TSTP Solution File: GRP001+6 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : GRP001+6 : TPTP v8.1.2. Released v3.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n022.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 12:09:38 EDT 2023

% Result   : Theorem 0.19s 0.49s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    1
% Syntax   : Number of formulae    :   20 (   9 unt;   0 def)
%            Number of atoms       :  107 (   0 equ)
%            Maximal formula atoms :   16 (   5 avg)
%            Number of connectives :  122 (  35   ~;  30   |;  47   &)
%                                         (   0 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   7 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-3 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :  144 (; 132   !;  12   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,conjecture,
    ! [E] :
      ( ( ! [X,Y] :
          ? [Z] : product(X,Y,Z)
        & ! [X,Y,Z,U,V,W] :
            ( ( product(X,Y,U)
              & product(Y,Z,V)
              & product(U,Z,W) )
           => product(X,V,W) )
        & ! [X,Y,Z,U,V,W] :
            ( ( product(X,Y,U)
              & product(Y,Z,V)
              & product(X,V,W) )
           => product(U,Z,W) )
        & ! [X] : product(X,E,X)
        & ! [X] : product(E,X,X)
        & ! [X] : product(X,inverse(X),E)
        & ! [X] : product(inverse(X),X,E) )
     => ( ! [X] : product(X,X,E)
       => ! [U,V,W] :
            ( product(U,V,W)
           => product(V,U,W) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f2,negated_conjecture,
    ~ ! [E] :
        ( ( ! [X,Y] :
            ? [Z] : product(X,Y,Z)
          & ! [X,Y,Z,U,V,W] :
              ( ( product(X,Y,U)
                & product(Y,Z,V)
                & product(U,Z,W) )
             => product(X,V,W) )
          & ! [X,Y,Z,U,V,W] :
              ( ( product(X,Y,U)
                & product(Y,Z,V)
                & product(X,V,W) )
             => product(U,Z,W) )
          & ! [X] : product(X,E,X)
          & ! [X] : product(E,X,X)
          & ! [X] : product(X,inverse(X),E)
          & ! [X] : product(inverse(X),X,E) )
       => ( ! [X] : product(X,X,E)
         => ! [U,V,W] :
              ( product(U,V,W)
             => product(V,U,W) ) ) ),
    inference(negated_conjecture,[status(cth)],[f1]) ).

fof(f3,plain,
    ? [E] :
      ( ! [X,Y] :
        ? [Z] : product(X,Y,Z)
      & ! [X,Y,Z,U,V,W] :
          ( ~ product(X,Y,U)
          | ~ product(Y,Z,V)
          | ~ product(U,Z,W)
          | product(X,V,W) )
      & ! [X,Y,Z,U,V,W] :
          ( ~ product(X,Y,U)
          | ~ product(Y,Z,V)
          | ~ product(X,V,W)
          | product(U,Z,W) )
      & ! [X] : product(X,E,X)
      & ! [X] : product(E,X,X)
      & ! [X] : product(X,inverse(X),E)
      & ! [X] : product(inverse(X),X,E)
      & ! [X] : product(X,X,E)
      & ? [U,V,W] :
          ( product(U,V,W)
          & ~ product(V,U,W) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f2]) ).

fof(f4,plain,
    ? [E] :
      ( ! [X,Y] :
        ? [Z] : product(X,Y,Z)
      & ! [X,V,W] :
          ( ! [Z,U] :
              ( ! [Y] :
                  ( ~ product(X,Y,U)
                  | ~ product(Y,Z,V) )
              | ~ product(U,Z,W) )
          | product(X,V,W) )
      & ! [Z,U,W] :
          ( ! [X,V] :
              ( ! [Y] :
                  ( ~ product(X,Y,U)
                  | ~ product(Y,Z,V) )
              | ~ product(X,V,W) )
          | product(U,Z,W) )
      & ! [X] : product(X,E,X)
      & ! [X] : product(E,X,X)
      & ! [X] : product(X,inverse(X),E)
      & ! [X] : product(inverse(X),X,E)
      & ! [X] : product(X,X,E)
      & ? [U,V,W] :
          ( product(U,V,W)
          & ~ product(V,U,W) ) ),
    inference(miniscoping,[status(esa)],[f3]) ).

fof(f5,plain,
    ( ! [X,Y] : product(X,Y,sk0_1(Y,X))
    & ! [X,V,W] :
        ( ! [Z,U] :
            ( ! [Y] :
                ( ~ product(X,Y,U)
                | ~ product(Y,Z,V) )
            | ~ product(U,Z,W) )
        | product(X,V,W) )
    & ! [Z,U,W] :
        ( ! [X,V] :
            ( ! [Y] :
                ( ~ product(X,Y,U)
                | ~ product(Y,Z,V) )
            | ~ product(X,V,W) )
        | product(U,Z,W) )
    & ! [X] : product(X,sk0_0,X)
    & ! [X] : product(sk0_0,X,X)
    & ! [X] : product(X,inverse(X),sk0_0)
    & ! [X] : product(inverse(X),X,sk0_0)
    & ! [X] : product(X,X,sk0_0)
    & product(sk0_2,sk0_3,sk0_4)
    & ~ product(sk0_3,sk0_2,sk0_4) ),
    inference(skolemization,[status(esa)],[f4]) ).

fof(f7,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)],[f5]) ).

fof(f8,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)],[f5]) ).

fof(f9,plain,
    ! [X0] : product(X0,sk0_0,X0),
    inference(cnf_transformation,[status(esa)],[f5]) ).

fof(f10,plain,
    ! [X0] : product(sk0_0,X0,X0),
    inference(cnf_transformation,[status(esa)],[f5]) ).

fof(f13,plain,
    ! [X0] : product(X0,X0,sk0_0),
    inference(cnf_transformation,[status(esa)],[f5]) ).

fof(f14,plain,
    product(sk0_2,sk0_3,sk0_4),
    inference(cnf_transformation,[status(esa)],[f5]) ).

fof(f15,plain,
    ~ product(sk0_3,sk0_2,sk0_4),
    inference(cnf_transformation,[status(esa)],[f5]) ).

fof(f25,plain,
    ! [X0,X1,X2,X3] :
      ( ~ product(X0,X1,sk0_0)
      | ~ product(X1,X2,X3)
      | product(X0,X3,X2) ),
    inference(resolution,[status(thm)],[f7,f10]) ).

fof(f69,plain,
    ! [X0,X1,X2,X3] :
      ( ~ product(X0,X1,X2)
      | ~ product(X0,sk0_0,X3)
      | product(X2,X1,X3) ),
    inference(resolution,[status(thm)],[f8,f13]) ).

fof(f423,plain,
    ! [X0,X1,X2] :
      ( ~ product(X0,X1,X2)
      | product(X0,X2,X1) ),
    inference(resolution,[status(thm)],[f25,f13]) ).

fof(f481,plain,
    product(sk0_2,sk0_4,sk0_3),
    inference(resolution,[status(thm)],[f423,f14]) ).

fof(f2251,plain,
    ! [X0,X1,X2] :
      ( ~ product(X0,X1,X2)
      | product(X2,X1,X0) ),
    inference(resolution,[status(thm)],[f69,f9]) ).

fof(f2344,plain,
    product(sk0_3,sk0_4,sk0_2),
    inference(resolution,[status(thm)],[f2251,f481]) ).

fof(f2449,plain,
    product(sk0_3,sk0_2,sk0_4),
    inference(resolution,[status(thm)],[f2344,f423]) ).

fof(f2450,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[f2449,f15]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GRP001+6 : TPTP v8.1.2. Released v3.1.0.
% 0.07/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34  % Computer : n022.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Tue May 30 11:26:57 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  % Drodi V3.5.1
% 0.19/0.49  % Refutation found
% 0.19/0.49  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.19/0.49  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/0.50  % Elapsed time: 0.161620 seconds
% 0.19/0.50  % CPU time: 1.190734 seconds
% 0.19/0.50  % Memory used: 40.002 MB
%------------------------------------------------------------------------------