TSTP Solution File: FLD064-1 by Drodi---3.6.0

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%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : FLD064-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n013.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 20:16:34 EDT 2024

% Result   : Unsatisfiable 67.41s 8.85s
% Output   : CNFRefutation 67.74s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   49 (  17 unt;   0 def)
%            Number of atoms       :  100 (   0 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  101 (  50   ~;  49   |;   0   &)
%                                         (   2 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    6 (   5 usr;   3 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :   52 (  52   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f2,axiom,
    ! [X] :
      ( equalish(add(additive_identity,X),X)
      | ~ defined(X) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f3,axiom,
    ! [X] :
      ( equalish(add(X,additive_inverse(X)),additive_identity)
      | ~ defined(X) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f11,axiom,
    defined(additive_identity),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f12,axiom,
    ! [X] :
      ( defined(additive_inverse(X))
      | ~ defined(X) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f17,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(f18,axiom,
    ! [X,Y] :
      ( less_or_equal(X,Y)
      | less_or_equal(Y,X)
      | ~ defined(X)
      | ~ defined(Y) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f19,axiom,
    ! [X,Z,Y] :
      ( less_or_equal(add(X,Z),add(Y,Z))
      | ~ defined(Z)
      | ~ less_or_equal(X,Y) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

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

fof(f26,axiom,
    ! [Y,Z,X] :
      ( less_or_equal(Y,Z)
      | ~ less_or_equal(X,Z)
      | ~ equalish(X,Y) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

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

fof(f33,plain,
    ! [X0] :
      ( equalish(add(additive_identity,X0),X0)
      | ~ defined(X0) ),
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f34,plain,
    ! [X0] :
      ( equalish(add(X0,additive_inverse(X0)),additive_identity)
      | ~ defined(X0) ),
    inference(cnf_transformation,[status(esa)],[f3]) ).

fof(f47,plain,
    defined(additive_identity),
    inference(cnf_transformation,[status(esa)],[f11]) ).

fof(f48,plain,
    ! [X0] :
      ( defined(additive_inverse(X0))
      | ~ defined(X0) ),
    inference(cnf_transformation,[status(esa)],[f12]) ).

fof(f54,plain,
    ! [Z,Y] :
      ( ! [X] :
          ( less_or_equal(X,Z)
          | ~ less_or_equal(X,Y) )
      | ~ less_or_equal(Y,Z) ),
    inference(miniscoping,[status(esa)],[f17]) ).

fof(f55,plain,
    ! [X0,X1,X2] :
      ( less_or_equal(X0,X1)
      | ~ less_or_equal(X0,X2)
      | ~ less_or_equal(X2,X1) ),
    inference(cnf_transformation,[status(esa)],[f54]) ).

fof(f56,plain,
    ! [Y] :
      ( ! [X] :
          ( less_or_equal(X,Y)
          | less_or_equal(Y,X)
          | ~ defined(X) )
      | ~ defined(Y) ),
    inference(miniscoping,[status(esa)],[f18]) ).

fof(f57,plain,
    ! [X0,X1] :
      ( less_or_equal(X0,X1)
      | less_or_equal(X1,X0)
      | ~ defined(X0)
      | ~ defined(X1) ),
    inference(cnf_transformation,[status(esa)],[f56]) ).

fof(f58,plain,
    ! [X,Y] :
      ( ! [Z] :
          ( less_or_equal(add(X,Z),add(Y,Z))
          | ~ defined(Z) )
      | ~ less_or_equal(X,Y) ),
    inference(miniscoping,[status(esa)],[f19]) ).

fof(f59,plain,
    ! [X0,X1,X2] :
      ( less_or_equal(add(X0,X1),add(X2,X1))
      | ~ defined(X1)
      | ~ less_or_equal(X0,X2) ),
    inference(cnf_transformation,[status(esa)],[f58]) ).

fof(f63,plain,
    ! [X0,X1] :
      ( equalish(X0,X1)
      | ~ equalish(X1,X0) ),
    inference(cnf_transformation,[status(esa)],[f22]) ).

fof(f70,plain,
    ! [Y,X] :
      ( ! [Z] :
          ( less_or_equal(Y,Z)
          | ~ less_or_equal(X,Z) )
      | ~ equalish(X,Y) ),
    inference(miniscoping,[status(esa)],[f26]) ).

fof(f71,plain,
    ! [X0,X1,X2] :
      ( less_or_equal(X0,X1)
      | ~ less_or_equal(X2,X1)
      | ~ equalish(X2,X0) ),
    inference(cnf_transformation,[status(esa)],[f70]) ).

fof(f73,plain,
    defined(a),
    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(additive_inverse(a),additive_identity),
    inference(cnf_transformation,[status(esa)],[f30]) ).

fof(f82,plain,
    defined(additive_inverse(a)),
    inference(resolution,[status(thm)],[f48,f73]) ).

fof(f97,plain,
    equalish(add(additive_identity,additive_inverse(a)),additive_inverse(a)),
    inference(resolution,[status(thm)],[f33,f82]) ).

fof(f107,plain,
    equalish(add(a,additive_inverse(a)),additive_identity),
    inference(resolution,[status(thm)],[f34,f73]) ).

fof(f135,plain,
    equalish(additive_identity,add(a,additive_inverse(a))),
    inference(resolution,[status(thm)],[f107,f63]) ).

fof(f986,plain,
    ( spl0_40
  <=> less_or_equal(additive_identity,additive_identity) ),
    introduced(split_symbol_definition) ).

fof(f2099,plain,
    ! [X0] :
      ( less_or_equal(X0,additive_identity)
      | less_or_equal(additive_identity,X0)
      | ~ defined(X0) ),
    inference(resolution,[status(thm)],[f57,f47]) ).

fof(f2128,plain,
    ! [X0] :
      ( ~ less_or_equal(X0,additive_identity)
      | ~ equalish(X0,additive_inverse(a)) ),
    inference(resolution,[status(thm)],[f71,f75]) ).

fof(f2130,plain,
    ! [X0,X1,X2,X3] :
      ( ~ less_or_equal(X0,X1)
      | ~ equalish(X0,X2)
      | less_or_equal(X3,X1)
      | ~ less_or_equal(X3,X2) ),
    inference(resolution,[status(thm)],[f71,f55]) ).

fof(f2133,plain,
    ~ less_or_equal(add(additive_identity,additive_inverse(a)),additive_identity),
    inference(resolution,[status(thm)],[f2128,f97]) ).

fof(f2345,plain,
    ( less_or_equal(additive_identity,additive_identity)
    | less_or_equal(additive_identity,additive_identity) ),
    inference(resolution,[status(thm)],[f2099,f47]) ).

fof(f2346,plain,
    spl0_40,
    inference(split_clause,[status(thm)],[f2345,f986]) ).

fof(f4847,plain,
    ! [X0] :
      ( less_or_equal(add(additive_identity,X0),add(a,X0))
      | ~ defined(X0) ),
    inference(resolution,[status(thm)],[f59,f74]) ).

fof(f5553,plain,
    less_or_equal(add(additive_identity,additive_inverse(a)),add(a,additive_inverse(a))),
    inference(resolution,[status(thm)],[f4847,f82]) ).

fof(f10199,plain,
    ( spl0_1345
  <=> less_or_equal(add(additive_identity,additive_inverse(a)),add(a,additive_inverse(a))) ),
    introduced(split_symbol_definition) ).

fof(f10201,plain,
    ( ~ less_or_equal(add(additive_identity,additive_inverse(a)),add(a,additive_inverse(a)))
    | spl0_1345 ),
    inference(component_clause,[status(thm)],[f10199]) ).

fof(f30692,plain,
    ! [X0,X1] :
      ( ~ less_or_equal(X0,additive_identity)
      | ~ equalish(X0,X1)
      | ~ less_or_equal(add(additive_identity,additive_inverse(a)),X1) ),
    inference(resolution,[status(thm)],[f2130,f2133]) ).

fof(f31528,plain,
    ( ~ less_or_equal(additive_identity,additive_identity)
    | ~ less_or_equal(add(additive_identity,additive_inverse(a)),add(a,additive_inverse(a))) ),
    inference(resolution,[status(thm)],[f30692,f135]) ).

fof(f31529,plain,
    ( ~ spl0_40
    | ~ spl0_1345 ),
    inference(split_clause,[status(thm)],[f31528,f986,f10199]) ).

fof(f31566,plain,
    ( $false
    | spl0_1345 ),
    inference(forward_subsumption_resolution,[status(thm)],[f10201,f5553]) ).

fof(f31567,plain,
    spl0_1345,
    inference(contradiction_clause,[status(thm)],[f31566]) ).

fof(f31568,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f2346,f31529,f31567]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem  : FLD064-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.04/0.14  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.35  % Computer : n013.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Mon Apr 29 23:13:19 EDT 2024
% 0.14/0.35  % CPUTime  : 
% 0.14/0.36  % Drodi V3.6.0
% 67.41/8.85  % Refutation found
% 67.41/8.85  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 67.41/8.85  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 67.74/8.92  % Elapsed time: 8.549768 seconds
% 67.74/8.92  % CPU time: 67.836264 seconds
% 67.74/8.92  % Total memory used: 322.790 MB
% 67.74/8.92  % Net memory used: 307.388 MB
%------------------------------------------------------------------------------