TSTP Solution File: GEO183+3 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : GEO183+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n025.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 05:15:55 EDT 2024

% Result   : Theorem 0.21s 0.38s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   59 (  16 unt;   0 def)
%            Number of atoms       :  140 (   0 equ)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives :  133 (  52   ~;  43   |;  24   &)
%                                         (   4 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    9 (   8 usr;   3 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :  104 (  92   !;  12   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f315,plain,
    $false,
    inference(avatar_sat_refutation,[],[f150,f305,f314]) ).

fof(f314,plain,
    spl5_2,
    inference(avatar_contradiction_clause,[],[f311]) ).

fof(f311,plain,
    ( $false
    | spl5_2 ),
    inference(resolution,[],[f310,f287]) ).

fof(f287,plain,
    ! [X0] : ~ apart_point_and_line(X0,sK2),
    inference(resolution,[],[f171,f205]) ).

fof(f205,plain,
    ! [X0] : ~ distinct_lines(sK2,parallel_through_point(line_connecting(sK0,sK1),X0)),
    inference(resolution,[],[f188,f110]) ).

fof(f110,plain,
    ! [X0,X1] :
      ( convergent_lines(X0,X1)
      | ~ distinct_lines(X0,X1) ),
    inference(cnf_transformation,[],[f56]) ).

fof(f56,plain,
    ! [X0,X1] :
      ( convergent_lines(X0,X1)
      | ~ distinct_lines(X0,X1) ),
    inference(ennf_transformation,[],[f15]) ).

fof(f15,axiom,
    ! [X0,X1] :
      ( distinct_lines(X0,X1)
     => convergent_lines(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).

fof(f188,plain,
    ! [X0] : ~ convergent_lines(sK2,parallel_through_point(line_connecting(sK0,sK1),X0)),
    inference(resolution,[],[f181,f162]) ).

fof(f162,plain,
    ! [X0] : ~ distinct_lines(parallel_through_point(line_connecting(sK0,sK1),X0),sK2),
    inference(resolution,[],[f158,f153]) ).

fof(f153,plain,
    ! [X0,X1] : ~ distinct_lines(parallel_through_point(X0,X1),X0),
    inference(resolution,[],[f110,f108]) ).

fof(f108,plain,
    ! [X0,X1] : ~ convergent_lines(parallel_through_point(X1,X0),X1),
    inference(cnf_transformation,[],[f16]) ).

fof(f16,axiom,
    ! [X0,X1] : ~ convergent_lines(parallel_through_point(X1,X0),X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cp1) ).

fof(f158,plain,
    ! [X0] :
      ( distinct_lines(X0,line_connecting(sK0,sK1))
      | ~ distinct_lines(X0,sK2) ),
    inference(resolution,[],[f122,f155]) ).

fof(f155,plain,
    ~ distinct_lines(sK2,line_connecting(sK0,sK1)),
    inference(resolution,[],[f120,f100]) ).

fof(f100,plain,
    equal_lines(sK2,line_connecting(sK0,sK1)),
    inference(cnf_transformation,[],[f97]) ).

fof(f97,plain,
    ( ( ~ incident_point_and_line(sK1,sK2)
      | ~ incident_point_and_line(sK0,sK2) )
    & equal_lines(sK2,line_connecting(sK0,sK1))
    & convergent_lines(sK2,sK3)
    & distinct_points(sK0,sK1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f55,f96]) ).

fof(f96,plain,
    ( ? [X0,X1,X2,X3] :
        ( ( ~ incident_point_and_line(X1,X2)
          | ~ incident_point_and_line(X0,X2) )
        & equal_lines(X2,line_connecting(X0,X1))
        & convergent_lines(X2,X3)
        & distinct_points(X0,X1) )
   => ( ( ~ incident_point_and_line(sK1,sK2)
        | ~ incident_point_and_line(sK0,sK2) )
      & equal_lines(sK2,line_connecting(sK0,sK1))
      & convergent_lines(sK2,sK3)
      & distinct_points(sK0,sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f55,plain,
    ? [X0,X1,X2,X3] :
      ( ( ~ incident_point_and_line(X1,X2)
        | ~ incident_point_and_line(X0,X2) )
      & equal_lines(X2,line_connecting(X0,X1))
      & convergent_lines(X2,X3)
      & distinct_points(X0,X1) ),
    inference(flattening,[],[f54]) ).

fof(f54,plain,
    ? [X0,X1,X2,X3] :
      ( ( ~ incident_point_and_line(X1,X2)
        | ~ incident_point_and_line(X0,X2) )
      & equal_lines(X2,line_connecting(X0,X1))
      & convergent_lines(X2,X3)
      & distinct_points(X0,X1) ),
    inference(ennf_transformation,[],[f38]) ).

fof(f38,plain,
    ~ ! [X0,X1,X2,X3] :
        ( ( equal_lines(X2,line_connecting(X0,X1))
          & convergent_lines(X2,X3)
          & distinct_points(X0,X1) )
       => ( incident_point_and_line(X1,X2)
          & incident_point_and_line(X0,X2) ) ),
    inference(rectify,[],[f37]) ).

fof(f37,negated_conjecture,
    ~ ! [X0,X1,X3,X4] :
        ( ( equal_lines(X3,line_connecting(X0,X1))
          & convergent_lines(X3,X4)
          & distinct_points(X0,X1) )
       => ( incident_point_and_line(X1,X3)
          & incident_point_and_line(X0,X3) ) ),
    inference(negated_conjecture,[],[f36]) ).

fof(f36,conjecture,
    ! [X0,X1,X3,X4] :
      ( ( equal_lines(X3,line_connecting(X0,X1))
        & convergent_lines(X3,X4)
        & distinct_points(X0,X1) )
     => ( incident_point_and_line(X1,X3)
        & incident_point_and_line(X0,X3) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).

fof(f120,plain,
    ! [X0,X1] :
      ( ~ equal_lines(X0,X1)
      | ~ distinct_lines(X0,X1) ),
    inference(cnf_transformation,[],[f70]) ).

fof(f70,plain,
    ! [X0,X1] :
      ( ~ distinct_lines(X0,X1)
      | ~ equal_lines(X0,X1) ),
    inference(ennf_transformation,[],[f53]) ).

fof(f53,plain,
    ! [X0,X1] :
      ( equal_lines(X0,X1)
     => ~ distinct_lines(X0,X1) ),
    inference(unused_predicate_definition_removal,[],[f32]) ).

fof(f32,axiom,
    ! [X0,X1] :
      ( equal_lines(X0,X1)
    <=> ~ distinct_lines(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).

fof(f122,plain,
    ! [X2,X0,X1] :
      ( distinct_lines(X1,X2)
      | distinct_lines(X0,X2)
      | ~ distinct_lines(X0,X1) ),
    inference(cnf_transformation,[],[f73]) ).

fof(f73,plain,
    ! [X0,X1,X2] :
      ( distinct_lines(X1,X2)
      | distinct_lines(X0,X2)
      | ~ distinct_lines(X0,X1) ),
    inference(flattening,[],[f72]) ).

fof(f72,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(f181,plain,
    ! [X0,X1] :
      ( distinct_lines(X0,X1)
      | ~ convergent_lines(X1,X0) ),
    inference(resolution,[],[f127,f104]) ).

fof(f104,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(f127,plain,
    ! [X2,X0,X1] :
      ( convergent_lines(X0,X2)
      | distinct_lines(X1,X2)
      | ~ convergent_lines(X0,X1) ),
    inference(cnf_transformation,[],[f83]) ).

fof(f83,plain,
    ! [X0,X1,X2] :
      ( convergent_lines(X0,X2)
      | distinct_lines(X1,X2)
      | ~ convergent_lines(X0,X1) ),
    inference(flattening,[],[f82]) ).

fof(f82,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(f171,plain,
    ! [X2,X0,X1] :
      ( distinct_lines(X0,parallel_through_point(X1,X2))
      | ~ apart_point_and_line(X2,X0) ),
    inference(resolution,[],[f126,f106]) ).

fof(f106,plain,
    ! [X0,X1] : ~ apart_point_and_line(X0,parallel_through_point(X1,X0)),
    inference(cnf_transformation,[],[f17]) ).

fof(f17,axiom,
    ! [X0,X1] : ~ apart_point_and_line(X0,parallel_through_point(X1,X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cp2) ).

fof(f126,plain,
    ! [X2,X0,X1] :
      ( apart_point_and_line(X0,X2)
      | distinct_lines(X1,X2)
      | ~ apart_point_and_line(X0,X1) ),
    inference(cnf_transformation,[],[f81]) ).

fof(f81,plain,
    ! [X0,X1,X2] :
      ( apart_point_and_line(X0,X2)
      | distinct_lines(X1,X2)
      | ~ apart_point_and_line(X0,X1) ),
    inference(flattening,[],[f80]) ).

fof(f80,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(f310,plain,
    ( apart_point_and_line(sK1,sK2)
    | spl5_2 ),
    inference(resolution,[],[f149,f119]) ).

fof(f119,plain,
    ! [X0,X1] :
      ( incident_point_and_line(X0,X1)
      | apart_point_and_line(X0,X1) ),
    inference(cnf_transformation,[],[f69]) ).

fof(f69,plain,
    ! [X0,X1] :
      ( incident_point_and_line(X0,X1)
      | apart_point_and_line(X0,X1) ),
    inference(ennf_transformation,[],[f52]) ).

fof(f52,plain,
    ! [X0,X1] :
      ( ~ apart_point_and_line(X0,X1)
     => incident_point_and_line(X0,X1) ),
    inference(unused_predicate_definition_removal,[],[f34]) ).

fof(f34,axiom,
    ! [X0,X1] :
      ( incident_point_and_line(X0,X1)
    <=> ~ apart_point_and_line(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a4) ).

fof(f149,plain,
    ( ~ incident_point_and_line(sK1,sK2)
    | spl5_2 ),
    inference(avatar_component_clause,[],[f147]) ).

fof(f147,plain,
    ( spl5_2
  <=> incident_point_and_line(sK1,sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_2])]) ).

fof(f305,plain,
    spl5_1,
    inference(avatar_contradiction_clause,[],[f300]) ).

fof(f300,plain,
    ( $false
    | spl5_1 ),
    inference(resolution,[],[f287,f154]) ).

fof(f154,plain,
    ( apart_point_and_line(sK0,sK2)
    | spl5_1 ),
    inference(resolution,[],[f119,f145]) ).

fof(f145,plain,
    ( ~ incident_point_and_line(sK0,sK2)
    | spl5_1 ),
    inference(avatar_component_clause,[],[f143]) ).

fof(f143,plain,
    ( spl5_1
  <=> incident_point_and_line(sK0,sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_1])]) ).

fof(f150,plain,
    ( ~ spl5_1
    | ~ spl5_2 ),
    inference(avatar_split_clause,[],[f101,f147,f143]) ).

fof(f101,plain,
    ( ~ incident_point_and_line(sK1,sK2)
    | ~ incident_point_and_line(sK0,sK2) ),
    inference(cnf_transformation,[],[f97]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : GEO183+3 : TPTP v8.1.2. Released v4.0.0.
% 0.15/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35  % Computer : n025.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit   : 300
% 0.15/0.35  % WCLimit    : 300
% 0.15/0.35  % DateTime   : Fri May  3 22:04:53 EDT 2024
% 0.15/0.35  % CPUTime    : 
% 0.15/0.35  % (27037)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.37  % (27043)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.21/0.37  % (27038)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.21/0.37  % (27040)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)
% 0.21/0.37  % (27041)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.21/0.37  % (27044)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)
% 0.21/0.37  % (27042)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.21/0.37  % (27039)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.21/0.37  TRYING [1]
% 0.21/0.37  TRYING [2]
% 0.21/0.37  TRYING [1]
% 0.21/0.37  TRYING [2]
% 0.21/0.37  TRYING [3]
% 0.21/0.37  TRYING [1,1]
% 0.21/0.37  TRYING [1,1]
% 0.21/0.37  TRYING [2,2]
% 0.21/0.37  TRYING [2,2]
% 0.21/0.37  TRYING [3]
% 0.21/0.38  TRYING [3,2]
% 0.21/0.38  TRYING [3,2]
% 0.21/0.38  TRYING [4]
% 0.21/0.38  % (27040)First to succeed.
% 0.21/0.38  TRYING [4,2]
% 0.21/0.38  TRYING [4,2]
% 0.21/0.38  TRYING [4]
% 0.21/0.38  % (27040)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-27037"
% 0.21/0.38  % (27040)Refutation found. Thanks to Tanya!
% 0.21/0.38  % SZS status Theorem for theBenchmark
% 0.21/0.38  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.38  % (27040)------------------------------
% 0.21/0.38  % (27040)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.38  % (27040)Termination reason: Refutation
% 0.21/0.38  
% 0.21/0.38  % (27040)Memory used [KB]: 994
% 0.21/0.38  % (27040)Time elapsed: 0.009 s
% 0.21/0.38  % (27040)Instructions burned: 10 (million)
% 0.21/0.38  % (27037)Success in time 0.026 s
%------------------------------------------------------------------------------