TSTP Solution File: SEU158+2 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SEU158+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s

% Computer : n026.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 Aug 31 18:26:58 EDT 2022

% Result   : Theorem 0.19s 0.55s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   34 (   5 unt;   0 def)
%            Number of atoms       :  128 (  29 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  149 (  55   ~;  52   |;  25   &)
%                                         (  11 <=>;   5  =>;   0  <=;   1 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   72 (  58   !;  14   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f452,plain,
    $false,
    inference(subsumption_resolution,[],[f438,f431]) ).

fof(f431,plain,
    subset(singleton(sK0),sK1),
    inference(subsumption_resolution,[],[f271,f430]) ).

fof(f430,plain,
    ~ in(sK0,sK1),
    inference(subsumption_resolution,[],[f272,f332]) ).

fof(f332,plain,
    ! [X0,X1] :
      ( subset(singleton(X0),X1)
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f214]) ).

fof(f214,plain,
    ! [X0,X1] :
      ( ( subset(singleton(X0),X1)
        | ~ in(X0,X1) )
      & ( in(X0,X1)
        | ~ subset(singleton(X0),X1) ) ),
    inference(nnf_transformation,[],[f41]) ).

fof(f41,axiom,
    ! [X0,X1] :
      ( subset(singleton(X0),X1)
    <=> in(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l2_zfmisc_1) ).

fof(f272,plain,
    ( ~ in(sK0,sK1)
    | ~ subset(singleton(sK0),sK1) ),
    inference(cnf_transformation,[],[f175]) ).

fof(f175,plain,
    ( ( ~ subset(singleton(sK0),sK1)
      | ~ in(sK0,sK1) )
    & ( subset(singleton(sK0),sK1)
      | in(sK0,sK1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f173,f174]) ).

fof(f174,plain,
    ( ? [X0,X1] :
        ( ( ~ subset(singleton(X0),X1)
          | ~ in(X0,X1) )
        & ( subset(singleton(X0),X1)
          | in(X0,X1) ) )
   => ( ( ~ subset(singleton(sK0),sK1)
        | ~ in(sK0,sK1) )
      & ( subset(singleton(sK0),sK1)
        | in(sK0,sK1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f173,plain,
    ? [X0,X1] :
      ( ( ~ subset(singleton(X0),X1)
        | ~ in(X0,X1) )
      & ( subset(singleton(X0),X1)
        | in(X0,X1) ) ),
    inference(rectify,[],[f172]) ).

fof(f172,plain,
    ? [X1,X0] :
      ( ( ~ subset(singleton(X1),X0)
        | ~ in(X1,X0) )
      & ( subset(singleton(X1),X0)
        | in(X1,X0) ) ),
    inference(nnf_transformation,[],[f140]) ).

fof(f140,plain,
    ? [X1,X0] :
      ( in(X1,X0)
    <~> subset(singleton(X1),X0) ),
    inference(ennf_transformation,[],[f91]) ).

fof(f91,plain,
    ~ ! [X1,X0] :
        ( subset(singleton(X1),X0)
      <=> in(X1,X0) ),
    inference(rectify,[],[f68]) ).

fof(f68,negated_conjecture,
    ~ ! [X1,X0] :
        ( in(X0,X1)
      <=> subset(singleton(X0),X1) ),
    inference(negated_conjecture,[],[f67]) ).

fof(f67,conjecture,
    ! [X1,X0] :
      ( in(X0,X1)
    <=> subset(singleton(X0),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_zfmisc_1) ).

fof(f271,plain,
    ( in(sK0,sK1)
    | subset(singleton(sK0),sK1) ),
    inference(cnf_transformation,[],[f175]) ).

fof(f438,plain,
    ~ subset(singleton(sK0),sK1),
    inference(unit_resulting_resolution,[],[f399,f430,f371]) ).

fof(f371,plain,
    ! [X2,X0,X1] :
      ( ~ subset(X0,X1)
      | ~ in(X2,X0)
      | in(X2,X1) ),
    inference(cnf_transformation,[],[f247]) ).

fof(f247,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( ~ in(X2,X0)
            | in(X2,X1) )
        | ~ subset(X0,X1) )
      & ( subset(X0,X1)
        | ( in(sK13(X0,X1),X0)
          & ~ in(sK13(X0,X1),X1) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f245,f246]) ).

fof(f246,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( in(X3,X0)
          & ~ in(X3,X1) )
     => ( in(sK13(X0,X1),X0)
        & ~ in(sK13(X0,X1),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f245,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( ~ in(X2,X0)
            | in(X2,X1) )
        | ~ subset(X0,X1) )
      & ( subset(X0,X1)
        | ? [X3] :
            ( in(X3,X0)
            & ~ in(X3,X1) ) ) ),
    inference(rectify,[],[f244]) ).

fof(f244,plain,
    ! [X1,X0] :
      ( ( ! [X2] :
            ( ~ in(X2,X1)
            | in(X2,X0) )
        | ~ subset(X1,X0) )
      & ( subset(X1,X0)
        | ? [X2] :
            ( in(X2,X1)
            & ~ in(X2,X0) ) ) ),
    inference(nnf_transformation,[],[f139]) ).

fof(f139,plain,
    ! [X1,X0] :
      ( ! [X2] :
          ( ~ in(X2,X1)
          | in(X2,X0) )
    <=> subset(X1,X0) ),
    inference(ennf_transformation,[],[f122]) ).

fof(f122,plain,
    ! [X0,X1] :
      ( subset(X1,X0)
    <=> ! [X2] :
          ( in(X2,X1)
         => in(X2,X0) ) ),
    inference(rectify,[],[f13]) ).

fof(f13,axiom,
    ! [X1,X0] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X0)
         => in(X2,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).

fof(f399,plain,
    ! [X3] : in(X3,singleton(X3)),
    inference(equality_resolution,[],[f398]) ).

fof(f398,plain,
    ! [X3,X1] :
      ( in(X3,X1)
      | singleton(X3) != X1 ),
    inference(equality_resolution,[],[f287]) ).

fof(f287,plain,
    ! [X3,X0,X1] :
      ( in(X3,X1)
      | X0 != X3
      | singleton(X0) != X1 ),
    inference(cnf_transformation,[],[f184]) ).

fof(f184,plain,
    ! [X0,X1] :
      ( ( singleton(X0) = X1
        | ( ( sK2(X0,X1) != X0
            | ~ in(sK2(X0,X1),X1) )
          & ( sK2(X0,X1) = X0
            | in(sK2(X0,X1),X1) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X1)
              | X0 != X3 )
            & ( X0 = X3
              | ~ in(X3,X1) ) )
        | singleton(X0) != X1 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f182,f183]) ).

fof(f183,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( X0 != X2
            | ~ in(X2,X1) )
          & ( X0 = X2
            | in(X2,X1) ) )
     => ( ( sK2(X0,X1) != X0
          | ~ in(sK2(X0,X1),X1) )
        & ( sK2(X0,X1) = X0
          | in(sK2(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f182,plain,
    ! [X0,X1] :
      ( ( singleton(X0) = X1
        | ? [X2] :
            ( ( X0 != X2
              | ~ in(X2,X1) )
            & ( X0 = X2
              | in(X2,X1) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X1)
              | X0 != X3 )
            & ( X0 = X3
              | ~ in(X3,X1) ) )
        | singleton(X0) != X1 ) ),
    inference(rectify,[],[f181]) ).

fof(f181,plain,
    ! [X1,X0] :
      ( ( singleton(X1) = X0
        | ? [X2] :
            ( ( X1 != X2
              | ~ in(X2,X0) )
            & ( X1 = X2
              | in(X2,X0) ) ) )
      & ( ! [X2] :
            ( ( in(X2,X0)
              | X1 != X2 )
            & ( X1 = X2
              | ~ in(X2,X0) ) )
        | singleton(X1) != X0 ) ),
    inference(nnf_transformation,[],[f117]) ).

fof(f117,plain,
    ! [X1,X0] :
      ( singleton(X1) = X0
    <=> ! [X2] :
          ( in(X2,X0)
        <=> X1 = X2 ) ),
    inference(rectify,[],[f7]) ).

fof(f7,axiom,
    ! [X1,X0] :
      ( ! [X2] :
          ( in(X2,X1)
        <=> X0 = X2 )
    <=> singleton(X0) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SEU158+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.12/0.34  % Computer : n026.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Tue Aug 30 14:57:06 EDT 2022
% 0.12/0.34  % CPUTime    : 
% 0.19/0.52  % (31278)lrs+10_5:1_br=off:fde=none:nwc=3.0:sd=1:sgt=10:sos=on:ss=axioms:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.53  % (31278)First to succeed.
% 0.19/0.55  % (31298)dis+1010_2:3_fs=off:fsr=off:nm=0:nwc=5.0:s2a=on:s2agt=32:i=82:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/82Mi)
% 0.19/0.55  % (31278)Refutation found. Thanks to Tanya!
% 0.19/0.55  % SZS status Theorem for theBenchmark
% 0.19/0.55  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.55  % (31278)------------------------------
% 0.19/0.55  % (31278)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.55  % (31278)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.55  % (31278)Termination reason: Refutation
% 0.19/0.55  
% 0.19/0.55  % (31278)Memory used [KB]: 6268
% 0.19/0.55  % (31278)Time elapsed: 0.122 s
% 0.19/0.55  % (31278)Instructions burned: 9 (million)
% 0.19/0.55  % (31278)------------------------------
% 0.19/0.55  % (31278)------------------------------
% 0.19/0.55  % (31274)Success in time 0.202 s
%------------------------------------------------------------------------------