TSTP Solution File: GEO197+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : GEO197+1 : 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 : 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 : Mon May 20 20:15:10 EDT 2024

% Result   : Theorem 0.14s 0.40s
% Output   : Refutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   68 (  13 unt;   0 def)
%            Number of atoms       :  192 (   0 equ)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives :  186 (  62   ~;  81   |;  28   &)
%                                         (   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   :   94 (  85   !;   9   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f483,plain,
    $false,
    inference(avatar_sat_refutation,[],[f405,f410,f418,f432,f458,f482]) ).

fof(f482,plain,
    ~ spl3_13,
    inference(avatar_contradiction_clause,[],[f481]) ).

fof(f481,plain,
    ( $false
    | ~ spl3_13 ),
    inference(subsumption_resolution,[],[f478,f40]) ).

fof(f40,plain,
    convergent_lines(sK0,sK1),
    inference(cnf_transformation,[],[f39]) ).

fof(f39,plain,
    ( apart_point_and_line(intersection_point(sK2,sK1),sK0)
    & ~ 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])],[f19,f38]) ).

fof(f38,plain,
    ( ? [X0,X1,X2] :
        ( apart_point_and_line(intersection_point(X2,X1),X0)
        & ~ 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(sK2,sK1),sK0)
      & ~ 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(f19,plain,
    ? [X0,X1,X2] :
      ( apart_point_and_line(intersection_point(X2,X1),X0)
      & ~ apart_point_and_line(intersection_point(X0,X1),X2)
      & convergent_lines(X0,X2)
      & convergent_lines(X2,X1)
      & convergent_lines(X0,X1) ),
    inference(flattening,[],[f18]) ).

fof(f18,plain,
    ? [X0,X1,X2] :
      ( apart_point_and_line(intersection_point(X2,X1),X0)
      & ~ apart_point_and_line(intersection_point(X0,X1),X2)
      & convergent_lines(X0,X2)
      & convergent_lines(X2,X1)
      & convergent_lines(X0,X1) ),
    inference(ennf_transformation,[],[f16]) ).

fof(f16,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(X2,X1),X0) ),
    inference(negated_conjecture,[],[f15]) ).

fof(f15,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(X2,X1),X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).

fof(f478,plain,
    ( ~ convergent_lines(sK0,sK1)
    | ~ spl3_13 ),
    inference(resolution,[],[f431,f51]) ).

fof(f51,plain,
    ! [X0,X1] :
      ( ~ apart_point_and_line(intersection_point(X0,X1),X1)
      | ~ convergent_lines(X0,X1) ),
    inference(cnf_transformation,[],[f23]) ).

fof(f23,plain,
    ! [X0,X1] :
      ( ~ apart_point_and_line(intersection_point(X0,X1),X1)
      | ~ convergent_lines(X0,X1) ),
    inference(ennf_transformation,[],[f10]) ).

fof(f10,axiom,
    ! [X0,X1] :
      ( convergent_lines(X0,X1)
     => ~ apart_point_and_line(intersection_point(X0,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ci4) ).

fof(f431,plain,
    ( apart_point_and_line(intersection_point(sK0,sK1),sK1)
    | ~ spl3_13 ),
    inference(avatar_component_clause,[],[f429]) ).

fof(f429,plain,
    ( spl3_13
  <=> apart_point_and_line(intersection_point(sK0,sK1),sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_13])]) ).

fof(f458,plain,
    ~ spl3_12,
    inference(avatar_contradiction_clause,[],[f457]) ).

fof(f457,plain,
    ( $false
    | ~ spl3_12 ),
    inference(subsumption_resolution,[],[f454,f40]) ).

fof(f454,plain,
    ( ~ convergent_lines(sK0,sK1)
    | ~ spl3_12 ),
    inference(resolution,[],[f427,f50]) ).

fof(f50,plain,
    ! [X0,X1] :
      ( ~ apart_point_and_line(intersection_point(X0,X1),X0)
      | ~ convergent_lines(X0,X1) ),
    inference(cnf_transformation,[],[f22]) ).

fof(f22,plain,
    ! [X0,X1] :
      ( ~ apart_point_and_line(intersection_point(X0,X1),X0)
      | ~ convergent_lines(X0,X1) ),
    inference(ennf_transformation,[],[f9]) ).

fof(f9,axiom,
    ! [X0,X1] :
      ( convergent_lines(X0,X1)
     => ~ apart_point_and_line(intersection_point(X0,X1),X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ci3) ).

fof(f427,plain,
    ( apart_point_and_line(intersection_point(sK0,sK1),sK0)
    | ~ spl3_12 ),
    inference(avatar_component_clause,[],[f425]) ).

fof(f425,plain,
    ( spl3_12
  <=> apart_point_and_line(intersection_point(sK0,sK1),sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_12])]) ).

fof(f432,plain,
    ( spl3_12
    | spl3_13
    | ~ spl3_4 ),
    inference(avatar_split_clause,[],[f419,f372,f429,f425]) ).

fof(f372,plain,
    ( spl3_4
  <=> ! [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_4])]) ).

fof(f419,plain,
    ( apart_point_and_line(intersection_point(sK0,sK1),sK1)
    | apart_point_and_line(intersection_point(sK0,sK1),sK0)
    | ~ spl3_4 ),
    inference(resolution,[],[f373,f43]) ).

fof(f43,plain,
    ~ apart_point_and_line(intersection_point(sK0,sK1),sK2),
    inference(cnf_transformation,[],[f39]) ).

fof(f373,plain,
    ( ! [X0] :
        ( apart_point_and_line(X0,sK2)
        | apart_point_and_line(X0,sK1)
        | apart_point_and_line(X0,sK0) )
    | ~ spl3_4 ),
    inference(avatar_component_clause,[],[f372]) ).

fof(f418,plain,
    ~ spl3_1,
    inference(avatar_contradiction_clause,[],[f417]) ).

fof(f417,plain,
    ( $false
    | ~ spl3_1 ),
    inference(subsumption_resolution,[],[f414,f41]) ).

fof(f41,plain,
    convergent_lines(sK2,sK1),
    inference(cnf_transformation,[],[f39]) ).

fof(f414,plain,
    ( ~ convergent_lines(sK2,sK1)
    | ~ spl3_1 ),
    inference(resolution,[],[f362,f50]) ).

fof(f362,plain,
    ( apart_point_and_line(intersection_point(sK2,sK1),sK2)
    | ~ spl3_1 ),
    inference(avatar_component_clause,[],[f360]) ).

fof(f360,plain,
    ( spl3_1
  <=> apart_point_and_line(intersection_point(sK2,sK1),sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).

fof(f410,plain,
    ~ spl3_3,
    inference(avatar_contradiction_clause,[],[f409]) ).

fof(f409,plain,
    ( $false
    | ~ spl3_3 ),
    inference(subsumption_resolution,[],[f406,f41]) ).

fof(f406,plain,
    ( ~ convergent_lines(sK2,sK1)
    | ~ spl3_3 ),
    inference(resolution,[],[f370,f51]) ).

fof(f370,plain,
    ( apart_point_and_line(intersection_point(sK2,sK1),sK1)
    | ~ spl3_3 ),
    inference(avatar_component_clause,[],[f368]) ).

fof(f368,plain,
    ( spl3_3
  <=> apart_point_and_line(intersection_point(sK2,sK1),sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_3])]) ).

fof(f405,plain,
    ( spl3_1
    | spl3_3
    | spl3_4 ),
    inference(avatar_split_clause,[],[f346,f372,f368,f360]) ).

fof(f346,plain,
    ! [X0] :
      ( apart_point_and_line(X0,sK2)
      | apart_point_and_line(intersection_point(sK2,sK1),sK1)
      | apart_point_and_line(intersection_point(sK2,sK1),sK2)
      | apart_point_and_line(X0,sK0)
      | apart_point_and_line(X0,sK1) ),
    inference(resolution,[],[f93,f123]) ).

fof(f123,plain,
    distinct_lines(sK2,sK1),
    inference(resolution,[],[f86,f47]) ).

fof(f47,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(f86,plain,
    ! [X0] :
      ( convergent_lines(sK1,X0)
      | distinct_lines(sK2,X0) ),
    inference(resolution,[],[f82,f54]) ).

fof(f54,plain,
    ! [X2,X0,X1] :
      ( ~ convergent_lines(X0,X1)
      | distinct_lines(X1,X2)
      | convergent_lines(X0,X2) ),
    inference(cnf_transformation,[],[f29]) ).

fof(f29,plain,
    ! [X0,X1,X2] :
      ( convergent_lines(X0,X2)
      | distinct_lines(X1,X2)
      | ~ convergent_lines(X0,X1) ),
    inference(flattening,[],[f28]) ).

fof(f28,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(f82,plain,
    convergent_lines(sK1,sK2),
    inference(resolution,[],[f65,f47]) ).

fof(f65,plain,
    ! [X0] :
      ( convergent_lines(sK2,X0)
      | convergent_lines(sK1,X0) ),
    inference(resolution,[],[f55,f41]) ).

fof(f55,plain,
    ! [X2,X0,X1] :
      ( ~ convergent_lines(X0,X1)
      | convergent_lines(X0,X2)
      | convergent_lines(X1,X2) ),
    inference(cnf_transformation,[],[f31]) ).

fof(f31,plain,
    ! [X0,X1,X2] :
      ( convergent_lines(X1,X2)
      | convergent_lines(X0,X2)
      | ~ convergent_lines(X0,X1) ),
    inference(flattening,[],[f30]) ).

fof(f30,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',ax6) ).

fof(f93,plain,
    ! [X2,X0,X1] :
      ( ~ distinct_lines(X1,X2)
      | apart_point_and_line(X0,X1)
      | apart_point_and_line(intersection_point(sK2,sK1),X2)
      | apart_point_and_line(intersection_point(sK2,sK1),X1)
      | apart_point_and_line(X0,sK0)
      | apart_point_and_line(X0,X2) ),
    inference(resolution,[],[f72,f58]) ).

fof(f58,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,[],[f37]) ).

fof(f37,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,[],[f36]) ).

fof(f36,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,[],[f17]) ).

fof(f17,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) ).

fof(f72,plain,
    ! [X0] :
      ( distinct_points(intersection_point(sK2,sK1),X0)
      | apart_point_and_line(X0,sK0) ),
    inference(resolution,[],[f56,f44]) ).

fof(f44,plain,
    apart_point_and_line(intersection_point(sK2,sK1),sK0),
    inference(cnf_transformation,[],[f39]) ).

fof(f56,plain,
    ! [X2,X0,X1] :
      ( ~ apart_point_and_line(X0,X1)
      | distinct_points(X0,X2)
      | apart_point_and_line(X2,X1) ),
    inference(cnf_transformation,[],[f33]) ).

fof(f33,plain,
    ! [X0,X1,X2] :
      ( apart_point_and_line(X2,X1)
      | distinct_points(X0,X2)
      | ~ apart_point_and_line(X0,X1) ),
    inference(flattening,[],[f32]) ).

fof(f32,plain,
    ! [X0,X1,X2] :
      ( apart_point_and_line(X2,X1)
      | distinct_points(X0,X2)
      | ~ apart_point_and_line(X0,X1) ),
    inference(ennf_transformation,[],[f12]) ).

fof(f12,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) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : GEO197+1 : TPTP v8.2.0. Released v3.3.0.
% 0.07/0.15  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36  % Computer : n018.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Sun May 19 14:42:53 EDT 2024
% 0.14/0.36  % CPUTime    : 
% 0.14/0.37  % (4994)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.38  % (4999)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.14/0.38  % (5001)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)
% 0.14/0.38  % (4997)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)
% 0.14/0.38  % (5000)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.14/0.38  % (4996)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.38  % (4998)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.14/0.39  TRYING [1]
% 0.14/0.39  % (4995)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.14/0.39  TRYING [1,1]
% 0.14/0.39  TRYING [2]
% 0.14/0.39  TRYING [1,1]
% 0.14/0.39  TRYING [2,2]
% 0.14/0.39  TRYING [2,2]
% 0.14/0.39  TRYING [3]
% 0.14/0.39  TRYING [3,3]
% 0.14/0.39  TRYING [3,3]
% 0.14/0.39  TRYING [1]
% 0.14/0.39  TRYING [4]
% 0.14/0.39  TRYING [3,4]
% 0.14/0.39  TRYING [3,4]
% 0.14/0.39  TRYING [2]
% 0.14/0.39  TRYING [3]
% 0.14/0.39  TRYING [3,5]
% 0.14/0.39  TRYING [4]
% 0.14/0.39  TRYING [3,5]
% 0.14/0.39  TRYING [5]
% 0.14/0.39  TRYING [3,6]
% 0.14/0.39  TRYING [3,6]
% 0.14/0.39  TRYING [5]
% 0.14/0.39  TRYING [3,7]
% 0.14/0.40  TRYING [3,7]
% 0.14/0.40  % (5000)First to succeed.
% 0.14/0.40  % (5000)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4994"
% 0.14/0.40  % (5000)Refutation found. Thanks to Tanya!
% 0.14/0.40  % SZS status Theorem for theBenchmark
% 0.14/0.40  % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.40  % (5000)------------------------------
% 0.14/0.40  % (5000)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.40  % (5000)Termination reason: Refutation
% 0.14/0.40  
% 0.14/0.40  % (5000)Memory used [KB]: 916
% 0.14/0.40  % (5000)Time elapsed: 0.015 s
% 0.14/0.40  % (5000)Instructions burned: 24 (million)
% 0.14/0.40  % (4994)Success in time 0.03 s
%------------------------------------------------------------------------------