TSTP Solution File: GEO190+2 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : GEO190+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 : n019.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 11:14:34 EDT 2024

% Result   : Theorem 0.15s 0.40s
% Output   : Refutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   69 (   9 unt;   0 def)
%            Number of atoms       :  210 (   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(f470,plain,
    $false,
    inference(avatar_sat_refutation,[],[f88,f304,f311,f401,f407,f421,f469]) ).

fof(f469,plain,
    ~ spl3_18,
    inference(avatar_contradiction_clause,[],[f468]) ).

fof(f468,plain,
    ( $false
    | ~ spl3_18 ),
    inference(subsumption_resolution,[],[f467,f37]) ).

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

fof(f36,plain,
    ( apart_point_and_line(sK2,line_connecting(sK1,sK0))
    & ~ 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(X2,line_connecting(X1,X0))
        & ~ 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(sK2,line_connecting(sK1,sK0))
      & ~ 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(X2,line_connecting(X1,X0))
      & ~ 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(X2,line_connecting(X1,X0))
      & ~ 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(X2,line_connecting(X1,X0)) ),
    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(X2,line_connecting(X1,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).

fof(f467,plain,
    ( ~ distinct_points(sK0,sK1)
    | ~ spl3_18 ),
    inference(subsumption_resolution,[],[f464,f44]) ).

fof(f44,plain,
    ! [X0] : ~ distinct_points(X0,X0),
    inference(cnf_transformation,[],[f1]) ).

fof(f1,axiom,
    ! [X0] : ~ distinct_points(X0,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart1) ).

fof(f464,plain,
    ( distinct_points(sK0,sK0)
    | ~ distinct_points(sK0,sK1)
    | ~ spl3_18 ),
    inference(resolution,[],[f393,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/sandbox/benchmark/theBenchmark.p',con1) ).

fof(f393,plain,
    ( apart_point_and_line(sK0,line_connecting(sK0,sK1))
    | ~ spl3_18 ),
    inference(avatar_component_clause,[],[f391]) ).

fof(f391,plain,
    ( spl3_18
  <=> apart_point_and_line(sK0,line_connecting(sK0,sK1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_18])]) ).

fof(f421,plain,
    ~ spl3_17,
    inference(avatar_contradiction_clause,[],[f420]) ).

fof(f420,plain,
    ( $false
    | ~ spl3_17 ),
    inference(subsumption_resolution,[],[f419,f37]) ).

fof(f419,plain,
    ( ~ distinct_points(sK0,sK1)
    | ~ spl3_17 ),
    inference(subsumption_resolution,[],[f415,f44]) ).

fof(f415,plain,
    ( distinct_points(sK1,sK1)
    | ~ distinct_points(sK0,sK1)
    | ~ spl3_17 ),
    inference(resolution,[],[f389,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(f389,plain,
    ( apart_point_and_line(sK1,line_connecting(sK0,sK1))
    | ~ spl3_17 ),
    inference(avatar_component_clause,[],[f387]) ).

fof(f387,plain,
    ( spl3_17
  <=> apart_point_and_line(sK1,line_connecting(sK0,sK1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_17])]) ).

fof(f407,plain,
    ( spl3_17
    | spl3_18
    | ~ spl3_9 ),
    inference(avatar_split_clause,[],[f402,f270,f391,f387]) ).

fof(f270,plain,
    ( spl3_9
  <=> ! [X0] :
        ( apart_point_and_line(sK0,X0)
        | apart_point_and_line(sK2,X0)
        | apart_point_and_line(sK1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_9])]) ).

fof(f402,plain,
    ( apart_point_and_line(sK0,line_connecting(sK0,sK1))
    | apart_point_and_line(sK1,line_connecting(sK0,sK1))
    | ~ spl3_9 ),
    inference(resolution,[],[f271,f40]) ).

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

fof(f271,plain,
    ( ! [X0] :
        ( apart_point_and_line(sK2,X0)
        | apart_point_and_line(sK0,X0)
        | apart_point_and_line(sK1,X0) )
    | ~ spl3_9 ),
    inference(avatar_component_clause,[],[f270]) ).

fof(f401,plain,
    ( ~ spl3_1
    | ~ spl3_5 ),
    inference(avatar_contradiction_clause,[],[f400]) ).

fof(f400,plain,
    ( $false
    | ~ spl3_1
    | ~ spl3_5 ),
    inference(subsumption_resolution,[],[f399,f75]) ).

fof(f75,plain,
    ( distinct_points(sK1,sK0)
    | ~ spl3_1 ),
    inference(avatar_component_clause,[],[f74]) ).

fof(f74,plain,
    ( spl3_1
  <=> distinct_points(sK1,sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).

fof(f399,plain,
    ( ~ distinct_points(sK1,sK0)
    | ~ spl3_5 ),
    inference(subsumption_resolution,[],[f396,f44]) ).

fof(f396,plain,
    ( distinct_points(sK1,sK1)
    | ~ distinct_points(sK1,sK0)
    | ~ spl3_5 ),
    inference(resolution,[],[f256,f53]) ).

fof(f256,plain,
    ( apart_point_and_line(sK1,line_connecting(sK1,sK0))
    | ~ spl3_5 ),
    inference(avatar_component_clause,[],[f254]) ).

fof(f254,plain,
    ( spl3_5
  <=> apart_point_and_line(sK1,line_connecting(sK1,sK0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_5])]) ).

fof(f311,plain,
    ( ~ spl3_1
    | ~ spl3_8 ),
    inference(avatar_contradiction_clause,[],[f310]) ).

fof(f310,plain,
    ( $false
    | ~ spl3_1
    | ~ spl3_8 ),
    inference(subsumption_resolution,[],[f309,f75]) ).

fof(f309,plain,
    ( ~ distinct_points(sK1,sK0)
    | ~ spl3_8 ),
    inference(subsumption_resolution,[],[f305,f44]) ).

fof(f305,plain,
    ( distinct_points(sK0,sK0)
    | ~ distinct_points(sK1,sK0)
    | ~ spl3_8 ),
    inference(resolution,[],[f268,f54]) ).

fof(f268,plain,
    ( apart_point_and_line(sK0,line_connecting(sK1,sK0))
    | ~ spl3_8 ),
    inference(avatar_component_clause,[],[f266]) ).

fof(f266,plain,
    ( spl3_8
  <=> apart_point_and_line(sK0,line_connecting(sK1,sK0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_8])]) ).

fof(f304,plain,
    ( spl3_8
    | spl3_5
    | spl3_9
    | ~ spl3_1 ),
    inference(avatar_split_clause,[],[f224,f74,f270,f254,f266]) ).

fof(f224,plain,
    ( ! [X0] :
        ( apart_point_and_line(sK1,X0)
        | apart_point_and_line(sK1,line_connecting(sK1,sK0))
        | apart_point_and_line(sK0,X0)
        | apart_point_and_line(sK0,line_connecting(sK1,sK0))
        | apart_point_and_line(sK2,X0) )
    | ~ spl3_1 ),
    inference(resolution,[],[f97,f75]) ).

fof(f97,plain,
    ! [X2,X0,X1] :
      ( ~ distinct_points(X1,X0)
      | apart_point_and_line(X1,X2)
      | apart_point_and_line(X1,line_connecting(sK1,sK0))
      | apart_point_and_line(X0,X2)
      | apart_point_and_line(X0,line_connecting(sK1,sK0))
      | apart_point_and_line(sK2,X2) ),
    inference(resolution,[],[f55,f56]) ).

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

fof(f41,plain,
    apart_point_and_line(sK2,line_connecting(sK1,sK0)),
    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/sandbox/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/sandbox/benchmark/theBenchmark.p',cu1) ).

fof(f88,plain,
    spl3_1,
    inference(avatar_contradiction_clause,[],[f87]) ).

fof(f87,plain,
    ( $false
    | spl3_1 ),
    inference(subsumption_resolution,[],[f86,f44]) ).

fof(f86,plain,
    ( distinct_points(sK0,sK0)
    | spl3_1 ),
    inference(resolution,[],[f76,f60]) ).

fof(f60,plain,
    ! [X0] :
      ( distinct_points(sK1,X0)
      | distinct_points(sK0,X0) ),
    inference(resolution,[],[f52,f37]) ).

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/sandbox/benchmark/theBenchmark.p',apart4) ).

fof(f76,plain,
    ( ~ distinct_points(sK1,sK0)
    | spl3_1 ),
    inference(avatar_component_clause,[],[f74]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem    : GEO190+2 : TPTP v8.1.2. Released v3.3.0.
% 0.12/0.15  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36  % Computer : n019.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Tue Apr 30 05:45:59 EDT 2024
% 0.15/0.36  % CPUTime    : 
% 0.15/0.37  % (30646)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38  % (30651)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.15/0.38  % (30647)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.15/0.38  % (30652)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.15/0.38  % (30650)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.15/0.38  % (30649)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)
% 0.15/0.38  % (30648)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.15/0.38  % (30653)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)
% 0.15/0.39  TRYING [1]
% 0.15/0.39  TRYING [1]
% 0.15/0.39  Detected minimum model sizes of [1,1,1,1]
% 0.15/0.39  Detected maximum model sizes of [max,3,max,max]
% 0.15/0.39  Detected minimum model sizes of [1,1,1,1]
% 0.15/0.39  Detected maximum model sizes of [max,3,max,max]
% 0.15/0.39  TRYING [1,1,1,1]
% 0.15/0.39  TRYING [2]
% 0.15/0.39  TRYING [1,1,1,1]
% 0.15/0.39  TRYING [2]
% 0.15/0.39  TRYING [2,2,1,1]
% 0.15/0.39  TRYING [2,2,1,1]
% 0.15/0.39  TRYING [3]
% 0.15/0.39  TRYING [3]
% 0.15/0.39  TRYING [3,3,1,1]
% 0.15/0.39  TRYING [3,3,1,1]
% 0.15/0.39  TRYING [4]
% 0.15/0.39  TRYING [4,3,1,1]
% 0.15/0.39  TRYING [4,3,1,1]
% 0.15/0.39  TRYING [4]
% 0.15/0.39  TRYING [5,3,1,1]
% 0.15/0.39  TRYING [5,3,1,1]
% 0.15/0.39  TRYING [5]
% 0.15/0.39  TRYING [6,3,1,1]
% 0.15/0.39  TRYING [6,3,1,1]
% 0.15/0.39  TRYING [5]
% 0.15/0.39  TRYING [7,3,1,1]
% 0.15/0.39  TRYING [7,3,1,1]
% 0.15/0.39  % (30652)First to succeed.
% 0.15/0.40  % (30652)Refutation found. Thanks to Tanya!
% 0.15/0.40  % SZS status Theorem for theBenchmark
% 0.15/0.40  % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.40  % (30652)------------------------------
% 0.15/0.40  % (30652)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.15/0.40  % (30652)Termination reason: Refutation
% 0.15/0.40  
% 0.15/0.40  % (30652)Memory used [KB]: 924
% 0.15/0.40  % (30652)Time elapsed: 0.013 s
% 0.15/0.40  % (30652)Instructions burned: 20 (million)
% 0.15/0.40  % (30652)------------------------------
% 0.15/0.40  % (30652)------------------------------
% 0.15/0.40  % (30646)Success in time 0.029 s
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