TSTP Solution File: GEO199+2 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : GEO199+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n018.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 : Tue Apr 30 11:14:39 EDT 2024

% Result   : Theorem 0.21s 0.41s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   69 (  11 unt;   0 def)
%            Number of atoms       :  213 (   0 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  229 (  85   ~;  99   |;  30   &)
%                                         (   5 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   10 (   9 usr;   6 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :  104 (  95   !;   9   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1511,plain,
    $false,
    inference(avatar_sat_refutation,[],[f102,f160,f1063,f1101,f1486,f1510]) ).

fof(f1510,plain,
    spl3_42,
    inference(avatar_contradiction_clause,[],[f1491]) ).

fof(f1491,plain,
    ( $false
    | spl3_42 ),
    inference(resolution,[],[f1485,f41]) ).

fof(f41,plain,
    apart_point_and_line(intersection_point(sK1,sK0),sK2),
    inference(cnf_transformation,[],[f36]) ).

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

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

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

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

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

fof(f13,conjecture,
    ! [X0,X1,X2] :
      ( ( ~ apart_point_and_line(intersection_point(X0,X1),X2)
        & convergent_lines(X0,X2)
        & convergent_lines(X2,X1)
        & convergent_lines(X0,X1) )
     => ~ apart_point_and_line(intersection_point(X1,X0),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).

fof(f1485,plain,
    ( ~ apart_point_and_line(intersection_point(sK1,sK0),sK2)
    | spl3_42 ),
    inference(avatar_component_clause,[],[f1483]) ).

fof(f1483,plain,
    ( spl3_42
  <=> apart_point_and_line(intersection_point(sK1,sK0),sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_42])]) ).

fof(f1486,plain,
    ( ~ spl3_1
    | ~ spl3_42
    | ~ spl3_30 ),
    inference(avatar_split_clause,[],[f1481,f1061,f1483,f81]) ).

fof(f81,plain,
    ( spl3_1
  <=> convergent_lines(sK1,sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).

fof(f1061,plain,
    ( spl3_30
  <=> ! [X0] :
        ( apart_point_and_line(X0,sK1)
        | ~ apart_point_and_line(X0,sK2)
        | apart_point_and_line(X0,sK0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_30])]) ).

fof(f1481,plain,
    ( ~ apart_point_and_line(intersection_point(sK1,sK0),sK2)
    | ~ convergent_lines(sK1,sK0)
    | ~ spl3_30 ),
    inference(duplicate_literal_removal,[],[f1474]) ).

fof(f1474,plain,
    ( ~ apart_point_and_line(intersection_point(sK1,sK0),sK2)
    | ~ convergent_lines(sK1,sK0)
    | ~ convergent_lines(sK1,sK0)
    | ~ spl3_30 ),
    inference(resolution,[],[f1133,f68]) ).

fof(f68,plain,
    ! [X0,X1] :
      ( ~ apart_point_and_line(intersection_point(X0,X1),X1)
      | ~ convergent_lines(X0,X1) ),
    inference(resolution,[],[f49,f44]) ).

fof(f44,plain,
    ! [X0] : ~ distinct_points(X0,X0),
    inference(cnf_transformation,[],[f1]) ).

fof(f1,axiom,
    ! [X0] : ~ distinct_points(X0,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart1) ).

fof(f49,plain,
    ! [X2,X0,X1] :
      ( distinct_points(X2,intersection_point(X0,X1))
      | ~ apart_point_and_line(X2,X1)
      | ~ convergent_lines(X0,X1) ),
    inference(cnf_transformation,[],[f24]) ).

fof(f24,plain,
    ! [X0,X1,X2] :
      ( distinct_points(X2,intersection_point(X0,X1))
      | ( ~ apart_point_and_line(X2,X1)
        & ~ apart_point_and_line(X2,X0) )
      | ~ convergent_lines(X0,X1) ),
    inference(flattening,[],[f23]) ).

fof(f23,plain,
    ! [X0,X1,X2] :
      ( distinct_points(X2,intersection_point(X0,X1))
      | ( ~ apart_point_and_line(X2,X1)
        & ~ apart_point_and_line(X2,X0) )
      | ~ convergent_lines(X0,X1) ),
    inference(ennf_transformation,[],[f8]) ).

fof(f8,axiom,
    ! [X0,X1,X2] :
      ( convergent_lines(X0,X1)
     => ( ( apart_point_and_line(X2,X1)
          | apart_point_and_line(X2,X0) )
       => distinct_points(X2,intersection_point(X0,X1)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con2) ).

fof(f1133,plain,
    ( ! [X0] :
        ( apart_point_and_line(intersection_point(sK1,X0),sK0)
        | ~ apart_point_and_line(intersection_point(sK1,X0),sK2)
        | ~ convergent_lines(sK1,X0) )
    | ~ spl3_30 ),
    inference(resolution,[],[f1062,f65]) ).

fof(f65,plain,
    ! [X0,X1] :
      ( ~ apart_point_and_line(intersection_point(X0,X1),X0)
      | ~ convergent_lines(X0,X1) ),
    inference(resolution,[],[f48,f44]) ).

fof(f48,plain,
    ! [X2,X0,X1] :
      ( distinct_points(X2,intersection_point(X0,X1))
      | ~ apart_point_and_line(X2,X0)
      | ~ convergent_lines(X0,X1) ),
    inference(cnf_transformation,[],[f24]) ).

fof(f1062,plain,
    ( ! [X0] :
        ( apart_point_and_line(X0,sK1)
        | ~ apart_point_and_line(X0,sK2)
        | apart_point_and_line(X0,sK0) )
    | ~ spl3_30 ),
    inference(avatar_component_clause,[],[f1061]) ).

fof(f1101,plain,
    ( ~ spl3_1
    | spl3_29 ),
    inference(avatar_contradiction_clause,[],[f1099]) ).

fof(f1099,plain,
    ( $false
    | ~ spl3_1
    | spl3_29 ),
    inference(resolution,[],[f1088,f82]) ).

fof(f82,plain,
    ( convergent_lines(sK1,sK0)
    | ~ spl3_1 ),
    inference(avatar_component_clause,[],[f81]) ).

fof(f1088,plain,
    ( ~ convergent_lines(sK1,sK0)
    | spl3_29 ),
    inference(resolution,[],[f1059,f45]) ).

fof(f45,plain,
    ! [X0,X1] :
      ( distinct_lines(X0,X1)
      | ~ convergent_lines(X0,X1) ),
    inference(cnf_transformation,[],[f18]) ).

fof(f18,plain,
    ! [X0,X1] :
      ( distinct_lines(X0,X1)
      | ~ convergent_lines(X0,X1) ),
    inference(ennf_transformation,[],[f12]) ).

fof(f12,axiom,
    ! [X0,X1] :
      ( convergent_lines(X0,X1)
     => distinct_lines(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ceq3) ).

fof(f1059,plain,
    ( ~ distinct_lines(sK1,sK0)
    | spl3_29 ),
    inference(avatar_component_clause,[],[f1057]) ).

fof(f1057,plain,
    ( spl3_29
  <=> distinct_lines(sK1,sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_29])]) ).

fof(f1063,plain,
    ( ~ spl3_4
    | ~ spl3_29
    | spl3_30 ),
    inference(avatar_split_clause,[],[f772,f1061,f1057,f147]) ).

fof(f147,plain,
    ( spl3_4
  <=> convergent_lines(sK0,sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_4])]) ).

fof(f772,plain,
    ! [X0] :
      ( apart_point_and_line(X0,sK1)
      | ~ distinct_lines(sK1,sK0)
      | apart_point_and_line(X0,sK0)
      | ~ convergent_lines(sK0,sK1)
      | ~ apart_point_and_line(X0,sK2) ),
    inference(resolution,[],[f271,f61]) ).

fof(f61,plain,
    ! [X0] :
      ( distinct_points(X0,intersection_point(sK0,sK1))
      | ~ apart_point_and_line(X0,sK2) ),
    inference(resolution,[],[f54,f40]) ).

fof(f40,plain,
    ~ apart_point_and_line(intersection_point(sK0,sK1),sK2),
    inference(cnf_transformation,[],[f36]) ).

fof(f54,plain,
    ! [X2,X0,X1] :
      ( apart_point_and_line(X2,X1)
      | distinct_points(X0,X2)
      | ~ apart_point_and_line(X0,X1) ),
    inference(cnf_transformation,[],[f32]) ).

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

fof(f31,plain,
    ! [X0,X1,X2] :
      ( apart_point_and_line(X2,X1)
      | distinct_points(X0,X2)
      | ~ apart_point_and_line(X0,X1) ),
    inference(ennf_transformation,[],[f10]) ).

fof(f10,axiom,
    ! [X0,X1,X2] :
      ( apart_point_and_line(X0,X1)
     => ( apart_point_and_line(X2,X1)
        | distinct_points(X0,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ceq1) ).

fof(f271,plain,
    ! [X2,X0,X1] :
      ( ~ distinct_points(X0,intersection_point(X1,X2))
      | apart_point_and_line(X0,X2)
      | ~ distinct_lines(X2,X1)
      | apart_point_and_line(X0,X1)
      | ~ convergent_lines(X1,X2) ),
    inference(duplicate_literal_removal,[],[f264]) ).

fof(f264,plain,
    ! [X2,X0,X1] :
      ( apart_point_and_line(X0,X1)
      | apart_point_and_line(X0,X2)
      | ~ distinct_lines(X2,X1)
      | ~ distinct_points(X0,intersection_point(X1,X2))
      | ~ convergent_lines(X1,X2)
      | ~ convergent_lines(X1,X2) ),
    inference(resolution,[],[f91,f68]) ).

fof(f91,plain,
    ! [X2,X3,X0,X1] :
      ( apart_point_and_line(intersection_point(X0,X1),X2)
      | apart_point_and_line(X3,X0)
      | apart_point_and_line(X3,X2)
      | ~ distinct_lines(X2,X0)
      | ~ distinct_points(X3,intersection_point(X0,X1))
      | ~ convergent_lines(X0,X1) ),
    inference(resolution,[],[f55,f65]) ).

fof(f55,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,[],[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/sandbox2/benchmark/theBenchmark.p',cu1) ).

fof(f160,plain,
    spl3_4,
    inference(avatar_contradiction_clause,[],[f158]) ).

fof(f158,plain,
    ( $false
    | spl3_4 ),
    inference(resolution,[],[f149,f37]) ).

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

fof(f149,plain,
    ( ~ convergent_lines(sK0,sK1)
    | spl3_4 ),
    inference(avatar_component_clause,[],[f147]) ).

fof(f102,plain,
    spl3_1,
    inference(avatar_contradiction_clause,[],[f100]) ).

fof(f100,plain,
    ( $false
    | spl3_1 ),
    inference(resolution,[],[f98,f37]) ).

fof(f98,plain,
    ( ~ convergent_lines(sK0,sK1)
    | spl3_1 ),
    inference(resolution,[],[f96,f43]) ).

fof(f43,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(f96,plain,
    ( ! [X0] :
        ( convergent_lines(X0,sK0)
        | ~ convergent_lines(X0,sK1) )
    | spl3_1 ),
    inference(resolution,[],[f83,f47]) ).

fof(f47,plain,
    ! [X2,X0,X1] :
      ( convergent_lines(X1,X2)
      | convergent_lines(X0,X2)
      | ~ convergent_lines(X0,X1) ),
    inference(cnf_transformation,[],[f22]) ).

fof(f22,plain,
    ! [X0,X1,X2] :
      ( convergent_lines(X1,X2)
      | convergent_lines(X0,X2)
      | ~ convergent_lines(X0,X1) ),
    inference(flattening,[],[f21]) ).

fof(f21,plain,
    ! [X0,X1,X2] :
      ( convergent_lines(X1,X2)
      | convergent_lines(X0,X2)
      | ~ convergent_lines(X0,X1) ),
    inference(ennf_transformation,[],[f6]) ).

fof(f6,axiom,
    ! [X0,X1,X2] :
      ( convergent_lines(X0,X1)
     => ( convergent_lines(X1,X2)
        | convergent_lines(X0,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart6) ).

fof(f83,plain,
    ( ~ convergent_lines(sK1,sK0)
    | spl3_1 ),
    inference(avatar_component_clause,[],[f81]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : GEO199+2 : TPTP v8.1.2. Released v3.3.0.
% 0.06/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35  % Computer : n018.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Tue Apr 30 05:55:58 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.14/0.35  % (12575)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37  % (12577)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.14/0.37  % (12579)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  % (12581)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.14/0.37  % (12580)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  % (12578)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.37  % (12583)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  % (12582)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.14/0.37  TRYING [1]
% 0.14/0.37  TRYING [2]
% 0.14/0.37  TRYING [1]
% 0.14/0.37  TRYING [1,1]
% 0.14/0.37  TRYING [1,1]
% 0.14/0.37  TRYING [2]
% 0.14/0.37  TRYING [3]
% 0.14/0.37  TRYING [2,2]
% 0.14/0.37  TRYING [2,2]
% 0.14/0.37  TRYING [3]
% 0.14/0.37  TRYING [3,3]
% 0.14/0.37  TRYING [3,3]
% 0.14/0.37  TRYING [4]
% 0.14/0.37  TRYING [4]
% 0.14/0.37  TRYING [3,4]
% 0.14/0.37  TRYING [3,4]
% 0.21/0.38  TRYING [5]
% 0.21/0.38  TRYING [3,5]
% 0.21/0.38  TRYING [3,5]
% 0.21/0.38  TRYING [5]
% 0.21/0.38  TRYING [3,6]
% 0.21/0.38  TRYING [3,6]
% 0.21/0.38  TRYING [6]
% 0.21/0.38  TRYING [3,7]
% 0.21/0.38  TRYING [3,7]
% 0.21/0.39  TRYING [6]
% 0.21/0.39  TRYING [3,8]
% 0.21/0.39  TRYING [3,8]
% 0.21/0.39  TRYING [7]
% 0.21/0.40  TRYING [3,9]
% 0.21/0.40  TRYING [3,9]
% 0.21/0.40  TRYING [7]
% 0.21/0.41  % (12579)First to succeed.
% 0.21/0.41  % (12579)Refutation found. Thanks to Tanya!
% 0.21/0.41  % SZS status Theorem for theBenchmark
% 0.21/0.41  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.41  % (12579)------------------------------
% 0.21/0.41  % (12579)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.21/0.41  % (12579)Termination reason: Refutation
% 0.21/0.41  
% 0.21/0.41  % (12579)Memory used [KB]: 1368
% 0.21/0.41  % (12579)Time elapsed: 0.042 s
% 0.21/0.41  % (12579)Instructions burned: 73 (million)
% 0.21/0.41  % (12579)------------------------------
% 0.21/0.41  % (12579)------------------------------
% 0.21/0.41  % (12575)Success in time 0.058 s
%------------------------------------------------------------------------------