TSTP Solution File: GRP012-3 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : GRP012-3 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n019.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 20:18:46 EDT 2024

% Result   : Unsatisfiable 0.18s 0.42s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   36 (  25 unt;   0 def)
%            Number of atoms       :   57 (  17 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   45 (  24   ~;  21   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-3 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   80 (  80   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X] : product(identity,X,X),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f2,axiom,
    ! [X] : product(X,identity,X),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f3,axiom,
    ! [X] : product(inverse(X),X,identity),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

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

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

fof(f7,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/sandbox2/benchmark/theBenchmark.p') ).

fof(f9,negated_conjecture,
    inverse(multiply(a,b)) != multiply(inverse(b),inverse(a)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f10,plain,
    ! [X0] : product(identity,X0,X0),
    inference(cnf_transformation,[status(esa)],[f1]) ).

fof(f11,plain,
    ! [X0] : product(X0,identity,X0),
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f12,plain,
    ! [X0] : product(inverse(X0),X0,identity),
    inference(cnf_transformation,[status(esa)],[f3]) ).

fof(f14,plain,
    ! [X0,X1] : product(X0,X1,multiply(X0,X1)),
    inference(cnf_transformation,[status(esa)],[f5]) ).

fof(f15,plain,
    ! [Z,W] :
      ( ! [X,Y] :
          ( ~ product(X,Y,Z)
          | ~ product(X,Y,W) )
      | Z = W ),
    inference(miniscoping,[status(esa)],[f6]) ).

fof(f16,plain,
    ! [X0,X1,X2,X3] :
      ( ~ product(X0,X1,X2)
      | ~ product(X0,X1,X3)
      | X2 = X3 ),
    inference(cnf_transformation,[status(esa)],[f15]) ).

fof(f17,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)],[f7]) ).

fof(f18,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)],[f17]) ).

fof(f21,plain,
    inverse(multiply(a,b)) != multiply(inverse(b),inverse(a)),
    inference(cnf_transformation,[status(esa)],[f9]) ).

fof(f25,plain,
    ! [X0,X1] :
      ( ~ product(X0,identity,X1)
      | X0 = X1 ),
    inference(resolution,[status(thm)],[f16,f11]) ).

fof(f26,plain,
    ! [X0,X1,X2] :
      ( ~ product(X0,X1,X2)
      | multiply(X0,X1) = X2 ),
    inference(resolution,[status(thm)],[f16,f14]) ).

fof(f27,plain,
    ! [X0] : multiply(inverse(X0),X0) = identity,
    inference(resolution,[status(thm)],[f26,f12]) ).

fof(f28,plain,
    ! [X0] : multiply(identity,X0) = X0,
    inference(resolution,[status(thm)],[f26,f10]) ).

fof(f51,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ product(X0,X1,X2)
      | ~ product(multiply(X3,X0),X1,X4)
      | product(X3,X2,X4) ),
    inference(resolution,[status(thm)],[f18,f14]) ).

fof(f52,plain,
    ! [X0,X1,X2] :
      ( ~ product(multiply(X0,inverse(X1)),X1,X2)
      | product(X0,identity,X2) ),
    inference(resolution,[status(thm)],[f51,f12]) ).

fof(f56,plain,
    ! [X0,X1,X2,X3] :
      ( ~ product(multiply(X0,X1),X2,X3)
      | product(X0,multiply(X1,X2),X3) ),
    inference(resolution,[status(thm)],[f51,f14]) ).

fof(f111,plain,
    ! [X0,X1] : product(X0,identity,multiply(multiply(X0,inverse(X1)),X1)),
    inference(resolution,[status(thm)],[f52,f14]) ).

fof(f147,plain,
    ! [X0,X1] : X0 = multiply(multiply(X0,inverse(X1)),X1),
    inference(resolution,[status(thm)],[f111,f25]) ).

fof(f172,plain,
    ! [X0] : inverse(inverse(X0)) = multiply(identity,X0),
    inference(paramodulation,[status(thm)],[f27,f147]) ).

fof(f173,plain,
    ! [X0] : inverse(inverse(X0)) = X0,
    inference(forward_demodulation,[status(thm)],[f28,f172]) ).

fof(f200,plain,
    ! [X0,X1] : X0 = multiply(multiply(X0,X1),inverse(X1)),
    inference(paramodulation,[status(thm)],[f173,f147]) ).

fof(f340,plain,
    ! [X0,X1,X2] : product(X0,multiply(X1,X2),multiply(multiply(X0,X1),X2)),
    inference(resolution,[status(thm)],[f56,f14]) ).

fof(f419,plain,
    ! [X0,X1] : product(inverse(X0),multiply(X0,X1),multiply(identity,X1)),
    inference(paramodulation,[status(thm)],[f27,f340]) ).

fof(f420,plain,
    ! [X0,X1] : product(inverse(X0),multiply(X0,X1),X1),
    inference(forward_demodulation,[status(thm)],[f28,f419]) ).

fof(f436,plain,
    ! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
    inference(resolution,[status(thm)],[f420,f26]) ).

fof(f480,plain,
    ! [X0,X1] : multiply(inverse(multiply(X0,X1)),X0) = inverse(X1),
    inference(paramodulation,[status(thm)],[f200,f436]) ).

fof(f676,plain,
    ! [X0,X1] : multiply(inverse(X0),inverse(X1)) = inverse(multiply(X1,X0)),
    inference(paramodulation,[status(thm)],[f436,f480]) ).

fof(f1668,plain,
    inverse(multiply(a,b)) != inverse(multiply(a,b)),
    inference(backward_demodulation,[status(thm)],[f676,f21]) ).

fof(f1669,plain,
    $false,
    inference(trivial_equality_resolution,[status(esa)],[f1668]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.13  % Problem  : GRP012-3 : TPTP v8.1.2. Released v1.0.0.
% 0.06/0.14  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.35  % Computer : n019.cluster.edu
% 0.10/0.35  % Model    : x86_64 x86_64
% 0.10/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35  % Memory   : 8042.1875MB
% 0.10/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.35  % CPULimit : 300
% 0.10/0.35  % WCLimit  : 300
% 0.10/0.35  % DateTime : Tue Apr 30 00:28:29 EDT 2024
% 0.10/0.35  % CPUTime  : 
% 0.10/0.36  % Drodi V3.6.0
% 0.18/0.42  % Refutation found
% 0.18/0.42  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.18/0.42  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.18/0.43  % Elapsed time: 0.076944 seconds
% 0.18/0.43  % CPU time: 0.482180 seconds
% 0.18/0.43  % Total memory used: 25.364 MB
% 0.18/0.43  % Net memory used: 23.974 MB
%------------------------------------------------------------------------------