%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : KLE089+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n021.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 12:15:45 EDT 2023

% Result   : Theorem 0.28s 0.61s
% Output   : CNFRefutation 0.28s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   21 (  17 unt;   0 def)
%            Number of atoms       :   25 (  24 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :    8 (   4   ~;   0   |;   2   &)
%                                         (   0 <=>;   0  =>;   2  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-2 aty)
%            Number of variables   :   25 (;  23   !;   2   ?)

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

fof(f3,axiom,
    ! [A] : addition(A,zero) = A,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

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

fof(f13,axiom,
    ! [X0] : multiplication(antidomain(X0),X0) = zero,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f21,conjecture,
    ! [X0,X1] :
      ( multiplication(domain(X0),X1) = zero
     <= addition(domain(X0),antidomain(X1)) = antidomain(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f22,negated_conjecture,
    ~ ! [X0,X1] :
        ( multiplication(domain(X0),X1) = zero
       <= addition(domain(X0),antidomain(X1)) = antidomain(X1) ),
    inference(negated_conjecture,[status(cth)],[f21]) ).

fof(f23,plain,
    ! [X0,X1] : addition(X0,X1) = addition(X1,X0),
    inference(cnf_transformation,[status(esa)],[f1]) ).

fof(f25,plain,
    ! [X0] : addition(X0,zero) = X0,
    inference(cnf_transformation,[status(esa)],[f3]) ).

fof(f31,plain,
    ! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
    inference(cnf_transformation,[status(esa)],[f9]) ).

fof(f38,plain,
    ! [X0] : multiplication(antidomain(X0),X0) = zero,
    inference(cnf_transformation,[status(esa)],[f13]) ).

fof(f46,plain,
    ? [X0,X1] :
      ( multiplication(domain(X0),X1) != zero
      & addition(domain(X0),antidomain(X1)) = antidomain(X1) ),
    inference(pre_NNF_transformation,[status(esa)],[f22]) ).

fof(f47,plain,
    ( multiplication(domain(sk0_0),sk0_1) != zero
    & addition(domain(sk0_0),antidomain(sk0_1)) = antidomain(sk0_1) ),
    inference(skolemization,[status(esa)],[f46]) ).

fof(f48,plain,
    multiplication(domain(sk0_0),sk0_1) != zero,
    inference(cnf_transformation,[status(esa)],[f47]) ).

fof(f49,plain,
    addition(domain(sk0_0),antidomain(sk0_1)) = antidomain(sk0_1),
    inference(cnf_transformation,[status(esa)],[f47]) ).

fof(f50,plain,
    antidomain(sk0_1) = addition(antidomain(sk0_1),domain(sk0_0)),
    inference(paramodulation,[status(thm)],[f49,f23]) ).

fof(f51,plain,
    ! [X0] : X0 = addition(zero,X0),
    inference(paramodulation,[status(thm)],[f25,f23]) ).

fof(f225,plain,
    ! [X0,X1] : multiplication(addition(antidomain(X0),X1),X0) = addition(zero,multiplication(X1,X0)),
    inference(paramodulation,[status(thm)],[f38,f31]) ).

fof(f226,plain,
    ! [X0,X1] : multiplication(addition(antidomain(X0),X1),X0) = multiplication(X1,X0),
    inference(forward_demodulation,[status(thm)],[f51,f225]) ).

fof(f2547,plain,
    multiplication(antidomain(sk0_1),sk0_1) = multiplication(domain(sk0_0),sk0_1),
    inference(paramodulation,[status(thm)],[f50,f226]) ).

fof(f2548,plain,
    zero = multiplication(domain(sk0_0),sk0_1),
    inference(forward_demodulation,[status(thm)],[f38,f2547]) ).

fof(f2549,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[f2548,f48]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10  % Problem  : KLE089+1 : TPTP v8.1.2. Released v4.0.0.
% 0.03/0.11  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.31  % Computer : n021.cluster.edu
% 0.11/0.31  % Model    : x86_64 x86_64
% 0.11/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31  % Memory   : 8042.1875MB
% 0.11/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31  % CPULimit : 300
% 0.11/0.31  % WCLimit  : 300
% 0.11/0.31  % DateTime : Tue May 30 11:46:07 EDT 2023
% 0.11/0.31  % CPUTime  : 
% 0.11/0.32  % Drodi V3.5.1
% 0.28/0.61  % Refutation found
% 0.28/0.61  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.28/0.61  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.28/0.61  % Elapsed time: 0.068200 seconds
% 0.28/0.61  % CPU time: 0.084268 seconds
% 0.28/0.61  % Memory used: 9.453 MB
%------------------------------------------------------------------------------