TSTP Solution File: NUM500+3 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : NUM500+3 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s

% Computer : n002.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 : Tue May 21 01:42:45 EDT 2024

% Result   : Theorem 0.58s 0.75s
% Output   : Refutation 0.58s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   49 (   6 unt;   0 def)
%            Number of atoms       :  229 (  86 equ)
%            Maximal formula atoms :   13 (   4 avg)
%            Number of connectives :  266 (  86   ~;  84   |;  87   &)
%                                         (   2 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   3 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   6 con; 0-2 aty)
%            Number of variables   :   51 (  26   !;  25   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f620,plain,
    $false,
    inference(avatar_sat_refutation,[],[f475,f501,f619]) ).

fof(f619,plain,
    ~ spl16_14,
    inference(avatar_contradiction_clause,[],[f618]) ).

fof(f618,plain,
    ( $false
    | ~ spl16_14 ),
    inference(subsumption_resolution,[],[f617,f210]) ).

fof(f210,plain,
    aNaturalNumber0(xk),
    inference(cnf_transformation,[],[f45]) ).

fof(f45,axiom,
    ( xk = sdtsldt0(sdtasdt0(xn,xm),xp)
    & sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
    & aNaturalNumber0(xk) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2306) ).

fof(f617,plain,
    ( ~ aNaturalNumber0(xk)
    | ~ spl16_14 ),
    inference(subsumption_resolution,[],[f616,f213]) ).

fof(f213,plain,
    sz00 != xk,
    inference(cnf_transformation,[],[f62]) ).

fof(f62,plain,
    ( sz10 != xk
    & sz00 != xk ),
    inference(ennf_transformation,[],[f46]) ).

fof(f46,axiom,
    ~ ( sz10 = xk
      | sz00 = xk ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2315) ).

fof(f616,plain,
    ( sz00 = xk
    | ~ aNaturalNumber0(xk)
    | ~ spl16_14 ),
    inference(subsumption_resolution,[],[f615,f214]) ).

fof(f214,plain,
    sz10 != xk,
    inference(cnf_transformation,[],[f62]) ).

fof(f615,plain,
    ( sz10 = xk
    | sz00 = xk
    | ~ aNaturalNumber0(xk)
    | ~ spl16_14 ),
    inference(resolution,[],[f502,f262]) ).

fof(f262,plain,
    ! [X0] :
      ( isPrime0(sK13(X0))
      | sz10 = X0
      | sz00 = X0
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f159]) ).

fof(f159,plain,
    ! [X0] :
      ( ( isPrime0(sK13(X0))
        & doDivides0(sK13(X0),X0)
        & aNaturalNumber0(sK13(X0)) )
      | sz10 = X0
      | sz00 = X0
      | ~ aNaturalNumber0(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f105,f158]) ).

fof(f158,plain,
    ! [X0] :
      ( ? [X1] :
          ( isPrime0(X1)
          & doDivides0(X1,X0)
          & aNaturalNumber0(X1) )
     => ( isPrime0(sK13(X0))
        & doDivides0(sK13(X0),X0)
        & aNaturalNumber0(sK13(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f105,plain,
    ! [X0] :
      ( ? [X1] :
          ( isPrime0(X1)
          & doDivides0(X1,X0)
          & aNaturalNumber0(X1) )
      | sz10 = X0
      | sz00 = X0
      | ~ aNaturalNumber0(X0) ),
    inference(flattening,[],[f104]) ).

fof(f104,plain,
    ! [X0] :
      ( ? [X1] :
          ( isPrime0(X1)
          & doDivides0(X1,X0)
          & aNaturalNumber0(X1) )
      | sz10 = X0
      | sz00 = X0
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f38]) ).

fof(f38,axiom,
    ! [X0] :
      ( ( sz10 != X0
        & sz00 != X0
        & aNaturalNumber0(X0) )
     => ? [X1] :
          ( isPrime0(X1)
          & doDivides0(X1,X0)
          & aNaturalNumber0(X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mPrimDiv) ).

fof(f502,plain,
    ( ~ isPrime0(sK13(xk))
    | ~ spl16_14 ),
    inference(resolution,[],[f474,f223]) ).

fof(f223,plain,
    ! [X0] :
      ( ~ sP2(X0)
      | ~ isPrime0(X0) ),
    inference(cnf_transformation,[],[f152]) ).

fof(f152,plain,
    ! [X0] :
      ( ( ~ isPrime0(X0)
        & ( ( sK10(X0) != X0
            & sz10 != sK10(X0)
            & doDivides0(sK10(X0),X0)
            & sdtasdt0(sK10(X0),sK11(X0)) = X0
            & aNaturalNumber0(sK11(X0))
            & aNaturalNumber0(sK10(X0)) )
          | sz10 = X0
          | sz00 = X0 ) )
      | ~ sP2(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11])],[f149,f151,f150]) ).

fof(f150,plain,
    ! [X0] :
      ( ? [X1] :
          ( X0 != X1
          & sz10 != X1
          & doDivides0(X1,X0)
          & ? [X2] :
              ( sdtasdt0(X1,X2) = X0
              & aNaturalNumber0(X2) )
          & aNaturalNumber0(X1) )
     => ( sK10(X0) != X0
        & sz10 != sK10(X0)
        & doDivides0(sK10(X0),X0)
        & ? [X2] :
            ( sdtasdt0(sK10(X0),X2) = X0
            & aNaturalNumber0(X2) )
        & aNaturalNumber0(sK10(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f151,plain,
    ! [X0] :
      ( ? [X2] :
          ( sdtasdt0(sK10(X0),X2) = X0
          & aNaturalNumber0(X2) )
     => ( sdtasdt0(sK10(X0),sK11(X0)) = X0
        & aNaturalNumber0(sK11(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f149,plain,
    ! [X0] :
      ( ( ~ isPrime0(X0)
        & ( ? [X1] :
              ( X0 != X1
              & sz10 != X1
              & doDivides0(X1,X0)
              & ? [X2] :
                  ( sdtasdt0(X1,X2) = X0
                  & aNaturalNumber0(X2) )
              & aNaturalNumber0(X1) )
          | sz10 = X0
          | sz00 = X0 ) )
      | ~ sP2(X0) ),
    inference(nnf_transformation,[],[f130]) ).

fof(f130,plain,
    ! [X0] :
      ( ( ~ isPrime0(X0)
        & ( ? [X1] :
              ( X0 != X1
              & sz10 != X1
              & doDivides0(X1,X0)
              & ? [X2] :
                  ( sdtasdt0(X1,X2) = X0
                  & aNaturalNumber0(X2) )
              & aNaturalNumber0(X1) )
          | sz10 = X0
          | sz00 = X0 ) )
      | ~ sP2(X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).

fof(f474,plain,
    ( sP2(sK13(xk))
    | ~ spl16_14 ),
    inference(avatar_component_clause,[],[f472]) ).

fof(f472,plain,
    ( spl16_14
  <=> sP2(sK13(xk)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl16_14])]) ).

fof(f501,plain,
    spl16_13,
    inference(avatar_contradiction_clause,[],[f500]) ).

fof(f500,plain,
    ( $false
    | spl16_13 ),
    inference(subsumption_resolution,[],[f499,f210]) ).

fof(f499,plain,
    ( ~ aNaturalNumber0(xk)
    | spl16_13 ),
    inference(subsumption_resolution,[],[f498,f213]) ).

fof(f498,plain,
    ( sz00 = xk
    | ~ aNaturalNumber0(xk)
    | spl16_13 ),
    inference(subsumption_resolution,[],[f497,f214]) ).

fof(f497,plain,
    ( sz10 = xk
    | sz00 = xk
    | ~ aNaturalNumber0(xk)
    | spl16_13 ),
    inference(resolution,[],[f470,f260]) ).

fof(f260,plain,
    ! [X0] :
      ( aNaturalNumber0(sK13(X0))
      | sz10 = X0
      | sz00 = X0
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f159]) ).

fof(f470,plain,
    ( ~ aNaturalNumber0(sK13(xk))
    | spl16_13 ),
    inference(avatar_component_clause,[],[f468]) ).

fof(f468,plain,
    ( spl16_13
  <=> aNaturalNumber0(sK13(xk)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl16_13])]) ).

fof(f475,plain,
    ( ~ spl16_13
    | spl16_14 ),
    inference(avatar_split_clause,[],[f466,f472,f468]) ).

fof(f466,plain,
    ( sP2(sK13(xk))
    | ~ aNaturalNumber0(sK13(xk)) ),
    inference(subsumption_resolution,[],[f465,f210]) ).

fof(f465,plain,
    ( sP2(sK13(xk))
    | ~ aNaturalNumber0(sK13(xk))
    | ~ aNaturalNumber0(xk) ),
    inference(subsumption_resolution,[],[f464,f213]) ).

fof(f464,plain,
    ( sP2(sK13(xk))
    | ~ aNaturalNumber0(sK13(xk))
    | sz00 = xk
    | ~ aNaturalNumber0(xk) ),
    inference(subsumption_resolution,[],[f430,f214]) ).

fof(f430,plain,
    ( sP2(sK13(xk))
    | ~ aNaturalNumber0(sK13(xk))
    | sz10 = xk
    | sz00 = xk
    | ~ aNaturalNumber0(xk) ),
    inference(resolution,[],[f225,f261]) ).

fof(f261,plain,
    ! [X0] :
      ( doDivides0(sK13(X0),X0)
      | sz10 = X0
      | sz00 = X0
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f159]) ).

fof(f225,plain,
    ! [X0] :
      ( ~ doDivides0(X0,xk)
      | sP2(X0)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f153]) ).

fof(f153,plain,
    ! [X0] :
      ( sP2(X0)
      | ( ~ doDivides0(X0,xk)
        & ! [X1] :
            ( sdtasdt0(X0,X1) != xk
            | ~ aNaturalNumber0(X1) ) )
      | ~ aNaturalNumber0(X0) ),
    inference(rectify,[],[f131]) ).

fof(f131,plain,
    ! [X0] :
      ( sP2(X0)
      | ( ~ doDivides0(X0,xk)
        & ! [X3] :
            ( xk != sdtasdt0(X0,X3)
            | ~ aNaturalNumber0(X3) ) )
      | ~ aNaturalNumber0(X0) ),
    inference(definition_folding,[],[f64,f130]) ).

fof(f64,plain,
    ! [X0] :
      ( ( ~ isPrime0(X0)
        & ( ? [X1] :
              ( X0 != X1
              & sz10 != X1
              & doDivides0(X1,X0)
              & ? [X2] :
                  ( sdtasdt0(X1,X2) = X0
                  & aNaturalNumber0(X2) )
              & aNaturalNumber0(X1) )
          | sz10 = X0
          | sz00 = X0 ) )
      | ( ~ doDivides0(X0,xk)
        & ! [X3] :
            ( xk != sdtasdt0(X0,X3)
            | ~ aNaturalNumber0(X3) ) )
      | ~ aNaturalNumber0(X0) ),
    inference(flattening,[],[f63]) ).

fof(f63,plain,
    ! [X0] :
      ( ( ~ isPrime0(X0)
        & ( ? [X1] :
              ( X0 != X1
              & sz10 != X1
              & doDivides0(X1,X0)
              & ? [X2] :
                  ( sdtasdt0(X1,X2) = X0
                  & aNaturalNumber0(X2) )
              & aNaturalNumber0(X1) )
          | sz10 = X0
          | sz00 = X0 ) )
      | ( ~ doDivides0(X0,xk)
        & ! [X3] :
            ( xk != sdtasdt0(X0,X3)
            | ~ aNaturalNumber0(X3) ) )
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f53]) ).

fof(f53,plain,
    ~ ? [X0] :
        ( ( isPrime0(X0)
          | ( ! [X1] :
                ( ( doDivides0(X1,X0)
                  & ? [X2] :
                      ( sdtasdt0(X1,X2) = X0
                      & aNaturalNumber0(X2) )
                  & aNaturalNumber0(X1) )
               => ( X0 = X1
                  | sz10 = X1 ) )
            & sz10 != X0
            & sz00 != X0 ) )
        & ( doDivides0(X0,xk)
          | ? [X3] :
              ( xk = sdtasdt0(X0,X3)
              & aNaturalNumber0(X3) ) )
        & aNaturalNumber0(X0) ),
    inference(rectify,[],[f49]) ).

fof(f49,negated_conjecture,
    ~ ? [X0] :
        ( ( isPrime0(X0)
          | ( ! [X1] :
                ( ( doDivides0(X1,X0)
                  & ? [X2] :
                      ( sdtasdt0(X1,X2) = X0
                      & aNaturalNumber0(X2) )
                  & aNaturalNumber0(X1) )
               => ( X0 = X1
                  | sz10 = X1 ) )
            & sz10 != X0
            & sz00 != X0 ) )
        & ( doDivides0(X0,xk)
          | ? [X1] :
              ( sdtasdt0(X0,X1) = xk
              & aNaturalNumber0(X1) ) )
        & aNaturalNumber0(X0) ),
    inference(negated_conjecture,[],[f48]) ).

fof(f48,conjecture,
    ? [X0] :
      ( ( isPrime0(X0)
        | ( ! [X1] :
              ( ( doDivides0(X1,X0)
                & ? [X2] :
                    ( sdtasdt0(X1,X2) = X0
                    & aNaturalNumber0(X2) )
                & aNaturalNumber0(X1) )
             => ( X0 = X1
                | sz10 = X1 ) )
          & sz10 != X0
          & sz00 != X0 ) )
      & ( doDivides0(X0,xk)
        | ? [X1] :
            ( sdtasdt0(X0,X1) = xk
            & aNaturalNumber0(X1) ) )
      & aNaturalNumber0(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : NUM500+3 : TPTP v8.2.0. Released v4.0.0.
% 0.07/0.14  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.14/0.36  % Computer : n002.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Mon May 20 06:16:23 EDT 2024
% 0.14/0.36  % CPUTime    : 
% 0.14/0.36  This is a FOF_THM_RFO_SEQ problem
% 0.14/0.36  Running vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.53/0.74  % (26749)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on theBenchmark for (2996ds/45Mi)
% 0.53/0.74  % (26750)lrs+21_1:5_sil=2000:sos=on:urr=on:newcnf=on:slsq=on:i=83:slsql=off:bd=off:nm=2:ss=axioms:st=1.5:sp=const_min:gsp=on:rawr=on_0 on theBenchmark for (2996ds/83Mi)
% 0.53/0.74  % (26744)dis-1011_2:1_sil=2000:lsd=20:nwc=5.0:flr=on:mep=off:st=3.0:i=34:sd=1:ep=RS:ss=axioms_0 on theBenchmark for (2996ds/34Mi)
% 0.53/0.74  % (26746)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on theBenchmark for (2996ds/78Mi)
% 0.53/0.74  % (26747)ott+1011_1:1_sil=2000:urr=on:i=33:sd=1:kws=inv_frequency:ss=axioms:sup=off_0 on theBenchmark for (2996ds/33Mi)
% 0.53/0.74  % (26748)lrs+2_1:1_sil=16000:fde=none:sos=all:nwc=5.0:i=34:ep=RS:s2pl=on:lma=on:afp=100000_0 on theBenchmark for (2996ds/34Mi)
% 0.53/0.74  % (26745)lrs+1011_461:32768_sil=16000:irw=on:sp=frequency:lsd=20:fd=preordered:nwc=10.0:s2agt=32:alpa=false:cond=fast:s2a=on:i=51:s2at=3.0:awrs=decay:awrsf=691:bd=off:nm=20:fsr=off:amm=sco:uhcvi=on:rawr=on_0 on theBenchmark for (2996ds/51Mi)
% 0.53/0.74  % (26751)lrs-21_1:1_to=lpo:sil=2000:sp=frequency:sos=on:lma=on:i=56:sd=2:ss=axioms:ep=R_0 on theBenchmark for (2996ds/56Mi)
% 0.58/0.75  % (26749)First to succeed.
% 0.58/0.75  % (26744)Also succeeded, but the first one will report.
% 0.58/0.75  % (26749)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-26743"
% 0.58/0.75  % (26749)Refutation found. Thanks to Tanya!
% 0.58/0.75  % SZS status Theorem for theBenchmark
% 0.58/0.75  % SZS output start Proof for theBenchmark
% See solution above
% 0.58/0.75  % (26749)------------------------------
% 0.58/0.75  % (26749)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.58/0.75  % (26749)Termination reason: Refutation
% 0.58/0.75  
% 0.58/0.75  % (26749)Memory used [KB]: 1257
% 0.58/0.75  % (26749)Time elapsed: 0.010 s
% 0.58/0.75  % (26749)Instructions burned: 21 (million)
% 0.58/0.75  % (26743)Success in time 0.373 s
% 0.58/0.75  % Vampire---4.8 exiting
%------------------------------------------------------------------------------