%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : GEO178+2 : 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 : n018.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 16:08:58 EDT 2022

% Result   : Theorem 0.21s 0.52s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   29 (   4 unt;   0 def)
%            Number of atoms       :   84 (   0 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :   87 (  32   ~;  24   |;  21   &)
%                                         (   3 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    6 (   5 usr;   4 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :   39 (  27   !;  12   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f125,plain,
    $false,
    inference(avatar_sat_refutation,[],[f79,f111,f118,f124]) ).

fof(f124,plain,
    spl3_3,
    inference(avatar_contradiction_clause,[],[f119]) ).

fof(f119,plain,
    ( $false
    | spl3_3 ),
    inference(resolution,[],[f106,f63]) ).

fof(f63,plain,
    distinct_points(sK1,sK0),
    inference(cnf_transformation,[],[f48]) ).

fof(f48,plain,
    ( distinct_points(sK1,sK0)
    & apart_point_and_line(sK2,line_connecting(sK1,sK0))
    & ( ~ distinct_points(sK2,sK0)
      | ~ distinct_points(sK2,sK1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f46,f47]) ).

fof(f47,plain,
    ( ? [X0,X1,X2] :
        ( distinct_points(X1,X0)
        & apart_point_and_line(X2,line_connecting(X1,X0))
        & ( ~ distinct_points(X2,X0)
          | ~ distinct_points(X2,X1) ) )
   => ( distinct_points(sK1,sK0)
      & apart_point_and_line(sK2,line_connecting(sK1,sK0))
      & ( ~ distinct_points(sK2,sK0)
        | ~ distinct_points(sK2,sK1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f46,plain,
    ? [X0,X1,X2] :
      ( distinct_points(X1,X0)
      & apart_point_and_line(X2,line_connecting(X1,X0))
      & ( ~ distinct_points(X2,X0)
        | ~ distinct_points(X2,X1) ) ),
    inference(rectify,[],[f29]) ).

fof(f29,plain,
    ? [X1,X0,X2] :
      ( distinct_points(X0,X1)
      & apart_point_and_line(X2,line_connecting(X0,X1))
      & ( ~ distinct_points(X2,X1)
        | ~ distinct_points(X2,X0) ) ),
    inference(flattening,[],[f28]) ).

fof(f28,plain,
    ? [X0,X1,X2] :
      ( ( ~ distinct_points(X2,X1)
        | ~ distinct_points(X2,X0) )
      & apart_point_and_line(X2,line_connecting(X0,X1))
      & distinct_points(X0,X1) ),
    inference(ennf_transformation,[],[f14]) ).

fof(f14,negated_conjecture,
    ~ ! [X0,X1,X2] :
        ( ( apart_point_and_line(X2,line_connecting(X0,X1))
          & distinct_points(X0,X1) )
       => ( distinct_points(X2,X1)
          & distinct_points(X2,X0) ) ),
    inference(negated_conjecture,[],[f13]) ).

fof(f13,conjecture,
    ! [X0,X1,X2] :
      ( ( apart_point_and_line(X2,line_connecting(X0,X1))
        & distinct_points(X0,X1) )
     => ( distinct_points(X2,X1)
        & distinct_points(X2,X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).

fof(f106,plain,
    ( ~ distinct_points(sK1,sK0)
    | spl3_3 ),
    inference(avatar_component_clause,[],[f104]) ).

fof(f104,plain,
    ( spl3_3
  <=> distinct_points(sK1,sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_3])]) ).

fof(f118,plain,
    ( ~ spl3_3
    | spl3_1 ),
    inference(avatar_split_clause,[],[f112,f72,f104]) ).

fof(f72,plain,
    ( spl3_1
  <=> distinct_points(sK2,sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).

fof(f112,plain,
    ( distinct_points(sK2,sK0)
    | ~ distinct_points(sK1,sK0) ),
    inference(resolution,[],[f68,f62]) ).

fof(f62,plain,
    apart_point_and_line(sK2,line_connecting(sK1,sK0)),
    inference(cnf_transformation,[],[f48]) ).

fof(f68,plain,
    ! [X2,X0,X1] :
      ( ~ apart_point_and_line(X2,line_connecting(X0,X1))
      | ~ distinct_points(X0,X1)
      | distinct_points(X2,X1) ),
    inference(cnf_transformation,[],[f52]) ).

fof(f52,plain,
    ! [X0,X1,X2] :
      ( ~ apart_point_and_line(X2,line_connecting(X0,X1))
      | ( distinct_points(X2,X1)
        & distinct_points(X2,X0) )
      | ~ distinct_points(X0,X1) ),
    inference(rectify,[],[f40]) ).

fof(f40,plain,
    ! [X1,X2,X0] :
      ( ~ apart_point_and_line(X0,line_connecting(X1,X2))
      | ( distinct_points(X0,X2)
        & distinct_points(X0,X1) )
      | ~ distinct_points(X1,X2) ),
    inference(flattening,[],[f39]) ).

fof(f39,plain,
    ! [X1,X2,X0] :
      ( ( distinct_points(X0,X2)
        & distinct_points(X0,X1) )
      | ~ apart_point_and_line(X0,line_connecting(X1,X2))
      | ~ distinct_points(X1,X2) ),
    inference(ennf_transformation,[],[f16]) ).

fof(f16,plain,
    ! [X1,X2,X0] :
      ( distinct_points(X1,X2)
     => ( apart_point_and_line(X0,line_connecting(X1,X2))
       => ( distinct_points(X0,X2)
          & distinct_points(X0,X1) ) ) ),
    inference(rectify,[],[f7]) ).

fof(f7,axiom,
    ! [X2,X0,X1] :
      ( distinct_points(X0,X1)
     => ( apart_point_and_line(X2,line_connecting(X0,X1))
       => ( distinct_points(X2,X0)
          & distinct_points(X2,X1) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con1) ).

fof(f111,plain,
    ( spl3_2
    | ~ spl3_3 ),
    inference(avatar_split_clause,[],[f101,f104,f76]) ).

fof(f76,plain,
    ( spl3_2
  <=> distinct_points(sK2,sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_2])]) ).

fof(f101,plain,
    ( ~ distinct_points(sK1,sK0)
    | distinct_points(sK2,sK1) ),
    inference(resolution,[],[f67,f62]) ).

fof(f67,plain,
    ! [X2,X0,X1] :
      ( ~ apart_point_and_line(X2,line_connecting(X0,X1))
      | distinct_points(X2,X0)
      | ~ distinct_points(X0,X1) ),
    inference(cnf_transformation,[],[f52]) ).

fof(f79,plain,
    ( ~ spl3_1
    | ~ spl3_2 ),
    inference(avatar_split_clause,[],[f61,f76,f72]) ).

fof(f61,plain,
    ( ~ distinct_points(sK2,sK1)
    | ~ distinct_points(sK2,sK0) ),
    inference(cnf_transformation,[],[f48]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem    : GEO178+2 : TPTP v8.1.0. Released v3.3.0.
% 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 : n018.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   : Mon Aug 29 21:28:39 EDT 2022
% 0.14/0.35  % CPUTime    : 
% 0.21/0.51  % (14474)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)
% 0.21/0.52  % (14482)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)
% 0.21/0.52  % (14466)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)
% 0.21/0.52  % (14482)First to succeed.
% 0.21/0.52  % (14477)fmb+10_1:1_nm=2:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.21/0.52  % (14461)lrs+10_1:1_gsp=on:sd=1:sgt=32:sos=on:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.21/0.52  % (14461)Also succeeded, but the first one will report.
% 0.21/0.52  % (14482)Refutation found. Thanks to Tanya!
% 0.21/0.52  % SZS status Theorem for theBenchmark
% 0.21/0.52  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.52  % (14482)------------------------------
% 0.21/0.52  % (14482)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.52  % (14482)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.52  % (14482)Termination reason: Refutation
% 0.21/0.52  
% 0.21/0.52  % (14482)Memory used [KB]: 5884
% 0.21/0.52  % (14482)Time elapsed: 0.114 s
% 0.21/0.52  % (14482)Instructions burned: 2 (million)
% 0.21/0.52  % (14482)------------------------------
% 0.21/0.52  % (14482)------------------------------
% 0.21/0.52  % (14459)Success in time 0.169 s
%------------------------------------------------------------------------------