TSTP Solution File: GEO202+3 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : GEO202+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 : n019.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 05:16:05 EDT 2024

% Result   : Theorem 1.49s 0.60s
% Output   : Refutation 1.49s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   67 (  16 unt;   0 def)
%            Number of atoms       :  180 (   0 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  180 (  67   ~;  78   |;  21   &)
%                                         (   3 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    9 (   8 usr;   4 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :  129 ( 120   !;   9   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f7029,plain,
    $false,
    inference(avatar_sat_refutation,[],[f6956,f6991,f7025,f7028]) ).

fof(f7028,plain,
    ~ spl4_1,
    inference(avatar_contradiction_clause,[],[f7027]) ).

fof(f7027,plain,
    ( $false
    | ~ spl4_1 ),
    inference(resolution,[],[f6947,f161]) ).

fof(f161,plain,
    ! [X0,X1] : ~ apart_point_and_line(X0,X1),
    inference(resolution,[],[f158,f99]) ).

fof(f99,plain,
    ! [X0] : ~ distinct_lines(X0,X0),
    inference(cnf_transformation,[],[f2]) ).

fof(f2,axiom,
    ! [X0] : ~ distinct_lines(X0,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart2) ).

fof(f158,plain,
    ! [X2,X0,X1] :
      ( distinct_lines(X1,X2)
      | ~ apart_point_and_line(X0,X1) ),
    inference(resolution,[],[f146,f143]) ).

fof(f143,plain,
    ! [X2,X0,X1] :
      ( ~ distinct_lines(X0,parallel_through_point(X1,X2))
      | distinct_lines(X0,X1) ),
    inference(resolution,[],[f118,f140]) ).

fof(f140,plain,
    ! [X0,X1] : ~ distinct_lines(parallel_through_point(X0,X1),X0),
    inference(resolution,[],[f107,f105]) ).

fof(f105,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(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/sandbox2/benchmark/theBenchmark.p',p1) ).

fof(f118,plain,
    ! [X2,X0,X1] :
      ( distinct_lines(X1,X2)
      | distinct_lines(X0,X2)
      | ~ distinct_lines(X0,X1) ),
    inference(cnf_transformation,[],[f70]) ).

fof(f70,plain,
    ! [X0,X1,X2] :
      ( distinct_lines(X1,X2)
      | distinct_lines(X0,X2)
      | ~ distinct_lines(X0,X1) ),
    inference(flattening,[],[f69]) ).

fof(f69,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(f146,plain,
    ! [X2,X0,X1] :
      ( distinct_lines(X0,parallel_through_point(X1,X2))
      | ~ apart_point_and_line(X2,X0) ),
    inference(resolution,[],[f121,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(f121,plain,
    ! [X2,X0,X1] :
      ( apart_point_and_line(X0,X2)
      | distinct_lines(X1,X2)
      | ~ apart_point_and_line(X0,X1) ),
    inference(cnf_transformation,[],[f76]) ).

fof(f76,plain,
    ! [X0,X1,X2] :
      ( apart_point_and_line(X0,X2)
      | distinct_lines(X1,X2)
      | ~ apart_point_and_line(X0,X1) ),
    inference(flattening,[],[f75]) ).

fof(f75,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(f6947,plain,
    ( apart_point_and_line(sK0,line_connecting(sK0,sK2))
    | ~ spl4_1 ),
    inference(avatar_component_clause,[],[f6945]) ).

fof(f6945,plain,
    ( spl4_1
  <=> apart_point_and_line(sK0,line_connecting(sK0,sK2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_1])]) ).

fof(f7025,plain,
    ~ spl4_3,
    inference(avatar_contradiction_clause,[],[f7024]) ).

fof(f7024,plain,
    ( $false
    | ~ spl4_3 ),
    inference(resolution,[],[f6955,f161]) ).

fof(f6955,plain,
    ( apart_point_and_line(sK1,line_connecting(sK0,sK2))
    | ~ spl4_3 ),
    inference(avatar_component_clause,[],[f6953]) ).

fof(f6953,plain,
    ( spl4_3
  <=> apart_point_and_line(sK1,line_connecting(sK0,sK2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_3])]) ).

fof(f6991,plain,
    spl4_2,
    inference(avatar_contradiction_clause,[],[f6989]) ).

fof(f6989,plain,
    ( $false
    | spl4_2 ),
    inference(resolution,[],[f6951,f95]) ).

fof(f95,plain,
    distinct_points(sK0,sK1),
    inference(cnf_transformation,[],[f94]) ).

fof(f94,plain,
    ( ~ equal_points(intersection_point(line_connecting(sK0,sK1),line_connecting(sK0,sK2)),sK0)
    & convergent_lines(line_connecting(sK0,sK1),line_connecting(sK0,sK2))
    & distinct_points(sK0,sK2)
    & distinct_points(sK0,sK1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f53,f93]) ).

fof(f93,plain,
    ( ? [X0,X1,X2] :
        ( ~ equal_points(intersection_point(line_connecting(X0,X1),line_connecting(X0,X2)),X0)
        & convergent_lines(line_connecting(X0,X1),line_connecting(X0,X2))
        & distinct_points(X0,X2)
        & distinct_points(X0,X1) )
   => ( ~ equal_points(intersection_point(line_connecting(sK0,sK1),line_connecting(sK0,sK2)),sK0)
      & convergent_lines(line_connecting(sK0,sK1),line_connecting(sK0,sK2))
      & distinct_points(sK0,sK2)
      & distinct_points(sK0,sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f53,plain,
    ? [X0,X1,X2] :
      ( ~ equal_points(intersection_point(line_connecting(X0,X1),line_connecting(X0,X2)),X0)
      & convergent_lines(line_connecting(X0,X1),line_connecting(X0,X2))
      & distinct_points(X0,X2)
      & distinct_points(X0,X1) ),
    inference(flattening,[],[f52]) ).

fof(f52,plain,
    ? [X0,X1,X2] :
      ( ~ equal_points(intersection_point(line_connecting(X0,X1),line_connecting(X0,X2)),X0)
      & convergent_lines(line_connecting(X0,X1),line_connecting(X0,X2))
      & distinct_points(X0,X2)
      & distinct_points(X0,X1) ),
    inference(ennf_transformation,[],[f37]) ).

fof(f37,negated_conjecture,
    ~ ! [X0,X1,X2] :
        ( ( convergent_lines(line_connecting(X0,X1),line_connecting(X0,X2))
          & distinct_points(X0,X2)
          & distinct_points(X0,X1) )
       => equal_points(intersection_point(line_connecting(X0,X1),line_connecting(X0,X2)),X0) ),
    inference(negated_conjecture,[],[f36]) ).

fof(f36,conjecture,
    ! [X0,X1,X2] :
      ( ( convergent_lines(line_connecting(X0,X1),line_connecting(X0,X2))
        & distinct_points(X0,X2)
        & distinct_points(X0,X1) )
     => equal_points(intersection_point(line_connecting(X0,X1),line_connecting(X0,X2)),X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).

fof(f6951,plain,
    ( ~ distinct_points(sK0,sK1)
    | spl4_2 ),
    inference(avatar_component_clause,[],[f6949]) ).

fof(f6949,plain,
    ( spl4_2
  <=> distinct_points(sK0,sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_2])]) ).

fof(f6956,plain,
    ( spl4_1
    | ~ spl4_2
    | spl4_3 ),
    inference(avatar_split_clause,[],[f2661,f6953,f6949,f6945]) ).

fof(f2661,plain,
    ( apart_point_and_line(sK1,line_connecting(sK0,sK2))
    | ~ distinct_points(sK0,sK1)
    | apart_point_and_line(sK0,line_connecting(sK0,sK2)) ),
    inference(resolution,[],[f712,f97]) ).

fof(f97,plain,
    convergent_lines(line_connecting(sK0,sK1),line_connecting(sK0,sK2)),
    inference(cnf_transformation,[],[f94]) ).

fof(f712,plain,
    ! [X2,X0,X1] :
      ( ~ convergent_lines(line_connecting(X0,X2),X1)
      | apart_point_and_line(X2,X1)
      | ~ distinct_points(X0,X2)
      | apart_point_and_line(X0,X1) ),
    inference(resolution,[],[f477,f164]) ).

fof(f164,plain,
    ! [X0,X1] :
      ( distinct_lines(X0,X1)
      | ~ convergent_lines(X1,X0) ),
    inference(resolution,[],[f123,f101]) ).

fof(f101,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(f123,plain,
    ! [X2,X0,X1] :
      ( convergent_lines(X0,X2)
      | distinct_lines(X1,X2)
      | ~ convergent_lines(X0,X1) ),
    inference(cnf_transformation,[],[f80]) ).

fof(f80,plain,
    ! [X0,X1,X2] :
      ( convergent_lines(X0,X2)
      | distinct_lines(X1,X2)
      | ~ convergent_lines(X0,X1) ),
    inference(flattening,[],[f79]) ).

fof(f79,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(f477,plain,
    ! [X2,X0,X1] :
      ( ~ distinct_lines(X1,line_connecting(X2,X0))
      | apart_point_and_line(X2,X1)
      | apart_point_and_line(X0,X1)
      | ~ distinct_points(X2,X0) ),
    inference(duplicate_literal_removal,[],[f473]) ).

fof(f473,plain,
    ! [X2,X0,X1] :
      ( apart_point_and_line(X0,X1)
      | apart_point_and_line(X2,X1)
      | ~ distinct_lines(X1,line_connecting(X2,X0))
      | ~ distinct_points(X2,X0)
      | ~ distinct_points(X2,X0)
      | ~ distinct_points(X2,X0) ),
    inference(resolution,[],[f262,f109]) ).

fof(f109,plain,
    ! [X0,X1] :
      ( ~ apart_point_and_line(X0,line_connecting(X0,X1))
      | ~ distinct_points(X0,X1) ),
    inference(cnf_transformation,[],[f56]) ).

fof(f56,plain,
    ! [X0,X1] :
      ( ~ apart_point_and_line(X0,line_connecting(X0,X1))
      | ~ distinct_points(X0,X1) ),
    inference(ennf_transformation,[],[f7]) ).

fof(f7,axiom,
    ! [X0,X1] :
      ( distinct_points(X0,X1)
     => ~ apart_point_and_line(X0,line_connecting(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ci1) ).

fof(f262,plain,
    ! [X2,X3,X0,X1] :
      ( apart_point_and_line(X2,line_connecting(X3,X0))
      | apart_point_and_line(X0,X1)
      | apart_point_and_line(X2,X1)
      | ~ distinct_lines(X1,line_connecting(X3,X0))
      | ~ distinct_points(X2,X0)
      | ~ distinct_points(X3,X0) ),
    inference(resolution,[],[f135,f108]) ).

fof(f108,plain,
    ! [X0,X1] :
      ( ~ apart_point_and_line(X1,line_connecting(X0,X1))
      | ~ distinct_points(X0,X1) ),
    inference(cnf_transformation,[],[f55]) ).

fof(f55,plain,
    ! [X0,X1] :
      ( ~ apart_point_and_line(X1,line_connecting(X0,X1))
      | ~ distinct_points(X0,X1) ),
    inference(ennf_transformation,[],[f8]) ).

fof(f8,axiom,
    ! [X0,X1] :
      ( distinct_points(X0,X1)
     => ~ apart_point_and_line(X1,line_connecting(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ci2) ).

fof(f135,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,[],[f92]) ).

fof(f92,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,[],[f91]) ).

fof(f91,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,[],[f50]) ).

fof(f50,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/sandbox2/benchmark/theBenchmark.p',cu1) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : GEO202+3 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.34  % Computer : n019.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Fri May  3 21:53:23 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.14/0.35  % (23410)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37  % (23411)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.14/0.37  % (23412)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.37  % (23413)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)
% 0.14/0.37  % (23415)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.14/0.37  % (23414)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.14/0.37  % (23416)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.14/0.37  % (23417)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)
% 0.14/0.37  TRYING [1]
% 0.14/0.37  TRYING [2]
% 0.14/0.37  TRYING [1]
% 0.14/0.37  TRYING [1]
% 0.14/0.37  TRYING [3]
% 0.14/0.37  TRYING [1]
% 0.14/0.37  TRYING [2]
% 0.14/0.37  TRYING [2]
% 0.14/0.37  TRYING [2]
% 0.14/0.37  TRYING [3]
% 0.14/0.37  TRYING [3]
% 0.14/0.37  TRYING [3]
% 0.14/0.37  TRYING [4]
% 0.14/0.37  TRYING [4]
% 0.14/0.37  TRYING [4]
% 0.14/0.37  TRYING [4]
% 0.20/0.38  TRYING [5]
% 0.20/0.38  TRYING [5]
% 0.20/0.38  TRYING [5]
% 0.20/0.38  TRYING [5]
% 0.20/0.39  TRYING [6]
% 0.20/0.39  TRYING [6]
% 0.20/0.39  TRYING [6]
% 0.20/0.40  TRYING [6]
% 0.20/0.41  TRYING [7]
% 0.20/0.41  TRYING [7]
% 0.20/0.41  TRYING [7]
% 0.20/0.43  TRYING [7]
% 0.20/0.45  TRYING [8]
% 0.20/0.45  TRYING [8]
% 0.20/0.46  TRYING [8]
% 0.20/0.48  TRYING [8]
% 0.20/0.50  TRYING [9]
% 0.20/0.51  TRYING [9]
% 0.20/0.51  TRYING [9]
% 1.49/0.55  TRYING [9]
% 1.49/0.57  TRYING [10]
% 1.49/0.57  TRYING [10]
% 1.49/0.59  TRYING [10]
% 1.49/0.60  % (23413)First to succeed.
% 1.49/0.60  % (23413)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-23410"
% 1.49/0.60  % (23413)Refutation found. Thanks to Tanya!
% 1.49/0.60  % SZS status Theorem for theBenchmark
% 1.49/0.60  % SZS output start Proof for theBenchmark
% See solution above
% 1.49/0.61  % (23413)------------------------------
% 1.49/0.61  % (23413)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 1.49/0.61  % (23413)Termination reason: Refutation
% 1.49/0.61  
% 1.49/0.61  % (23413)Memory used [KB]: 3287
% 1.49/0.61  % (23413)Time elapsed: 0.238 s
% 1.49/0.61  % (23413)Instructions burned: 662 (million)
% 1.49/0.61  % (23410)Success in time 0.244 s
%------------------------------------------------------------------------------