,W11,D5,L1,V1,M1} I { addition( X, multiplication( 
% 0.49/1.01    domain( X ), X ) ) ==> multiplication( domain( X ), X ) }.
% 0.49/1.01  parent0: (2426) {G0,W11,D5,L1,V1,M1}  { addition( X, multiplication( domain
% 0.49/1.01    ( X ), X ) ) = multiplication( domain( X ), X ) }.
% 0.49/1.01  substitution0:
% 0.49/1.01     X := X
% 0.49/1.01  end
% 0.49/1.01  permutation0:
% 0.49/1.01     0 ==> 0
% 0.49/1.01  end
% 0.49/1.01  
% 0.49/1.01  subsumption: (15) {G0,W6,D4,L1,V1,M1} I { addition( domain( X ), one ) ==> 
% 0.49/1.01    one }.
% 0.49/1.01  parent0: (2428) {G0,W6,D4,L1,V1,M1}  { addition( domain( X ), one ) = one
% 0.49/1.01     }.
% 0.49/1.01  substitution0:
% 0.49/1.01     X := X
% 0.49/1.01  end
% 0.49/1.01  permutation0:
% 0.49/1.01     0 ==> 0
% 0.49/1.01  end
% 0.49/1.01  
% 0.49/1.01  subsumption: (18) {G0,W6,D4,L1,V0,M1} I { ! multiplication( domain( skol1 )
% 0.49/1.01    , skol1 ) ==> skol1 }.
% 0.49/1.01  parent0: (2431) {G0,W6,D4,L1,V0,M1}  { ! multiplication( domain( skol1 ), 
% 0.49/1.01    skol1 ) = skol1 }.
% 0.49/1.01  substitution0:
% 0.49/1.01  end
% 0.49/1.01  permutation0:
% 0.49/1.01     0 ==> 0
% 0.49/1.01  end
% 0.49/1.01  
% 0.49/1.01  eqswap: (2492) {G0,W6,D4,L1,V1,M1}  { one ==> addition( domain( X ), one )
% 0.49/1.01     }.
% 0.49/1.01  parent0[0]: (15) {G0,W6,D4,L1,V1,M1} I { addition( domain( X ), one ) ==> 
% 0.49/1.01    one }.
% 0.49/1.01  substitution0:
% 0.49/1.01     X := X
% 0.49/1.01  end
% 0.49/1.01  
% 0.49/1.01  paramod: (2493) {G1,W6,D4,L1,V1,M1}  { one ==> addition( one, domain( X ) )
% 0.49/1.01     }.
% 0.49/1.01  parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 0.49/1.01     }.
% 0.49/1.01  parent1[0; 2]: (2492) {G0,W6,D4,L1,V1,M1}  { one ==> addition( domain( X )
% 0.49/1.01    , one ) }.
% 0.49/1.01  substitution0:
% 0.49/1.01     X := domain( X )
% 0.49/1.01     Y := one
% 0.49/1.01  end
% 0.49/1.01  substitution1:
% 0.49/1.01     X := X
% 0.49/1.01  end
% 0.49/1.01  
% 0.49/1.01  eqswap: (2496) {G1,W6,D4,L1,V1,M1}  { addition( one, domain( X ) ) ==> one
% 0.49/1.01     }.
% 0.49/1.01  parent0[0]: (2493) {G1,W6,D4,L1,V1,M1}  { one ==> addition( one, domain( X
% 0.49/1.01     ) ) }.
% 0.49/1.01  substitution0:
% 0.49/1.01     X := X
% 0.49/1.01  end
% 0.49/1.01  
% 0.49/1.01  subsumption: (20) {G1,W6,D4,L1,V1,M1} P(15,0) { addition( one, domain( X )
% 0.49/1.01     ) ==> one }.
% 0.49/1.01  parent0: (2496) {G1,W6,D4,L1,V1,M1}  { addition( one, domain( X ) ) ==> one
% 0.49/1.01     }.
% 0.49/1.01  substitution0:
% 0.49/1.01     X := X
% 0.49/1.01  end
% 0.49/1.01  permutation0:
% 0.49/1.01     0 ==> 0
% 0.49/1.01  end
% 0.49/1.01  
% 0.49/1.01  eqswap: (2498) {G0,W13,D4,L1,V3,M1}  { multiplication( addition( X, Z ), Y
% 0.49/1.01     ) ==> addition( multiplication( X, Y ), multiplication( Z, Y ) ) }.
% 0.49/1.01  parent0[0]: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ), 
% 0.49/1.01    multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 0.49/1.01  substitution0:
% 0.49/1.01     X := X
% 0.49/1.01     Y := Z
% 0.49/1.01     Z := Y
% 0.49/1.01  end
% 0.49/1.01  
% 0.49/1.01  paramod: (2499) {G1,W11,D4,L1,V2,M1}  { multiplication( addition( one, X )
% 0.49/1.01    , Y ) ==> addition( Y, multiplication( X, Y ) ) }.
% 0.49/1.01  parent0[0]: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 0.49/1.01  parent1[0; 7]: (2498) {G0,W13,D4,L1,V3,M1}  { multiplication( addition( X, 
% 0.49/1.01    Z ), Y ) ==> addition( multiplication( X, Y ), multiplication( Z, Y ) )
% 0.49/1.01     }.
% 0.49/1.01  substitution0:
% 0.49/1.01     X := Y
% 0.49/1.01  end
% 0.49/1.01  substitution1:
% 0.49/1.01     X := one
% 0.49/1.01     Y := Y
% 0.49/1.01     Z := X
% 0.49/1.01  end
% 0.49/1.01  
% 0.49/1.01  eqswap: (2501) {G1,W11,D4,L1,V2,M1}  { addition( Y, multiplication( X, Y )
% 0.49/1.01     ) ==> multiplication( addition( one, X ), Y ) }.
% 0.49/1.01  parent0[0]: (2499) {G1,W11,D4,L1,V2,M1}  { multiplication( addition( one, X
% 0.49/1.01     ), Y ) ==> addition( Y, multiplication( X, Y ) ) }.
% 0.49/1.01  substitution0:
% 0.49/1.01     X := X
% 0.49/1.01     Y := Y
% 0.49/1.01  end
% 0.49/1.01  
% 0.49/1.01  subsumption: (78) {G1,W11,D4,L1,V2,M1} P(6,8) { addition( X, multiplication
% 0.49/1.01    ( Y, X ) ) = multiplication( addition( one, Y ), X ) }.
% 0.49/1.01  parent0: (2501) {G1,W11,D4,L1,V2,M1}  { addition( Y, multiplication( X, Y )
% 0.49/1.01     ) ==> multiplication( addition( one, X ), Y ) }.
% 0.49/1.01  substitution0:
% 0.49/1.01     X := Y
% 0.49/1.01     Y := X
% 0.49/1.01  end
% 0.49/1.01  permutation0:
% 0.49/1.01     0 ==> 0
% 0.49/1.01  end
% 0.49/1.01  
% 0.49/1.01  eqswap: (2503) {G1,W11,D4,L1,V2,M1}  { multiplication( addition( one, Y ), 
% 0.49/1.01    X ) = addition( X, multiplication( Y, X ) ) }.
% 0.49/1.01  parent0[0]: (78) {G1,W11,D4,L1,V2,M1} P(6,8) { addition( X, multiplication
% 0.49/1.01    ( Y, X ) ) = multiplication( addition( one, Y ), X ) }.
% 0.49/1.01  substitution0:
% 0.49/1.01     X := X
% 0.49/1.01     Y := Y
% 0.49/1.01  end
% 0.49/1.01  
% 0.49/1.01  paramod: (2508) {G1,W11,D5,L1,V1,M1}  { multiplication( addition( one, 
% 0.49/1.01    domain( X ) ), X ) = multiplication( domain( X ), X ) }.
% 0.49/1.01  parent0[0]: (13) {G0,W11,D5,L1,V1,M1} I { addition( X, multiplication( 
% 0.49/1.01    domain( X ), X ) ) ==> multiplication( domain( X ), X ) }.
% 0.49/1.01  parent1[0; 7]: (2503) {G1,W11,D4,L1,V2,M1}  { multiplication( addition( one
% 0.49/1.01    , Y ), X ) = addition( X, multiplication( Y, X ) ) }.
% 0.49/1.01  substitution0:
% 0.49/1.01     X := X
% 0.49/1.01  end
% 0.49/1.01  substitution1:
% 0.49/1.01     X := X
% 0.49/1.01     Y := domain( X )
% 0.49/1.01  end
% 0.49/1.01  
% 0.49/1.01  paramod: (2509) {G2,W8,D4,L1,V1,M1}  { multiplication( one, X ) = 
% 0.49/1.01    multiplication( domain( X ), X ) }.
% 0.49/1.01  parent0[0]: (20) {G1,W6,D4,L1,V1,M1} P(15,0) { addition( one, domain( X ) )
% 0.49/1.01     ==> one }.
% 0.49/1.01  parent1[0; 2]: (2508) {G1,W11,D5,L1,V1,M1}  { multiplication( addition( one
% 0.49/1.01    , domain( X ) ), X ) = multiplication( domain( X ), X ) }.
% 0.49/1.01  substitution0:
% 0.49/1.01     X := X
% 0.49/1.01  end
% 0.49/1.01  substitution1:
% 0.49/1.01     X := X
% 0.49/1.01  end
% 0.49/1.01  
% 0.49/1.01  paramod: (2510) {G1,W6,D4,L1,V1,M1}  { X = multiplication( domain( X ), X )
% 0.49/1.01     }.
% 0.49/1.01  parent0[0]: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 0.49/1.01  parent1[0; 1]: (2509) {G2,W8,D4,L1,V1,M1}  { multiplication( one, X ) = 
% 0.49/1.01    multiplication( domain( X ), X ) }.
% 0.49/1.01  substitution0:
% 0.49/1.01     X := X
% 0.49/1.01  end
% 0.49/1.01  substitution1:
% 0.49/1.01     X := X
% 0.49/1.01  end
% 0.49/1.01  
% 0.49/1.01  eqswap: (2511) {G1,W6,D4,L1,V1,M1}  { multiplication( domain( X ), X ) = X
% 0.49/1.01     }.
% 0.49/1.01  parent0[0]: (2510) {G1,W6,D4,L1,V1,M1}  { X = multiplication( domain( X ), 
% 0.49/1.01    X ) }.
% 0.49/1.01  substitution0:
% 0.49/1.01     X := X
% 0.49/1.01  end
% 0.49/1.01  
% 0.49/1.01  subsumption: (2400) {G2,W6,D4,L1,V1,M1} P(78,13);d(20);d(6) { 
% 0.49/1.01    multiplication( domain( X ), X ) ==> X }.
% 0.49/1.01  parent0: (2511) {G1,W6,D4,L1,V1,M1}  { multiplication( domain( X ), X ) = X
% 0.49/1.01     }.
% 0.49/1.01  substitution0:
% 0.49/1.01     X := X
% 0.49/1.01  end
% 0.49/1.01  permutation0:
% 0.49/1.01     0 ==> 0
% 0.49/1.01  end
% 0.49/1.01  
% 0.49/1.01  eqswap: (2512) {G2,W6,D4,L1,V1,M1}  { X ==> multiplication( domain( X ), X
% 0.49/1.01     ) }.
% 0.49/1.01  parent0[0]: (2400) {G2,W6,D4,L1,V1,M1} P(78,13);d(20);d(6) { multiplication
% 0.49/1.01    ( domain( X ), X ) ==> X }.
% 0.49/1.01  substitution0:
% 0.49/1.01     X := X
% 0.49/1.01  end
% 0.49/1.01  
% 0.49/1.01  eqswap: (2513) {G0,W6,D4,L1,V0,M1}  { ! skol1 ==> multiplication( domain( 
% 0.49/1.01    skol1 ), skol1 ) }.
% 0.49/1.01  parent0[0]: (18) {G0,W6,D4,L1,V0,M1} I { ! multiplication( domain( skol1 )
% 0.49/1.01    , skol1 ) ==> skol1 }.
% 0.49/1.01  substitution0:
% 0.49/1.01  end
% 0.49/1.01  
% 0.49/1.01  resolution: (2514) {G1,W0,D0,L0,V0,M0}  {  }.
% 0.49/1.01  parent0[0]: (2513) {G0,W6,D4,L1,V0,M1}  { ! skol1 ==> multiplication( 
% 0.49/1.01    domain( skol1 ), skol1 ) }.
% 0.49/1.01  parent1[0]: (2512) {G2,W6,D4,L1,V1,M1}  { X ==> multiplication( domain( X )
% 0.49/1.01    , X ) }.
% 0.49/1.01  substitution0:
% 0.49/1.01  end
% 0.49/1.01  substitution1:
% 0.49/1.01     X := skol1
% 0.49/1.01  end
% 0.49/1.01  
% 0.49/1.01  subsumption: (2411) {G3,W0,D0,L0,V0,M0} R(2400,18) {  }.
% 0.49/1.01  parent0: (2514) {G1,W0,D0,L0,V0,M0}  {  }.
% 0.49/1.01  substitution0:
% 0.49/1.01  end
% 0.49/1.01  permutation0:
% 0.49/1.01  end
% 0.49/1.01  
% 0.49/1.01  Proof check complete!
% 0.49/1.01  
% 0.49/1.01  Memory use:
% 0.49/1.01  
% 0.49/1.01  space for terms:        30448
% 0.49/1.01  space for clauses:      124707
% 0.49/1.01  
% 0.49/1.01  
% 0.49/1.01  clauses generated:      17992
% 0.49/1.01  clauses kept:           2412
% 0.49/1.01  clauses selected:       250
% 0.49/1.01  clauses deleted:        18
% 0.49/1.01  clauses inuse deleted:  6
% 0.49/1.01  
% 0.49/1.01  subsentry:          38292
% 0.49/1.01  literals s-matched: 26182
% 0.49/1.01  literals matched:   25050
% 0.49/1.01  full subsumption:   3121
% 0.49/1.01  
% 0.49/1.01  checksum:           -1593391094
% 0.49/1.01  
% 0.49/1.01  
% 0.49/1.01  Bliksem ended
%------------------------------------------------------------------------------