TSTP Solution File: GEO182+2 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : GEO182+2 : 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 : 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 : Fri Sep  1 14:43:18 EDT 2023

% Result   : Theorem 0.20s 0.43s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   65 (  10 unt;   0 def)
%            Number of atoms       :  183 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  181 (  63   ~;  87   |;  15   &)
%                                         (   5 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    9 (   8 usr;   6 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :   84 (;  75   !;   9   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f483,plain,
    $false,
    inference(avatar_sat_refutation,[],[f211,f231,f288,f379,f404,f480]) ).

fof(f480,plain,
    ~ spl3_14,
    inference(avatar_contradiction_clause,[],[f479]) ).

fof(f479,plain,
    ( $false
    | ~ spl3_14 ),
    inference(subsumption_resolution,[],[f454,f42]) ).

fof(f42,plain,
    ! [X0] : ~ distinct_points(X0,X0),
    inference(cnf_transformation,[],[f1]) ).

fof(f1,axiom,
    ! [X0] : ~ distinct_points(X0,X0),
    file('/export/starexec/sandbox/tmp/tmp.noX9AnMp5H/Vampire---4.8_15545',apart1) ).

fof(f454,plain,
    ( distinct_points(sK0,sK0)
    | ~ spl3_14 ),
    inference(resolution,[],[f434,f54]) ).

fof(f54,plain,
    ! [X0] :
      ( distinct_points(sK1,X0)
      | distinct_points(sK0,X0) ),
    inference(resolution,[],[f48,f37]) ).

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

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

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

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

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

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

fof(f13,conjecture,
    ! [X0,X1,X2] :
      ( distinct_points(X0,X1)
     => ( apart_point_and_line(X2,line_connecting(X0,X1))
       => apart_point_and_line(X2,line_connecting(X1,X0)) ) ),
    file('/export/starexec/sandbox/tmp/tmp.noX9AnMp5H/Vampire---4.8_15545',con) ).

fof(f48,plain,
    ! [X2,X0,X1] :
      ( ~ distinct_points(X0,X1)
      | distinct_points(X0,X2)
      | distinct_points(X1,X2) ),
    inference(cnf_transformation,[],[f26]) ).

fof(f26,plain,
    ! [X0,X1,X2] :
      ( distinct_points(X1,X2)
      | distinct_points(X0,X2)
      | ~ distinct_points(X0,X1) ),
    inference(flattening,[],[f25]) ).

fof(f25,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.noX9AnMp5H/Vampire---4.8_15545',apart4) ).

fof(f434,plain,
    ( ~ distinct_points(sK1,sK0)
    | ~ spl3_14 ),
    inference(subsumption_resolution,[],[f430,f42]) ).

fof(f430,plain,
    ( distinct_points(sK0,sK0)
    | ~ distinct_points(sK1,sK0)
    | ~ spl3_14 ),
    inference(resolution,[],[f378,f50]) ).

fof(f50,plain,
    ! [X2,X0,X1] :
      ( ~ apart_point_and_line(X2,line_connecting(X0,X1))
      | distinct_points(X2,X1)
      | ~ distinct_points(X0,X1) ),
    inference(cnf_transformation,[],[f28]) ).

fof(f28,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,[],[f27]) ).

fof(f27,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/sandbox/tmp/tmp.noX9AnMp5H/Vampire---4.8_15545',con1) ).

fof(f378,plain,
    ( apart_point_and_line(sK0,line_connecting(sK1,sK0))
    | ~ spl3_14 ),
    inference(avatar_component_clause,[],[f376]) ).

fof(f376,plain,
    ( spl3_14
  <=> apart_point_and_line(sK0,line_connecting(sK1,sK0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_14])]) ).

fof(f404,plain,
    ~ spl3_13,
    inference(avatar_contradiction_clause,[],[f403]) ).

fof(f403,plain,
    ( $false
    | ~ spl3_13 ),
    inference(subsumption_resolution,[],[f389,f42]) ).

fof(f389,plain,
    ( distinct_points(sK0,sK0)
    | ~ spl3_13 ),
    inference(resolution,[],[f384,f54]) ).

fof(f384,plain,
    ( ~ distinct_points(sK1,sK0)
    | ~ spl3_13 ),
    inference(subsumption_resolution,[],[f381,f42]) ).

fof(f381,plain,
    ( distinct_points(sK1,sK1)
    | ~ distinct_points(sK1,sK0)
    | ~ spl3_13 ),
    inference(resolution,[],[f374,f49]) ).

fof(f49,plain,
    ! [X2,X0,X1] :
      ( ~ apart_point_and_line(X2,line_connecting(X0,X1))
      | distinct_points(X2,X0)
      | ~ distinct_points(X0,X1) ),
    inference(cnf_transformation,[],[f28]) ).

fof(f374,plain,
    ( apart_point_and_line(sK1,line_connecting(sK1,sK0))
    | ~ spl3_13 ),
    inference(avatar_component_clause,[],[f372]) ).

fof(f372,plain,
    ( spl3_13
  <=> apart_point_and_line(sK1,line_connecting(sK1,sK0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_13])]) ).

fof(f379,plain,
    ( spl3_13
    | spl3_14
    | ~ spl3_5 ),
    inference(avatar_split_clause,[],[f366,f209,f376,f372]) ).

fof(f209,plain,
    ( spl3_5
  <=> ! [X21] :
        ( apart_point_and_line(sK0,X21)
        | apart_point_and_line(sK2,X21)
        | apart_point_and_line(sK1,X21) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_5])]) ).

fof(f366,plain,
    ( apart_point_and_line(sK0,line_connecting(sK1,sK0))
    | apart_point_and_line(sK1,line_connecting(sK1,sK0))
    | ~ spl3_5 ),
    inference(resolution,[],[f210,f39]) ).

fof(f39,plain,
    ~ apart_point_and_line(sK2,line_connecting(sK1,sK0)),
    inference(cnf_transformation,[],[f36]) ).

fof(f210,plain,
    ( ! [X21] :
        ( apart_point_and_line(sK2,X21)
        | apart_point_and_line(sK0,X21)
        | apart_point_and_line(sK1,X21) )
    | ~ spl3_5 ),
    inference(avatar_component_clause,[],[f209]) ).

fof(f288,plain,
    ~ spl3_1,
    inference(avatar_contradiction_clause,[],[f287]) ).

fof(f287,plain,
    ( $false
    | ~ spl3_1 ),
    inference(subsumption_resolution,[],[f286,f37]) ).

fof(f286,plain,
    ( ~ distinct_points(sK0,sK1)
    | ~ spl3_1 ),
    inference(subsumption_resolution,[],[f282,f42]) ).

fof(f282,plain,
    ( distinct_points(sK1,sK1)
    | ~ distinct_points(sK0,sK1)
    | ~ spl3_1 ),
    inference(resolution,[],[f195,f50]) ).

fof(f195,plain,
    ( apart_point_and_line(sK1,line_connecting(sK0,sK1))
    | ~ spl3_1 ),
    inference(avatar_component_clause,[],[f193]) ).

fof(f193,plain,
    ( spl3_1
  <=> apart_point_and_line(sK1,line_connecting(sK0,sK1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).

fof(f231,plain,
    ~ spl3_3,
    inference(avatar_contradiction_clause,[],[f230]) ).

fof(f230,plain,
    ( $false
    | ~ spl3_3 ),
    inference(subsumption_resolution,[],[f229,f37]) ).

fof(f229,plain,
    ( ~ distinct_points(sK0,sK1)
    | ~ spl3_3 ),
    inference(subsumption_resolution,[],[f226,f42]) ).

fof(f226,plain,
    ( distinct_points(sK0,sK0)
    | ~ distinct_points(sK0,sK1)
    | ~ spl3_3 ),
    inference(resolution,[],[f203,f49]) ).

fof(f203,plain,
    ( apart_point_and_line(sK0,line_connecting(sK0,sK1))
    | ~ spl3_3 ),
    inference(avatar_component_clause,[],[f201]) ).

fof(f201,plain,
    ( spl3_3
  <=> apart_point_and_line(sK0,line_connecting(sK0,sK1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_3])]) ).

fof(f211,plain,
    ( spl3_1
    | spl3_3
    | spl3_5 ),
    inference(avatar_split_clause,[],[f163,f209,f201,f193]) ).

fof(f163,plain,
    ! [X21] :
      ( apart_point_and_line(sK0,X21)
      | apart_point_and_line(sK0,line_connecting(sK0,sK1))
      | apart_point_and_line(sK1,X21)
      | apart_point_and_line(sK1,line_connecting(sK0,sK1))
      | apart_point_and_line(sK2,X21) ),
    inference(resolution,[],[f85,f37]) ).

fof(f85,plain,
    ! [X2,X0,X1] :
      ( ~ distinct_points(X1,X0)
      | apart_point_and_line(X1,X2)
      | apart_point_and_line(X1,line_connecting(sK0,sK1))
      | apart_point_and_line(X0,X2)
      | apart_point_and_line(X0,line_connecting(sK0,sK1))
      | apart_point_and_line(sK2,X2) ),
    inference(resolution,[],[f53,f55]) ).

fof(f55,plain,
    ! [X0] :
      ( distinct_lines(line_connecting(sK0,sK1),X0)
      | apart_point_and_line(sK2,X0) ),
    inference(resolution,[],[f51,f38]) ).

fof(f38,plain,
    apart_point_and_line(sK2,line_connecting(sK0,sK1)),
    inference(cnf_transformation,[],[f36]) ).

fof(f51,plain,
    ! [X2,X0,X1] :
      ( ~ apart_point_and_line(X0,X1)
      | distinct_lines(X1,X2)
      | apart_point_and_line(X0,X2) ),
    inference(cnf_transformation,[],[f30]) ).

fof(f30,plain,
    ! [X0,X1,X2] :
      ( apart_point_and_line(X0,X2)
      | distinct_lines(X1,X2)
      | ~ apart_point_and_line(X0,X1) ),
    inference(flattening,[],[f29]) ).

fof(f29,plain,
    ! [X0,X1,X2] :
      ( apart_point_and_line(X0,X2)
      | distinct_lines(X1,X2)
      | ~ apart_point_and_line(X0,X1) ),
    inference(ennf_transformation,[],[f11]) ).

fof(f11,axiom,
    ! [X0,X1,X2] :
      ( apart_point_and_line(X0,X1)
     => ( apart_point_and_line(X0,X2)
        | distinct_lines(X1,X2) ) ),
    file('/export/starexec/sandbox/tmp/tmp.noX9AnMp5H/Vampire---4.8_15545',ceq2) ).

fof(f53,plain,
    ! [X2,X3,X0,X1] :
      ( ~ distinct_lines(X2,X3)
      | apart_point_and_line(X1,X2)
      | apart_point_and_line(X0,X3)
      | apart_point_and_line(X0,X2)
      | apart_point_and_line(X1,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/tmp/tmp.noX9AnMp5H/Vampire---4.8_15545',cu1) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.12  % Problem    : GEO182+2 : TPTP v8.1.2. Released v3.3.0.
% 0.09/0.13  % Command    : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.13/0.35  % Computer : n014.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   : Wed Aug 30 18:05:44 EDT 2023
% 0.13/0.35  % CPUTime    : 
% 0.20/0.41  % (15702)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.42  % (15706)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on Vampire---4 for (470ds/0Mi)
% 0.20/0.42  % (15704)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on Vampire---4 for (569ds/0Mi)
% 0.20/0.42  % (15707)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on Vampire---4 for (396ds/0Mi)
% 0.20/0.42  % (15705)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)
% 0.20/0.42  % (15708)dis+11_4:5_nm=4_216 on Vampire---4 for (216ds/0Mi)
% 0.20/0.42  % (15703)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on Vampire---4 for (1451ds/0Mi)
% 0.20/0.42  % (15709)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)
% 0.20/0.42  TRYING [1]
% 0.20/0.42  TRYING [1,1]
% 0.20/0.42  TRYING [1,1]
% 0.20/0.42  TRYING [1]
% 0.20/0.42  TRYING [2]
% 0.20/0.42  TRYING [2,2]
% 0.20/0.42  TRYING [2]
% 0.20/0.42  TRYING [2,2]
% 0.20/0.42  TRYING [3]
% 0.20/0.42  TRYING [3,2]
% 0.20/0.42  TRYING [3,2]
% 0.20/0.42  TRYING [3]
% 0.20/0.42  TRYING [4,2]
% 0.20/0.42  TRYING [4,2]
% 0.20/0.42  TRYING [4]
% 0.20/0.42  TRYING [4]
% 0.20/0.42  TRYING [3,3]
% 0.20/0.42  TRYING [3,3]
% 0.20/0.42  TRYING [5]
% 0.20/0.42  TRYING [5,2]
% 0.20/0.42  TRYING [5,2]
% 0.20/0.42  TRYING [4,3]
% 0.20/0.42  TRYING [4,3]
% 0.20/0.42  TRYING [5]
% 0.20/0.43  TRYING [6]
% 0.20/0.43  TRYING [6,2]
% 0.20/0.43  TRYING [6,2]
% 0.20/0.43  % (15708)First to succeed.
% 0.20/0.43  TRYING [5,3]
% 0.20/0.43  TRYING [5,3]
% 0.20/0.43  % (15708)Refutation found. Thanks to Tanya!
% 0.20/0.43  % SZS status Theorem for Vampire---4
% 0.20/0.43  % SZS output start Proof for Vampire---4
% See solution above
% 0.20/0.43  % (15708)------------------------------
% 0.20/0.43  % (15708)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.20/0.43  % (15708)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.20/0.43  % (15708)Termination reason: Refutation
% 0.20/0.43  
% 0.20/0.43  % (15708)Memory used [KB]: 5500
% 0.20/0.43  % (15708)Time elapsed: 0.012 s
% 0.20/0.43  % (15708)------------------------------
% 0.20/0.43  % (15708)------------------------------
% 0.20/0.43  % (15702)Success in time 0.074 s
% 0.20/0.43  % Vampire---4.8 exiting
%------------------------------------------------------------------------------