TSTP Solution File: GEO197+2 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : GEO197+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 : n003.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 11:14:38 EDT 2024

% Result   : Theorem 0.15s 0.40s
% Output   : Refutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   66 (  13 unt;   0 def)
%            Number of atoms       :  200 (   0 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  212 (  78   ~;  89   |;  30   &)
%                                         (   6 <=>;   9  =>;   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   :   86 (  77   !;   9   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f728,plain,
    $false,
    inference(avatar_sat_refutation,[],[f98,f153,f170,f212,f325,f701,f727]) ).

fof(f727,plain,
    spl3_22,
    inference(avatar_contradiction_clause,[],[f716]) ).

fof(f716,plain,
    ( $false
    | spl3_22 ),
    inference(resolution,[],[f700,f41]) ).

fof(f41,plain,
    apart_point_and_line(intersection_point(sK2,sK1),sK0),
    inference(cnf_transformation,[],[f36]) ).

fof(f36,plain,
    ( apart_point_and_line(intersection_point(sK2,sK1),sK0)
    & ~ 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])],[f17,f35]) ).

fof(f35,plain,
    ( ? [X0,X1,X2] :
        ( apart_point_and_line(intersection_point(X2,X1),X0)
        & ~ 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(sK2,sK1),sK0)
      & ~ 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(f17,plain,
    ? [X0,X1,X2] :
      ( apart_point_and_line(intersection_point(X2,X1),X0)
      & ~ apart_point_and_line(intersection_point(X0,X1),X2)
      & convergent_lines(X0,X2)
      & convergent_lines(X2,X1)
      & convergent_lines(X0,X1) ),
    inference(flattening,[],[f16]) ).

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

fof(f14,negated_conjecture,
    ~ ! [X0,X1,X2] :
        ( ( ~ 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(X2,X1),X0) ),
    inference(negated_conjecture,[],[f13]) ).

fof(f13,conjecture,
    ! [X0,X1,X2] :
      ( ( ~ 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(X2,X1),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).

fof(f700,plain,
    ( ~ apart_point_and_line(intersection_point(sK2,sK1),sK0)
    | spl3_22 ),
    inference(avatar_component_clause,[],[f698]) ).

fof(f698,plain,
    ( spl3_22
  <=> apart_point_and_line(intersection_point(sK2,sK1),sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_22])]) ).

fof(f701,plain,
    ( ~ spl3_1
    | ~ spl3_22
    | ~ spl3_11 ),
    inference(avatar_split_clause,[],[f691,f323,f698,f81]) ).

fof(f81,plain,
    ( spl3_1
  <=> convergent_lines(sK2,sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).

fof(f323,plain,
    ( spl3_11
  <=> ! [X0] :
        ( apart_point_and_line(X0,sK2)
        | ~ apart_point_and_line(X0,sK0)
        | apart_point_and_line(X0,sK1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_11])]) ).

fof(f691,plain,
    ( ~ apart_point_and_line(intersection_point(sK2,sK1),sK0)
    | ~ convergent_lines(sK2,sK1)
    | ~ spl3_11 ),
    inference(duplicate_literal_removal,[],[f684]) ).

fof(f684,plain,
    ( ~ apart_point_and_line(intersection_point(sK2,sK1),sK0)
    | ~ convergent_lines(sK2,sK1)
    | ~ convergent_lines(sK2,sK1)
    | ~ spl3_11 ),
    inference(resolution,[],[f339,f68]) ).

fof(f68,plain,
    ! [X0,X1] :
      ( ~ apart_point_and_line(intersection_point(X0,X1),X1)
      | ~ convergent_lines(X0,X1) ),
    inference(resolution,[],[f49,f44]) ).

fof(f44,plain,
    ! [X0] : ~ distinct_points(X0,X0),
    inference(cnf_transformation,[],[f1]) ).

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

fof(f49,plain,
    ! [X2,X0,X1] :
      ( distinct_points(X2,intersection_point(X0,X1))
      | ~ apart_point_and_line(X2,X1)
      | ~ convergent_lines(X0,X1) ),
    inference(cnf_transformation,[],[f24]) ).

fof(f24,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,[],[f23]) ).

fof(f23,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/sandbox/benchmark/theBenchmark.p',con2) ).

fof(f339,plain,
    ( ! [X0] :
        ( apart_point_and_line(intersection_point(sK2,X0),sK1)
        | ~ apart_point_and_line(intersection_point(sK2,X0),sK0)
        | ~ convergent_lines(sK2,X0) )
    | ~ spl3_11 ),
    inference(resolution,[],[f324,f65]) ).

fof(f65,plain,
    ! [X0,X1] :
      ( ~ apart_point_and_line(intersection_point(X0,X1),X0)
      | ~ convergent_lines(X0,X1) ),
    inference(resolution,[],[f48,f44]) ).

fof(f48,plain,
    ! [X2,X0,X1] :
      ( distinct_points(X2,intersection_point(X0,X1))
      | ~ apart_point_and_line(X2,X0)
      | ~ convergent_lines(X0,X1) ),
    inference(cnf_transformation,[],[f24]) ).

fof(f324,plain,
    ( ! [X0] :
        ( apart_point_and_line(X0,sK2)
        | ~ apart_point_and_line(X0,sK0)
        | apart_point_and_line(X0,sK1) )
    | ~ spl3_11 ),
    inference(avatar_component_clause,[],[f323]) ).

fof(f325,plain,
    ( ~ spl3_4
    | spl3_11
    | ~ spl3_7 ),
    inference(avatar_split_clause,[],[f218,f168,f323,f144]) ).

fof(f144,plain,
    ( spl3_4
  <=> convergent_lines(sK0,sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_4])]) ).

fof(f168,plain,
    ( spl3_7
  <=> ! [X0] :
        ( apart_point_and_line(X0,sK2)
        | ~ distinct_points(X0,intersection_point(sK0,sK1))
        | apart_point_and_line(X0,sK1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_7])]) ).

fof(f218,plain,
    ( ! [X0] :
        ( apart_point_and_line(X0,sK2)
        | apart_point_and_line(X0,sK1)
        | ~ apart_point_and_line(X0,sK0)
        | ~ convergent_lines(sK0,sK1) )
    | ~ spl3_7 ),
    inference(resolution,[],[f169,f48]) ).

fof(f169,plain,
    ( ! [X0] :
        ( ~ distinct_points(X0,intersection_point(sK0,sK1))
        | apart_point_and_line(X0,sK2)
        | apart_point_and_line(X0,sK1) )
    | ~ spl3_7 ),
    inference(avatar_component_clause,[],[f168]) ).

fof(f212,plain,
    spl3_6,
    inference(avatar_contradiction_clause,[],[f210]) ).

fof(f210,plain,
    ( $false
    | spl3_6 ),
    inference(resolution,[],[f200,f38]) ).

fof(f38,plain,
    convergent_lines(sK2,sK1),
    inference(cnf_transformation,[],[f36]) ).

fof(f200,plain,
    ( ~ convergent_lines(sK2,sK1)
    | spl3_6 ),
    inference(resolution,[],[f185,f45]) ).

fof(f45,plain,
    ! [X0,X1] :
      ( distinct_lines(X0,X1)
      | ~ convergent_lines(X0,X1) ),
    inference(cnf_transformation,[],[f18]) ).

fof(f18,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/sandbox/benchmark/theBenchmark.p',ceq3) ).

fof(f185,plain,
    ( ~ distinct_lines(sK2,sK1)
    | spl3_6 ),
    inference(resolution,[],[f174,f42]) ).

fof(f42,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(f174,plain,
    ( ! [X0] :
        ( distinct_lines(X0,sK2)
        | ~ distinct_lines(X0,sK1) )
    | spl3_6 ),
    inference(resolution,[],[f166,f46]) ).

fof(f46,plain,
    ! [X2,X0,X1] :
      ( distinct_lines(X1,X2)
      | distinct_lines(X0,X2)
      | ~ distinct_lines(X0,X1) ),
    inference(cnf_transformation,[],[f20]) ).

fof(f20,plain,
    ! [X0,X1,X2] :
      ( distinct_lines(X1,X2)
      | distinct_lines(X0,X2)
      | ~ distinct_lines(X0,X1) ),
    inference(flattening,[],[f19]) ).

fof(f19,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(f166,plain,
    ( ~ distinct_lines(sK1,sK2)
    | spl3_6 ),
    inference(avatar_component_clause,[],[f164]) ).

fof(f164,plain,
    ( spl3_6
  <=> distinct_lines(sK1,sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_6])]) ).

fof(f170,plain,
    ( ~ spl3_4
    | ~ spl3_6
    | spl3_7 ),
    inference(avatar_split_clause,[],[f115,f168,f164,f144]) ).

fof(f115,plain,
    ! [X0] :
      ( apart_point_and_line(X0,sK2)
      | apart_point_and_line(X0,sK1)
      | ~ distinct_lines(sK1,sK2)
      | ~ distinct_points(X0,intersection_point(sK0,sK1))
      | ~ convergent_lines(sK0,sK1) ),
    inference(resolution,[],[f89,f68]) ).

fof(f89,plain,
    ! [X0,X1] :
      ( apart_point_and_line(intersection_point(sK0,sK1),X0)
      | apart_point_and_line(X1,sK2)
      | apart_point_and_line(X1,X0)
      | ~ distinct_lines(X0,sK2)
      | ~ distinct_points(X1,intersection_point(sK0,sK1)) ),
    inference(resolution,[],[f55,f40]) ).

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

fof(f55,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,[],[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/sandbox/benchmark/theBenchmark.p',cu1) ).

fof(f153,plain,
    spl3_4,
    inference(avatar_contradiction_clause,[],[f151]) ).

fof(f151,plain,
    ( $false
    | spl3_4 ),
    inference(resolution,[],[f146,f37]) ).

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

fof(f146,plain,
    ( ~ convergent_lines(sK0,sK1)
    | spl3_4 ),
    inference(avatar_component_clause,[],[f144]) ).

fof(f98,plain,
    spl3_1,
    inference(avatar_contradiction_clause,[],[f96]) ).

fof(f96,plain,
    ( $false
    | spl3_1 ),
    inference(resolution,[],[f83,f38]) ).

fof(f83,plain,
    ( ~ convergent_lines(sK2,sK1)
    | spl3_1 ),
    inference(avatar_component_clause,[],[f81]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : GEO197+2 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.15  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36  % Computer : n003.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Tue Apr 30 05:53:03 EDT 2024
% 0.15/0.36  % CPUTime    : 
% 0.15/0.36  % (6532)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38  % (6533)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.15/0.38  % (6534)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.15/0.38  % (6537)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.15/0.38  % (6536)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.15/0.38  % (6535)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)
% 0.15/0.38  % (6538)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.15/0.38  % (6539)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)
% 0.15/0.38  TRYING [1]
% 0.15/0.38  TRYING [2]
% 0.15/0.38  TRYING [1,1]
% 0.15/0.38  TRYING [1]
% 0.15/0.38  TRYING [1,1]
% 0.15/0.38  TRYING [3]
% 0.15/0.38  TRYING [2,2]
% 0.15/0.38  TRYING [2]
% 0.15/0.38  TRYING [2,2]
% 0.15/0.38  TRYING [3]
% 0.15/0.38  TRYING [3,3]
% 0.15/0.38  TRYING [3,3]
% 0.15/0.39  TRYING [4]
% 0.15/0.39  TRYING [4]
% 0.15/0.39  TRYING [3,4]
% 0.15/0.39  TRYING [3,4]
% 0.15/0.39  TRYING [5]
% 0.15/0.39  TRYING [3,5]
% 0.15/0.39  TRYING [3,5]
% 0.15/0.39  TRYING [5]
% 0.15/0.39  TRYING [3,6]
% 0.15/0.39  TRYING [3,6]
% 0.15/0.39  TRYING [6]
% 0.15/0.40  TRYING [3,7]
% 0.15/0.40  TRYING [3,7]
% 0.15/0.40  % (6535)First to succeed.
% 0.15/0.40  TRYING [6]
% 0.15/0.40  % (6535)Refutation found. Thanks to Tanya!
% 0.15/0.40  % SZS status Theorem for theBenchmark
% 0.15/0.40  % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.40  % (6535)------------------------------
% 0.15/0.40  % (6535)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.15/0.40  % (6535)Termination reason: Refutation
% 0.15/0.40  
% 0.15/0.40  % (6535)Memory used [KB]: 1113
% 0.15/0.40  % (6535)Time elapsed: 0.020 s
% 0.15/0.40  % (6535)Instructions burned: 32 (million)
% 0.15/0.40  % (6535)------------------------------
% 0.15/0.40  % (6535)------------------------------
% 0.15/0.40  % (6532)Success in time 0.036 s
%------------------------------------------------------------------------------