TSTP Solution File: LCL106-1 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : LCL106-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n006.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 20:26:22 EDT 2024

% Result   : Unsatisfiable 0.13s 0.33s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   21 (  13 unt;   0 def)
%            Number of atoms       :   32 (   0 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   24 (  13   ~;  11   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-1 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :   67 (  67   !;   0   ?)

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

fof(f2,axiom,
    ! [X,Y,Z] : is_a_theorem(equivalent(X,equivalent(equivalent(Y,Z),equivalent(equivalent(Z,Y),X)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f3,axiom,
    ! [X,Y,Z] : is_a_theorem(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),equivalent(Y,Z))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f4,negated_conjecture,
    ~ is_a_theorem(equivalent(equivalent(a,b),equivalent(equivalent(c,a),equivalent(c,b)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f5,plain,
    ! [Y] :
      ( ! [X] :
          ( ~ is_a_theorem(equivalent(X,Y))
          | ~ is_a_theorem(X) )
      | is_a_theorem(Y) ),
    inference(miniscoping,[status(esa)],[f1]) ).

fof(f6,plain,
    ! [X0,X1] :
      ( ~ is_a_theorem(equivalent(X0,X1))
      | ~ is_a_theorem(X0)
      | is_a_theorem(X1) ),
    inference(cnf_transformation,[status(esa)],[f5]) ).

fof(f7,plain,
    ! [X0,X1,X2] : is_a_theorem(equivalent(X0,equivalent(equivalent(X1,X2),equivalent(equivalent(X2,X1),X0)))),
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f8,plain,
    ! [X0,X1,X2] : is_a_theorem(equivalent(equivalent(equivalent(X0,X1),equivalent(X0,X2)),equivalent(X1,X2))),
    inference(cnf_transformation,[status(esa)],[f3]) ).

fof(f9,plain,
    ~ is_a_theorem(equivalent(equivalent(a,b),equivalent(equivalent(c,a),equivalent(c,b)))),
    inference(cnf_transformation,[status(esa)],[f4]) ).

fof(f10,plain,
    ! [X0,X1,X2] :
      ( ~ is_a_theorem(X0)
      | is_a_theorem(equivalent(equivalent(X1,X2),equivalent(equivalent(X2,X1),X0))) ),
    inference(resolution,[status(thm)],[f7,f6]) ).

fof(f11,plain,
    ! [X0,X1,X2] :
      ( ~ is_a_theorem(equivalent(equivalent(X0,X1),equivalent(X0,X2)))
      | is_a_theorem(equivalent(X1,X2)) ),
    inference(resolution,[status(thm)],[f8,f6]) ).

fof(f12,plain,
    ! [X0,X1,X2,X3,X4] : is_a_theorem(equivalent(equivalent(X0,X1),equivalent(equivalent(X1,X0),equivalent(equivalent(equivalent(X2,X3),equivalent(X2,X4)),equivalent(X3,X4))))),
    inference(resolution,[status(thm)],[f10,f8]) ).

fof(f13,plain,
    ! [X0,X1,X2,X3,X4] : is_a_theorem(equivalent(equivalent(X0,X1),equivalent(equivalent(X1,X0),equivalent(X2,equivalent(equivalent(X3,X4),equivalent(equivalent(X4,X3),X2)))))),
    inference(resolution,[status(thm)],[f10,f7]) ).

fof(f15,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ is_a_theorem(equivalent(X0,X1))
      | is_a_theorem(equivalent(equivalent(X1,X0),equivalent(equivalent(equivalent(X2,X3),equivalent(X2,X4)),equivalent(X3,X4)))) ),
    inference(resolution,[status(thm)],[f12,f6]) ).

fof(f17,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ is_a_theorem(equivalent(X0,X1))
      | is_a_theorem(equivalent(equivalent(X1,X0),equivalent(X2,equivalent(equivalent(X3,X4),equivalent(equivalent(X4,X3),X2))))) ),
    inference(resolution,[status(thm)],[f13,f6]) ).

fof(f19,plain,
    ! [X0,X1,X2,X3,X4,X5] : is_a_theorem(equivalent(equivalent(equivalent(X0,X1),equivalent(equivalent(X2,X0),equivalent(X2,X1))),equivalent(equivalent(equivalent(X3,X4),equivalent(X3,X5)),equivalent(X4,X5)))),
    inference(resolution,[status(thm)],[f15,f8]) ).

fof(f23,plain,
    ! [X0,X1,X2,X3,X4,X5] : is_a_theorem(equivalent(equivalent(equivalent(X0,X1),equivalent(equivalent(X2,X0),equivalent(X2,X1))),equivalent(X3,equivalent(equivalent(X4,X5),equivalent(equivalent(X5,X4),X3))))),
    inference(resolution,[status(thm)],[f17,f8]) ).

fof(f27,plain,
    ! [X0,X1,X2,X3] : is_a_theorem(equivalent(equivalent(equivalent(X0,equivalent(X1,X2)),equivalent(X0,equivalent(X1,X3))),equivalent(X2,X3))),
    inference(resolution,[status(thm)],[f19,f11]) ).

fof(f41,plain,
    ! [X0,X1,X2,X3] :
      ( ~ is_a_theorem(equivalent(equivalent(X0,equivalent(X1,X2)),equivalent(X0,equivalent(X1,X3))))
      | is_a_theorem(equivalent(X2,X3)) ),
    inference(resolution,[status(thm)],[f27,f6]) ).

fof(f52,plain,
    ! [X0,X1,X2] : is_a_theorem(equivalent(equivalent(X0,X1),equivalent(equivalent(X2,X0),equivalent(X2,X1)))),
    inference(resolution,[status(thm)],[f23,f41]) ).

fof(f62,plain,
    $false,
    inference(backward_subsumption_resolution,[status(thm)],[f9,f52]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : LCL106-1 : TPTP v8.1.2. Released v1.0.0.
% 0.12/0.12  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.32  % Computer : n006.cluster.edu
% 0.13/0.32  % Model    : x86_64 x86_64
% 0.13/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32  % Memory   : 8042.1875MB
% 0.13/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32  % CPULimit : 300
% 0.13/0.32  % WCLimit  : 300
% 0.13/0.32  % DateTime : Mon Apr 29 20:22:35 EDT 2024
% 0.13/0.33  % CPUTime  : 
% 0.13/0.33  % Drodi V3.6.0
% 0.13/0.33  % Refutation found
% 0.13/0.33  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.33  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/0.35  % Elapsed time: 0.017015 seconds
% 0.19/0.35  % CPU time: 0.025768 seconds
% 0.19/0.35  % Total memory used: 6.638 MB
% 0.19/0.35  % Net memory used: 6.622 MB
%------------------------------------------------------------------------------