TSTP Solution File: GEO221+2 by Vampire-SAT---4.8

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%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : GEO221+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 : n005.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 05:16:13 EDT 2024

% Result   : Theorem 0.13s 0.37s
% Output   : Refutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   32 (  11 unt;   0 def)
%            Number of atoms       :   76 (   0 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :   74 (  30   ~;  32   |;   4   &)
%                                         (   2 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    6 (   5 usr;   3 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :   53 (  47   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f159,plain,
    $false,
    inference(avatar_sat_refutation,[],[f120,f151,f158]) ).

fof(f158,plain,
    ~ spl3_4,
    inference(avatar_contradiction_clause,[],[f157]) ).

fof(f157,plain,
    ( $false
    | ~ spl3_4 ),
    inference(subsumption_resolution,[],[f153,f61]) ).

fof(f61,plain,
    ! [X0,X1] : ~ unorthogonal_lines(orthogonal_through_point(X1,X0),X1),
    inference(cnf_transformation,[],[f24]) ).

fof(f24,plain,
    ! [X0,X1] : ~ unorthogonal_lines(orthogonal_through_point(X1,X0),X1),
    inference(rectify,[],[f18]) ).

fof(f18,axiom,
    ! [X8,X5] : ~ unorthogonal_lines(orthogonal_through_point(X5,X8),X5),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ooc1) ).

fof(f153,plain,
    ( unorthogonal_lines(orthogonal_through_point(sK2,sK0),sK2)
    | ~ spl3_4 ),
    inference(resolution,[],[f150,f61]) ).

fof(f150,plain,
    ( ! [X0] :
        ( unorthogonal_lines(orthogonal_through_point(sK2,sK1),X0)
        | unorthogonal_lines(orthogonal_through_point(sK2,sK0),X0) )
    | ~ spl3_4 ),
    inference(avatar_component_clause,[],[f149]) ).

fof(f149,plain,
    ( spl3_4
  <=> ! [X0] :
        ( unorthogonal_lines(orthogonal_through_point(sK2,sK0),X0)
        | unorthogonal_lines(orthogonal_through_point(sK2,sK1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_4])]) ).

fof(f151,plain,
    ( spl3_2
    | spl3_4 ),
    inference(avatar_split_clause,[],[f143,f149,f111]) ).

fof(f111,plain,
    ( spl3_2
  <=> ! [X0] :
        ( apart_point_and_line(X0,orthogonal_through_point(sK2,sK1))
        | apart_point_and_line(X0,orthogonal_through_point(sK2,sK0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_2])]) ).

fof(f143,plain,
    ! [X0,X1] :
      ( unorthogonal_lines(orthogonal_through_point(sK2,sK0),X0)
      | apart_point_and_line(X1,orthogonal_through_point(sK2,sK1))
      | apart_point_and_line(X1,orthogonal_through_point(sK2,sK0))
      | unorthogonal_lines(orthogonal_through_point(sK2,sK1),X0) ),
    inference(resolution,[],[f81,f57]) ).

fof(f57,plain,
    distinct_lines(orthogonal_through_point(sK2,sK0),orthogonal_through_point(sK2,sK1)),
    inference(cnf_transformation,[],[f55]) ).

fof(f55,plain,
    ( distinct_lines(orthogonal_through_point(sK2,sK0),orthogonal_through_point(sK2,sK1))
    & ~ apart_point_and_line(sK1,orthogonal_through_point(sK2,sK0)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f30,f54]) ).

fof(f54,plain,
    ( ? [X0,X1,X2] :
        ( distinct_lines(orthogonal_through_point(X2,X0),orthogonal_through_point(X2,X1))
        & ~ apart_point_and_line(X1,orthogonal_through_point(X2,X0)) )
   => ( distinct_lines(orthogonal_through_point(sK2,sK0),orthogonal_through_point(sK2,sK1))
      & ~ apart_point_and_line(sK1,orthogonal_through_point(sK2,sK0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f30,plain,
    ? [X0,X1,X2] :
      ( distinct_lines(orthogonal_through_point(X2,X0),orthogonal_through_point(X2,X1))
      & ~ apart_point_and_line(X1,orthogonal_through_point(X2,X0)) ),
    inference(ennf_transformation,[],[f23]) ).

fof(f23,plain,
    ~ ! [X0,X1,X2] :
        ( ~ apart_point_and_line(X1,orthogonal_through_point(X2,X0))
       => ~ distinct_lines(orthogonal_through_point(X2,X0),orthogonal_through_point(X2,X1)) ),
    inference(rectify,[],[f22]) ).

fof(f22,negated_conjecture,
    ~ ! [X8,X9,X5] :
        ( ~ apart_point_and_line(X9,orthogonal_through_point(X5,X8))
       => ~ distinct_lines(orthogonal_through_point(X5,X8),orthogonal_through_point(X5,X9)) ),
    inference(negated_conjecture,[],[f21]) ).

fof(f21,conjecture,
    ! [X8,X9,X5] :
      ( ~ apart_point_and_line(X9,orthogonal_through_point(X5,X8))
     => ~ distinct_lines(orthogonal_through_point(X5,X8),orthogonal_through_point(X5,X9)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).

fof(f81,plain,
    ! [X2,X3,X0,X1] :
      ( ~ distinct_lines(X1,X2)
      | unorthogonal_lines(X1,X3)
      | apart_point_and_line(X0,X2)
      | apart_point_and_line(X0,X1)
      | unorthogonal_lines(X2,X3) ),
    inference(cnf_transformation,[],[f51]) ).

fof(f51,plain,
    ! [X0,X1,X2,X3] :
      ( unorthogonal_lines(X2,X3)
      | unorthogonal_lines(X1,X3)
      | apart_point_and_line(X0,X2)
      | apart_point_and_line(X0,X1)
      | ~ distinct_lines(X1,X2) ),
    inference(flattening,[],[f50]) ).

fof(f50,plain,
    ! [X0,X1,X2,X3] :
      ( unorthogonal_lines(X2,X3)
      | unorthogonal_lines(X1,X3)
      | apart_point_and_line(X0,X2)
      | apart_point_and_line(X0,X1)
      | ~ distinct_lines(X1,X2) ),
    inference(ennf_transformation,[],[f28]) ).

fof(f28,plain,
    ! [X0,X1,X2,X3] :
      ( distinct_lines(X1,X2)
     => ( unorthogonal_lines(X2,X3)
        | unorthogonal_lines(X1,X3)
        | apart_point_and_line(X0,X2)
        | apart_point_and_line(X0,X1) ) ),
    inference(rectify,[],[f20]) ).

fof(f20,axiom,
    ! [X8,X5,X6,X7] :
      ( distinct_lines(X5,X6)
     => ( unorthogonal_lines(X6,X7)
        | unorthogonal_lines(X5,X7)
        | apart_point_and_line(X8,X6)
        | apart_point_and_line(X8,X5) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ouo1) ).

fof(f120,plain,
    ~ spl3_2,
    inference(avatar_contradiction_clause,[],[f119]) ).

fof(f119,plain,
    ( $false
    | ~ spl3_2 ),
    inference(subsumption_resolution,[],[f114,f56]) ).

fof(f56,plain,
    ~ apart_point_and_line(sK1,orthogonal_through_point(sK2,sK0)),
    inference(cnf_transformation,[],[f55]) ).

fof(f114,plain,
    ( apart_point_and_line(sK1,orthogonal_through_point(sK2,sK0))
    | ~ spl3_2 ),
    inference(resolution,[],[f112,f64]) ).

fof(f64,plain,
    ! [X0,X1] : ~ apart_point_and_line(X0,orthogonal_through_point(X1,X0)),
    inference(cnf_transformation,[],[f25]) ).

fof(f25,plain,
    ! [X0,X1] : ~ apart_point_and_line(X0,orthogonal_through_point(X1,X0)),
    inference(rectify,[],[f19]) ).

fof(f19,axiom,
    ! [X8,X5] : ~ apart_point_and_line(X8,orthogonal_through_point(X5,X8)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ooc2) ).

fof(f112,plain,
    ( ! [X0] :
        ( apart_point_and_line(X0,orthogonal_through_point(sK2,sK1))
        | apart_point_and_line(X0,orthogonal_through_point(sK2,sK0)) )
    | ~ spl3_2 ),
    inference(avatar_component_clause,[],[f111]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : GEO221+2 : TPTP v8.1.2. Released v3.3.0.
% 0.11/0.13  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.35  % Computer : n005.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Fri May  3 22:04:38 EDT 2024
% 0.13/0.35  % CPUTime    : 
% 0.13/0.35  % (811)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.37  % (816)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.13/0.37  % (814)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)
% 0.13/0.37  % (813)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.13/0.37  % (818)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)
% 0.13/0.37  % (817)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.13/0.37  % (812)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.13/0.37  TRYING [1,1]
% 0.13/0.37  TRYING [1]
% 0.13/0.37  TRYING [2,1]
% 0.13/0.37  TRYING [2]
% 0.13/0.37  TRYING [3,1]
% 0.13/0.37  TRYING [3]
% 0.13/0.37  TRYING [1]
% 0.13/0.37  TRYING [2,2]
% 0.13/0.37  % (815)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.13/0.37  TRYING [2]
% 0.13/0.37  % (817)First to succeed.
% 0.13/0.37  TRYING [3,2]
% 0.13/0.37  % (817)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-811"
% 0.13/0.37  TRYING [3]
% 0.13/0.37  TRYING [1,1]
% 0.13/0.37  TRYING [4]
% 0.13/0.37  TRYING [2,1]
% 0.13/0.37  % (817)Refutation found. Thanks to Tanya!
% 0.13/0.37  % SZS status Theorem for theBenchmark
% 0.13/0.37  % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.37  % (817)------------------------------
% 0.13/0.37  % (817)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.13/0.37  % (817)Termination reason: Refutation
% 0.13/0.37  
% 0.13/0.37  % (817)Memory used [KB]: 898
% 0.13/0.37  % (817)Time elapsed: 0.005 s
% 0.13/0.37  % (817)Instructions burned: 7 (million)
% 0.13/0.37  % (811)Success in time 0.009 s
%------------------------------------------------------------------------------