TSTP Solution File: GEO172+1 by Vampire-SAT---4.8

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%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : GEO172+1 : 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 : n026.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 11:14:25 EDT 2024

% Result   : Theorem 0.15s 0.37s
% Output   : Refutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   53 (  13 unt;   0 def)
%            Number of atoms       :  143 (   0 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  146 (  56   ~;  58   |;  21   &)
%                                         (   2 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    7 (   6 usr;   3 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :   79 (  70   !;   9   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f129,plain,
    $false,
    inference(avatar_sat_refutation,[],[f111,f123,f128]) ).

fof(f128,plain,
    ~ spl3_1,
    inference(avatar_contradiction_clause,[],[f127]) ).

fof(f127,plain,
    ( $false
    | ~ spl3_1 ),
    inference(subsumption_resolution,[],[f124,f40]) ).

fof(f40,plain,
    convergent_lines(sK0,sK1),
    inference(cnf_transformation,[],[f39]) ).

fof(f39,plain,
    ( distinct_points(sK2,intersection_point(sK0,sK1))
    & ~ apart_point_and_line(sK2,sK1)
    & ~ apart_point_and_line(sK2,sK0)
    & convergent_lines(sK0,sK1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f19,f38]) ).

fof(f38,plain,
    ( ? [X0,X1,X2] :
        ( distinct_points(X2,intersection_point(X0,X1))
        & ~ apart_point_and_line(X2,X1)
        & ~ apart_point_and_line(X2,X0)
        & convergent_lines(X0,X1) )
   => ( distinct_points(sK2,intersection_point(sK0,sK1))
      & ~ apart_point_and_line(sK2,sK1)
      & ~ apart_point_and_line(sK2,sK0)
      & convergent_lines(sK0,sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f19,plain,
    ? [X0,X1,X2] :
      ( distinct_points(X2,intersection_point(X0,X1))
      & ~ apart_point_and_line(X2,X1)
      & ~ apart_point_and_line(X2,X0)
      & convergent_lines(X0,X1) ),
    inference(flattening,[],[f18]) ).

fof(f18,plain,
    ? [X0,X1,X2] :
      ( distinct_points(X2,intersection_point(X0,X1))
      & ~ apart_point_and_line(X2,X1)
      & ~ apart_point_and_line(X2,X0)
      & convergent_lines(X0,X1) ),
    inference(ennf_transformation,[],[f16]) ).

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

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

fof(f124,plain,
    ( ~ convergent_lines(sK0,sK1)
    | ~ spl3_1 ),
    inference(resolution,[],[f93,f49]) ).

fof(f49,plain,
    ! [X0,X1] :
      ( ~ apart_point_and_line(intersection_point(X0,X1),X0)
      | ~ convergent_lines(X0,X1) ),
    inference(cnf_transformation,[],[f22]) ).

fof(f22,plain,
    ! [X0,X1] :
      ( ~ apart_point_and_line(intersection_point(X0,X1),X0)
      | ~ convergent_lines(X0,X1) ),
    inference(ennf_transformation,[],[f9]) ).

fof(f9,axiom,
    ! [X0,X1] :
      ( convergent_lines(X0,X1)
     => ~ apart_point_and_line(intersection_point(X0,X1),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ci3) ).

fof(f93,plain,
    ( apart_point_and_line(intersection_point(sK0,sK1),sK0)
    | ~ spl3_1 ),
    inference(avatar_component_clause,[],[f91]) ).

fof(f91,plain,
    ( spl3_1
  <=> apart_point_and_line(intersection_point(sK0,sK1),sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).

fof(f123,plain,
    ~ spl3_2,
    inference(avatar_contradiction_clause,[],[f122]) ).

fof(f122,plain,
    ( $false
    | ~ spl3_2 ),
    inference(subsumption_resolution,[],[f119,f40]) ).

fof(f119,plain,
    ( ~ convergent_lines(sK0,sK1)
    | ~ spl3_2 ),
    inference(resolution,[],[f97,f50]) ).

fof(f50,plain,
    ! [X0,X1] :
      ( ~ apart_point_and_line(intersection_point(X0,X1),X1)
      | ~ convergent_lines(X0,X1) ),
    inference(cnf_transformation,[],[f23]) ).

fof(f23,plain,
    ! [X0,X1] :
      ( ~ apart_point_and_line(intersection_point(X0,X1),X1)
      | ~ convergent_lines(X0,X1) ),
    inference(ennf_transformation,[],[f10]) ).

fof(f10,axiom,
    ! [X0,X1] :
      ( convergent_lines(X0,X1)
     => ~ apart_point_and_line(intersection_point(X0,X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ci4) ).

fof(f97,plain,
    ( apart_point_and_line(intersection_point(sK0,sK1),sK1)
    | ~ spl3_2 ),
    inference(avatar_component_clause,[],[f95]) ).

fof(f95,plain,
    ( spl3_2
  <=> apart_point_and_line(intersection_point(sK0,sK1),sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_2])]) ).

fof(f111,plain,
    ( spl3_2
    | spl3_1 ),
    inference(avatar_split_clause,[],[f110,f91,f95]) ).

fof(f110,plain,
    ( apart_point_and_line(intersection_point(sK0,sK1),sK0)
    | apart_point_and_line(intersection_point(sK0,sK1),sK1) ),
    inference(subsumption_resolution,[],[f109,f41]) ).

fof(f41,plain,
    ~ apart_point_and_line(sK2,sK0),
    inference(cnf_transformation,[],[f39]) ).

fof(f109,plain,
    ( apart_point_and_line(sK2,sK0)
    | apart_point_and_line(intersection_point(sK0,sK1),sK0)
    | apart_point_and_line(intersection_point(sK0,sK1),sK1) ),
    inference(subsumption_resolution,[],[f86,f42]) ).

fof(f42,plain,
    ~ apart_point_and_line(sK2,sK1),
    inference(cnf_transformation,[],[f39]) ).

fof(f86,plain,
    ( apart_point_and_line(sK2,sK1)
    | apart_point_and_line(sK2,sK0)
    | apart_point_and_line(intersection_point(sK0,sK1),sK0)
    | apart_point_and_line(intersection_point(sK0,sK1),sK1) ),
    inference(resolution,[],[f73,f68]) ).

fof(f68,plain,
    distinct_lines(sK0,sK1),
    inference(resolution,[],[f63,f44]) ).

fof(f44,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(f63,plain,
    ! [X0] :
      ( distinct_lines(sK1,X0)
      | distinct_lines(sK0,X0) ),
    inference(resolution,[],[f59,f51]) ).

fof(f51,plain,
    ! [X2,X0,X1] :
      ( ~ distinct_lines(X0,X1)
      | distinct_lines(X0,X2)
      | distinct_lines(X1,X2) ),
    inference(cnf_transformation,[],[f25]) ).

fof(f25,plain,
    ! [X0,X1,X2] :
      ( distinct_lines(X1,X2)
      | distinct_lines(X0,X2)
      | ~ distinct_lines(X0,X1) ),
    inference(flattening,[],[f24]) ).

fof(f24,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(f59,plain,
    distinct_lines(sK1,sK0),
    inference(resolution,[],[f58,f46]) ).

fof(f46,plain,
    ! [X0] : ~ convergent_lines(X0,X0),
    inference(cnf_transformation,[],[f3]) ).

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

fof(f58,plain,
    ! [X0] :
      ( convergent_lines(sK0,X0)
      | distinct_lines(sK1,X0) ),
    inference(resolution,[],[f52,f40]) ).

fof(f52,plain,
    ! [X2,X0,X1] :
      ( ~ convergent_lines(X0,X1)
      | distinct_lines(X1,X2)
      | convergent_lines(X0,X2) ),
    inference(cnf_transformation,[],[f27]) ).

fof(f27,plain,
    ! [X0,X1,X2] :
      ( convergent_lines(X0,X2)
      | distinct_lines(X1,X2)
      | ~ convergent_lines(X0,X1) ),
    inference(flattening,[],[f26]) ).

fof(f26,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/sandbox/benchmark/theBenchmark.p',ceq3) ).

fof(f73,plain,
    ! [X0,X1] :
      ( ~ distinct_lines(X0,X1)
      | apart_point_and_line(sK2,X1)
      | apart_point_and_line(sK2,X0)
      | apart_point_and_line(intersection_point(sK0,sK1),X0)
      | apart_point_and_line(intersection_point(sK0,sK1),X1) ),
    inference(resolution,[],[f57,f43]) ).

fof(f43,plain,
    distinct_points(sK2,intersection_point(sK0,sK1)),
    inference(cnf_transformation,[],[f39]) ).

fof(f57,plain,
    ! [X2,X3,X0,X1] :
      ( ~ distinct_points(X0,X1)
      | apart_point_and_line(X1,X2)
      | apart_point_and_line(X0,X3)
      | apart_point_and_line(X0,X2)
      | ~ distinct_lines(X2,X3)
      | apart_point_and_line(X1,X3) ),
    inference(cnf_transformation,[],[f37]) ).

fof(f37,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,[],[f36]) ).

fof(f36,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,[],[f17]) ).

fof(f17,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,[],[f11]) ).

fof(f11,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) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : GEO172+1 : TPTP v8.1.2. Released v3.3.0.
% 0.03/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35  % Computer : n026.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 06:02:34 EDT 2024
% 0.15/0.35  % CPUTime    : 
% 0.15/0.35  % (29120)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.36  % (29126)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.15/0.37  % (29126)First to succeed.
% 0.15/0.37  % (29126)Refutation found. Thanks to Tanya!
% 0.15/0.37  % SZS status Theorem for theBenchmark
% 0.15/0.37  % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.37  % (29126)------------------------------
% 0.15/0.37  % (29126)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.15/0.37  % (29126)Termination reason: Refutation
% 0.15/0.37  
% 0.15/0.37  % (29126)Memory used [KB]: 788
% 0.15/0.37  % (29126)Time elapsed: 0.003 s
% 0.15/0.37  % (29126)Instructions burned: 6 (million)
% 0.15/0.37  % (29126)------------------------------
% 0.15/0.37  % (29126)------------------------------
% 0.15/0.37  % (29120)Success in time 0.003 s
%------------------------------------------------------------------------------