TSTP Solution File: SET676+3 by Drodi---3.5.1

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%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SET676+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n020.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 12:35:00 EDT 2023

% Result   : Theorem 0.13s 0.37s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   20 (   5 unt;   0 def)
%            Number of atoms       :   50 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   53 (  23   ~;  19   |;   3   &)
%                                         (   2 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   26 (;  25   !;   1   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [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/sandbox/benchmark/theBenchmark.p') ).

fof(f4,axiom,
    ! [B] :
      ( ilf_type(B,set_type)
     => ! [C] :
          ( ilf_type(C,set_type)
         => ( ilf_type(C,identity_relation_of_type(B))
          <=> ilf_type(C,relation_type(B,B)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

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

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

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

fof(f22,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)],[f1]) ).

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

fof(f35,plain,
    ! [B] :
      ( ~ ilf_type(B,set_type)
      | ! [C] :
          ( ~ ilf_type(C,set_type)
          | ( ilf_type(C,identity_relation_of_type(B))
          <=> ilf_type(C,relation_type(B,B)) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f4]) ).

fof(f36,plain,
    ! [B] :
      ( ~ ilf_type(B,set_type)
      | ! [C] :
          ( ~ ilf_type(C,set_type)
          | ( ( ~ ilf_type(C,identity_relation_of_type(B))
              | ilf_type(C,relation_type(B,B)) )
            & ( ilf_type(C,identity_relation_of_type(B))
              | ~ ilf_type(C,relation_type(B,B)) ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f35]) ).

fof(f38,plain,
    ! [X0,X1] :
      ( ~ ilf_type(X0,set_type)
      | ~ ilf_type(X1,set_type)
      | ilf_type(X1,identity_relation_of_type(X0))
      | ~ ilf_type(X1,relation_type(X0,X0)) ),
    inference(cnf_transformation,[status(esa)],[f36]) ).

fof(f93,plain,
    ! [X0] : ilf_type(X0,set_type),
    inference(cnf_transformation,[status(esa)],[f19]) ).

fof(f94,plain,
    ? [B] :
      ( ilf_type(B,set_type)
      & ~ ilf_type(cross_product(B,B),identity_relation_of_type(B)) ),
    inference(pre_NNF_transformation,[status(esa)],[f21]) ).

fof(f95,plain,
    ( ilf_type(sk0_11,set_type)
    & ~ ilf_type(cross_product(sk0_11,sk0_11),identity_relation_of_type(sk0_11)) ),
    inference(skolemization,[status(esa)],[f94]) ).

fof(f97,plain,
    ~ ilf_type(cross_product(sk0_11,sk0_11),identity_relation_of_type(sk0_11)),
    inference(cnf_transformation,[status(esa)],[f95]) ).

fof(f100,plain,
    ! [X0,X1] :
      ( ~ ilf_type(X0,set_type)
      | ilf_type(X0,identity_relation_of_type(X1))
      | ~ ilf_type(X0,relation_type(X1,X1)) ),
    inference(forward_subsumption_resolution,[status(thm)],[f38,f93]) ).

fof(f110,plain,
    ! [X0,X1] :
      ( ~ ilf_type(X0,set_type)
      | ilf_type(cross_product(X1,X0),relation_type(X1,X0)) ),
    inference(forward_subsumption_resolution,[status(thm)],[f23,f93]) ).

fof(f111,plain,
    ! [X0] :
      ( ~ ilf_type(X0,set_type)
      | ~ ilf_type(cross_product(X0,X0),set_type)
      | ilf_type(cross_product(X0,X0),identity_relation_of_type(X0)) ),
    inference(resolution,[status(thm)],[f110,f100]) ).

fof(f112,plain,
    ! [X0] :
      ( ~ ilf_type(cross_product(X0,X0),set_type)
      | ilf_type(cross_product(X0,X0),identity_relation_of_type(X0)) ),
    inference(forward_subsumption_resolution,[status(thm)],[f111,f93]) ).

fof(f113,plain,
    ! [X0] : ilf_type(cross_product(X0,X0),identity_relation_of_type(X0)),
    inference(forward_subsumption_resolution,[status(thm)],[f112,f93]) ).

fof(f114,plain,
    $false,
    inference(backward_subsumption_resolution,[status(thm)],[f97,f113]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SET676+3 : TPTP v8.1.2. Released v2.2.0.
% 0.07/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34  % Computer : n020.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 10:16:58 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.13/0.35  % Drodi V3.5.1
% 0.13/0.37  % Refutation found
% 0.13/0.37  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.37  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.37  % Elapsed time: 0.023177 seconds
% 0.13/0.37  % CPU time: 0.032405 seconds
% 0.13/0.37  % Memory used: 11.731 MB
%------------------------------------------------------------------------------