TSTP Solution File: NUM405+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : NUM405+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n003.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 Apr 30 14:21:59 EDT 2024

% Result   : Theorem 0.11s 0.34s
% Output   : Refutation 0.11s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   27 (   4 unt;   0 def)
%            Number of atoms       :   87 (   0 equ)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :  104 (  44   ~;  37   |;  15   &)
%                                         (   2 <=>;   5  =>;   0  <=;   1 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   1 con; 0-1 aty)
%            Number of variables   :   46 (  37   !;   9   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f253,plain,
    $false,
    inference(subsumption_resolution,[],[f250,f196]) ).

fof(f196,plain,
    ! [X0] : ordinal(sK1(sK3(X0))),
    inference(duplicate_literal_removal,[],[f195]) ).

fof(f195,plain,
    ! [X0] :
      ( ordinal(sK1(sK3(X0)))
      | ordinal(sK1(sK3(X0))) ),
    inference(resolution,[],[f121,f125]) ).

fof(f125,plain,
    ! [X2,X0] :
      ( ~ in(X2,sK3(X0))
      | ordinal(X2) ),
    inference(cnf_transformation,[],[f71]) ).

fof(f71,plain,
    ! [X0,X2] :
      ( ( in(X2,sK3(X0))
        | ~ ordinal(X2)
        | ~ in(X2,X0) )
      & ( ( ordinal(X2)
          & in(X2,X0) )
        | ~ in(X2,sK3(X0)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f69,f70]) ).

fof(f70,plain,
    ! [X0] :
      ( ? [X1] :
        ! [X2] :
          ( ( in(X2,X1)
            | ~ ordinal(X2)
            | ~ in(X2,X0) )
          & ( ( ordinal(X2)
              & in(X2,X0) )
            | ~ in(X2,X1) ) )
     => ! [X2] :
          ( ( in(X2,sK3(X0))
            | ~ ordinal(X2)
            | ~ in(X2,X0) )
          & ( ( ordinal(X2)
              & in(X2,X0) )
            | ~ in(X2,sK3(X0)) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f69,plain,
    ! [X0] :
    ? [X1] :
    ! [X2] :
      ( ( in(X2,X1)
        | ~ ordinal(X2)
        | ~ in(X2,X0) )
      & ( ( ordinal(X2)
          & in(X2,X0) )
        | ~ in(X2,X1) ) ),
    inference(flattening,[],[f68]) ).

fof(f68,plain,
    ! [X0] :
    ? [X1] :
    ! [X2] :
      ( ( in(X2,X1)
        | ~ ordinal(X2)
        | ~ in(X2,X0) )
      & ( ( ordinal(X2)
          & in(X2,X0) )
        | ~ in(X2,X1) ) ),
    inference(nnf_transformation,[],[f26]) ).

fof(f26,axiom,
    ! [X0] :
    ? [X1] :
    ! [X2] :
      ( in(X2,X1)
    <=> ( ordinal(X2)
        & in(X2,X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_xboole_0__e2_43__ordinal1) ).

fof(f121,plain,
    ! [X0] :
      ( in(sK1(X0),X0)
      | ordinal(sK1(X0)) ),
    inference(cnf_transformation,[],[f65]) ).

fof(f65,plain,
    ! [X0] :
      ( ( ~ ordinal(sK1(X0))
        | ~ in(sK1(X0),X0) )
      & ( ordinal(sK1(X0))
        | in(sK1(X0),X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f63,f64]) ).

fof(f64,plain,
    ! [X0] :
      ( ? [X1] :
          ( ( ~ ordinal(X1)
            | ~ in(X1,X0) )
          & ( ordinal(X1)
            | in(X1,X0) ) )
     => ( ( ~ ordinal(sK1(X0))
          | ~ in(sK1(X0),X0) )
        & ( ordinal(sK1(X0))
          | in(sK1(X0),X0) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f63,plain,
    ! [X0] :
    ? [X1] :
      ( ( ~ ordinal(X1)
        | ~ in(X1,X0) )
      & ( ordinal(X1)
        | in(X1,X0) ) ),
    inference(nnf_transformation,[],[f54]) ).

fof(f54,plain,
    ! [X0] :
    ? [X1] :
      ( in(X1,X0)
    <~> ordinal(X1) ),
    inference(ennf_transformation,[],[f29]) ).

fof(f29,axiom,
    ! [X0] :
      ~ ! [X1] :
          ( in(X1,X0)
        <=> ordinal(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_ordinal1) ).

fof(f250,plain,
    ~ ordinal(sK1(sK3(sK0))),
    inference(resolution,[],[f249,f98]) ).

fof(f98,plain,
    ! [X1] :
      ( in(X1,sK0)
      | ~ ordinal(X1) ),
    inference(cnf_transformation,[],[f62]) ).

fof(f62,plain,
    ! [X1] :
      ( in(X1,sK0)
      | ~ ordinal(X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f44,f61]) ).

fof(f61,plain,
    ( ? [X0] :
      ! [X1] :
        ( in(X1,X0)
        | ~ ordinal(X1) )
   => ! [X1] :
        ( in(X1,sK0)
        | ~ ordinal(X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f44,plain,
    ? [X0] :
    ! [X1] :
      ( in(X1,X0)
      | ~ ordinal(X1) ),
    inference(ennf_transformation,[],[f31]) ).

fof(f31,negated_conjecture,
    ~ ! [X0] :
        ~ ! [X1] :
            ( ordinal(X1)
           => in(X1,X0) ),
    inference(negated_conjecture,[],[f30]) ).

fof(f30,conjecture,
    ! [X0] :
      ~ ! [X1] :
          ( ordinal(X1)
         => in(X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_ordinal1) ).

fof(f249,plain,
    ! [X0] : ~ in(sK1(sK3(X0)),X0),
    inference(subsumption_resolution,[],[f248,f196]) ).

fof(f248,plain,
    ! [X0] :
      ( ~ ordinal(sK1(sK3(X0)))
      | ~ in(sK1(sK3(X0)),X0) ),
    inference(duplicate_literal_removal,[],[f246]) ).

fof(f246,plain,
    ! [X0] :
      ( ~ ordinal(sK1(sK3(X0)))
      | ~ in(sK1(sK3(X0)),X0)
      | ~ ordinal(sK1(sK3(X0))) ),
    inference(resolution,[],[f126,f122]) ).

fof(f122,plain,
    ! [X0] :
      ( ~ in(sK1(X0),X0)
      | ~ ordinal(sK1(X0)) ),
    inference(cnf_transformation,[],[f65]) ).

fof(f126,plain,
    ! [X2,X0] :
      ( in(X2,sK3(X0))
      | ~ ordinal(X2)
      | ~ in(X2,X0) ),
    inference(cnf_transformation,[],[f71]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10  % Problem    : NUM405+1 : TPTP v8.1.2. Released v3.2.0.
% 0.02/0.11  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.32  % Computer : n003.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit   : 300
% 0.11/0.32  % WCLimit    : 300
% 0.11/0.32  % DateTime   : Mon Apr 29 23:43:33 EDT 2024
% 0.11/0.32  % CPUTime    : 
% 0.11/0.32  % (29320)Running in auto input_syntax mode. Trying TPTP
% 0.11/0.33  % (29323)WARNING: value z3 for option sas not known
% 0.11/0.34  % (29324)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.11/0.34  % (29321)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.11/0.34  % (29325)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)
% 0.11/0.34  % (29322)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.11/0.34  % (29323)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)
% 0.11/0.34  % (29327)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)
% 0.11/0.34  % (29326)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)
% 0.11/0.34  TRYING [1]
% 0.11/0.34  TRYING [2]
% 0.11/0.34  TRYING [3]
% 0.11/0.34  TRYING [1]
% 0.11/0.34  TRYING [4]
% 0.11/0.34  TRYING [2]
% 0.11/0.34  TRYING [5]
% 0.11/0.34  TRYING [1]
% 0.11/0.34  TRYING [2]
% 0.11/0.34  % (29323)First to succeed.
% 0.11/0.34  TRYING [3]
% 0.11/0.34  TRYING [4]
% 0.11/0.34  TRYING [3]
% 0.11/0.34  % (29323)Refutation found. Thanks to Tanya!
% 0.11/0.34  % SZS status Theorem for theBenchmark
% 0.11/0.34  % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.34  % (29323)------------------------------
% 0.11/0.34  % (29323)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.11/0.34  % (29323)Termination reason: Refutation
% 0.11/0.34  
% 0.11/0.34  % (29323)Memory used [KB]: 869
% 0.11/0.34  % (29323)Time elapsed: 0.007 s
% 0.11/0.34  % (29323)Instructions burned: 8 (million)
% 0.11/0.34  % (29323)------------------------------
% 0.11/0.34  % (29323)------------------------------
% 0.11/0.34  % (29320)Success in time 0.022 s
%------------------------------------------------------------------------------