TSTP Solution File: GEO201+2 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : GEO201+2 : TPTP v8.2.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n014.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 : Mon May 20 20:15:12 EDT 2024

% Result   : Theorem 0.12s 0.36s
% Output   : Refutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   57 (  11 unt;   0 def)
%            Number of atoms       :  153 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  157 (  61   ~;  75   |;   8   &)
%                                         (   4 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    9 (   8 usr;   5 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   2 con; 0-2 aty)
%            Number of variables   :   80 (  76   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f244,plain,
    $false,
    inference(avatar_sat_refutation,[],[f154,f176,f203,f231,f243]) ).

fof(f243,plain,
    ~ spl2_2,
    inference(avatar_contradiction_clause,[],[f241]) ).

fof(f241,plain,
    ( $false
    | ~ spl2_2 ),
    inference(resolution,[],[f232,f36]) ).

fof(f36,plain,
    convergent_lines(sK0,sK1),
    inference(cnf_transformation,[],[f35]) ).

fof(f35,plain,
    ( distinct_points(intersection_point(sK0,sK1),intersection_point(sK1,sK0))
    & convergent_lines(sK0,sK1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f16,f34]) ).

fof(f34,plain,
    ( ? [X0,X1] :
        ( distinct_points(intersection_point(X0,X1),intersection_point(X1,X0))
        & convergent_lines(X0,X1) )
   => ( distinct_points(intersection_point(sK0,sK1),intersection_point(sK1,sK0))
      & convergent_lines(sK0,sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f16,plain,
    ? [X0,X1] :
      ( distinct_points(intersection_point(X0,X1),intersection_point(X1,X0))
      & convergent_lines(X0,X1) ),
    inference(ennf_transformation,[],[f14]) ).

fof(f14,negated_conjecture,
    ~ ! [X0,X1] :
        ( convergent_lines(X0,X1)
       => ~ distinct_points(intersection_point(X0,X1),intersection_point(X1,X0)) ),
    inference(negated_conjecture,[],[f13]) ).

fof(f13,conjecture,
    ! [X0,X1] :
      ( convergent_lines(X0,X1)
     => ~ distinct_points(intersection_point(X0,X1),intersection_point(X1,X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).

fof(f232,plain,
    ( ~ convergent_lines(sK0,sK1)
    | ~ spl2_2 ),
    inference(resolution,[],[f145,f59]) ).

fof(f59,plain,
    ! [X0,X1] :
      ( ~ apart_point_and_line(intersection_point(X0,X1),X1)
      | ~ convergent_lines(X0,X1) ),
    inference(resolution,[],[f44,f40]) ).

fof(f40,plain,
    ! [X0] : ~ distinct_points(X0,X0),
    inference(cnf_transformation,[],[f1]) ).

fof(f1,axiom,
    ! [X0] : ~ distinct_points(X0,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart1) ).

fof(f44,plain,
    ! [X2,X0,X1] :
      ( distinct_points(X2,intersection_point(X0,X1))
      | ~ apart_point_and_line(X2,X1)
      | ~ convergent_lines(X0,X1) ),
    inference(cnf_transformation,[],[f21]) ).

fof(f21,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,[],[f20]) ).

fof(f20,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,[],[f8]) ).

fof(f8,axiom,
    ! [X0,X1,X2] :
      ( convergent_lines(X0,X1)
     => ( ( apart_point_and_line(X2,X1)
          | apart_point_and_line(X2,X0) )
       => distinct_points(X2,intersection_point(X0,X1)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con2) ).

fof(f145,plain,
    ( apart_point_and_line(intersection_point(sK0,sK1),sK1)
    | ~ spl2_2 ),
    inference(avatar_component_clause,[],[f143]) ).

fof(f143,plain,
    ( spl2_2
  <=> apart_point_and_line(intersection_point(sK0,sK1),sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_2])]) ).

fof(f231,plain,
    ~ spl2_4,
    inference(avatar_contradiction_clause,[],[f229]) ).

fof(f229,plain,
    ( $false
    | ~ spl2_4 ),
    inference(resolution,[],[f214,f36]) ).

fof(f214,plain,
    ( ~ convergent_lines(sK0,sK1)
    | ~ spl2_4 ),
    inference(resolution,[],[f153,f56]) ).

fof(f56,plain,
    ! [X0,X1] :
      ( ~ apart_point_and_line(intersection_point(X0,X1),X0)
      | ~ convergent_lines(X0,X1) ),
    inference(resolution,[],[f43,f40]) ).

fof(f43,plain,
    ! [X2,X0,X1] :
      ( distinct_points(X2,intersection_point(X0,X1))
      | ~ apart_point_and_line(X2,X0)
      | ~ convergent_lines(X0,X1) ),
    inference(cnf_transformation,[],[f21]) ).

fof(f153,plain,
    ( apart_point_and_line(intersection_point(sK0,sK1),sK0)
    | ~ spl2_4 ),
    inference(avatar_component_clause,[],[f151]) ).

fof(f151,plain,
    ( spl2_4
  <=> apart_point_and_line(intersection_point(sK0,sK1),sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_4])]) ).

fof(f203,plain,
    spl2_3,
    inference(avatar_contradiction_clause,[],[f201]) ).

fof(f201,plain,
    ( $false
    | spl2_3 ),
    inference(resolution,[],[f190,f36]) ).

fof(f190,plain,
    ( ~ convergent_lines(sK0,sK1)
    | spl2_3 ),
    inference(resolution,[],[f149,f41]) ).

fof(f41,plain,
    ! [X0,X1] :
      ( distinct_lines(X0,X1)
      | ~ convergent_lines(X0,X1) ),
    inference(cnf_transformation,[],[f17]) ).

fof(f17,plain,
    ! [X0,X1] :
      ( distinct_lines(X0,X1)
      | ~ convergent_lines(X0,X1) ),
    inference(ennf_transformation,[],[f12]) ).

fof(f12,axiom,
    ! [X0,X1] :
      ( convergent_lines(X0,X1)
     => distinct_lines(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ceq3) ).

fof(f149,plain,
    ( ~ distinct_lines(sK0,sK1)
    | spl2_3 ),
    inference(avatar_component_clause,[],[f147]) ).

fof(f147,plain,
    ( spl2_3
  <=> distinct_lines(sK0,sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_3])]) ).

fof(f176,plain,
    spl2_1,
    inference(avatar_contradiction_clause,[],[f174]) ).

fof(f174,plain,
    ( $false
    | spl2_1 ),
    inference(resolution,[],[f162,f36]) ).

fof(f162,plain,
    ( ~ convergent_lines(sK0,sK1)
    | spl2_1 ),
    inference(resolution,[],[f155,f38]) ).

fof(f38,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(f155,plain,
    ( ! [X0] :
        ( convergent_lines(X0,sK0)
        | ~ convergent_lines(X0,sK1) )
    | spl2_1 ),
    inference(resolution,[],[f141,f42]) ).

fof(f42,plain,
    ! [X2,X0,X1] :
      ( convergent_lines(X1,X2)
      | convergent_lines(X0,X2)
      | ~ convergent_lines(X0,X1) ),
    inference(cnf_transformation,[],[f19]) ).

fof(f19,plain,
    ! [X0,X1,X2] :
      ( convergent_lines(X1,X2)
      | convergent_lines(X0,X2)
      | ~ convergent_lines(X0,X1) ),
    inference(flattening,[],[f18]) ).

fof(f18,plain,
    ! [X0,X1,X2] :
      ( convergent_lines(X1,X2)
      | convergent_lines(X0,X2)
      | ~ convergent_lines(X0,X1) ),
    inference(ennf_transformation,[],[f6]) ).

fof(f6,axiom,
    ! [X0,X1,X2] :
      ( convergent_lines(X0,X1)
     => ( convergent_lines(X1,X2)
        | convergent_lines(X0,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart6) ).

fof(f141,plain,
    ( ~ convergent_lines(sK1,sK0)
    | spl2_1 ),
    inference(avatar_component_clause,[],[f139]) ).

fof(f139,plain,
    ( spl2_1
  <=> convergent_lines(sK1,sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_1])]) ).

fof(f154,plain,
    ( ~ spl2_1
    | spl2_2
    | ~ spl2_3
    | spl2_4 ),
    inference(avatar_split_clause,[],[f120,f151,f147,f143,f139]) ).

fof(f120,plain,
    ( apart_point_and_line(intersection_point(sK0,sK1),sK0)
    | ~ distinct_lines(sK0,sK1)
    | apart_point_and_line(intersection_point(sK0,sK1),sK1)
    | ~ convergent_lines(sK1,sK0) ),
    inference(resolution,[],[f108,f37]) ).

fof(f37,plain,
    distinct_points(intersection_point(sK0,sK1),intersection_point(sK1,sK0)),
    inference(cnf_transformation,[],[f35]) ).

fof(f108,plain,
    ! [X2,X0,X1] :
      ( ~ distinct_points(X0,intersection_point(X1,X2))
      | apart_point_and_line(X0,X2)
      | ~ distinct_lines(X2,X1)
      | apart_point_and_line(X0,X1)
      | ~ convergent_lines(X1,X2) ),
    inference(duplicate_literal_removal,[],[f101]) ).

fof(f101,plain,
    ! [X2,X0,X1] :
      ( apart_point_and_line(X0,X1)
      | apart_point_and_line(X0,X2)
      | ~ distinct_lines(X2,X1)
      | ~ distinct_points(X0,intersection_point(X1,X2))
      | ~ convergent_lines(X1,X2)
      | ~ convergent_lines(X1,X2) ),
    inference(resolution,[],[f68,f59]) ).

fof(f68,plain,
    ! [X2,X3,X0,X1] :
      ( apart_point_and_line(intersection_point(X0,X1),X2)
      | apart_point_and_line(X3,X0)
      | apart_point_and_line(X3,X2)
      | ~ distinct_lines(X2,X0)
      | ~ distinct_points(X3,intersection_point(X0,X1))
      | ~ convergent_lines(X0,X1) ),
    inference(resolution,[],[f51,f56]) ).

fof(f51,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,[],[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(flattening,[],[f32]) ).

fof(f32,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/sandbox2/benchmark/theBenchmark.p',cu1) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : GEO201+2 : TPTP v8.2.0. Released v3.3.0.
% 0.06/0.13  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.12/0.33  % Computer : n014.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Sun May 19 13:41:23 EDT 2024
% 0.12/0.33  % CPUTime    : 
% 0.12/0.34  % (1899)Running in auto input_syntax mode. Trying TPTP
% 0.12/0.35  % (1904)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.12/0.35  % (1901)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.12/0.35  % (1903)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.12/0.35  % (1905)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.12/0.35  TRYING [1,1]
% 0.12/0.35  % (1902)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)
% 0.12/0.35  TRYING [1,2]
% 0.12/0.35  TRYING [2,2]
% 0.12/0.35  TRYING [1,1]
% 0.12/0.35  % (1906)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)
% 0.12/0.35  TRYING [1,2]
% 0.12/0.35  TRYING [2,3]
% 0.12/0.35  TRYING [2,2]
% 0.12/0.35  TRYING [2,3]
% 0.12/0.35  TRYING [2,4]
% 0.12/0.35  TRYING [1]
% 0.12/0.35  TRYING [2]
% 0.12/0.35  TRYING [2,4]
% 0.12/0.35  TRYING [3]
% 0.12/0.35  TRYING [2,5]
% 0.12/0.35  % (1900)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.12/0.35  TRYING [2,5]
% 0.12/0.36  TRYING [4]
% 0.12/0.36  TRYING [2,6]
% 0.12/0.36  TRYING [1]
% 0.12/0.36  TRYING [2,6]
% 0.12/0.36  TRYING [2]
% 0.12/0.36  % (1902)First to succeed.
% 0.12/0.36  TRYING [3]
% 0.12/0.36  % (1902)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1899"
% 0.12/0.36  TRYING [2,7]
% 0.12/0.36  TRYING [2,7]
% 0.12/0.36  TRYING [4]
% 0.12/0.36  % (1902)Refutation found. Thanks to Tanya!
% 0.12/0.36  % SZS status Theorem for theBenchmark
% 0.12/0.36  % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.36  % (1902)------------------------------
% 0.12/0.36  % (1902)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.12/0.36  % (1902)Termination reason: Refutation
% 0.12/0.36  
% 0.12/0.36  % (1902)Memory used [KB]: 894
% 0.12/0.36  % (1902)Time elapsed: 0.007 s
% 0.12/0.36  % (1902)Instructions burned: 12 (million)
% 0.12/0.36  % (1899)Success in time 0.021 s
%------------------------------------------------------------------------------