TSTP Solution File: GEO177+3 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : GEO177+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 : n023.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 05:15:52 EDT 2024

% Result   : Theorem 0.21s 0.39s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   41 (  13 unt;   0 def)
%            Number of atoms       :  111 (   0 equ)
%            Maximal formula atoms :   12 (   2 avg)
%            Number of connectives :  108 (  38   ~;  35   |;  23   &)
%                                         (   2 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    2 (   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   :   77 (  65   !;  12   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f212,plain,
    $false,
    inference(avatar_sat_refutation,[],[f148,f209,f211]) ).

fof(f211,plain,
    ~ spl5_1,
    inference(avatar_contradiction_clause,[],[f210]) ).

fof(f210,plain,
    ( $false
    | ~ spl5_1 ),
    inference(resolution,[],[f143,f203]) ).

fof(f203,plain,
    ! [X0,X1] : ~ apart_point_and_line(X0,X1),
    inference(resolution,[],[f169,f162]) ).

fof(f162,plain,
    ! [X0,X1] : ~ distinct_lines(X0,parallel_through_point(X0,X1)),
    inference(resolution,[],[f158,f107]) ).

fof(f107,plain,
    ! [X0,X1] :
      ( convergent_lines(X0,X1)
      | ~ distinct_lines(X0,X1) ),
    inference(cnf_transformation,[],[f54]) ).

fof(f54,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/sandbox/benchmark/theBenchmark.p',p1) ).

fof(f158,plain,
    ! [X0,X1] : ~ convergent_lines(X0,parallel_through_point(X0,X1)),
    inference(resolution,[],[f153,f139]) ).

fof(f139,plain,
    ! [X0,X1] : ~ distinct_lines(parallel_through_point(X0,X1),X0),
    inference(resolution,[],[f107,f103]) ).

fof(f103,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/sandbox/benchmark/theBenchmark.p',cp1) ).

fof(f153,plain,
    ! [X0,X1] :
      ( distinct_lines(X0,X1)
      | ~ convergent_lines(X1,X0) ),
    inference(resolution,[],[f120,f101]) ).

fof(f101,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(f120,plain,
    ! [X2,X0,X1] :
      ( convergent_lines(X0,X2)
      | distinct_lines(X1,X2)
      | ~ convergent_lines(X0,X1) ),
    inference(cnf_transformation,[],[f75]) ).

fof(f75,plain,
    ! [X0,X1,X2] :
      ( convergent_lines(X0,X2)
      | distinct_lines(X1,X2)
      | ~ convergent_lines(X0,X1) ),
    inference(flattening,[],[f74]) ).

fof(f74,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(f169,plain,
    ! [X2,X0,X1] :
      ( distinct_lines(X0,parallel_through_point(X1,X2))
      | ~ apart_point_and_line(X2,X0) ),
    inference(resolution,[],[f122,f104]) ).

fof(f104,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/sandbox/benchmark/theBenchmark.p',cp2) ).

fof(f122,plain,
    ! [X2,X0,X1] :
      ( apart_point_and_line(X0,X2)
      | distinct_lines(X1,X2)
      | ~ apart_point_and_line(X0,X1) ),
    inference(cnf_transformation,[],[f79]) ).

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

fof(f78,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/sandbox/benchmark/theBenchmark.p',ceq2) ).

fof(f143,plain,
    ( apart_point_and_line(sK0,line_connecting(sK2,sK3))
    | ~ spl5_1 ),
    inference(avatar_component_clause,[],[f141]) ).

fof(f141,plain,
    ( spl5_1
  <=> apart_point_and_line(sK0,line_connecting(sK2,sK3)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_1])]) ).

fof(f209,plain,
    ~ spl5_2,
    inference(avatar_contradiction_clause,[],[f206]) ).

fof(f206,plain,
    ( $false
    | ~ spl5_2 ),
    inference(resolution,[],[f203,f147]) ).

fof(f147,plain,
    ( apart_point_and_line(sK1,line_connecting(sK2,sK3))
    | ~ spl5_2 ),
    inference(avatar_component_clause,[],[f145]) ).

fof(f145,plain,
    ( spl5_2
  <=> apart_point_and_line(sK1,line_connecting(sK2,sK3)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_2])]) ).

fof(f148,plain,
    ( spl5_1
    | spl5_2 ),
    inference(avatar_split_clause,[],[f96,f145,f141]) ).

fof(f96,plain,
    ( apart_point_and_line(sK1,line_connecting(sK2,sK3))
    | apart_point_and_line(sK0,line_connecting(sK2,sK3)) ),
    inference(cnf_transformation,[],[f93]) ).

fof(f93,plain,
    ( ~ apart_point_and_line(sK3,line_connecting(sK0,sK1))
    & ~ apart_point_and_line(sK2,line_connecting(sK0,sK1))
    & ( apart_point_and_line(sK1,line_connecting(sK2,sK3))
      | apart_point_and_line(sK0,line_connecting(sK2,sK3)) )
    & distinct_points(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] :
        ( ~ apart_point_and_line(X3,line_connecting(X0,X1))
        & ~ apart_point_and_line(X2,line_connecting(X0,X1))
        & ( apart_point_and_line(X1,line_connecting(X2,X3))
          | apart_point_and_line(X0,line_connecting(X2,X3)) )
        & distinct_points(X2,X3)
        & distinct_points(X0,X1) )
   => ( ~ apart_point_and_line(sK3,line_connecting(sK0,sK1))
      & ~ apart_point_and_line(sK2,line_connecting(sK0,sK1))
      & ( apart_point_and_line(sK1,line_connecting(sK2,sK3))
        | apart_point_and_line(sK0,line_connecting(sK2,sK3)) )
      & distinct_points(sK2,sK3)
      & distinct_points(sK0,sK1) ) ),
    introduced(choice_axiom,[]) ).

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

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

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

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

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.14  % Problem    : GEO177+3 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.16  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36  % Computer : n023.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   : Fri May  3 21:58:53 EDT 2024
% 0.15/0.36  % CPUTime    : 
% 0.15/0.37  % (6244)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.38  % (6248)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.21/0.38  % (6249)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.21/0.38  % (6246)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.21/0.38  % (6247)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)
% 0.21/0.38  % (6250)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.21/0.38  % (6251)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)
% 0.21/0.39  TRYING [1,1]
% 0.21/0.39  TRYING [1,1]
% 0.21/0.39  TRYING [1]
% 0.21/0.39  TRYING [2,2]
% 0.21/0.39  TRYING [2,2]
% 0.21/0.39  TRYING [2]
% 0.21/0.39  % (6247)First to succeed.
% 0.21/0.39  TRYING [3,2]
% 0.21/0.39  TRYING [3,2]
% 0.21/0.39  TRYING [3]
% 0.21/0.39  % (6245)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.21/0.39  % (6247)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-6244"
% 0.21/0.39  TRYING [4,2]
% 0.21/0.39  TRYING [4,2]
% 0.21/0.39  % (6247)Refutation found. Thanks to Tanya!
% 0.21/0.39  % SZS status Theorem for theBenchmark
% 0.21/0.39  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.39  % (6247)------------------------------
% 0.21/0.39  % (6247)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.39  % (6247)Termination reason: Refutation
% 0.21/0.39  
% 0.21/0.39  % (6247)Memory used [KB]: 969
% 0.21/0.39  % (6247)Time elapsed: 0.006 s
% 0.21/0.39  % (6247)Instructions burned: 8 (million)
% 0.21/0.39  % (6244)Success in time 0.019 s
%------------------------------------------------------------------------------