%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : GEO178+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_sat --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 16:12:07 EDT 2022

% Result   : Theorem 0.20s 0.51s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   37 (   4 unt;   0 def)
%            Number of atoms       :   93 (   0 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :   96 (  40   ~;  29   |;  16   &)
%                                         (   3 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 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   :   52 (  43   !;   9   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f95,plain,
    $false,
    inference(avatar_sat_refutation,[],[f80,f90,f91,f94]) ).

fof(f94,plain,
    spl3_3,
    inference(avatar_contradiction_clause,[],[f93]) ).

fof(f93,plain,
    ( $false
    | spl3_3 ),
    inference(resolution,[],[f89,f60]) ).

fof(f60,plain,
    distinct_points(sK0,sK2),
    inference(cnf_transformation,[],[f47]) ).

fof(f47,plain,
    ( distinct_points(sK0,sK2)
    & apart_point_and_line(sK1,line_connecting(sK0,sK2))
    & ( ~ distinct_points(sK1,sK0)
      | ~ distinct_points(sK1,sK2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f35,f46]) ).

fof(f46,plain,
    ( ? [X0,X1,X2] :
        ( distinct_points(X0,X2)
        & apart_point_and_line(X1,line_connecting(X0,X2))
        & ( ~ distinct_points(X1,X0)
          | ~ distinct_points(X1,X2) ) )
   => ( distinct_points(sK0,sK2)
      & apart_point_and_line(sK1,line_connecting(sK0,sK2))
      & ( ~ distinct_points(sK1,sK0)
        | ~ distinct_points(sK1,sK2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f35,plain,
    ? [X0,X1,X2] :
      ( distinct_points(X0,X2)
      & apart_point_and_line(X1,line_connecting(X0,X2))
      & ( ~ distinct_points(X1,X0)
        | ~ distinct_points(X1,X2) ) ),
    inference(flattening,[],[f34]) ).

fof(f34,plain,
    ? [X1,X2,X0] :
      ( ( ~ distinct_points(X1,X0)
        | ~ distinct_points(X1,X2) )
      & distinct_points(X0,X2)
      & apart_point_and_line(X1,line_connecting(X0,X2)) ),
    inference(ennf_transformation,[],[f20]) ).

fof(f20,plain,
    ~ ! [X1,X2,X0] :
        ( ( distinct_points(X0,X2)
          & apart_point_and_line(X1,line_connecting(X0,X2)) )
       => ( distinct_points(X1,X2)
          & distinct_points(X1,X0) ) ),
    inference(rectify,[],[f16]) ).

fof(f16,negated_conjecture,
    ~ ! [X0,X2,X1] :
        ( ( apart_point_and_line(X2,line_connecting(X0,X1))
          & distinct_points(X0,X1) )
       => ( distinct_points(X2,X1)
          & distinct_points(X2,X0) ) ),
    inference(negated_conjecture,[],[f15]) ).

fof(f15,conjecture,
    ! [X0,X2,X1] :
      ( ( apart_point_and_line(X2,line_connecting(X0,X1))
        & distinct_points(X0,X1) )
     => ( distinct_points(X2,X1)
        & distinct_points(X2,X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).

fof(f89,plain,
    ( ~ distinct_points(sK0,sK2)
    | spl3_3 ),
    inference(avatar_component_clause,[],[f87]) ).

fof(f87,plain,
    ( spl3_3
  <=> distinct_points(sK0,sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_3])]) ).

fof(f91,plain,
    ( spl3_1
    | ~ spl3_3 ),
    inference(avatar_split_clause,[],[f83,f87,f73]) ).

fof(f73,plain,
    ( spl3_1
  <=> distinct_points(sK1,sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).

fof(f83,plain,
    ( ~ distinct_points(sK0,sK2)
    | distinct_points(sK1,sK2) ),
    inference(resolution,[],[f81,f71]) ).

fof(f71,plain,
    ! [X0,X1] :
      ( ~ apart_point_and_line(X0,line_connecting(X1,X0))
      | ~ distinct_points(X1,X0) ),
    inference(cnf_transformation,[],[f54]) ).

fof(f54,plain,
    ! [X0,X1] :
      ( ~ apart_point_and_line(X0,line_connecting(X1,X0))
      | ~ distinct_points(X1,X0) ),
    inference(rectify,[],[f36]) ).

fof(f36,plain,
    ! [X1,X0] :
      ( ~ apart_point_and_line(X1,line_connecting(X0,X1))
      | ~ distinct_points(X0,X1) ),
    inference(ennf_transformation,[],[f8]) ).

fof(f8,axiom,
    ! [X0,X1] :
      ( distinct_points(X0,X1)
     => ~ apart_point_and_line(X1,line_connecting(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ci2) ).

fof(f81,plain,
    ! [X0] :
      ( apart_point_and_line(X0,line_connecting(sK0,sK2))
      | distinct_points(sK1,X0) ),
    inference(resolution,[],[f64,f59]) ).

fof(f59,plain,
    apart_point_and_line(sK1,line_connecting(sK0,sK2)),
    inference(cnf_transformation,[],[f47]) ).

fof(f64,plain,
    ! [X2,X0,X1] :
      ( ~ apart_point_and_line(X1,X0)
      | distinct_points(X1,X2)
      | apart_point_and_line(X2,X0) ),
    inference(cnf_transformation,[],[f50]) ).

fof(f50,plain,
    ! [X0,X1,X2] :
      ( distinct_points(X1,X2)
      | apart_point_and_line(X2,X0)
      | ~ apart_point_and_line(X1,X0) ),
    inference(rectify,[],[f28]) ).

fof(f28,plain,
    ! [X1,X0,X2] :
      ( distinct_points(X0,X2)
      | apart_point_and_line(X2,X1)
      | ~ apart_point_and_line(X0,X1) ),
    inference(flattening,[],[f27]) ).

fof(f27,plain,
    ! [X1,X0,X2] :
      ( distinct_points(X0,X2)
      | apart_point_and_line(X2,X1)
      | ~ apart_point_and_line(X0,X1) ),
    inference(ennf_transformation,[],[f12]) ).

fof(f12,axiom,
    ! [X1,X0,X2] :
      ( apart_point_and_line(X0,X1)
     => ( distinct_points(X0,X2)
        | apart_point_and_line(X2,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ceq1) ).

fof(f90,plain,
    ( ~ spl3_3
    | spl3_2 ),
    inference(avatar_split_clause,[],[f82,f77,f87]) ).

fof(f77,plain,
    ( spl3_2
  <=> distinct_points(sK1,sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_2])]) ).

fof(f82,plain,
    ( distinct_points(sK1,sK0)
    | ~ distinct_points(sK0,sK2) ),
    inference(resolution,[],[f81,f62]) ).

fof(f62,plain,
    ! [X0,X1] :
      ( ~ apart_point_and_line(X0,line_connecting(X0,X1))
      | ~ distinct_points(X0,X1) ),
    inference(cnf_transformation,[],[f49]) ).

fof(f49,plain,
    ! [X0,X1] :
      ( ~ distinct_points(X0,X1)
      | ~ apart_point_and_line(X0,line_connecting(X0,X1)) ),
    inference(rectify,[],[f33]) ).

fof(f33,plain,
    ! [X1,X0] :
      ( ~ distinct_points(X1,X0)
      | ~ apart_point_and_line(X1,line_connecting(X1,X0)) ),
    inference(ennf_transformation,[],[f19]) ).

fof(f19,plain,
    ! [X1,X0] :
      ( distinct_points(X1,X0)
     => ~ apart_point_and_line(X1,line_connecting(X1,X0)) ),
    inference(rectify,[],[f7]) ).

fof(f7,axiom,
    ! [X1,X0] :
      ( distinct_points(X0,X1)
     => ~ apart_point_and_line(X0,line_connecting(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ci1) ).

fof(f80,plain,
    ( ~ spl3_1
    | ~ spl3_2 ),
    inference(avatar_split_clause,[],[f58,f77,f73]) ).

fof(f58,plain,
    ( ~ distinct_points(sK1,sK0)
    | ~ distinct_points(sK1,sK2) ),
    inference(cnf_transformation,[],[f47]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem    : GEO178+1 : TPTP v8.1.0. Released v3.3.0.
% 0.10/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --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   : Mon Aug 29 21:23:40 EDT 2022
% 0.14/0.34  % CPUTime    : 
% 0.20/0.50  % (25145)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 0.20/0.50  % (25154)ott+10_7:2_awrs=decay:awrsf=8:bd=preordered:drc=off:fd=preordered:fde=unused:fsr=off:slsq=on:slsqc=2:slsqr=5,8:sp=const_min:spb=units:to=lpo:i=355:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/355Mi)
% 0.20/0.50  % (25154)First to succeed.
% 0.20/0.51  % (25125)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.20/0.51  % (25154)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  % (25154)------------------------------
% 0.20/0.51  % (25154)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.51  % (25154)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.51  % (25154)Termination reason: Refutation
% 0.20/0.51  
% 0.20/0.51  % (25154)Memory used [KB]: 5373
% 0.20/0.51  % (25154)Time elapsed: 0.097 s
% 0.20/0.51  % (25154)Instructions burned: 2 (million)
% 0.20/0.51  % (25154)------------------------------
% 0.20/0.51  % (25154)------------------------------
% 0.20/0.51  % (25123)Success in time 0.159 s
%------------------------------------------------------------------------------