TSTP Solution File: SWW600_2 by Vampire---4.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.9
% Problem  : SWW600_2 : TPTP v8.2.0. Released v6.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_vampire %s %d THM

% Computer : n022.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  : 300s
% DateTime : Mon Jun 24 18:35:04 EDT 2024

% Result   : Theorem 0.22s 0.43s
% Output   : Refutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   13 (   3 unt;   0 typ;   0 def)
%            Number of atoms       :  107 (  50 equ)
%            Maximal formula atoms :   18 (   8 avg)
%            Number of connectives :  154 (  60   ~;   0   |;  80   &)
%                                         (   0 <=>;  14  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   19 (  13 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number arithmetic     :  328 (  56 atm; 114 fun;  56 num; 102 var)
%            Number of types       :    6 (   4 usr;   1 ari)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :    8 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   30 (  27 usr;  17 con; 0-4 aty)
%            Number of variables   :  102 (  50   !;  52   ?; 102   :)

% Comments : 
%------------------------------------------------------------------------------
tff(type_def_5,type,
    uni: $tType ).

tff(type_def_6,type,
    ty: $tType ).

tff(type_def_7,type,
    bool: $tType ).

tff(type_def_8,type,
    tuple0: $tType ).

tff(func_def_0,type,
    witness: ty > uni ).

tff(func_def_1,type,
    int: ty ).

tff(func_def_2,type,
    real: ty ).

tff(func_def_3,type,
    bool1: ty ).

tff(func_def_4,type,
    true: bool ).

tff(func_def_5,type,
    false: bool ).

tff(func_def_6,type,
    match_bool: ( ty * bool * uni * uni ) > uni ).

tff(func_def_7,type,
    tuple01: ty ).

tff(func_def_8,type,
    tuple02: tuple0 ).

tff(func_def_9,type,
    qtmark: ty ).

tff(func_def_12,type,
    abs: $int > $int ).

tff(func_def_14,type,
    div: ( $int * $int ) > $int ).

tff(func_def_15,type,
    mod: ( $int * $int ) > $int ).

tff(func_def_22,type,
    gcd: ( $int * $int ) > $int ).

tff(func_def_23,type,
    ref: ty > ty ).

tff(func_def_24,type,
    mk_ref: ( ty * uni ) > uni ).

tff(func_def_25,type,
    contents: ( ty * uni ) > uni ).

tff(func_def_27,type,
    sK0: $int ).

tff(func_def_28,type,
    sK1: $int ).

tff(func_def_29,type,
    sK2: $int ).

tff(func_def_30,type,
    sK3: $int ).

tff(func_def_31,type,
    sK4: $int ).

tff(func_def_32,type,
    sK5: $int ).

tff(func_def_33,type,
    sK6: $int ).

tff(func_def_34,type,
    sK7: $int ).

tff(func_def_35,type,
    sK8: ( $int * $int ) > $int ).

tff(func_def_36,type,
    sK9: ( $int * $int * $int ) > $int ).

tff(pred_def_1,type,
    sort: ( ty * uni ) > $o ).

tff(pred_def_4,type,
    divides: ( $int * $int ) > $o ).

tff(pred_def_5,type,
    even: $int > $o ).

tff(pred_def_6,type,
    odd: $int > $o ).

tff(f223,plain,
    $false,
    inference(subsumption_resolution,[],[f199,f198]) ).

tff(f198,plain,
    ! [X8: $int,X9: $int] : ( $sum($product(X9,sK0),$product(X8,sK1)) != sK5 ),
    inference(cnf_transformation,[],[f173]) ).

tff(f173,plain,
    ( ~ $less(sK0,0)
    & ~ $less(sK1,0)
    & ( sK5 = $sum($product(sK6,sK0),$product(sK4,sK1)) )
    & ! [X8: $int,X9: $int] : ( $sum($product(X9,sK0),$product(X8,sK1)) != sK5 )
    & ~ $less(sK3,0)
    & ( sK3 = $sum($product(sK7,sK0),$product(sK2,sK1)) )
    & ~ $less(0,sK3)
    & ~ $less(sK5,0)
    & ( gcd(sK0,sK1) = gcd(sK5,sK3) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7])],[f170,f172,f171]) ).

tff(f171,plain,
    ( ? [X0: $int,X1: $int] :
        ( ~ $less(X0,0)
        & ~ $less(X1,0)
        & ? [X2: $int,X3: $int,X4: $int,X5: $int,X6: $int,X7: $int] :
            ( ( $sum($product(X6,X0),$product(X4,X1)) = X5 )
            & ! [X8: $int,X9: $int] : ( $sum($product(X9,X0),$product(X8,X1)) != X5 )
            & ~ $less(X3,0)
            & ( $sum($product(X7,X0),$product(X2,X1)) = X3 )
            & ~ $less(0,X3)
            & ~ $less(X5,0)
            & ( gcd(X0,X1) = gcd(X5,X3) ) ) )
   => ( ~ $less(sK0,0)
      & ~ $less(sK1,0)
      & ? [X7: $int,X6: $int,X5: $int,X4: $int,X3: $int,X2: $int] :
          ( ( $sum($product(X6,sK0),$product(X4,sK1)) = X5 )
          & ! [X9: $int,X8: $int] : ( $sum($product(X9,sK0),$product(X8,sK1)) != X5 )
          & ~ $less(X3,0)
          & ( $sum($product(X7,sK0),$product(X2,sK1)) = X3 )
          & ~ $less(0,X3)
          & ~ $less(X5,0)
          & ( gcd(X5,X3) = gcd(sK0,sK1) ) ) ) ),
    introduced(choice_axiom,[]) ).

tff(f172,plain,
    ( ? [X7: $int,X6: $int,X5: $int,X4: $int,X3: $int,X2: $int] :
        ( ( $sum($product(X6,sK0),$product(X4,sK1)) = X5 )
        & ! [X9: $int,X8: $int] : ( $sum($product(X9,sK0),$product(X8,sK1)) != X5 )
        & ~ $less(X3,0)
        & ( $sum($product(X7,sK0),$product(X2,sK1)) = X3 )
        & ~ $less(0,X3)
        & ~ $less(X5,0)
        & ( gcd(X5,X3) = gcd(sK0,sK1) ) )
   => ( ( sK5 = $sum($product(sK6,sK0),$product(sK4,sK1)) )
      & ! [X9: $int,X8: $int] : ( $sum($product(X9,sK0),$product(X8,sK1)) != sK5 )
      & ~ $less(sK3,0)
      & ( sK3 = $sum($product(sK7,sK0),$product(sK2,sK1)) )
      & ~ $less(0,sK3)
      & ~ $less(sK5,0)
      & ( gcd(sK0,sK1) = gcd(sK5,sK3) ) ) ),
    introduced(choice_axiom,[]) ).

tff(f170,plain,
    ? [X0: $int,X1: $int] :
      ( ~ $less(X0,0)
      & ~ $less(X1,0)
      & ? [X2: $int,X3: $int,X4: $int,X5: $int,X6: $int,X7: $int] :
          ( ( $sum($product(X6,X0),$product(X4,X1)) = X5 )
          & ! [X8: $int,X9: $int] : ( $sum($product(X9,X0),$product(X8,X1)) != X5 )
          & ~ $less(X3,0)
          & ( $sum($product(X7,X0),$product(X2,X1)) = X3 )
          & ~ $less(0,X3)
          & ~ $less(X5,0)
          & ( gcd(X0,X1) = gcd(X5,X3) ) ) ),
    inference(rectify,[],[f154]) ).

tff(f154,plain,
    ? [X1: $int,X0: $int] :
      ( ~ $less(X1,0)
      & ~ $less(X0,0)
      & ? [X3: $int,X7: $int,X5: $int,X6: $int,X4: $int,X2: $int] :
          ( ( $sum($product(X4,X1),$product(X5,X0)) = X6 )
          & ! [X8: $int,X9: $int] : ( $sum($product(X9,X1),$product(X8,X0)) != X6 )
          & ~ $less(X7,0)
          & ( $sum($product(X2,X1),$product(X3,X0)) = X7 )
          & ~ $less(0,X7)
          & ~ $less(X6,0)
          & ( gcd(X1,X0) = gcd(X6,X7) ) ) ),
    inference(flattening,[],[f153]) ).

tff(f153,plain,
    ? [X0: $int,X1: $int] :
      ( ? [X5: $int,X6: $int,X2: $int,X3: $int,X7: $int,X4: $int] :
          ( ! [X8: $int,X9: $int] : ( $sum($product(X9,X1),$product(X8,X0)) != X6 )
          & ~ $less(0,X7)
          & ( $sum($product(X4,X1),$product(X5,X0)) = X6 )
          & ( $sum($product(X2,X1),$product(X3,X0)) = X7 )
          & ~ $less(X7,0)
          & ( gcd(X1,X0) = gcd(X6,X7) )
          & ~ $less(X6,0) )
      & ~ $less(X1,0)
      & ~ $less(X0,0) ),
    inference(ennf_transformation,[],[f130]) ).

tff(f130,plain,
    ~ ! [X0: $int,X1: $int] :
        ( ( ~ $less(X1,0)
          & ~ $less(X0,0) )
       => ! [X5: $int,X6: $int,X2: $int,X3: $int,X7: $int,X4: $int] :
            ( ( ( $sum($product(X4,X1),$product(X5,X0)) = X6 )
              & ( $sum($product(X2,X1),$product(X3,X0)) = X7 )
              & ~ $less(X7,0)
              & ( gcd(X1,X0) = gcd(X6,X7) )
              & ~ $less(X6,0) )
           => ( ~ $less(0,X7)
             => ? [X9: $int,X8: $int] : ( $sum($product(X9,X1),$product(X8,X0)) = X6 ) ) ) ),
    inference(rectify,[],[f88]) ).

tff(f88,plain,
    ~ ! [X7: $int,X1: $int] :
        ( ( ~ $less(X7,0)
          & ~ $less(X1,0) )
       => ! [X12: $int,X8: $int,X0: $int,X11: $int,X2: $int,X14: $int] :
            ( ( ~ $less(X2,0)
              & ( gcd(X1,X7) = gcd(X2,X14) )
              & ~ $less(X14,0)
              & ( $sum($product(X0,X1),$product(X11,X7)) = X2 )
              & ( $sum($product(X12,X1),$product(X8,X7)) = X14 ) )
           => ( ~ $less(0,X14)
             => ? [X16: $int,X15: $int] : ( $sum($product(X15,X1),$product(X16,X7)) = X2 ) ) ) ),
    inference(theory_normalization,[],[f84]) ).

tff(f84,negated_conjecture,
    ~ ! [X7: $int,X1: $int] :
        ( ( $lesseq(0,X7)
          & $lesseq(0,X1) )
       => ! [X12: $int,X8: $int,X0: $int,X11: $int,X2: $int,X14: $int] :
            ( ( $lesseq(0,X2)
              & ( gcd(X1,X7) = gcd(X2,X14) )
              & $lesseq(0,X14)
              & ( $sum($product(X0,X1),$product(X11,X7)) = X2 )
              & ( $sum($product(X12,X1),$product(X8,X7)) = X14 ) )
           => ( ~ $less(0,X14)
             => ? [X16: $int,X15: $int] : ( $sum($product(X15,X1),$product(X16,X7)) = X2 ) ) ) ),
    inference(negated_conjecture,[],[f83]) ).

tff(f83,conjecture,
    ! [X7: $int,X1: $int] :
      ( ( $lesseq(0,X7)
        & $lesseq(0,X1) )
     => ! [X12: $int,X8: $int,X0: $int,X11: $int,X2: $int,X14: $int] :
          ( ( $lesseq(0,X2)
            & ( gcd(X1,X7) = gcd(X2,X14) )
            & $lesseq(0,X14)
            & ( $sum($product(X0,X1),$product(X11,X7)) = X2 )
            & ( $sum($product(X12,X1),$product(X8,X7)) = X14 ) )
         => ( ~ $less(0,X14)
           => ? [X16: $int,X15: $int] : ( $sum($product(X15,X1),$product(X16,X7)) = X2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).

tff(f199,plain,
    sK5 = $sum($product(sK6,sK0),$product(sK4,sK1)),
    inference(cnf_transformation,[],[f173]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem    : SWW600_2 : TPTP v8.2.0. Released v6.1.0.
% 0.12/0.12  % Command    : run_vampire %s %d THM
% 0.12/0.34  % Computer : n022.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  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Wed Jun 19 08:02:09 EDT 2024
% 0.12/0.34  % CPUTime    : 
% 0.12/0.36  This is a TF0_THM_EQU_ARI problem
% 0.12/0.36  Running first-order theorem proving
% 0.12/0.36  Running /export/starexec/sandbox2/solver/bin/vampire --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.43  % (20712)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.43  % (20720)lrs+10_1:32_s2a=on:s2agt=10:sgt=8:ss=axioms:i=15:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/15Mi)
% 0.22/0.43  % (20712)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.43  % (20719)ott+1011_1:2_br=off:bs=unit_only:bsr=unit_only:nwc=5.0:s2a=on:s2agt=32:urr=on:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/37Mi)
% 0.22/0.43  % (20712)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.43  % (20718)ott+21_1:1_erd=off:s2a=on:sac=on:sd=1:sgt=64:sos=on:ss=included:st=3.0:to=lpo:urr=on:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/2Mi)
% 0.22/0.43  % (20712)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.43  % (20715)dis+1010_1:4_aac=none:abs=on:atotf=0.5:avsq=on:avsqc=2:avsqr=215,247:awrs=converge:awrsf=128:bsd=on:erd=off:fde=none:gve=cautious:newcnf=on:nwc=5.0:rnwc=on:sac=on:sas=z3:sp=const_min:tgt=ground:thsq=on:thsqc=64:thsqr=1,4:i=59848:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/59848Mi)
% 0.22/0.43  % (20712)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.43  % (20721)lrs+10_5:1_br=off:fde=none:nwc=3.0:sd=1:sgt=10:sos=on:ss=axioms:urr=on:i=32:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/32Mi)
% 0.22/0.43  % (20712)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.43  % (20716)lrs+1010_1:1_aac=none:bce=on:nicw=on:nm=0:plsq=on:plsql=on:sac=on:sos=on:sp=frequency:spb=units:to=lpo:i=34:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/34Mi)
% 0.22/0.43  % (20712)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.43  % (20717)dis+1011_1:64_drc=off:flr=on:nwc=2.0:sac=on:urr=ec_only:i=8:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/8Mi)
% 0.22/0.43  % (20718)Instruction limit reached!
% 0.22/0.43  % (20718)------------------------------
% 0.22/0.43  % (20718)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.22/0.43  % (20718)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.22/0.43  % (20718)Termination reason: Time limit
% 0.22/0.43  % (20718)Termination phase: Property scanning
% 0.22/0.43  
% 0.22/0.43  % (20718)Memory used [KB]: 825
% 0.22/0.43  % (20718)Time elapsed: 0.003 s
% 0.22/0.43  % (20718)Instructions burned: 3 (million)
% 0.22/0.43  % (20717)Instruction limit reached!
% 0.22/0.43  % (20717)------------------------------
% 0.22/0.43  % (20717)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.22/0.43  % (20717)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.22/0.43  % (20717)Termination reason: Time limit
% 0.22/0.43  % (20717)Termination phase: Saturation
% 0.22/0.43  
% 0.22/0.43  % (20717)Memory used [KB]: 1143
% 0.22/0.43  % (20717)Time elapsed: 0.007 s
% 0.22/0.43  % (20717)Instructions burned: 8 (million)
% 0.22/0.43  % (20721)First to succeed.
% 0.22/0.43  % (20720)Also succeeded, but the first one will report.
% 0.22/0.43  % (20721)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-20712"
% 0.22/0.43  % (20719)Also succeeded, but the first one will report.
% 0.22/0.43  % (20712)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.43  % (20721)Refutation found. Thanks to Tanya!
% 0.22/0.43  % SZS status Theorem for theBenchmark
% 0.22/0.43  % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.44  % (20721)------------------------------
% 0.22/0.44  % (20721)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.22/0.44  % (20721)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.22/0.44  % (20721)Termination reason: Refutation
% 0.22/0.44  
% 0.22/0.44  % (20721)Memory used [KB]: 895
% 0.22/0.44  % (20721)Time elapsed: 0.008 s
% 0.22/0.44  % (20721)Instructions burned: 9 (million)
% 0.22/0.44  % (20721)------------------------------
% 0.22/0.44  % (20721)------------------------------
% 0.22/0.44  % (20712)Success in time 0.065 s
%------------------------------------------------------------------------------