TSTP Solution File: GEO172+2 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : GEO172+2 : TPTP v8.2.0. Released v3.3.0.
% 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 : Mon May 20 20:14:55 EDT 2024

% Result   : Theorem 0.08s 0.30s
% Output   : Refutation 0.08s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   52 (  12 unt;   0 def)
%            Number of atoms       :  148 (   0 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  155 (  59   ~;  62   |;  23   &)
%                                         (   2 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    7 (   6 usr;   3 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :   78 (  69   !;   9   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f285,plain,
    $false,
    inference(avatar_sat_refutation,[],[f127,f265,f284]) ).

fof(f284,plain,
    ~ spl3_1,
    inference(avatar_contradiction_clause,[],[f283]) ).

fof(f283,plain,
    ( $false
    | ~ spl3_1 ),
    inference(subsumption_resolution,[],[f280,f37]) ).

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

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

fof(f35,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) )
   => ( distinct_points(sK2,intersection_point(sK0,sK1))
      & ~ apart_point_and_line(sK2,sK1)
      & ~ apart_point_and_line(sK2,sK0)
      & convergent_lines(sK0,sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f17,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,[],[f16]) ).

fof(f16,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,[],[f14]) ).

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

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

fof(f280,plain,
    ( ~ convergent_lines(sK0,sK1)
    | ~ spl3_1 ),
    inference(resolution,[],[f158,f43]) ).

fof(f43,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(f158,plain,
    ( ! [X0] :
        ( distinct_points(intersection_point(sK0,sK1),intersection_point(X0,sK1))
        | ~ convergent_lines(X0,sK1) )
    | ~ spl3_1 ),
    inference(resolution,[],[f109,f47]) ).

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

fof(f22,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,[],[f21]) ).

fof(f21,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(f109,plain,
    ( apart_point_and_line(intersection_point(sK0,sK1),sK1)
    | ~ spl3_1 ),
    inference(avatar_component_clause,[],[f107]) ).

fof(f107,plain,
    ( spl3_1
  <=> apart_point_and_line(intersection_point(sK0,sK1),sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).

fof(f265,plain,
    ~ spl3_2,
    inference(avatar_contradiction_clause,[],[f264]) ).

fof(f264,plain,
    ( $false
    | ~ spl3_2 ),
    inference(subsumption_resolution,[],[f261,f37]) ).

fof(f261,plain,
    ( ~ convergent_lines(sK0,sK1)
    | ~ spl3_2 ),
    inference(resolution,[],[f131,f43]) ).

fof(f131,plain,
    ( ! [X0] :
        ( distinct_points(intersection_point(sK0,sK1),intersection_point(sK0,X0))
        | ~ convergent_lines(sK0,X0) )
    | ~ spl3_2 ),
    inference(resolution,[],[f113,f46]) ).

fof(f46,plain,
    ! [X2,X0,X1] :
      ( ~ apart_point_and_line(X2,X0)
      | distinct_points(X2,intersection_point(X0,X1))
      | ~ convergent_lines(X0,X1) ),
    inference(cnf_transformation,[],[f22]) ).

fof(f113,plain,
    ( apart_point_and_line(intersection_point(sK0,sK1),sK0)
    | ~ spl3_2 ),
    inference(avatar_component_clause,[],[f111]) ).

fof(f111,plain,
    ( spl3_2
  <=> apart_point_and_line(intersection_point(sK0,sK1),sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_2])]) ).

fof(f127,plain,
    ( spl3_2
    | spl3_1 ),
    inference(avatar_split_clause,[],[f126,f107,f111]) ).

fof(f126,plain,
    ( apart_point_and_line(intersection_point(sK0,sK1),sK1)
    | apart_point_and_line(intersection_point(sK0,sK1),sK0) ),
    inference(subsumption_resolution,[],[f125,f39]) ).

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

fof(f125,plain,
    ( apart_point_and_line(sK2,sK1)
    | apart_point_and_line(intersection_point(sK0,sK1),sK1)
    | apart_point_and_line(intersection_point(sK0,sK1),sK0) ),
    inference(subsumption_resolution,[],[f102,f38]) ).

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

fof(f102,plain,
    ( apart_point_and_line(sK2,sK0)
    | apart_point_and_line(sK2,sK1)
    | apart_point_and_line(intersection_point(sK0,sK1),sK1)
    | apart_point_and_line(intersection_point(sK0,sK1),sK0) ),
    inference(resolution,[],[f97,f63]) ).

fof(f63,plain,
    distinct_lines(sK1,sK0),
    inference(resolution,[],[f60,f41]) ).

fof(f41,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(f60,plain,
    ! [X0] :
      ( convergent_lines(sK0,X0)
      | distinct_lines(sK1,X0) ),
    inference(resolution,[],[f56,f44]) ).

fof(f44,plain,
    ! [X0,X1] :
      ( ~ convergent_lines(X0,X1)
      | distinct_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(f56,plain,
    ! [X0] :
      ( convergent_lines(sK1,X0)
      | convergent_lines(sK0,X0) ),
    inference(resolution,[],[f45,f37]) ).

fof(f45,plain,
    ! [X2,X0,X1] :
      ( ~ convergent_lines(X0,X1)
      | convergent_lines(X0,X2)
      | convergent_lines(X1,X2) ),
    inference(cnf_transformation,[],[f20]) ).

fof(f20,plain,
    ! [X0,X1,X2] :
      ( convergent_lines(X1,X2)
      | convergent_lines(X0,X2)
      | ~ convergent_lines(X0,X1) ),
    inference(flattening,[],[f19]) ).

fof(f19,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(f97,plain,
    ! [X0,X1] :
      ( ~ distinct_lines(X0,X1)
      | apart_point_and_line(sK2,X1)
      | apart_point_and_line(sK2,X0)
      | apart_point_and_line(intersection_point(sK0,sK1),X0)
      | apart_point_and_line(intersection_point(sK0,sK1),X1) ),
    inference(resolution,[],[f54,f40]) ).

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

fof(f54,plain,
    ! [X2,X3,X0,X1] :
      ( ~ distinct_points(X0,X1)
      | apart_point_and_line(X1,X2)
      | apart_point_and_line(X0,X3)
      | apart_point_and_line(X0,X2)
      | ~ distinct_lines(X2,X3)
      | apart_point_and_line(X1,X3) ),
    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) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.08  % Problem    : GEO172+2 : TPTP v8.2.0. Released v3.3.0.
% 0.03/0.09  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.08/0.28  % Computer : n032.cluster.edu
% 0.08/0.28  % Model    : x86_64 x86_64
% 0.08/0.28  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.28  % Memory   : 8042.1875MB
% 0.08/0.28  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.08/0.28  % CPULimit   : 300
% 0.08/0.28  % WCLimit    : 300
% 0.08/0.28  % DateTime   : Sun May 19 14:25:23 EDT 2024
% 0.08/0.28  % CPUTime    : 
% 0.08/0.28  % (10928)Running in auto input_syntax mode. Trying TPTP
% 0.08/0.29  % (10931)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  % (10932)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  % (10935)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.08/0.29  % (10933)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.08/0.29  % (10930)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.08/0.29  TRYING [1,1]
% 0.08/0.29  TRYING [1,2]
% 0.08/0.29  TRYING [1,1]
% 0.08/0.29  TRYING [2,2]
% 0.08/0.29  TRYING [1,2]
% 0.08/0.29  TRYING [2,2]
% 0.08/0.29  TRYING [2,3]
% 0.08/0.29  TRYING [2,3]
% 0.08/0.29  TRYING [2,4]
% 0.08/0.29  TRYING [2,4]
% 0.08/0.29  % (10936)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)
% 0.08/0.29  TRYING [2,5]
% 0.08/0.30  TRYING [2,5]
% 0.08/0.30  TRYING [1]
% 0.08/0.30  TRYING [2]
% 0.08/0.30  TRYING [3]
% 0.08/0.30  TRYING [2,6]
% 0.08/0.30  % (10935)First to succeed.
% 0.08/0.30  TRYING [2,6]
% 0.08/0.30  % (10931)Also succeeded, but the first one will report.
% 0.08/0.30  % (10935)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-10928"
% 0.08/0.30  TRYING [4]
% 0.08/0.30  % (10935)Refutation found. Thanks to Tanya!
% 0.08/0.30  % SZS status Theorem for theBenchmark
% 0.08/0.30  % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.30  % (10935)------------------------------
% 0.08/0.30  % (10935)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.08/0.30  % (10935)Termination reason: Refutation
% 0.08/0.30  
% 0.08/0.30  % (10935)Memory used [KB]: 883
% 0.08/0.30  % (10935)Time elapsed: 0.005 s
% 0.08/0.30  % (10935)Instructions burned: 13 (million)
% 0.08/0.30  % (10928)Success in time 0.015 s
%------------------------------------------------------------------------------