TSTP Solution File: NUM425+1 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : NUM425+1 : 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/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s

% Computer : n023.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 : Wed May  1 03:31:01 EDT 2024

% Result   : Theorem 0.63s 0.80s
% Output   : Refutation 0.63s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   57 (  10 unt;   0 def)
%            Number of atoms       :  195 (  35 equ)
%            Maximal formula atoms :   11 (   3 avg)
%            Number of connectives :  235 (  97   ~;  91   |;  34   &)
%                                         (   8 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   3 prp; 0-3 aty)
%            Number of functors    :    8 (   8 usr;   4 con; 0-2 aty)
%            Number of variables   :   70 (  62   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f360,plain,
    $false,
    inference(avatar_sat_refutation,[],[f136,f237,f359]) ).

fof(f359,plain,
    spl2_2,
    inference(avatar_contradiction_clause,[],[f358]) ).

fof(f358,plain,
    ( $false
    | spl2_2 ),
    inference(subsumption_resolution,[],[f357,f90]) ).

fof(f90,plain,
    aInteger0(xa),
    inference(cnf_transformation,[],[f21]) ).

fof(f21,axiom,
    ( sz00 != xq
    & aInteger0(xq)
    & aInteger0(xb)
    & aInteger0(xa) ),
    file('/export/starexec/sandbox/tmp/tmp.4O4YiMNGJG/Vampire---4.8_3642',m__704) ).

fof(f357,plain,
    ( ~ aInteger0(xa)
    | spl2_2 ),
    inference(subsumption_resolution,[],[f356,f91]) ).

fof(f91,plain,
    aInteger0(xb),
    inference(cnf_transformation,[],[f21]) ).

fof(f356,plain,
    ( ~ aInteger0(xb)
    | ~ aInteger0(xa)
    | spl2_2 ),
    inference(subsumption_resolution,[],[f351,f94]) ).

fof(f94,plain,
    sdteqdtlpzmzozddtrp0(xa,xb,xq),
    inference(cnf_transformation,[],[f22]) ).

fof(f22,axiom,
    sdteqdtlpzmzozddtrp0(xa,xb,xq),
    file('/export/starexec/sandbox/tmp/tmp.4O4YiMNGJG/Vampire---4.8_3642',m__724) ).

fof(f351,plain,
    ( ~ sdteqdtlpzmzozddtrp0(xa,xb,xq)
    | ~ aInteger0(xb)
    | ~ aInteger0(xa)
    | spl2_2 ),
    inference(resolution,[],[f340,f135]) ).

fof(f135,plain,
    ( ~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
    | spl2_2 ),
    inference(avatar_component_clause,[],[f133]) ).

fof(f133,plain,
    ( spl2_2
  <=> aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_2])]) ).

fof(f340,plain,
    ! [X0,X1] :
      ( aDivisorOf0(xq,sdtpldt0(X0,smndt0(X1)))
      | ~ sdteqdtlpzmzozddtrp0(X0,X1,xq)
      | ~ aInteger0(X1)
      | ~ aInteger0(X0) ),
    inference(subsumption_resolution,[],[f333,f92]) ).

fof(f92,plain,
    aInteger0(xq),
    inference(cnf_transformation,[],[f21]) ).

fof(f333,plain,
    ! [X0,X1] :
      ( aDivisorOf0(xq,sdtpldt0(X0,smndt0(X1)))
      | ~ sdteqdtlpzmzozddtrp0(X0,X1,xq)
      | ~ aInteger0(xq)
      | ~ aInteger0(X1)
      | ~ aInteger0(X0) ),
    inference(resolution,[],[f121,f119]) ).

fof(f119,plain,
    ! [X2,X0,X1] :
      ( aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1)))
      | ~ sdteqdtlpzmzozddtrp0(X0,X1,X2)
      | sQ1_eqProxy(sz00,X2)
      | ~ aInteger0(X2)
      | ~ aInteger0(X1)
      | ~ aInteger0(X0) ),
    inference(equality_proxy_replacement,[],[f87,f98]) ).

fof(f98,plain,
    ! [X0,X1] :
      ( sQ1_eqProxy(X0,X1)
    <=> X0 = X1 ),
    introduced(equality_proxy_definition,[new_symbols(naming,[sQ1_eqProxy])]) ).

fof(f87,plain,
    ! [X2,X0,X1] :
      ( aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1)))
      | ~ sdteqdtlpzmzozddtrp0(X0,X1,X2)
      | sz00 = X2
      | ~ aInteger0(X2)
      | ~ aInteger0(X1)
      | ~ aInteger0(X0) ),
    inference(cnf_transformation,[],[f59]) ).

fof(f59,plain,
    ! [X0,X1,X2] :
      ( ( ( sdteqdtlpzmzozddtrp0(X0,X1,X2)
          | ~ aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1))) )
        & ( aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1)))
          | ~ sdteqdtlpzmzozddtrp0(X0,X1,X2) ) )
      | sz00 = X2
      | ~ aInteger0(X2)
      | ~ aInteger0(X1)
      | ~ aInteger0(X0) ),
    inference(nnf_transformation,[],[f50]) ).

fof(f50,plain,
    ! [X0,X1,X2] :
      ( ( sdteqdtlpzmzozddtrp0(X0,X1,X2)
      <=> aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1))) )
      | sz00 = X2
      | ~ aInteger0(X2)
      | ~ aInteger0(X1)
      | ~ aInteger0(X0) ),
    inference(flattening,[],[f49]) ).

fof(f49,plain,
    ! [X0,X1,X2] :
      ( ( sdteqdtlpzmzozddtrp0(X0,X1,X2)
      <=> aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1))) )
      | sz00 = X2
      | ~ aInteger0(X2)
      | ~ aInteger0(X1)
      | ~ aInteger0(X0) ),
    inference(ennf_transformation,[],[f19]) ).

fof(f19,axiom,
    ! [X0,X1,X2] :
      ( ( sz00 != X2
        & aInteger0(X2)
        & aInteger0(X1)
        & aInteger0(X0) )
     => ( sdteqdtlpzmzozddtrp0(X0,X1,X2)
      <=> aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1))) ) ),
    file('/export/starexec/sandbox/tmp/tmp.4O4YiMNGJG/Vampire---4.8_3642',mEquMod) ).

fof(f121,plain,
    ~ sQ1_eqProxy(sz00,xq),
    inference(equality_proxy_replacement,[],[f93,f98]) ).

fof(f93,plain,
    sz00 != xq,
    inference(cnf_transformation,[],[f21]) ).

fof(f237,plain,
    spl2_1,
    inference(avatar_contradiction_clause,[],[f236]) ).

fof(f236,plain,
    ( $false
    | spl2_1 ),
    inference(subsumption_resolution,[],[f234,f91]) ).

fof(f234,plain,
    ( ~ aInteger0(xb)
    | spl2_1 ),
    inference(resolution,[],[f186,f62]) ).

fof(f62,plain,
    ! [X0] :
      ( aInteger0(smndt0(X0))
      | ~ aInteger0(X0) ),
    inference(cnf_transformation,[],[f26]) ).

fof(f26,plain,
    ! [X0] :
      ( aInteger0(smndt0(X0))
      | ~ aInteger0(X0) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X0] :
      ( aInteger0(X0)
     => aInteger0(smndt0(X0)) ),
    file('/export/starexec/sandbox/tmp/tmp.4O4YiMNGJG/Vampire---4.8_3642',mIntNeg) ).

fof(f186,plain,
    ( ~ aInteger0(smndt0(xb))
    | spl2_1 ),
    inference(subsumption_resolution,[],[f184,f90]) ).

fof(f184,plain,
    ( ~ aInteger0(smndt0(xb))
    | ~ aInteger0(xa)
    | spl2_1 ),
    inference(resolution,[],[f131,f63]) ).

fof(f63,plain,
    ! [X0,X1] :
      ( aInteger0(sdtpldt0(X0,X1))
      | ~ aInteger0(X1)
      | ~ aInteger0(X0) ),
    inference(cnf_transformation,[],[f28]) ).

fof(f28,plain,
    ! [X0,X1] :
      ( aInteger0(sdtpldt0(X0,X1))
      | ~ aInteger0(X1)
      | ~ aInteger0(X0) ),
    inference(flattening,[],[f27]) ).

fof(f27,plain,
    ! [X0,X1] :
      ( aInteger0(sdtpldt0(X0,X1))
      | ~ aInteger0(X1)
      | ~ aInteger0(X0) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f5,axiom,
    ! [X0,X1] :
      ( ( aInteger0(X1)
        & aInteger0(X0) )
     => aInteger0(sdtpldt0(X0,X1)) ),
    file('/export/starexec/sandbox/tmp/tmp.4O4YiMNGJG/Vampire---4.8_3642',mIntPlus) ).

fof(f131,plain,
    ( ~ aInteger0(sdtpldt0(xa,smndt0(xb)))
    | spl2_1 ),
    inference(avatar_component_clause,[],[f129]) ).

fof(f129,plain,
    ( spl2_1
  <=> aInteger0(sdtpldt0(xa,smndt0(xb))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_1])]) ).

fof(f136,plain,
    ( ~ spl2_1
    | ~ spl2_2 ),
    inference(avatar_split_clause,[],[f127,f133,f129]) ).

fof(f127,plain,
    ( ~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
    | ~ aInteger0(sdtpldt0(xa,smndt0(xb))) ),
    inference(subsumption_resolution,[],[f125,f84]) ).

fof(f84,plain,
    ! [X0,X1] :
      ( aInteger0(sK0(X0,X1))
      | ~ aDivisorOf0(X1,X0)
      | ~ aInteger0(X0) ),
    inference(cnf_transformation,[],[f58]) ).

fof(f58,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( aDivisorOf0(X1,X0)
            | ! [X2] :
                ( sdtasdt0(X1,X2) != X0
                | ~ aInteger0(X2) )
            | sz00 = X1
            | ~ aInteger0(X1) )
          & ( ( sdtasdt0(X1,sK0(X0,X1)) = X0
              & aInteger0(sK0(X0,X1))
              & sz00 != X1
              & aInteger0(X1) )
            | ~ aDivisorOf0(X1,X0) ) )
      | ~ aInteger0(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f56,f57]) ).

fof(f57,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( sdtasdt0(X1,X3) = X0
          & aInteger0(X3) )
     => ( sdtasdt0(X1,sK0(X0,X1)) = X0
        & aInteger0(sK0(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f56,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( aDivisorOf0(X1,X0)
            | ! [X2] :
                ( sdtasdt0(X1,X2) != X0
                | ~ aInteger0(X2) )
            | sz00 = X1
            | ~ aInteger0(X1) )
          & ( ( ? [X3] :
                  ( sdtasdt0(X1,X3) = X0
                  & aInteger0(X3) )
              & sz00 != X1
              & aInteger0(X1) )
            | ~ aDivisorOf0(X1,X0) ) )
      | ~ aInteger0(X0) ),
    inference(rectify,[],[f55]) ).

fof(f55,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( aDivisorOf0(X1,X0)
            | ! [X2] :
                ( sdtasdt0(X1,X2) != X0
                | ~ aInteger0(X2) )
            | sz00 = X1
            | ~ aInteger0(X1) )
          & ( ( ? [X2] :
                  ( sdtasdt0(X1,X2) = X0
                  & aInteger0(X2) )
              & sz00 != X1
              & aInteger0(X1) )
            | ~ aDivisorOf0(X1,X0) ) )
      | ~ aInteger0(X0) ),
    inference(flattening,[],[f54]) ).

fof(f54,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( aDivisorOf0(X1,X0)
            | ! [X2] :
                ( sdtasdt0(X1,X2) != X0
                | ~ aInteger0(X2) )
            | sz00 = X1
            | ~ aInteger0(X1) )
          & ( ( ? [X2] :
                  ( sdtasdt0(X1,X2) = X0
                  & aInteger0(X2) )
              & sz00 != X1
              & aInteger0(X1) )
            | ~ aDivisorOf0(X1,X0) ) )
      | ~ aInteger0(X0) ),
    inference(nnf_transformation,[],[f48]) ).

fof(f48,plain,
    ! [X0] :
      ( ! [X1] :
          ( aDivisorOf0(X1,X0)
        <=> ( ? [X2] :
                ( sdtasdt0(X1,X2) = X0
                & aInteger0(X2) )
            & sz00 != X1
            & aInteger0(X1) ) )
      | ~ aInteger0(X0) ),
    inference(ennf_transformation,[],[f18]) ).

fof(f18,axiom,
    ! [X0] :
      ( aInteger0(X0)
     => ! [X1] :
          ( aDivisorOf0(X1,X0)
        <=> ( ? [X2] :
                ( sdtasdt0(X1,X2) = X0
                & aInteger0(X2) )
            & sz00 != X1
            & aInteger0(X1) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.4O4YiMNGJG/Vampire---4.8_3642',mDivisor) ).

fof(f125,plain,
    ( ~ aInteger0(sK0(sdtpldt0(xa,smndt0(xb)),xq))
    | ~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
    | ~ aInteger0(sdtpldt0(xa,smndt0(xb))) ),
    inference(resolution,[],[f122,f117]) ).

fof(f117,plain,
    ! [X0,X1] :
      ( sQ1_eqProxy(sdtasdt0(X1,sK0(X0,X1)),X0)
      | ~ aDivisorOf0(X1,X0)
      | ~ aInteger0(X0) ),
    inference(equality_proxy_replacement,[],[f85,f98]) ).

fof(f85,plain,
    ! [X0,X1] :
      ( sdtasdt0(X1,sK0(X0,X1)) = X0
      | ~ aDivisorOf0(X1,X0)
      | ~ aInteger0(X0) ),
    inference(cnf_transformation,[],[f58]) ).

fof(f122,plain,
    ! [X0] :
      ( ~ sQ1_eqProxy(sdtasdt0(xq,X0),sdtpldt0(xa,smndt0(xb)))
      | ~ aInteger0(X0) ),
    inference(equality_proxy_replacement,[],[f95,f98]) ).

fof(f95,plain,
    ! [X0] :
      ( sdtasdt0(xq,X0) != sdtpldt0(xa,smndt0(xb))
      | ~ aInteger0(X0) ),
    inference(cnf_transformation,[],[f53]) ).

fof(f53,plain,
    ! [X0] :
      ( sdtasdt0(xq,X0) != sdtpldt0(xa,smndt0(xb))
      | ~ aInteger0(X0) ),
    inference(ennf_transformation,[],[f24]) ).

fof(f24,negated_conjecture,
    ~ ? [X0] :
        ( sdtasdt0(xq,X0) = sdtpldt0(xa,smndt0(xb))
        & aInteger0(X0) ),
    inference(negated_conjecture,[],[f23]) ).

fof(f23,conjecture,
    ? [X0] :
      ( sdtasdt0(xq,X0) = sdtpldt0(xa,smndt0(xb))
      & aInteger0(X0) ),
    file('/export/starexec/sandbox/tmp/tmp.4O4YiMNGJG/Vampire---4.8_3642',m__) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem    : NUM425+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.11  % 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
% 0.11/0.31  % Computer : n023.cluster.edu
% 0.11/0.31  % Model    : x86_64 x86_64
% 0.11/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31  % Memory   : 8042.1875MB
% 0.11/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31  % CPULimit   : 300
% 0.11/0.31  % WCLimit    : 300
% 0.11/0.31  % DateTime   : Tue Apr 30 17:09:25 EDT 2024
% 0.11/0.31  % CPUTime    : 
% 0.11/0.31  This is a FOF_THM_RFO_SEQ problem
% 0.17/0.31  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/tmp/tmp.4O4YiMNGJG/Vampire---4.8_3642
% 0.63/0.80  % (3757)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2995ds/78Mi)
% 0.63/0.80  % (3759)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 (2995ds/34Mi)
% 0.63/0.80  % (3758)ott+1011_1:1_sil=2000:urr=on:i=33:sd=1:kws=inv_frequency:ss=axioms:sup=off_0 on Vampire---4 for (2995ds/33Mi)
% 0.63/0.80  % (3755)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 (2995ds/34Mi)
% 0.63/0.80  % (3760)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on Vampire---4 for (2995ds/45Mi)
% 0.63/0.80  % (3756)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 (2995ds/51Mi)
% 0.63/0.80  % (3761)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 (2995ds/83Mi)
% 0.63/0.80  % (3762)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 (2995ds/56Mi)
% 0.63/0.80  % (3762)Refutation not found, incomplete strategy% (3762)------------------------------
% 0.63/0.80  % (3762)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.63/0.80  % (3762)Termination reason: Refutation not found, incomplete strategy
% 0.63/0.80  
% 0.63/0.80  % (3762)Memory used [KB]: 961
% 0.63/0.80  % (3762)Time elapsed: 0.003 s
% 0.63/0.80  % (3762)Instructions burned: 3 (million)
% 0.63/0.80  % (3762)------------------------------
% 0.63/0.80  % (3762)------------------------------
% 0.63/0.80  % (3755)Refutation not found, incomplete strategy% (3755)------------------------------
% 0.63/0.80  % (3755)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.63/0.80  % (3755)Termination reason: Refutation not found, incomplete strategy
% 0.63/0.80  
% 0.63/0.80  % (3755)Memory used [KB]: 1045
% 0.63/0.80  % (3755)Time elapsed: 0.004 s
% 0.63/0.80  % (3755)Instructions burned: 4 (million)
% 0.63/0.80  % (3755)------------------------------
% 0.63/0.80  % (3755)------------------------------
% 0.63/0.80  % (3759)First to succeed.
% 0.63/0.80  % (3759)Refutation found. Thanks to Tanya!
% 0.63/0.80  % SZS status Theorem for Vampire---4
% 0.63/0.80  % SZS output start Proof for Vampire---4
% See solution above
% 0.63/0.80  % (3759)------------------------------
% 0.63/0.80  % (3759)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.63/0.80  % (3759)Termination reason: Refutation
% 0.63/0.80  
% 0.63/0.80  % (3759)Memory used [KB]: 1080
% 0.63/0.80  % (3759)Time elapsed: 0.005 s
% 0.63/0.80  % (3759)Instructions burned: 7 (million)
% 0.63/0.80  % (3759)------------------------------
% 0.63/0.80  % (3759)------------------------------
% 0.63/0.80  % (3752)Success in time 0.484 s
% 0.63/0.80  % Vampire---4.8 exiting
%------------------------------------------------------------------------------