TSTP Solution File: SET947+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SET947+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 : 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 : Tue Apr 30 15:14:04 EDT 2024

% Result   : Theorem 0.14s 0.37s
% Output   : Refutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   29 (  10 unt;   0 def)
%            Number of atoms       :   96 (   8 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  113 (  46   ~;  39   |;  19   &)
%                                         (   4 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   1 con; 0-2 aty)
%            Number of variables   :   56 (  48   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f78,plain,
    $false,
    inference(resolution,[],[f77,f29]) ).

fof(f29,plain,
    ~ subset(sK0,powerset(union(sK0))),
    inference(cnf_transformation,[],[f16]) ).

fof(f16,plain,
    ~ subset(sK0,powerset(union(sK0))),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f11,f15]) ).

fof(f15,plain,
    ( ? [X0] : ~ subset(X0,powerset(union(X0)))
   => ~ subset(sK0,powerset(union(sK0))) ),
    introduced(choice_axiom,[]) ).

fof(f11,plain,
    ? [X0] : ~ subset(X0,powerset(union(X0))),
    inference(ennf_transformation,[],[f9]) ).

fof(f9,negated_conjecture,
    ~ ! [X0] : subset(X0,powerset(union(X0))),
    inference(negated_conjecture,[],[f8]) ).

fof(f8,conjecture,
    ! [X0] : subset(X0,powerset(union(X0))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t100_zfmisc_1) ).

fof(f77,plain,
    subset(sK0,powerset(union(sK0))),
    inference(resolution,[],[f74,f34]) ).

fof(f34,plain,
    ! [X0,X1] :
      ( in(sK1(X0,X1),X0)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f20]) ).

fof(f20,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ( ~ in(sK1(X0,X1),X1)
          & in(sK1(X0,X1),X0) ) )
      & ( ! [X3] :
            ( in(X3,X1)
            | ~ in(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f18,f19]) ).

fof(f19,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ in(X2,X1)
          & in(X2,X0) )
     => ( ~ in(sK1(X0,X1),X1)
        & in(sK1(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f18,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ in(X2,X1)
            & in(X2,X0) ) )
      & ( ! [X3] :
            ( in(X3,X1)
            | ~ in(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(rectify,[],[f17]) ).

fof(f17,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ in(X2,X1)
            & in(X2,X0) ) )
      & ( ! [X2] :
            ( in(X2,X1)
            | ~ in(X2,X0) )
        | ~ subset(X0,X1) ) ),
    inference(nnf_transformation,[],[f14]) ).

fof(f14,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X1)
          | ~ in(X2,X0) ) ),
    inference(ennf_transformation,[],[f3]) ).

fof(f3,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X0)
         => in(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).

fof(f74,plain,
    ~ in(sK1(sK0,powerset(union(sK0))),sK0),
    inference(resolution,[],[f73,f32]) ).

fof(f32,plain,
    ! [X0,X1] :
      ( subset(X0,union(X1))
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f13]) ).

fof(f13,plain,
    ! [X0,X1] :
      ( subset(X0,union(X1))
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X0,X1] :
      ( in(X0,X1)
     => subset(X0,union(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l50_zfmisc_1) ).

fof(f73,plain,
    ~ subset(sK1(sK0,powerset(union(sK0))),union(sK0)),
    inference(resolution,[],[f67,f42]) ).

fof(f42,plain,
    ! [X3,X0] :
      ( in(X3,powerset(X0))
      | ~ subset(X3,X0) ),
    inference(equality_resolution,[],[f37]) ).

fof(f37,plain,
    ! [X3,X0,X1] :
      ( in(X3,X1)
      | ~ subset(X3,X0)
      | powerset(X0) != X1 ),
    inference(cnf_transformation,[],[f24]) ).

fof(f24,plain,
    ! [X0,X1] :
      ( ( powerset(X0) = X1
        | ( ( ~ subset(sK2(X0,X1),X0)
            | ~ in(sK2(X0,X1),X1) )
          & ( subset(sK2(X0,X1),X0)
            | in(sK2(X0,X1),X1) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X1)
              | ~ subset(X3,X0) )
            & ( subset(X3,X0)
              | ~ in(X3,X1) ) )
        | powerset(X0) != X1 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f22,f23]) ).

fof(f23,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( ~ subset(X2,X0)
            | ~ in(X2,X1) )
          & ( subset(X2,X0)
            | in(X2,X1) ) )
     => ( ( ~ subset(sK2(X0,X1),X0)
          | ~ in(sK2(X0,X1),X1) )
        & ( subset(sK2(X0,X1),X0)
          | in(sK2(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f22,plain,
    ! [X0,X1] :
      ( ( powerset(X0) = X1
        | ? [X2] :
            ( ( ~ subset(X2,X0)
              | ~ in(X2,X1) )
            & ( subset(X2,X0)
              | in(X2,X1) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X1)
              | ~ subset(X3,X0) )
            & ( subset(X3,X0)
              | ~ in(X3,X1) ) )
        | powerset(X0) != X1 ) ),
    inference(rectify,[],[f21]) ).

fof(f21,plain,
    ! [X0,X1] :
      ( ( powerset(X0) = X1
        | ? [X2] :
            ( ( ~ subset(X2,X0)
              | ~ in(X2,X1) )
            & ( subset(X2,X0)
              | in(X2,X1) ) ) )
      & ( ! [X2] :
            ( ( in(X2,X1)
              | ~ subset(X2,X0) )
            & ( subset(X2,X0)
              | ~ in(X2,X1) ) )
        | powerset(X0) != X1 ) ),
    inference(nnf_transformation,[],[f2]) ).

fof(f2,axiom,
    ! [X0,X1] :
      ( powerset(X0) = X1
    <=> ! [X2] :
          ( in(X2,X1)
        <=> subset(X2,X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_zfmisc_1) ).

fof(f67,plain,
    ~ in(sK1(sK0,powerset(union(sK0))),powerset(union(sK0))),
    inference(resolution,[],[f35,f29]) ).

fof(f35,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ in(sK1(X0,X1),X1) ),
    inference(cnf_transformation,[],[f20]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SET947+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.34  % Computer : n006.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Tue Apr 30 01:29:20 EDT 2024
% 0.14/0.34  % CPUTime    : 
% 0.14/0.34  % (21147)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37  % (21153)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)
% 0.14/0.37  % (21151)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.37  % (21154)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)
% 0.14/0.37  % (21152)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)
% 0.14/0.37  % (21153)First to succeed.
% 0.14/0.37  TRYING [1]
% 0.14/0.37  TRYING [2]
% 0.14/0.37  % (21154)Also succeeded, but the first one will report.
% 0.14/0.37  TRYING [3]
% 0.14/0.37  % (21153)Refutation found. Thanks to Tanya!
% 0.14/0.37  % SZS status Theorem for theBenchmark
% 0.14/0.37  % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.37  % (21153)------------------------------
% 0.14/0.37  % (21153)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.14/0.37  % (21153)Termination reason: Refutation
% 0.14/0.37  
% 0.14/0.37  % (21153)Memory used [KB]: 762
% 0.14/0.37  % (21153)Time elapsed: 0.005 s
% 0.14/0.37  % (21153)Instructions burned: 5 (million)
% 0.14/0.37  % (21153)------------------------------
% 0.14/0.37  % (21153)------------------------------
% 0.14/0.37  % (21147)Success in time 0.03 s
%------------------------------------------------------------------------------