TSTP Solution File: GEO174+3 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : GEO174+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n032.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 05:15:50 EDT 2024

% Result   : Theorem 0.08s 0.29s
% Output   : Refutation 0.08s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   48 (  15 unt;   0 def)
%            Number of atoms       :  119 (   0 equ)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives :  110 (  39   ~;  40   |;  21   &)
%                                         (   2 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    7 (   6 usr;   3 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :   88 (  76   !;  12   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f310,plain,
    $false,
    inference(avatar_sat_refutation,[],[f144,f301,f309]) ).

fof(f309,plain,
    ~ spl5_1,
    inference(avatar_contradiction_clause,[],[f306]) ).

fof(f306,plain,
    ( $false
    | ~ spl5_1 ),
    inference(resolution,[],[f139,f295]) ).

fof(f295,plain,
    ! [X0] : ~ apart_point_and_line(X0,sK2),
    inference(resolution,[],[f163,f195]) ).

fof(f195,plain,
    ! [X0] : ~ distinct_lines(sK2,parallel_through_point(line_connecting(sK0,sK1),X0)),
    inference(resolution,[],[f177,f108]) ).

fof(f108,plain,
    ! [X0,X1] :
      ( convergent_lines(X0,X1)
      | ~ distinct_lines(X0,X1) ),
    inference(cnf_transformation,[],[f56]) ).

fof(f56,plain,
    ! [X0,X1] :
      ( convergent_lines(X0,X1)
      | ~ distinct_lines(X0,X1) ),
    inference(ennf_transformation,[],[f15]) ).

fof(f15,axiom,
    ! [X0,X1] :
      ( distinct_lines(X0,X1)
     => convergent_lines(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).

fof(f177,plain,
    ! [X0] : ~ convergent_lines(sK2,parallel_through_point(line_connecting(sK0,sK1),X0)),
    inference(resolution,[],[f171,f154]) ).

fof(f154,plain,
    ! [X0] : ~ distinct_lines(parallel_through_point(line_connecting(sK0,sK1),X0),sK2),
    inference(resolution,[],[f150,f147]) ).

fof(f147,plain,
    ! [X0,X1] : ~ distinct_lines(parallel_through_point(X0,X1),X0),
    inference(resolution,[],[f108,f104]) ).

fof(f104,plain,
    ! [X0,X1] : ~ convergent_lines(parallel_through_point(X1,X0),X1),
    inference(cnf_transformation,[],[f16]) ).

fof(f16,axiom,
    ! [X0,X1] : ~ convergent_lines(parallel_through_point(X1,X0),X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cp1) ).

fof(f150,plain,
    ! [X0] :
      ( distinct_lines(X0,line_connecting(sK0,sK1))
      | ~ distinct_lines(X0,sK2) ),
    inference(resolution,[],[f117,f97]) ).

fof(f97,plain,
    ~ distinct_lines(sK2,line_connecting(sK0,sK1)),
    inference(cnf_transformation,[],[f93]) ).

fof(f93,plain,
    ( ~ distinct_lines(sK2,line_connecting(sK0,sK1))
    & ( apart_point_and_line(sK1,sK2)
      | 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])],[f53,f92]) ).

fof(f92,plain,
    ( ? [X0,X1,X2,X3] :
        ( ~ distinct_lines(X2,line_connecting(X0,X1))
        & ( apart_point_and_line(X1,X2)
          | apart_point_and_line(X0,X2) )
        & convergent_lines(X2,X3)
        & distinct_points(X0,X1) )
   => ( ~ distinct_lines(sK2,line_connecting(sK0,sK1))
      & ( apart_point_and_line(sK1,sK2)
        | apart_point_and_line(sK0,sK2) )
      & convergent_lines(sK2,sK3)
      & distinct_points(sK0,sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f53,plain,
    ? [X0,X1,X2,X3] :
      ( ~ distinct_lines(X2,line_connecting(X0,X1))
      & ( apart_point_and_line(X1,X2)
        | apart_point_and_line(X0,X2) )
      & convergent_lines(X2,X3)
      & distinct_points(X0,X1) ),
    inference(flattening,[],[f52]) ).

fof(f52,plain,
    ? [X0,X1,X2,X3] :
      ( ~ distinct_lines(X2,line_connecting(X0,X1))
      & ( apart_point_and_line(X1,X2)
        | apart_point_and_line(X0,X2) )
      & convergent_lines(X2,X3)
      & distinct_points(X0,X1) ),
    inference(ennf_transformation,[],[f38]) ).

fof(f38,plain,
    ~ ! [X0,X1,X2,X3] :
        ( ( ( apart_point_and_line(X1,X2)
            | apart_point_and_line(X0,X2) )
          & convergent_lines(X2,X3)
          & distinct_points(X0,X1) )
       => distinct_lines(X2,line_connecting(X0,X1)) ),
    inference(rectify,[],[f37]) ).

fof(f37,negated_conjecture,
    ~ ! [X0,X1,X3,X4] :
        ( ( ( apart_point_and_line(X1,X3)
            | apart_point_and_line(X0,X3) )
          & convergent_lines(X3,X4)
          & distinct_points(X0,X1) )
       => distinct_lines(X3,line_connecting(X0,X1)) ),
    inference(negated_conjecture,[],[f36]) ).

fof(f36,conjecture,
    ! [X0,X1,X3,X4] :
      ( ( ( apart_point_and_line(X1,X3)
          | apart_point_and_line(X0,X3) )
        & convergent_lines(X3,X4)
        & distinct_points(X0,X1) )
     => distinct_lines(X3,line_connecting(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).

fof(f117,plain,
    ! [X2,X0,X1] :
      ( distinct_lines(X1,X2)
      | distinct_lines(X0,X2)
      | ~ distinct_lines(X0,X1) ),
    inference(cnf_transformation,[],[f71]) ).

fof(f71,plain,
    ! [X0,X1,X2] :
      ( distinct_lines(X1,X2)
      | distinct_lines(X0,X2)
      | ~ distinct_lines(X0,X1) ),
    inference(flattening,[],[f70]) ).

fof(f70,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(f171,plain,
    ! [X0,X1] :
      ( distinct_lines(X0,X1)
      | ~ convergent_lines(X1,X0) ),
    inference(resolution,[],[f121,f100]) ).

fof(f100,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(f121,plain,
    ! [X2,X0,X1] :
      ( convergent_lines(X0,X2)
      | distinct_lines(X1,X2)
      | ~ convergent_lines(X0,X1) ),
    inference(cnf_transformation,[],[f79]) ).

fof(f79,plain,
    ! [X0,X1,X2] :
      ( convergent_lines(X0,X2)
      | distinct_lines(X1,X2)
      | ~ convergent_lines(X0,X1) ),
    inference(flattening,[],[f78]) ).

fof(f78,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(f163,plain,
    ! [X2,X0,X1] :
      ( distinct_lines(X0,parallel_through_point(X1,X2))
      | ~ apart_point_and_line(X2,X0) ),
    inference(resolution,[],[f120,f103]) ).

fof(f103,plain,
    ! [X0,X1] : ~ apart_point_and_line(X0,parallel_through_point(X1,X0)),
    inference(cnf_transformation,[],[f17]) ).

fof(f17,axiom,
    ! [X0,X1] : ~ apart_point_and_line(X0,parallel_through_point(X1,X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cp2) ).

fof(f120,plain,
    ! [X2,X0,X1] :
      ( apart_point_and_line(X0,X2)
      | distinct_lines(X1,X2)
      | ~ apart_point_and_line(X0,X1) ),
    inference(cnf_transformation,[],[f77]) ).

fof(f77,plain,
    ! [X0,X1,X2] :
      ( apart_point_and_line(X0,X2)
      | distinct_lines(X1,X2)
      | ~ apart_point_and_line(X0,X1) ),
    inference(flattening,[],[f76]) ).

fof(f76,plain,
    ! [X0,X1,X2] :
      ( apart_point_and_line(X0,X2)
      | distinct_lines(X1,X2)
      | ~ apart_point_and_line(X0,X1) ),
    inference(ennf_transformation,[],[f13]) ).

fof(f13,axiom,
    ! [X0,X1,X2] :
      ( apart_point_and_line(X0,X1)
     => ( apart_point_and_line(X0,X2)
        | distinct_lines(X1,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ceq2) ).

fof(f139,plain,
    ( apart_point_and_line(sK0,sK2)
    | ~ spl5_1 ),
    inference(avatar_component_clause,[],[f137]) ).

fof(f137,plain,
    ( spl5_1
  <=> apart_point_and_line(sK0,sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_1])]) ).

fof(f301,plain,
    ~ spl5_2,
    inference(avatar_contradiction_clause,[],[f296]) ).

fof(f296,plain,
    ( $false
    | ~ spl5_2 ),
    inference(resolution,[],[f295,f143]) ).

fof(f143,plain,
    ( apart_point_and_line(sK1,sK2)
    | ~ spl5_2 ),
    inference(avatar_component_clause,[],[f141]) ).

fof(f141,plain,
    ( spl5_2
  <=> apart_point_and_line(sK1,sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_2])]) ).

fof(f144,plain,
    ( spl5_1
    | spl5_2 ),
    inference(avatar_split_clause,[],[f96,f141,f137]) ).

fof(f96,plain,
    ( apart_point_and_line(sK1,sK2)
    | apart_point_and_line(sK0,sK2) ),
    inference(cnf_transformation,[],[f93]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07  % Problem    : GEO174+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.08  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.08/0.27  % Computer : n032.cluster.edu
% 0.08/0.27  % Model    : x86_64 x86_64
% 0.08/0.27  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.27  % Memory   : 8042.1875MB
% 0.08/0.27  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.08/0.27  % CPULimit   : 300
% 0.08/0.27  % WCLimit    : 300
% 0.08/0.27  % DateTime   : Fri May  3 22:03:08 EDT 2024
% 0.08/0.27  % CPUTime    : 
% 0.08/0.27  % (21679)Running in auto input_syntax mode. Trying TPTP
% 0.08/0.29  % (21681)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.08/0.29  % (21684)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.08/0.29  % (21682)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)
% 0.08/0.29  TRYING [1,1]
% 0.08/0.29  TRYING [2,2]
% 0.08/0.29  TRYING [3,2]
% 0.08/0.29  % (21682)First to succeed.
% 0.08/0.29  % (21683)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.08/0.29  TRYING [4,2]
% 0.08/0.29  % (21682)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-21679"
% 0.08/0.29  % (21682)Refutation found. Thanks to Tanya!
% 0.08/0.29  % SZS status Theorem for theBenchmark
% 0.08/0.29  % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.29  % (21682)------------------------------
% 0.08/0.29  % (21682)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.08/0.29  % (21682)Termination reason: Refutation
% 0.08/0.29  
% 0.08/0.29  % (21682)Memory used [KB]: 994
% 0.08/0.29  % (21682)Time elapsed: 0.005 s
% 0.08/0.29  % (21682)Instructions burned: 10 (million)
% 0.08/0.29  % (21679)Success in time 0.004 s
%------------------------------------------------------------------------------