%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : KLE146+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n022.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 20:24:30 EDT 2024

% Result   : Theorem 0.13s 0.37s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   22 (  18 unt;   0 def)
%            Number of atoms       :   30 (  16 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   17 (   9   ~;   5   |;   2   &)
%                                         (   1 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   33 (  32   !;   1   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [A,B] : addition(A,B) = addition(B,A),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f2,axiom,
    ! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f4,axiom,
    ! [A] : addition(A,A) = A,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f15,axiom,
    ! [A] : strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f18,axiom,
    ! [A,B] :
      ( leq(A,B)
    <=> addition(A,B) = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f19,conjecture,
    ! [X0] : leq(one,strong_iteration(X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f20,negated_conjecture,
    ~ ! [X0] : leq(one,strong_iteration(X0)),
    inference(negated_conjecture,[status(cth)],[f19]) ).

fof(f21,plain,
    ! [X0,X1] : addition(X0,X1) = addition(X1,X0),
    inference(cnf_transformation,[status(esa)],[f1]) ).

fof(f22,plain,
    ! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X0,X1),X2),
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f24,plain,
    ! [X0] : addition(X0,X0) = X0,
    inference(cnf_transformation,[status(esa)],[f4]) ).

fof(f37,plain,
    ! [X0] : strong_iteration(X0) = addition(multiplication(X0,strong_iteration(X0)),one),
    inference(cnf_transformation,[status(esa)],[f15]) ).

fof(f41,plain,
    ! [A,B] :
      ( ( ~ leq(A,B)
        | addition(A,B) = B )
      & ( leq(A,B)
        | addition(A,B) != B ) ),
    inference(NNF_transformation,[status(esa)],[f18]) ).

fof(f42,plain,
    ( ! [A,B] :
        ( ~ leq(A,B)
        | addition(A,B) = B )
    & ! [A,B] :
        ( leq(A,B)
        | addition(A,B) != B ) ),
    inference(miniscoping,[status(esa)],[f41]) ).

fof(f44,plain,
    ! [X0,X1] :
      ( leq(X0,X1)
      | addition(X0,X1) != X1 ),
    inference(cnf_transformation,[status(esa)],[f42]) ).

fof(f45,plain,
    ? [X0] : ~ leq(one,strong_iteration(X0)),
    inference(pre_NNF_transformation,[status(esa)],[f20]) ).

fof(f46,plain,
    ~ leq(one,strong_iteration(sk0_0)),
    inference(skolemization,[status(esa)],[f45]) ).

fof(f47,plain,
    ~ leq(one,strong_iteration(sk0_0)),
    inference(cnf_transformation,[status(esa)],[f46]) ).

fof(f158,plain,
    ! [X0] : strong_iteration(X0) = addition(one,multiplication(X0,strong_iteration(X0))),
    inference(paramodulation,[status(thm)],[f37,f21]) ).

fof(f204,plain,
    ! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X0,X1),
    inference(paramodulation,[status(thm)],[f24,f22]) ).

fof(f387,plain,
    ! [X0,X1] : leq(X0,addition(X0,X1)),
    inference(resolution,[status(thm)],[f204,f44]) ).

fof(f435,plain,
    ! [X0] : leq(one,strong_iteration(X0)),
    inference(paramodulation,[status(thm)],[f158,f387]) ).

fof(f444,plain,
    $false,
    inference(backward_subsumption_resolution,[status(thm)],[f47,f435]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem  : KLE146+1 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.14  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.35  % Computer : n022.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Tue Apr 30 00:58:58 EDT 2024
% 0.13/0.35  % CPUTime  : 
% 0.13/0.36  % Drodi V3.6.0
% 0.13/0.37  % Refutation found
% 0.13/0.37  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.37  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.38  % Elapsed time: 0.024036 seconds
% 0.13/0.38  % CPU time: 0.063506 seconds
% 0.13/0.38  % Total memory used: 10.306 MB
% 0.13/0.38  % Net memory used: 10.262 MB
%------------------------------------------------------------------------------