TSTP Solution File: NUM469+2 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : NUM469+2 : TPTP v8.1.2. 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/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s

% Computer : n005.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 : Sun May  5 08:12:18 EDT 2024

% Result   : Theorem 0.60s 0.76s
% Output   : Refutation 0.60s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   67 (   9 unt;   0 def)
%            Number of atoms       :  171 (  51 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  158 (  54   ~;  53   |;  37   &)
%                                         (   8 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   12 (  10 usr;   9 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   6 con; 0-2 aty)
%            Number of variables   :   24 (  16   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f452,plain,
    $false,
    inference(avatar_sat_refutation,[],[f197,f207,f217,f294,f297,f423,f425,f443,f451]) ).

fof(f451,plain,
    ( ~ spl4_6
    | ~ spl4_4
    | ~ spl4_2 ),
    inference(avatar_split_clause,[],[f446,f194,f204,f214]) ).

fof(f214,plain,
    ( spl4_6
  <=> aNaturalNumber0(sdtsldt0(xm,xl)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_6])]) ).

fof(f204,plain,
    ( spl4_4
  <=> aNaturalNumber0(sdtsldt0(xn,xl)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_4])]) ).

fof(f194,plain,
    ( spl4_2
  <=> sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_2])]) ).

fof(f446,plain,
    ( ~ aNaturalNumber0(sdtsldt0(xn,xl))
    | ~ aNaturalNumber0(sdtsldt0(xm,xl))
    | ~ spl4_2 ),
    inference(resolution,[],[f112,f249]) ).

fof(f249,plain,
    ( ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)))
    | ~ spl4_2 ),
    inference(trivial_inequality_removal,[],[f248]) ).

fof(f248,plain,
    ( sdtpldt0(xm,xn) != sdtpldt0(xm,xn)
    | ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)))
    | ~ spl4_2 ),
    inference(superposition,[],[f176,f196]) ).

fof(f196,plain,
    ( sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)))
    | ~ spl4_2 ),
    inference(avatar_component_clause,[],[f194]) ).

fof(f176,plain,
    ! [X0] :
      ( sdtasdt0(xl,X0) != sdtpldt0(xm,xn)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f93]) ).

fof(f93,plain,
    ( ~ doDivides0(xl,sdtpldt0(xm,xn))
    & ! [X0] :
        ( sdtasdt0(xl,X0) != sdtpldt0(xm,xn)
        | ~ aNaturalNumber0(X0) ) ),
    inference(ennf_transformation,[],[f37]) ).

fof(f37,negated_conjecture,
    ~ ( doDivides0(xl,sdtpldt0(xm,xn))
      | ? [X0] :
          ( sdtasdt0(xl,X0) = sdtpldt0(xm,xn)
          & aNaturalNumber0(X0) ) ),
    inference(negated_conjecture,[],[f36]) ).

fof(f36,conjecture,
    ( doDivides0(xl,sdtpldt0(xm,xn))
    | ? [X0] :
        ( sdtasdt0(xl,X0) = sdtpldt0(xm,xn)
        & aNaturalNumber0(X0) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.7k2UxQ4SdP/Vampire---4.8_4972',m__) ).

fof(f112,plain,
    ! [X0,X1] :
      ( aNaturalNumber0(sdtpldt0(X0,X1))
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f43]) ).

fof(f43,plain,
    ! [X0,X1] :
      ( aNaturalNumber0(sdtpldt0(X0,X1))
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(flattening,[],[f42]) ).

fof(f42,plain,
    ! [X0,X1] :
      ( aNaturalNumber0(sdtpldt0(X0,X1))
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X0,X1] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X0) )
     => aNaturalNumber0(sdtpldt0(X0,X1)) ),
    file('/export/starexec/sandbox2/tmp/tmp.7k2UxQ4SdP/Vampire---4.8_4972',mSortsB) ).

fof(f443,plain,
    ~ spl4_8,
    inference(avatar_contradiction_clause,[],[f442]) ).

fof(f442,plain,
    ( $false
    | ~ spl4_8 ),
    inference(resolution,[],[f441,f167]) ).

fof(f167,plain,
    doDivides0(xl,xm),
    inference(cnf_transformation,[],[f108]) ).

fof(f108,plain,
    ( doDivides0(xl,xn)
    & xn = sdtasdt0(xl,sK2)
    & aNaturalNumber0(sK2)
    & doDivides0(xl,xm)
    & xm = sdtasdt0(xl,sK3)
    & aNaturalNumber0(sK3) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f40,f107,f106]) ).

fof(f106,plain,
    ( ? [X0] :
        ( xn = sdtasdt0(xl,X0)
        & aNaturalNumber0(X0) )
   => ( xn = sdtasdt0(xl,sK2)
      & aNaturalNumber0(sK2) ) ),
    introduced(choice_axiom,[]) ).

fof(f107,plain,
    ( ? [X1] :
        ( xm = sdtasdt0(xl,X1)
        & aNaturalNumber0(X1) )
   => ( xm = sdtasdt0(xl,sK3)
      & aNaturalNumber0(sK3) ) ),
    introduced(choice_axiom,[]) ).

fof(f40,plain,
    ( doDivides0(xl,xn)
    & ? [X0] :
        ( xn = sdtasdt0(xl,X0)
        & aNaturalNumber0(X0) )
    & doDivides0(xl,xm)
    & ? [X1] :
        ( xm = sdtasdt0(xl,X1)
        & aNaturalNumber0(X1) ) ),
    inference(rectify,[],[f34]) ).

fof(f34,axiom,
    ( doDivides0(xl,xn)
    & ? [X0] :
        ( xn = sdtasdt0(xl,X0)
        & aNaturalNumber0(X0) )
    & doDivides0(xl,xm)
    & ? [X0] :
        ( xm = sdtasdt0(xl,X0)
        & aNaturalNumber0(X0) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.7k2UxQ4SdP/Vampire---4.8_4972',m__1240_04) ).

fof(f441,plain,
    ( ~ doDivides0(xl,xm)
    | ~ spl4_8 ),
    inference(superposition,[],[f177,f239]) ).

fof(f239,plain,
    ( xm = sdtpldt0(xm,xn)
    | ~ spl4_8 ),
    inference(avatar_component_clause,[],[f238]) ).

fof(f238,plain,
    ( spl4_8
  <=> xm = sdtpldt0(xm,xn) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_8])]) ).

fof(f177,plain,
    ~ doDivides0(xl,sdtpldt0(xm,xn)),
    inference(cnf_transformation,[],[f93]) ).

fof(f425,plain,
    spl4_19,
    inference(avatar_contradiction_clause,[],[f424]) ).

fof(f424,plain,
    ( $false
    | spl4_19 ),
    inference(resolution,[],[f417,f163]) ).

fof(f163,plain,
    aNaturalNumber0(xm),
    inference(cnf_transformation,[],[f33]) ).

fof(f33,axiom,
    ( aNaturalNumber0(xn)
    & aNaturalNumber0(xm)
    & aNaturalNumber0(xl) ),
    file('/export/starexec/sandbox2/tmp/tmp.7k2UxQ4SdP/Vampire---4.8_4972',m__1240) ).

fof(f417,plain,
    ( ~ aNaturalNumber0(xm)
    | spl4_19 ),
    inference(avatar_component_clause,[],[f415]) ).

fof(f415,plain,
    ( spl4_19
  <=> aNaturalNumber0(xm) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_19])]) ).

fof(f423,plain,
    ( ~ spl4_19
    | spl4_8
    | ~ spl4_12 ),
    inference(avatar_split_clause,[],[f422,f270,f238,f415]) ).

fof(f270,plain,
    ( spl4_12
  <=> sz00 = xn ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_12])]) ).

fof(f422,plain,
    ( ~ aNaturalNumber0(xm)
    | spl4_8
    | ~ spl4_12 ),
    inference(trivial_inequality_removal,[],[f421]) ).

fof(f421,plain,
    ( xm != xm
    | ~ aNaturalNumber0(xm)
    | spl4_8
    | ~ spl4_12 ),
    inference(superposition,[],[f407,f116]) ).

fof(f116,plain,
    ! [X0] :
      ( sdtpldt0(X0,sz00) = X0
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f50]) ).

fof(f50,plain,
    ! [X0] :
      ( ( sdtpldt0(sz00,X0) = X0
        & sdtpldt0(X0,sz00) = X0 )
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f8]) ).

fof(f8,axiom,
    ! [X0] :
      ( aNaturalNumber0(X0)
     => ( sdtpldt0(sz00,X0) = X0
        & sdtpldt0(X0,sz00) = X0 ) ),
    file('/export/starexec/sandbox2/tmp/tmp.7k2UxQ4SdP/Vampire---4.8_4972',m_AddZero) ).

fof(f407,plain,
    ( xm != sdtpldt0(xm,sz00)
    | spl4_8
    | ~ spl4_12 ),
    inference(forward_demodulation,[],[f240,f272]) ).

fof(f272,plain,
    ( sz00 = xn
    | ~ spl4_12 ),
    inference(avatar_component_clause,[],[f270]) ).

fof(f240,plain,
    ( xm != sdtpldt0(xm,xn)
    | spl4_8 ),
    inference(avatar_component_clause,[],[f238]) ).

fof(f297,plain,
    spl4_11,
    inference(avatar_contradiction_clause,[],[f296]) ).

fof(f296,plain,
    ( $false
    | spl4_11 ),
    inference(resolution,[],[f268,f168]) ).

fof(f168,plain,
    aNaturalNumber0(sK2),
    inference(cnf_transformation,[],[f108]) ).

fof(f268,plain,
    ( ~ aNaturalNumber0(sK2)
    | spl4_11 ),
    inference(avatar_component_clause,[],[f266]) ).

fof(f266,plain,
    ( spl4_11
  <=> aNaturalNumber0(sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_11])]) ).

fof(f294,plain,
    ( ~ spl4_11
    | spl4_12
    | ~ spl4_1 ),
    inference(avatar_split_clause,[],[f257,f190,f270,f266]) ).

fof(f190,plain,
    ( spl4_1
  <=> sz00 = xl ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_1])]) ).

fof(f257,plain,
    ( sz00 = xn
    | ~ aNaturalNumber0(sK2)
    | ~ spl4_1 ),
    inference(superposition,[],[f227,f123]) ).

fof(f123,plain,
    ! [X0] :
      ( sz00 = sdtasdt0(sz00,X0)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f56]) ).

fof(f56,plain,
    ! [X0] :
      ( ( sz00 = sdtasdt0(sz00,X0)
        & sz00 = sdtasdt0(X0,sz00) )
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f12]) ).

fof(f12,axiom,
    ! [X0] :
      ( aNaturalNumber0(X0)
     => ( sz00 = sdtasdt0(sz00,X0)
        & sz00 = sdtasdt0(X0,sz00) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.7k2UxQ4SdP/Vampire---4.8_4972',m_MulZero) ).

fof(f227,plain,
    ( xn = sdtasdt0(sz00,sK2)
    | ~ spl4_1 ),
    inference(superposition,[],[f169,f192]) ).

fof(f192,plain,
    ( sz00 = xl
    | ~ spl4_1 ),
    inference(avatar_component_clause,[],[f190]) ).

fof(f169,plain,
    xn = sdtasdt0(xl,sK2),
    inference(cnf_transformation,[],[f108]) ).

fof(f217,plain,
    ( spl4_1
    | spl4_6 ),
    inference(avatar_split_clause,[],[f171,f214,f190]) ).

fof(f171,plain,
    ( aNaturalNumber0(sdtsldt0(xm,xl))
    | sz00 = xl ),
    inference(cnf_transformation,[],[f92]) ).

fof(f92,plain,
    ( ( sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)))
      & xn = sdtasdt0(xl,sdtsldt0(xn,xl))
      & aNaturalNumber0(sdtsldt0(xn,xl))
      & xm = sdtasdt0(xl,sdtsldt0(xm,xl))
      & aNaturalNumber0(sdtsldt0(xm,xl)) )
    | sz00 = xl ),
    inference(ennf_transformation,[],[f35]) ).

fof(f35,axiom,
    ( sz00 != xl
   => ( sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)))
      & xn = sdtasdt0(xl,sdtsldt0(xn,xl))
      & aNaturalNumber0(sdtsldt0(xn,xl))
      & xm = sdtasdt0(xl,sdtsldt0(xm,xl))
      & aNaturalNumber0(sdtsldt0(xm,xl)) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.7k2UxQ4SdP/Vampire---4.8_4972',m__1298) ).

fof(f207,plain,
    ( spl4_1
    | spl4_4 ),
    inference(avatar_split_clause,[],[f173,f204,f190]) ).

fof(f173,plain,
    ( aNaturalNumber0(sdtsldt0(xn,xl))
    | sz00 = xl ),
    inference(cnf_transformation,[],[f92]) ).

fof(f197,plain,
    ( spl4_1
    | spl4_2 ),
    inference(avatar_split_clause,[],[f175,f194,f190]) ).

fof(f175,plain,
    ( sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)))
    | sz00 = xl ),
    inference(cnf_transformation,[],[f92]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem    : NUM469+2 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.15  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.15/0.36  % Computer : n005.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Fri May  3 13:45:53 EDT 2024
% 0.22/0.36  % CPUTime    : 
% 0.22/0.36  This is a FOF_THM_RFO_SEQ problem
% 0.22/0.36  Running vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/tmp/tmp.7k2UxQ4SdP/Vampire---4.8_4972
% 0.57/0.75  % (5155)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 Vampire---4 for (2996ds/34Mi)
% 0.57/0.75  % (5162)lrs-21_1:1_to=lpo:sil=2000:sp=frequency:sos=on:lma=on:i=56:sd=2:ss=axioms:ep=R_0 on Vampire---4 for (2996ds/56Mi)
% 0.57/0.75  % (5157)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2996ds/78Mi)
% 0.57/0.75  % (5156)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 Vampire---4 for (2996ds/51Mi)
% 0.57/0.75  % (5158)ott+1011_1:1_sil=2000:urr=on:i=33:sd=1:kws=inv_frequency:ss=axioms:sup=off_0 on Vampire---4 for (2996ds/33Mi)
% 0.57/0.75  % (5159)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 Vampire---4 for (2996ds/34Mi)
% 0.57/0.75  % (5160)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on Vampire---4 for (2996ds/45Mi)
% 0.57/0.75  % (5161)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 Vampire---4 for (2996ds/83Mi)
% 0.60/0.76  % (5156)First to succeed.
% 0.60/0.76  % (5157)Also succeeded, but the first one will report.
% 0.60/0.76  % (5155)Instruction limit reached!
% 0.60/0.76  % (5155)------------------------------
% 0.60/0.76  % (5155)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.60/0.76  % (5155)Termination reason: Unknown
% 0.60/0.76  % (5156)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-5136"
% 0.60/0.76  % (5155)Termination phase: Saturation
% 0.60/0.76  
% 0.60/0.76  % (5155)Memory used [KB]: 1356
% 0.60/0.76  % (5155)Time elapsed: 0.012 s
% 0.60/0.76  % (5155)Instructions burned: 37 (million)
% 0.60/0.76  % (5155)------------------------------
% 0.60/0.76  % (5155)------------------------------
% 0.60/0.76  % (5156)Refutation found. Thanks to Tanya!
% 0.60/0.76  % SZS status Theorem for Vampire---4
% 0.60/0.76  % SZS output start Proof for Vampire---4
% See solution above
% 0.60/0.76  % (5156)------------------------------
% 0.60/0.76  % (5156)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.60/0.76  % (5156)Termination reason: Refutation
% 0.60/0.76  
% 0.60/0.76  % (5156)Memory used [KB]: 1200
% 0.60/0.76  % (5156)Time elapsed: 0.010 s
% 0.60/0.76  % (5156)Instructions burned: 14 (million)
% 0.60/0.76  % (5136)Success in time 0.385 s
% 0.60/0.76  % Vampire---4.8 exiting
%------------------------------------------------------------------------------