TSTP Solution File: GEO203+2 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : GEO203+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 : 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 : Tue Apr 30 11:14:41 EDT 2024

% Result   : Theorem 0.14s 0.39s
% Output   : Refutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   66 (  14 unt;   0 def)
%            Number of atoms       :  188 (   0 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  185 (  63   ~;  82   |;  26   &)
%                                         (   4 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    9 (   8 usr;   5 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   83 (  74   !;   9   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f632,plain,
    $false,
    inference(avatar_sat_refutation,[],[f246,f259,f483,f530,f631]) ).

fof(f631,plain,
    ~ spl3_7,
    inference(avatar_contradiction_clause,[],[f630]) ).

fof(f630,plain,
    ( $false
    | ~ spl3_7 ),
    inference(subsumption_resolution,[],[f627,f37]) ).

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

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

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

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

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

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

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

fof(f627,plain,
    ( ~ convergent_lines(sK0,sK1)
    | ~ spl3_7 ),
    inference(resolution,[],[f534,f43]) ).

fof(f43,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(f534,plain,
    ( ! [X0] :
        ( distinct_points(intersection_point(sK0,sK1),intersection_point(sK0,X0))
        | ~ convergent_lines(sK0,X0) )
    | ~ spl3_7 ),
    inference(resolution,[],[f151,f46]) ).

fof(f46,plain,
    ! [X2,X0,X1] :
      ( ~ apart_point_and_line(X2,X0)
      | distinct_points(X2,intersection_point(X0,X1))
      | ~ convergent_lines(X0,X1) ),
    inference(cnf_transformation,[],[f22]) ).

fof(f22,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,[],[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(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(f151,plain,
    ( apart_point_and_line(intersection_point(sK0,sK1),sK0)
    | ~ spl3_7 ),
    inference(avatar_component_clause,[],[f149]) ).

fof(f149,plain,
    ( spl3_7
  <=> apart_point_and_line(intersection_point(sK0,sK1),sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_7])]) ).

fof(f530,plain,
    ( spl3_4
    | spl3_7
    | spl3_5
    | spl3_6 ),
    inference(avatar_split_clause,[],[f529,f145,f141,f149,f137]) ).

fof(f137,plain,
    ( spl3_4
  <=> apart_point_and_line(intersection_point(sK0,sK2),sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_4])]) ).

fof(f141,plain,
    ( spl3_5
  <=> apart_point_and_line(intersection_point(sK0,sK2),line_connecting(intersection_point(sK0,sK1),intersection_point(sK0,sK2))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_5])]) ).

fof(f145,plain,
    ( spl3_6
  <=> apart_point_and_line(intersection_point(sK0,sK1),line_connecting(intersection_point(sK0,sK1),intersection_point(sK0,sK2))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_6])]) ).

fof(f529,plain,
    ( apart_point_and_line(intersection_point(sK0,sK1),sK0)
    | apart_point_and_line(intersection_point(sK0,sK2),sK0)
    | spl3_5
    | spl3_6 ),
    inference(subsumption_resolution,[],[f528,f142]) ).

fof(f142,plain,
    ( ~ apart_point_and_line(intersection_point(sK0,sK2),line_connecting(intersection_point(sK0,sK1),intersection_point(sK0,sK2)))
    | spl3_5 ),
    inference(avatar_component_clause,[],[f141]) ).

fof(f528,plain,
    ( apart_point_and_line(intersection_point(sK0,sK1),sK0)
    | apart_point_and_line(intersection_point(sK0,sK2),sK0)
    | apart_point_and_line(intersection_point(sK0,sK2),line_connecting(intersection_point(sK0,sK1),intersection_point(sK0,sK2)))
    | spl3_6 ),
    inference(subsumption_resolution,[],[f193,f146]) ).

fof(f146,plain,
    ( ~ apart_point_and_line(intersection_point(sK0,sK1),line_connecting(intersection_point(sK0,sK1),intersection_point(sK0,sK2)))
    | spl3_6 ),
    inference(avatar_component_clause,[],[f145]) ).

fof(f193,plain,
    ( apart_point_and_line(intersection_point(sK0,sK1),line_connecting(intersection_point(sK0,sK1),intersection_point(sK0,sK2)))
    | apart_point_and_line(intersection_point(sK0,sK1),sK0)
    | apart_point_and_line(intersection_point(sK0,sK2),sK0)
    | apart_point_and_line(intersection_point(sK0,sK2),line_connecting(intersection_point(sK0,sK1),intersection_point(sK0,sK2))) ),
    inference(resolution,[],[f105,f92]) ).

fof(f92,plain,
    ! [X0,X1] :
      ( ~ distinct_lines(X0,X1)
      | apart_point_and_line(intersection_point(sK0,sK1),X1)
      | apart_point_and_line(intersection_point(sK0,sK1),X0)
      | apart_point_and_line(intersection_point(sK0,sK2),X0)
      | apart_point_and_line(intersection_point(sK0,sK2),X1) ),
    inference(resolution,[],[f54,f39]) ).

fof(f39,plain,
    distinct_points(intersection_point(sK0,sK1),intersection_point(sK0,sK2)),
    inference(cnf_transformation,[],[f36]) ).

fof(f54,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,[],[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/sandbox2/benchmark/theBenchmark.p',cu1) ).

fof(f105,plain,
    distinct_lines(sK0,line_connecting(intersection_point(sK0,sK1),intersection_point(sK0,sK2))),
    inference(resolution,[],[f64,f42]) ).

fof(f42,plain,
    ! [X0] : ~ distinct_lines(X0,X0),
    inference(cnf_transformation,[],[f2]) ).

fof(f2,axiom,
    ! [X0] : ~ distinct_lines(X0,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart2) ).

fof(f64,plain,
    ! [X0] :
      ( distinct_lines(line_connecting(intersection_point(sK0,sK1),intersection_point(sK0,sK2)),X0)
      | distinct_lines(sK0,X0) ),
    inference(resolution,[],[f48,f40]) ).

fof(f40,plain,
    distinct_lines(line_connecting(intersection_point(sK0,sK1),intersection_point(sK0,sK2)),sK0),
    inference(cnf_transformation,[],[f36]) ).

fof(f48,plain,
    ! [X2,X0,X1] :
      ( ~ distinct_lines(X0,X1)
      | distinct_lines(X0,X2)
      | distinct_lines(X1,X2) ),
    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/sandbox2/benchmark/theBenchmark.p',apart5) ).

fof(f483,plain,
    ~ spl3_4,
    inference(avatar_contradiction_clause,[],[f482]) ).

fof(f482,plain,
    ( $false
    | ~ spl3_4 ),
    inference(subsumption_resolution,[],[f479,f38]) ).

fof(f38,plain,
    convergent_lines(sK0,sK2),
    inference(cnf_transformation,[],[f36]) ).

fof(f479,plain,
    ( ~ convergent_lines(sK0,sK2)
    | ~ spl3_4 ),
    inference(resolution,[],[f173,f43]) ).

fof(f173,plain,
    ( ! [X0] :
        ( distinct_points(intersection_point(sK0,sK2),intersection_point(sK0,X0))
        | ~ convergent_lines(sK0,X0) )
    | ~ spl3_4 ),
    inference(resolution,[],[f139,f46]) ).

fof(f139,plain,
    ( apart_point_and_line(intersection_point(sK0,sK2),sK0)
    | ~ spl3_4 ),
    inference(avatar_component_clause,[],[f137]) ).

fof(f259,plain,
    ~ spl3_6,
    inference(avatar_contradiction_clause,[],[f258]) ).

fof(f258,plain,
    ( $false
    | ~ spl3_6 ),
    inference(subsumption_resolution,[],[f257,f39]) ).

fof(f257,plain,
    ( ~ distinct_points(intersection_point(sK0,sK1),intersection_point(sK0,sK2))
    | ~ spl3_6 ),
    inference(subsumption_resolution,[],[f252,f43]) ).

fof(f252,plain,
    ( distinct_points(intersection_point(sK0,sK1),intersection_point(sK0,sK1))
    | ~ distinct_points(intersection_point(sK0,sK1),intersection_point(sK0,sK2))
    | ~ spl3_6 ),
    inference(resolution,[],[f147,f52]) ).

fof(f52,plain,
    ! [X2,X0,X1] :
      ( ~ apart_point_and_line(X2,line_connecting(X0,X1))
      | distinct_points(X2,X0)
      | ~ distinct_points(X0,X1) ),
    inference(cnf_transformation,[],[f32]) ).

fof(f32,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,[],[f31]) ).

fof(f31,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/sandbox2/benchmark/theBenchmark.p',con1) ).

fof(f147,plain,
    ( apart_point_and_line(intersection_point(sK0,sK1),line_connecting(intersection_point(sK0,sK1),intersection_point(sK0,sK2)))
    | ~ spl3_6 ),
    inference(avatar_component_clause,[],[f145]) ).

fof(f246,plain,
    ~ spl3_5,
    inference(avatar_contradiction_clause,[],[f245]) ).

fof(f245,plain,
    ( $false
    | ~ spl3_5 ),
    inference(subsumption_resolution,[],[f244,f39]) ).

fof(f244,plain,
    ( ~ distinct_points(intersection_point(sK0,sK1),intersection_point(sK0,sK2))
    | ~ spl3_5 ),
    inference(subsumption_resolution,[],[f238,f43]) ).

fof(f238,plain,
    ( distinct_points(intersection_point(sK0,sK2),intersection_point(sK0,sK2))
    | ~ distinct_points(intersection_point(sK0,sK1),intersection_point(sK0,sK2))
    | ~ spl3_5 ),
    inference(resolution,[],[f143,f53]) ).

fof(f53,plain,
    ! [X2,X0,X1] :
      ( ~ apart_point_and_line(X2,line_connecting(X0,X1))
      | distinct_points(X2,X1)
      | ~ distinct_points(X0,X1) ),
    inference(cnf_transformation,[],[f32]) ).

fof(f143,plain,
    ( apart_point_and_line(intersection_point(sK0,sK2),line_connecting(intersection_point(sK0,sK1),intersection_point(sK0,sK2)))
    | ~ spl3_5 ),
    inference(avatar_component_clause,[],[f141]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem    : GEO203+2 : TPTP v8.1.2. Released v3.3.0.
% 0.12/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35  % Computer : n014.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   : Tue Apr 30 05:29:49 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.14/0.36  % (5221)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37  % (5224)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)
% 0.14/0.37  % (5222)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.14/0.37  % (5225)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.14/0.37  % (5223)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.37  % (5226)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.14/0.37  % (5227)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.14/0.37  % (5228)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)
% 0.14/0.38  TRYING [1]
% 0.14/0.38  TRYING [2]
% 0.14/0.38  TRYING [1]
% 0.14/0.38  TRYING [1]
% 0.14/0.38  TRYING [3]
% 0.14/0.38  TRYING [1]
% 0.14/0.38  TRYING [2]
% 0.14/0.38  TRYING [2]
% 0.14/0.38  TRYING [2]
% 0.14/0.38  TRYING [3]
% 0.14/0.38  TRYING [3]
% 0.14/0.38  TRYING [3]
% 0.14/0.38  TRYING [4]
% 0.14/0.38  TRYING [4]
% 0.14/0.38  TRYING [4]
% 0.14/0.38  TRYING [4]
% 0.14/0.38  TRYING [5]
% 0.14/0.38  TRYING [5]
% 0.14/0.38  TRYING [5]
% 0.14/0.38  TRYING [5]
% 0.14/0.39  TRYING [6]
% 0.14/0.39  % (5227)First to succeed.
% 0.14/0.39  TRYING [6]
% 0.14/0.39  TRYING [6]
% 0.14/0.39  % (5227)Refutation found. Thanks to Tanya!
% 0.14/0.39  % SZS status Theorem for theBenchmark
% 0.14/0.39  % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.39  % (5227)------------------------------
% 0.14/0.39  % (5227)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.14/0.39  % (5227)Termination reason: Refutation
% 0.14/0.39  
% 0.14/0.39  % (5227)Memory used [KB]: 956
% 0.14/0.39  % (5227)Time elapsed: 0.017 s
% 0.14/0.39  % (5227)Instructions burned: 28 (million)
% 0.14/0.39  % (5227)------------------------------
% 0.14/0.39  % (5227)------------------------------
% 0.14/0.39  % (5221)Success in time 0.022 s
%------------------------------------------------------------------------------