TSTP Solution File: CAT002-1 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : CAT002-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n023.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 20:13:15 EDT 2024

% Result   : Unsatisfiable 4.59s 0.87s
% Output   : CNFRefutation 4.59s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   43 (  20 unt;   0 def)
%            Number of atoms       :   82 (  12 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   80 (  41   ~;  39   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   6 con; 0-2 aty)
%            Number of variables   :   69 (  69   !;   0   ?)

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

fof(f2,axiom,
    ! [X,Y,Z] :
      ( ~ product(X,Y,Z)
      | defined(X,Y) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

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

fof(f5,axiom,
    ! [X,Y,Xy,Z,Xyz,Yz] :
      ( ~ product(X,Y,Xy)
      | ~ product(Xy,Z,Xyz)
      | ~ product(Y,Z,Yz)
      | product(X,Yz,Xyz) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f19,hypothesis,
    ! [X,W,Y] :
      ( ~ product(a,X,W)
      | ~ product(a,Y,W)
      | X = Y ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f20,hypothesis,
    ! [X,W,Y] :
      ( ~ product(b,X,W)
      | ~ product(b,Y,W)
      | X = Y ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f21,hypothesis,
    product(a,b,c),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f22,hypothesis,
    product(c,h,d),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f23,hypothesis,
    product(c,g,d),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f24,negated_conjecture,
    h != g,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f25,plain,
    ! [X0,X1] :
      ( ~ defined(X0,X1)
      | product(X0,X1,compose(X0,X1)) ),
    inference(cnf_transformation,[status(esa)],[f1]) ).

fof(f26,plain,
    ! [X,Y] :
      ( ! [Z] : ~ product(X,Y,Z)
      | defined(X,Y) ),
    inference(miniscoping,[status(esa)],[f2]) ).

fof(f27,plain,
    ! [X0,X1,X2] :
      ( ~ product(X0,X1,X2)
      | defined(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f26]) ).

fof(f28,plain,
    ! [Y,Z] :
      ( ! [Xy] :
          ( ! [X] : ~ product(X,Y,Xy)
          | ~ defined(Xy,Z) )
      | defined(Y,Z) ),
    inference(miniscoping,[status(esa)],[f3]) ).

fof(f29,plain,
    ! [X0,X1,X2,X3] :
      ( ~ product(X0,X1,X2)
      | ~ defined(X2,X3)
      | defined(X1,X3) ),
    inference(cnf_transformation,[status(esa)],[f28]) ).

fof(f32,plain,
    ! [X,Xyz,Yz] :
      ( ! [Y,Z] :
          ( ! [Xy] :
              ( ~ product(X,Y,Xy)
              | ~ product(Xy,Z,Xyz) )
          | ~ product(Y,Z,Yz) )
      | product(X,Yz,Xyz) ),
    inference(miniscoping,[status(esa)],[f5]) ).

fof(f33,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( ~ product(X0,X1,X2)
      | ~ product(X2,X3,X4)
      | ~ product(X1,X3,X5)
      | product(X0,X5,X4) ),
    inference(cnf_transformation,[status(esa)],[f32]) ).

fof(f52,plain,
    ! [X,Y] :
      ( ! [W] :
          ( ~ product(a,X,W)
          | ~ product(a,Y,W) )
      | X = Y ),
    inference(miniscoping,[status(esa)],[f19]) ).

fof(f53,plain,
    ! [X0,X1,X2] :
      ( ~ product(a,X0,X1)
      | ~ product(a,X2,X1)
      | X0 = X2 ),
    inference(cnf_transformation,[status(esa)],[f52]) ).

fof(f54,plain,
    ! [X,Y] :
      ( ! [W] :
          ( ~ product(b,X,W)
          | ~ product(b,Y,W) )
      | X = Y ),
    inference(miniscoping,[status(esa)],[f20]) ).

fof(f55,plain,
    ! [X0,X1,X2] :
      ( ~ product(b,X0,X1)
      | ~ product(b,X2,X1)
      | X0 = X2 ),
    inference(cnf_transformation,[status(esa)],[f54]) ).

fof(f56,plain,
    product(a,b,c),
    inference(cnf_transformation,[status(esa)],[f21]) ).

fof(f57,plain,
    product(c,h,d),
    inference(cnf_transformation,[status(esa)],[f22]) ).

fof(f58,plain,
    product(c,g,d),
    inference(cnf_transformation,[status(esa)],[f23]) ).

fof(f59,plain,
    h != g,
    inference(cnf_transformation,[status(esa)],[f24]) ).

fof(f64,plain,
    defined(c,g),
    inference(resolution,[status(thm)],[f27,f58]) ).

fof(f65,plain,
    defined(c,h),
    inference(resolution,[status(thm)],[f27,f57]) ).

fof(f71,plain,
    ! [X0] :
      ( ~ defined(c,X0)
      | defined(b,X0) ),
    inference(resolution,[status(thm)],[f29,f56]) ).

fof(f80,plain,
    defined(b,h),
    inference(resolution,[status(thm)],[f71,f65]) ).

fof(f81,plain,
    defined(b,g),
    inference(resolution,[status(thm)],[f71,f64]) ).

fof(f83,plain,
    product(b,h,compose(b,h)),
    inference(resolution,[status(thm)],[f80,f25]) ).

fof(f84,plain,
    product(b,g,compose(b,g)),
    inference(resolution,[status(thm)],[f81,f25]) ).

fof(f118,plain,
    ! [X0,X1,X2] :
      ( ~ product(c,X0,X1)
      | ~ product(b,X0,X2)
      | product(a,X2,X1) ),
    inference(resolution,[status(thm)],[f33,f56]) ).

fof(f1470,plain,
    ! [X0] :
      ( ~ product(b,X0,compose(b,h))
      | h = X0 ),
    inference(resolution,[status(thm)],[f55,f83]) ).

fof(f2322,plain,
    ! [X0] :
      ( ~ product(b,g,X0)
      | product(a,X0,d) ),
    inference(resolution,[status(thm)],[f118,f58]) ).

fof(f2323,plain,
    ! [X0] :
      ( ~ product(b,h,X0)
      | product(a,X0,d) ),
    inference(resolution,[status(thm)],[f118,f57]) ).

fof(f2638,plain,
    product(a,compose(b,g),d),
    inference(resolution,[status(thm)],[f2322,f84]) ).

fof(f2972,plain,
    product(a,compose(b,h),d),
    inference(resolution,[status(thm)],[f2323,f83]) ).

fof(f8135,plain,
    ! [X0] :
      ( ~ product(a,X0,d)
      | compose(b,g) = X0 ),
    inference(resolution,[status(thm)],[f2638,f53]) ).

fof(f16087,plain,
    compose(b,g) = compose(b,h),
    inference(resolution,[status(thm)],[f8135,f2972]) ).

fof(f16106,plain,
    product(b,g,compose(b,h)),
    inference(backward_demodulation,[status(thm)],[f16087,f84]) ).

fof(f16108,plain,
    h = g,
    inference(resolution,[status(thm)],[f16106,f1470]) ).

fof(f16109,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[f16108,f59]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.07  % Problem  : CAT002-1 : TPTP v8.1.2. Released v1.0.0.
% 0.06/0.07  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.07/0.26  % Computer : n023.cluster.edu
% 0.07/0.26  % Model    : x86_64 x86_64
% 0.07/0.26  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.26  % Memory   : 8042.1875MB
% 0.07/0.26  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.07/0.26  % CPULimit : 300
% 0.07/0.26  % WCLimit  : 300
% 0.07/0.26  % DateTime : Mon Apr 29 22:28:25 EDT 2024
% 0.07/0.26  % CPUTime  : 
% 0.07/0.26  % Drodi V3.6.0
% 4.59/0.87  % Refutation found
% 4.59/0.87  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 4.59/0.87  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 4.59/0.89  % Elapsed time: 0.626395 seconds
% 4.59/0.89  % CPU time: 4.909345 seconds
% 4.59/0.89  % Total memory used: 104.227 MB
% 4.59/0.89  % Net memory used: 96.775 MB
%------------------------------------------------------------------------------