%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : GEO219+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n002.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 May 31 12:08:23 EDT 2023

% Result   : Theorem 0.15s 0.32s
% Output   : CNFRefutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   30 (   6 unt;   0 def)
%            Number of atoms       :   84 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   97 (  43   ~;  33   |;  16   &)
%                                         (   0 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   3 con; 0-0 aty)
%            Number of variables   :   57 (;  51   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f6,axiom,
    ! [X,Y,Z] :
      ( convergent_lines(X,Y)
     => ( convergent_lines(X,Z)
        | convergent_lines(Y,Z) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f15,axiom,
    ! [L,M] :
      ~ ( ~ convergent_lines(L,M)
        & ~ unorthogonal_lines(L,M) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f16,axiom,
    ! [L,M,N] :
      ( ( ( ~ convergent_lines(L,M)
          | ~ unorthogonal_lines(L,M) )
        & ( ~ convergent_lines(L,N)
          | ~ unorthogonal_lines(L,N) ) )
     => ( ~ convergent_lines(M,N)
        | ~ unorthogonal_lines(M,N) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f18,conjecture,
    ! [L,M,N] :
      ( ( ~ unorthogonal_lines(L,M)
        & ~ convergent_lines(L,N) )
     => ~ unorthogonal_lines(M,N) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f19,negated_conjecture,
    ~ ! [L,M,N] :
        ( ( ~ unorthogonal_lines(L,M)
          & ~ convergent_lines(L,N) )
       => ~ unorthogonal_lines(M,N) ),
    inference(negated_conjecture,[status(cth)],[f18]) ).

fof(f29,plain,
    ! [X,Y,Z] :
      ( ~ convergent_lines(X,Y)
      | convergent_lines(X,Z)
      | convergent_lines(Y,Z) ),
    inference(pre_NNF_transformation,[status(esa)],[f6]) ).

fof(f30,plain,
    ! [X,Y] :
      ( ~ convergent_lines(X,Y)
      | ! [Z] :
          ( convergent_lines(X,Z)
          | convergent_lines(Y,Z) ) ),
    inference(miniscoping,[status(esa)],[f29]) ).

fof(f31,plain,
    ! [X0,X1,X2] :
      ( ~ convergent_lines(X0,X1)
      | convergent_lines(X0,X2)
      | convergent_lines(X1,X2) ),
    inference(cnf_transformation,[status(esa)],[f30]) ).

fof(f51,plain,
    ! [L,M] :
      ( convergent_lines(L,M)
      | unorthogonal_lines(L,M) ),
    inference(pre_NNF_transformation,[status(esa)],[f15]) ).

fof(f52,plain,
    ! [X0,X1] :
      ( convergent_lines(X0,X1)
      | unorthogonal_lines(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f51]) ).

fof(f53,plain,
    ! [L,M,N] :
      ( ( convergent_lines(L,M)
        & unorthogonal_lines(L,M) )
      | ( convergent_lines(L,N)
        & unorthogonal_lines(L,N) )
      | ~ convergent_lines(M,N)
      | ~ unorthogonal_lines(M,N) ),
    inference(pre_NNF_transformation,[status(esa)],[f16]) ).

fof(f54,plain,
    ! [L,M] :
      ( pd0_0(M,L)
     => ( convergent_lines(L,M)
        & unorthogonal_lines(L,M) ) ),
    introduced(predicate_definition,[f53]) ).

fof(f55,plain,
    ! [L,M,N] :
      ( pd0_0(M,L)
      | ( convergent_lines(L,N)
        & unorthogonal_lines(L,N) )
      | ~ convergent_lines(M,N)
      | ~ unorthogonal_lines(M,N) ),
    inference(formula_renaming,[status(thm)],[f53,f54]) ).

fof(f56,plain,
    ! [M,N] :
      ( ! [L] :
          ( pd0_0(M,L)
          | ( convergent_lines(L,N)
            & unorthogonal_lines(L,N) ) )
      | ~ convergent_lines(M,N)
      | ~ unorthogonal_lines(M,N) ),
    inference(miniscoping,[status(esa)],[f55]) ).

fof(f57,plain,
    ! [X0,X1,X2] :
      ( pd0_0(X0,X1)
      | convergent_lines(X1,X2)
      | ~ convergent_lines(X0,X2)
      | ~ unorthogonal_lines(X0,X2) ),
    inference(cnf_transformation,[status(esa)],[f56]) ).

fof(f62,plain,
    ? [L,M,N] :
      ( ~ unorthogonal_lines(L,M)
      & ~ convergent_lines(L,N)
      & unorthogonal_lines(M,N) ),
    inference(pre_NNF_transformation,[status(esa)],[f19]) ).

fof(f63,plain,
    ? [M,N] :
      ( ? [L] :
          ( ~ unorthogonal_lines(L,M)
          & ~ convergent_lines(L,N) )
      & unorthogonal_lines(M,N) ),
    inference(miniscoping,[status(esa)],[f62]) ).

fof(f64,plain,
    ( ~ unorthogonal_lines(sk0_2,sk0_0)
    & ~ convergent_lines(sk0_2,sk0_1)
    & unorthogonal_lines(sk0_0,sk0_1) ),
    inference(skolemization,[status(esa)],[f63]) ).

fof(f65,plain,
    ~ unorthogonal_lines(sk0_2,sk0_0),
    inference(cnf_transformation,[status(esa)],[f64]) ).

fof(f66,plain,
    ~ convergent_lines(sk0_2,sk0_1),
    inference(cnf_transformation,[status(esa)],[f64]) ).

fof(f67,plain,
    unorthogonal_lines(sk0_0,sk0_1),
    inference(cnf_transformation,[status(esa)],[f64]) ).

fof(f68,plain,
    ! [L,M] :
      ( ~ pd0_0(M,L)
      | ( convergent_lines(L,M)
        & unorthogonal_lines(L,M) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f54]) ).

fof(f70,plain,
    ! [X0,X1] :
      ( ~ pd0_0(X0,X1)
      | unorthogonal_lines(X1,X0) ),
    inference(cnf_transformation,[status(esa)],[f68]) ).

fof(f71,plain,
    convergent_lines(sk0_2,sk0_0),
    inference(resolution,[status(thm)],[f52,f65]) ).

fof(f72,plain,
    ! [X0] :
      ( convergent_lines(sk0_2,X0)
      | convergent_lines(sk0_0,X0) ),
    inference(resolution,[status(thm)],[f31,f71]) ).

fof(f94,plain,
    ! [X0,X1,X2] :
      ( convergent_lines(X0,X1)
      | ~ convergent_lines(X2,X1)
      | ~ unorthogonal_lines(X2,X1)
      | unorthogonal_lines(X0,X2) ),
    inference(resolution,[status(thm)],[f57,f70]) ).

fof(f99,plain,
    ! [X0] :
      ( convergent_lines(sk0_2,X0)
      | ~ convergent_lines(sk0_0,X0)
      | ~ unorthogonal_lines(sk0_0,X0) ),
    inference(resolution,[status(thm)],[f94,f65]) ).

fof(f100,plain,
    ! [X0] :
      ( convergent_lines(sk0_2,X0)
      | ~ unorthogonal_lines(sk0_0,X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[f99,f72]) ).

fof(f101,plain,
    ~ unorthogonal_lines(sk0_0,sk0_1),
    inference(resolution,[status(thm)],[f100,f66]) ).

fof(f102,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[f101,f67]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem  : GEO219+1 : TPTP v8.1.2. Released v3.3.0.
% 0.09/0.10  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.30  % Computer : n002.cluster.edu
% 0.10/0.30  % Model    : x86_64 x86_64
% 0.10/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30  % Memory   : 8042.1875MB
% 0.10/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30  % CPULimit : 300
% 0.10/0.30  % WCLimit  : 300
% 0.10/0.30  % DateTime : Tue May 30 12:18:28 EDT 2023
% 0.10/0.31  % CPUTime  : 
% 0.10/0.31  % Drodi V3.5.1
% 0.15/0.32  % Refutation found
% 0.15/0.32  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.32  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.53  % Elapsed time: 0.010613 seconds
% 0.15/0.53  % CPU time: 0.013127 seconds
% 0.15/0.53  % Memory used: 548.599 KB
%------------------------------------------------------------------------------