%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : KLE002+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n002.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 : Wed May 31 12:15:25 EDT 2023

% Result   : Theorem 0.20s 0.36s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   19 (   9 unt;   0 def)
%            Number of atoms       :   33 (  13 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   28 (  14   ~;   6   |;   5   &)
%                                         (   1 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   30 (;  24   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f9,axiom,
    ! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f12,axiom,
    ! [A,B] :
      ( leq(A,B)
    <=> addition(A,B) = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f13,conjecture,
    ! [X0,X1,X2] :
      ( leq(X0,X1)
     => leq(multiplication(X0,X2),multiplication(X1,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f14,negated_conjecture,
    ~ ! [X0,X1,X2] :
        ( leq(X0,X1)
       => leq(multiplication(X0,X2),multiplication(X1,X2)) ),
    inference(negated_conjecture,[status(cth)],[f13]) ).

fof(f23,plain,
    ! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
    inference(cnf_transformation,[status(esa)],[f9]) ).

fof(f26,plain,
    ! [A,B] :
      ( ( ~ leq(A,B)
        | addition(A,B) = B )
      & ( leq(A,B)
        | addition(A,B) != B ) ),
    inference(NNF_transformation,[status(esa)],[f12]) ).

fof(f27,plain,
    ( ! [A,B] :
        ( ~ leq(A,B)
        | addition(A,B) = B )
    & ! [A,B] :
        ( leq(A,B)
        | addition(A,B) != B ) ),
    inference(miniscoping,[status(esa)],[f26]) ).

fof(f28,plain,
    ! [X0,X1] :
      ( ~ leq(X0,X1)
      | addition(X0,X1) = X1 ),
    inference(cnf_transformation,[status(esa)],[f27]) ).

fof(f29,plain,
    ! [X0,X1] :
      ( leq(X0,X1)
      | addition(X0,X1) != X1 ),
    inference(cnf_transformation,[status(esa)],[f27]) ).

fof(f30,plain,
    ? [X0,X1,X2] :
      ( leq(X0,X1)
      & ~ leq(multiplication(X0,X2),multiplication(X1,X2)) ),
    inference(pre_NNF_transformation,[status(esa)],[f14]) ).

fof(f31,plain,
    ? [X0,X1] :
      ( leq(X0,X1)
      & ? [X2] : ~ leq(multiplication(X0,X2),multiplication(X1,X2)) ),
    inference(miniscoping,[status(esa)],[f30]) ).

fof(f32,plain,
    ( leq(sk0_0,sk0_1)
    & ~ leq(multiplication(sk0_0,sk0_2),multiplication(sk0_1,sk0_2)) ),
    inference(skolemization,[status(esa)],[f31]) ).

fof(f33,plain,
    leq(sk0_0,sk0_1),
    inference(cnf_transformation,[status(esa)],[f32]) ).

fof(f34,plain,
    ~ leq(multiplication(sk0_0,sk0_2),multiplication(sk0_1,sk0_2)),
    inference(cnf_transformation,[status(esa)],[f32]) ).

fof(f35,plain,
    addition(sk0_0,sk0_1) = sk0_1,
    inference(resolution,[status(thm)],[f28,f33]) ).

fof(f46,plain,
    addition(multiplication(sk0_0,sk0_2),multiplication(sk0_1,sk0_2)) != multiplication(sk0_1,sk0_2),
    inference(resolution,[status(thm)],[f29,f34]) ).

fof(f47,plain,
    multiplication(addition(sk0_0,sk0_1),sk0_2) != multiplication(sk0_1,sk0_2),
    inference(forward_demodulation,[status(thm)],[f23,f46]) ).

fof(f48,plain,
    multiplication(sk0_1,sk0_2) != multiplication(sk0_1,sk0_2),
    inference(forward_demodulation,[status(thm)],[f35,f47]) ).

fof(f49,plain,
    $false,
    inference(trivial_equality_resolution,[status(esa)],[f48]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : KLE002+1 : TPTP v8.1.2. Released v4.0.0.
% 0.03/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34  % Computer : n002.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 : Tue May 30 12:01:58 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  % Drodi V3.5.1
% 0.20/0.36  % Refutation found
% 0.20/0.36  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.20/0.36  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.24/0.58  % Elapsed time: 0.015627 seconds
% 0.24/0.58  % CPU time: 0.027111 seconds
% 0.24/0.58  % Memory used: 9.069 MB
%------------------------------------------------------------------------------