TSTP Solution File: SEU143+1 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SEU143+1 : 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_sat --cores 0 -t %d %s

% Computer : n012.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 18:32:07 EDT 2022

% Result   : Theorem 0.19s 0.49s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   23 (   9 unt;   0 def)
%            Number of atoms       :   75 (  42 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :   87 (  35   ~;  32   |;  14   &)
%                                         (   3 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   42 (  34   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f45,plain,
    $false,
    inference(resolution,[],[f44,f40]) ).

fof(f40,plain,
    ! [X2] : ~ in(X2,empty_set),
    inference(equality_resolution,[],[f32]) ).

fof(f32,plain,
    ! [X2,X0] :
      ( ~ in(X2,X0)
      | empty_set != X0 ),
    inference(cnf_transformation,[],[f22]) ).

fof(f22,plain,
    ! [X0] :
      ( ( empty_set = X0
        | in(sK2(X0),X0) )
      & ( ! [X2] : ~ in(X2,X0)
        | empty_set != X0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f20,f21]) ).

fof(f21,plain,
    ! [X0] :
      ( ? [X1] : in(X1,X0)
     => in(sK2(X0),X0) ),
    introduced(choice_axiom,[]) ).

fof(f20,plain,
    ! [X0] :
      ( ( empty_set = X0
        | ? [X1] : in(X1,X0) )
      & ( ! [X2] : ~ in(X2,X0)
        | empty_set != X0 ) ),
    inference(rectify,[],[f19]) ).

fof(f19,plain,
    ! [X0] :
      ( ( empty_set = X0
        | ? [X1] : in(X1,X0) )
      & ( ! [X1] : ~ in(X1,X0)
        | empty_set != X0 ) ),
    inference(nnf_transformation,[],[f3]) ).

fof(f3,axiom,
    ! [X0] :
      ( empty_set = X0
    <=> ! [X1] : ~ in(X1,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).

fof(f44,plain,
    in(sK0,empty_set),
    inference(superposition,[],[f43,f29]) ).

fof(f29,plain,
    empty_set = singleton(sK0),
    inference(cnf_transformation,[],[f15]) ).

fof(f15,plain,
    empty_set = singleton(sK0),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f12,f14]) ).

fof(f14,plain,
    ( ? [X0] : singleton(X0) = empty_set
   => empty_set = singleton(sK0) ),
    introduced(choice_axiom,[]) ).

fof(f12,plain,
    ? [X0] : singleton(X0) = empty_set,
    inference(ennf_transformation,[],[f8]) ).

fof(f8,negated_conjecture,
    ~ ! [X0] : singleton(X0) != empty_set,
    inference(negated_conjecture,[],[f7]) ).

fof(f7,conjecture,
    ! [X0] : singleton(X0) != empty_set,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1_zfmisc_1) ).

fof(f43,plain,
    ! [X2] : in(X2,singleton(X2)),
    inference(equality_resolution,[],[f42]) ).

fof(f42,plain,
    ! [X2,X1] :
      ( in(X2,X1)
      | singleton(X2) != X1 ),
    inference(equality_resolution,[],[f37]) ).

fof(f37,plain,
    ! [X2,X0,X1] :
      ( in(X2,X1)
      | X0 != X2
      | singleton(X0) != X1 ),
    inference(cnf_transformation,[],[f26]) ).

fof(f26,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( ( X0 = X2
              | ~ in(X2,X1) )
            & ( in(X2,X1)
              | X0 != X2 ) )
        | singleton(X0) != X1 )
      & ( singleton(X0) = X1
        | ( ( ~ in(sK3(X0,X1),X1)
            | sK3(X0,X1) != X0 )
          & ( in(sK3(X0,X1),X1)
            | sK3(X0,X1) = X0 ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f24,f25]) ).

fof(f25,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( ( ~ in(X3,X1)
            | X0 != X3 )
          & ( in(X3,X1)
            | X0 = X3 ) )
     => ( ( ~ in(sK3(X0,X1),X1)
          | sK3(X0,X1) != X0 )
        & ( in(sK3(X0,X1),X1)
          | sK3(X0,X1) = X0 ) ) ),
    introduced(choice_axiom,[]) ).

fof(f24,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( ( X0 = X2
              | ~ in(X2,X1) )
            & ( in(X2,X1)
              | X0 != X2 ) )
        | singleton(X0) != X1 )
      & ( singleton(X0) = X1
        | ? [X3] :
            ( ( ~ in(X3,X1)
              | X0 != X3 )
            & ( in(X3,X1)
              | X0 = X3 ) ) ) ),
    inference(rectify,[],[f23]) ).

fof(f23,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( ( X0 = X2
              | ~ in(X2,X1) )
            & ( in(X2,X1)
              | X0 != X2 ) )
        | singleton(X0) != X1 )
      & ( singleton(X0) = X1
        | ? [X2] :
            ( ( ~ in(X2,X1)
              | X0 != X2 )
            & ( in(X2,X1)
              | X0 = X2 ) ) ) ),
    inference(nnf_transformation,[],[f2]) ).

fof(f2,axiom,
    ! [X0,X1] :
      ( ! [X2] :
          ( X0 = X2
        <=> in(X2,X1) )
    <=> singleton(X0) = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SEU143+1 : 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_sat --cores 0 -t %d %s
% 0.13/0.34  % Computer : n012.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Tue Aug 30 14:43:05 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.19/0.48  % (16430)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/50Mi)
% 0.19/0.48  % (16442)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/498Mi)
% 0.19/0.48  % (16430)First to succeed.
% 0.19/0.48  % (16421)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/37Mi)
% 0.19/0.49  % (16430)Refutation found. Thanks to Tanya!
% 0.19/0.49  % SZS status Theorem for theBenchmark
% 0.19/0.49  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.49  % (16430)------------------------------
% 0.19/0.49  % (16430)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.49  % (16430)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.49  % (16430)Termination reason: Refutation
% 0.19/0.49  
% 0.19/0.49  % (16430)Memory used [KB]: 5373
% 0.19/0.49  % (16430)Time elapsed: 0.091 s
% 0.19/0.49  % (16430)Instructions burned: 1 (million)
% 0.19/0.49  % (16430)------------------------------
% 0.19/0.49  % (16430)------------------------------
% 0.19/0.49  % (16415)Success in time 0.135 s
%------------------------------------------------------------------------------