%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : NUM016-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n019.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 20:30:11 EDT 2024

% Result   : Unsatisfiable 0.13s 0.35s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   39 (   6 unt;   0 def)
%            Number of atoms       :   78 (   0 equ)
%            Maximal formula atoms :    3 (   2 avg)
%            Number of connectives :   65 (  26   ~;  35   |;   0   &)
%                                         (   4 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    8 (   7 usr;   5 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   1 con; 0-1 aty)
%            Number of variables   :   22 (  22   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X] : ~ less(X,X),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f2,axiom,
    ! [X,Y] :
      ( ~ less(X,Y)
      | ~ less(Y,X) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f6,axiom,
    ! [X] : less(X,factorial_plus_one(X)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f7,axiom,
    ! [X,Y] :
      ( ~ divides(X,factorial_plus_one(Y))
      | less(Y,X) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f8,axiom,
    ! [X] :
      ( prime(X)
      | divides(prime_divisor(X),X) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f9,axiom,
    ! [X] :
      ( prime(X)
      | prime(prime_divisor(X)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f10,axiom,
    ! [X] :
      ( prime(X)
      | less(prime_divisor(X),X) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f12,negated_conjecture,
    ! [X] :
      ( ~ prime(X)
      | ~ less(a,X)
      | less(factorial_plus_one(a),X) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f13,plain,
    ! [X0] : ~ less(X0,X0),
    inference(cnf_transformation,[status(esa)],[f1]) ).

fof(f14,plain,
    ! [X0,X1] :
      ( ~ less(X0,X1)
      | ~ less(X1,X0) ),
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f19,plain,
    ! [X0] : less(X0,factorial_plus_one(X0)),
    inference(cnf_transformation,[status(esa)],[f6]) ).

fof(f20,plain,
    ! [X0,X1] :
      ( ~ divides(X0,factorial_plus_one(X1))
      | less(X1,X0) ),
    inference(cnf_transformation,[status(esa)],[f7]) ).

fof(f21,plain,
    ! [X0] :
      ( prime(X0)
      | divides(prime_divisor(X0),X0) ),
    inference(cnf_transformation,[status(esa)],[f8]) ).

fof(f22,plain,
    ! [X0] :
      ( prime(X0)
      | prime(prime_divisor(X0)) ),
    inference(cnf_transformation,[status(esa)],[f9]) ).

fof(f23,plain,
    ! [X0] :
      ( prime(X0)
      | less(prime_divisor(X0),X0) ),
    inference(cnf_transformation,[status(esa)],[f10]) ).

fof(f25,plain,
    ! [X0] :
      ( ~ prime(X0)
      | ~ less(a,X0)
      | less(factorial_plus_one(a),X0) ),
    inference(cnf_transformation,[status(esa)],[f12]) ).

fof(f26,plain,
    ( spl0_0
  <=> prime(factorial_plus_one(a)) ),
    introduced(split_symbol_definition) ).

fof(f28,plain,
    ( ~ prime(factorial_plus_one(a))
    | spl0_0 ),
    inference(component_clause,[status(thm)],[f26]) ).

fof(f29,plain,
    ( spl0_1
  <=> less(factorial_plus_one(a),factorial_plus_one(a)) ),
    introduced(split_symbol_definition) ).

fof(f30,plain,
    ( less(factorial_plus_one(a),factorial_plus_one(a))
    | ~ spl0_1 ),
    inference(component_clause,[status(thm)],[f29]) ).

fof(f32,plain,
    ( ~ prime(factorial_plus_one(a))
    | less(factorial_plus_one(a),factorial_plus_one(a)) ),
    inference(resolution,[status(thm)],[f19,f25]) ).

fof(f33,plain,
    ( ~ spl0_0
    | spl0_1 ),
    inference(split_clause,[status(thm)],[f32,f26,f29]) ).

fof(f37,plain,
    ! [X0] :
      ( prime(X0)
      | ~ less(X0,prime_divisor(X0)) ),
    inference(resolution,[status(thm)],[f23,f14]) ).

fof(f38,plain,
    ! [X0] :
      ( prime(factorial_plus_one(X0))
      | less(X0,prime_divisor(factorial_plus_one(X0))) ),
    inference(resolution,[status(thm)],[f21,f20]) ).

fof(f40,plain,
    ( spl0_2
  <=> prime(prime_divisor(factorial_plus_one(a))) ),
    introduced(split_symbol_definition) ).

fof(f42,plain,
    ( ~ prime(prime_divisor(factorial_plus_one(a)))
    | spl0_2 ),
    inference(component_clause,[status(thm)],[f40]) ).

fof(f43,plain,
    ( spl0_3
  <=> less(factorial_plus_one(a),prime_divisor(factorial_plus_one(a))) ),
    introduced(split_symbol_definition) ).

fof(f44,plain,
    ( less(factorial_plus_one(a),prime_divisor(factorial_plus_one(a)))
    | ~ spl0_3 ),
    inference(component_clause,[status(thm)],[f43]) ).

fof(f46,plain,
    ( prime(factorial_plus_one(a))
    | ~ prime(prime_divisor(factorial_plus_one(a)))
    | less(factorial_plus_one(a),prime_divisor(factorial_plus_one(a))) ),
    inference(resolution,[status(thm)],[f38,f25]) ).

fof(f47,plain,
    ( spl0_0
    | ~ spl0_2
    | spl0_3 ),
    inference(split_clause,[status(thm)],[f46,f26,f40,f43]) ).

fof(f49,plain,
    ( $false
    | ~ spl0_1 ),
    inference(forward_subsumption_resolution,[status(thm)],[f30,f13]) ).

fof(f50,plain,
    ~ spl0_1,
    inference(contradiction_clause,[status(thm)],[f49]) ).

fof(f54,plain,
    ( prime(factorial_plus_one(a))
    | spl0_2 ),
    inference(resolution,[status(thm)],[f42,f22]) ).

fof(f55,plain,
    ( $false
    | spl0_0
    | spl0_2 ),
    inference(forward_subsumption_resolution,[status(thm)],[f54,f28]) ).

fof(f56,plain,
    ( spl0_0
    | spl0_2 ),
    inference(contradiction_clause,[status(thm)],[f55]) ).

fof(f57,plain,
    ( prime(factorial_plus_one(a))
    | ~ spl0_3 ),
    inference(resolution,[status(thm)],[f44,f37]) ).

fof(f58,plain,
    ( $false
    | spl0_0
    | ~ spl0_3 ),
    inference(forward_subsumption_resolution,[status(thm)],[f57,f28]) ).

fof(f59,plain,
    ( spl0_0
    | ~ spl0_3 ),
    inference(contradiction_clause,[status(thm)],[f58]) ).

fof(f60,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f33,f47,f50,f56,f59]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : NUM016-1 : TPTP v8.1.2. Released v1.0.0.
% 0.12/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34  % Computer : n019.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 : Mon Apr 29 20:41:44 EDT 2024
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  % Drodi V3.6.0
% 0.13/0.35  % Refutation found
% 0.13/0.35  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.35  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.37  % Elapsed time: 0.016181 seconds
% 0.13/0.37  % CPU time: 0.032277 seconds
% 0.13/0.37  % Total memory used: 1.939 MB
% 0.13/0.37  % Net memory used: 1.889 MB
%------------------------------------------------------------------------------