TSTP Solution File: GEO191+3 by Vampire-SAT---4.8

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%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : GEO191+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n008.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 : Tue Apr 30 11:14:35 EDT 2024

% Result   : Theorem 0.13s 0.36s
% Output   : Refutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   41 (  13 unt;   0 def)
%            Number of atoms       :  111 (   0 equ)
%            Maximal formula atoms :   12 (   2 avg)
%            Number of connectives :  108 (  38   ~;  35   |;  26   &)
%                                         (   2 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    6 (   5 usr;   3 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :   77 (  65   !;  12   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f203,plain,
    $false,
    inference(avatar_sat_refutation,[],[f148,f200,f202]) ).

fof(f202,plain,
    ~ spl5_1,
    inference(avatar_contradiction_clause,[],[f201]) ).

fof(f201,plain,
    ( $false
    | ~ spl5_1 ),
    inference(resolution,[],[f143,f194]) ).

fof(f194,plain,
    ! [X0,X1] : ~ apart_point_and_line(X0,X1),
    inference(resolution,[],[f166,f180]) ).

fof(f180,plain,
    ! [X0,X1] : ~ distinct_lines(X0,parallel_through_point(X0,X1)),
    inference(resolution,[],[f175,f109]) ).

fof(f109,plain,
    ! [X0,X1] :
      ( convergent_lines(X0,X1)
      | ~ distinct_lines(X0,X1) ),
    inference(cnf_transformation,[],[f56]) ).

fof(f56,plain,
    ! [X0,X1] :
      ( convergent_lines(X0,X1)
      | ~ distinct_lines(X0,X1) ),
    inference(ennf_transformation,[],[f15]) ).

fof(f15,axiom,
    ! [X0,X1] :
      ( distinct_lines(X0,X1)
     => convergent_lines(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).

fof(f175,plain,
    ! [X0,X1] : ~ convergent_lines(X0,parallel_through_point(X0,X1)),
    inference(resolution,[],[f172,f139]) ).

fof(f139,plain,
    ! [X0,X1] : ~ distinct_lines(parallel_through_point(X0,X1),X0),
    inference(resolution,[],[f109,f105]) ).

fof(f105,plain,
    ! [X0,X1] : ~ convergent_lines(parallel_through_point(X1,X0),X1),
    inference(cnf_transformation,[],[f16]) ).

fof(f16,axiom,
    ! [X0,X1] : ~ convergent_lines(parallel_through_point(X1,X0),X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cp1) ).

fof(f172,plain,
    ! [X0,X1] :
      ( distinct_lines(X0,X1)
      | ~ convergent_lines(X1,X0) ),
    inference(resolution,[],[f122,f101]) ).

fof(f101,plain,
    ! [X0] : ~ convergent_lines(X0,X0),
    inference(cnf_transformation,[],[f3]) ).

fof(f3,axiom,
    ! [X0] : ~ convergent_lines(X0,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart3) ).

fof(f122,plain,
    ! [X2,X0,X1] :
      ( convergent_lines(X0,X2)
      | distinct_lines(X1,X2)
      | ~ convergent_lines(X0,X1) ),
    inference(cnf_transformation,[],[f79]) ).

fof(f79,plain,
    ! [X0,X1,X2] :
      ( convergent_lines(X0,X2)
      | distinct_lines(X1,X2)
      | ~ convergent_lines(X0,X1) ),
    inference(flattening,[],[f78]) ).

fof(f78,plain,
    ! [X0,X1,X2] :
      ( convergent_lines(X0,X2)
      | distinct_lines(X1,X2)
      | ~ convergent_lines(X0,X1) ),
    inference(ennf_transformation,[],[f14]) ).

fof(f14,axiom,
    ! [X0,X1,X2] :
      ( convergent_lines(X0,X1)
     => ( convergent_lines(X0,X2)
        | distinct_lines(X1,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ceq3) ).

fof(f166,plain,
    ! [X2,X0,X1] :
      ( distinct_lines(X0,parallel_through_point(X1,X2))
      | ~ apart_point_and_line(X2,X0) ),
    inference(resolution,[],[f121,f104]) ).

fof(f104,plain,
    ! [X0,X1] : ~ apart_point_and_line(X0,parallel_through_point(X1,X0)),
    inference(cnf_transformation,[],[f17]) ).

fof(f17,axiom,
    ! [X0,X1] : ~ apart_point_and_line(X0,parallel_through_point(X1,X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cp2) ).

fof(f121,plain,
    ! [X2,X0,X1] :
      ( apart_point_and_line(X0,X2)
      | distinct_lines(X1,X2)
      | ~ apart_point_and_line(X0,X1) ),
    inference(cnf_transformation,[],[f77]) ).

fof(f77,plain,
    ! [X0,X1,X2] :
      ( apart_point_and_line(X0,X2)
      | distinct_lines(X1,X2)
      | ~ apart_point_and_line(X0,X1) ),
    inference(flattening,[],[f76]) ).

fof(f76,plain,
    ! [X0,X1,X2] :
      ( apart_point_and_line(X0,X2)
      | distinct_lines(X1,X2)
      | ~ apart_point_and_line(X0,X1) ),
    inference(ennf_transformation,[],[f13]) ).

fof(f13,axiom,
    ! [X0,X1,X2] :
      ( apart_point_and_line(X0,X1)
     => ( apart_point_and_line(X0,X2)
        | distinct_lines(X1,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ceq2) ).

fof(f143,plain,
    ( apart_point_and_line(intersection_point(sK0,sK1),sK2)
    | ~ spl5_1 ),
    inference(avatar_component_clause,[],[f141]) ).

fof(f141,plain,
    ( spl5_1
  <=> apart_point_and_line(intersection_point(sK0,sK1),sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_1])]) ).

fof(f200,plain,
    ~ spl5_2,
    inference(avatar_contradiction_clause,[],[f197]) ).

fof(f197,plain,
    ( $false
    | ~ spl5_2 ),
    inference(resolution,[],[f194,f147]) ).

fof(f147,plain,
    ( apart_point_and_line(intersection_point(sK0,sK1),sK3)
    | ~ spl5_2 ),
    inference(avatar_component_clause,[],[f145]) ).

fof(f145,plain,
    ( spl5_2
  <=> apart_point_and_line(intersection_point(sK0,sK1),sK3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_2])]) ).

fof(f148,plain,
    ( spl5_1
    | spl5_2 ),
    inference(avatar_split_clause,[],[f96,f145,f141]) ).

fof(f96,plain,
    ( apart_point_and_line(intersection_point(sK0,sK1),sK3)
    | apart_point_and_line(intersection_point(sK0,sK1),sK2) ),
    inference(cnf_transformation,[],[f93]) ).

fof(f93,plain,
    ( ~ apart_point_and_line(intersection_point(sK2,sK3),sK1)
    & ~ apart_point_and_line(intersection_point(sK2,sK3),sK0)
    & ( apart_point_and_line(intersection_point(sK0,sK1),sK3)
      | apart_point_and_line(intersection_point(sK0,sK1),sK2) )
    & convergent_lines(sK2,sK3)
    & convergent_lines(sK0,sK1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f53,f92]) ).

fof(f92,plain,
    ( ? [X0,X1,X2,X3] :
        ( ~ apart_point_and_line(intersection_point(X2,X3),X1)
        & ~ apart_point_and_line(intersection_point(X2,X3),X0)
        & ( apart_point_and_line(intersection_point(X0,X1),X3)
          | apart_point_and_line(intersection_point(X0,X1),X2) )
        & convergent_lines(X2,X3)
        & convergent_lines(X0,X1) )
   => ( ~ apart_point_and_line(intersection_point(sK2,sK3),sK1)
      & ~ apart_point_and_line(intersection_point(sK2,sK3),sK0)
      & ( apart_point_and_line(intersection_point(sK0,sK1),sK3)
        | apart_point_and_line(intersection_point(sK0,sK1),sK2) )
      & convergent_lines(sK2,sK3)
      & convergent_lines(sK0,sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f53,plain,
    ? [X0,X1,X2,X3] :
      ( ~ apart_point_and_line(intersection_point(X2,X3),X1)
      & ~ apart_point_and_line(intersection_point(X2,X3),X0)
      & ( apart_point_and_line(intersection_point(X0,X1),X3)
        | apart_point_and_line(intersection_point(X0,X1),X2) )
      & convergent_lines(X2,X3)
      & convergent_lines(X0,X1) ),
    inference(flattening,[],[f52]) ).

fof(f52,plain,
    ? [X0,X1,X2,X3] :
      ( ~ apart_point_and_line(intersection_point(X2,X3),X1)
      & ~ apart_point_and_line(intersection_point(X2,X3),X0)
      & ( apart_point_and_line(intersection_point(X0,X1),X3)
        | apart_point_and_line(intersection_point(X0,X1),X2) )
      & convergent_lines(X2,X3)
      & convergent_lines(X0,X1) ),
    inference(ennf_transformation,[],[f38]) ).

fof(f38,plain,
    ~ ! [X0,X1,X2,X3] :
        ( ( ( apart_point_and_line(intersection_point(X0,X1),X3)
            | apart_point_and_line(intersection_point(X0,X1),X2) )
          & convergent_lines(X2,X3)
          & convergent_lines(X0,X1) )
       => ( apart_point_and_line(intersection_point(X2,X3),X1)
          | apart_point_and_line(intersection_point(X2,X3),X0) ) ),
    inference(rectify,[],[f37]) ).

fof(f37,negated_conjecture,
    ~ ! [X0,X1,X3,X4] :
        ( ( ( apart_point_and_line(intersection_point(X0,X1),X4)
            | apart_point_and_line(intersection_point(X0,X1),X3) )
          & convergent_lines(X3,X4)
          & convergent_lines(X0,X1) )
       => ( apart_point_and_line(intersection_point(X3,X4),X1)
          | apart_point_and_line(intersection_point(X3,X4),X0) ) ),
    inference(negated_conjecture,[],[f36]) ).

fof(f36,conjecture,
    ! [X0,X1,X3,X4] :
      ( ( ( apart_point_and_line(intersection_point(X0,X1),X4)
          | apart_point_and_line(intersection_point(X0,X1),X3) )
        & convergent_lines(X3,X4)
        & convergent_lines(X0,X1) )
     => ( apart_point_and_line(intersection_point(X3,X4),X1)
        | apart_point_and_line(intersection_point(X3,X4),X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : GEO191+3 : TPTP v8.1.2. Released v4.0.0.
% 0.03/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.34  % Computer : n008.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 Apr 30 05:47:28 EDT 2024
% 0.13/0.34  % CPUTime    : 
% 0.13/0.35  % (15098)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.36  % (15103)dis-2_2:3_amm=sco:anc=none:bce=on:fsr=off:gsp=on:nm=16:nwc=1.2:nicw=on:sac=on:sp=weighted_frequency_476 on theBenchmark for (476ds/0Mi)
% 0.13/0.36  % (15103)First to succeed.
% 0.13/0.36  % (15103)Refutation found. Thanks to Tanya!
% 0.13/0.36  % SZS status Theorem for theBenchmark
% 0.13/0.36  % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.36  % (15103)------------------------------
% 0.13/0.36  % (15103)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.13/0.36  % (15103)Termination reason: Refutation
% 0.13/0.36  
% 0.13/0.36  % (15103)Memory used [KB]: 974
% 0.13/0.36  % (15103)Time elapsed: 0.004 s
% 0.13/0.36  % (15103)Instructions burned: 7 (million)
% 0.13/0.36  % (15103)------------------------------
% 0.13/0.36  % (15103)------------------------------
% 0.13/0.36  % (15098)Success in time 0.013 s
%------------------------------------------------------------------------------