TSTP Solution File: SET975+1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SET975+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 : 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 : Wed Aug 31 18:22:55 EDT 2022

% Result   : Theorem 0.20s 0.50s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   49 (   3 unt;   0 def)
%            Number of atoms       :  178 (  52 equ)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :  208 (  79   ~;  82   |;  35   &)
%                                         (   9 <=>;   2  =>;   0  <=;   1 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   3 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   4 con; 0-2 aty)
%            Number of variables   :   92 (  69   !;  23   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f91,plain,
    $false,
    inference(avatar_sat_refutation,[],[f55,f57,f76,f90]) ).

fof(f90,plain,
    ( ~ spl5_1
    | spl5_2 ),
    inference(avatar_contradiction_clause,[],[f89]) ).

fof(f89,plain,
    ( $false
    | ~ spl5_1
    | spl5_2 ),
    inference(subsumption_resolution,[],[f80,f78]) ).

fof(f78,plain,
    ( ~ in(sK0,singleton(sK3))
    | spl5_2 ),
    inference(unit_resulting_resolution,[],[f53,f45]) ).

fof(f45,plain,
    ! [X2,X0] :
      ( ~ in(X2,singleton(X0))
      | X0 = X2 ),
    inference(equality_resolution,[],[f37]) ).

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

fof(f26,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( ( in(X2,X1)
              | X0 != X2 )
            & ( X0 = X2
              | ~ in(X2,X1) ) )
        | singleton(X0) != X1 )
      & ( singleton(X0) = X1
        | ( ( sK4(X0,X1) != X0
            | ~ in(sK4(X0,X1),X1) )
          & ( sK4(X0,X1) = X0
            | in(sK4(X0,X1),X1) ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f24,f25]) ).

fof(f25,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( ( X0 != X3
            | ~ in(X3,X1) )
          & ( X0 = X3
            | in(X3,X1) ) )
     => ( ( sK4(X0,X1) != X0
          | ~ in(sK4(X0,X1),X1) )
        & ( sK4(X0,X1) = X0
          | in(sK4(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

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

fof(f23,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( ( in(X2,X1)
              | X0 != X2 )
            & ( X0 = X2
              | ~ in(X2,X1) ) )
        | singleton(X0) != X1 )
      & ( singleton(X0) = X1
        | ? [X2] :
            ( ( X0 != X2
              | ~ in(X2,X1) )
            & ( X0 = X2
              | in(X2,X1) ) ) ) ),
    inference(nnf_transformation,[],[f3]) ).

fof(f3,axiom,
    ! [X0,X1] :
      ( ! [X2] :
          ( in(X2,X1)
        <=> X0 = X2 )
    <=> singleton(X0) = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).

fof(f53,plain,
    ( sK0 != sK3
    | spl5_2 ),
    inference(avatar_component_clause,[],[f52]) ).

fof(f52,plain,
    ( spl5_2
  <=> sK0 = sK3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_2])]) ).

fof(f80,plain,
    ( in(sK0,singleton(sK3))
    | ~ spl5_1 ),
    inference(unit_resulting_resolution,[],[f50,f40]) ).

fof(f40,plain,
    ! [X2,X3,X0,X1] :
      ( ~ in(ordered_pair(X2,X3),cartesian_product2(X1,X0))
      | in(X2,X1) ),
    inference(cnf_transformation,[],[f29]) ).

fof(f29,plain,
    ! [X0,X1,X2,X3] :
      ( ( in(ordered_pair(X2,X3),cartesian_product2(X1,X0))
        | ~ in(X3,X0)
        | ~ in(X2,X1) )
      & ( ( in(X3,X0)
          & in(X2,X1) )
        | ~ in(ordered_pair(X2,X3),cartesian_product2(X1,X0)) ) ),
    inference(rectify,[],[f28]) ).

fof(f28,plain,
    ! [X2,X3,X1,X0] :
      ( ( in(ordered_pair(X1,X0),cartesian_product2(X3,X2))
        | ~ in(X0,X2)
        | ~ in(X1,X3) )
      & ( ( in(X0,X2)
          & in(X1,X3) )
        | ~ in(ordered_pair(X1,X0),cartesian_product2(X3,X2)) ) ),
    inference(flattening,[],[f27]) ).

fof(f27,plain,
    ! [X2,X3,X1,X0] :
      ( ( in(ordered_pair(X1,X0),cartesian_product2(X3,X2))
        | ~ in(X0,X2)
        | ~ in(X1,X3) )
      & ( ( in(X0,X2)
          & in(X1,X3) )
        | ~ in(ordered_pair(X1,X0),cartesian_product2(X3,X2)) ) ),
    inference(nnf_transformation,[],[f12]) ).

fof(f12,plain,
    ! [X2,X3,X1,X0] :
      ( in(ordered_pair(X1,X0),cartesian_product2(X3,X2))
    <=> ( in(X0,X2)
        & in(X1,X3) ) ),
    inference(rectify,[],[f6]) ).

fof(f6,axiom,
    ! [X1,X0,X3,X2] :
      ( ( in(X1,X3)
        & in(X0,X2) )
    <=> in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l55_zfmisc_1) ).

fof(f50,plain,
    ( in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK3),sK2))
    | ~ spl5_1 ),
    inference(avatar_component_clause,[],[f48]) ).

fof(f48,plain,
    ( spl5_1
  <=> in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK3),sK2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_1])]) ).

fof(f76,plain,
    ( spl5_1
    | ~ spl5_2 ),
    inference(avatar_contradiction_clause,[],[f75]) ).

fof(f75,plain,
    ( $false
    | spl5_1
    | ~ spl5_2 ),
    inference(subsumption_resolution,[],[f68,f46]) ).

fof(f46,plain,
    in(sK1,sK2),
    inference(subsumption_resolution,[],[f32,f41]) ).

fof(f41,plain,
    ! [X2,X3,X0,X1] :
      ( ~ in(ordered_pair(X2,X3),cartesian_product2(X1,X0))
      | in(X3,X0) ),
    inference(cnf_transformation,[],[f29]) ).

fof(f32,plain,
    ( in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK3),sK2))
    | in(sK1,sK2) ),
    inference(cnf_transformation,[],[f22]) ).

fof(f22,plain,
    ( ( ~ in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK3),sK2))
      | ~ in(sK1,sK2)
      | sK0 != sK3 )
    & ( in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK3),sK2))
      | ( in(sK1,sK2)
        & sK0 = sK3 ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f20,f21]) ).

fof(f21,plain,
    ( ? [X0,X1,X2,X3] :
        ( ( ~ in(ordered_pair(X0,X1),cartesian_product2(singleton(X3),X2))
          | ~ in(X1,X2)
          | X0 != X3 )
        & ( in(ordered_pair(X0,X1),cartesian_product2(singleton(X3),X2))
          | ( in(X1,X2)
            & X0 = X3 ) ) )
   => ( ( ~ in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK3),sK2))
        | ~ in(sK1,sK2)
        | sK0 != sK3 )
      & ( in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK3),sK2))
        | ( in(sK1,sK2)
          & sK0 = sK3 ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f20,plain,
    ? [X0,X1,X2,X3] :
      ( ( ~ in(ordered_pair(X0,X1),cartesian_product2(singleton(X3),X2))
        | ~ in(X1,X2)
        | X0 != X3 )
      & ( in(ordered_pair(X0,X1),cartesian_product2(singleton(X3),X2))
        | ( in(X1,X2)
          & X0 = X3 ) ) ),
    inference(rectify,[],[f19]) ).

fof(f19,plain,
    ? [X1,X2,X3,X0] :
      ( ( ~ in(ordered_pair(X1,X2),cartesian_product2(singleton(X0),X3))
        | ~ in(X2,X3)
        | X0 != X1 )
      & ( in(ordered_pair(X1,X2),cartesian_product2(singleton(X0),X3))
        | ( in(X2,X3)
          & X0 = X1 ) ) ),
    inference(flattening,[],[f18]) ).

fof(f18,plain,
    ? [X1,X2,X3,X0] :
      ( ( ~ in(ordered_pair(X1,X2),cartesian_product2(singleton(X0),X3))
        | ~ in(X2,X3)
        | X0 != X1 )
      & ( in(ordered_pair(X1,X2),cartesian_product2(singleton(X0),X3))
        | ( in(X2,X3)
          & X0 = X1 ) ) ),
    inference(nnf_transformation,[],[f16]) ).

fof(f16,plain,
    ? [X1,X2,X3,X0] :
      ( ( in(X2,X3)
        & X0 = X1 )
    <~> in(ordered_pair(X1,X2),cartesian_product2(singleton(X0),X3)) ),
    inference(ennf_transformation,[],[f11]) ).

fof(f11,plain,
    ~ ! [X0,X1,X2,X3] :
        ( in(ordered_pair(X1,X2),cartesian_product2(singleton(X0),X3))
      <=> ( in(X2,X3)
          & X0 = X1 ) ),
    inference(rectify,[],[f10]) ).

fof(f10,negated_conjecture,
    ~ ! [X2,X0,X1,X3] :
        ( ( in(X1,X3)
          & X0 = X2 )
      <=> in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),X3)) ),
    inference(negated_conjecture,[],[f9]) ).

fof(f9,conjecture,
    ! [X2,X0,X1,X3] :
      ( ( in(X1,X3)
        & X0 = X2 )
    <=> in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t128_zfmisc_1) ).

fof(f68,plain,
    ( ~ in(sK1,sK2)
    | spl5_1
    | ~ spl5_2 ),
    inference(unit_resulting_resolution,[],[f44,f58,f42]) ).

fof(f42,plain,
    ! [X2,X3,X0,X1] :
      ( in(ordered_pair(X2,X3),cartesian_product2(X1,X0))
      | ~ in(X2,X1)
      | ~ in(X3,X0) ),
    inference(cnf_transformation,[],[f29]) ).

fof(f58,plain,
    ( ~ in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK0),sK2))
    | spl5_1
    | ~ spl5_2 ),
    inference(backward_demodulation,[],[f49,f54]) ).

fof(f54,plain,
    ( sK0 = sK3
    | ~ spl5_2 ),
    inference(avatar_component_clause,[],[f52]) ).

fof(f49,plain,
    ( ~ in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK3),sK2))
    | spl5_1 ),
    inference(avatar_component_clause,[],[f48]) ).

fof(f44,plain,
    ! [X2] : in(X2,singleton(X2)),
    inference(equality_resolution,[],[f43]) ).

fof(f43,plain,
    ! [X2,X1] :
      ( in(X2,X1)
      | singleton(X2) != X1 ),
    inference(equality_resolution,[],[f38]) ).

fof(f38,plain,
    ! [X2,X0,X1] :
      ( in(X2,X1)
      | X0 != X2
      | singleton(X0) != X1 ),
    inference(cnf_transformation,[],[f26]) ).

fof(f57,plain,
    ( ~ spl5_2
    | ~ spl5_1 ),
    inference(avatar_split_clause,[],[f56,f48,f52]) ).

fof(f56,plain,
    ( ~ in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK3),sK2))
    | sK0 != sK3 ),
    inference(subsumption_resolution,[],[f33,f46]) ).

fof(f33,plain,
    ( ~ in(sK1,sK2)
    | sK0 != sK3
    | ~ in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK3),sK2)) ),
    inference(cnf_transformation,[],[f22]) ).

fof(f55,plain,
    ( spl5_1
    | spl5_2 ),
    inference(avatar_split_clause,[],[f31,f52,f48]) ).

fof(f31,plain,
    ( sK0 = sK3
    | in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK3),sK2)) ),
    inference(cnf_transformation,[],[f22]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SET975+1 : TPTP v8.1.0. Released v3.2.0.
% 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
% 0.14/0.34  % 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 Aug 30 14:31:55 EDT 2022
% 0.14/0.34  % CPUTime    : 
% 0.20/0.49  % (13580)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)
% 0.20/0.49  % (13561)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)
% 0.20/0.50  % (13561)First to succeed.
% 0.20/0.50  % (13572)lrs+10_1:1_ins=3:sp=reverse_frequency:spb=goal:to=lpo:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.20/0.50  % (13561)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  % (13561)------------------------------
% 0.20/0.50  % (13561)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.50  % (13561)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.50  % (13561)Termination reason: Refutation
% 0.20/0.50  
% 0.20/0.50  % (13561)Memory used [KB]: 6012
% 0.20/0.50  % (13561)Time elapsed: 0.098 s
% 0.20/0.50  % (13561)Instructions burned: 3 (million)
% 0.20/0.50  % (13561)------------------------------
% 0.20/0.50  % (13561)------------------------------
% 0.20/0.50  % (13552)Success in time 0.155 s
%------------------------------------------------------------------------------