TSTP Solution File: GEO170+2 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : GEO170+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 : n007.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 20:14:54 EDT 2024

% Result   : Theorem 0.14s 0.37s
% Output   : Refutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   66 (  14 unt;   0 def)
%            Number of atoms       :  206 (   0 equ)
%            Maximal formula atoms :    8 (   3 avg)
%            Number of connectives :  224 (  84   ~; 101   |;  24   &)
%                                         (   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   :   99 (  90   !;   9   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f206,plain,
    $false,
    inference(avatar_sat_refutation,[],[f126,f156,f189,f195,f199,f203,f205]) ).

fof(f205,plain,
    ~ spl3_4,
    inference(avatar_contradiction_clause,[],[f204]) ).

fof(f204,plain,
    ( $false
    | ~ spl3_4 ),
    inference(resolution,[],[f176,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(f176,plain,
    ( distinct_points(sK1,sK1)
    | ~ spl3_4 ),
    inference(avatar_component_clause,[],[f174]) ).

fof(f174,plain,
    ( spl3_4
  <=> distinct_points(sK1,sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_4])]) ).

fof(f203,plain,
    ~ spl3_6,
    inference(avatar_contradiction_clause,[],[f202]) ).

fof(f202,plain,
    ( $false
    | ~ spl3_6 ),
    inference(resolution,[],[f184,f43]) ).

fof(f184,plain,
    ( distinct_points(sK0,sK0)
    | ~ spl3_6 ),
    inference(avatar_component_clause,[],[f182]) ).

fof(f182,plain,
    ( spl3_6
  <=> distinct_points(sK0,sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_6])]) ).

fof(f199,plain,
    ~ spl3_5,
    inference(avatar_contradiction_clause,[],[f198]) ).

fof(f198,plain,
    ( $false
    | ~ spl3_5 ),
    inference(resolution,[],[f180,f42]) ).

fof(f42,plain,
    ! [X0] : ~ distinct_lines(X0,X0),
    inference(cnf_transformation,[],[f2]) ).

fof(f2,axiom,
    ! [X0] : ~ distinct_lines(X0,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart2) ).

fof(f180,plain,
    ( distinct_lines(sK2,sK2)
    | ~ spl3_5 ),
    inference(avatar_component_clause,[],[f178]) ).

fof(f178,plain,
    ( spl3_5
  <=> distinct_lines(sK2,sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_5])]) ).

fof(f195,plain,
    spl3_7,
    inference(avatar_contradiction_clause,[],[f190]) ).

fof(f190,plain,
    ( $false
    | spl3_7 ),
    inference(resolution,[],[f188,f37]) ).

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

fof(f36,plain,
    ( distinct_lines(sK2,line_connecting(sK0,sK1))
    & ~ apart_point_and_line(sK1,sK2)
    & ~ apart_point_and_line(sK0,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(X2,line_connecting(X0,X1))
        & ~ apart_point_and_line(X1,X2)
        & ~ apart_point_and_line(X0,X2)
        & distinct_points(X0,X1) )
   => ( distinct_lines(sK2,line_connecting(sK0,sK1))
      & ~ apart_point_and_line(sK1,sK2)
      & ~ apart_point_and_line(sK0,sK2)
      & distinct_points(sK0,sK1) ) ),
    introduced(choice_axiom,[]) ).

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

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

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

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

fof(f188,plain,
    ( ~ distinct_points(sK0,sK1)
    | spl3_7 ),
    inference(avatar_component_clause,[],[f186]) ).

fof(f186,plain,
    ( spl3_7
  <=> distinct_points(sK0,sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_7])]) ).

fof(f189,plain,
    ( spl3_4
    | spl3_5
    | spl3_6
    | ~ spl3_7
    | ~ spl3_3 ),
    inference(avatar_split_clause,[],[f165,f154,f186,f182,f178,f174]) ).

fof(f154,plain,
    ( spl3_3
  <=> ! [X0,X1] :
        ( ~ distinct_lines(line_connecting(X0,X1),sK2)
        | distinct_points(sK1,X1)
        | ~ distinct_points(X0,X1)
        | distinct_points(sK0,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_3])]) ).

fof(f165,plain,
    ( ~ distinct_points(sK0,sK1)
    | distinct_points(sK0,sK0)
    | distinct_lines(sK2,sK2)
    | distinct_points(sK1,sK1)
    | ~ spl3_3 ),
    inference(resolution,[],[f162,f40]) ).

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

fof(f162,plain,
    ( ! [X2,X0,X1] :
        ( ~ distinct_lines(X2,line_connecting(X1,X0))
        | ~ distinct_points(X1,X0)
        | distinct_points(sK0,X1)
        | distinct_lines(X2,sK2)
        | distinct_points(sK1,X0) )
    | ~ spl3_3 ),
    inference(resolution,[],[f155,f48]) ).

fof(f48,plain,
    ! [X2,X0,X1] :
      ( distinct_lines(X1,X2)
      | distinct_lines(X0,X2)
      | ~ distinct_lines(X0,X1) ),
    inference(cnf_transformation,[],[f24]) ).

fof(f24,plain,
    ! [X0,X1,X2] :
      ( distinct_lines(X1,X2)
      | distinct_lines(X0,X2)
      | ~ distinct_lines(X0,X1) ),
    inference(flattening,[],[f23]) ).

fof(f23,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/sandbox2/benchmark/theBenchmark.p',apart5) ).

fof(f155,plain,
    ( ! [X0,X1] :
        ( ~ distinct_lines(line_connecting(X0,X1),sK2)
        | distinct_points(sK1,X1)
        | ~ distinct_points(X0,X1)
        | distinct_points(sK0,X0) )
    | ~ spl3_3 ),
    inference(avatar_component_clause,[],[f154]) ).

fof(f156,plain,
    ( ~ spl3_1
    | spl3_3 ),
    inference(avatar_split_clause,[],[f152,f154,f100]) ).

fof(f100,plain,
    ( spl3_1
  <=> distinct_points(sK1,sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).

fof(f152,plain,
    ! [X0,X1] :
      ( ~ distinct_lines(line_connecting(X0,X1),sK2)
      | ~ distinct_points(sK1,sK0)
      | distinct_points(sK0,X0)
      | ~ distinct_points(X0,X1)
      | distinct_points(sK1,X1) ),
    inference(resolution,[],[f110,f39]) ).

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

fof(f110,plain,
    ! [X2,X0,X1] :
      ( apart_point_and_line(X0,sK2)
      | ~ distinct_lines(line_connecting(X1,X2),sK2)
      | ~ distinct_points(X0,sK0)
      | distinct_points(sK0,X1)
      | ~ distinct_points(X1,X2)
      | distinct_points(X0,X2) ),
    inference(duplicate_literal_removal,[],[f107]) ).

fof(f107,plain,
    ! [X2,X0,X1] :
      ( apart_point_and_line(X0,sK2)
      | ~ distinct_lines(line_connecting(X1,X2),sK2)
      | ~ distinct_points(X0,sK0)
      | distinct_points(sK0,X1)
      | ~ distinct_points(X1,X2)
      | distinct_points(X0,X2)
      | ~ distinct_points(X1,X2) ),
    inference(resolution,[],[f75,f53]) ).

fof(f53,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(f75,plain,
    ! [X2,X0,X1] :
      ( apart_point_and_line(X0,line_connecting(X1,X2))
      | apart_point_and_line(X0,sK2)
      | ~ distinct_lines(line_connecting(X1,X2),sK2)
      | ~ distinct_points(X0,sK0)
      | distinct_points(sK0,X1)
      | ~ distinct_points(X1,X2) ),
    inference(resolution,[],[f69,f52]) ).

fof(f52,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(f69,plain,
    ! [X0,X1] :
      ( apart_point_and_line(sK0,X0)
      | apart_point_and_line(X1,sK2)
      | apart_point_and_line(X1,X0)
      | ~ distinct_lines(X0,sK2)
      | ~ distinct_points(X1,sK0) ),
    inference(resolution,[],[f54,f38]) ).

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

fof(f54,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,[],[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(f126,plain,
    spl3_1,
    inference(avatar_contradiction_clause,[],[f121]) ).

fof(f121,plain,
    ( $false
    | spl3_1 ),
    inference(resolution,[],[f115,f37]) ).

fof(f115,plain,
    ( ~ distinct_points(sK0,sK1)
    | spl3_1 ),
    inference(resolution,[],[f114,f43]) ).

fof(f114,plain,
    ( ! [X0] :
        ( distinct_points(X0,sK0)
        | ~ distinct_points(X0,sK1) )
    | spl3_1 ),
    inference(resolution,[],[f102,f51]) ).

fof(f51,plain,
    ! [X2,X0,X1] :
      ( distinct_points(X1,X2)
      | distinct_points(X0,X2)
      | ~ distinct_points(X0,X1) ),
    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(f102,plain,
    ( ~ distinct_points(sK1,sK0)
    | spl3_1 ),
    inference(avatar_component_clause,[],[f100]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem    : GEO170+2 : TPTP v8.2.0. Released v3.3.0.
% 0.08/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.34  % Computer : n007.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Sun May 19 13:52:38 EDT 2024
% 0.14/0.34  % CPUTime    : 
% 0.14/0.34  % (16782)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.35  % (16789)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.14/0.35  Detected minimum model sizes of [1,1,1,1]
% 0.14/0.35  Detected maximum model sizes of [max,2,max,max]
% 0.14/0.35  TRYING [1,1,1,1]
% 0.14/0.35  TRYING [2,2,1,1]
% 0.14/0.35  TRYING [3,2,1,1]
% 0.14/0.36  TRYING [4,2,1,1]
% 0.14/0.36  TRYING [5,2,1,1]
% 0.14/0.36  TRYING [6,2,1,1]
% 0.14/0.36  TRYING [7,2,1,1]
% 0.14/0.36  TRYING [8,2,1,1]
% 0.14/0.36  TRYING [9,2,1,1]
% 0.14/0.36  % (16786)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.14/0.36  % (16787)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.36  % (16790)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.14/0.36  % (16792)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)
% 0.14/0.36  % (16788)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)
% 0.14/0.36  TRYING [10,2,1,1]
% 0.14/0.36  TRYING [1]
% 0.14/0.36  TRYING [2]
% 0.14/0.36  Detected minimum model sizes of [1,1,1,1]
% 0.14/0.36  Detected maximum model sizes of [max,2,max,max]
% 0.14/0.36  TRYING [1,1,1,1]
% 0.14/0.36  TRYING [2,2,1,1]
% 0.14/0.36  TRYING [3]
% 0.14/0.36  TRYING [1]
% 0.14/0.36  TRYING [3,2,1,1]
% 0.14/0.36  TRYING [2]
% 0.14/0.36  TRYING [4,2,1,1]
% 0.14/0.36  TRYING [3]
% 0.14/0.36  TRYING [11,2,1,1]
% 0.14/0.36  TRYING [4]
% 0.14/0.36  TRYING [5,2,1,1]
% 0.14/0.36  TRYING [4]
% 0.14/0.36  TRYING [6,2,1,1]
% 0.14/0.37  TRYING [12,2,1,1]
% 0.14/0.37  TRYING [7,2,1,1]
% 0.14/0.37  % (16788)First to succeed.
% 0.14/0.37  TRYING [5]
% 0.14/0.37  % (16791)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.14/0.37  % (16788)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-16782"
% 0.14/0.37  TRYING [13,2,1,1]
% 0.14/0.37  % (16788)Refutation found. Thanks to Tanya!
% 0.14/0.37  % SZS status Theorem for theBenchmark
% 0.14/0.37  % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.37  % (16788)------------------------------
% 0.14/0.37  % (16788)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.37  % (16788)Termination reason: Refutation
% 0.14/0.37  
% 0.14/0.37  % (16788)Memory used [KB]: 890
% 0.14/0.37  % (16788)Time elapsed: 0.008 s
% 0.14/0.37  % (16788)Instructions burned: 10 (million)
% 0.14/0.37  % (16782)Success in time 0.025 s
%------------------------------------------------------------------------------