TSTP Solution File: GEO205+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : GEO205+1 : 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 : n017.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 11:14:42 EDT 2024

% Result   : Theorem 0.20s 0.38s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   82 (  12 unt;   0 def)
%            Number of atoms       :  226 (   0 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  241 (  97   ~; 111   |;  16   &)
%                                         (   7 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   12 (  11 usr;   8 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :  111 ( 102   !;   9   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f650,plain,
    $false,
    inference(avatar_sat_refutation,[],[f65,f83,f309,f481,f525,f613,f647,f649]) ).

fof(f649,plain,
    ~ spl3_7,
    inference(avatar_contradiction_clause,[],[f648]) ).

fof(f648,plain,
    ( $false
    | ~ spl3_7 ),
    inference(resolution,[],[f612,f43]) ).

fof(f43,plain,
    ! [X0] : ~ distinct_lines(X0,X0),
    inference(cnf_transformation,[],[f2]) ).

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

fof(f612,plain,
    ( distinct_lines(sK1,sK1)
    | ~ spl3_7 ),
    inference(avatar_component_clause,[],[f610]) ).

fof(f610,plain,
    ( spl3_7
  <=> distinct_lines(sK1,sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_7])]) ).

fof(f647,plain,
    spl3_6,
    inference(avatar_contradiction_clause,[],[f643]) ).

fof(f643,plain,
    ( $false
    | spl3_6 ),
    inference(resolution,[],[f608,f40]) ).

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

fof(f39,plain,
    ( ( distinct_points(intersection_point(sK0,sK1),intersection_point(sK0,sK2))
      | ~ convergent_lines(sK0,sK2) )
    & ~ distinct_lines(sK1,sK2)
    & convergent_lines(sK0,sK1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f19,f38]) ).

fof(f38,plain,
    ( ? [X0,X1,X2] :
        ( ( distinct_points(intersection_point(X0,X1),intersection_point(X0,X2))
          | ~ convergent_lines(X0,X2) )
        & ~ distinct_lines(X1,X2)
        & convergent_lines(X0,X1) )
   => ( ( distinct_points(intersection_point(sK0,sK1),intersection_point(sK0,sK2))
        | ~ convergent_lines(sK0,sK2) )
      & ~ distinct_lines(sK1,sK2)
      & convergent_lines(sK0,sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f19,plain,
    ? [X0,X1,X2] :
      ( ( distinct_points(intersection_point(X0,X1),intersection_point(X0,X2))
        | ~ convergent_lines(X0,X2) )
      & ~ distinct_lines(X1,X2)
      & convergent_lines(X0,X1) ),
    inference(flattening,[],[f18]) ).

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

fof(f16,negated_conjecture,
    ~ ! [X0,X1,X2] :
        ( ( ~ distinct_lines(X1,X2)
          & convergent_lines(X0,X1) )
       => ( ~ distinct_points(intersection_point(X0,X1),intersection_point(X0,X2))
          & convergent_lines(X0,X2) ) ),
    inference(negated_conjecture,[],[f15]) ).

fof(f15,conjecture,
    ! [X0,X1,X2] :
      ( ( ~ distinct_lines(X1,X2)
        & convergent_lines(X0,X1) )
     => ( ~ distinct_points(intersection_point(X0,X1),intersection_point(X0,X2))
        & convergent_lines(X0,X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).

fof(f608,plain,
    ( ~ convergent_lines(sK0,sK1)
    | spl3_6 ),
    inference(avatar_component_clause,[],[f606]) ).

fof(f606,plain,
    ( spl3_6
  <=> convergent_lines(sK0,sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_6])]) ).

fof(f613,plain,
    ( ~ spl3_6
    | spl3_7
    | ~ spl3_3 ),
    inference(avatar_split_clause,[],[f555,f298,f610,f606]) ).

fof(f298,plain,
    ( spl3_3
  <=> apart_point_and_line(intersection_point(sK0,sK1),sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_3])]) ).

fof(f555,plain,
    ( distinct_lines(sK1,sK1)
    | ~ convergent_lines(sK0,sK1)
    | ~ spl3_3 ),
    inference(resolution,[],[f300,f142]) ).

fof(f142,plain,
    ! [X0,X1] :
      ( ~ apart_point_and_line(intersection_point(X0,X1),sK2)
      | distinct_lines(sK1,X1)
      | ~ convergent_lines(X0,X1) ),
    inference(resolution,[],[f115,f69]) ).

fof(f69,plain,
    ~ distinct_lines(sK2,sK1),
    inference(resolution,[],[f66,f43]) ).

fof(f66,plain,
    ! [X0] :
      ( distinct_lines(X0,sK2)
      | ~ distinct_lines(X0,sK1) ),
    inference(resolution,[],[f50,f41]) ).

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

fof(f50,plain,
    ! [X2,X0,X1] :
      ( distinct_lines(X1,X2)
      | distinct_lines(X0,X2)
      | ~ distinct_lines(X0,X1) ),
    inference(cnf_transformation,[],[f25]) ).

fof(f25,plain,
    ! [X0,X1,X2] :
      ( distinct_lines(X1,X2)
      | distinct_lines(X0,X2)
      | ~ distinct_lines(X0,X1) ),
    inference(flattening,[],[f24]) ).

fof(f24,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/sandbox/benchmark/theBenchmark.p',apart5) ).

fof(f115,plain,
    ! [X2,X3,X0,X1] :
      ( distinct_lines(X3,X0)
      | ~ convergent_lines(X2,X1)
      | distinct_lines(X0,X1)
      | ~ apart_point_and_line(intersection_point(X2,X1),X3) ),
    inference(resolution,[],[f89,f54]) ).

fof(f54,plain,
    ! [X2,X0,X1] :
      ( apart_point_and_line(X0,X2)
      | distinct_lines(X1,X2)
      | ~ apart_point_and_line(X0,X1) ),
    inference(cnf_transformation,[],[f33]) ).

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

fof(f32,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(f89,plain,
    ! [X2,X0,X1] :
      ( ~ apart_point_and_line(intersection_point(X2,X1),X0)
      | distinct_lines(X0,X1)
      | ~ convergent_lines(X2,X1) ),
    inference(resolution,[],[f54,f48]) ).

fof(f48,plain,
    ! [X0,X1] :
      ( ~ apart_point_and_line(intersection_point(X0,X1),X1)
      | ~ convergent_lines(X0,X1) ),
    inference(cnf_transformation,[],[f22]) ).

fof(f22,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/sandbox/benchmark/theBenchmark.p',ci4) ).

fof(f300,plain,
    ( apart_point_and_line(intersection_point(sK0,sK1),sK2)
    | ~ spl3_3 ),
    inference(avatar_component_clause,[],[f298]) ).

fof(f525,plain,
    ~ spl3_5,
    inference(avatar_contradiction_clause,[],[f521]) ).

fof(f521,plain,
    ( $false
    | ~ spl3_5 ),
    inference(resolution,[],[f498,f40]) ).

fof(f498,plain,
    ( ~ convergent_lines(sK0,sK1)
    | ~ spl3_5 ),
    inference(resolution,[],[f308,f49]) ).

fof(f49,plain,
    ! [X0,X1] :
      ( ~ apart_point_and_line(intersection_point(X0,X1),X0)
      | ~ convergent_lines(X0,X1) ),
    inference(cnf_transformation,[],[f23]) ).

fof(f23,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/sandbox/benchmark/theBenchmark.p',ci3) ).

fof(f308,plain,
    ( apart_point_and_line(intersection_point(sK0,sK1),sK0)
    | ~ spl3_5 ),
    inference(avatar_component_clause,[],[f306]) ).

fof(f306,plain,
    ( spl3_5
  <=> apart_point_and_line(intersection_point(sK0,sK1),sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_5])]) ).

fof(f481,plain,
    ( ~ spl3_1
    | spl3_4 ),
    inference(avatar_contradiction_clause,[],[f477]) ).

fof(f477,plain,
    ( $false
    | ~ spl3_1
    | spl3_4 ),
    inference(resolution,[],[f443,f59]) ).

fof(f59,plain,
    ( convergent_lines(sK0,sK2)
    | ~ spl3_1 ),
    inference(avatar_component_clause,[],[f58]) ).

fof(f58,plain,
    ( spl3_1
  <=> convergent_lines(sK0,sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).

fof(f443,plain,
    ( ~ convergent_lines(sK0,sK2)
    | spl3_4 ),
    inference(resolution,[],[f410,f74]) ).

fof(f74,plain,
    ! [X0,X1] :
      ( distinct_lines(X0,X1)
      | ~ convergent_lines(X1,X0) ),
    inference(resolution,[],[f52,f45]) ).

fof(f45,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(f52,plain,
    ! [X2,X0,X1] :
      ( convergent_lines(X0,X2)
      | distinct_lines(X1,X2)
      | ~ convergent_lines(X0,X1) ),
    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/sandbox/benchmark/theBenchmark.p',ceq3) ).

fof(f410,plain,
    ( ~ distinct_lines(sK2,sK0)
    | spl3_4 ),
    inference(resolution,[],[f335,f43]) ).

fof(f335,plain,
    ( ! [X0] :
        ( distinct_lines(X0,sK2)
        | ~ distinct_lines(X0,sK0) )
    | spl3_4 ),
    inference(resolution,[],[f304,f50]) ).

fof(f304,plain,
    ( ~ distinct_lines(sK0,sK2)
    | spl3_4 ),
    inference(avatar_component_clause,[],[f302]) ).

fof(f302,plain,
    ( spl3_4
  <=> distinct_lines(sK0,sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_4])]) ).

fof(f309,plain,
    ( ~ spl3_1
    | spl3_3
    | ~ spl3_4
    | spl3_5
    | ~ spl3_2 ),
    inference(avatar_split_clause,[],[f285,f62,f306,f302,f298,f58]) ).

fof(f62,plain,
    ( spl3_2
  <=> distinct_points(intersection_point(sK0,sK1),intersection_point(sK0,sK2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_2])]) ).

fof(f285,plain,
    ( apart_point_and_line(intersection_point(sK0,sK1),sK0)
    | ~ distinct_lines(sK0,sK2)
    | apart_point_and_line(intersection_point(sK0,sK1),sK2)
    | ~ convergent_lines(sK0,sK2)
    | ~ spl3_2 ),
    inference(resolution,[],[f176,f64]) ).

fof(f64,plain,
    ( distinct_points(intersection_point(sK0,sK1),intersection_point(sK0,sK2))
    | ~ spl3_2 ),
    inference(avatar_component_clause,[],[f62]) ).

fof(f176,plain,
    ! [X2,X0,X1] :
      ( ~ distinct_points(X0,intersection_point(X2,X1))
      | apart_point_and_line(X0,X2)
      | ~ distinct_lines(X2,X1)
      | apart_point_and_line(X0,X1)
      | ~ convergent_lines(X2,X1) ),
    inference(duplicate_literal_removal,[],[f161]) ).

fof(f161,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(X2,X1))
      | ~ convergent_lines(X2,X1)
      | ~ convergent_lines(X2,X1) ),
    inference(resolution,[],[f103,f49]) ).

fof(f103,plain,
    ! [X2,X3,X0,X1] :
      ( apart_point_and_line(intersection_point(X0,X1),X2)
      | apart_point_and_line(X3,X1)
      | apart_point_and_line(X3,X2)
      | ~ distinct_lines(X2,X1)
      | ~ distinct_points(X3,intersection_point(X0,X1))
      | ~ convergent_lines(X0,X1) ),
    inference(resolution,[],[f56,f48]) ).

fof(f56,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,[],[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/sandbox/benchmark/theBenchmark.p',cu1) ).

fof(f83,plain,
    spl3_1,
    inference(avatar_contradiction_clause,[],[f80]) ).

fof(f80,plain,
    ( $false
    | spl3_1 ),
    inference(resolution,[],[f76,f40]) ).

fof(f76,plain,
    ( ~ convergent_lines(sK0,sK1)
    | spl3_1 ),
    inference(resolution,[],[f75,f41]) ).

fof(f75,plain,
    ( ! [X0] :
        ( distinct_lines(X0,sK2)
        | ~ convergent_lines(sK0,X0) )
    | spl3_1 ),
    inference(resolution,[],[f52,f60]) ).

fof(f60,plain,
    ( ~ convergent_lines(sK0,sK2)
    | spl3_1 ),
    inference(avatar_component_clause,[],[f58]) ).

fof(f65,plain,
    ( ~ spl3_1
    | spl3_2 ),
    inference(avatar_split_clause,[],[f42,f62,f58]) ).

fof(f42,plain,
    ( distinct_points(intersection_point(sK0,sK1),intersection_point(sK0,sK2))
    | ~ convergent_lines(sK0,sK2) ),
    inference(cnf_transformation,[],[f39]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem    : GEO205+1 : TPTP v8.1.2. Released v3.3.0.
% 0.04/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.35  % Computer : n017.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Tue Apr 30 05:22:19 EDT 2024
% 0.13/0.35  % CPUTime    : 
% 0.13/0.36  % (19709)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.37  % (19712)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)
% 0.20/0.37  % (19711)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.20/0.37  % (19710)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.20/0.37  % (19713)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.20/0.37  % (19715)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.20/0.37  % (19716)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)
% 0.20/0.37  % (19714)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.20/0.37  TRYING [1]
% 0.20/0.37  TRYING [2]
% 0.20/0.37  TRYING [1]
% 0.20/0.37  TRYING [2]
% 0.20/0.37  TRYING [3]
% 0.20/0.37  % (19712)First to succeed.
% 0.20/0.37  TRYING [1,1]
% 0.20/0.38  TRYING [3]
% 0.20/0.38  TRYING [2,2]
% 0.20/0.38  TRYING [1,1]
% 0.20/0.38  TRYING [2,2]
% 0.20/0.38  TRYING [2,3]
% 0.20/0.38  TRYING [4]
% 0.20/0.38  TRYING [2,3]
% 0.20/0.38  % (19712)Refutation found. Thanks to Tanya!
% 0.20/0.38  % SZS status Theorem for theBenchmark
% 0.20/0.38  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.38  % (19712)------------------------------
% 0.20/0.38  % (19712)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.20/0.38  % (19712)Termination reason: Refutation
% 0.20/0.38  
% 0.20/0.38  % (19712)Memory used [KB]: 1028
% 0.20/0.38  % (19712)Time elapsed: 0.010 s
% 0.20/0.38  % (19712)Instructions burned: 32 (million)
% 0.20/0.38  % (19712)------------------------------
% 0.20/0.38  % (19712)------------------------------
% 0.20/0.38  % (19709)Success in time 0.017 s
%------------------------------------------------------------------------------