TSTP Solution File: GRP031-2 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : GRP031-2 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n004.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 20:18:51 EDT 2024

% Result   : Unsatisfiable 0.16s 0.46s
% Output   : CNFRefutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   24 (  12 unt;   0 def)
%            Number of atoms       :   51 (   0 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   59 (  32   ~;  27   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-3 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :   68 (  68   !;   0   ?)

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

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

fof(f4,axiom,
    ! [X,Y,U,Z,V,W] :
      ( ~ product(X,Y,U)
      | ~ product(Y,Z,V)
      | ~ product(X,V,W)
      | product(U,Z,W) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f5,hypothesis,
    ! [A] : product(A,inverse(A),identity),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f6,hypothesis,
    ! [A] : product(A,identity,A),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f7,negated_conjecture,
    ! [A] : ~ product(A,a,identity),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f8,plain,
    ! [X0,X1] : product(X0,X1,multiply(X0,X1)),
    inference(cnf_transformation,[status(esa)],[f1]) ).

fof(f11,plain,
    ! [X,V,W] :
      ( ! [U,Z] :
          ( ! [Y] :
              ( ~ product(X,Y,U)
              | ~ product(Y,Z,V) )
          | ~ product(U,Z,W) )
      | product(X,V,W) ),
    inference(miniscoping,[status(esa)],[f3]) ).

fof(f12,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( ~ product(X0,X1,X2)
      | ~ product(X1,X3,X4)
      | ~ product(X2,X3,X5)
      | product(X0,X4,X5) ),
    inference(cnf_transformation,[status(esa)],[f11]) ).

fof(f13,plain,
    ! [U,Z,W] :
      ( ! [X,V] :
          ( ! [Y] :
              ( ~ product(X,Y,U)
              | ~ product(Y,Z,V) )
          | ~ product(X,V,W) )
      | product(U,Z,W) ),
    inference(miniscoping,[status(esa)],[f4]) ).

fof(f14,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( ~ product(X0,X1,X2)
      | ~ product(X1,X3,X4)
      | ~ product(X0,X4,X5)
      | product(X2,X3,X5) ),
    inference(cnf_transformation,[status(esa)],[f13]) ).

fof(f15,plain,
    ! [X0] : product(X0,inverse(X0),identity),
    inference(cnf_transformation,[status(esa)],[f5]) ).

fof(f16,plain,
    ! [X0] : product(X0,identity,X0),
    inference(cnf_transformation,[status(esa)],[f6]) ).

fof(f17,plain,
    ! [X0] : ~ product(X0,a,identity),
    inference(cnf_transformation,[status(esa)],[f7]) ).

fof(f23,plain,
    ! [X0,X1,X2,X3] :
      ( ~ product(X0,X1,X2)
      | ~ product(X1,X3,a)
      | ~ product(X2,X3,identity) ),
    inference(resolution,[status(thm)],[f12,f17]) ).

fof(f36,plain,
    ! [X0,X1,X2,X3] :
      ( ~ product(X0,X1,X2)
      | ~ product(X0,X1,X3)
      | product(X2,identity,X3) ),
    inference(resolution,[status(thm)],[f14,f16]) ).

fof(f39,plain,
    ! [X0,X1,X2,X3] :
      ( ~ product(X0,X1,X2)
      | ~ product(X1,X3,identity)
      | product(X2,X3,X0) ),
    inference(resolution,[status(thm)],[f14,f16]) ).

fof(f43,plain,
    ! [X0,X1] :
      ( ~ product(X0,identity,X1)
      | product(X1,identity,X0) ),
    inference(resolution,[status(thm)],[f36,f16]) ).

fof(f70,plain,
    ! [X0] : product(multiply(X0,identity),identity,X0),
    inference(resolution,[status(thm)],[f8,f43]) ).

fof(f90,plain,
    ! [X0,X1,X2] :
      ( ~ product(X0,X1,X2)
      | product(X2,inverse(X1),X0) ),
    inference(resolution,[status(thm)],[f15,f39]) ).

fof(f144,plain,
    ! [X0] : product(identity,inverse(inverse(X0)),X0),
    inference(resolution,[status(thm)],[f90,f15]) ).

fof(f168,plain,
    ! [X0,X1] :
      ( ~ product(X0,identity,X1)
      | ~ product(X1,inverse(inverse(a)),identity) ),
    inference(resolution,[status(thm)],[f144,f23]) ).

fof(f426,plain,
    ! [X0] : ~ product(X0,identity,inverse(a)),
    inference(resolution,[status(thm)],[f168,f15]) ).

fof(f428,plain,
    $false,
    inference(resolution,[status(thm)],[f426,f70]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10  % Problem  : GRP031-2 : TPTP v8.1.2. Released v1.0.0.
% 0.05/0.11  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.32  % Computer : n004.cluster.edu
% 0.10/0.32  % Model    : x86_64 x86_64
% 0.10/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32  % Memory   : 8042.1875MB
% 0.10/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32  % CPULimit : 300
% 0.10/0.32  % WCLimit  : 300
% 0.10/0.32  % DateTime : Tue Apr 30 00:27:18 EDT 2024
% 0.10/0.32  % CPUTime  : 
% 0.10/0.32  % Drodi V3.6.0
% 0.16/0.46  % Refutation found
% 0.16/0.46  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.16/0.46  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.46  % Elapsed time: 0.140999 seconds
% 0.16/0.46  % CPU time: 1.044715 seconds
% 0.16/0.46  % Total memory used: 45.257 MB
% 0.16/0.46  % Net memory used: 41.152 MB
%------------------------------------------------------------------------------