TSTP Solution File: FLD058-3 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : FLD058-3 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n031.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 0.10s 0.27s
% Output   : CNFRefutation 0.10s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   62 (  19 unt;   0 def)
%            Number of atoms       :  121 (   0 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :  112 (  53   ~;  52   |;   0   &)
%                                         (   7 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   3 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :   11 (  10 usr;   8 prp; 0-3 aty)
%            Number of functors    :    3 (   3 usr;   3 con; 0-0 aty)
%            Number of variables   :   42 (  42   !;   0   ?)

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

fof(f5,axiom,
    ! [Y,X,Z] :
      ( sum(Y,X,Z)
      | ~ sum(X,Y,Z) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

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

fof(f21,axiom,
    ! [X,Y] :
      ( sum(additive_identity,X,Y)
      | ~ less_or_equal(X,Y)
      | ~ less_or_equal(Y,X) ),
    file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p') ).

fof(f28,hypothesis,
    defined(b),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

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

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

fof(f31,negated_conjecture,
    ~ sum(additive_identity,a,additive_identity),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f32,negated_conjecture,
    sum(additive_identity,b,additive_identity),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f37,plain,
    ! [X0] :
      ( sum(additive_identity,X0,X0)
      | ~ defined(X0) ),
    inference(cnf_transformation,[status(esa)],[f3]) ).

fof(f39,plain,
    ! [X0,X1,X2] :
      ( sum(X0,X1,X2)
      | ~ sum(X1,X0,X2) ),
    inference(cnf_transformation,[status(esa)],[f5]) ).

fof(f53,plain,
    defined(additive_identity),
    inference(cnf_transformation,[status(esa)],[f14]) ).

fof(f63,plain,
    ! [X0,X1] :
      ( sum(additive_identity,X0,X1)
      | ~ less_or_equal(X0,X1)
      | ~ less_or_equal(X1,X0) ),
    inference(cnf_transformation,[status(esa)],[f21]) ).

fof(f64,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(f65,plain,
    ! [X0,X1,X2] :
      ( less_or_equal(X0,X1)
      | ~ less_or_equal(X0,X2)
      | ~ less_or_equal(X2,X1) ),
    inference(cnf_transformation,[status(esa)],[f64]) ).

fof(f68,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(f69,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)],[f68]) ).

fof(f73,plain,
    defined(b),
    inference(cnf_transformation,[status(esa)],[f28]) ).

fof(f74,plain,
    less_or_equal(additive_identity,a),
    inference(cnf_transformation,[status(esa)],[f29]) ).

fof(f75,plain,
    less_or_equal(a,b),
    inference(cnf_transformation,[status(esa)],[f30]) ).

fof(f76,plain,
    ~ sum(additive_identity,a,additive_identity),
    inference(cnf_transformation,[status(esa)],[f31]) ).

fof(f77,plain,
    sum(additive_identity,b,additive_identity),
    inference(cnf_transformation,[status(esa)],[f32]) ).

fof(f81,plain,
    sum(b,additive_identity,additive_identity),
    inference(resolution,[status(thm)],[f39,f77]) ).

fof(f82,plain,
    ! [X0] :
      ( less_or_equal(X0,b)
      | ~ less_or_equal(X0,a) ),
    inference(resolution,[status(thm)],[f65,f75]) ).

fof(f83,plain,
    ! [X0] :
      ( less_or_equal(X0,a)
      | ~ less_or_equal(X0,additive_identity) ),
    inference(resolution,[status(thm)],[f65,f74]) ).

fof(f84,plain,
    less_or_equal(additive_identity,b),
    inference(resolution,[status(thm)],[f82,f74]) ).

fof(f85,plain,
    ( spl0_0
  <=> sum(additive_identity,b,a) ),
    introduced(split_symbol_definition) ).

fof(f86,plain,
    ( sum(additive_identity,b,a)
    | ~ spl0_0 ),
    inference(component_clause,[status(thm)],[f85]) ).

fof(f88,plain,
    ( spl0_1
  <=> less_or_equal(b,a) ),
    introduced(split_symbol_definition) ).

fof(f90,plain,
    ( ~ less_or_equal(b,a)
    | spl0_1 ),
    inference(component_clause,[status(thm)],[f88]) ).

fof(f91,plain,
    ( sum(additive_identity,b,a)
    | ~ less_or_equal(b,a) ),
    inference(resolution,[status(thm)],[f63,f75]) ).

fof(f92,plain,
    ( spl0_0
    | ~ spl0_1 ),
    inference(split_clause,[status(thm)],[f91,f85,f88]) ).

fof(f93,plain,
    ( spl0_2
  <=> sum(additive_identity,a,additive_identity) ),
    introduced(split_symbol_definition) ).

fof(f94,plain,
    ( sum(additive_identity,a,additive_identity)
    | ~ spl0_2 ),
    inference(component_clause,[status(thm)],[f93]) ).

fof(f96,plain,
    ( spl0_3
  <=> less_or_equal(a,additive_identity) ),
    introduced(split_symbol_definition) ).

fof(f99,plain,
    ( sum(additive_identity,a,additive_identity)
    | ~ less_or_equal(a,additive_identity) ),
    inference(resolution,[status(thm)],[f63,f74]) ).

fof(f100,plain,
    ( spl0_2
    | ~ spl0_3 ),
    inference(split_clause,[status(thm)],[f99,f93,f96]) ).

fof(f101,plain,
    ! [X0,X1] :
      ( less_or_equal(X0,additive_identity)
      | ~ less_or_equal(X1,additive_identity)
      | ~ sum(X1,b,X0) ),
    inference(resolution,[status(thm)],[f69,f77]) ).

fof(f106,plain,
    sum(additive_identity,additive_identity,additive_identity),
    inference(resolution,[status(thm)],[f53,f37]) ).

fof(f124,plain,
    sum(additive_identity,b,b),
    inference(resolution,[status(thm)],[f73,f37]) ).

fof(f132,plain,
    ( spl0_5
  <=> less_or_equal(b,additive_identity) ),
    introduced(split_symbol_definition) ).

fof(f133,plain,
    ( less_or_equal(b,additive_identity)
    | ~ spl0_5 ),
    inference(component_clause,[status(thm)],[f132]) ).

fof(f184,plain,
    ! [X0,X1] :
      ( less_or_equal(X0,additive_identity)
      | ~ less_or_equal(X1,b)
      | ~ sum(X1,additive_identity,X0) ),
    inference(resolution,[status(thm)],[f81,f69]) ).

fof(f191,plain,
    ( spl0_6
  <=> less_or_equal(additive_identity,additive_identity) ),
    introduced(split_symbol_definition) ).

fof(f208,plain,
    ( spl0_8
  <=> less_or_equal(additive_identity,b) ),
    introduced(split_symbol_definition) ).

fof(f210,plain,
    ( ~ less_or_equal(additive_identity,b)
    | spl0_8 ),
    inference(component_clause,[status(thm)],[f208]) ).

fof(f211,plain,
    ( less_or_equal(additive_identity,additive_identity)
    | ~ less_or_equal(additive_identity,b) ),
    inference(resolution,[status(thm)],[f106,f184]) ).

fof(f212,plain,
    ( spl0_6
    | ~ spl0_8 ),
    inference(split_clause,[status(thm)],[f211,f191,f208]) ).

fof(f221,plain,
    ( $false
    | spl0_8 ),
    inference(forward_subsumption_resolution,[status(thm)],[f210,f84]) ).

fof(f222,plain,
    spl0_8,
    inference(contradiction_clause,[status(thm)],[f221]) ).

fof(f261,plain,
    ( less_or_equal(b,additive_identity)
    | ~ less_or_equal(additive_identity,additive_identity) ),
    inference(resolution,[status(thm)],[f124,f101]) ).

fof(f262,plain,
    ( spl0_5
    | ~ spl0_6 ),
    inference(split_clause,[status(thm)],[f261,f132,f191]) ).

fof(f276,plain,
    ( less_or_equal(b,a)
    | ~ spl0_5 ),
    inference(resolution,[status(thm)],[f133,f83]) ).

fof(f277,plain,
    ( $false
    | spl0_1
    | ~ spl0_5 ),
    inference(forward_subsumption_resolution,[status(thm)],[f276,f90]) ).

fof(f278,plain,
    ( spl0_1
    | ~ spl0_5 ),
    inference(contradiction_clause,[status(thm)],[f277]) ).

fof(f289,plain,
    ( less_or_equal(a,additive_identity)
    | ~ less_or_equal(additive_identity,additive_identity)
    | ~ spl0_0 ),
    inference(resolution,[status(thm)],[f86,f101]) ).

fof(f290,plain,
    ( spl0_3
    | ~ spl0_6
    | ~ spl0_0 ),
    inference(split_clause,[status(thm)],[f289,f96,f191,f85]) ).

fof(f301,plain,
    ( $false
    | ~ spl0_2 ),
    inference(forward_subsumption_resolution,[status(thm)],[f94,f76]) ).

fof(f302,plain,
    ~ spl0_2,
    inference(contradiction_clause,[status(thm)],[f301]) ).

fof(f303,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f92,f100,f212,f222,f262,f278,f290,f302]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.07  % Problem  : FLD058-3 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.02/0.07  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.06/0.26  % Computer : n031.cluster.edu
% 0.06/0.26  % Model    : x86_64 x86_64
% 0.06/0.26  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.26  % Memory   : 8042.1875MB
% 0.06/0.26  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.06/0.26  % CPULimit : 300
% 0.06/0.26  % WCLimit  : 300
% 0.06/0.26  % DateTime : Mon Apr 29 23:53:13 EDT 2024
% 0.06/0.26  % CPUTime  : 
% 0.06/0.26  % Drodi V3.6.0
% 0.10/0.27  % Refutation found
% 0.10/0.27  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.10/0.27  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.28  % Elapsed time: 0.019353 seconds
% 0.10/0.28  % CPU time: 0.099364 seconds
% 0.10/0.28  % Total memory used: 5.851 MB
% 0.10/0.28  % Net memory used: 5.714 MB
%------------------------------------------------------------------------------