%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : GEO037-2 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n026.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 20:16:53 EDT 2024

% Result   : Unsatisfiable 0.15s 0.36s
% Output   : CNFRefutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   43 (  19 unt;   0 def)
%            Number of atoms       :   73 (   9 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   59 (  29   ~;  27   |;   0   &)
%                                         (   3 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   4 prp; 0-4 aty)
%            Number of functors    :    8 (   8 usr;   7 con; 0-4 aty)
%            Number of variables   :   88 (  88   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X,Y] : equidistant(X,Y,Y,X),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f2,axiom,
    ! [X,Y,Z,V,V2,W] :
      ( ~ equidistant(X,Y,Z,V)
      | ~ equidistant(X,Y,V2,W)
      | equidistant(Z,V,V2,W) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f3,axiom,
    ! [X,Y,Z] :
      ( ~ equidistant(X,Y,Z,Z)
      | X = Y ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f4,axiom,
    ! [X,Y,W,V] : between(X,Y,extension(X,Y,W,V)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f5,axiom,
    ! [Y,X,W,V] : equidistant(Y,extension(X,Y,W,V),W,V),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f12,axiom,
    ~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f19,negated_conjecture,
    ( v = extension(u,v,lower_dimension_point_1,lower_dimension_point_2)
    | ~ equidistant(v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2),x,extension(w,x,lower_dimension_point_1,lower_dimension_point_2))
    | ~ between(u,v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f20,plain,
    ! [X0,X1] : equidistant(X0,X1,X1,X0),
    inference(cnf_transformation,[status(esa)],[f1]) ).

fof(f21,plain,
    ! [Z,V,V2,W] :
      ( ! [X,Y] :
          ( ~ equidistant(X,Y,Z,V)
          | ~ equidistant(X,Y,V2,W) )
      | equidistant(Z,V,V2,W) ),
    inference(miniscoping,[status(esa)],[f2]) ).

fof(f22,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( ~ equidistant(X0,X1,X2,X3)
      | ~ equidistant(X0,X1,X4,X5)
      | equidistant(X2,X3,X4,X5) ),
    inference(cnf_transformation,[status(esa)],[f21]) ).

fof(f23,plain,
    ! [X,Y] :
      ( ! [Z] : ~ equidistant(X,Y,Z,Z)
      | X = Y ),
    inference(miniscoping,[status(esa)],[f3]) ).

fof(f24,plain,
    ! [X0,X1,X2] :
      ( ~ equidistant(X0,X1,X2,X2)
      | X0 = X1 ),
    inference(cnf_transformation,[status(esa)],[f23]) ).

fof(f25,plain,
    ! [X0,X1,X2,X3] : between(X0,X1,extension(X0,X1,X2,X3)),
    inference(cnf_transformation,[status(esa)],[f4]) ).

fof(f26,plain,
    ! [X0,X1,X2,X3] : equidistant(X0,extension(X1,X0,X2,X3),X2,X3),
    inference(cnf_transformation,[status(esa)],[f5]) ).

fof(f34,plain,
    ~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2),
    inference(cnf_transformation,[status(esa)],[f12]) ).

fof(f42,plain,
    ( v = extension(u,v,lower_dimension_point_1,lower_dimension_point_2)
    | ~ equidistant(v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2),x,extension(w,x,lower_dimension_point_1,lower_dimension_point_2))
    | ~ between(u,v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2)) ),
    inference(cnf_transformation,[status(esa)],[f19]) ).

fof(f43,plain,
    ( spl0_0
  <=> v = extension(u,v,lower_dimension_point_1,lower_dimension_point_2) ),
    introduced(split_symbol_definition) ).

fof(f44,plain,
    ( v = extension(u,v,lower_dimension_point_1,lower_dimension_point_2)
    | ~ spl0_0 ),
    inference(component_clause,[status(thm)],[f43]) ).

fof(f46,plain,
    ( spl0_1
  <=> equidistant(v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2),x,extension(w,x,lower_dimension_point_1,lower_dimension_point_2)) ),
    introduced(split_symbol_definition) ).

fof(f48,plain,
    ( ~ equidistant(v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2),x,extension(w,x,lower_dimension_point_1,lower_dimension_point_2))
    | spl0_1 ),
    inference(component_clause,[status(thm)],[f46]) ).

fof(f49,plain,
    ( spl0_2
  <=> between(u,v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2)) ),
    introduced(split_symbol_definition) ).

fof(f51,plain,
    ( ~ between(u,v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2))
    | spl0_2 ),
    inference(component_clause,[status(thm)],[f49]) ).

fof(f52,plain,
    ( spl0_0
    | ~ spl0_1
    | ~ spl0_2 ),
    inference(split_clause,[status(thm)],[f42,f43,f46,f49]) ).

fof(f53,plain,
    ( $false
    | spl0_2 ),
    inference(forward_subsumption_resolution,[status(thm)],[f51,f25]) ).

fof(f54,plain,
    spl0_2,
    inference(contradiction_clause,[status(thm)],[f53]) ).

fof(f55,plain,
    ! [X0,X1,X2] : X0 = extension(X1,X0,X2,X2),
    inference(resolution,[status(thm)],[f26,f24]) ).

fof(f56,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( ~ equidistant(X0,extension(X1,X0,X2,X3),X4,X5)
      | equidistant(X2,X3,X4,X5) ),
    inference(resolution,[status(thm)],[f22,f26]) ).

fof(f57,plain,
    ! [X0,X1,X2,X3] :
      ( ~ equidistant(X0,X1,X2,X3)
      | equidistant(X1,X0,X2,X3) ),
    inference(resolution,[status(thm)],[f22,f20]) ).

fof(f59,plain,
    ! [X0,X1] : between(X0,X1,X1),
    inference(paramodulation,[status(thm)],[f55,f25]) ).

fof(f63,plain,
    ! [X0,X1] : equidistant(X0,X1,X0,X1),
    inference(resolution,[status(thm)],[f57,f20]) ).

fof(f73,plain,
    ! [X0,X1,X2,X3] : equidistant(X0,X1,X2,extension(X3,X2,X0,X1)),
    inference(resolution,[status(thm)],[f56,f63]) ).

fof(f74,plain,
    ! [X0,X1,X2,X3] : equidistant(X0,X1,extension(X2,X3,X0,X1),X3),
    inference(resolution,[status(thm)],[f56,f20]) ).

fof(f80,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( ~ equidistant(X0,X1,X2,X3)
      | equidistant(X4,extension(X5,X4,X0,X1),X2,X3) ),
    inference(resolution,[status(thm)],[f73,f22]) ).

fof(f85,plain,
    ! [X0,X1,X2,X3] : equidistant(X0,X1,extension(X2,X3,X1,X0),X3),
    inference(resolution,[status(thm)],[f74,f57]) ).

fof(f124,plain,
    ! [X0,X1,X2,X3,X4,X5] : equidistant(X0,extension(X1,X0,X2,X3),X4,extension(X5,X4,X2,X3)),
    inference(resolution,[status(thm)],[f80,f73]) ).

fof(f129,plain,
    ( $false
    | spl0_1 ),
    inference(backward_subsumption_resolution,[status(thm)],[f48,f124]) ).

fof(f130,plain,
    spl0_1,
    inference(contradiction_clause,[status(thm)],[f129]) ).

fof(f214,plain,
    ( equidistant(lower_dimension_point_2,lower_dimension_point_1,v,v)
    | ~ spl0_0 ),
    inference(paramodulation,[status(thm)],[f44,f85]) ).

fof(f271,plain,
    ( lower_dimension_point_2 = lower_dimension_point_1
    | ~ spl0_0 ),
    inference(resolution,[status(thm)],[f214,f24]) ).

fof(f275,plain,
    ( ~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_1)
    | ~ spl0_0 ),
    inference(backward_demodulation,[status(thm)],[f271,f34]) ).

fof(f276,plain,
    ( $false
    | ~ spl0_0 ),
    inference(forward_subsumption_resolution,[status(thm)],[f275,f59]) ).

fof(f277,plain,
    ~ spl0_0,
    inference(contradiction_clause,[status(thm)],[f276]) ).

fof(f278,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f52,f54,f130,f277]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09  % Problem  : GEO037-2 : TPTP v8.1.2. Released v1.0.0.
% 0.02/0.10  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.30  % Computer : n026.cluster.edu
% 0.09/0.30  % Model    : x86_64 x86_64
% 0.09/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30  % Memory   : 8042.1875MB
% 0.09/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30  % CPULimit : 300
% 0.09/0.30  % WCLimit  : 300
% 0.09/0.30  % DateTime : Tue Apr 30 01:48:34 EDT 2024
% 0.09/0.30  % CPUTime  : 
% 0.09/0.31  % Drodi V3.6.0
% 0.15/0.36  % Refutation found
% 0.15/0.36  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.15/0.36  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.37  % Elapsed time: 0.056887 seconds
% 0.15/0.37  % CPU time: 0.366217 seconds
% 0.15/0.37  % Total memory used: 53.473 MB
% 0.15/0.37  % Net memory used: 53.073 MB
%------------------------------------------------------------------------------