TSTP Solution File: GEO221+1 by Vampire-SAT---4.8

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%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : GEO221+1 : 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 : n022.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 11:14:50 EDT 2024

% Result   : Theorem 0.15s 0.39s
% Output   : Refutation 0.15s
% 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(f162,plain,
    $false,
    inference(avatar_sat_refutation,[],[f125,f144,f161]) ).

fof(f161,plain,
    ~ spl3_3,
    inference(avatar_contradiction_clause,[],[f160]) ).

fof(f160,plain,
    ( $false
    | ~ spl3_3 ),
    inference(subsumption_resolution,[],[f156,f64]) ).

fof(f64,plain,
    ! [X0,X1] : ~ unorthogonal_lines(orthogonal_through_point(X1,X0),X1),
    inference(cnf_transformation,[],[f26]) ).

fof(f26,plain,
    ! [X0,X1] : ~ unorthogonal_lines(orthogonal_through_point(X1,X0),X1),
    inference(rectify,[],[f20]) ).

fof(f20,axiom,
    ! [X8,X5] : ~ unorthogonal_lines(orthogonal_through_point(X5,X8),X5),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ooc1) ).

fof(f156,plain,
    ( unorthogonal_lines(orthogonal_through_point(sK2,sK0),sK2)
    | ~ spl3_3 ),
    inference(resolution,[],[f143,f64]) ).

fof(f143,plain,
    ( ! [X0] :
        ( unorthogonal_lines(orthogonal_through_point(sK2,sK1),X0)
        | unorthogonal_lines(orthogonal_through_point(sK2,sK0),X0) )
    | ~ spl3_3 ),
    inference(avatar_component_clause,[],[f142]) ).

fof(f142,plain,
    ( spl3_3
  <=> ! [X0] :
        ( unorthogonal_lines(orthogonal_through_point(sK2,sK0),X0)
        | unorthogonal_lines(orthogonal_through_point(sK2,sK1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_3])]) ).

fof(f144,plain,
    ( spl3_2
    | spl3_3 ),
    inference(avatar_split_clause,[],[f136,f142,f106]) ).

fof(f106,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(f136,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,[],[f84,f60]) ).

fof(f60,plain,
    distinct_lines(orthogonal_through_point(sK2,sK0),orthogonal_through_point(sK2,sK1)),
    inference(cnf_transformation,[],[f58]) ).

fof(f58,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])],[f32,f57]) ).

fof(f57,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(f32,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,[],[f25]) ).

fof(f25,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,[],[f24]) ).

fof(f24,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,[],[f23]) ).

fof(f23,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(f84,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,[],[f54]) ).

fof(f54,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,[],[f53]) ).

fof(f53,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,[],[f30]) ).

fof(f30,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,[],[f22]) ).

fof(f22,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(f125,plain,
    ~ spl3_2,
    inference(avatar_contradiction_clause,[],[f124]) ).

fof(f124,plain,
    ( $false
    | ~ spl3_2 ),
    inference(subsumption_resolution,[],[f119,f59]) ).

fof(f59,plain,
    ~ apart_point_and_line(sK1,orthogonal_through_point(sK2,sK0)),
    inference(cnf_transformation,[],[f58]) ).

fof(f119,plain,
    ( apart_point_and_line(sK1,orthogonal_through_point(sK2,sK0))
    | ~ spl3_2 ),
    inference(resolution,[],[f107,f67]) ).

fof(f67,plain,
    ! [X0,X1] : ~ apart_point_and_line(X0,orthogonal_through_point(X1,X0)),
    inference(cnf_transformation,[],[f27]) ).

fof(f27,plain,
    ! [X0,X1] : ~ apart_point_and_line(X0,orthogonal_through_point(X1,X0)),
    inference(rectify,[],[f21]) ).

fof(f21,axiom,
    ! [X8,X5] : ~ apart_point_and_line(X8,orthogonal_through_point(X5,X8)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ooc2) ).

fof(f107,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,[],[f106]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : GEO221+1 : TPTP v8.1.2. Released v3.3.0.
% 0.14/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36  % Computer : n022.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 05:34:43 EDT 2024
% 0.15/0.36  % CPUTime    : 
% 0.15/0.36  % (9015)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38  % (9017)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.15/0.38  TRYING [1,1]
% 0.15/0.38  TRYING [2,1]
% 0.15/0.38  TRYING [3,1]
% 0.15/0.38  TRYING [2,2]
% 0.15/0.38  TRYING [3,2]
% 0.15/0.38  TRYING [4,1]
% 0.15/0.38  % (9016)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.15/0.38  % (9018)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  % (9020)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.15/0.38  % (9019)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  % (9021)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.15/0.38  % (9022)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)
% 0.15/0.38  TRYING [4,2]
% 0.15/0.38  TRYING [1]
% 0.15/0.38  TRYING [2]
% 0.15/0.38  TRYING [1]
% 0.15/0.38  TRYING [2]
% 0.15/0.38  TRYING [1,1]
% 0.15/0.38  TRYING [3]
% 0.15/0.38  TRYING [2,1]
% 0.15/0.38  TRYING [5,1]
% 0.15/0.38  TRYING [3]
% 0.15/0.38  TRYING [3,1]
% 0.15/0.38  % (9021)First to succeed.
% 0.15/0.38  TRYING [2,2]
% 0.15/0.38  TRYING [4]
% 0.15/0.38  TRYING [5,2]
% 0.15/0.38  TRYING [3,2]
% 0.15/0.39  % (9021)Refutation found. Thanks to Tanya!
% 0.15/0.39  % SZS status Theorem for theBenchmark
% 0.15/0.39  % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.39  % (9021)------------------------------
% 0.15/0.39  % (9021)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.15/0.39  % (9021)Termination reason: Refutation
% 0.15/0.39  
% 0.15/0.39  % (9021)Memory used [KB]: 899
% 0.15/0.39  % (9021)Time elapsed: 0.006 s
% 0.15/0.39  % (9021)Instructions burned: 7 (million)
% 0.15/0.39  % (9021)------------------------------
% 0.15/0.39  % (9021)------------------------------
% 0.15/0.39  % (9015)Success in time 0.022 s
%------------------------------------------------------------------------------