TSTP Solution File: GEO194+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : GEO194+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 : n018.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 : Sun May  5 05:16:00 EDT 2024

% Result   : Theorem 0.10s 0.37s
% Output   : Refutation 0.10s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   72 (  13 unt;   0 def)
%            Number of atoms       :  213 (   0 equ)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives :  218 (  77   ~;  97   |;  26   &)
%                                         (   6 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   11 (  10 usr;   7 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :  102 (  93   !;   9   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1297,plain,
    $false,
    inference(avatar_sat_refutation,[],[f109,f218,f222,f253,f275,f1258,f1296]) ).

fof(f1296,plain,
    spl3_27,
    inference(avatar_contradiction_clause,[],[f1278]) ).

fof(f1278,plain,
    ( $false
    | spl3_27 ),
    inference(resolution,[],[f1257,f43]) ).

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

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

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

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

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

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

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

fof(f1257,plain,
    ( ~ apart_point_and_line(intersection_point(sK0,sK1),sK2)
    | spl3_27 ),
    inference(avatar_component_clause,[],[f1255]) ).

fof(f1255,plain,
    ( spl3_27
  <=> apart_point_and_line(intersection_point(sK0,sK1),sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_27])]) ).

fof(f1258,plain,
    ( ~ spl3_1
    | ~ spl3_27
    | ~ spl3_9 ),
    inference(avatar_split_clause,[],[f1252,f273,f1255,f98]) ).

fof(f98,plain,
    ( spl3_1
  <=> convergent_lines(sK0,sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).

fof(f273,plain,
    ( spl3_9
  <=> ! [X0] :
        ( apart_point_and_line(X0,sK1)
        | ~ apart_point_and_line(X0,sK2)
        | apart_point_and_line(X0,sK0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_9])]) ).

fof(f1252,plain,
    ( ~ apart_point_and_line(intersection_point(sK0,sK1),sK2)
    | ~ convergent_lines(sK0,sK1)
    | ~ spl3_9 ),
    inference(duplicate_literal_removal,[],[f1246]) ).

fof(f1246,plain,
    ( ~ apart_point_and_line(intersection_point(sK0,sK1),sK2)
    | ~ convergent_lines(sK0,sK1)
    | ~ convergent_lines(sK0,sK1)
    | ~ spl3_9 ),
    inference(resolution,[],[f279,f50]) ).

fof(f50,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(f279,plain,
    ( ! [X0] :
        ( apart_point_and_line(intersection_point(X0,sK1),sK0)
        | ~ apart_point_and_line(intersection_point(X0,sK1),sK2)
        | ~ convergent_lines(X0,sK1) )
    | ~ spl3_9 ),
    inference(resolution,[],[f274,f51]) ).

fof(f51,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(f274,plain,
    ( ! [X0] :
        ( apart_point_and_line(X0,sK1)
        | ~ apart_point_and_line(X0,sK2)
        | apart_point_and_line(X0,sK0) )
    | ~ spl3_9 ),
    inference(avatar_component_clause,[],[f273]) ).

fof(f275,plain,
    ( ~ spl3_4
    | spl3_9
    | ~ spl3_6 ),
    inference(avatar_split_clause,[],[f258,f216,f273,f208]) ).

fof(f208,plain,
    ( spl3_4
  <=> convergent_lines(sK0,sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_4])]) ).

fof(f216,plain,
    ( spl3_6
  <=> ! [X0] :
        ( apart_point_and_line(X0,sK1)
        | ~ distinct_points(X0,intersection_point(sK0,sK2))
        | apart_point_and_line(X0,sK0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_6])]) ).

fof(f258,plain,
    ( ! [X0] :
        ( apart_point_and_line(X0,sK1)
        | apart_point_and_line(X0,sK0)
        | ~ apart_point_and_line(X0,sK2)
        | ~ convergent_lines(sK0,sK2) )
    | ~ spl3_6 ),
    inference(resolution,[],[f217,f66]) ).

fof(f66,plain,
    ! [X2,X0,X1] :
      ( distinct_points(X0,intersection_point(X1,X2))
      | ~ apart_point_and_line(X0,X2)
      | ~ convergent_lines(X1,X2) ),
    inference(resolution,[],[f56,f51]) ).

fof(f56,plain,
    ! [X2,X0,X1] :
      ( apart_point_and_line(X2,X1)
      | distinct_points(X0,X2)
      | ~ apart_point_and_line(X0,X1) ),
    inference(cnf_transformation,[],[f33]) ).

fof(f33,plain,
    ! [X0,X1,X2] :
      ( apart_point_and_line(X2,X1)
      | distinct_points(X0,X2)
      | ~ apart_point_and_line(X0,X1) ),
    inference(flattening,[],[f32]) ).

fof(f32,plain,
    ! [X0,X1,X2] :
      ( apart_point_and_line(X2,X1)
      | distinct_points(X0,X2)
      | ~ apart_point_and_line(X0,X1) ),
    inference(ennf_transformation,[],[f12]) ).

fof(f12,axiom,
    ! [X0,X1,X2] :
      ( apart_point_and_line(X0,X1)
     => ( apart_point_and_line(X2,X1)
        | distinct_points(X0,X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ceq1) ).

fof(f217,plain,
    ( ! [X0] :
        ( ~ distinct_points(X0,intersection_point(sK0,sK2))
        | apart_point_and_line(X0,sK1)
        | apart_point_and_line(X0,sK0) )
    | ~ spl3_6 ),
    inference(avatar_component_clause,[],[f216]) ).

fof(f253,plain,
    spl3_5,
    inference(avatar_contradiction_clause,[],[f250]) ).

fof(f250,plain,
    ( $false
    | spl3_5 ),
    inference(resolution,[],[f239,f40]) ).

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

fof(f239,plain,
    ( ~ convergent_lines(sK0,sK1)
    | spl3_5 ),
    inference(resolution,[],[f230,f61]) ).

fof(f61,plain,
    ! [X0,X1] :
      ( distinct_lines(X0,X1)
      | ~ convergent_lines(X1,X0) ),
    inference(resolution,[],[f54,f47]) ).

fof(f47,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(f54,plain,
    ! [X2,X0,X1] :
      ( convergent_lines(X0,X2)
      | distinct_lines(X1,X2)
      | ~ convergent_lines(X0,X1) ),
    inference(cnf_transformation,[],[f29]) ).

fof(f29,plain,
    ! [X0,X1,X2] :
      ( convergent_lines(X0,X2)
      | distinct_lines(X1,X2)
      | ~ convergent_lines(X0,X1) ),
    inference(flattening,[],[f28]) ).

fof(f28,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(f230,plain,
    ( ~ distinct_lines(sK1,sK0)
    | spl3_5 ),
    inference(resolution,[],[f227,f46]) ).

fof(f46,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(f227,plain,
    ( ! [X0] :
        ( distinct_lines(X0,sK1)
        | ~ distinct_lines(X0,sK0) )
    | spl3_5 ),
    inference(resolution,[],[f214,f53]) ).

fof(f53,plain,
    ! [X2,X0,X1] :
      ( distinct_lines(X1,X2)
      | distinct_lines(X0,X2)
      | ~ distinct_lines(X0,X1) ),
    inference(cnf_transformation,[],[f27]) ).

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

fof(f26,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(f214,plain,
    ( ~ distinct_lines(sK0,sK1)
    | spl3_5 ),
    inference(avatar_component_clause,[],[f212]) ).

fof(f212,plain,
    ( spl3_5
  <=> distinct_lines(sK0,sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_5])]) ).

fof(f222,plain,
    spl3_4,
    inference(avatar_contradiction_clause,[],[f219]) ).

fof(f219,plain,
    ( $false
    | spl3_4 ),
    inference(resolution,[],[f210,f42]) ).

fof(f42,plain,
    convergent_lines(sK0,sK2),
    inference(cnf_transformation,[],[f39]) ).

fof(f210,plain,
    ( ~ convergent_lines(sK0,sK2)
    | spl3_4 ),
    inference(avatar_component_clause,[],[f208]) ).

fof(f218,plain,
    ( ~ spl3_4
    | ~ spl3_5
    | spl3_6 ),
    inference(avatar_split_clause,[],[f123,f216,f212,f208]) ).

fof(f123,plain,
    ! [X0] :
      ( apart_point_and_line(X0,sK1)
      | apart_point_and_line(X0,sK0)
      | ~ distinct_lines(sK0,sK1)
      | ~ distinct_points(X0,intersection_point(sK0,sK2))
      | ~ convergent_lines(sK0,sK2) ),
    inference(resolution,[],[f77,f50]) ).

fof(f77,plain,
    ! [X0,X1] :
      ( apart_point_and_line(intersection_point(sK0,sK2),X0)
      | apart_point_and_line(X1,sK1)
      | apart_point_and_line(X1,X0)
      | ~ distinct_lines(X0,sK1)
      | ~ distinct_points(X1,intersection_point(sK0,sK2)) ),
    inference(resolution,[],[f58,f44]) ).

fof(f44,plain,
    ~ apart_point_and_line(intersection_point(sK0,sK2),sK1),
    inference(cnf_transformation,[],[f39]) ).

fof(f58,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,[],[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) ).

fof(f109,plain,
    spl3_1,
    inference(avatar_contradiction_clause,[],[f106]) ).

fof(f106,plain,
    ( $false
    | spl3_1 ),
    inference(resolution,[],[f100,f40]) ).

fof(f100,plain,
    ( ~ convergent_lines(sK0,sK1)
    | spl3_1 ),
    inference(avatar_component_clause,[],[f98]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem    : GEO194+1 : TPTP v8.1.2. Released v3.3.0.
% 0.10/0.11  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.10/0.31  % Computer : n018.cluster.edu
% 0.10/0.31  % Model    : x86_64 x86_64
% 0.10/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31  % Memory   : 8042.1875MB
% 0.10/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32  % CPULimit   : 300
% 0.10/0.32  % WCLimit    : 300
% 0.10/0.32  % DateTime   : Fri May  3 22:03:38 EDT 2024
% 0.10/0.32  % CPUTime    : 
% 0.10/0.32  % (2798)Running in auto input_syntax mode. Trying TPTP
% 0.10/0.33  % (2805)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.10/0.33  % (2800)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.10/0.33  % (2803)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.10/0.33  % (2806)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)
% 0.10/0.33  % (2799)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.10/0.33  % (2801)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)
% 0.10/0.34  % (2804)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.10/0.34  TRYING [1]
% 0.10/0.34  TRYING [1,1]
% 0.10/0.34  TRYING [1,1]
% 0.10/0.34  TRYING [1]
% 0.10/0.34  TRYING [2]
% 0.10/0.34  TRYING [2]
% 0.10/0.34  TRYING [2,2]
% 0.10/0.34  TRYING [2,2]
% 0.10/0.34  TRYING [3]
% 0.10/0.34  TRYING [3]
% 0.10/0.34  TRYING [3,3]
% 0.10/0.34  TRYING [3,3]
% 0.10/0.34  TRYING [4]
% 0.10/0.34  TRYING [3,4]
% 0.10/0.34  TRYING [3,4]
% 0.10/0.34  TRYING [4]
% 0.10/0.34  TRYING [3,5]
% 0.10/0.34  TRYING [3,5]
% 0.10/0.34  TRYING [5]
% 0.10/0.34  TRYING [5]
% 0.10/0.34  TRYING [3,6]
% 0.10/0.34  TRYING [3,6]
% 0.10/0.34  TRYING [3,7]
% 0.10/0.34  TRYING [3,7]
% 0.10/0.35  TRYING [6]
% 0.10/0.35  TRYING [6]
% 0.10/0.35  TRYING [3,8]
% 0.10/0.35  TRYING [3,8]
% 0.10/0.35  TRYING [3,9]
% 0.10/0.35  TRYING [3,9]
% 0.10/0.36  TRYING [7]
% 0.10/0.36  TRYING [3,10]
% 0.10/0.36  TRYING [3,10]
% 0.10/0.37  TRYING [7]
% 0.10/0.37  % (2801)First to succeed.
% 0.10/0.37  % (2801)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2798"
% 0.10/0.37  TRYING [3,11]
% 0.10/0.37  TRYING [3,11]
% 0.10/0.37  % (2801)Refutation found. Thanks to Tanya!
% 0.10/0.37  % SZS status Theorem for theBenchmark
% 0.10/0.37  % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.37  % (2801)------------------------------
% 0.10/0.37  % (2801)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.10/0.37  % (2801)Termination reason: Refutation
% 0.10/0.37  
% 0.10/0.37  % (2801)Memory used [KB]: 1316
% 0.10/0.37  % (2801)Time elapsed: 0.036 s
% 0.10/0.37  % (2801)Instructions burned: 71 (million)
% 0.10/0.37  % (2798)Success in time 0.049 s
%------------------------------------------------------------------------------