TSTP Solution File: SET643+3 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SET643+3 : TPTP v8.1.2. Released v2.2.0.
% 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 12:34:54 EDT 2023

% Result   : Theorem 0.21s 0.60s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   19 (   6 unt;   0 def)
%            Number of atoms       :   48 (   0 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :   49 (  20   ~;  16   |;   4   &)
%                                         (   0 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   30 (;  28   !;   2   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [B] :
      ( ilf_type(B,set_type)
     => ! [C] :
          ( ilf_type(C,set_type)
         => ! [D] :
              ( ilf_type(D,set_type)
             => ( subset(B,cross_product(C,D))
               => ilf_type(B,relation_type(C,D)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f10,axiom,
    ! [B] :
      ( ilf_type(B,set_type)
     => subset(B,B) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f19,axiom,
    ! [B] : ilf_type(B,set_type),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f20,conjecture,
    ! [B] :
      ( ilf_type(B,set_type)
     => ! [C] :
          ( ilf_type(C,set_type)
         => ilf_type(cross_product(B,C),relation_type(B,C)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f21,negated_conjecture,
    ~ ! [B] :
        ( ilf_type(B,set_type)
       => ! [C] :
            ( ilf_type(C,set_type)
           => ilf_type(cross_product(B,C),relation_type(B,C)) ) ),
    inference(negated_conjecture,[status(cth)],[f20]) ).

fof(f22,plain,
    ! [B] :
      ( ~ ilf_type(B,set_type)
      | ! [C] :
          ( ~ ilf_type(C,set_type)
          | ! [D] :
              ( ~ ilf_type(D,set_type)
              | ~ subset(B,cross_product(C,D))
              | ilf_type(B,relation_type(C,D)) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f1]) ).

fof(f23,plain,
    ! [X0,X1,X2] :
      ( ~ ilf_type(X0,set_type)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X2,set_type)
      | ~ subset(X0,cross_product(X1,X2))
      | ilf_type(X0,relation_type(X1,X2)) ),
    inference(cnf_transformation,[status(esa)],[f22]) ).

fof(f57,plain,
    ! [B] :
      ( ~ ilf_type(B,set_type)
      | subset(B,B) ),
    inference(pre_NNF_transformation,[status(esa)],[f10]) ).

fof(f58,plain,
    ! [X0] :
      ( ~ ilf_type(X0,set_type)
      | subset(X0,X0) ),
    inference(cnf_transformation,[status(esa)],[f57]) ).

fof(f95,plain,
    ! [X0] : ilf_type(X0,set_type),
    inference(cnf_transformation,[status(esa)],[f19]) ).

fof(f96,plain,
    ? [B] :
      ( ilf_type(B,set_type)
      & ? [C] :
          ( ilf_type(C,set_type)
          & ~ ilf_type(cross_product(B,C),relation_type(B,C)) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f21]) ).

fof(f97,plain,
    ( ilf_type(sk0_11,set_type)
    & ilf_type(sk0_12,set_type)
    & ~ ilf_type(cross_product(sk0_11,sk0_12),relation_type(sk0_11,sk0_12)) ),
    inference(skolemization,[status(esa)],[f96]) ).

fof(f100,plain,
    ~ ilf_type(cross_product(sk0_11,sk0_12),relation_type(sk0_11,sk0_12)),
    inference(cnf_transformation,[status(esa)],[f97]) ).

fof(f102,plain,
    ! [X0,X1,X2] :
      ( ~ ilf_type(X0,set_type)
      | ~ ilf_type(X1,set_type)
      | ~ subset(X2,cross_product(X0,X1))
      | ilf_type(X2,relation_type(X0,X1)) ),
    inference(forward_subsumption_resolution,[status(thm)],[f23,f95]) ).

fof(f105,plain,
    ! [X0] : subset(X0,X0),
    inference(forward_subsumption_resolution,[status(thm)],[f58,f95]) ).

fof(f106,plain,
    ! [X0,X1] :
      ( ~ ilf_type(X0,set_type)
      | ~ ilf_type(X1,set_type)
      | ilf_type(cross_product(X0,X1),relation_type(X0,X1)) ),
    inference(resolution,[status(thm)],[f105,f102]) ).

fof(f107,plain,
    ! [X0,X1] :
      ( ~ ilf_type(X0,set_type)
      | ilf_type(cross_product(X1,X0),relation_type(X1,X0)) ),
    inference(forward_subsumption_resolution,[status(thm)],[f106,f95]) ).

fof(f108,plain,
    ! [X0,X1] : ilf_type(cross_product(X0,X1),relation_type(X0,X1)),
    inference(forward_subsumption_resolution,[status(thm)],[f107,f95]) ).

fof(f109,plain,
    $false,
    inference(backward_subsumption_resolution,[status(thm)],[f100,f108]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SET643+3 : TPTP v8.1.2. Released v2.2.0.
% 0.11/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.35  % Computer : n022.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Tue May 30 10:13:42 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.13/0.36  % Drodi V3.5.1
% 0.21/0.60  % Refutation found
% 0.21/0.60  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.21/0.60  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.21/0.60  % Elapsed time: 0.033010 seconds
% 0.21/0.60  % CPU time: 0.023375 seconds
% 0.21/0.60  % Memory used: 2.956 MB
%------------------------------------------------------------------------------