TSTP Solution File: SET962+1 by Bliksem---1.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Bliksem---1.12
% Problem  : SET962+1 : TPTP v8.1.0. Bugfixed v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : bliksem %s

% Computer : n028.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 22:53:38 EDT 2022

% Result   : Theorem 0.71s 1.11s
% Output   : Refutation 0.71s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : SET962+1 : TPTP v8.1.0. Bugfixed v4.0.0.
% 0.07/0.13  % Command  : bliksem %s
% 0.13/0.35  % Computer : n028.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % DateTime : Sat Jul  9 18:46:26 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.71/1.11  *** allocated 10000 integers for termspace/termends
% 0.71/1.11  *** allocated 10000 integers for clauses
% 0.71/1.11  *** allocated 10000 integers for justifications
% 0.71/1.11  Bliksem 1.12
% 0.71/1.11  
% 0.71/1.11  
% 0.71/1.11  Automatic Strategy Selection
% 0.71/1.11  
% 0.71/1.11  
% 0.71/1.11  Clauses:
% 0.71/1.11  
% 0.71/1.11  { ! in( X, Y ), ! in( Y, X ) }.
% 0.71/1.11  { unordered_pair( X, Y ) = unordered_pair( Y, X ) }.
% 0.71/1.11  { ordered_pair( X, Y ) = unordered_pair( unordered_pair( X, Y ), singleton
% 0.71/1.11    ( X ) ) }.
% 0.71/1.11  { ! empty( ordered_pair( X, Y ) ) }.
% 0.71/1.11  { ! in( ordered_pair( X, Y ), cartesian_product2( Z, T ) ), in( X, Z ) }.
% 0.71/1.11  { ! in( ordered_pair( X, Y ), cartesian_product2( Z, T ) ), in( Y, T ) }.
% 0.71/1.11  { ! in( X, Z ), ! in( Y, T ), in( ordered_pair( X, Y ), cartesian_product2
% 0.71/1.11    ( Z, T ) ) }.
% 0.71/1.11  { empty( skol1 ) }.
% 0.71/1.11  { ! empty( skol2 ) }.
% 0.71/1.11  { cartesian_product2( skol3, skol3 ) = cartesian_product2( skol5, skol5 ) }
% 0.71/1.11    .
% 0.71/1.11  { ! skol3 = skol5 }.
% 0.71/1.11  { alpha1( X, Y, skol4( X, Y ) ), in( skol4( X, Y ), Y ), X = Y }.
% 0.71/1.11  { alpha1( X, Y, skol4( X, Y ) ), ! in( skol4( X, Y ), X ), X = Y }.
% 0.71/1.11  { ! alpha1( X, Y, Z ), in( Z, X ) }.
% 0.71/1.11  { ! alpha1( X, Y, Z ), ! in( Z, Y ) }.
% 0.71/1.11  { ! in( Z, X ), in( Z, Y ), alpha1( X, Y, Z ) }.
% 0.71/1.11  
% 0.71/1.11  percentage equality = 0.206897, percentage horn = 0.812500
% 0.71/1.11  This is a problem with some equality
% 0.71/1.11  
% 0.71/1.11  
% 0.71/1.11  
% 0.71/1.11  Options Used:
% 0.71/1.11  
% 0.71/1.11  useres =            1
% 0.71/1.11  useparamod =        1
% 0.71/1.11  useeqrefl =         1
% 0.71/1.11  useeqfact =         1
% 0.71/1.11  usefactor =         1
% 0.71/1.11  usesimpsplitting =  0
% 0.71/1.11  usesimpdemod =      5
% 0.71/1.11  usesimpres =        3
% 0.71/1.11  
% 0.71/1.11  resimpinuse      =  1000
% 0.71/1.11  resimpclauses =     20000
% 0.71/1.11  substype =          eqrewr
% 0.71/1.11  backwardsubs =      1
% 0.71/1.11  selectoldest =      5
% 0.71/1.11  
% 0.71/1.11  litorderings [0] =  split
% 0.71/1.11  litorderings [1] =  extend the termordering, first sorting on arguments
% 0.71/1.11  
% 0.71/1.11  termordering =      kbo
% 0.71/1.11  
% 0.71/1.11  litapriori =        0
% 0.71/1.11  termapriori =       1
% 0.71/1.11  litaposteriori =    0
% 0.71/1.11  termaposteriori =   0
% 0.71/1.11  demodaposteriori =  0
% 0.71/1.11  ordereqreflfact =   0
% 0.71/1.11  
% 0.71/1.11  litselect =         negord
% 0.71/1.11  
% 0.71/1.11  maxweight =         15
% 0.71/1.11  maxdepth =          30000
% 0.71/1.11  maxlength =         115
% 0.71/1.11  maxnrvars =         195
% 0.71/1.11  excuselevel =       1
% 0.71/1.11  increasemaxweight = 1
% 0.71/1.11  
% 0.71/1.11  maxselected =       10000000
% 0.71/1.11  maxnrclauses =      10000000
% 0.71/1.11  
% 0.71/1.11  showgenerated =    0
% 0.71/1.11  showkept =         0
% 0.71/1.11  showselected =     0
% 0.71/1.11  showdeleted =      0
% 0.71/1.11  showresimp =       1
% 0.71/1.11  showstatus =       2000
% 0.71/1.11  
% 0.71/1.11  prologoutput =     0
% 0.71/1.11  nrgoals =          5000000
% 0.71/1.11  totalproof =       1
% 0.71/1.11  
% 0.71/1.11  Symbols occurring in the translation:
% 0.71/1.11  
% 0.71/1.11  {}  [0, 0]      (w:1, o:2, a:1, s:1, b:0), 
% 0.71/1.11  .  [1, 2]      (w:1, o:21, a:1, s:1, b:0), 
% 0.71/1.11  !  [4, 1]      (w:0, o:14, a:1, s:1, b:0), 
% 0.71/1.11  =  [13, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 0.71/1.11  ==>  [14, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 0.71/1.11  in  [37, 2]      (w:1, o:45, a:1, s:1, b:0), 
% 0.71/1.11  unordered_pair  [38, 2]      (w:1, o:46, a:1, s:1, b:0), 
% 0.71/1.11  ordered_pair  [39, 2]      (w:1, o:47, a:1, s:1, b:0), 
% 0.71/1.11  singleton  [40, 1]      (w:1, o:19, a:1, s:1, b:0), 
% 0.71/1.11  empty  [41, 1]      (w:1, o:20, a:1, s:1, b:0), 
% 0.71/1.11  cartesian_product2  [44, 2]      (w:1, o:48, a:1, s:1, b:0), 
% 0.71/1.11  alpha1  [45, 3]      (w:1, o:50, a:1, s:1, b:1), 
% 0.71/1.11  skol1  [46, 0]      (w:1, o:10, a:1, s:1, b:1), 
% 0.71/1.11  skol2  [47, 0]      (w:1, o:11, a:1, s:1, b:1), 
% 0.71/1.11  skol3  [48, 0]      (w:1, o:12, a:1, s:1, b:1), 
% 0.71/1.11  skol4  [49, 2]      (w:1, o:49, a:1, s:1, b:1), 
% 0.71/1.11  skol5  [50, 0]      (w:1, o:13, a:1, s:1, b:1).
% 0.71/1.11  
% 0.71/1.11  
% 0.71/1.11  Starting Search:
% 0.71/1.11  
% 0.71/1.11  *** allocated 15000 integers for clauses
% 0.71/1.11  *** allocated 22500 integers for clauses
% 0.71/1.11  *** allocated 33750 integers for clauses
% 0.71/1.11  
% 0.71/1.11  Bliksems!, er is een bewijs:
% 0.71/1.11  % SZS status Theorem
% 0.71/1.11  % SZS output start Refutation
% 0.71/1.11  
% 0.71/1.11  (5) {G0,W10,D3,L2,V4,M2} I { ! in( ordered_pair( X, Y ), cartesian_product2
% 0.71/1.11    ( Z, T ) ), in( Y, T ) }.
% 0.71/1.11  (6) {G0,W13,D3,L3,V4,M3} I { ! in( X, Z ), ! in( Y, T ), in( ordered_pair( 
% 0.71/1.11    X, Y ), cartesian_product2( Z, T ) ) }.
% 0.71/1.11  (9) {G0,W7,D3,L1,V0,M1} I { cartesian_product2( skol5, skol5 ) ==> 
% 0.71/1.11    cartesian_product2( skol3, skol3 ) }.
% 0.71/1.11  (10) {G0,W3,D2,L1,V0,M1} I { ! skol5 ==> skol3 }.
% 0.71/1.11  (11) {G0,W14,D3,L3,V2,M3} I { alpha1( X, Y, skol4( X, Y ) ), in( skol4( X, 
% 0.71/1.11    Y ), Y ), X = Y }.
% 0.71/1.11  (12) {G0,W14,D3,L3,V2,M3} I { alpha1( X, Y, skol4( X, Y ) ), ! in( skol4( X
% 0.71/1.11    , Y ), X ), X = Y }.
% 0.71/1.11  (13) {G0,W7,D2,L2,V3,M2} I { ! alpha1( X, Y, Z ), in( Z, X ) }.
% 0.71/1.11  (14) {G0,W7,D2,L2,V3,M2} I { ! alpha1( X, Y, Z ), ! in( Z, Y ) }.
% 0.71/1.11  (17) {G1,W10,D3,L2,V2,M2} F(6) { ! in( X, Y ), in( ordered_pair( X, X ), 
% 0.71/1.11    cartesian_product2( Y, Y ) ) }.
% 0.71/1.11  (71) {G1,W10,D3,L2,V2,M2} P(9,5) { ! in( ordered_pair( X, Y ), 
% 0.71/1.11    cartesian_product2( skol3, skol3 ) ), in( Y, skol5 ) }.
% 0.71/1.11  (320) {G2,W6,D2,L2,V1,M2} R(71,17) { in( X, skol5 ), ! in( X, skol3 ) }.
% 0.71/1.11  (340) {G3,W7,D2,L2,V2,M2} R(320,13) { in( X, skol5 ), ! alpha1( skol3, Y, X
% 0.71/1.11     ) }.
% 0.71/1.11  (352) {G4,W13,D3,L3,V1,M3} R(340,11) { in( skol4( skol3, X ), skol5 ), in( 
% 0.71/1.11    skol4( skol3, X ), X ), skol3 = X }.
% 0.71/1.11  (358) {G4,W8,D2,L2,V3,M2} R(340,14) { ! alpha1( skol3, X, Y ), ! alpha1( Z
% 0.71/1.11    , skol5, Y ) }.
% 0.71/1.11  (359) {G5,W4,D2,L1,V1,M1} F(358) { ! alpha1( skol3, skol5, X ) }.
% 0.71/1.11  (360) {G5,W8,D3,L2,V0,M2} F(352) { in( skol4( skol3, skol5 ), skol5 ), 
% 0.71/1.11    skol5 ==> skol3 }.
% 0.71/1.11  (361) {G6,W8,D3,L2,V0,M2} R(359,12) { ! in( skol4( skol3, skol5 ), skol3 )
% 0.71/1.11    , skol5 ==> skol3 }.
% 0.71/1.11  (407) {G7,W5,D3,L1,V0,M1} S(361);r(10) { ! in( skol4( skol3, skol5 ), skol3
% 0.71/1.11     ) }.
% 0.71/1.11  (415) {G8,W9,D4,L1,V2,M1} R(407,5) { ! in( ordered_pair( X, skol4( skol3, 
% 0.71/1.11    skol5 ) ), cartesian_product2( Y, skol3 ) ) }.
% 0.71/1.11  (421) {G6,W5,D3,L1,V0,M1} S(360);r(10) { in( skol4( skol3, skol5 ), skol5 )
% 0.71/1.11     }.
% 0.71/1.11  (433) {G9,W0,D0,L0,V0,M0} R(421,17);d(9);r(415) {  }.
% 0.71/1.11  
% 0.71/1.11  
% 0.71/1.11  % SZS output end Refutation
% 0.71/1.11  found a proof!
% 0.71/1.11  
% 0.71/1.11  
% 0.71/1.11  Unprocessed initial clauses:
% 0.71/1.11  
% 0.71/1.11  (435) {G0,W6,D2,L2,V2,M2}  { ! in( X, Y ), ! in( Y, X ) }.
% 0.71/1.11  (436) {G0,W7,D3,L1,V2,M1}  { unordered_pair( X, Y ) = unordered_pair( Y, X
% 0.71/1.11     ) }.
% 0.71/1.11  (437) {G0,W10,D4,L1,V2,M1}  { ordered_pair( X, Y ) = unordered_pair( 
% 0.71/1.11    unordered_pair( X, Y ), singleton( X ) ) }.
% 0.71/1.11  (438) {G0,W4,D3,L1,V2,M1}  { ! empty( ordered_pair( X, Y ) ) }.
% 0.71/1.11  (439) {G0,W10,D3,L2,V4,M2}  { ! in( ordered_pair( X, Y ), 
% 0.71/1.11    cartesian_product2( Z, T ) ), in( X, Z ) }.
% 0.71/1.11  (440) {G0,W10,D3,L2,V4,M2}  { ! in( ordered_pair( X, Y ), 
% 0.71/1.11    cartesian_product2( Z, T ) ), in( Y, T ) }.
% 0.71/1.11  (441) {G0,W13,D3,L3,V4,M3}  { ! in( X, Z ), ! in( Y, T ), in( ordered_pair
% 0.71/1.11    ( X, Y ), cartesian_product2( Z, T ) ) }.
% 0.71/1.11  (442) {G0,W2,D2,L1,V0,M1}  { empty( skol1 ) }.
% 0.71/1.11  (443) {G0,W2,D2,L1,V0,M1}  { ! empty( skol2 ) }.
% 0.71/1.11  (444) {G0,W7,D3,L1,V0,M1}  { cartesian_product2( skol3, skol3 ) = 
% 0.71/1.11    cartesian_product2( skol5, skol5 ) }.
% 0.71/1.11  (445) {G0,W3,D2,L1,V0,M1}  { ! skol3 = skol5 }.
% 0.71/1.11  (446) {G0,W14,D3,L3,V2,M3}  { alpha1( X, Y, skol4( X, Y ) ), in( skol4( X, 
% 0.71/1.11    Y ), Y ), X = Y }.
% 0.71/1.11  (447) {G0,W14,D3,L3,V2,M3}  { alpha1( X, Y, skol4( X, Y ) ), ! in( skol4( X
% 0.71/1.11    , Y ), X ), X = Y }.
% 0.71/1.11  (448) {G0,W7,D2,L2,V3,M2}  { ! alpha1( X, Y, Z ), in( Z, X ) }.
% 0.71/1.11  (449) {G0,W7,D2,L2,V3,M2}  { ! alpha1( X, Y, Z ), ! in( Z, Y ) }.
% 0.71/1.11  (450) {G0,W10,D2,L3,V3,M3}  { ! in( Z, X ), in( Z, Y ), alpha1( X, Y, Z )
% 0.71/1.11     }.
% 0.71/1.11  
% 0.71/1.11  
% 0.71/1.11  Total Proof:
% 0.71/1.11  
% 0.71/1.11  subsumption: (5) {G0,W10,D3,L2,V4,M2} I { ! in( ordered_pair( X, Y ), 
% 0.71/1.11    cartesian_product2( Z, T ) ), in( Y, T ) }.
% 0.71/1.11  parent0: (440) {G0,W10,D3,L2,V4,M2}  { ! in( ordered_pair( X, Y ), 
% 0.71/1.11    cartesian_product2( Z, T ) ), in( Y, T ) }.
% 0.71/1.11  substitution0:
% 0.71/1.11     X := X
% 0.71/1.11     Y := Y
% 0.71/1.11     Z := Z
% 0.71/1.11     T := T
% 0.71/1.11  end
% 0.71/1.11  permutation0:
% 0.71/1.11     0 ==> 0
% 0.71/1.11     1 ==> 1
% 0.71/1.11  end
% 0.71/1.11  
% 0.71/1.11  subsumption: (6) {G0,W13,D3,L3,V4,M3} I { ! in( X, Z ), ! in( Y, T ), in( 
% 0.71/1.11    ordered_pair( X, Y ), cartesian_product2( Z, T ) ) }.
% 0.71/1.11  parent0: (441) {G0,W13,D3,L3,V4,M3}  { ! in( X, Z ), ! in( Y, T ), in( 
% 0.71/1.11    ordered_pair( X, Y ), cartesian_product2( Z, T ) ) }.
% 0.71/1.11  substitution0:
% 0.71/1.11     X := X
% 0.71/1.11     Y := Y
% 0.71/1.11     Z := Z
% 0.71/1.11     T := T
% 0.71/1.11  end
% 0.71/1.11  permutation0:
% 0.71/1.11     0 ==> 0
% 0.71/1.11     1 ==> 1
% 0.71/1.11     2 ==> 2
% 0.71/1.11  end
% 0.71/1.11  
% 0.71/1.11  eqswap: (459) {G0,W7,D3,L1,V0,M1}  { cartesian_product2( skol5, skol5 ) = 
% 0.71/1.11    cartesian_product2( skol3, skol3 ) }.
% 0.71/1.11  parent0[0]: (444) {G0,W7,D3,L1,V0,M1}  { cartesian_product2( skol3, skol3 )
% 0.71/1.11     = cartesian_product2( skol5, skol5 ) }.
% 0.71/1.11  substitution0:
% 0.71/1.11  end
% 0.71/1.11  
% 0.71/1.11  subsumption: (9) {G0,W7,D3,L1,V0,M1} I { cartesian_product2( skol5, skol5 )
% 0.71/1.11     ==> cartesian_product2( skol3, skol3 ) }.
% 0.71/1.11  parent0: (459) {G0,W7,D3,L1,V0,M1}  { cartesian_product2( skol5, skol5 ) = 
% 0.71/1.11    cartesian_product2( skol3, skol3 ) }.
% 0.71/1.11  substitution0:
% 0.71/1.11  end
% 0.71/1.11  permutation0:
% 0.71/1.11     0 ==> 0
% 0.71/1.11  end
% 0.71/1.11  
% 0.71/1.11  eqswap: (464) {G0,W3,D2,L1,V0,M1}  { ! skol5 = skol3 }.
% 0.71/1.11  parent0[0]: (445) {G0,W3,D2,L1,V0,M1}  { ! skol3 = skol5 }.
% 0.71/1.11  substitution0:
% 0.71/1.11  end
% 0.71/1.11  
% 0.71/1.11  subsumption: (10) {G0,W3,D2,L1,V0,M1} I { ! skol5 ==> skol3 }.
% 0.71/1.11  parent0: (464) {G0,W3,D2,L1,V0,M1}  { ! skol5 = skol3 }.
% 0.71/1.11  substitution0:
% 0.71/1.11  end
% 0.71/1.11  permutation0:
% 0.71/1.11     0 ==> 0
% 0.71/1.11  end
% 0.71/1.11  
% 0.71/1.11  subsumption: (11) {G0,W14,D3,L3,V2,M3} I { alpha1( X, Y, skol4( X, Y ) ), 
% 0.71/1.11    in( skol4( X, Y ), Y ), X = Y }.
% 0.71/1.11  parent0: (446) {G0,W14,D3,L3,V2,M3}  { alpha1( X, Y, skol4( X, Y ) ), in( 
% 0.71/1.11    skol4( X, Y ), Y ), X = Y }.
% 0.71/1.11  substitution0:
% 0.71/1.11     X := X
% 0.71/1.11     Y := Y
% 0.71/1.11  end
% 0.71/1.11  permutation0:
% 0.71/1.11     0 ==> 0
% 0.71/1.11     1 ==> 1
% 0.71/1.11     2 ==> 2
% 0.71/1.11  end
% 0.71/1.11  
% 0.71/1.11  subsumption: (12) {G0,W14,D3,L3,V2,M3} I { alpha1( X, Y, skol4( X, Y ) ), !
% 0.71/1.11     in( skol4( X, Y ), X ), X = Y }.
% 0.71/1.11  parent0: (447) {G0,W14,D3,L3,V2,M3}  { alpha1( X, Y, skol4( X, Y ) ), ! in
% 0.71/1.11    ( skol4( X, Y ), X ), X = Y }.
% 0.71/1.11  substitution0:
% 0.71/1.11     X := X
% 0.71/1.11     Y := Y
% 0.71/1.11  end
% 0.71/1.11  permutation0:
% 0.71/1.11     0 ==> 0
% 0.71/1.11     1 ==> 1
% 0.71/1.11     2 ==> 2
% 0.71/1.11  end
% 0.71/1.11  
% 0.71/1.11  subsumption: (13) {G0,W7,D2,L2,V3,M2} I { ! alpha1( X, Y, Z ), in( Z, X )
% 0.71/1.11     }.
% 0.71/1.11  parent0: (448) {G0,W7,D2,L2,V3,M2}  { ! alpha1( X, Y, Z ), in( Z, X ) }.
% 0.71/1.11  substitution0:
% 0.71/1.11     X := X
% 0.71/1.11     Y := Y
% 0.71/1.11     Z := Z
% 0.71/1.11  end
% 0.71/1.11  permutation0:
% 0.71/1.11     0 ==> 0
% 0.71/1.11     1 ==> 1
% 0.71/1.11  end
% 0.71/1.11  
% 0.71/1.11  subsumption: (14) {G0,W7,D2,L2,V3,M2} I { ! alpha1( X, Y, Z ), ! in( Z, Y )
% 0.71/1.11     }.
% 0.71/1.11  parent0: (449) {G0,W7,D2,L2,V3,M2}  { ! alpha1( X, Y, Z ), ! in( Z, Y ) }.
% 0.71/1.11  substitution0:
% 0.71/1.11     X := X
% 0.71/1.11     Y := Y
% 0.71/1.11     Z := Z
% 0.71/1.11  end
% 0.71/1.11  permutation0:
% 0.71/1.11     0 ==> 0
% 0.71/1.11     1 ==> 1
% 0.71/1.11  end
% 0.71/1.11  
% 0.71/1.11  factor: (492) {G0,W10,D3,L2,V2,M2}  { ! in( X, Y ), in( ordered_pair( X, X
% 0.71/1.11     ), cartesian_product2( Y, Y ) ) }.
% 0.71/1.11  parent0[0, 1]: (6) {G0,W13,D3,L3,V4,M3} I { ! in( X, Z ), ! in( Y, T ), in
% 0.71/1.11    ( ordered_pair( X, Y ), cartesian_product2( Z, T ) ) }.
% 0.71/1.11  substitution0:
% 0.71/1.11     X := X
% 0.71/1.11     Y := X
% 0.71/1.11     Z := Y
% 0.71/1.11     T := Y
% 0.71/1.11  end
% 0.71/1.11  
% 0.71/1.11  subsumption: (17) {G1,W10,D3,L2,V2,M2} F(6) { ! in( X, Y ), in( 
% 0.71/1.11    ordered_pair( X, X ), cartesian_product2( Y, Y ) ) }.
% 0.71/1.11  parent0: (492) {G0,W10,D3,L2,V2,M2}  { ! in( X, Y ), in( ordered_pair( X, X
% 0.71/1.11     ), cartesian_product2( Y, Y ) ) }.
% 0.71/1.11  substitution0:
% 0.71/1.11     X := X
% 0.71/1.11     Y := Y
% 0.71/1.11  end
% 0.71/1.11  permutation0:
% 0.71/1.11     0 ==> 0
% 0.71/1.11     1 ==> 1
% 0.71/1.11  end
% 0.71/1.11  
% 0.71/1.11  paramod: (494) {G1,W10,D3,L2,V2,M2}  { ! in( ordered_pair( X, Y ), 
% 0.71/1.11    cartesian_product2( skol3, skol3 ) ), in( Y, skol5 ) }.
% 0.71/1.11  parent0[0]: (9) {G0,W7,D3,L1,V0,M1} I { cartesian_product2( skol5, skol5 ) 
% 0.71/1.11    ==> cartesian_product2( skol3, skol3 ) }.
% 0.71/1.11  parent1[0; 5]: (5) {G0,W10,D3,L2,V4,M2} I { ! in( ordered_pair( X, Y ), 
% 0.71/1.11    cartesian_product2( Z, T ) ), in( Y, T ) }.
% 0.71/1.11  substitution0:
% 0.71/1.11  end
% 0.71/1.11  substitution1:
% 0.71/1.11     X := X
% 0.71/1.11     Y := Y
% 0.71/1.11     Z := skol5
% 0.71/1.11     T := skol5
% 0.71/1.11  end
% 0.71/1.11  
% 0.71/1.11  subsumption: (71) {G1,W10,D3,L2,V2,M2} P(9,5) { ! in( ordered_pair( X, Y )
% 0.71/1.11    , cartesian_product2( skol3, skol3 ) ), in( Y, skol5 ) }.
% 0.71/1.11  parent0: (494) {G1,W10,D3,L2,V2,M2}  { ! in( ordered_pair( X, Y ), 
% 0.71/1.11    cartesian_product2( skol3, skol3 ) ), in( Y, skol5 ) }.
% 0.71/1.11  substitution0:
% 0.71/1.11     X := X
% 0.71/1.11     Y := Y
% 0.71/1.11  end
% 0.71/1.11  permutation0:
% 0.71/1.11     0 ==> 0
% 0.71/1.11     1 ==> 1
% 0.71/1.11  end
% 0.71/1.11  
% 0.71/1.11  resolution: (495) {G2,W6,D2,L2,V1,M2}  { in( X, skol5 ), ! in( X, skol3 )
% 0.71/1.11     }.
% 0.71/1.11  parent0[0]: (71) {G1,W10,D3,L2,V2,M2} P(9,5) { ! in( ordered_pair( X, Y ), 
% 0.71/1.11    cartesian_product2( skol3, skol3 ) ), in( Y, skol5 ) }.
% 0.71/1.11  parent1[1]: (17) {G1,W10,D3,L2,V2,M2} F(6) { ! in( X, Y ), in( ordered_pair
% 0.71/1.11    ( X, X ), cartesian_product2( Y, Y ) ) }.
% 0.71/1.11  substitution0:
% 0.71/1.11     X := X
% 0.71/1.11     Y := X
% 0.71/1.11  end
% 0.71/1.11  substitution1:
% 0.71/1.11     X := X
% 0.71/1.11     Y := skol3
% 0.71/1.11  end
% 0.71/1.11  
% 0.71/1.11  subsumption: (320) {G2,W6,D2,L2,V1,M2} R(71,17) { in( X, skol5 ), ! in( X, 
% 0.71/1.11    skol3 ) }.
% 0.71/1.11  parent0: (495) {G2,W6,D2,L2,V1,M2}  { in( X, skol5 ), ! in( X, skol3 ) }.
% 0.71/1.11  substitution0:
% 0.71/1.11     X := X
% 0.71/1.11  end
% 0.71/1.11  permutation0:
% 0.71/1.11     0 ==> 0
% 0.71/1.11     1 ==> 1
% 0.71/1.11  end
% 0.71/1.11  
% 0.71/1.11  resolution: (496) {G1,W7,D2,L2,V2,M2}  { in( X, skol5 ), ! alpha1( skol3, Y
% 0.71/1.11    , X ) }.
% 0.71/1.11  parent0[1]: (320) {G2,W6,D2,L2,V1,M2} R(71,17) { in( X, skol5 ), ! in( X, 
% 0.71/1.11    skol3 ) }.
% 0.71/1.11  parent1[1]: (13) {G0,W7,D2,L2,V3,M2} I { ! alpha1( X, Y, Z ), in( Z, X )
% 0.71/1.11     }.
% 0.71/1.11  substitution0:
% 0.71/1.11     X := X
% 0.71/1.11  end
% 0.71/1.11  substitution1:
% 0.71/1.11     X := skol3
% 0.71/1.11     Y := Y
% 0.71/1.11     Z := X
% 0.71/1.11  end
% 0.71/1.11  
% 0.71/1.11  subsumption: (340) {G3,W7,D2,L2,V2,M2} R(320,13) { in( X, skol5 ), ! alpha1
% 0.71/1.11    ( skol3, Y, X ) }.
% 0.71/1.11  parent0: (496) {G1,W7,D2,L2,V2,M2}  { in( X, skol5 ), ! alpha1( skol3, Y, X
% 0.71/1.11     ) }.
% 0.71/1.11  substitution0:
% 0.71/1.11     X := X
% 0.71/1.11     Y := Y
% 0.71/1.11  end
% 0.71/1.11  permutation0:
% 0.71/1.11     0 ==> 0
% 0.71/1.11     1 ==> 1
% 0.71/1.11  end
% 0.71/1.11  
% 0.71/1.11  eqswap: (497) {G0,W14,D3,L3,V2,M3}  { Y = X, alpha1( X, Y, skol4( X, Y ) )
% 0.71/1.11    , in( skol4( X, Y ), Y ) }.
% 0.71/1.11  parent0[2]: (11) {G0,W14,D3,L3,V2,M3} I { alpha1( X, Y, skol4( X, Y ) ), in
% 0.71/1.11    ( skol4( X, Y ), Y ), X = Y }.
% 0.71/1.11  substitution0:
% 0.71/1.11     X := X
% 0.71/1.11     Y := Y
% 0.71/1.11  end
% 0.71/1.11  
% 0.71/1.11  resolution: (498) {G1,W13,D3,L3,V1,M3}  { in( skol4( skol3, X ), skol5 ), X
% 0.71/1.11     = skol3, in( skol4( skol3, X ), X ) }.
% 0.71/1.11  parent0[1]: (340) {G3,W7,D2,L2,V2,M2} R(320,13) { in( X, skol5 ), ! alpha1
% 0.71/1.11    ( skol3, Y, X ) }.
% 0.71/1.11  parent1[1]: (497) {G0,W14,D3,L3,V2,M3}  { Y = X, alpha1( X, Y, skol4( X, Y
% 0.71/1.11     ) ), in( skol4( X, Y ), Y ) }.
% 0.71/1.11  substitution0:
% 0.71/1.11     X := skol4( skol3, X )
% 0.71/1.11     Y := X
% 0.71/1.11  end
% 0.71/1.11  substitution1:
% 0.71/1.11     X := skol3
% 0.71/1.11     Y := X
% 0.71/1.11  end
% 0.71/1.11  
% 0.71/1.11  eqswap: (499) {G1,W13,D3,L3,V1,M3}  { skol3 = X, in( skol4( skol3, X ), 
% 0.71/1.11    skol5 ), in( skol4( skol3, X ), X ) }.
% 0.71/1.11  parent0[1]: (498) {G1,W13,D3,L3,V1,M3}  { in( skol4( skol3, X ), skol5 ), X
% 0.71/1.11     = skol3, in( skol4( skol3, X ), X ) }.
% 0.71/1.11  substitution0:
% 0.71/1.11     X := X
% 0.71/1.11  end
% 0.71/1.11  
% 0.71/1.11  subsumption: (352) {G4,W13,D3,L3,V1,M3} R(340,11) { in( skol4( skol3, X ), 
% 0.71/1.11    skol5 ), in( skol4( skol3, X ), X ), skol3 = X }.
% 0.71/1.11  parent0: (499) {G1,W13,D3,L3,V1,M3}  { skol3 = X, in( skol4( skol3, X ), 
% 0.71/1.11    skol5 ), in( skol4( skol3, X ), X ) }.
% 0.71/1.11  substitution0:
% 0.71/1.11     X := X
% 0.71/1.11  end
% 0.71/1.11  permutation0:
% 0.71/1.11     0 ==> 2
% 0.71/1.11     1 ==> 0
% 0.71/1.11     2 ==> 1
% 0.71/1.11  end
% 0.71/1.11  
% 0.71/1.11  resolution: (502) {G1,W8,D2,L2,V3,M2}  { ! alpha1( X, skol5, Y ), ! alpha1
% 0.71/1.11    ( skol3, Z, Y ) }.
% 0.71/1.11  parent0[1]: (14) {G0,W7,D2,L2,V3,M2} I { ! alpha1( X, Y, Z ), ! in( Z, Y )
% 0.71/1.11     }.
% 0.71/1.11  parent1[0]: (340) {G3,W7,D2,L2,V2,M2} R(320,13) { in( X, skol5 ), ! alpha1
% 0.71/1.11    ( skol3, Y, X ) }.
% 0.71/1.11  substitution0:
% 0.71/1.11     X := X
% 0.71/1.11     Y := skol5
% 0.71/1.11     Z := Y
% 0.71/1.11  end
% 0.71/1.11  substitution1:
% 0.71/1.11     X := Y
% 0.71/1.11     Y := Z
% 0.71/1.11  end
% 0.71/1.11  
% 0.71/1.11  subsumption: (358) {G4,W8,D2,L2,V3,M2} R(340,14) { ! alpha1( skol3, X, Y )
% 0.71/1.11    , ! alpha1( Z, skol5, Y ) }.
% 0.71/1.11  parent0: (502) {G1,W8,D2,L2,V3,M2}  { ! alpha1( X, skol5, Y ), ! alpha1( 
% 0.71/1.11    skol3, Z, Y ) }.
% 0.71/1.11  substitution0:
% 0.71/1.11     X := Z
% 0.71/1.11     Y := Y
% 0.71/1.11     Z := X
% 0.71/1.11  end
% 0.71/1.11  permutation0:
% 0.71/1.11     0 ==> 1
% 0.71/1.11     1 ==> 0
% 0.71/1.11  end
% 0.71/1.11  
% 0.71/1.11  factor: (504) {G4,W4,D2,L1,V1,M1}  { ! alpha1( skol3, skol5, X ) }.
% 0.71/1.11  parent0[0, 1]: (358) {G4,W8,D2,L2,V3,M2} R(340,14) { ! alpha1( skol3, X, Y
% 0.71/1.11     ), ! alpha1( Z, skol5, Y ) }.
% 0.71/1.11  substitution0:
% 0.71/1.11     X := skol5
% 0.71/1.11     Y := X
% 0.71/1.11     Z := skol3
% 0.71/1.11  end
% 0.71/1.11  
% 0.71/1.11  subsumption: (359) {G5,W4,D2,L1,V1,M1} F(358) { ! alpha1( skol3, skol5, X )
% 0.71/1.11     }.
% 0.71/1.11  parent0: (504) {G4,W4,D2,L1,V1,M1}  { ! alpha1( skol3, skol5, X ) }.
% 0.71/1.11  substitution0:
% 0.71/1.11     X := X
% 0.71/1.11  end
% 0.71/1.11  permutation0:
% 0.71/1.11     0 ==> 0
% 0.71/1.11  end
% 0.71/1.11  
% 0.71/1.11  eqswap: (505) {G4,W13,D3,L3,V1,M3}  { X = skol3, in( skol4( skol3, X ), 
% 0.71/1.11    skol5 ), in( skol4( skol3, X ), X ) }.
% 0.71/1.11  parent0[2]: (352) {G4,W13,D3,L3,V1,M3} R(340,11) { in( skol4( skol3, X ), 
% 0.71/1.11    skol5 ), in( skol4( skol3, X ), X ), skol3 = X }.
% 0.71/1.11  substitution0:
% 0.71/1.11     X := X
% 0.71/1.11  end
% 0.71/1.11  
% 0.71/1.11  factor: (507) {G4,W8,D3,L2,V0,M2}  { skol5 = skol3, in( skol4( skol3, skol5
% 0.71/1.11     ), skol5 ) }.
% 0.71/1.11  parent0[1, 2]: (505) {G4,W13,D3,L3,V1,M3}  { X = skol3, in( skol4( skol3, X
% 0.71/1.11     ), skol5 ), in( skol4( skol3, X ), X ) }.
% 0.71/1.11  substitution0:
% 0.71/1.11     X := skol5
% 0.71/1.11  end
% 0.71/1.11  
% 0.71/1.11  subsumption: (360) {G5,W8,D3,L2,V0,M2} F(352) { in( skol4( skol3, skol5 ), 
% 0.71/1.11    skol5 ), skol5 ==> skol3 }.
% 0.71/1.11  parent0: (507) {G4,W8,D3,L2,V0,M2}  { skol5 = skol3, in( skol4( skol3, 
% 0.71/1.11    skol5 ), skol5 ) }.
% 0.71/1.11  substitution0:
% 0.71/1.11  end
% 0.71/1.11  permutation0:
% 0.71/1.11     0 ==> 1
% 0.71/1.11     1 ==> 0
% 0.71/1.11  end
% 0.71/1.11  
% 0.71/1.11  eqswap: (508) {G0,W14,D3,L3,V2,M3}  { Y = X, alpha1( X, Y, skol4( X, Y ) )
% 0.71/1.11    , ! in( skol4( X, Y ), X ) }.
% 0.71/1.11  parent0[2]: (12) {G0,W14,D3,L3,V2,M3} I { alpha1( X, Y, skol4( X, Y ) ), ! 
% 0.71/1.11    in( skol4( X, Y ), X ), X = Y }.
% 0.71/1.11  substitution0:
% 0.71/1.11     X := X
% 0.71/1.11     Y := Y
% 0.71/1.11  end
% 0.71/1.11  
% 0.71/1.11  resolution: (509) {G1,W8,D3,L2,V0,M2}  { skol5 = skol3, ! in( skol4( skol3
% 0.71/1.11    , skol5 ), skol3 ) }.
% 0.71/1.11  parent0[0]: (359) {G5,W4,D2,L1,V1,M1} F(358) { ! alpha1( skol3, skol5, X )
% 0.71/1.11     }.
% 0.71/1.11  parent1[1]: (508) {G0,W14,D3,L3,V2,M3}  { Y = X, alpha1( X, Y, skol4( X, Y
% 0.71/1.11     ) ), ! in( skol4( X, Y ), X ) }.
% 0.71/1.11  substitution0:
% 0.71/1.11     X := skol4( skol3, skol5 )
% 0.71/1.11  end
% 0.71/1.11  substitution1:
% 0.71/1.11     X := skol3
% 0.71/1.11     Y := skol5
% 0.71/1.11  end
% 0.71/1.11  
% 0.71/1.11  subsumption: (361) {G6,W8,D3,L2,V0,M2} R(359,12) { ! in( skol4( skol3, 
% 0.71/1.11    skol5 ), skol3 ), skol5 ==> skol3 }.
% 0.71/1.11  parent0: (509) {G1,W8,D3,L2,V0,M2}  { skol5 = skol3, ! in( skol4( skol3, 
% 0.71/1.11    skol5 ), skol3 ) }.
% 0.71/1.11  substitution0:
% 0.71/1.11  end
% 0.71/1.11  permutation0:
% 0.71/1.11     0 ==> 1
% 0.71/1.11     1 ==> 0
% 0.71/1.11  end
% 0.71/1.11  
% 0.71/1.11  resolution: (513) {G1,W5,D3,L1,V0,M1}  { ! in( skol4( skol3, skol5 ), skol3
% 0.71/1.11     ) }.
% 0.71/1.11  parent0[0]: (10) {G0,W3,D2,L1,V0,M1} I { ! skol5 ==> skol3 }.
% 0.71/1.11  parent1[1]: (361) {G6,W8,D3,L2,V0,M2} R(359,12) { ! in( skol4( skol3, skol5
% 0.71/1.11     ), skol3 ), skol5 ==> skol3 }.
% 0.71/1.11  substitution0:
% 0.71/1.11  end
% 0.71/1.11  substitution1:
% 0.71/1.11  end
% 0.71/1.11  
% 0.71/1.11  subsumption: (407) {G7,W5,D3,L1,V0,M1} S(361);r(10) { ! in( skol4( skol3, 
% 0.71/1.11    skol5 ), skol3 ) }.
% 0.71/1.11  parent0: (513) {G1,W5,D3,L1,V0,M1}  { ! in( skol4( skol3, skol5 ), skol3 )
% 0.71/1.11     }.
% 0.71/1.11  substitution0:
% 0.71/1.11  end
% 0.71/1.11  permutation0:
% 0.71/1.11     0 ==> 0
% 0.71/1.11  end
% 0.71/1.11  
% 0.71/1.11  resolution: (514) {G1,W9,D4,L1,V2,M1}  { ! in( ordered_pair( X, skol4( 
% 0.71/1.11    skol3, skol5 ) ), cartesian_product2( Y, skol3 ) ) }.
% 0.71/1.11  parent0[0]: (407) {G7,W5,D3,L1,V0,M1} S(361);r(10) { ! in( skol4( skol3, 
% 0.71/1.11    skol5 ), skol3 ) }.
% 0.71/1.11  parent1[1]: (5) {G0,W10,D3,L2,V4,M2} I { ! in( ordered_pair( X, Y ), 
% 0.71/1.11    cartesian_product2( Z, T ) ), in( Y, T ) }.
% 0.71/1.11  substitution0:
% 0.71/1.11  end
% 0.71/1.11  substitution1:
% 0.71/1.11     X := X
% 0.71/1.11     Y := skol4( skol3, skol5 )
% 0.71/1.11     Z := Y
% 0.71/1.11     T := skol3
% 0.71/1.11  end
% 0.71/1.11  
% 0.71/1.11  subsumption: (415) {G8,W9,D4,L1,V2,M1} R(407,5) { ! in( ordered_pair( X, 
% 0.71/1.11    skol4( skol3, skol5 ) ), cartesian_product2( Y, skol3 ) ) }.
% 0.71/1.11  parent0: (514) {G1,W9,D4,L1,V2,M1}  { ! in( ordered_pair( X, skol4( skol3, 
% 0.71/1.11    skol5 ) ), cartesian_product2( Y, skol3 ) ) }.
% 0.71/1.11  substitution0:
% 0.71/1.11     X := X
% 0.71/1.11     Y := Y
% 0.71/1.11  end
% 0.71/1.11  permutation0:
% 0.71/1.11     0 ==> 0
% 0.71/1.11  end
% 0.71/1.11  
% 0.71/1.11  resolution: (517) {G1,W5,D3,L1,V0,M1}  { in( skol4( skol3, skol5 ), skol5 )
% 0.71/1.11     }.
% 0.71/1.11  parent0[0]: (10) {G0,W3,D2,L1,V0,M1} I { ! skol5 ==> skol3 }.
% 0.71/1.11  parent1[1]: (360) {G5,W8,D3,L2,V0,M2} F(352) { in( skol4( skol3, skol5 ), 
% 0.71/1.11    skol5 ), skol5 ==> skol3 }.
% 0.71/1.11  substitution0:
% 0.71/1.11  end
% 0.71/1.11  substitution1:
% 0.71/1.11  end
% 0.71/1.11  
% 0.71/1.11  subsumption: (421) {G6,W5,D3,L1,V0,M1} S(360);r(10) { in( skol4( skol3, 
% 0.71/1.11    skol5 ), skol5 ) }.
% 0.71/1.11  parent0: (517) {G1,W5,D3,L1,V0,M1}  { in( skol4( skol3, skol5 ), skol5 )
% 0.71/1.11     }.
% 0.71/1.11  substitution0:
% 0.71/1.11  end
% 0.71/1.11  permutation0:
% 0.71/1.11     0 ==> 0
% 0.71/1.11  end
% 0.71/1.11  
% 0.71/1.11  resolution: (519) {G2,W11,D4,L1,V0,M1}  { in( ordered_pair( skol4( skol3, 
% 0.71/1.11    skol5 ), skol4( skol3, skol5 ) ), cartesian_product2( skol5, skol5 ) )
% 0.71/1.11     }.
% 0.71/1.11  parent0[0]: (17) {G1,W10,D3,L2,V2,M2} F(6) { ! in( X, Y ), in( ordered_pair
% 0.71/1.11    ( X, X ), cartesian_product2( Y, Y ) ) }.
% 0.71/1.11  parent1[0]: (421) {G6,W5,D3,L1,V0,M1} S(360);r(10) { in( skol4( skol3, 
% 0.71/1.11    skol5 ), skol5 ) }.
% 0.71/1.11  substitution0:
% 0.71/1.11     X := skol4( skol3, skol5 )
% 0.71/1.11     Y := skol5
% 0.71/1.11  end
% 0.71/1.11  substitution1:
% 0.71/1.11  end
% 0.71/1.11  
% 0.71/1.11  paramod: (520) {G1,W11,D4,L1,V0,M1}  { in( ordered_pair( skol4( skol3, 
% 0.71/1.11    skol5 ), skol4( skol3, skol5 ) ), cartesian_product2( skol3, skol3 ) )
% 0.71/1.11     }.
% 0.71/1.11  parent0[0]: (9) {G0,W7,D3,L1,V0,M1} I { cartesian_product2( skol5, skol5 ) 
% 0.71/1.11    ==> cartesian_product2( skol3, skol3 ) }.
% 0.71/1.11  parent1[0; 8]: (519) {G2,W11,D4,L1,V0,M1}  { in( ordered_pair( skol4( skol3
% 0.71/1.11    , skol5 ), skol4( skol3, skol5 ) ), cartesian_product2( skol5, skol5 ) )
% 0.71/1.11     }.
% 0.71/1.11  substitution0:
% 0.71/1.11  end
% 0.71/1.11  substitution1:
% 0.71/1.11  end
% 0.71/1.11  
% 0.71/1.11  resolution: (521) {G2,W0,D0,L0,V0,M0}  {  }.
% 0.71/1.11  parent0[0]: (415) {G8,W9,D4,L1,V2,M1} R(407,5) { ! in( ordered_pair( X, 
% 0.71/1.11    skol4( skol3, skol5 ) ), cartesian_product2( Y, skol3 ) ) }.
% 0.71/1.11  parent1[0]: (520) {G1,W11,D4,L1,V0,M1}  { in( ordered_pair( skol4( skol3, 
% 0.71/1.11    skol5 ), skol4( skol3, skol5 ) ), cartesian_product2( skol3, skol3 ) )
% 0.71/1.11     }.
% 0.71/1.11  substitution0:
% 0.71/1.11     X := skol4( skol3, skol5 )
% 0.71/1.11     Y := skol3
% 0.71/1.11  end
% 0.71/1.11  substitution1:
% 0.71/1.11  end
% 0.71/1.11  
% 0.71/1.11  subsumption: (433) {G9,W0,D0,L0,V0,M0} R(421,17);d(9);r(415) {  }.
% 0.71/1.11  parent0: (521) {G2,W0,D0,L0,V0,M0}  {  }.
% 0.71/1.11  substitution0:
% 0.71/1.11  end
% 0.71/1.11  permutation0:
% 0.71/1.11  end
% 0.71/1.11  
% 0.71/1.11  Proof check complete!
% 0.71/1.11  
% 0.71/1.11  Memory use:
% 0.71/1.11  
% 0.71/1.11  space for terms:        6791
% 0.71/1.11  space for clauses:      23091
% 0.71/1.11  
% 0.71/1.11  
% 0.71/1.11  clauses generated:      1878
% 0.71/1.11  clauses kept:           434
% 0.71/1.11  clauses selected:       83
% 0.71/1.11  clauses deleted:        4
% 0.71/1.11  clauses inuse deleted:  0
% 0.71/1.11  
% 0.71/1.11  subsentry:          8848
% 0.71/1.11  literals s-matched: 6541
% 0.71/1.11  literals matched:   5899
% 0.71/1.11  full subsumption:   2132
% 0.71/1.11  
% 0.71/1.11  checksum:           390239500
% 0.71/1.11  
% 0.71/1.11  
% 0.71/1.11  Bliksem ended
%------------------------------------------------------------------------------