%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : FLD059-4 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n014.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 20:16:32 EDT 2024

% Result   : Unsatisfiable 0.20s 0.39s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   40 (  14 unt;   0 def)
%            Number of atoms       :   76 (   0 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   69 (  33   ~;  32   |;   0   &)
%                                         (   4 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   3 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    8 (   7 usr;   5 prp; 0-3 aty)
%            Number of functors    :    4 (   4 usr;   4 con; 0-0 aty)
%            Number of variables   :   31 (  31   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f3,axiom,
    ! [X] :
      ( sum(additive_identity,X,X)
      | ~ defined(X) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f17,axiom,
    defined(multiplicative_identity),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f22,axiom,
    ! [X,Z,Y] :
      ( less_or_equal(X,Z)
      | ~ less_or_equal(X,Y)
      | ~ less_or_equal(Y,Z) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f24,axiom,
    ! [U,V,X,Y,Z] :
      ( less_or_equal(U,V)
      | ~ less_or_equal(X,Y)
      | ~ sum(X,Z,U)
      | ~ sum(Y,Z,V) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f27,hypothesis,
    defined(a),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f29,negated_conjecture,
    less_or_equal(additive_identity,a),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f30,negated_conjecture,
    sum(a,a,u),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f31,negated_conjecture,
    ~ less_or_equal(additive_identity,u),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f36,plain,
    ! [X0] :
      ( sum(additive_identity,X0,X0)
      | ~ defined(X0) ),
    inference(cnf_transformation,[status(esa)],[f3]) ).

fof(f56,plain,
    defined(multiplicative_identity),
    inference(cnf_transformation,[status(esa)],[f17]) ).

fof(f63,plain,
    ! [Z,Y] :
      ( ! [X] :
          ( less_or_equal(X,Z)
          | ~ less_or_equal(X,Y) )
      | ~ less_or_equal(Y,Z) ),
    inference(miniscoping,[status(esa)],[f22]) ).

fof(f64,plain,
    ! [X0,X1,X2] :
      ( less_or_equal(X0,X1)
      | ~ less_or_equal(X0,X2)
      | ~ less_or_equal(X2,X1) ),
    inference(cnf_transformation,[status(esa)],[f63]) ).

fof(f67,plain,
    ! [V,Y,Z] :
      ( ! [U,X] :
          ( less_or_equal(U,V)
          | ~ less_or_equal(X,Y)
          | ~ sum(X,Z,U) )
      | ~ sum(Y,Z,V) ),
    inference(miniscoping,[status(esa)],[f24]) ).

fof(f68,plain,
    ! [X0,X1,X2,X3,X4] :
      ( less_or_equal(X0,X1)
      | ~ less_or_equal(X2,X3)
      | ~ sum(X2,X4,X0)
      | ~ sum(X3,X4,X1) ),
    inference(cnf_transformation,[status(esa)],[f67]) ).

fof(f71,plain,
    defined(a),
    inference(cnf_transformation,[status(esa)],[f27]) ).

fof(f73,plain,
    less_or_equal(additive_identity,a),
    inference(cnf_transformation,[status(esa)],[f29]) ).

fof(f74,plain,
    sum(a,a,u),
    inference(cnf_transformation,[status(esa)],[f30]) ).

fof(f75,plain,
    ~ less_or_equal(additive_identity,u),
    inference(cnf_transformation,[status(esa)],[f31]) ).

fof(f76,plain,
    ! [X0] :
      ( less_or_equal(additive_identity,X0)
      | ~ less_or_equal(a,X0) ),
    inference(resolution,[status(thm)],[f64,f73]) ).

fof(f81,plain,
    ( spl0_0
  <=> less_or_equal(additive_identity,u) ),
    introduced(split_symbol_definition) ).

fof(f82,plain,
    ( less_or_equal(additive_identity,u)
    | ~ spl0_0 ),
    inference(component_clause,[status(thm)],[f81]) ).

fof(f108,plain,
    ( $false
    | ~ spl0_0 ),
    inference(forward_subsumption_resolution,[status(thm)],[f82,f75]) ).

fof(f109,plain,
    ~ spl0_0,
    inference(contradiction_clause,[status(thm)],[f108]) ).

fof(f113,plain,
    ( spl0_6
  <=> defined(a) ),
    introduced(split_symbol_definition) ).

fof(f115,plain,
    ( ~ defined(a)
    | spl0_6 ),
    inference(component_clause,[status(thm)],[f113]) ).

fof(f127,plain,
    ( $false
    | spl0_6 ),
    inference(forward_subsumption_resolution,[status(thm)],[f115,f71]) ).

fof(f128,plain,
    spl0_6,
    inference(contradiction_clause,[status(thm)],[f127]) ).

fof(f130,plain,
    ! [X0,X1,X2] :
      ( less_or_equal(X0,X1)
      | ~ sum(additive_identity,X2,X0)
      | ~ sum(a,X2,X1) ),
    inference(resolution,[status(thm)],[f68,f73]) ).

fof(f173,plain,
    ( spl0_14
  <=> defined(multiplicative_identity) ),
    introduced(split_symbol_definition) ).

fof(f175,plain,
    ( ~ defined(multiplicative_identity)
    | spl0_14 ),
    inference(component_clause,[status(thm)],[f173]) ).

fof(f182,plain,
    ( $false
    | spl0_14 ),
    inference(forward_subsumption_resolution,[status(thm)],[f175,f56]) ).

fof(f183,plain,
    spl0_14,
    inference(contradiction_clause,[status(thm)],[f182]) ).

fof(f184,plain,
    ! [X0] :
      ( less_or_equal(X0,u)
      | ~ sum(additive_identity,a,X0) ),
    inference(resolution,[status(thm)],[f130,f74]) ).

fof(f193,plain,
    ( spl0_16
  <=> sum(additive_identity,a,a) ),
    introduced(split_symbol_definition) ).

fof(f195,plain,
    ( ~ sum(additive_identity,a,a)
    | spl0_16 ),
    inference(component_clause,[status(thm)],[f193]) ).

fof(f196,plain,
    ( ~ sum(additive_identity,a,a)
    | less_or_equal(additive_identity,u) ),
    inference(resolution,[status(thm)],[f184,f76]) ).

fof(f197,plain,
    ( ~ spl0_16
    | spl0_0 ),
    inference(split_clause,[status(thm)],[f196,f193,f81]) ).

fof(f245,plain,
    ( ~ defined(a)
    | spl0_16 ),
    inference(resolution,[status(thm)],[f195,f36]) ).

fof(f246,plain,
    ( ~ spl0_6
    | spl0_16 ),
    inference(split_clause,[status(thm)],[f245,f113,f193]) ).

fof(f250,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f109,f128,f183,f197,f246]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.14  % Problem  : FLD059-4 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.03/0.14  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.36  % Computer : n014.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Mon Apr 29 23:13:19 EDT 2024
% 0.14/0.36  % CPUTime  : 
% 0.20/0.38  % Drodi V3.6.0
% 0.20/0.39  % Refutation found
% 0.20/0.39  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.20/0.39  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.20/0.41  % Elapsed time: 0.023331 seconds
% 0.20/0.41  % CPU time: 0.064067 seconds
% 0.20/0.41  % Total memory used: 2.914 MB
% 0.20/0.41  % Net memory used: 2.857 MB
%------------------------------------------------------------------------------