TSTP Solution File: GEO186+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : GEO186+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s

% Computer : n012.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 : Fri Sep  1 14:43:19 EDT 2023

% Result   : Theorem 0.22s 0.43s
% Output   : Refutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   60 (  12 unt;   0 def)
%            Number of atoms       :  178 (   0 equ)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives :  194 (  76   ~;  73   |;  31   &)
%                                         (   4 <=>;  10  =>;   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    :    5 (   5 usr;   4 con; 0-2 aty)
%            Number of variables   :   93 (;  81   !;  12   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f233,plain,
    $false,
    inference(avatar_sat_refutation,[],[f124,f143,f199,f204,f232]) ).

fof(f232,plain,
    spl4_4,
    inference(avatar_contradiction_clause,[],[f231]) ).

fof(f231,plain,
    ( $false
    | spl4_4 ),
    inference(resolution,[],[f225,f48]) ).

fof(f48,plain,
    ! [X0] : ~ distinct_points(X0,X0),
    inference(cnf_transformation,[],[f1]) ).

fof(f1,axiom,
    ! [X0] : ~ distinct_points(X0,X0),
    file('/export/starexec/sandbox/tmp/tmp.32Ll9gJnwQ/Vampire---4.8_17550',apart1) ).

fof(f225,plain,
    ( distinct_points(sK0,sK0)
    | spl4_4 ),
    inference(resolution,[],[f208,f45]) ).

fof(f45,plain,
    distinct_points(sK0,intersection_point(sK2,sK3)),
    inference(cnf_transformation,[],[f40]) ).

fof(f40,plain,
    ( distinct_points(sK0,intersection_point(sK2,sK3))
    & ~ apart_point_and_line(sK0,sK3)
    & ~ apart_point_and_line(sK0,sK2)
    & convergent_lines(sK2,sK3)
    & distinct_points(sK0,sK1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f20,f39]) ).

fof(f39,plain,
    ( ? [X0,X1,X2,X3] :
        ( distinct_points(X0,intersection_point(X2,X3))
        & ~ apart_point_and_line(X0,X3)
        & ~ apart_point_and_line(X0,X2)
        & convergent_lines(X2,X3)
        & distinct_points(X0,X1) )
   => ( distinct_points(sK0,intersection_point(sK2,sK3))
      & ~ apart_point_and_line(sK0,sK3)
      & ~ apart_point_and_line(sK0,sK2)
      & convergent_lines(sK2,sK3)
      & distinct_points(sK0,sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f20,plain,
    ? [X0,X1,X2,X3] :
      ( distinct_points(X0,intersection_point(X2,X3))
      & ~ apart_point_and_line(X0,X3)
      & ~ apart_point_and_line(X0,X2)
      & convergent_lines(X2,X3)
      & distinct_points(X0,X1) ),
    inference(flattening,[],[f19]) ).

fof(f19,plain,
    ? [X0,X1,X2,X3] :
      ( distinct_points(X0,intersection_point(X2,X3))
      & ~ apart_point_and_line(X0,X3)
      & ~ apart_point_and_line(X0,X2)
      & convergent_lines(X2,X3)
      & distinct_points(X0,X1) ),
    inference(ennf_transformation,[],[f17]) ).

fof(f17,plain,
    ~ ! [X0,X1,X2,X3] :
        ( ( ~ apart_point_and_line(X0,X3)
          & ~ apart_point_and_line(X0,X2)
          & convergent_lines(X2,X3)
          & distinct_points(X0,X1) )
       => ~ distinct_points(X0,intersection_point(X2,X3)) ),
    inference(rectify,[],[f16]) ).

fof(f16,negated_conjecture,
    ~ ! [X0,X1,X3,X4] :
        ( ( ~ apart_point_and_line(X0,X4)
          & ~ apart_point_and_line(X0,X3)
          & convergent_lines(X3,X4)
          & distinct_points(X0,X1) )
       => ~ distinct_points(X0,intersection_point(X3,X4)) ),
    inference(negated_conjecture,[],[f15]) ).

fof(f15,conjecture,
    ! [X0,X1,X3,X4] :
      ( ( ~ apart_point_and_line(X0,X4)
        & ~ apart_point_and_line(X0,X3)
        & convergent_lines(X3,X4)
        & distinct_points(X0,X1) )
     => ~ distinct_points(X0,intersection_point(X3,X4)) ),
    file('/export/starexec/sandbox/tmp/tmp.32Ll9gJnwQ/Vampire---4.8_17550',con) ).

fof(f208,plain,
    ( ! [X0] :
        ( ~ distinct_points(X0,intersection_point(sK2,sK3))
        | distinct_points(X0,sK0) )
    | spl4_4 ),
    inference(resolution,[],[f198,f56]) ).

fof(f56,plain,
    ! [X2,X0,X1] :
      ( distinct_points(X1,X2)
      | distinct_points(X0,X2)
      | ~ distinct_points(X0,X1) ),
    inference(cnf_transformation,[],[f32]) ).

fof(f32,plain,
    ! [X0,X1,X2] :
      ( distinct_points(X1,X2)
      | distinct_points(X0,X2)
      | ~ distinct_points(X0,X1) ),
    inference(flattening,[],[f31]) ).

fof(f31,plain,
    ! [X0,X1,X2] :
      ( distinct_points(X1,X2)
      | distinct_points(X0,X2)
      | ~ distinct_points(X0,X1) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X0,X1,X2] :
      ( distinct_points(X0,X1)
     => ( distinct_points(X1,X2)
        | distinct_points(X0,X2) ) ),
    file('/export/starexec/sandbox/tmp/tmp.32Ll9gJnwQ/Vampire---4.8_17550',apart4) ).

fof(f198,plain,
    ( ~ distinct_points(intersection_point(sK2,sK3),sK0)
    | spl4_4 ),
    inference(avatar_component_clause,[],[f196]) ).

fof(f196,plain,
    ( spl4_4
  <=> distinct_points(intersection_point(sK2,sK3),sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_4])]) ).

fof(f204,plain,
    spl4_3,
    inference(avatar_contradiction_clause,[],[f201]) ).

fof(f201,plain,
    ( $false
    | spl4_3 ),
    inference(resolution,[],[f194,f42]) ).

fof(f42,plain,
    convergent_lines(sK2,sK3),
    inference(cnf_transformation,[],[f40]) ).

fof(f194,plain,
    ( ~ convergent_lines(sK2,sK3)
    | spl4_3 ),
    inference(avatar_component_clause,[],[f192]) ).

fof(f192,plain,
    ( spl4_3
  <=> convergent_lines(sK2,sK3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_3])]) ).

fof(f199,plain,
    ( ~ spl4_3
    | ~ spl4_4
    | ~ spl4_2 ),
    inference(avatar_split_clause,[],[f190,f122,f196,f192]) ).

fof(f122,plain,
    ( spl4_2
  <=> ! [X1] :
        ( apart_point_and_line(X1,sK2)
        | ~ distinct_points(X1,sK0)
        | apart_point_and_line(X1,sK3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_2])]) ).

fof(f190,plain,
    ( ~ distinct_points(intersection_point(sK2,sK3),sK0)
    | ~ convergent_lines(sK2,sK3)
    | ~ spl4_2 ),
    inference(duplicate_literal_removal,[],[f185]) ).

fof(f185,plain,
    ( ~ distinct_points(intersection_point(sK2,sK3),sK0)
    | ~ convergent_lines(sK2,sK3)
    | ~ convergent_lines(sK2,sK3)
    | ~ spl4_2 ),
    inference(resolution,[],[f157,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/tmp/tmp.32Ll9gJnwQ/Vampire---4.8_17550',ci3) ).

fof(f157,plain,
    ( ! [X0] :
        ( apart_point_and_line(intersection_point(X0,sK3),sK2)
        | ~ distinct_points(intersection_point(X0,sK3),sK0)
        | ~ convergent_lines(X0,sK3) )
    | ~ spl4_2 ),
    inference(resolution,[],[f123,f49]) ).

fof(f49,plain,
    ! [X0,X1] :
      ( ~ apart_point_and_line(intersection_point(X0,X1),X1)
      | ~ convergent_lines(X0,X1) ),
    inference(cnf_transformation,[],[f21]) ).

fof(f21,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/tmp/tmp.32Ll9gJnwQ/Vampire---4.8_17550',ci4) ).

fof(f123,plain,
    ( ! [X1] :
        ( apart_point_and_line(X1,sK3)
        | ~ distinct_points(X1,sK0)
        | apart_point_and_line(X1,sK2) )
    | ~ spl4_2 ),
    inference(avatar_component_clause,[],[f122]) ).

fof(f143,plain,
    spl4_1,
    inference(avatar_contradiction_clause,[],[f140]) ).

fof(f140,plain,
    ( $false
    | spl4_1 ),
    inference(resolution,[],[f126,f42]) ).

fof(f126,plain,
    ( ~ convergent_lines(sK2,sK3)
    | spl4_1 ),
    inference(resolution,[],[f120,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/tmp/tmp.32Ll9gJnwQ/Vampire---4.8_17550',apart3) ).

fof(f54,plain,
    ! [X2,X0,X1] :
      ( convergent_lines(X0,X2)
      | distinct_lines(X1,X2)
      | ~ convergent_lines(X0,X1) ),
    inference(cnf_transformation,[],[f28]) ).

fof(f28,plain,
    ! [X0,X1,X2] :
      ( convergent_lines(X0,X2)
      | distinct_lines(X1,X2)
      | ~ convergent_lines(X0,X1) ),
    inference(flattening,[],[f27]) ).

fof(f27,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/tmp/tmp.32Ll9gJnwQ/Vampire---4.8_17550',ceq3) ).

fof(f120,plain,
    ( ~ distinct_lines(sK3,sK2)
    | spl4_1 ),
    inference(avatar_component_clause,[],[f118]) ).

fof(f118,plain,
    ( spl4_1
  <=> distinct_lines(sK3,sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_1])]) ).

fof(f124,plain,
    ( ~ spl4_1
    | spl4_2 ),
    inference(avatar_split_clause,[],[f104,f122,f118]) ).

fof(f104,plain,
    ! [X1] :
      ( apart_point_and_line(X1,sK2)
      | apart_point_and_line(X1,sK3)
      | ~ distinct_lines(sK3,sK2)
      | ~ distinct_points(X1,sK0) ),
    inference(resolution,[],[f79,f44]) ).

fof(f44,plain,
    ~ apart_point_and_line(sK0,sK3),
    inference(cnf_transformation,[],[f40]) ).

fof(f79,plain,
    ! [X0,X1] :
      ( apart_point_and_line(sK0,X0)
      | apart_point_and_line(X1,sK2)
      | apart_point_and_line(X1,X0)
      | ~ distinct_lines(X0,sK2)
      | ~ distinct_points(X1,sK0) ),
    inference(resolution,[],[f59,f43]) ).

fof(f43,plain,
    ~ apart_point_and_line(sK0,sK2),
    inference(cnf_transformation,[],[f40]) ).

fof(f59,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,[],[f38]) ).

fof(f38,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,[],[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(ennf_transformation,[],[f18]) ).

fof(f18,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/tmp/tmp.32Ll9gJnwQ/Vampire---4.8_17550',cu1) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.13  % Problem    : GEO186+1 : TPTP v8.1.2. Released v3.3.0.
% 0.10/0.14  % Command    : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.15/0.36  % Computer : n012.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   : Wed Aug 30 18:02:23 EDT 2023
% 0.15/0.36  % CPUTime    : 
% 0.22/0.42  % (17801)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.42  % (17823)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on Vampire---4 for (1451ds/0Mi)
% 0.22/0.42  % (17824)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on Vampire---4 for (569ds/0Mi)
% 0.22/0.42  % (17825)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 Vampire---4 for (476ds/0Mi)
% 0.22/0.42  % (17826)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on Vampire---4 for (470ds/0Mi)
% 0.22/0.42  % (17828)dis+11_4:5_nm=4_216 on Vampire---4 for (216ds/0Mi)
% 0.22/0.42  % (17827)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on Vampire---4 for (396ds/0Mi)
% 0.22/0.42  % (17829)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_1451 on Vampire---4 for (1451ds/0Mi)
% 0.22/0.42  TRYING [1,1]
% 0.22/0.42  TRYING [1]
% 0.22/0.42  TRYING [2]
% 0.22/0.42  TRYING [1,1]
% 0.22/0.42  TRYING [1,2]
% 0.22/0.42  TRYING [2,2]
% 0.22/0.42  TRYING [1,2]
% 0.22/0.42  TRYING [3]
% 0.22/0.42  TRYING [2,2]
% 0.22/0.42  TRYING [2,3]
% 0.22/0.42  TRYING [2,3]
% 0.22/0.42  TRYING [1]
% 0.22/0.42  TRYING [2]
% 0.22/0.42  TRYING [2,4]
% 0.22/0.42  TRYING [4]
% 0.22/0.42  TRYING [2,4]
% 0.22/0.42  TRYING [3]
% 0.22/0.42  TRYING [2,5]
% 0.22/0.42  TRYING [2,5]
% 0.22/0.43  TRYING [4]
% 0.22/0.43  % (17825)First to succeed.
% 0.22/0.43  TRYING [2,6]
% 0.22/0.43  TRYING [5]
% 0.22/0.43  TRYING [2,6]
% 0.22/0.43  TRYING [2,7]
% 0.22/0.43  % (17825)Refutation found. Thanks to Tanya!
% 0.22/0.43  % SZS status Theorem for Vampire---4
% 0.22/0.43  % SZS output start Proof for Vampire---4
% See solution above
% 0.22/0.43  % (17825)------------------------------
% 0.22/0.43  % (17825)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.22/0.43  % (17825)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.22/0.43  % (17825)Termination reason: Refutation
% 0.22/0.43  
% 0.22/0.43  % (17825)Memory used [KB]: 5500
% 0.22/0.43  % (17825)Time elapsed: 0.007 s
% 0.22/0.43  % (17825)------------------------------
% 0.22/0.43  % (17825)------------------------------
% 0.22/0.43  % (17801)Success in time 0.065 s
% 0.22/0.43  % Vampire---4.8 exiting
%------------------------------------------------------------------------------