TSTP Solution File: GEO204+2 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : GEO204+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 : n008.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 0.12s 0.36s
% Output   : Refutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   66 (  10 unt;   0 def)
%            Number of atoms       :  188 (   0 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  197 (  75   ~;  89   |;  19   &)
%                                         (   6 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   10 (   9 usr;   7 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :   73 (  64   !;   9   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f267,plain,
    $false,
    inference(avatar_sat_refutation,[],[f62,f69,f216,f228,f237,f246,f266]) ).

fof(f266,plain,
    ( ~ spl3_1
    | ~ spl3_12 ),
    inference(avatar_contradiction_clause,[],[f265]) ).

fof(f265,plain,
    ( $false
    | ~ spl3_1
    | ~ spl3_12 ),
    inference(subsumption_resolution,[],[f264,f56]) ).

fof(f56,plain,
    ( distinct_points(sK0,sK2)
    | ~ spl3_1 ),
    inference(avatar_component_clause,[],[f55]) ).

fof(f55,plain,
    ( spl3_1
  <=> distinct_points(sK0,sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).

fof(f264,plain,
    ( ~ distinct_points(sK0,sK2)
    | ~ spl3_12 ),
    inference(subsumption_resolution,[],[f258,f38]) ).

fof(f38,plain,
    ~ distinct_points(sK1,sK2),
    inference(cnf_transformation,[],[f36]) ).

fof(f36,plain,
    ( ( distinct_lines(line_connecting(sK0,sK1),line_connecting(sK0,sK2))
      | ~ distinct_points(sK0,sK2) )
    & ~ distinct_points(sK1,sK2)
    & distinct_points(sK0,sK1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f17,f35]) ).

fof(f35,plain,
    ( ? [X0,X1,X2] :
        ( ( distinct_lines(line_connecting(X0,X1),line_connecting(X0,X2))
          | ~ distinct_points(X0,X2) )
        & ~ distinct_points(X1,X2)
        & distinct_points(X0,X1) )
   => ( ( distinct_lines(line_connecting(sK0,sK1),line_connecting(sK0,sK2))
        | ~ distinct_points(sK0,sK2) )
      & ~ distinct_points(sK1,sK2)
      & distinct_points(sK0,sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f17,plain,
    ? [X0,X1,X2] :
      ( ( distinct_lines(line_connecting(X0,X1),line_connecting(X0,X2))
        | ~ distinct_points(X0,X2) )
      & ~ distinct_points(X1,X2)
      & distinct_points(X0,X1) ),
    inference(flattening,[],[f16]) ).

fof(f16,plain,
    ? [X0,X1,X2] :
      ( ( distinct_lines(line_connecting(X0,X1),line_connecting(X0,X2))
        | ~ distinct_points(X0,X2) )
      & ~ distinct_points(X1,X2)
      & distinct_points(X0,X1) ),
    inference(ennf_transformation,[],[f14]) ).

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

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

fof(f258,plain,
    ( distinct_points(sK1,sK2)
    | ~ distinct_points(sK0,sK2)
    | ~ spl3_12 ),
    inference(resolution,[],[f182,f52]) ).

fof(f52,plain,
    ! [X2,X0,X1] :
      ( ~ apart_point_and_line(X2,line_connecting(X0,X1))
      | distinct_points(X2,X1)
      | ~ distinct_points(X0,X1) ),
    inference(cnf_transformation,[],[f32]) ).

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

fof(f31,plain,
    ! [X0,X1,X2] :
      ( ( distinct_points(X2,X1)
        & distinct_points(X2,X0) )
      | ~ apart_point_and_line(X2,line_connecting(X0,X1))
      | ~ distinct_points(X0,X1) ),
    inference(ennf_transformation,[],[f7]) ).

fof(f7,axiom,
    ! [X0,X1,X2] :
      ( distinct_points(X0,X1)
     => ( apart_point_and_line(X2,line_connecting(X0,X1))
       => ( distinct_points(X2,X1)
          & distinct_points(X2,X0) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con1) ).

fof(f182,plain,
    ( apart_point_and_line(sK1,line_connecting(sK0,sK2))
    | ~ spl3_12 ),
    inference(avatar_component_clause,[],[f180]) ).

fof(f180,plain,
    ( spl3_12
  <=> apart_point_and_line(sK1,line_connecting(sK0,sK2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_12])]) ).

fof(f246,plain,
    ~ spl3_11,
    inference(avatar_contradiction_clause,[],[f245]) ).

fof(f245,plain,
    ( $false
    | ~ spl3_11 ),
    inference(subsumption_resolution,[],[f244,f37]) ).

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

fof(f244,plain,
    ( ~ distinct_points(sK0,sK1)
    | ~ spl3_11 ),
    inference(subsumption_resolution,[],[f238,f42]) ).

fof(f42,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(f238,plain,
    ( distinct_points(sK1,sK1)
    | ~ distinct_points(sK0,sK1)
    | ~ spl3_11 ),
    inference(resolution,[],[f178,f52]) ).

fof(f178,plain,
    ( apart_point_and_line(sK1,line_connecting(sK0,sK1))
    | ~ spl3_11 ),
    inference(avatar_component_clause,[],[f176]) ).

fof(f176,plain,
    ( spl3_11
  <=> apart_point_and_line(sK1,line_connecting(sK0,sK1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_11])]) ).

fof(f237,plain,
    ( ~ spl3_1
    | ~ spl3_14 ),
    inference(avatar_contradiction_clause,[],[f236]) ).

fof(f236,plain,
    ( $false
    | ~ spl3_1
    | ~ spl3_14 ),
    inference(subsumption_resolution,[],[f235,f56]) ).

fof(f235,plain,
    ( ~ distinct_points(sK0,sK2)
    | ~ spl3_14 ),
    inference(subsumption_resolution,[],[f230,f42]) ).

fof(f230,plain,
    ( distinct_points(sK0,sK0)
    | ~ distinct_points(sK0,sK2)
    | ~ spl3_14 ),
    inference(resolution,[],[f191,f51]) ).

fof(f51,plain,
    ! [X2,X0,X1] :
      ( ~ apart_point_and_line(X2,line_connecting(X0,X1))
      | distinct_points(X2,X0)
      | ~ distinct_points(X0,X1) ),
    inference(cnf_transformation,[],[f32]) ).

fof(f191,plain,
    ( apart_point_and_line(sK0,line_connecting(sK0,sK2))
    | ~ spl3_14 ),
    inference(avatar_component_clause,[],[f189]) ).

fof(f189,plain,
    ( spl3_14
  <=> apart_point_and_line(sK0,line_connecting(sK0,sK2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_14])]) ).

fof(f228,plain,
    ~ spl3_13,
    inference(avatar_contradiction_clause,[],[f227]) ).

fof(f227,plain,
    ( $false
    | ~ spl3_13 ),
    inference(subsumption_resolution,[],[f226,f37]) ).

fof(f226,plain,
    ( ~ distinct_points(sK0,sK1)
    | ~ spl3_13 ),
    inference(subsumption_resolution,[],[f221,f42]) ).

fof(f221,plain,
    ( distinct_points(sK0,sK0)
    | ~ distinct_points(sK0,sK1)
    | ~ spl3_13 ),
    inference(resolution,[],[f187,f51]) ).

fof(f187,plain,
    ( apart_point_and_line(sK0,line_connecting(sK0,sK1))
    | ~ spl3_13 ),
    inference(avatar_component_clause,[],[f185]) ).

fof(f185,plain,
    ( spl3_13
  <=> apart_point_and_line(sK0,line_connecting(sK0,sK1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_13])]) ).

fof(f216,plain,
    ( spl3_13
    | spl3_14
    | spl3_11
    | spl3_12
    | ~ spl3_2 ),
    inference(avatar_split_clause,[],[f139,f59,f180,f176,f189,f185]) ).

fof(f59,plain,
    ( spl3_2
  <=> distinct_lines(line_connecting(sK0,sK1),line_connecting(sK0,sK2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_2])]) ).

fof(f139,plain,
    ( apart_point_and_line(sK1,line_connecting(sK0,sK2))
    | apart_point_and_line(sK1,line_connecting(sK0,sK1))
    | apart_point_and_line(sK0,line_connecting(sK0,sK2))
    | apart_point_and_line(sK0,line_connecting(sK0,sK1))
    | ~ spl3_2 ),
    inference(resolution,[],[f114,f115]) ).

fof(f115,plain,
    distinct_points(sK1,sK0),
    inference(resolution,[],[f105,f38]) ).

fof(f105,plain,
    ! [X0] :
      ( distinct_points(X0,sK2)
      | distinct_points(X0,sK0) ),
    inference(resolution,[],[f85,f42]) ).

fof(f85,plain,
    ! [X0,X1] :
      ( distinct_points(X0,sK2)
      | distinct_points(sK0,X1)
      | distinct_points(X0,X1) ),
    inference(resolution,[],[f76,f50]) ).

fof(f50,plain,
    ! [X2,X0,X1] :
      ( ~ distinct_points(X0,X1)
      | distinct_points(X0,X2)
      | distinct_points(X1,X2) ),
    inference(cnf_transformation,[],[f30]) ).

fof(f30,plain,
    ! [X0,X1,X2] :
      ( distinct_points(X1,X2)
      | distinct_points(X0,X2)
      | ~ distinct_points(X0,X1) ),
    inference(flattening,[],[f29]) ).

fof(f29,plain,
    ! [X0,X1,X2] :
      ( distinct_points(X1,X2)
      | distinct_points(X0,X2)
      | ~ distinct_points(X0,X1) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X0,X1,X2] :
      ( distinct_points(X0,X1)
     => ( distinct_points(X1,X2)
        | distinct_points(X0,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart4) ).

fof(f76,plain,
    ! [X0] :
      ( distinct_points(sK0,X0)
      | distinct_points(X0,sK2) ),
    inference(resolution,[],[f66,f38]) ).

fof(f66,plain,
    ! [X0,X1] :
      ( distinct_points(sK0,X0)
      | distinct_points(sK1,X1)
      | distinct_points(X0,X1) ),
    inference(resolution,[],[f63,f50]) ).

fof(f63,plain,
    ! [X0] :
      ( distinct_points(sK1,X0)
      | distinct_points(sK0,X0) ),
    inference(resolution,[],[f50,f37]) ).

fof(f114,plain,
    ( ! [X0,X1] :
        ( ~ distinct_points(X1,X0)
        | apart_point_and_line(X1,line_connecting(sK0,sK2))
        | apart_point_and_line(X1,line_connecting(sK0,sK1))
        | apart_point_and_line(X0,line_connecting(sK0,sK2))
        | apart_point_and_line(X0,line_connecting(sK0,sK1)) )
    | ~ spl3_2 ),
    inference(resolution,[],[f53,f61]) ).

fof(f61,plain,
    ( distinct_lines(line_connecting(sK0,sK1),line_connecting(sK0,sK2))
    | ~ spl3_2 ),
    inference(avatar_component_clause,[],[f59]) ).

fof(f53,plain,
    ! [X2,X3,X0,X1] :
      ( ~ distinct_lines(X2,X3)
      | apart_point_and_line(X1,X2)
      | apart_point_and_line(X0,X3)
      | apart_point_and_line(X0,X2)
      | apart_point_and_line(X1,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(f69,plain,
    spl3_1,
    inference(avatar_split_clause,[],[f64,f55]) ).

fof(f64,plain,
    distinct_points(sK0,sK2),
    inference(resolution,[],[f63,f38]) ).

fof(f62,plain,
    ( ~ spl3_1
    | spl3_2 ),
    inference(avatar_split_clause,[],[f39,f59,f55]) ).

fof(f39,plain,
    ( distinct_lines(line_connecting(sK0,sK1),line_connecting(sK0,sK2))
    | ~ distinct_points(sK0,sK2) ),
    inference(cnf_transformation,[],[f36]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem    : GEO204+2 : TPTP v8.1.2. Released v3.3.0.
% 0.10/0.13  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.12/0.33  % Computer : n008.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Fri May  3 21:59:38 EDT 2024
% 0.12/0.33  % CPUTime    : 
% 0.12/0.34  % (13467)Running in auto input_syntax mode. Trying TPTP
% 0.12/0.35  % (13468)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.12/0.35  % (13471)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.12/0.35  % (13470)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)
% 0.12/0.35  % (13474)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)
% 0.12/0.35  % (13472)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.12/0.35  % (13469)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.12/0.35  % (13473)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.12/0.35  TRYING [1]
% 0.12/0.35  Detected minimum model sizes of [1,1,1,1]
% 0.12/0.35  Detected maximum model sizes of [max,3,max,max]
% 0.12/0.35  TRYING [2]
% 0.12/0.35  TRYING [1,1,1,1]
% 0.12/0.35  TRYING [2,2,1,1]
% 0.12/0.35  TRYING [1]
% 0.12/0.35  Detected minimum model sizes of [1,1,1,1]
% 0.12/0.35  TRYING [3]
% 0.12/0.35  Detected maximum model sizes of [max,3,max,max]
% 0.12/0.35  TRYING [1,1,1,1]
% 0.12/0.35  TRYING [2]
% 0.12/0.35  TRYING [3,2,1,1]
% 0.12/0.36  TRYING [2,2,1,1]
% 0.12/0.36  TRYING [3]
% 0.12/0.36  TRYING [3,2,1,1]
% 0.12/0.36  TRYING [4,2,1,1]
% 0.12/0.36  TRYING [4]
% 0.12/0.36  TRYING [4,2,1,1]
% 0.12/0.36  TRYING [3,3,1,1]
% 0.12/0.36  TRYING [3,3,1,1]
% 0.12/0.36  TRYING [4]
% 0.12/0.36  TRYING [5,2,1,1]
% 0.12/0.36  % (13473)First to succeed.
% 0.12/0.36  TRYING [5,2,1,1]
% 0.12/0.36  TRYING [4,3,1,1]
% 0.12/0.36  TRYING [5]
% 0.12/0.36  % (13473)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-13467"
% 0.12/0.36  TRYING [4,3,1,1]
% 0.12/0.36  TRYING [6,2,1,1]
% 0.12/0.36  % (13473)Refutation found. Thanks to Tanya!
% 0.12/0.36  % SZS status Theorem for theBenchmark
% 0.12/0.36  % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.36  % (13473)------------------------------
% 0.12/0.36  % (13473)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.12/0.36  % (13473)Termination reason: Refutation
% 0.12/0.36  
% 0.12/0.36  % (13473)Memory used [KB]: 888
% 0.12/0.36  % (13473)Time elapsed: 0.007 s
% 0.12/0.36  % (13473)Instructions burned: 10 (million)
% 0.12/0.36  % (13467)Success in time 0.022 s
%------------------------------------------------------------------------------