%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : GEO042-2 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%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 : Tue Apr 30 20:16:54 EDT 2024

% Result   : Unsatisfiable 0.14s 0.37s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   41 (  16 unt;   0 def)
%            Number of atoms       :   71 (  11 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   60 (  30   ~;  28   |;   0   &)
%                                         (   2 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   3 prp; 0-4 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-5 aty)
%            Number of variables   :   69 (  69   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
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(f7,axiom,
    ! [X,Y] :
      ( ~ between(X,Y,X)
      | X = Y ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f8,axiom,
    ! [U,V,W,Y,X] :
      ( ~ between(U,V,W)
      | ~ between(Y,X,W)
      | between(V,inner_pasch(U,V,W,X,Y),Y) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f9,axiom,
    ! [U,V,W,Y,X] :
      ( ~ between(U,V,W)
      | ~ between(Y,X,W)
      | between(X,inner_pasch(U,V,W,X,Y),U) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f19,hypothesis,
    between(u,v,x),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f20,hypothesis,
    between(v,w,x),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f21,negated_conjecture,
    ~ between(u,v,w),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f25,plain,
    ! [X,Y] :
      ( ! [Z] : ~ equidistant(X,Y,Z,Z)
      | X = Y ),
    inference(miniscoping,[status(esa)],[f3]) ).

fof(f26,plain,
    ! [X0,X1,X2] :
      ( ~ equidistant(X0,X1,X2,X2)
      | X0 = X1 ),
    inference(cnf_transformation,[status(esa)],[f25]) ).

fof(f27,plain,
    ! [X0,X1,X2,X3] : between(X0,X1,extension(X0,X1,X2,X3)),
    inference(cnf_transformation,[status(esa)],[f4]) ).

fof(f28,plain,
    ! [X0,X1,X2,X3] : equidistant(X0,extension(X1,X0,X2,X3),X2,X3),
    inference(cnf_transformation,[status(esa)],[f5]) ).

fof(f31,plain,
    ! [X0,X1] :
      ( ~ between(X0,X1,X0)
      | X0 = X1 ),
    inference(cnf_transformation,[status(esa)],[f7]) ).

fof(f32,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ between(X0,X1,X2)
      | ~ between(X3,X4,X2)
      | between(X1,inner_pasch(X0,X1,X2,X4,X3),X3) ),
    inference(cnf_transformation,[status(esa)],[f8]) ).

fof(f33,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ between(X0,X1,X2)
      | ~ between(X3,X4,X2)
      | between(X4,inner_pasch(X0,X1,X2,X4,X3),X0) ),
    inference(cnf_transformation,[status(esa)],[f9]) ).

fof(f44,plain,
    between(u,v,x),
    inference(cnf_transformation,[status(esa)],[f19]) ).

fof(f45,plain,
    between(v,w,x),
    inference(cnf_transformation,[status(esa)],[f20]) ).

fof(f46,plain,
    ~ between(u,v,w),
    inference(cnf_transformation,[status(esa)],[f21]) ).

fof(f48,plain,
    ! [X0,X1,X2] : X0 = extension(X1,X0,X2,X2),
    inference(resolution,[status(thm)],[f28,f26]) ).

fof(f50,plain,
    ! [X0,X1] : between(X0,X1,X1),
    inference(paramodulation,[status(thm)],[f48,f27]) ).

fof(f58,plain,
    ! [X0,X1,X2,X3] :
      ( ~ between(X0,X1,X2)
      | ~ between(X1,X3,X2)
      | X1 = inner_pasch(X0,X1,X2,X3,X1) ),
    inference(resolution,[status(thm)],[f32,f31]) ).

fof(f61,plain,
    ! [X0] :
      ( ~ between(X0,v,x)
      | v = inner_pasch(X0,v,x,w,v) ),
    inference(resolution,[status(thm)],[f58,f45]) ).

fof(f65,plain,
    ! [X0,X1,X2] :
      ( ~ between(X0,X1,X2)
      | X1 = inner_pasch(X0,X1,X2,X2,X1) ),
    inference(resolution,[status(thm)],[f58,f50]) ).

fof(f86,plain,
    ( spl0_3
  <=> between(u,v,x) ),
    introduced(split_symbol_definition) ).

fof(f88,plain,
    ( ~ between(u,v,x)
    | spl0_3 ),
    inference(component_clause,[status(thm)],[f86]) ).

fof(f99,plain,
    ( $false
    | spl0_3 ),
    inference(forward_subsumption_resolution,[status(thm)],[f88,f44]) ).

fof(f100,plain,
    spl0_3,
    inference(contradiction_clause,[status(thm)],[f99]) ).

fof(f116,plain,
    v = inner_pasch(u,v,x,w,v),
    inference(resolution,[status(thm)],[f61,f44]) ).

fof(f119,plain,
    ! [X0,X1] :
      ( ~ between(X0,X1,x)
      | between(w,inner_pasch(X0,X1,x,w,v),X0) ),
    inference(resolution,[status(thm)],[f33,f45]) ).

fof(f123,plain,
    ! [X0,X1,X2,X3] :
      ( ~ between(X0,X1,X2)
      | between(X2,inner_pasch(X0,X1,X2,X2,X3),X0) ),
    inference(resolution,[status(thm)],[f33,f50]) ).

fof(f188,plain,
    ( spl0_6
  <=> between(w,v,u) ),
    introduced(split_symbol_definition) ).

fof(f189,plain,
    ( between(w,v,u)
    | ~ spl0_6 ),
    inference(component_clause,[status(thm)],[f188]) ).

fof(f191,plain,
    ( ~ between(u,v,x)
    | between(w,v,u) ),
    inference(paramodulation,[status(thm)],[f116,f119]) ).

fof(f192,plain,
    ( ~ spl0_3
    | spl0_6 ),
    inference(split_clause,[status(thm)],[f191,f86,f188]) ).

fof(f194,plain,
    ! [X0] :
      ( between(u,inner_pasch(w,v,u,u,X0),w)
      | ~ spl0_6 ),
    inference(resolution,[status(thm)],[f189,f123]) ).

fof(f196,plain,
    ( v = inner_pasch(w,v,u,u,v)
    | ~ spl0_6 ),
    inference(resolution,[status(thm)],[f189,f65]) ).

fof(f213,plain,
    ( between(u,v,w)
    | ~ spl0_6 ),
    inference(paramodulation,[status(thm)],[f196,f194]) ).

fof(f214,plain,
    ( $false
    | ~ spl0_6 ),
    inference(forward_subsumption_resolution,[status(thm)],[f213,f46]) ).

fof(f215,plain,
    ~ spl0_6,
    inference(contradiction_clause,[status(thm)],[f214]) ).

fof(f216,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f100,f192,f215]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : GEO042-2 : TPTP v8.1.2. Released v1.0.0.
% 0.03/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.34  % Computer : n005.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Tue Apr 30 01:25:11 EDT 2024
% 0.14/0.34  % CPUTime  : 
% 0.14/0.35  % Drodi V3.6.0
% 0.14/0.37  % Refutation found
% 0.14/0.37  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.37  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.21/0.38  % Elapsed time: 0.031572 seconds
% 0.21/0.38  % CPU time: 0.123900 seconds
% 0.21/0.38  % Total memory used: 18.843 MB
% 0.21/0.38  % Net memory used: 18.768 MB
%------------------------------------------------------------------------------