TSTP Solution File: GEO188+2 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : GEO188+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 : n020.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 05:15:57 EDT 2024

% Result   : Theorem 0.14s 0.39s
% Output   : Refutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   70 (  10 unt;   0 def)
%            Number of atoms       :  211 (   0 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  214 (  73   ~;  95   |;  31   &)
%                                         (   6 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 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   :   84 (  75   !;   9   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f435,plain,
    $false,
    inference(avatar_sat_refutation,[],[f84,f252,f262,f349,f356,f385,f434]) ).

fof(f434,plain,
    ( ~ spl3_1
    | ~ spl3_4 ),
    inference(avatar_contradiction_clause,[],[f433]) ).

fof(f433,plain,
    ( $false
    | ~ spl3_1
    | ~ spl3_4 ),
    inference(subsumption_resolution,[],[f432,f75]) ).

fof(f75,plain,
    ( distinct_points(sK2,sK1)
    | ~ spl3_1 ),
    inference(avatar_component_clause,[],[f74]) ).

fof(f74,plain,
    ( spl3_1
  <=> distinct_points(sK2,sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).

fof(f432,plain,
    ( ~ distinct_points(sK2,sK1)
    | ~ spl3_4 ),
    inference(subsumption_resolution,[],[f429,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(f429,plain,
    ( distinct_points(sK2,sK2)
    | ~ distinct_points(sK2,sK1)
    | ~ spl3_4 ),
    inference(resolution,[],[f215,f53]) ).

fof(f53,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(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(f215,plain,
    ( apart_point_and_line(sK2,line_connecting(sK2,sK1))
    | ~ spl3_4 ),
    inference(avatar_component_clause,[],[f213]) ).

fof(f213,plain,
    ( spl3_4
  <=> apart_point_and_line(sK2,line_connecting(sK2,sK1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_4])]) ).

fof(f385,plain,
    ~ spl3_16,
    inference(avatar_contradiction_clause,[],[f384]) ).

fof(f384,plain,
    ( $false
    | ~ spl3_16 ),
    inference(subsumption_resolution,[],[f383,f37]) ).

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

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

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

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

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

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

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

fof(f383,plain,
    ( ~ distinct_points(sK0,sK1)
    | ~ spl3_16 ),
    inference(subsumption_resolution,[],[f380,f44]) ).

fof(f380,plain,
    ( distinct_points(sK0,sK0)
    | ~ distinct_points(sK0,sK1)
    | ~ spl3_16 ),
    inference(resolution,[],[f348,f53]) ).

fof(f348,plain,
    ( apart_point_and_line(sK0,line_connecting(sK0,sK1))
    | ~ spl3_16 ),
    inference(avatar_component_clause,[],[f346]) ).

fof(f346,plain,
    ( spl3_16
  <=> apart_point_and_line(sK0,line_connecting(sK0,sK1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_16])]) ).

fof(f356,plain,
    ~ spl3_15,
    inference(avatar_contradiction_clause,[],[f355]) ).

fof(f355,plain,
    ( $false
    | ~ spl3_15 ),
    inference(subsumption_resolution,[],[f354,f37]) ).

fof(f354,plain,
    ( ~ distinct_points(sK0,sK1)
    | ~ spl3_15 ),
    inference(subsumption_resolution,[],[f350,f44]) ).

fof(f350,plain,
    ( distinct_points(sK1,sK1)
    | ~ distinct_points(sK0,sK1)
    | ~ spl3_15 ),
    inference(resolution,[],[f344,f54]) ).

fof(f54,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(f344,plain,
    ( apart_point_and_line(sK1,line_connecting(sK0,sK1))
    | ~ spl3_15 ),
    inference(avatar_component_clause,[],[f342]) ).

fof(f342,plain,
    ( spl3_15
  <=> apart_point_and_line(sK1,line_connecting(sK0,sK1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_15])]) ).

fof(f349,plain,
    ( spl3_15
    | spl3_16
    | ~ spl3_10 ),
    inference(avatar_split_clause,[],[f336,f236,f346,f342]) ).

fof(f236,plain,
    ( spl3_10
  <=> ! [X0] :
        ( apart_point_and_line(sK1,X0)
        | apart_point_and_line(sK0,X0)
        | apart_point_and_line(sK2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_10])]) ).

fof(f336,plain,
    ( apart_point_and_line(sK0,line_connecting(sK0,sK1))
    | apart_point_and_line(sK1,line_connecting(sK0,sK1))
    | ~ spl3_10 ),
    inference(resolution,[],[f237,f40]) ).

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

fof(f237,plain,
    ( ! [X0] :
        ( apart_point_and_line(sK2,X0)
        | apart_point_and_line(sK0,X0)
        | apart_point_and_line(sK1,X0) )
    | ~ spl3_10 ),
    inference(avatar_component_clause,[],[f236]) ).

fof(f262,plain,
    ( ~ spl3_1
    | ~ spl3_9 ),
    inference(avatar_contradiction_clause,[],[f261]) ).

fof(f261,plain,
    ( $false
    | ~ spl3_1
    | ~ spl3_9 ),
    inference(subsumption_resolution,[],[f260,f75]) ).

fof(f260,plain,
    ( ~ distinct_points(sK2,sK1)
    | ~ spl3_9 ),
    inference(subsumption_resolution,[],[f256,f44]) ).

fof(f256,plain,
    ( distinct_points(sK1,sK1)
    | ~ distinct_points(sK2,sK1)
    | ~ spl3_9 ),
    inference(resolution,[],[f234,f54]) ).

fof(f234,plain,
    ( apart_point_and_line(sK1,line_connecting(sK2,sK1))
    | ~ spl3_9 ),
    inference(avatar_component_clause,[],[f232]) ).

fof(f232,plain,
    ( spl3_9
  <=> apart_point_and_line(sK1,line_connecting(sK2,sK1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_9])]) ).

fof(f252,plain,
    ( spl3_9
    | spl3_4
    | spl3_10
    | ~ spl3_1 ),
    inference(avatar_split_clause,[],[f201,f74,f236,f213,f232]) ).

fof(f201,plain,
    ( ! [X0] :
        ( apart_point_and_line(sK2,X0)
        | apart_point_and_line(sK2,line_connecting(sK2,sK1))
        | apart_point_and_line(sK1,X0)
        | apart_point_and_line(sK1,line_connecting(sK2,sK1))
        | apart_point_and_line(sK0,X0) )
    | ~ spl3_1 ),
    inference(resolution,[],[f92,f75]) ).

fof(f92,plain,
    ! [X2,X0,X1] :
      ( ~ distinct_points(X1,X0)
      | apart_point_and_line(X1,X2)
      | apart_point_and_line(X1,line_connecting(sK2,sK1))
      | apart_point_and_line(X0,X2)
      | apart_point_and_line(X0,line_connecting(sK2,sK1))
      | apart_point_and_line(sK0,X2) ),
    inference(resolution,[],[f55,f56]) ).

fof(f56,plain,
    ! [X0] :
      ( distinct_lines(line_connecting(sK2,sK1),X0)
      | apart_point_and_line(sK0,X0) ),
    inference(resolution,[],[f50,f41]) ).

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

fof(f50,plain,
    ! [X2,X0,X1] :
      ( ~ apart_point_and_line(X0,X1)
      | distinct_lines(X1,X2)
      | apart_point_and_line(X0,X2) ),
    inference(cnf_transformation,[],[f26]) ).

fof(f26,plain,
    ! [X0,X1,X2] :
      ( apart_point_and_line(X0,X2)
      | distinct_lines(X1,X2)
      | ~ apart_point_and_line(X0,X1) ),
    inference(flattening,[],[f25]) ).

fof(f25,plain,
    ! [X0,X1,X2] :
      ( apart_point_and_line(X0,X2)
      | distinct_lines(X1,X2)
      | ~ apart_point_and_line(X0,X1) ),
    inference(ennf_transformation,[],[f11]) ).

fof(f11,axiom,
    ! [X0,X1,X2] :
      ( apart_point_and_line(X0,X1)
     => ( apart_point_and_line(X0,X2)
        | distinct_lines(X1,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ceq2) ).

fof(f55,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(f84,plain,
    spl3_1,
    inference(avatar_contradiction_clause,[],[f83]) ).

fof(f83,plain,
    ( $false
    | spl3_1 ),
    inference(subsumption_resolution,[],[f81,f44]) ).

fof(f81,plain,
    ( distinct_points(sK1,sK1)
    | spl3_1 ),
    inference(resolution,[],[f76,f62]) ).

fof(f62,plain,
    ! [X0] :
      ( distinct_points(sK2,X0)
      | distinct_points(sK1,X0) ),
    inference(resolution,[],[f52,f39]) ).

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

fof(f52,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,
    ( ~ distinct_points(sK2,sK1)
    | spl3_1 ),
    inference(avatar_component_clause,[],[f74]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : GEO188+2 : TPTP v8.1.2. Released v3.3.0.
% 0.12/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35  % Computer : n020.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   : Fri May  3 22:04:38 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.14/0.36  % (31892)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37  % (31894)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.14/0.37  TRYING [1]
% 0.14/0.37  TRYING [2]
% 0.14/0.37  TRYING [3]
% 0.14/0.37  TRYING [4]
% 0.14/0.37  TRYING [5]
% 0.14/0.38  TRYING [6]
% 0.14/0.38  % (31896)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  % (31898)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.14/0.38  % (31899)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.14/0.38  % (31895)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.38  % (31900)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  % (31897)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.14/0.38  Detected minimum model sizes of [1,1,1,1]
% 0.14/0.38  Detected maximum model sizes of [max,3,max,max]
% 0.14/0.38  Detected minimum model sizes of [1,1,1,1]
% 0.14/0.38  Detected maximum model sizes of [max,3,max,max]
% 0.14/0.38  TRYING [1]
% 0.14/0.38  TRYING [1,1,1,1]
% 0.14/0.38  TRYING [2]
% 0.14/0.38  TRYING [1,1,1,1]
% 0.14/0.38  TRYING [2,2,1,1]
% 0.14/0.38  TRYING [2,2,1,1]
% 0.14/0.38  TRYING [3]
% 0.14/0.38  TRYING [3,3,1,1]
% 0.14/0.38  TRYING [3,3,1,1]
% 0.14/0.38  TRYING [4,3,1,1]
% 0.14/0.38  TRYING [4,3,1,1]
% 0.14/0.38  TRYING [4]
% 0.14/0.38  TRYING [5,3,1,1]
% 0.14/0.38  TRYING [7]
% 0.14/0.38  TRYING [5,3,1,1]
% 0.14/0.38  TRYING [6,3,1,1]
% 0.14/0.38  TRYING [6,3,1,1]
% 0.14/0.38  TRYING [5]
% 0.14/0.38  % (31899)First to succeed.
% 0.14/0.39  TRYING [7,3,1,1]
% 0.14/0.39  % (31899)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-31892"
% 0.14/0.39  TRYING [7,3,1,1]
% 0.14/0.39  % (31899)Refutation found. Thanks to Tanya!
% 0.14/0.39  % SZS status Theorem for theBenchmark
% 0.14/0.39  % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.39  % (31899)------------------------------
% 0.14/0.39  % (31899)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.39  % (31899)Termination reason: Refutation
% 0.14/0.39  
% 0.14/0.39  % (31899)Memory used [KB]: 914
% 0.14/0.39  % (31899)Time elapsed: 0.012 s
% 0.14/0.39  % (31899)Instructions burned: 19 (million)
% 0.14/0.39  % (31892)Success in time 0.029 s
%------------------------------------------------------------------------------