%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : GEO219+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -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 : Wed Aug 31 16:09:19 EDT 2022

% Result   : Theorem 0.19s 0.55s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   36 (   8 unt;   0 def)
%            Number of atoms       :  103 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  126 (  59   ~;  33   |;  25   &)
%                                         (   1 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   2 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   3 con; 0-0 aty)
%            Number of variables   :   65 (  53   !;  12   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f102,plain,
    $false,
    inference(avatar_sat_refutation,[],[f100,f101]) ).

fof(f101,plain,
    ~ spl3_2,
    inference(avatar_split_clause,[],[f75,f57]) ).

fof(f57,plain,
    ( spl3_2
  <=> convergent_lines(sK0,sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_2])]) ).

fof(f75,plain,
    ~ convergent_lines(sK0,sK2),
    inference(unit_resulting_resolution,[],[f40,f39,f41,f45]) ).

fof(f45,plain,
    ! [X2,X0,X1] :
      ( unorthogonal_lines(X1,X0)
      | ~ convergent_lines(X0,X2)
      | ~ unorthogonal_lines(X0,X2)
      | convergent_lines(X1,X2) ),
    inference(cnf_transformation,[],[f36]) ).

fof(f36,plain,
    ! [X0,X1,X2] :
      ( ( convergent_lines(X1,X2)
        & unorthogonal_lines(X1,X2) )
      | ( convergent_lines(X1,X0)
        & unorthogonal_lines(X1,X0) )
      | ~ unorthogonal_lines(X0,X2)
      | ~ convergent_lines(X0,X2) ),
    inference(rectify,[],[f31]) ).

fof(f31,plain,
    ! [X1,X2,X0] :
      ( ( convergent_lines(X2,X0)
        & unorthogonal_lines(X2,X0) )
      | ( convergent_lines(X2,X1)
        & unorthogonal_lines(X2,X1) )
      | ~ unorthogonal_lines(X1,X0)
      | ~ convergent_lines(X1,X0) ),
    inference(flattening,[],[f30]) ).

fof(f30,plain,
    ! [X1,X2,X0] :
      ( ~ unorthogonal_lines(X1,X0)
      | ~ convergent_lines(X1,X0)
      | ( convergent_lines(X2,X1)
        & unorthogonal_lines(X2,X1) )
      | ( convergent_lines(X2,X0)
        & unorthogonal_lines(X2,X0) ) ),
    inference(ennf_transformation,[],[f20]) ).

fof(f20,plain,
    ! [X1,X2,X0] :
      ( ( ( ~ unorthogonal_lines(X2,X1)
          | ~ convergent_lines(X2,X1) )
        & ( ~ unorthogonal_lines(X2,X0)
          | ~ convergent_lines(X2,X0) ) )
     => ( ~ unorthogonal_lines(X1,X0)
        | ~ convergent_lines(X1,X0) ) ),
    inference(rectify,[],[f14]) ).

fof(f14,axiom,
    ! [X7,X6,X5] :
      ( ( ( ~ convergent_lines(X5,X7)
          | ~ unorthogonal_lines(X5,X7) )
        & ( ~ convergent_lines(X5,X6)
          | ~ unorthogonal_lines(X5,X6) ) )
     => ( ~ convergent_lines(X6,X7)
        | ~ unorthogonal_lines(X6,X7) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cotno1) ).

fof(f41,plain,
    ~ convergent_lines(sK1,sK2),
    inference(cnf_transformation,[],[f35]) ).

fof(f35,plain,
    ( ~ convergent_lines(sK1,sK2)
    & ~ unorthogonal_lines(sK1,sK0)
    & unorthogonal_lines(sK0,sK2) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f33,f34]) ).

fof(f34,plain,
    ( ? [X0,X1,X2] :
        ( ~ convergent_lines(X1,X2)
        & ~ unorthogonal_lines(X1,X0)
        & unorthogonal_lines(X0,X2) )
   => ( ~ convergent_lines(sK1,sK2)
      & ~ unorthogonal_lines(sK1,sK0)
      & unorthogonal_lines(sK0,sK2) ) ),
    introduced(choice_axiom,[]) ).

fof(f33,plain,
    ? [X0,X1,X2] :
      ( ~ convergent_lines(X1,X2)
      & ~ unorthogonal_lines(X1,X0)
      & unorthogonal_lines(X0,X2) ),
    inference(rectify,[],[f28]) ).

fof(f28,plain,
    ? [X2,X0,X1] :
      ( ~ convergent_lines(X0,X1)
      & ~ unorthogonal_lines(X0,X2)
      & unorthogonal_lines(X2,X1) ),
    inference(flattening,[],[f27]) ).

fof(f27,plain,
    ? [X1,X2,X0] :
      ( unorthogonal_lines(X2,X1)
      & ~ unorthogonal_lines(X0,X2)
      & ~ convergent_lines(X0,X1) ),
    inference(ennf_transformation,[],[f18]) ).

fof(f18,plain,
    ~ ! [X1,X2,X0] :
        ( ( ~ unorthogonal_lines(X0,X2)
          & ~ convergent_lines(X0,X1) )
       => ~ unorthogonal_lines(X2,X1) ),
    inference(rectify,[],[f17]) ).

fof(f17,negated_conjecture,
    ~ ! [X5,X7,X6] :
        ( ( ~ unorthogonal_lines(X5,X6)
          & ~ convergent_lines(X5,X7) )
       => ~ unorthogonal_lines(X6,X7) ),
    inference(negated_conjecture,[],[f16]) ).

fof(f16,conjecture,
    ! [X5,X7,X6] :
      ( ( ~ unorthogonal_lines(X5,X6)
        & ~ convergent_lines(X5,X7) )
     => ~ unorthogonal_lines(X6,X7) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).

fof(f39,plain,
    unorthogonal_lines(sK0,sK2),
    inference(cnf_transformation,[],[f35]) ).

fof(f40,plain,
    ~ unorthogonal_lines(sK1,sK0),
    inference(cnf_transformation,[],[f35]) ).

fof(f100,plain,
    spl3_2,
    inference(avatar_contradiction_clause,[],[f99]) ).

fof(f99,plain,
    ( $false
    | spl3_2 ),
    inference(subsumption_resolution,[],[f88,f61]) ).

fof(f61,plain,
    convergent_lines(sK1,sK0),
    inference(unit_resulting_resolution,[],[f40,f47]) ).

fof(f47,plain,
    ! [X0,X1] :
      ( unorthogonal_lines(X1,X0)
      | convergent_lines(X1,X0) ),
    inference(cnf_transformation,[],[f29]) ).

fof(f29,plain,
    ! [X0,X1] :
      ( unorthogonal_lines(X1,X0)
      | convergent_lines(X1,X0) ),
    inference(ennf_transformation,[],[f19]) ).

fof(f19,plain,
    ! [X0,X1] :
      ~ ( ~ unorthogonal_lines(X1,X0)
        & ~ convergent_lines(X1,X0) ),
    inference(rectify,[],[f13]) ).

fof(f13,axiom,
    ! [X6,X5] :
      ~ ( ~ unorthogonal_lines(X5,X6)
        & ~ convergent_lines(X5,X6) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',coipo1) ).

fof(f88,plain,
    ( ~ convergent_lines(sK1,sK0)
    | spl3_2 ),
    inference(unit_resulting_resolution,[],[f41,f59,f38]) ).

fof(f38,plain,
    ! [X2,X0,X1] :
      ( convergent_lines(X2,X1)
      | ~ convergent_lines(X0,X2)
      | convergent_lines(X0,X1) ),
    inference(cnf_transformation,[],[f32]) ).

fof(f32,plain,
    ! [X0,X1,X2] :
      ( ~ convergent_lines(X0,X2)
      | convergent_lines(X2,X1)
      | convergent_lines(X0,X1) ),
    inference(rectify,[],[f24]) ).

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

fof(f23,plain,
    ! [X2,X1,X0] :
      ( convergent_lines(X2,X0)
      | convergent_lines(X1,X0)
      | ~ convergent_lines(X1,X2) ),
    inference(ennf_transformation,[],[f22]) ).

fof(f22,plain,
    ! [X2,X1,X0] :
      ( convergent_lines(X1,X2)
     => ( convergent_lines(X2,X0)
        | convergent_lines(X1,X0) ) ),
    inference(rectify,[],[f6]) ).

fof(f6,axiom,
    ! [X2,X0,X1] :
      ( convergent_lines(X0,X1)
     => ( convergent_lines(X1,X2)
        | convergent_lines(X0,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart6) ).

fof(f59,plain,
    ( ~ convergent_lines(sK0,sK2)
    | spl3_2 ),
    inference(avatar_component_clause,[],[f57]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : GEO219+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.12/0.34  % Computer : n022.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Mon Aug 29 21:31:41 EDT 2022
% 0.12/0.34  % CPUTime    : 
% 0.19/0.52  % (4219)lrs+2_1:1_lcm=reverse:lma=on:sos=all:spb=goal_then_units:ss=included:urr=on:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.19/0.53  % (4218)dis+1010_1:50_awrs=decay:awrsf=128:nwc=10.0:s2pl=no:sp=frequency:ss=axioms:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.19/0.54  % (4226)lrs+10_1:1_ins=3:sp=reverse_frequency:spb=goal:to=lpo:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.19/0.55  % (4219)First to succeed.
% 0.19/0.55  % (4219)Refutation found. Thanks to Tanya!
% 0.19/0.55  % SZS status Theorem for theBenchmark
% 0.19/0.55  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.55  % (4219)------------------------------
% 0.19/0.55  % (4219)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.55  % (4219)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.55  % (4219)Termination reason: Refutation
% 0.19/0.55  
% 0.19/0.55  % (4219)Memory used [KB]: 5884
% 0.19/0.55  % (4219)Time elapsed: 0.128 s
% 0.19/0.55  % (4219)Instructions burned: 3 (million)
% 0.19/0.55  % (4219)------------------------------
% 0.19/0.55  % (4219)------------------------------
% 0.19/0.55  % (4211)Success in time 0.198 s
%------------------------------------------------------------------------------