TSTP Solution File: NUM560+2 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : NUM560+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n006.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 08:38:02 EDT 2024

% Result   : Theorem 0.20s 0.38s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   19
% Syntax   : Number of formulae    :   62 (  24 unt;   0 def)
%            Number of atoms       :  182 (  26 equ)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives :  178 (  58   ~;  39   |;  54   &)
%                                         (  19 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   21 (  19 usr;  13 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   5 con; 0-2 aty)
%            Number of variables   :   41 (  30   !;  11   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f475,plain,
    $false,
    inference(avatar_sat_refutation,[],[f419,f424,f429,f434,f439,f444,f449,f454,f459,f464,f468,f473,f474]) ).

fof(f474,plain,
    ( spl22_2
    | ~ spl22_3
    | ~ spl22_11 ),
    inference(avatar_split_clause,[],[f469,f466,f426,f421]) ).

fof(f421,plain,
    ( spl22_2
  <=> aElementOf0(sK8,szDzozmdt0(xF)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl22_2])]) ).

fof(f426,plain,
    ( spl22_3
  <=> aElementOf0(sK8,sdtlbdtrb0(xF,xy)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl22_3])]) ).

fof(f466,plain,
    ( spl22_11
  <=> ! [X1] :
        ( aElementOf0(X1,szDzozmdt0(xF))
        | ~ aElementOf0(X1,sdtlbdtrb0(xF,xy)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl22_11])]) ).

fof(f469,plain,
    ( aElementOf0(sK8,szDzozmdt0(xF))
    | ~ spl22_3
    | ~ spl22_11 ),
    inference(resolution,[],[f467,f428]) ).

fof(f428,plain,
    ( aElementOf0(sK8,sdtlbdtrb0(xF,xy))
    | ~ spl22_3 ),
    inference(avatar_component_clause,[],[f426]) ).

fof(f467,plain,
    ( ! [X1] :
        ( ~ aElementOf0(X1,sdtlbdtrb0(xF,xy))
        | aElementOf0(X1,szDzozmdt0(xF)) )
    | ~ spl22_11 ),
    inference(avatar_component_clause,[],[f466]) ).

fof(f473,plain,
    spl22_12,
    inference(avatar_split_clause,[],[f256,f471]) ).

fof(f471,plain,
    ( spl22_12
  <=> ! [X1] :
        ( xy = sdtlpdtrp0(xF,X1)
        | ~ aElementOf0(X1,sdtlbdtrb0(xF,xy)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl22_12])]) ).

fof(f256,plain,
    ! [X1] :
      ( xy = sdtlpdtrp0(xF,X1)
      | ~ aElementOf0(X1,sdtlbdtrb0(xF,xy)) ),
    inference(cnf_transformation,[],[f187]) ).

fof(f187,plain,
    ( ~ aSubsetOf0(sdtlbdtrb0(xF,xy),szDzozmdt0(xF))
    & ~ aElementOf0(sK8,szDzozmdt0(xF))
    & aElementOf0(sK8,sdtlbdtrb0(xF,xy))
    & ! [X1] :
        ( ( aElementOf0(X1,sdtlbdtrb0(xF,xy))
          | xy != sdtlpdtrp0(xF,X1)
          | ~ aElementOf0(X1,szDzozmdt0(xF)) )
        & ( ( xy = sdtlpdtrp0(xF,X1)
            & aElementOf0(X1,szDzozmdt0(xF)) )
          | ~ aElementOf0(X1,sdtlbdtrb0(xF,xy)) ) )
    & aSet0(sdtlbdtrb0(xF,xy)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f185,f186]) ).

fof(f186,plain,
    ( ? [X0] :
        ( ~ aElementOf0(X0,szDzozmdt0(xF))
        & aElementOf0(X0,sdtlbdtrb0(xF,xy)) )
   => ( ~ aElementOf0(sK8,szDzozmdt0(xF))
      & aElementOf0(sK8,sdtlbdtrb0(xF,xy)) ) ),
    introduced(choice_axiom,[]) ).

fof(f185,plain,
    ( ~ aSubsetOf0(sdtlbdtrb0(xF,xy),szDzozmdt0(xF))
    & ? [X0] :
        ( ~ aElementOf0(X0,szDzozmdt0(xF))
        & aElementOf0(X0,sdtlbdtrb0(xF,xy)) )
    & ! [X1] :
        ( ( aElementOf0(X1,sdtlbdtrb0(xF,xy))
          | xy != sdtlpdtrp0(xF,X1)
          | ~ aElementOf0(X1,szDzozmdt0(xF)) )
        & ( ( xy = sdtlpdtrp0(xF,X1)
            & aElementOf0(X1,szDzozmdt0(xF)) )
          | ~ aElementOf0(X1,sdtlbdtrb0(xF,xy)) ) )
    & aSet0(sdtlbdtrb0(xF,xy)) ),
    inference(rectify,[],[f184]) ).

fof(f184,plain,
    ( ~ aSubsetOf0(sdtlbdtrb0(xF,xy),szDzozmdt0(xF))
    & ? [X1] :
        ( ~ aElementOf0(X1,szDzozmdt0(xF))
        & aElementOf0(X1,sdtlbdtrb0(xF,xy)) )
    & ! [X0] :
        ( ( aElementOf0(X0,sdtlbdtrb0(xF,xy))
          | xy != sdtlpdtrp0(xF,X0)
          | ~ aElementOf0(X0,szDzozmdt0(xF)) )
        & ( ( xy = sdtlpdtrp0(xF,X0)
            & aElementOf0(X0,szDzozmdt0(xF)) )
          | ~ aElementOf0(X0,sdtlbdtrb0(xF,xy)) ) )
    & aSet0(sdtlbdtrb0(xF,xy)) ),
    inference(flattening,[],[f183]) ).

fof(f183,plain,
    ( ~ aSubsetOf0(sdtlbdtrb0(xF,xy),szDzozmdt0(xF))
    & ? [X1] :
        ( ~ aElementOf0(X1,szDzozmdt0(xF))
        & aElementOf0(X1,sdtlbdtrb0(xF,xy)) )
    & ! [X0] :
        ( ( aElementOf0(X0,sdtlbdtrb0(xF,xy))
          | xy != sdtlpdtrp0(xF,X0)
          | ~ aElementOf0(X0,szDzozmdt0(xF)) )
        & ( ( xy = sdtlpdtrp0(xF,X0)
            & aElementOf0(X0,szDzozmdt0(xF)) )
          | ~ aElementOf0(X0,sdtlbdtrb0(xF,xy)) ) )
    & aSet0(sdtlbdtrb0(xF,xy)) ),
    inference(nnf_transformation,[],[f80]) ).

fof(f80,plain,
    ( ~ aSubsetOf0(sdtlbdtrb0(xF,xy),szDzozmdt0(xF))
    & ? [X1] :
        ( ~ aElementOf0(X1,szDzozmdt0(xF))
        & aElementOf0(X1,sdtlbdtrb0(xF,xy)) )
    & ! [X0] :
        ( aElementOf0(X0,sdtlbdtrb0(xF,xy))
      <=> ( xy = sdtlpdtrp0(xF,X0)
          & aElementOf0(X0,szDzozmdt0(xF)) ) )
    & aSet0(sdtlbdtrb0(xF,xy)) ),
    inference(flattening,[],[f79]) ).

fof(f79,plain,
    ( ~ aSubsetOf0(sdtlbdtrb0(xF,xy),szDzozmdt0(xF))
    & ? [X1] :
        ( ~ aElementOf0(X1,szDzozmdt0(xF))
        & aElementOf0(X1,sdtlbdtrb0(xF,xy)) )
    & ! [X0] :
        ( aElementOf0(X0,sdtlbdtrb0(xF,xy))
      <=> ( xy = sdtlpdtrp0(xF,X0)
          & aElementOf0(X0,szDzozmdt0(xF)) ) )
    & aSet0(sdtlbdtrb0(xF,xy)) ),
    inference(ennf_transformation,[],[f70]) ).

fof(f70,plain,
    ~ ( ( ! [X0] :
            ( aElementOf0(X0,sdtlbdtrb0(xF,xy))
          <=> ( xy = sdtlpdtrp0(xF,X0)
              & aElementOf0(X0,szDzozmdt0(xF)) ) )
        & aSet0(sdtlbdtrb0(xF,xy)) )
     => ( aSubsetOf0(sdtlbdtrb0(xF,xy),szDzozmdt0(xF))
        | ! [X1] :
            ( aElementOf0(X1,sdtlbdtrb0(xF,xy))
           => aElementOf0(X1,szDzozmdt0(xF)) ) ) ),
    inference(rectify,[],[f69]) ).

fof(f69,negated_conjecture,
    ~ ( ( ! [X0] :
            ( aElementOf0(X0,sdtlbdtrb0(xF,xy))
          <=> ( xy = sdtlpdtrp0(xF,X0)
              & aElementOf0(X0,szDzozmdt0(xF)) ) )
        & aSet0(sdtlbdtrb0(xF,xy)) )
     => ( aSubsetOf0(sdtlbdtrb0(xF,xy),szDzozmdt0(xF))
        | ! [X0] :
            ( aElementOf0(X0,sdtlbdtrb0(xF,xy))
           => aElementOf0(X0,szDzozmdt0(xF)) ) ) ),
    inference(negated_conjecture,[],[f68]) ).

fof(f68,conjecture,
    ( ( ! [X0] :
          ( aElementOf0(X0,sdtlbdtrb0(xF,xy))
        <=> ( xy = sdtlpdtrp0(xF,X0)
            & aElementOf0(X0,szDzozmdt0(xF)) ) )
      & aSet0(sdtlbdtrb0(xF,xy)) )
   => ( aSubsetOf0(sdtlbdtrb0(xF,xy),szDzozmdt0(xF))
      | ! [X0] :
          ( aElementOf0(X0,sdtlbdtrb0(xF,xy))
         => aElementOf0(X0,szDzozmdt0(xF)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

fof(f468,plain,
    spl22_11,
    inference(avatar_split_clause,[],[f255,f466]) ).

fof(f255,plain,
    ! [X1] :
      ( aElementOf0(X1,szDzozmdt0(xF))
      | ~ aElementOf0(X1,sdtlbdtrb0(xF,xy)) ),
    inference(cnf_transformation,[],[f187]) ).

fof(f464,plain,
    spl22_10,
    inference(avatar_split_clause,[],[f400,f461]) ).

fof(f461,plain,
    ( spl22_10
  <=> aSet0(slcrc0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl22_10])]) ).

fof(f400,plain,
    aSet0(slcrc0),
    inference(equality_resolution,[],[f327]) ).

fof(f327,plain,
    ! [X0] :
      ( aSet0(X0)
      | slcrc0 != X0 ),
    inference(cnf_transformation,[],[f219]) ).

fof(f219,plain,
    ! [X0] :
      ( ( slcrc0 = X0
        | aElementOf0(sK15(X0),X0)
        | ~ aSet0(X0) )
      & ( ( ! [X2] : ~ aElementOf0(X2,X0)
          & aSet0(X0) )
        | slcrc0 != X0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK15])],[f217,f218]) ).

fof(f218,plain,
    ! [X0] :
      ( ? [X1] : aElementOf0(X1,X0)
     => aElementOf0(sK15(X0),X0) ),
    introduced(choice_axiom,[]) ).

fof(f217,plain,
    ! [X0] :
      ( ( slcrc0 = X0
        | ? [X1] : aElementOf0(X1,X0)
        | ~ aSet0(X0) )
      & ( ( ! [X2] : ~ aElementOf0(X2,X0)
          & aSet0(X0) )
        | slcrc0 != X0 ) ),
    inference(rectify,[],[f216]) ).

fof(f216,plain,
    ! [X0] :
      ( ( slcrc0 = X0
        | ? [X1] : aElementOf0(X1,X0)
        | ~ aSet0(X0) )
      & ( ( ! [X1] : ~ aElementOf0(X1,X0)
          & aSet0(X0) )
        | slcrc0 != X0 ) ),
    inference(flattening,[],[f215]) ).

fof(f215,plain,
    ! [X0] :
      ( ( slcrc0 = X0
        | ? [X1] : aElementOf0(X1,X0)
        | ~ aSet0(X0) )
      & ( ( ! [X1] : ~ aElementOf0(X1,X0)
          & aSet0(X0) )
        | slcrc0 != X0 ) ),
    inference(nnf_transformation,[],[f135]) ).

fof(f135,plain,
    ! [X0] :
      ( slcrc0 = X0
    <=> ( ! [X1] : ~ aElementOf0(X1,X0)
        & aSet0(X0) ) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f5,axiom,
    ! [X0] :
      ( slcrc0 = X0
    <=> ( ~ ? [X1] : aElementOf0(X1,X0)
        & aSet0(X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefEmp) ).

fof(f459,plain,
    spl22_9,
    inference(avatar_split_clause,[],[f267,f456]) ).

fof(f456,plain,
    ( spl22_9
  <=> isCountable0(szNzAzT0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl22_9])]) ).

fof(f267,plain,
    isCountable0(szNzAzT0),
    inference(cnf_transformation,[],[f23]) ).

fof(f23,axiom,
    ( isCountable0(szNzAzT0)
    & aSet0(szNzAzT0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNATSet) ).

fof(f454,plain,
    spl22_8,
    inference(avatar_split_clause,[],[f266,f451]) ).

fof(f451,plain,
    ( spl22_8
  <=> aSet0(szNzAzT0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl22_8])]) ).

fof(f266,plain,
    aSet0(szNzAzT0),
    inference(cnf_transformation,[],[f23]) ).

fof(f449,plain,
    spl22_7,
    inference(avatar_split_clause,[],[f263,f446]) ).

fof(f446,plain,
    ( spl22_7
  <=> isFinite0(slcrc0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl22_7])]) ).

fof(f263,plain,
    isFinite0(slcrc0),
    inference(cnf_transformation,[],[f6]) ).

fof(f6,axiom,
    isFinite0(slcrc0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEmpFin) ).

fof(f444,plain,
    spl22_6,
    inference(avatar_split_clause,[],[f262,f441]) ).

fof(f441,plain,
    ( spl22_6
  <=> aElement0(xy) ),
    introduced(avatar_definition,[new_symbols(naming,[spl22_6])]) ).

fof(f262,plain,
    aElement0(xy),
    inference(cnf_transformation,[],[f67]) ).

fof(f67,axiom,
    ( aElement0(xy)
    & aFunction0(xF) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2693) ).

fof(f439,plain,
    spl22_5,
    inference(avatar_split_clause,[],[f261,f436]) ).

fof(f436,plain,
    ( spl22_5
  <=> aFunction0(xF) ),
    introduced(avatar_definition,[new_symbols(naming,[spl22_5])]) ).

fof(f261,plain,
    aFunction0(xF),
    inference(cnf_transformation,[],[f67]) ).

fof(f434,plain,
    ~ spl22_4,
    inference(avatar_split_clause,[],[f260,f431]) ).

fof(f431,plain,
    ( spl22_4
  <=> aSubsetOf0(sdtlbdtrb0(xF,xy),szDzozmdt0(xF)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl22_4])]) ).

fof(f260,plain,
    ~ aSubsetOf0(sdtlbdtrb0(xF,xy),szDzozmdt0(xF)),
    inference(cnf_transformation,[],[f187]) ).

fof(f429,plain,
    spl22_3,
    inference(avatar_split_clause,[],[f258,f426]) ).

fof(f258,plain,
    aElementOf0(sK8,sdtlbdtrb0(xF,xy)),
    inference(cnf_transformation,[],[f187]) ).

fof(f424,plain,
    ~ spl22_2,
    inference(avatar_split_clause,[],[f259,f421]) ).

fof(f259,plain,
    ~ aElementOf0(sK8,szDzozmdt0(xF)),
    inference(cnf_transformation,[],[f187]) ).

fof(f419,plain,
    spl22_1,
    inference(avatar_split_clause,[],[f254,f416]) ).

fof(f416,plain,
    ( spl22_1
  <=> aSet0(sdtlbdtrb0(xF,xy)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl22_1])]) ).

fof(f254,plain,
    aSet0(sdtlbdtrb0(xF,xy)),
    inference(cnf_transformation,[],[f187]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : NUM560+2 : TPTP v8.1.2. Released v4.0.0.
% 0.03/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.35  % Computer : n006.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  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Fri May  3 14:11:23 EDT 2024
% 0.13/0.35  % CPUTime    : 
% 0.13/0.35  % (7698)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.37  % (7704)WARNING: value z3 for option sas not known
% 0.20/0.37  % (7706)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.20/0.37  % (7707)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.20/0.37  % (7702)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.20/0.37  % (7703)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.20/0.37  % (7705)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.20/0.37  % (7704)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.20/0.38  % (7708)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.20/0.38  % (7706)First to succeed.
% 0.20/0.38  % (7707)Also succeeded, but the first one will report.
% 0.20/0.38  % (7706)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-7698"
% 0.20/0.38  % (7706)Refutation found. Thanks to Tanya!
% 0.20/0.38  % SZS status Theorem for theBenchmark
% 0.20/0.38  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.38  % (7706)------------------------------
% 0.20/0.38  % (7706)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.20/0.38  % (7706)Termination reason: Refutation
% 0.20/0.38  
% 0.20/0.38  % (7706)Memory used [KB]: 1029
% 0.20/0.38  % (7706)Time elapsed: 0.010 s
% 0.20/0.38  % (7706)Instructions burned: 13 (million)
% 0.20/0.38  % (7698)Success in time 0.027 s
%------------------------------------------------------------------------------