TSTP Solution File: HEN005-1 by Drodi---3.5.1

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%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : HEN005-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n029.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 12:12:46 EDT 2023

% Result   : Unsatisfiable 0.05s 0.27s
% Output   : CNFRefutation 0.05s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   58 (  26 unt;   0 def)
%            Number of atoms       :  113 (  16 equ)
%            Maximal formula atoms :    6 (   1 avg)
%            Number of connectives :  110 (  55   ~;  53   |;   0   &)
%                                         (   2 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   3 prp; 0-3 aty)
%            Number of functors    :    5 (   5 usr;   4 con; 0-2 aty)
%            Number of variables   :   97 (;  97   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X,Y] :
      ( ~ less_equal(X,Y)
      | quotient(X,Y,zero) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f2,axiom,
    ! [X,Y] :
      ( ~ quotient(X,Y,zero)
      | less_equal(X,Y) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f3,axiom,
    ! [X,Y,Z] :
      ( ~ quotient(X,Y,Z)
      | less_equal(Z,X) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f4,axiom,
    ! [X,Y,V1,Z,V2,V3,V4,V5] :
      ( ~ quotient(X,Y,V1)
      | ~ quotient(Y,Z,V2)
      | ~ quotient(X,Z,V3)
      | ~ quotient(V3,V2,V4)
      | ~ quotient(V1,Z,V5)
      | less_equal(V4,V5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f5,axiom,
    ! [X] : less_equal(zero,X),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f6,axiom,
    ! [X,Y] :
      ( ~ less_equal(X,Y)
      | ~ less_equal(Y,X)
      | X = Y ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f8,axiom,
    ! [X,Y] : quotient(X,Y,divide(X,Y)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f9,axiom,
    ! [X,Y,Z,W] :
      ( ~ quotient(X,Y,Z)
      | ~ quotient(X,Y,W)
      | Z = W ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f10,hypothesis,
    less_equal(x,y),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f11,hypothesis,
    less_equal(y,z),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f12,negated_conjecture,
    ~ less_equal(x,z),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f13,plain,
    ! [X0,X1] :
      ( ~ less_equal(X0,X1)
      | quotient(X0,X1,zero) ),
    inference(cnf_transformation,[status(esa)],[f1]) ).

fof(f14,plain,
    ! [X0,X1] :
      ( ~ quotient(X0,X1,zero)
      | less_equal(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f15,plain,
    ! [X,Z] :
      ( ! [Y] : ~ quotient(X,Y,Z)
      | less_equal(Z,X) ),
    inference(miniscoping,[status(esa)],[f3]) ).

fof(f16,plain,
    ! [X0,X1,X2] :
      ( ~ quotient(X0,X1,X2)
      | less_equal(X2,X0) ),
    inference(cnf_transformation,[status(esa)],[f15]) ).

fof(f17,plain,
    ! [V4,V5] :
      ( ! [V1,Z] :
          ( ! [V2,V3] :
              ( ! [X] :
                  ( ! [Y] :
                      ( ~ quotient(X,Y,V1)
                      | ~ quotient(Y,Z,V2) )
                  | ~ quotient(X,Z,V3) )
              | ~ quotient(V3,V2,V4) )
          | ~ quotient(V1,Z,V5) )
      | less_equal(V4,V5) ),
    inference(miniscoping,[status(esa)],[f4]) ).

fof(f18,plain,
    ! [X0,X1,X2,X3,X4,X5,X6,X7] :
      ( ~ quotient(X0,X1,X2)
      | ~ quotient(X1,X3,X4)
      | ~ quotient(X0,X3,X5)
      | ~ quotient(X5,X4,X6)
      | ~ quotient(X2,X3,X7)
      | less_equal(X6,X7) ),
    inference(cnf_transformation,[status(esa)],[f17]) ).

fof(f19,plain,
    ! [X0] : less_equal(zero,X0),
    inference(cnf_transformation,[status(esa)],[f5]) ).

fof(f20,plain,
    ! [X0,X1] :
      ( ~ less_equal(X0,X1)
      | ~ less_equal(X1,X0)
      | X0 = X1 ),
    inference(cnf_transformation,[status(esa)],[f6]) ).

fof(f22,plain,
    ! [X0,X1] : quotient(X0,X1,divide(X0,X1)),
    inference(cnf_transformation,[status(esa)],[f8]) ).

fof(f23,plain,
    ! [Z,W] :
      ( ! [X,Y] :
          ( ~ quotient(X,Y,Z)
          | ~ quotient(X,Y,W) )
      | Z = W ),
    inference(miniscoping,[status(esa)],[f9]) ).

fof(f24,plain,
    ! [X0,X1,X2,X3] :
      ( ~ quotient(X0,X1,X2)
      | ~ quotient(X0,X1,X3)
      | X2 = X3 ),
    inference(cnf_transformation,[status(esa)],[f23]) ).

fof(f25,plain,
    less_equal(x,y),
    inference(cnf_transformation,[status(esa)],[f10]) ).

fof(f26,plain,
    less_equal(y,z),
    inference(cnf_transformation,[status(esa)],[f11]) ).

fof(f27,plain,
    ~ less_equal(x,z),
    inference(cnf_transformation,[status(esa)],[f12]) ).

fof(f44,plain,
    ! [X0] :
      ( ~ less_equal(X0,zero)
      | zero = X0 ),
    inference(resolution,[status(thm)],[f19,f20]) ).

fof(f46,plain,
    ! [X0,X1,X2,X3,X4,X5,X6] :
      ( ~ quotient(X0,X1,X2)
      | ~ quotient(X3,X1,X4)
      | ~ quotient(X4,X2,X5)
      | ~ quotient(divide(X3,X0),X1,X6)
      | less_equal(X5,X6) ),
    inference(resolution,[status(thm)],[f22,f18]) ).

fof(f47,plain,
    ! [X0,X1] : less_equal(divide(X0,X1),X0),
    inference(resolution,[status(thm)],[f22,f16]) ).

fof(f48,plain,
    ! [X0] : zero = divide(zero,X0),
    inference(resolution,[status(thm)],[f47,f44]) ).

fof(f68,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( ~ quotient(X0,X1,X2)
      | ~ quotient(X2,divide(X3,X1),X4)
      | ~ quotient(divide(X0,X3),X1,X5)
      | less_equal(X4,X5) ),
    inference(resolution,[status(thm)],[f46,f22]) ).

fof(f71,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ quotient(divide(X0,X1),divide(X2,X1),X3)
      | ~ quotient(divide(X0,X2),X1,X4)
      | less_equal(X3,X4) ),
    inference(resolution,[status(thm)],[f68,f22]) ).

fof(f74,plain,
    quotient(y,z,zero),
    inference(resolution,[status(thm)],[f13,f26]) ).

fof(f75,plain,
    quotient(x,y,zero),
    inference(resolution,[status(thm)],[f13,f25]) ).

fof(f104,plain,
    ! [X0] :
      ( ~ quotient(x,y,X0)
      | zero = X0 ),
    inference(resolution,[status(thm)],[f24,f75]) ).

fof(f105,plain,
    ! [X0] :
      ( ~ quotient(y,z,X0)
      | zero = X0 ),
    inference(resolution,[status(thm)],[f24,f74]) ).

fof(f116,plain,
    zero = divide(x,y),
    inference(resolution,[status(thm)],[f104,f22]) ).

fof(f128,plain,
    zero = divide(y,z),
    inference(resolution,[status(thm)],[f105,f22]) ).

fof(f216,plain,
    ! [X0,X1,X2,X3] :
      ( ~ quotient(divide(X0,X1),X2,X3)
      | less_equal(divide(divide(X0,X2),divide(X1,X2)),X3) ),
    inference(resolution,[status(thm)],[f71,f22]) ).

fof(f234,plain,
    ! [X0,X1,X2] : less_equal(divide(divide(X0,X1),divide(X2,X1)),divide(divide(X0,X2),X1)),
    inference(resolution,[status(thm)],[f216,f22]) ).

fof(f444,plain,
    ! [X0] : less_equal(divide(divide(x,X0),divide(y,X0)),divide(zero,X0)),
    inference(paramodulation,[status(thm)],[f116,f234]) ).

fof(f445,plain,
    ! [X0] : less_equal(divide(divide(x,X0),divide(y,X0)),zero),
    inference(forward_demodulation,[status(thm)],[f48,f444]) ).

fof(f662,plain,
    ! [X0] : zero = divide(divide(x,X0),divide(y,X0)),
    inference(resolution,[status(thm)],[f445,f44]) ).

fof(f683,plain,
    zero = divide(divide(x,z),zero),
    inference(paramodulation,[status(thm)],[f128,f662]) ).

fof(f744,plain,
    quotient(divide(x,z),zero,zero),
    inference(paramodulation,[status(thm)],[f683,f22]) ).

fof(f746,plain,
    less_equal(divide(x,z),zero),
    inference(resolution,[status(thm)],[f744,f14]) ).

fof(f760,plain,
    ( spl0_12
  <=> less_equal(zero,divide(x,z)) ),
    introduced(split_symbol_definition) ).

fof(f762,plain,
    ( ~ less_equal(zero,divide(x,z))
    | spl0_12 ),
    inference(component_clause,[status(thm)],[f760]) ).

fof(f763,plain,
    ( spl0_13
  <=> divide(x,z) = zero ),
    introduced(split_symbol_definition) ).

fof(f764,plain,
    ( divide(x,z) = zero
    | ~ spl0_13 ),
    inference(component_clause,[status(thm)],[f763]) ).

fof(f766,plain,
    ( ~ less_equal(zero,divide(x,z))
    | divide(x,z) = zero ),
    inference(resolution,[status(thm)],[f746,f20]) ).

fof(f767,plain,
    ( ~ spl0_12
    | spl0_13 ),
    inference(split_clause,[status(thm)],[f766,f760,f763]) ).

fof(f768,plain,
    ( $false
    | spl0_12 ),
    inference(forward_subsumption_resolution,[status(thm)],[f762,f19]) ).

fof(f769,plain,
    spl0_12,
    inference(contradiction_clause,[status(thm)],[f768]) ).

fof(f815,plain,
    ( quotient(x,z,zero)
    | ~ spl0_13 ),
    inference(paramodulation,[status(thm)],[f764,f22]) ).

fof(f818,plain,
    ( less_equal(x,z)
    | ~ spl0_13 ),
    inference(resolution,[status(thm)],[f815,f14]) ).

fof(f819,plain,
    ( $false
    | ~ spl0_13 ),
    inference(forward_subsumption_resolution,[status(thm)],[f818,f27]) ).

fof(f820,plain,
    ~ spl0_13,
    inference(contradiction_clause,[status(thm)],[f819]) ).

fof(f821,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f767,f769,f820]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06  % Problem  : HEN005-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.00/0.06  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.05/0.25  % Computer : n029.cluster.edu
% 0.05/0.25  % Model    : x86_64 x86_64
% 0.05/0.25  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.25  % Memory   : 8042.1875MB
% 0.05/0.25  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.05/0.25  % CPULimit : 300
% 0.05/0.25  % WCLimit  : 300
% 0.05/0.25  % DateTime : Tue May 30 09:48:36 EDT 2023
% 0.05/0.25  % CPUTime  : 
% 0.05/0.26  % Drodi V3.5.1
% 0.05/0.27  % Refutation found
% 0.05/0.27  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.05/0.27  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.49  % Elapsed time: 0.026354 seconds
% 0.09/0.49  % CPU time: 0.065694 seconds
% 0.09/0.49  % Memory used: 3.156 MB
%------------------------------------------------------------------------------