TSTP Solution File: GEO172+3 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : GEO172+3 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n005.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 20:14:55 EDT 2024

% Result   : Theorem 0.19s 0.39s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   70 (  16 unt;   0 def)
%            Number of atoms       :  175 (   0 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  167 (  62   ~;  67   |;  21   &)
%                                         (   6 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   11 (  10 usr;   5 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :   95 (  86   !;   9   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f643,plain,
    $false,
    inference(avatar_sat_refutation,[],[f608,f626,f631,f637,f642]) ).

fof(f642,plain,
    ~ spl3_10,
    inference(avatar_contradiction_clause,[],[f641]) ).

fof(f641,plain,
    ( $false
    | ~ spl3_10 ),
    inference(subsumption_resolution,[],[f640,f99]) ).

fof(f99,plain,
    incident_point_and_line(sK2,sK1),
    inference(cnf_transformation,[],[f96]) ).

fof(f96,plain,
    ( ~ equal_points(sK2,intersection_point(sK0,sK1))
    & incident_point_and_line(sK2,sK1)
    & incident_point_and_line(sK2,sK0)
    & convergent_lines(sK0,sK1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f54,f95]) ).

fof(f95,plain,
    ( ? [X0,X1,X2] :
        ( ~ equal_points(X2,intersection_point(X0,X1))
        & incident_point_and_line(X2,X1)
        & incident_point_and_line(X2,X0)
        & convergent_lines(X0,X1) )
   => ( ~ equal_points(sK2,intersection_point(sK0,sK1))
      & incident_point_and_line(sK2,sK1)
      & incident_point_and_line(sK2,sK0)
      & convergent_lines(sK0,sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f54,plain,
    ? [X0,X1,X2] :
      ( ~ equal_points(X2,intersection_point(X0,X1))
      & incident_point_and_line(X2,X1)
      & incident_point_and_line(X2,X0)
      & convergent_lines(X0,X1) ),
    inference(flattening,[],[f53]) ).

fof(f53,plain,
    ? [X0,X1,X2] :
      ( ~ equal_points(X2,intersection_point(X0,X1))
      & incident_point_and_line(X2,X1)
      & incident_point_and_line(X2,X0)
      & convergent_lines(X0,X1) ),
    inference(ennf_transformation,[],[f37]) ).

fof(f37,negated_conjecture,
    ~ ! [X0,X1,X2] :
        ( ( incident_point_and_line(X2,X1)
          & incident_point_and_line(X2,X0)
          & convergent_lines(X0,X1) )
       => equal_points(X2,intersection_point(X0,X1)) ),
    inference(negated_conjecture,[],[f36]) ).

fof(f36,conjecture,
    ! [X0,X1,X2] :
      ( ( incident_point_and_line(X2,X1)
        & incident_point_and_line(X2,X0)
        & convergent_lines(X0,X1) )
     => equal_points(X2,intersection_point(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).

fof(f640,plain,
    ( ~ incident_point_and_line(sK2,sK1)
    | ~ spl3_10 ),
    inference(resolution,[],[f582,f119]) ).

fof(f119,plain,
    ! [X0,X1] :
      ( ~ apart_point_and_line(X0,X1)
      | ~ incident_point_and_line(X0,X1) ),
    inference(cnf_transformation,[],[f69]) ).

fof(f69,plain,
    ! [X0,X1] :
      ( ~ apart_point_and_line(X0,X1)
      | ~ incident_point_and_line(X0,X1) ),
    inference(ennf_transformation,[],[f51]) ).

fof(f51,plain,
    ! [X0,X1] :
      ( incident_point_and_line(X0,X1)
     => ~ apart_point_and_line(X0,X1) ),
    inference(unused_predicate_definition_removal,[],[f34]) ).

fof(f34,axiom,
    ! [X0,X1] :
      ( incident_point_and_line(X0,X1)
    <=> ~ apart_point_and_line(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a4) ).

fof(f582,plain,
    ( apart_point_and_line(sK2,sK1)
    | ~ spl3_10 ),
    inference(avatar_component_clause,[],[f580]) ).

fof(f580,plain,
    ( spl3_10
  <=> apart_point_and_line(sK2,sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_10])]) ).

fof(f637,plain,
    ~ spl3_9,
    inference(avatar_contradiction_clause,[],[f636]) ).

fof(f636,plain,
    ( $false
    | ~ spl3_9 ),
    inference(subsumption_resolution,[],[f632,f97]) ).

fof(f97,plain,
    convergent_lines(sK0,sK1),
    inference(cnf_transformation,[],[f96]) ).

fof(f632,plain,
    ( ~ convergent_lines(sK0,sK1)
    | ~ spl3_9 ),
    inference(resolution,[],[f578,f113]) ).

fof(f113,plain,
    ! [X0,X1] :
      ( ~ apart_point_and_line(intersection_point(X0,X1),X1)
      | ~ convergent_lines(X0,X1) ),
    inference(cnf_transformation,[],[f59]) ).

fof(f59,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/sandbox2/benchmark/theBenchmark.p',ci4) ).

fof(f578,plain,
    ( apart_point_and_line(intersection_point(sK0,sK1),sK1)
    | ~ spl3_9 ),
    inference(avatar_component_clause,[],[f576]) ).

fof(f576,plain,
    ( spl3_9
  <=> apart_point_and_line(intersection_point(sK0,sK1),sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_9])]) ).

fof(f631,plain,
    ~ spl3_11,
    inference(avatar_contradiction_clause,[],[f630]) ).

fof(f630,plain,
    ( $false
    | ~ spl3_11 ),
    inference(subsumption_resolution,[],[f629,f98]) ).

fof(f98,plain,
    incident_point_and_line(sK2,sK0),
    inference(cnf_transformation,[],[f96]) ).

fof(f629,plain,
    ( ~ incident_point_and_line(sK2,sK0)
    | ~ spl3_11 ),
    inference(resolution,[],[f586,f119]) ).

fof(f586,plain,
    ( apart_point_and_line(sK2,sK0)
    | ~ spl3_11 ),
    inference(avatar_component_clause,[],[f584]) ).

fof(f584,plain,
    ( spl3_11
  <=> apart_point_and_line(sK2,sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_11])]) ).

fof(f626,plain,
    ~ spl3_8,
    inference(avatar_contradiction_clause,[],[f625]) ).

fof(f625,plain,
    ( $false
    | ~ spl3_8 ),
    inference(subsumption_resolution,[],[f621,f97]) ).

fof(f621,plain,
    ( ~ convergent_lines(sK0,sK1)
    | ~ spl3_8 ),
    inference(resolution,[],[f574,f112]) ).

fof(f112,plain,
    ! [X0,X1] :
      ( ~ apart_point_and_line(intersection_point(X0,X1),X0)
      | ~ convergent_lines(X0,X1) ),
    inference(cnf_transformation,[],[f58]) ).

fof(f58,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/sandbox2/benchmark/theBenchmark.p',ci3) ).

fof(f574,plain,
    ( apart_point_and_line(intersection_point(sK0,sK1),sK0)
    | ~ spl3_8 ),
    inference(avatar_component_clause,[],[f572]) ).

fof(f572,plain,
    ( spl3_8
  <=> apart_point_and_line(intersection_point(sK0,sK1),sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_8])]) ).

fof(f608,plain,
    ( spl3_9
    | spl3_8
    | spl3_11
    | spl3_10 ),
    inference(avatar_split_clause,[],[f566,f580,f584,f572,f576]) ).

fof(f566,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,[],[f222,f164]) ).

fof(f164,plain,
    distinct_lines(sK0,sK1),
    inference(resolution,[],[f154,f102]) ).

fof(f102,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(f154,plain,
    ! [X0] :
      ( distinct_lines(sK1,X0)
      | distinct_lines(sK0,X0) ),
    inference(resolution,[],[f148,f122]) ).

fof(f122,plain,
    ! [X2,X0,X1] :
      ( ~ distinct_lines(X0,X1)
      | distinct_lines(X0,X2)
      | distinct_lines(X1,X2) ),
    inference(cnf_transformation,[],[f74]) ).

fof(f74,plain,
    ! [X0,X1,X2] :
      ( distinct_lines(X1,X2)
      | distinct_lines(X0,X2)
      | ~ distinct_lines(X0,X1) ),
    inference(flattening,[],[f73]) ).

fof(f73,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(f148,plain,
    distinct_lines(sK1,sK0),
    inference(resolution,[],[f144,f103]) ).

fof(f103,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(f144,plain,
    ! [X0] :
      ( convergent_lines(sK0,X0)
      | distinct_lines(sK1,X0) ),
    inference(resolution,[],[f126,f97]) ).

fof(f126,plain,
    ! [X2,X0,X1] :
      ( ~ convergent_lines(X0,X1)
      | distinct_lines(X1,X2)
      | convergent_lines(X0,X2) ),
    inference(cnf_transformation,[],[f82]) ).

fof(f82,plain,
    ! [X0,X1,X2] :
      ( convergent_lines(X0,X2)
      | distinct_lines(X1,X2)
      | ~ convergent_lines(X0,X1) ),
    inference(flattening,[],[f81]) ).

fof(f81,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/sandbox2/benchmark/theBenchmark.p',ceq3) ).

fof(f222,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,[],[f138,f140]) ).

fof(f140,plain,
    distinct_points(sK2,intersection_point(sK0,sK1)),
    inference(resolution,[],[f118,f100]) ).

fof(f100,plain,
    ~ equal_points(sK2,intersection_point(sK0,sK1)),
    inference(cnf_transformation,[],[f96]) ).

fof(f118,plain,
    ! [X0,X1] :
      ( equal_points(X0,X1)
      | distinct_points(X0,X1) ),
    inference(cnf_transformation,[],[f68]) ).

fof(f68,plain,
    ! [X0,X1] :
      ( equal_points(X0,X1)
      | distinct_points(X0,X1) ),
    inference(ennf_transformation,[],[f52]) ).

fof(f52,plain,
    ! [X0,X1] :
      ( ~ distinct_points(X0,X1)
     => equal_points(X0,X1) ),
    inference(unused_predicate_definition_removal,[],[f31]) ).

fof(f31,axiom,
    ! [X0,X1] :
      ( equal_points(X0,X1)
    <=> ~ distinct_points(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).

fof(f138,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,[],[f94]) ).

fof(f94,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,[],[f93]) ).

fof(f93,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,[],[f50]) ).

fof(f50,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/sandbox2/benchmark/theBenchmark.p',cu1) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : GEO172+3 : TPTP v8.2.0. Released v4.0.0.
% 0.07/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.35  % Computer : n005.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Sun May 19 14:07:53 EDT 2024
% 0.13/0.35  % CPUTime    : 
% 0.13/0.35  % (11064)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.37  % (11065)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.13/0.37  % (11068)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.13/0.37  % (11067)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)
% 0.13/0.37  % (11066)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.13/0.37  % (11069)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.13/0.37  % (11070)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.13/0.37  % (11071)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)
% 0.13/0.37  TRYING [1]
% 0.13/0.37  TRYING [2]
% 0.13/0.37  TRYING [1]
% 0.13/0.37  TRYING [3]
% 0.13/0.37  TRYING [1,1]
% 0.13/0.37  TRYING [1,1]
% 0.13/0.37  TRYING [2]
% 0.13/0.37  TRYING [1,2]
% 0.13/0.37  TRYING [1,2]
% 0.13/0.37  TRYING [2,2]
% 0.13/0.37  TRYING [2,2]
% 0.13/0.37  TRYING [3]
% 0.13/0.37  TRYING [2,3]
% 0.13/0.37  TRYING [2,3]
% 0.19/0.37  TRYING [4]
% 0.19/0.37  TRYING [2,4]
% 0.19/0.37  TRYING [2,4]
% 0.19/0.38  TRYING [4]
% 0.19/0.38  TRYING [2,5]
% 0.19/0.38  TRYING [2,5]
% 0.19/0.38  TRYING [2,6]
% 0.19/0.38  TRYING [2,6]
% 0.19/0.38  TRYING [5]
% 0.19/0.38  TRYING [2,7]
% 0.19/0.38  TRYING [2,7]
% 0.19/0.38  TRYING [5]
% 0.19/0.38  % (11070)First to succeed.
% 0.19/0.38  % (11067)Also succeeded, but the first one will report.
% 0.19/0.38  % (11070)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-11064"
% 0.19/0.38  TRYING [2,8]
% 0.19/0.39  TRYING [2,8]
% 0.19/0.39  % (11070)Refutation found. Thanks to Tanya!
% 0.19/0.39  % SZS status Theorem for theBenchmark
% 0.19/0.39  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.39  % (11070)------------------------------
% 0.19/0.39  % (11070)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.19/0.39  % (11070)Termination reason: Refutation
% 0.19/0.39  
% 0.19/0.39  % (11070)Memory used [KB]: 1116
% 0.19/0.39  % (11070)Time elapsed: 0.018 s
% 0.19/0.39  % (11070)Instructions burned: 30 (million)
% 0.19/0.39  % (11064)Success in time 0.022 s
%------------------------------------------------------------------------------