TSTP Solution File: SET900+1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SET900+1 : TPTP v8.1.0. Released v3.2.0.
% 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 : n009.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 18:22:42 EDT 2022

% Result   : Theorem 0.20s 0.50s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   22 (   4 unt;   0 def)
%            Number of atoms       :   70 (  55 equ)
%            Maximal formula atoms :    8 (   3 avg)
%            Number of connectives :   90 (  42   ~;  23   |;  23   &)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   6 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   38 (  30   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f45,plain,
    $false,
    inference(subsumption_resolution,[],[f44,f28]) ).

fof(f28,plain,
    sK4 != singleton(sK3),
    inference(cnf_transformation,[],[f20]) ).

fof(f20,plain,
    ( empty_set != sK4
    & sK4 != singleton(sK3)
    & ! [X2] :
        ( sK3 = X2
        | ~ in(X2,sK4) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f18,f19]) ).

fof(f19,plain,
    ( ? [X0,X1] :
        ( empty_set != X1
        & singleton(X0) != X1
        & ! [X2] :
            ( X0 = X2
            | ~ in(X2,X1) ) )
   => ( empty_set != sK4
      & sK4 != singleton(sK3)
      & ! [X2] :
          ( sK3 = X2
          | ~ in(X2,sK4) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f18,plain,
    ? [X0,X1] :
      ( empty_set != X1
      & singleton(X0) != X1
      & ! [X2] :
          ( X0 = X2
          | ~ in(X2,X1) ) ),
    inference(rectify,[],[f10]) ).

fof(f10,plain,
    ? [X1,X0] :
      ( empty_set != X0
      & singleton(X1) != X0
      & ! [X2] :
          ( X1 = X2
          | ~ in(X2,X0) ) ),
    inference(ennf_transformation,[],[f6]) ).

fof(f6,negated_conjecture,
    ~ ! [X1,X0] :
        ~ ( singleton(X1) != X0
          & empty_set != X0
          & ! [X2] :
              ~ ( in(X2,X0)
                & X1 != X2 ) ),
    inference(negated_conjecture,[],[f5]) ).

fof(f5,conjecture,
    ! [X1,X0] :
      ~ ( singleton(X1) != X0
        & empty_set != X0
        & ! [X2] :
            ~ ( in(X2,X0)
              & X1 != X2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_zfmisc_1) ).

fof(f44,plain,
    sK4 = singleton(sK3),
    inference(equality_resolution,[],[f39]) ).

fof(f39,plain,
    ! [X1] :
      ( sK3 != X1
      | singleton(X1) = sK4 ),
    inference(subsumption_resolution,[],[f36,f29]) ).

fof(f29,plain,
    empty_set != sK4,
    inference(cnf_transformation,[],[f20]) ).

fof(f36,plain,
    ! [X1] :
      ( sK3 != X1
      | empty_set = sK4
      | singleton(X1) = sK4 ),
    inference(duplicate_literal_removal,[],[f34]) ).

fof(f34,plain,
    ! [X1] :
      ( singleton(X1) = sK4
      | singleton(X1) = sK4
      | empty_set = sK4
      | sK3 != X1 ),
    inference(superposition,[],[f24,f31]) ).

fof(f31,plain,
    ! [X0] :
      ( sK1(sK4,X0) = sK3
      | singleton(X0) = sK4 ),
    inference(subsumption_resolution,[],[f30,f29]) ).

fof(f30,plain,
    ! [X0] :
      ( empty_set = sK4
      | singleton(X0) = sK4
      | sK1(sK4,X0) = sK3 ),
    inference(resolution,[],[f27,f25]) ).

fof(f25,plain,
    ! [X0,X1] :
      ( in(sK1(X0,X1),X0)
      | empty_set = X0
      | singleton(X1) = X0 ),
    inference(cnf_transformation,[],[f15]) ).

fof(f15,plain,
    ! [X0,X1] :
      ( singleton(X1) = X0
      | empty_set = X0
      | ( in(sK1(X0,X1),X0)
        & sK1(X0,X1) != X1 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f9,f14]) ).

fof(f14,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( in(X2,X0)
          & X1 != X2 )
     => ( in(sK1(X0,X1),X0)
        & sK1(X0,X1) != X1 ) ),
    introduced(choice_axiom,[]) ).

fof(f9,plain,
    ! [X0,X1] :
      ( singleton(X1) = X0
      | empty_set = X0
      | ? [X2] :
          ( in(X2,X0)
          & X1 != X2 ) ),
    inference(ennf_transformation,[],[f7]) ).

fof(f7,axiom,
    ! [X1,X0] :
      ~ ( ! [X2] :
            ~ ( in(X2,X0)
              & X1 != X2 )
        & empty_set != X0
        & singleton(X1) != X0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l45_zfmisc_1) ).

fof(f27,plain,
    ! [X2] :
      ( ~ in(X2,sK4)
      | sK3 = X2 ),
    inference(cnf_transformation,[],[f20]) ).

fof(f24,plain,
    ! [X0,X1] :
      ( sK1(X0,X1) != X1
      | singleton(X1) = X0
      | empty_set = X0 ),
    inference(cnf_transformation,[],[f15]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem    : SET900+1 : TPTP v8.1.0. Released v3.2.0.
% 0.08/0.14  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.14/0.35  % Computer : n009.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Tue Aug 30 14:26:05 EDT 2022
% 0.14/0.35  % CPUTime    : 
% 0.20/0.48  % (21904)dis+21_1:1_av=off:sos=on:sp=frequency:ss=included:to=lpo:i=15:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.20/0.50  % (21905)dis+1010_1:50_awrs=decay:awrsf=128:nwc=10.0:s2pl=no:sp=frequency:ss=axioms:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.20/0.50  % (21904)First to succeed.
% 0.20/0.50  % (21905)Also succeeded, but the first one will report.
% 0.20/0.50  % (21904)Refutation found. Thanks to Tanya!
% 0.20/0.50  % SZS status Theorem for theBenchmark
% 0.20/0.50  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.50  % (21904)------------------------------
% 0.20/0.50  % (21904)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.50  % (21904)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.50  % (21904)Termination reason: Refutation
% 0.20/0.50  
% 0.20/0.50  % (21904)Memory used [KB]: 1407
% 0.20/0.50  % (21904)Time elapsed: 0.103 s
% 0.20/0.50  % (21904)Instructions burned: 2 (million)
% 0.20/0.50  % (21904)------------------------------
% 0.20/0.50  % (21904)------------------------------
% 0.20/0.50  % (21898)Success in time 0.147 s
%------------------------------------------------------------------------------