%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : CAT011-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n017.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  : 600s
% DateTime : Fri Jul 15 00:04:34 EDT 2022

% Result   : Unsatisfiable 0.12s 0.34s
% Output   : CNFRefutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    7
% Syntax   : Number of clauses     :   16 (  10 unt;   0 nHn;  11 RR)
%            Number of literals    :   25 (  24 equ;  11 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    3 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   1 con; 0-1 aty)
%            Number of variables   :    9 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(codomain_of_domain_is_domain,axiom,
    codomain(domain(X)) = domain(X) ).

cnf(domain_of_codomain_is_codomain,axiom,
    domain(codomain(X)) = codomain(X) ).

cnf(prove_domain_is_idempotent,negated_conjecture,
    domain(domain(a)) != domain(a) ).

cnf(refute_0_0,plain,
    domain(codomain(domain(X))) = codomain(domain(X)),
    inference(subst,[],[domain_of_codomain_is_codomain:[bind(X,$fot(domain(X)))]]) ).

cnf(refute_0_1,plain,
    ( codomain(domain(X)) != domain(X)
    | domain(codomain(domain(X))) != codomain(domain(X))
    | domain(domain(X)) = codomain(domain(X)) ),
    introduced(tautology,[equality,[$cnf( $equal(domain(codomain(domain(X))),codomain(domain(X))) ),[0,0],$fot(domain(X))]]) ).

cnf(refute_0_2,plain,
    ( domain(codomain(domain(X))) != codomain(domain(X))
    | domain(domain(X)) = codomain(domain(X)) ),
    inference(resolve,[$cnf( $equal(codomain(domain(X)),domain(X)) )],[codomain_of_domain_is_domain,refute_0_1]) ).

cnf(refute_0_3,plain,
    domain(domain(X)) = codomain(domain(X)),
    inference(resolve,[$cnf( $equal(domain(codomain(domain(X))),codomain(domain(X))) )],[refute_0_0,refute_0_2]) ).

cnf(refute_0_4,plain,
    ( codomain(domain(X)) != domain(X)
    | domain(domain(X)) != codomain(domain(X))
    | domain(domain(X)) = domain(X) ),
    introduced(tautology,[equality,[$cnf( $equal(domain(domain(X)),codomain(domain(X))) ),[1],$fot(domain(X))]]) ).

cnf(refute_0_5,plain,
    ( domain(domain(X)) != codomain(domain(X))
    | domain(domain(X)) = domain(X) ),
    inference(resolve,[$cnf( $equal(codomain(domain(X)),domain(X)) )],[codomain_of_domain_is_domain,refute_0_4]) ).

cnf(refute_0_6,plain,
    domain(domain(X)) = domain(X),
    inference(resolve,[$cnf( $equal(domain(domain(X)),codomain(domain(X))) )],[refute_0_3,refute_0_5]) ).

cnf(refute_0_7,plain,
    domain(domain(a)) = domain(a),
    inference(subst,[],[refute_0_6:[bind(X,$fot(a))]]) ).

cnf(refute_0_8,plain,
    ( domain(a) != domain(a)
    | domain(domain(a)) != domain(a)
    | domain(domain(a)) = domain(a) ),
    introduced(tautology,[equality,[$cnf( $equal(domain(domain(a)),domain(a)) ),[0,0],$fot(domain(a))]]) ).

cnf(refute_0_9,plain,
    ( domain(a) != domain(a)
    | domain(domain(a)) = domain(a) ),
    inference(resolve,[$cnf( $equal(domain(domain(a)),domain(a)) )],[refute_0_7,refute_0_8]) ).

cnf(refute_0_10,plain,
    domain(a) != domain(a),
    inference(resolve,[$cnf( $equal(domain(domain(a)),domain(a)) )],[refute_0_9,prove_domain_is_idempotent]) ).

cnf(refute_0_11,plain,
    domain(a) = domain(a),
    introduced(tautology,[refl,[$fot(domain(a))]]) ).

cnf(refute_0_12,plain,
    $false,
    inference(resolve,[$cnf( $equal(domain(a),domain(a)) )],[refute_0_11,refute_0_10]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : CAT011-2 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12  % Command  : metis --show proof --show saturation %s
% 0.12/0.33  % Computer : n017.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Sun May 29 23:47:24 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.34  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.34  
% 0.12/0.34  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.12/0.34  
%------------------------------------------------------------------------------