TSTP Solution File: GEO181+2 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : GEO181+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n020.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 11:14:30 EDT 2024

% Result   : Theorem 0.21s 0.40s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   20
% Syntax   : Number of formulae    :   99 (  11 unt;   0 def)
%            Number of atoms       :  352 (   0 equ)
%            Maximal formula atoms :    8 (   3 avg)
%            Number of connectives :  415 ( 162   ~; 215   |;  15   &)
%                                         (  11 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   6 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   15 (  14 usr;  12 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :  151 ( 142   !;   9   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1082,plain,
    $false,
    inference(avatar_sat_refutation,[],[f72,f78,f87,f112,f130,f138,f245,f323,f934,f1076,f1079,f1081]) ).

fof(f1081,plain,
    ~ spl3_29,
    inference(avatar_contradiction_clause,[],[f1080]) ).

fof(f1080,plain,
    ( $false
    | ~ spl3_29 ),
    inference(resolution,[],[f1071,f42]) ).

fof(f42,plain,
    ! [X0] : ~ distinct_points(X0,X0),
    inference(cnf_transformation,[],[f1]) ).

fof(f1,axiom,
    ! [X0] : ~ distinct_points(X0,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart1) ).

fof(f1071,plain,
    ( distinct_points(sK0,sK0)
    | ~ spl3_29 ),
    inference(avatar_component_clause,[],[f1069]) ).

fof(f1069,plain,
    ( spl3_29
  <=> distinct_points(sK0,sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_29])]) ).

fof(f1079,plain,
    ~ spl3_30,
    inference(avatar_contradiction_clause,[],[f1078]) ).

fof(f1078,plain,
    ( $false
    | ~ spl3_30 ),
    inference(resolution,[],[f1075,f42]) ).

fof(f1075,plain,
    ( distinct_points(sK2,sK2)
    | ~ spl3_30 ),
    inference(avatar_component_clause,[],[f1073]) ).

fof(f1073,plain,
    ( spl3_30
  <=> distinct_points(sK2,sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_30])]) ).

fof(f1076,plain,
    ( spl3_29
    | spl3_30
    | ~ spl3_1
    | ~ spl3_14
    | ~ spl3_26 ),
    inference(avatar_split_clause,[],[f1008,f932,f321,f65,f1073,f1069]) ).

fof(f65,plain,
    ( spl3_1
  <=> distinct_points(sK0,sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).

fof(f321,plain,
    ( spl3_14
  <=> ! [X0] :
        ( distinct_points(X0,sK2)
        | ~ apart_point_and_line(X0,line_connecting(sK0,sK2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_14])]) ).

fof(f932,plain,
    ( spl3_26
  <=> ! [X0] :
        ( ~ distinct_lines(line_connecting(X0,sK1),line_connecting(sK0,sK2))
        | distinct_points(sK0,X0)
        | ~ distinct_points(X0,sK1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_26])]) ).

fof(f1008,plain,
    ( ~ distinct_points(sK0,sK1)
    | distinct_points(sK2,sK2)
    | distinct_points(sK0,sK0)
    | ~ spl3_14
    | ~ spl3_26 ),
    inference(resolution,[],[f937,f38]) ).

fof(f38,plain,
    apart_point_and_line(sK2,line_connecting(sK0,sK1)),
    inference(cnf_transformation,[],[f36]) ).

fof(f36,plain,
    ( ~ apart_point_and_line(sK1,line_connecting(sK0,sK2))
    & apart_point_and_line(sK2,line_connecting(sK0,sK1))
    & distinct_points(sK0,sK1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f17,f35]) ).

fof(f35,plain,
    ( ? [X0,X1,X2] :
        ( ~ apart_point_and_line(X1,line_connecting(X0,X2))
        & apart_point_and_line(X2,line_connecting(X0,X1))
        & distinct_points(X0,X1) )
   => ( ~ apart_point_and_line(sK1,line_connecting(sK0,sK2))
      & apart_point_and_line(sK2,line_connecting(sK0,sK1))
      & distinct_points(sK0,sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f17,plain,
    ? [X0,X1,X2] :
      ( ~ apart_point_and_line(X1,line_connecting(X0,X2))
      & apart_point_and_line(X2,line_connecting(X0,X1))
      & distinct_points(X0,X1) ),
    inference(flattening,[],[f16]) ).

fof(f16,plain,
    ? [X0,X1,X2] :
      ( ~ apart_point_and_line(X1,line_connecting(X0,X2))
      & apart_point_and_line(X2,line_connecting(X0,X1))
      & distinct_points(X0,X1) ),
    inference(ennf_transformation,[],[f14]) ).

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

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

fof(f937,plain,
    ( ! [X0,X1] :
        ( ~ apart_point_and_line(X1,line_connecting(X0,sK1))
        | ~ distinct_points(X0,sK1)
        | distinct_points(X1,sK2)
        | distinct_points(sK0,X0) )
    | ~ spl3_14
    | ~ spl3_26 ),
    inference(resolution,[],[f933,f347]) ).

fof(f347,plain,
    ( ! [X0,X1] :
        ( distinct_lines(X1,line_connecting(sK0,sK2))
        | distinct_points(X0,sK2)
        | ~ apart_point_and_line(X0,X1) )
    | ~ spl3_14 ),
    inference(resolution,[],[f322,f51]) ).

fof(f51,plain,
    ! [X2,X0,X1] :
      ( apart_point_and_line(X0,X2)
      | distinct_lines(X1,X2)
      | ~ apart_point_and_line(X0,X1) ),
    inference(cnf_transformation,[],[f30]) ).

fof(f30,plain,
    ! [X0,X1,X2] :
      ( apart_point_and_line(X0,X2)
      | distinct_lines(X1,X2)
      | ~ apart_point_and_line(X0,X1) ),
    inference(flattening,[],[f29]) ).

fof(f29,plain,
    ! [X0,X1,X2] :
      ( apart_point_and_line(X0,X2)
      | distinct_lines(X1,X2)
      | ~ apart_point_and_line(X0,X1) ),
    inference(ennf_transformation,[],[f11]) ).

fof(f11,axiom,
    ! [X0,X1,X2] :
      ( apart_point_and_line(X0,X1)
     => ( apart_point_and_line(X0,X2)
        | distinct_lines(X1,X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ceq2) ).

fof(f322,plain,
    ( ! [X0] :
        ( ~ apart_point_and_line(X0,line_connecting(sK0,sK2))
        | distinct_points(X0,sK2) )
    | ~ spl3_14 ),
    inference(avatar_component_clause,[],[f321]) ).

fof(f933,plain,
    ( ! [X0] :
        ( ~ distinct_lines(line_connecting(X0,sK1),line_connecting(sK0,sK2))
        | distinct_points(sK0,X0)
        | ~ distinct_points(X0,sK1) )
    | ~ spl3_26 ),
    inference(avatar_component_clause,[],[f932]) ).

fof(f934,plain,
    ( ~ spl3_1
    | spl3_26
    | ~ spl3_6 ),
    inference(avatar_split_clause,[],[f929,f136,f932,f65]) ).

fof(f136,plain,
    ( spl3_6
  <=> ! [X0,X1] :
        ( apart_point_and_line(sK1,X0)
        | distinct_points(X1,sK0)
        | ~ distinct_points(X1,sK1)
        | ~ distinct_lines(X0,line_connecting(sK0,sK2))
        | apart_point_and_line(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_6])]) ).

fof(f929,plain,
    ( ! [X0] :
        ( ~ distinct_lines(line_connecting(X0,sK1),line_connecting(sK0,sK2))
        | ~ distinct_points(sK0,sK1)
        | ~ distinct_points(X0,sK1)
        | distinct_points(sK0,X0) )
    | ~ spl3_6 ),
    inference(resolution,[],[f632,f42]) ).

fof(f632,plain,
    ( ! [X0,X1] :
        ( distinct_points(X1,sK0)
        | ~ distinct_lines(line_connecting(X0,sK1),line_connecting(sK0,sK2))
        | ~ distinct_points(X1,sK1)
        | ~ distinct_points(X0,sK1)
        | distinct_points(X1,X0) )
    | ~ spl3_6 ),
    inference(resolution,[],[f240,f42]) ).

fof(f240,plain,
    ( ! [X2,X0,X1] :
        ( distinct_points(sK1,X2)
        | ~ distinct_lines(line_connecting(X1,X2),line_connecting(sK0,sK2))
        | distinct_points(X0,sK0)
        | ~ distinct_points(X0,sK1)
        | ~ distinct_points(X1,X2)
        | distinct_points(X0,X1) )
    | ~ spl3_6 ),
    inference(duplicate_literal_removal,[],[f239]) ).

fof(f239,plain,
    ( ! [X2,X0,X1] :
        ( ~ distinct_points(X0,sK1)
        | ~ distinct_lines(line_connecting(X1,X2),line_connecting(sK0,sK2))
        | distinct_points(X0,sK0)
        | distinct_points(sK1,X2)
        | ~ distinct_points(X1,X2)
        | distinct_points(X0,X1)
        | ~ distinct_points(X1,X2) )
    | ~ spl3_6 ),
    inference(resolution,[],[f141,f49]) ).

fof(f49,plain,
    ! [X2,X0,X1] :
      ( ~ apart_point_and_line(X2,line_connecting(X0,X1))
      | distinct_points(X2,X0)
      | ~ distinct_points(X0,X1) ),
    inference(cnf_transformation,[],[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(flattening,[],[f27]) ).

fof(f27,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,[],[f7]) ).

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

fof(f141,plain,
    ( ! [X2,X0,X1] :
        ( apart_point_and_line(X0,line_connecting(X1,X2))
        | ~ distinct_points(X0,sK1)
        | ~ distinct_lines(line_connecting(X1,X2),line_connecting(sK0,sK2))
        | distinct_points(X0,sK0)
        | distinct_points(sK1,X2)
        | ~ distinct_points(X1,X2) )
    | ~ spl3_6 ),
    inference(resolution,[],[f137,f50]) ).

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

fof(f137,plain,
    ( ! [X0,X1] :
        ( apart_point_and_line(sK1,X0)
        | distinct_points(X1,sK0)
        | ~ distinct_points(X1,sK1)
        | ~ distinct_lines(X0,line_connecting(sK0,sK2))
        | apart_point_and_line(X1,X0) )
    | ~ spl3_6 ),
    inference(avatar_component_clause,[],[f136]) ).

fof(f323,plain,
    ( spl3_14
    | ~ spl3_3
    | ~ spl3_13 ),
    inference(avatar_split_clause,[],[f319,f243,f84,f321]) ).

fof(f84,plain,
    ( spl3_3
  <=> distinct_points(sK2,sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_3])]) ).

fof(f243,plain,
    ( spl3_13
  <=> ! [X0] :
        ( ~ distinct_lines(line_connecting(X0,sK1),line_connecting(sK0,sK2))
        | distinct_points(sK2,X0)
        | ~ distinct_points(X0,sK1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_13])]) ).

fof(f319,plain,
    ( ! [X0] :
        ( ~ distinct_points(sK2,sK1)
        | distinct_points(X0,sK2)
        | ~ apart_point_and_line(X0,line_connecting(sK0,sK2)) )
    | ~ spl3_13 ),
    inference(resolution,[],[f308,f42]) ).

fof(f308,plain,
    ( ! [X0,X1] :
        ( distinct_points(sK2,X0)
        | ~ distinct_points(X0,sK1)
        | distinct_points(X1,X0)
        | ~ apart_point_and_line(X1,line_connecting(sK0,sK2)) )
    | ~ spl3_13 ),
    inference(duplicate_literal_removal,[],[f306]) ).

fof(f306,plain,
    ( ! [X0,X1] :
        ( distinct_points(sK2,X0)
        | ~ distinct_points(X0,sK1)
        | ~ distinct_points(X0,sK1)
        | distinct_points(X1,X0)
        | ~ apart_point_and_line(X1,line_connecting(sK0,sK2)) )
    | ~ spl3_13 ),
    inference(resolution,[],[f294,f63]) ).

fof(f63,plain,
    ! [X2,X3,X0,X1] :
      ( distinct_lines(X3,line_connecting(X1,X2))
      | ~ distinct_points(X1,X2)
      | distinct_points(X0,X1)
      | ~ apart_point_and_line(X0,X3) ),
    inference(resolution,[],[f49,f51]) ).

fof(f294,plain,
    ( ! [X0] :
        ( ~ distinct_lines(line_connecting(sK0,sK2),line_connecting(X0,sK1))
        | distinct_points(sK2,X0)
        | ~ distinct_points(X0,sK1) )
    | ~ spl3_13 ),
    inference(resolution,[],[f250,f41]) ).

fof(f41,plain,
    ! [X0] : ~ distinct_lines(X0,X0),
    inference(cnf_transformation,[],[f2]) ).

fof(f2,axiom,
    ! [X0] : ~ distinct_lines(X0,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart2) ).

fof(f250,plain,
    ( ! [X0,X1] :
        ( distinct_lines(X1,line_connecting(sK0,sK2))
        | ~ distinct_points(X0,sK1)
        | distinct_points(sK2,X0)
        | ~ distinct_lines(X1,line_connecting(X0,sK1)) )
    | ~ spl3_13 ),
    inference(resolution,[],[f244,f47]) ).

fof(f47,plain,
    ! [X2,X0,X1] :
      ( distinct_lines(X1,X2)
      | distinct_lines(X0,X2)
      | ~ distinct_lines(X0,X1) ),
    inference(cnf_transformation,[],[f24]) ).

fof(f24,plain,
    ! [X0,X1,X2] :
      ( distinct_lines(X1,X2)
      | distinct_lines(X0,X2)
      | ~ distinct_lines(X0,X1) ),
    inference(flattening,[],[f23]) ).

fof(f23,plain,
    ! [X0,X1,X2] :
      ( distinct_lines(X1,X2)
      | distinct_lines(X0,X2)
      | ~ distinct_lines(X0,X1) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f5,axiom,
    ! [X0,X1,X2] :
      ( distinct_lines(X0,X1)
     => ( distinct_lines(X1,X2)
        | distinct_lines(X0,X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart5) ).

fof(f244,plain,
    ( ! [X0] :
        ( ~ distinct_lines(line_connecting(X0,sK1),line_connecting(sK0,sK2))
        | distinct_points(sK2,X0)
        | ~ distinct_points(X0,sK1) )
    | ~ spl3_13 ),
    inference(avatar_component_clause,[],[f243]) ).

fof(f245,plain,
    ( ~ spl3_3
    | spl3_13
    | ~ spl3_5 ),
    inference(avatar_split_clause,[],[f235,f110,f243,f84]) ).

fof(f110,plain,
    ( spl3_5
  <=> ! [X0,X1] :
        ( apart_point_and_line(sK1,X0)
        | distinct_points(X1,sK2)
        | ~ distinct_points(X1,sK1)
        | ~ distinct_lines(X0,line_connecting(sK0,sK2))
        | apart_point_and_line(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_5])]) ).

fof(f235,plain,
    ( ! [X0] :
        ( ~ distinct_lines(line_connecting(X0,sK1),line_connecting(sK0,sK2))
        | ~ distinct_points(sK2,sK1)
        | ~ distinct_points(X0,sK1)
        | distinct_points(sK2,X0) )
    | ~ spl3_5 ),
    inference(resolution,[],[f228,f42]) ).

fof(f228,plain,
    ( ! [X0,X1] :
        ( distinct_points(X1,sK2)
        | ~ distinct_lines(line_connecting(X0,sK1),line_connecting(sK0,sK2))
        | ~ distinct_points(X1,sK1)
        | ~ distinct_points(X0,sK1)
        | distinct_points(X1,X0) )
    | ~ spl3_5 ),
    inference(resolution,[],[f224,f42]) ).

fof(f224,plain,
    ( ! [X2,X0,X1] :
        ( distinct_points(sK1,X2)
        | ~ distinct_lines(line_connecting(X1,X2),line_connecting(sK0,sK2))
        | distinct_points(X0,sK2)
        | ~ distinct_points(X0,sK1)
        | ~ distinct_points(X1,X2)
        | distinct_points(X0,X1) )
    | ~ spl3_5 ),
    inference(duplicate_literal_removal,[],[f223]) ).

fof(f223,plain,
    ( ! [X2,X0,X1] :
        ( ~ distinct_points(X0,sK1)
        | ~ distinct_lines(line_connecting(X1,X2),line_connecting(sK0,sK2))
        | distinct_points(X0,sK2)
        | distinct_points(sK1,X2)
        | ~ distinct_points(X1,X2)
        | distinct_points(X0,X1)
        | ~ distinct_points(X1,X2) )
    | ~ spl3_5 ),
    inference(resolution,[],[f133,f49]) ).

fof(f133,plain,
    ( ! [X2,X0,X1] :
        ( apart_point_and_line(X0,line_connecting(X1,X2))
        | ~ distinct_points(X0,sK1)
        | ~ distinct_lines(line_connecting(X1,X2),line_connecting(sK0,sK2))
        | distinct_points(X0,sK2)
        | distinct_points(sK1,X2)
        | ~ distinct_points(X1,X2) )
    | ~ spl3_5 ),
    inference(resolution,[],[f111,f50]) ).

fof(f111,plain,
    ( ! [X0,X1] :
        ( apart_point_and_line(sK1,X0)
        | distinct_points(X1,sK2)
        | ~ distinct_points(X1,sK1)
        | ~ distinct_lines(X0,line_connecting(sK0,sK2))
        | apart_point_and_line(X1,X0) )
    | ~ spl3_5 ),
    inference(avatar_component_clause,[],[f110]) ).

fof(f138,plain,
    ( ~ spl3_4
    | spl3_6 ),
    inference(avatar_split_clause,[],[f97,f136,f106]) ).

fof(f106,plain,
    ( spl3_4
  <=> distinct_points(sK0,sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_4])]) ).

fof(f97,plain,
    ! [X0,X1] :
      ( apart_point_and_line(sK1,X0)
      | apart_point_and_line(X1,X0)
      | ~ distinct_lines(X0,line_connecting(sK0,sK2))
      | ~ distinct_points(X1,sK1)
      | distinct_points(X1,sK0)
      | ~ distinct_points(sK0,sK2) ),
    inference(resolution,[],[f79,f49]) ).

fof(f79,plain,
    ! [X0,X1] :
      ( apart_point_and_line(X1,line_connecting(sK0,sK2))
      | apart_point_and_line(sK1,X0)
      | apart_point_and_line(X1,X0)
      | ~ distinct_lines(X0,line_connecting(sK0,sK2))
      | ~ distinct_points(X1,sK1) ),
    inference(resolution,[],[f53,f39]) ).

fof(f39,plain,
    ~ apart_point_and_line(sK1,line_connecting(sK0,sK2)),
    inference(cnf_transformation,[],[f36]) ).

fof(f53,plain,
    ! [X2,X3,X0,X1] :
      ( apart_point_and_line(X1,X3)
      | apart_point_and_line(X1,X2)
      | apart_point_and_line(X0,X3)
      | apart_point_and_line(X0,X2)
      | ~ distinct_lines(X2,X3)
      | ~ distinct_points(X0,X1) ),
    inference(cnf_transformation,[],[f34]) ).

fof(f34,plain,
    ! [X0,X1,X2,X3] :
      ( apart_point_and_line(X1,X3)
      | apart_point_and_line(X1,X2)
      | apart_point_and_line(X0,X3)
      | apart_point_and_line(X0,X2)
      | ~ distinct_lines(X2,X3)
      | ~ distinct_points(X0,X1) ),
    inference(flattening,[],[f33]) ).

fof(f33,plain,
    ! [X0,X1,X2,X3] :
      ( apart_point_and_line(X1,X3)
      | apart_point_and_line(X1,X2)
      | apart_point_and_line(X0,X3)
      | apart_point_and_line(X0,X2)
      | ~ distinct_lines(X2,X3)
      | ~ distinct_points(X0,X1) ),
    inference(ennf_transformation,[],[f15]) ).

fof(f15,plain,
    ! [X0,X1,X2,X3] :
      ( ( distinct_lines(X2,X3)
        & distinct_points(X0,X1) )
     => ( apart_point_and_line(X1,X3)
        | apart_point_and_line(X1,X2)
        | apart_point_and_line(X0,X3)
        | apart_point_and_line(X0,X2) ) ),
    inference(rectify,[],[f9]) ).

fof(f9,axiom,
    ! [X0,X1,X3,X4] :
      ( ( distinct_lines(X3,X4)
        & distinct_points(X0,X1) )
     => ( apart_point_and_line(X1,X4)
        | apart_point_and_line(X1,X3)
        | apart_point_and_line(X0,X4)
        | apart_point_and_line(X0,X3) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cu1) ).

fof(f130,plain,
    ( ~ spl3_2
    | spl3_4 ),
    inference(avatar_contradiction_clause,[],[f125]) ).

fof(f125,plain,
    ( $false
    | ~ spl3_2
    | spl3_4 ),
    inference(resolution,[],[f123,f71]) ).

fof(f71,plain,
    ( distinct_points(sK2,sK0)
    | ~ spl3_2 ),
    inference(avatar_component_clause,[],[f69]) ).

fof(f69,plain,
    ( spl3_2
  <=> distinct_points(sK2,sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_2])]) ).

fof(f123,plain,
    ( ~ distinct_points(sK2,sK0)
    | spl3_4 ),
    inference(resolution,[],[f122,f42]) ).

fof(f122,plain,
    ( ! [X0] :
        ( distinct_points(X0,sK2)
        | ~ distinct_points(X0,sK0) )
    | spl3_4 ),
    inference(resolution,[],[f108,f48]) ).

fof(f48,plain,
    ! [X2,X0,X1] :
      ( distinct_points(X1,X2)
      | distinct_points(X0,X2)
      | ~ distinct_points(X0,X1) ),
    inference(cnf_transformation,[],[f26]) ).

fof(f26,plain,
    ! [X0,X1,X2] :
      ( distinct_points(X1,X2)
      | distinct_points(X0,X2)
      | ~ distinct_points(X0,X1) ),
    inference(flattening,[],[f25]) ).

fof(f25,plain,
    ! [X0,X1,X2] :
      ( distinct_points(X1,X2)
      | distinct_points(X0,X2)
      | ~ distinct_points(X0,X1) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X0,X1,X2] :
      ( distinct_points(X0,X1)
     => ( distinct_points(X1,X2)
        | distinct_points(X0,X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart4) ).

fof(f108,plain,
    ( ~ distinct_points(sK0,sK2)
    | spl3_4 ),
    inference(avatar_component_clause,[],[f106]) ).

fof(f112,plain,
    ( ~ spl3_4
    | spl3_5 ),
    inference(avatar_split_clause,[],[f96,f110,f106]) ).

fof(f96,plain,
    ! [X0,X1] :
      ( apart_point_and_line(sK1,X0)
      | apart_point_and_line(X1,X0)
      | ~ distinct_lines(X0,line_connecting(sK0,sK2))
      | ~ distinct_points(X1,sK1)
      | distinct_points(X1,sK2)
      | ~ distinct_points(sK0,sK2) ),
    inference(resolution,[],[f79,f50]) ).

fof(f87,plain,
    ( ~ spl3_1
    | spl3_3 ),
    inference(avatar_split_clause,[],[f73,f84,f65]) ).

fof(f73,plain,
    ( distinct_points(sK2,sK1)
    | ~ distinct_points(sK0,sK1) ),
    inference(resolution,[],[f50,f38]) ).

fof(f78,plain,
    spl3_1,
    inference(avatar_contradiction_clause,[],[f76]) ).

fof(f76,plain,
    ( $false
    | spl3_1 ),
    inference(resolution,[],[f67,f37]) ).

fof(f37,plain,
    distinct_points(sK0,sK1),
    inference(cnf_transformation,[],[f36]) ).

fof(f67,plain,
    ( ~ distinct_points(sK0,sK1)
    | spl3_1 ),
    inference(avatar_component_clause,[],[f65]) ).

fof(f72,plain,
    ( ~ spl3_1
    | spl3_2 ),
    inference(avatar_split_clause,[],[f61,f69,f65]) ).

fof(f61,plain,
    ( distinct_points(sK2,sK0)
    | ~ distinct_points(sK0,sK1) ),
    inference(resolution,[],[f49,f38]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem    : GEO181+2 : TPTP v8.1.2. Released v3.3.0.
% 0.14/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35  % Computer : n020.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit   : 300
% 0.15/0.35  % WCLimit    : 300
% 0.15/0.35  % DateTime   : Tue Apr 30 05:45:32 EDT 2024
% 0.15/0.35  % CPUTime    : 
% 0.15/0.36  % (16691)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.37  % (16698)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_1451 on theBenchmark for (1451ds/0Mi)
% 0.21/0.37  TRYING [1]
% 0.21/0.37  TRYING [2]
% 0.21/0.37  TRYING [3]
% 0.21/0.37  TRYING [4]
% 0.21/0.37  TRYING [5]
% 0.21/0.37  % (16692)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.21/0.37  % (16695)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.21/0.37  % (16694)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)
% 0.21/0.37  % (16693)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.21/0.37  % (16696)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.21/0.37  % (16697)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.21/0.37  TRYING [1]
% 0.21/0.37  TRYING [2]
% 0.21/0.37  Detected minimum model sizes of [1,1,1,1]
% 0.21/0.37  Detected maximum model sizes of [max,3,max,max]
% 0.21/0.37  Detected minimum model sizes of [1,1,1,1]
% 0.21/0.37  Detected maximum model sizes of [max,3,max,max]
% 0.21/0.37  TRYING [1,1,1,1]
% 0.21/0.37  TRYING [1,1,1,1]
% 0.21/0.37  TRYING [2,2,1,1]
% 0.21/0.37  TRYING [2,2,1,1]
% 0.21/0.37  TRYING [3]
% 0.21/0.37  TRYING [3,2,1,1]
% 0.21/0.37  TRYING [3,2,1,1]
% 0.21/0.37  TRYING [4,2,1,1]
% 0.21/0.38  TRYING [4,2,1,1]
% 0.21/0.38  TRYING [4]
% 0.21/0.38  TRYING [3,3,1,1]
% 0.21/0.38  TRYING [3,3,1,1]
% 0.21/0.38  TRYING [6]
% 0.21/0.38  TRYING [5,2,1,1]
% 0.21/0.38  TRYING [5,2,1,1]
% 0.21/0.38  TRYING [4,3,1,1]
% 0.21/0.38  TRYING [5]
% 0.21/0.38  TRYING [4,3,1,1]
% 0.21/0.38  TRYING [6,2,1,1]
% 0.21/0.38  TRYING [6,2,1,1]
% 0.21/0.38  TRYING [5,3,1,1]
% 0.21/0.38  TRYING [5,3,1,1]
% 0.21/0.38  TRYING [7,2,1,1]
% 0.21/0.38  TRYING [6]
% 0.21/0.38  TRYING [7,2,1,1]
% 0.21/0.39  TRYING [6,3,1,1]
% 0.21/0.39  TRYING [7]
% 0.21/0.39  TRYING [6,3,1,1]
% 0.21/0.39  TRYING [8,2,1,1]
% 0.21/0.39  TRYING [8,2,1,1]
% 0.21/0.39  TRYING [7,3,1,1]
% 0.21/0.39  TRYING [7,3,1,1]
% 0.21/0.40  TRYING [7]
% 0.21/0.40  TRYING [9,2,1,1]
% 0.21/0.40  TRYING [9,2,1,1]
% 0.21/0.40  % (16694)First to succeed.
% 0.21/0.40  TRYING [8,3,1,1]
% 0.21/0.40  TRYING [8,3,1,1]
% 0.21/0.40  % (16694)Refutation found. Thanks to Tanya!
% 0.21/0.40  % SZS status Theorem for theBenchmark
% 0.21/0.40  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.40  % (16694)------------------------------
% 0.21/0.40  % (16694)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.21/0.40  % (16694)Termination reason: Refutation
% 0.21/0.40  
% 0.21/0.40  % (16694)Memory used [KB]: 1213
% 0.21/0.40  % (16694)Time elapsed: 0.030 s
% 0.21/0.40  % (16694)Instructions burned: 54 (million)
% 0.21/0.40  % (16694)------------------------------
% 0.21/0.40  % (16694)------------------------------
% 0.21/0.40  % (16691)Success in time 0.047 s
%------------------------------------------------------------------------------