%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : FLD002-3 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n015.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 20:16:17 EDT 2024

% Result   : Unsatisfiable 147.40s 18.90s
% Output   : CNFRefutation 147.40s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   36 (  17 unt;   0 def)
%            Number of atoms       :   67 (   0 equ)
%            Maximal formula atoms :    5 (   1 avg)
%            Number of connectives :   64 (  33   ~;  29   |;   0   &)
%                                         (   2 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   3 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    6 (   5 usr;   3 prp; 0-3 aty)
%            Number of functors    :    4 (   4 usr;   4 con; 0-0 aty)
%            Number of variables   :   36 (  36   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f3,axiom,
    ! [X] :
      ( sum(additive_identity,X,X)
      | ~ defined(X) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f8,axiom,
    ! [X] :
      ( product(multiplicative_identity,X,X)
      | ~ defined(X) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f10,axiom,
    ! [Y,X,Z] :
      ( product(Y,X,Z)
      | ~ product(X,Y,Z) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f11,axiom,
    ! [C,D,B,X,Y,A,Z] :
      ( sum(C,D,B)
      | ~ sum(X,Y,A)
      | ~ product(A,Z,B)
      | ~ product(X,Z,C)
      | ~ product(Y,Z,D) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f14,axiom,
    defined(additive_identity),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f27,hypothesis,
    defined(a),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f29,hypothesis,
    product(multiplicative_identity,a,b),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f30,negated_conjecture,
    ~ sum(additive_identity,a,b),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f35,plain,
    ! [X0] :
      ( sum(additive_identity,X0,X0)
      | ~ defined(X0) ),
    inference(cnf_transformation,[status(esa)],[f3]) ).

fof(f42,plain,
    ! [X0] :
      ( product(multiplicative_identity,X0,X0)
      | ~ defined(X0) ),
    inference(cnf_transformation,[status(esa)],[f8]) ).

fof(f44,plain,
    ! [X0,X1,X2] :
      ( product(X0,X1,X2)
      | ~ product(X1,X0,X2) ),
    inference(cnf_transformation,[status(esa)],[f10]) ).

fof(f45,plain,
    ! [D,Y,Z] :
      ( ! [C,X] :
          ( ! [B,A] :
              ( sum(C,D,B)
              | ~ sum(X,Y,A)
              | ~ product(A,Z,B) )
          | ~ product(X,Z,C) )
      | ~ product(Y,Z,D) ),
    inference(miniscoping,[status(esa)],[f11]) ).

fof(f46,plain,
    ! [X0,X1,X2,X3,X4,X5,X6] :
      ( sum(X0,X1,X2)
      | ~ sum(X3,X4,X5)
      | ~ product(X5,X6,X2)
      | ~ product(X3,X6,X0)
      | ~ product(X4,X6,X1) ),
    inference(cnf_transformation,[status(esa)],[f45]) ).

fof(f51,plain,
    defined(additive_identity),
    inference(cnf_transformation,[status(esa)],[f14]) ).

fof(f70,plain,
    defined(a),
    inference(cnf_transformation,[status(esa)],[f27]) ).

fof(f72,plain,
    product(multiplicative_identity,a,b),
    inference(cnf_transformation,[status(esa)],[f29]) ).

fof(f73,plain,
    ~ sum(additive_identity,a,b),
    inference(cnf_transformation,[status(esa)],[f30]) ).

fof(f76,plain,
    sum(additive_identity,a,a),
    inference(resolution,[status(thm)],[f35,f70]) ).

fof(f828,plain,
    product(multiplicative_identity,a,a),
    inference(resolution,[status(thm)],[f42,f70]) ).

fof(f829,plain,
    product(multiplicative_identity,additive_identity,additive_identity),
    inference(resolution,[status(thm)],[f42,f51]) ).

fof(f859,plain,
    product(a,multiplicative_identity,b),
    inference(resolution,[status(thm)],[f44,f72]) ).

fof(f1013,plain,
    product(a,multiplicative_identity,a),
    inference(resolution,[status(thm)],[f828,f44]) ).

fof(f1018,plain,
    product(additive_identity,multiplicative_identity,additive_identity),
    inference(resolution,[status(thm)],[f829,f44]) ).

fof(f1372,plain,
    ! [X0,X1,X2,X3] :
      ( ~ sum(X0,X1,X2)
      | ~ product(X2,X3,b)
      | ~ product(X0,X3,additive_identity)
      | ~ product(X1,X3,a) ),
    inference(resolution,[status(thm)],[f46,f73]) ).

fof(f1656,plain,
    ! [X0] :
      ( ~ product(a,X0,b)
      | ~ product(additive_identity,X0,additive_identity)
      | ~ product(a,X0,a) ),
    inference(resolution,[status(thm)],[f1372,f76]) ).

fof(f11760,plain,
    ( spl0_767
  <=> product(additive_identity,multiplicative_identity,additive_identity) ),
    introduced(split_symbol_definition) ).

fof(f11762,plain,
    ( ~ product(additive_identity,multiplicative_identity,additive_identity)
    | spl0_767 ),
    inference(component_clause,[status(thm)],[f11760]) ).

fof(f11785,plain,
    ( $false
    | spl0_767 ),
    inference(forward_subsumption_resolution,[status(thm)],[f11762,f1018]) ).

fof(f11786,plain,
    spl0_767,
    inference(contradiction_clause,[status(thm)],[f11785]) ).

fof(f32503,plain,
    ( spl0_1983
  <=> product(a,multiplicative_identity,a) ),
    introduced(split_symbol_definition) ).

fof(f32505,plain,
    ( ~ product(a,multiplicative_identity,a)
    | spl0_1983 ),
    inference(component_clause,[status(thm)],[f32503]) ).

fof(f32506,plain,
    ( ~ product(additive_identity,multiplicative_identity,additive_identity)
    | ~ product(a,multiplicative_identity,a) ),
    inference(resolution,[status(thm)],[f1656,f859]) ).

fof(f32507,plain,
    ( ~ spl0_767
    | ~ spl0_1983 ),
    inference(split_clause,[status(thm)],[f32506,f11760,f32503]) ).

fof(f32521,plain,
    ( $false
    | spl0_1983 ),
    inference(forward_subsumption_resolution,[status(thm)],[f32505,f1013]) ).

fof(f32522,plain,
    spl0_1983,
    inference(contradiction_clause,[status(thm)],[f32521]) ).

fof(f32523,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f11786,f32507,f32522]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem  : FLD002-3 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.11  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.31  % Computer : n015.cluster.edu
% 0.11/0.31  % Model    : x86_64 x86_64
% 0.11/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31  % Memory   : 8042.1875MB
% 0.11/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31  % CPULimit : 300
% 0.11/0.31  % WCLimit  : 300
% 0.11/0.31  % DateTime : Mon Apr 29 23:38:47 EDT 2024
% 0.11/0.31  % CPUTime  : 
% 0.11/0.32  % Drodi V3.6.0
% 147.40/18.90  % Refutation found
% 147.40/18.90  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 147.40/18.90  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 148.21/19.00  % Elapsed time: 18.671320 seconds
% 148.21/19.00  % CPU time: 148.160180 seconds
% 148.21/19.00  % Total memory used: 442.183 MB
% 148.21/19.00  % Net memory used: 429.555 MB
%------------------------------------------------------------------------------