TSTP Solution File: SET962+1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SET962+1 : TPTP v8.1.0. Bugfixed v4.0.0.
% 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 : n020.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 18:22:52 EDT 2022

% Result   : Theorem 0.20s 0.51s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   62 (   3 unt;   0 def)
%            Number of atoms       :  182 (  35 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  208 (  88   ~;  87   |;  17   &)
%                                         (   8 <=>;   7  =>;   0  <=;   1 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   5 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   85 (  76   !;   9   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f121,plain,
    $false,
    inference(avatar_sat_refutation,[],[f57,f70,f81,f108,f112,f120]) ).

fof(f120,plain,
    ( ~ spl5_1
    | ~ spl5_3 ),
    inference(avatar_contradiction_clause,[],[f119]) ).

fof(f119,plain,
    ( $false
    | ~ spl5_1
    | ~ spl5_3 ),
    inference(subsumption_resolution,[],[f117,f31]) ).

fof(f31,plain,
    sK0 != sK1,
    inference(cnf_transformation,[],[f20]) ).

fof(f20,plain,
    ( cartesian_product2(sK1,sK1) = cartesian_product2(sK0,sK0)
    & sK0 != sK1 ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f18,f19]) ).

fof(f19,plain,
    ( ? [X0,X1] :
        ( cartesian_product2(X0,X0) = cartesian_product2(X1,X1)
        & X0 != X1 )
   => ( cartesian_product2(sK1,sK1) = cartesian_product2(sK0,sK0)
      & sK0 != sK1 ) ),
    introduced(choice_axiom,[]) ).

fof(f18,plain,
    ? [X0,X1] :
      ( cartesian_product2(X0,X0) = cartesian_product2(X1,X1)
      & X0 != X1 ),
    inference(rectify,[],[f17]) ).

fof(f17,plain,
    ? [X1,X0] :
      ( cartesian_product2(X0,X0) = cartesian_product2(X1,X1)
      & X0 != X1 ),
    inference(ennf_transformation,[],[f11]) ).

fof(f11,plain,
    ~ ! [X1,X0] :
        ( cartesian_product2(X0,X0) = cartesian_product2(X1,X1)
       => X0 = X1 ),
    inference(rectify,[],[f9]) ).

fof(f9,negated_conjecture,
    ~ ! [X1,X0] :
        ( cartesian_product2(X0,X0) = cartesian_product2(X1,X1)
       => X0 = X1 ),
    inference(negated_conjecture,[],[f8]) ).

fof(f8,conjecture,
    ! [X1,X0] :
      ( cartesian_product2(X0,X0) = cartesian_product2(X1,X1)
     => X0 = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t115_zfmisc_1) ).

fof(f117,plain,
    ( sK0 = sK1
    | ~ spl5_1
    | ~ spl5_3 ),
    inference(resolution,[],[f111,f65]) ).

fof(f65,plain,
    ( ! [X7] : ~ in(X7,sK1)
    | ~ spl5_3 ),
    inference(avatar_component_clause,[],[f64]) ).

fof(f64,plain,
    ( spl5_3
  <=> ! [X7] : ~ in(X7,sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_3])]) ).

fof(f111,plain,
    ( ! [X1] :
        ( in(sK2(X1,sK0),X1)
        | sK0 = X1 )
    | ~ spl5_1 ),
    inference(resolution,[],[f52,f37]) ).

fof(f37,plain,
    ! [X0,X1] :
      ( in(sK2(X0,X1),X1)
      | X0 = X1
      | in(sK2(X0,X1),X0) ),
    inference(cnf_transformation,[],[f26]) ).

fof(f26,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ( ( ~ in(sK2(X0,X1),X0)
          | ~ in(sK2(X0,X1),X1) )
        & ( in(sK2(X0,X1),X0)
          | in(sK2(X0,X1),X1) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f24,f25]) ).

fof(f25,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( ~ in(X2,X0)
            | ~ in(X2,X1) )
          & ( in(X2,X0)
            | in(X2,X1) ) )
     => ( ( ~ in(sK2(X0,X1),X0)
          | ~ in(sK2(X0,X1),X1) )
        & ( in(sK2(X0,X1),X0)
          | in(sK2(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f24,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ? [X2] :
          ( ( ~ in(X2,X0)
            | ~ in(X2,X1) )
          & ( in(X2,X0)
            | in(X2,X1) ) ) ),
    inference(nnf_transformation,[],[f16]) ).

fof(f16,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ? [X2] :
          ( in(X2,X1)
        <~> in(X2,X0) ) ),
    inference(ennf_transformation,[],[f13]) ).

fof(f13,plain,
    ! [X1,X0] :
      ( ! [X2] :
          ( in(X2,X0)
        <=> in(X2,X1) )
     => X0 = X1 ),
    inference(rectify,[],[f10]) ).

fof(f10,axiom,
    ! [X1,X0] :
      ( ! [X2] :
          ( in(X2,X0)
        <=> in(X2,X1) )
     => X0 = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).

fof(f52,plain,
    ( ! [X9] : ~ in(X9,sK0)
    | ~ spl5_1 ),
    inference(avatar_component_clause,[],[f51]) ).

fof(f51,plain,
    ( spl5_1
  <=> ! [X9] : ~ in(X9,sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_1])]) ).

fof(f112,plain,
    ( ~ spl5_1
    | ~ spl5_4 ),
    inference(avatar_contradiction_clause,[],[f109]) ).

fof(f109,plain,
    ( $false
    | ~ spl5_1
    | ~ spl5_4 ),
    inference(resolution,[],[f52,f94]) ).

fof(f94,plain,
    ( in(sK2(sK0,sK1),sK0)
    | ~ spl5_4 ),
    inference(subsumption_resolution,[],[f93,f31]) ).

fof(f93,plain,
    ( in(sK2(sK0,sK1),sK0)
    | sK0 = sK1
    | ~ spl5_4 ),
    inference(factoring,[],[f82]) ).

fof(f82,plain,
    ( ! [X0] :
        ( in(sK2(X0,sK1),sK0)
        | sK1 = X0
        | in(sK2(X0,sK1),X0) )
    | ~ spl5_4 ),
    inference(resolution,[],[f68,f37]) ).

fof(f68,plain,
    ( ! [X6] :
        ( ~ in(X6,sK1)
        | in(X6,sK0) )
    | ~ spl5_4 ),
    inference(avatar_component_clause,[],[f67]) ).

fof(f67,plain,
    ( spl5_4
  <=> ! [X6] :
        ( ~ in(X6,sK1)
        | in(X6,sK0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_4])]) ).

fof(f108,plain,
    ( ~ spl5_2
    | ~ spl5_4 ),
    inference(avatar_contradiction_clause,[],[f107]) ).

fof(f107,plain,
    ( $false
    | ~ spl5_2
    | ~ spl5_4 ),
    inference(subsumption_resolution,[],[f106,f86]) ).

fof(f86,plain,
    ( in(sK2(sK1,sK0),sK1)
    | ~ spl5_2 ),
    inference(subsumption_resolution,[],[f85,f31]) ).

fof(f85,plain,
    ( sK0 = sK1
    | in(sK2(sK1,sK0),sK1)
    | ~ spl5_2 ),
    inference(factoring,[],[f72]) ).

fof(f72,plain,
    ( ! [X2] :
        ( in(sK2(X2,sK0),sK1)
        | in(sK2(X2,sK0),X2)
        | sK0 = X2 )
    | ~ spl5_2 ),
    inference(resolution,[],[f37,f55]) ).

fof(f55,plain,
    ( ! [X8] :
        ( ~ in(X8,sK0)
        | in(X8,sK1) )
    | ~ spl5_2 ),
    inference(avatar_component_clause,[],[f54]) ).

fof(f54,plain,
    ( spl5_2
  <=> ! [X8] :
        ( ~ in(X8,sK0)
        | in(X8,sK1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_2])]) ).

fof(f106,plain,
    ( ~ in(sK2(sK1,sK0),sK1)
    | ~ spl5_2
    | ~ spl5_4 ),
    inference(subsumption_resolution,[],[f100,f31]) ).

fof(f100,plain,
    ( sK0 = sK1
    | ~ in(sK2(sK1,sK0),sK1)
    | ~ spl5_2
    | ~ spl5_4 ),
    inference(resolution,[],[f38,f87]) ).

fof(f87,plain,
    ( in(sK2(sK1,sK0),sK0)
    | ~ spl5_2
    | ~ spl5_4 ),
    inference(resolution,[],[f86,f68]) ).

fof(f38,plain,
    ! [X0,X1] :
      ( ~ in(sK2(X0,X1),X1)
      | ~ in(sK2(X0,X1),X0)
      | X0 = X1 ),
    inference(cnf_transformation,[],[f26]) ).

fof(f81,plain,
    ( ~ spl5_2
    | ~ spl5_3 ),
    inference(avatar_contradiction_clause,[],[f80]) ).

fof(f80,plain,
    ( $false
    | ~ spl5_2
    | ~ spl5_3 ),
    inference(subsumption_resolution,[],[f79,f31]) ).

fof(f79,plain,
    ( sK0 = sK1
    | ~ spl5_2
    | ~ spl5_3 ),
    inference(subsumption_resolution,[],[f77,f65]) ).

fof(f77,plain,
    ( in(sK2(sK0,sK1),sK1)
    | sK0 = sK1
    | ~ spl5_2
    | ~ spl5_3 ),
    inference(resolution,[],[f73,f55]) ).

fof(f73,plain,
    ( ! [X3] :
        ( in(sK2(X3,sK1),X3)
        | sK1 = X3 )
    | ~ spl5_3 ),
    inference(resolution,[],[f37,f65]) ).

fof(f70,plain,
    ( spl5_4
    | spl5_3 ),
    inference(avatar_split_clause,[],[f60,f64,f67]) ).

fof(f60,plain,
    ! [X4,X5] :
      ( ~ in(X4,sK1)
      | ~ in(X5,sK1)
      | in(X5,sK0) ),
    inference(resolution,[],[f49,f35]) ).

fof(f35,plain,
    ! [X2,X3,X0,X1] :
      ( ~ in(ordered_pair(X1,X3),cartesian_product2(X0,X2))
      | in(X3,X2) ),
    inference(cnf_transformation,[],[f23]) ).

fof(f23,plain,
    ! [X0,X1,X2,X3] :
      ( ( in(ordered_pair(X1,X3),cartesian_product2(X0,X2))
        | ~ in(X3,X2)
        | ~ in(X1,X0) )
      & ( ( in(X3,X2)
          & in(X1,X0) )
        | ~ in(ordered_pair(X1,X3),cartesian_product2(X0,X2)) ) ),
    inference(rectify,[],[f22]) ).

fof(f22,plain,
    ! [X0,X3,X2,X1] :
      ( ( in(ordered_pair(X3,X1),cartesian_product2(X0,X2))
        | ~ in(X1,X2)
        | ~ in(X3,X0) )
      & ( ( in(X1,X2)
          & in(X3,X0) )
        | ~ in(ordered_pair(X3,X1),cartesian_product2(X0,X2)) ) ),
    inference(flattening,[],[f21]) ).

fof(f21,plain,
    ! [X0,X3,X2,X1] :
      ( ( in(ordered_pair(X3,X1),cartesian_product2(X0,X2))
        | ~ in(X1,X2)
        | ~ in(X3,X0) )
      & ( ( in(X1,X2)
          & in(X3,X0) )
        | ~ in(ordered_pair(X3,X1),cartesian_product2(X0,X2)) ) ),
    inference(nnf_transformation,[],[f12]) ).

fof(f12,plain,
    ! [X0,X3,X2,X1] :
      ( in(ordered_pair(X3,X1),cartesian_product2(X0,X2))
    <=> ( in(X1,X2)
        & in(X3,X0) ) ),
    inference(rectify,[],[f5]) ).

fof(f5,axiom,
    ! [X2,X1,X3,X0] :
      ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
    <=> ( in(X0,X2)
        & in(X1,X3) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l55_zfmisc_1) ).

fof(f49,plain,
    ! [X0,X1] :
      ( in(ordered_pair(X0,X1),cartesian_product2(sK0,sK0))
      | ~ in(X0,sK1)
      | ~ in(X1,sK1) ),
    inference(superposition,[],[f36,f32]) ).

fof(f32,plain,
    cartesian_product2(sK1,sK1) = cartesian_product2(sK0,sK0),
    inference(cnf_transformation,[],[f20]) ).

fof(f36,plain,
    ! [X2,X3,X0,X1] :
      ( in(ordered_pair(X1,X3),cartesian_product2(X0,X2))
      | ~ in(X3,X2)
      | ~ in(X1,X0) ),
    inference(cnf_transformation,[],[f23]) ).

fof(f57,plain,
    ( spl5_2
    | spl5_1 ),
    inference(avatar_split_clause,[],[f47,f51,f54]) ).

fof(f47,plain,
    ! [X10,X11] :
      ( ~ in(X10,sK0)
      | ~ in(X11,sK0)
      | in(X11,sK1) ),
    inference(resolution,[],[f36,f42]) ).

fof(f42,plain,
    ! [X0,X1] :
      ( ~ in(ordered_pair(X0,X1),cartesian_product2(sK0,sK0))
      | in(X0,sK1) ),
    inference(superposition,[],[f34,f32]) ).

fof(f34,plain,
    ! [X2,X3,X0,X1] :
      ( ~ in(ordered_pair(X1,X3),cartesian_product2(X0,X2))
      | in(X1,X0) ),
    inference(cnf_transformation,[],[f23]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem    : SET962+1 : TPTP v8.1.0. Bugfixed v4.0.0.
% 0.04/0.14  % 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 : n020.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 14:34:30 EDT 2022
% 0.14/0.35  % CPUTime    : 
% 0.20/0.49  % (27103)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)
% 0.20/0.50  % (27087)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  % (27087)First to succeed.
% 0.20/0.51  % (27087)Refutation found. Thanks to Tanya!
% 0.20/0.51  % SZS status Theorem for theBenchmark
% 0.20/0.51  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.51  % (27087)------------------------------
% 0.20/0.51  % (27087)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.51  % (27087)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.51  % (27087)Termination reason: Refutation
% 0.20/0.51  
% 0.20/0.51  % (27087)Memory used [KB]: 6012
% 0.20/0.51  % (27087)Time elapsed: 0.041 s
% 0.20/0.51  % (27087)Instructions burned: 4 (million)
% 0.20/0.51  % (27087)------------------------------
% 0.20/0.51  % (27087)------------------------------
% 0.20/0.51  % (27080)Success in time 0.149 s
%------------------------------------------------------------------------------