TSTP Solution File: SYN334+1 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SYN334+1 : TPTP v8.1.2. Released v2.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n002.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 12:46:33 EDT 2023

% Result   : Theorem 0.11s 0.34s
% Output   : CNFRefutation 0.11s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :    1
% Syntax   : Number of formulae    :   25 (   4 unt;   0 def)
%            Number of atoms       :   96 (   0 equ)
%            Maximal formula atoms :   15 (   3 avg)
%            Number of connectives :  104 (  33   ~;  40   |;  14   &)
%                                         (   8 <=>;   8  =>;   0  <=;   1 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    1 (   1 usr;   0 con; 2-2 aty)
%            Number of variables   :   52 (;  46   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,conjecture,
    ? [X,Y] :
    ! [Z] :
      ( ( big_f(X,Y)
       => ( big_f(X,Z)
        <=> big_g(Y,Z) ) )
     => ( ( big_f(X,Y)
        <=> ( big_f(Z,Z)
           => big_g(Z,Z) ) )
       => ( big_g(X,Y)
        <=> big_g(Z,Z) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f2,negated_conjecture,
    ~ ? [X,Y] :
      ! [Z] :
        ( ( big_f(X,Y)
         => ( big_f(X,Z)
          <=> big_g(Y,Z) ) )
       => ( ( big_f(X,Y)
          <=> ( big_f(Z,Z)
             => big_g(Z,Z) ) )
         => ( big_g(X,Y)
          <=> big_g(Z,Z) ) ) ),
    inference(negated_conjecture,[status(cth)],[f1]) ).

fof(f3,plain,
    ! [X,Y] :
    ? [Z] :
      ( ( ~ big_f(X,Y)
        | ( big_f(X,Z)
        <=> big_g(Y,Z) ) )
      & ( big_f(X,Y)
      <=> ( ~ big_f(Z,Z)
          | big_g(Z,Z) ) )
      & ( big_g(X,Y)
      <~> big_g(Z,Z) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f2]) ).

fof(f4,plain,
    ! [X,Y] :
    ? [Z] :
      ( ( ~ big_f(X,Y)
        | ( ( ~ big_f(X,Z)
            | big_g(Y,Z) )
          & ( big_f(X,Z)
            | ~ big_g(Y,Z) ) ) )
      & ( ~ big_f(X,Y)
        | ~ big_f(Z,Z)
        | big_g(Z,Z) )
      & ( big_f(X,Y)
        | ( big_f(Z,Z)
          & ~ big_g(Z,Z) ) )
      & ( big_g(X,Y)
        | big_g(Z,Z) )
      & ( ~ big_g(X,Y)
        | ~ big_g(Z,Z) ) ),
    inference(NNF_transformation,[status(esa)],[f3]) ).

fof(f5,plain,
    ! [X,Y] :
      ( ( ~ big_f(X,Y)
        | ( ( ~ big_f(X,sk0_0(Y,X))
            | big_g(Y,sk0_0(Y,X)) )
          & ( big_f(X,sk0_0(Y,X))
            | ~ big_g(Y,sk0_0(Y,X)) ) ) )
      & ( ~ big_f(X,Y)
        | ~ big_f(sk0_0(Y,X),sk0_0(Y,X))
        | big_g(sk0_0(Y,X),sk0_0(Y,X)) )
      & ( big_f(X,Y)
        | ( big_f(sk0_0(Y,X),sk0_0(Y,X))
          & ~ big_g(sk0_0(Y,X),sk0_0(Y,X)) ) )
      & ( big_g(X,Y)
        | big_g(sk0_0(Y,X),sk0_0(Y,X)) )
      & ( ~ big_g(X,Y)
        | ~ big_g(sk0_0(Y,X),sk0_0(Y,X)) ) ),
    inference(skolemization,[status(esa)],[f4]) ).

fof(f6,plain,
    ! [X0,X1] :
      ( ~ big_f(X0,X1)
      | ~ big_f(X0,sk0_0(X1,X0))
      | big_g(X1,sk0_0(X1,X0)) ),
    inference(cnf_transformation,[status(esa)],[f5]) ).

fof(f7,plain,
    ! [X0,X1] :
      ( ~ big_f(X0,X1)
      | big_f(X0,sk0_0(X1,X0))
      | ~ big_g(X1,sk0_0(X1,X0)) ),
    inference(cnf_transformation,[status(esa)],[f5]) ).

fof(f8,plain,
    ! [X0,X1] :
      ( ~ big_f(X0,X1)
      | ~ big_f(sk0_0(X1,X0),sk0_0(X1,X0))
      | big_g(sk0_0(X1,X0),sk0_0(X1,X0)) ),
    inference(cnf_transformation,[status(esa)],[f5]) ).

fof(f9,plain,
    ! [X0,X1] :
      ( big_f(X0,X1)
      | big_f(sk0_0(X1,X0),sk0_0(X1,X0)) ),
    inference(cnf_transformation,[status(esa)],[f5]) ).

fof(f10,plain,
    ! [X0,X1] :
      ( big_f(X0,X1)
      | ~ big_g(sk0_0(X1,X0),sk0_0(X1,X0)) ),
    inference(cnf_transformation,[status(esa)],[f5]) ).

fof(f11,plain,
    ! [X0,X1] :
      ( big_g(X0,X1)
      | big_g(sk0_0(X1,X0),sk0_0(X1,X0)) ),
    inference(cnf_transformation,[status(esa)],[f5]) ).

fof(f12,plain,
    ! [X0,X1] :
      ( ~ big_g(X0,X1)
      | ~ big_g(sk0_0(X1,X0),sk0_0(X1,X0)) ),
    inference(cnf_transformation,[status(esa)],[f5]) ).

fof(f13,plain,
    ! [X0,X1] :
      ( big_g(X0,X1)
      | big_f(X0,X1) ),
    inference(resolution,[status(thm)],[f11,f10]) ).

fof(f14,plain,
    ! [X0,X1] :
      ( ~ big_f(X0,X1)
      | big_g(sk0_0(X1,X0),sk0_0(X1,X0)) ),
    inference(backward_subsumption_resolution,[status(thm)],[f8,f13]) ).

fof(f20,plain,
    ! [X0,X1] :
      ( ~ big_f(X0,X1)
      | big_f(X0,sk0_0(X1,X0))
      | big_f(X1,sk0_0(X1,X0)) ),
    inference(resolution,[status(thm)],[f7,f13]) ).

fof(f21,plain,
    ! [X0,X1] :
      ( big_f(sk0_0(X0,X1),sk0_0(sk0_0(X0,X1),sk0_0(X0,X1)))
      | big_f(sk0_0(X0,X1),sk0_0(sk0_0(X0,X1),sk0_0(X0,X1)))
      | big_f(X1,X0) ),
    inference(resolution,[status(thm)],[f20,f9]) ).

fof(f22,plain,
    ! [X0,X1] :
      ( big_f(sk0_0(X0,X1),sk0_0(sk0_0(X0,X1),sk0_0(X0,X1)))
      | big_f(X1,X0) ),
    inference(duplicate_literals_removal,[status(esa)],[f21]) ).

fof(f23,plain,
    ! [X0,X1] :
      ( big_f(X0,X1)
      | ~ big_f(sk0_0(X1,X0),sk0_0(X1,X0))
      | big_g(sk0_0(X1,X0),sk0_0(sk0_0(X1,X0),sk0_0(X1,X0))) ),
    inference(resolution,[status(thm)],[f22,f6]) ).

fof(f24,plain,
    ! [X0,X1] :
      ( big_f(X0,X1)
      | big_g(sk0_0(X1,X0),sk0_0(sk0_0(X1,X0),sk0_0(X1,X0))) ),
    inference(forward_subsumption_resolution,[status(thm)],[f23,f9]) ).

fof(f26,plain,
    ! [X0,X1] :
      ( big_f(X0,X1)
      | big_g(sk0_0(sk0_0(sk0_0(X1,X0),sk0_0(X1,X0)),sk0_0(X1,X0)),sk0_0(sk0_0(sk0_0(X1,X0),sk0_0(X1,X0)),sk0_0(X1,X0))) ),
    inference(resolution,[status(thm)],[f22,f14]) ).

fof(f35,plain,
    ! [X0,X1] :
      ( big_f(X0,X1)
      | ~ big_g(sk0_0(X1,X0),sk0_0(sk0_0(X1,X0),sk0_0(X1,X0))) ),
    inference(resolution,[status(thm)],[f26,f12]) ).

fof(f36,plain,
    ! [X0,X1] : big_f(X0,X1),
    inference(forward_subsumption_resolution,[status(thm)],[f35,f24]) ).

fof(f41,plain,
    ! [X0,X1] : big_g(sk0_0(X0,X1),sk0_0(X0,X1)),
    inference(backward_subsumption_resolution,[status(thm)],[f14,f36]) ).

fof(f42,plain,
    ! [X0,X1] : ~ big_g(X0,X1),
    inference(backward_subsumption_resolution,[status(thm)],[f12,f41]) ).

fof(f43,plain,
    $false,
    inference(backward_subsumption_resolution,[status(thm)],[f41,f42]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : SYN334+1 : TPTP v8.1.2. Released v2.0.0.
% 0.10/0.12  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.33  % Computer : n002.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit : 300
% 0.11/0.33  % WCLimit  : 300
% 0.11/0.33  % DateTime : Tue May 30 10:39:43 EDT 2023
% 0.11/0.33  % CPUTime  : 
% 0.11/0.33  % Drodi V3.5.1
% 0.11/0.34  % Refutation found
% 0.11/0.34  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.34  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/0.56  % Elapsed time: 0.010978 seconds
% 0.17/0.56  % CPU time: 0.014293 seconds
% 0.17/0.56  % Memory used: 517.620 KB
%------------------------------------------------------------------------------