TSTP Solution File: SEU129+1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SEU129+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_uns --cores 0 -t %d %s

% Computer : n017.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 18:26:47 EDT 2022

% Result   : Theorem 1.34s 0.56s
% Output   : Refutation 1.34s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   47 (  10 unt;   0 def)
%            Number of atoms       :  171 (  13 equ)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives :  199 (  75   ~;  68   |;  39   &)
%                                         (   9 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   3 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-3 aty)
%            Number of variables   :  101 (  85   !;  16   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f136,plain,
    $false,
    inference(avatar_sat_refutation,[],[f108,f117,f135]) ).

fof(f135,plain,
    spl8_1,
    inference(avatar_contradiction_clause,[],[f134]) ).

fof(f134,plain,
    ( $false
    | spl8_1 ),
    inference(subsumption_resolution,[],[f127,f103]) ).

fof(f103,plain,
    ( ~ in(sK5(set_intersection2(sK3,sK4),set_intersection2(sK2,sK4)),sK3)
    | spl8_1 ),
    inference(avatar_component_clause,[],[f101]) ).

fof(f101,plain,
    ( spl8_1
  <=> in(sK5(set_intersection2(sK3,sK4),set_intersection2(sK2,sK4)),sK3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_1])]) ).

fof(f127,plain,
    in(sK5(set_intersection2(sK3,sK4),set_intersection2(sK2,sK4)),sK3),
    inference(resolution,[],[f109,f85]) ).

fof(f85,plain,
    ! [X0] :
      ( ~ in(X0,sK2)
      | in(X0,sK3) ),
    inference(resolution,[],[f61,f63]) ).

fof(f63,plain,
    ! [X3,X0,X1] :
      ( in(X3,X0)
      | ~ subset(X1,X0)
      | ~ in(X3,X1) ),
    inference(cnf_transformation,[],[f45]) ).

fof(f45,plain,
    ! [X0,X1] :
      ( ( subset(X1,X0)
        | ( in(sK5(X0,X1),X1)
          & ~ in(sK5(X0,X1),X0) ) )
      & ( ! [X3] :
            ( ~ in(X3,X1)
            | in(X3,X0) )
        | ~ subset(X1,X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f43,f44]) ).

fof(f44,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( in(X2,X1)
          & ~ in(X2,X0) )
     => ( in(sK5(X0,X1),X1)
        & ~ in(sK5(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f43,plain,
    ! [X0,X1] :
      ( ( subset(X1,X0)
        | ? [X2] :
            ( in(X2,X1)
            & ~ in(X2,X0) ) )
      & ( ! [X3] :
            ( ~ in(X3,X1)
            | in(X3,X0) )
        | ~ subset(X1,X0) ) ),
    inference(rectify,[],[f42]) ).

fof(f42,plain,
    ! [X0,X1] :
      ( ( subset(X1,X0)
        | ? [X2] :
            ( in(X2,X1)
            & ~ in(X2,X0) ) )
      & ( ! [X2] :
            ( ~ in(X2,X1)
            | in(X2,X0) )
        | ~ subset(X1,X0) ) ),
    inference(nnf_transformation,[],[f26]) ).

fof(f26,plain,
    ! [X0,X1] :
      ( subset(X1,X0)
    <=> ! [X2] :
          ( ~ in(X2,X1)
          | in(X2,X0) ) ),
    inference(ennf_transformation,[],[f21]) ).

fof(f21,plain,
    ! [X0,X1] :
      ( subset(X1,X0)
    <=> ! [X2] :
          ( in(X2,X1)
         => in(X2,X0) ) ),
    inference(rectify,[],[f3]) ).

fof(f3,axiom,
    ! [X1,X0] :
      ( ! [X2] :
          ( in(X2,X0)
         => in(X2,X1) )
    <=> subset(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).

fof(f61,plain,
    subset(sK2,sK3),
    inference(cnf_transformation,[],[f41]) ).

fof(f41,plain,
    ( ~ subset(set_intersection2(sK2,sK4),set_intersection2(sK3,sK4))
    & subset(sK2,sK3) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f39,f40]) ).

fof(f40,plain,
    ( ? [X0,X1,X2] :
        ( ~ subset(set_intersection2(X0,X2),set_intersection2(X1,X2))
        & subset(X0,X1) )
   => ( ~ subset(set_intersection2(sK2,sK4),set_intersection2(sK3,sK4))
      & subset(sK2,sK3) ) ),
    introduced(choice_axiom,[]) ).

fof(f39,plain,
    ? [X0,X1,X2] :
      ( ~ subset(set_intersection2(X0,X2),set_intersection2(X1,X2))
      & subset(X0,X1) ),
    inference(rectify,[],[f27]) ).

fof(f27,plain,
    ? [X1,X0,X2] :
      ( ~ subset(set_intersection2(X1,X2),set_intersection2(X0,X2))
      & subset(X1,X0) ),
    inference(ennf_transformation,[],[f19]) ).

fof(f19,plain,
    ~ ! [X2,X0,X1] :
        ( subset(X1,X0)
       => subset(set_intersection2(X1,X2),set_intersection2(X0,X2)) ),
    inference(rectify,[],[f13]) ).

fof(f13,negated_conjecture,
    ~ ! [X1,X0,X2] :
        ( subset(X0,X1)
       => subset(set_intersection2(X0,X2),set_intersection2(X1,X2)) ),
    inference(negated_conjecture,[],[f12]) ).

fof(f12,conjecture,
    ! [X1,X0,X2] :
      ( subset(X0,X1)
     => subset(set_intersection2(X0,X2),set_intersection2(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_xboole_1) ).

fof(f109,plain,
    in(sK5(set_intersection2(sK3,sK4),set_intersection2(sK2,sK4)),sK2),
    inference(resolution,[],[f95,f73]) ).

fof(f73,plain,
    ! [X3,X0,X1] :
      ( in(X3,X0)
      | ~ in(X3,set_intersection2(X0,X1)) ),
    inference(equality_resolution,[],[f54]) ).

fof(f54,plain,
    ! [X2,X3,X0,X1] :
      ( in(X3,X0)
      | ~ in(X3,X2)
      | set_intersection2(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f34]) ).

fof(f34,plain,
    ! [X0,X1,X2] :
      ( ( ! [X3] :
            ( ( in(X3,X2)
              | ~ in(X3,X0)
              | ~ in(X3,X1) )
            & ( ( in(X3,X0)
                & in(X3,X1) )
              | ~ in(X3,X2) ) )
        | set_intersection2(X0,X1) != X2 )
      & ( set_intersection2(X0,X1) = X2
        | ( ( ~ in(sK0(X0,X1,X2),X0)
            | ~ in(sK0(X0,X1,X2),X1)
            | ~ in(sK0(X0,X1,X2),X2) )
          & ( ( in(sK0(X0,X1,X2),X0)
              & in(sK0(X0,X1,X2),X1) )
            | in(sK0(X0,X1,X2),X2) ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f32,f33]) ).

fof(f33,plain,
    ! [X0,X1,X2] :
      ( ? [X4] :
          ( ( ~ in(X4,X0)
            | ~ in(X4,X1)
            | ~ in(X4,X2) )
          & ( ( in(X4,X0)
              & in(X4,X1) )
            | in(X4,X2) ) )
     => ( ( ~ in(sK0(X0,X1,X2),X0)
          | ~ in(sK0(X0,X1,X2),X1)
          | ~ in(sK0(X0,X1,X2),X2) )
        & ( ( in(sK0(X0,X1,X2),X0)
            & in(sK0(X0,X1,X2),X1) )
          | in(sK0(X0,X1,X2),X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f32,plain,
    ! [X0,X1,X2] :
      ( ( ! [X3] :
            ( ( in(X3,X2)
              | ~ in(X3,X0)
              | ~ in(X3,X1) )
            & ( ( in(X3,X0)
                & in(X3,X1) )
              | ~ in(X3,X2) ) )
        | set_intersection2(X0,X1) != X2 )
      & ( set_intersection2(X0,X1) = X2
        | ? [X4] :
            ( ( ~ in(X4,X0)
              | ~ in(X4,X1)
              | ~ in(X4,X2) )
            & ( ( in(X4,X0)
                & in(X4,X1) )
              | in(X4,X2) ) ) ) ),
    inference(rectify,[],[f31]) ).

fof(f31,plain,
    ! [X0,X2,X1] :
      ( ( ! [X3] :
            ( ( in(X3,X1)
              | ~ in(X3,X0)
              | ~ in(X3,X2) )
            & ( ( in(X3,X0)
                & in(X3,X2) )
              | ~ in(X3,X1) ) )
        | set_intersection2(X0,X2) != X1 )
      & ( set_intersection2(X0,X2) = X1
        | ? [X3] :
            ( ( ~ in(X3,X0)
              | ~ in(X3,X2)
              | ~ in(X3,X1) )
            & ( ( in(X3,X0)
                & in(X3,X2) )
              | in(X3,X1) ) ) ) ),
    inference(flattening,[],[f30]) ).

fof(f30,plain,
    ! [X0,X2,X1] :
      ( ( ! [X3] :
            ( ( in(X3,X1)
              | ~ in(X3,X0)
              | ~ in(X3,X2) )
            & ( ( in(X3,X0)
                & in(X3,X2) )
              | ~ in(X3,X1) ) )
        | set_intersection2(X0,X2) != X1 )
      & ( set_intersection2(X0,X2) = X1
        | ? [X3] :
            ( ( ~ in(X3,X0)
              | ~ in(X3,X2)
              | ~ in(X3,X1) )
            & ( ( in(X3,X0)
                & in(X3,X2) )
              | in(X3,X1) ) ) ) ),
    inference(nnf_transformation,[],[f20]) ).

fof(f20,plain,
    ! [X0,X2,X1] :
      ( ! [X3] :
          ( in(X3,X1)
        <=> ( in(X3,X0)
            & in(X3,X2) ) )
    <=> set_intersection2(X0,X2) = X1 ),
    inference(rectify,[],[f4]) ).

fof(f4,axiom,
    ! [X0,X2,X1] :
      ( ! [X3] :
          ( ( in(X3,X1)
            & in(X3,X0) )
        <=> in(X3,X2) )
    <=> set_intersection2(X0,X1) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).

fof(f95,plain,
    in(sK5(set_intersection2(sK3,sK4),set_intersection2(sK2,sK4)),set_intersection2(sK2,sK4)),
    inference(resolution,[],[f62,f65]) ).

fof(f65,plain,
    ! [X0,X1] :
      ( subset(X1,X0)
      | in(sK5(X0,X1),X1) ),
    inference(cnf_transformation,[],[f45]) ).

fof(f62,plain,
    ~ subset(set_intersection2(sK2,sK4),set_intersection2(sK3,sK4)),
    inference(cnf_transformation,[],[f41]) ).

fof(f117,plain,
    spl8_2,
    inference(avatar_split_clause,[],[f110,f105]) ).

fof(f105,plain,
    ( spl8_2
  <=> in(sK5(set_intersection2(sK3,sK4),set_intersection2(sK2,sK4)),sK4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_2])]) ).

fof(f110,plain,
    in(sK5(set_intersection2(sK3,sK4),set_intersection2(sK2,sK4)),sK4),
    inference(resolution,[],[f95,f74]) ).

fof(f74,plain,
    ! [X3,X0,X1] :
      ( in(X3,X1)
      | ~ in(X3,set_intersection2(X0,X1)) ),
    inference(equality_resolution,[],[f53]) ).

fof(f53,plain,
    ! [X2,X3,X0,X1] :
      ( in(X3,X1)
      | ~ in(X3,X2)
      | set_intersection2(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f34]) ).

fof(f108,plain,
    ( ~ spl8_1
    | ~ spl8_2 ),
    inference(avatar_split_clause,[],[f96,f105,f101]) ).

fof(f96,plain,
    ( ~ in(sK5(set_intersection2(sK3,sK4),set_intersection2(sK2,sK4)),sK4)
    | ~ in(sK5(set_intersection2(sK3,sK4),set_intersection2(sK2,sK4)),sK3) ),
    inference(resolution,[],[f94,f72]) ).

fof(f72,plain,
    ! [X3,X0,X1] :
      ( ~ in(X3,X0)
      | in(X3,set_intersection2(X0,X1))
      | ~ in(X3,X1) ),
    inference(equality_resolution,[],[f55]) ).

fof(f55,plain,
    ! [X2,X3,X0,X1] :
      ( in(X3,X2)
      | ~ in(X3,X0)
      | ~ in(X3,X1)
      | set_intersection2(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f34]) ).

fof(f94,plain,
    ~ in(sK5(set_intersection2(sK3,sK4),set_intersection2(sK2,sK4)),set_intersection2(sK3,sK4)),
    inference(resolution,[],[f62,f64]) ).

fof(f64,plain,
    ! [X0,X1] :
      ( ~ in(sK5(X0,X1),X0)
      | subset(X1,X0) ),
    inference(cnf_transformation,[],[f45]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SEU129+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_uns --cores 0 -t %d %s
% 0.13/0.34  % Computer : n017.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 14:04:35 EDT 2022
% 0.13/0.35  % CPUTime    : 
% 1.34/0.55  % (19511)lrs+10_1:1_ep=R:lcm=predicate:lma=on:sos=all:spb=goal:ss=included:i=12:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/12Mi)
% 1.34/0.56  % (19511)First to succeed.
% 1.34/0.56  % (19511)Refutation found. Thanks to Tanya!
% 1.34/0.56  % SZS status Theorem for theBenchmark
% 1.34/0.56  % SZS output start Proof for theBenchmark
% See solution above
% 1.34/0.56  % (19511)------------------------------
% 1.34/0.56  % (19511)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.34/0.56  % (19511)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.34/0.56  % (19511)Termination reason: Refutation
% 1.34/0.56  
% 1.34/0.56  % (19511)Memory used [KB]: 5884
% 1.34/0.56  % (19511)Time elapsed: 0.134 s
% 1.34/0.56  % (19511)Instructions burned: 2 (million)
% 1.34/0.56  % (19511)------------------------------
% 1.34/0.56  % (19511)------------------------------
% 1.34/0.56  % (19500)Success in time 0.206 s
%------------------------------------------------------------------------------