%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : CAT014-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n026.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 00:04:35 EDT 2022

% Result   : Unsatisfiable 0.11s 0.33s
% Output   : CNFRefutation 0.11s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    7
% Syntax   : Number of clauses     :   17 (  11 unt;   0 nHn;  11 RR)
%            Number of literals    :   26 (  25 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   :   10 (   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_codomain_is_idempotent,negated_conjecture,
    codomain(codomain(a)) != codomain(a) ).

cnf(refute_0_0,plain,
    codomain(domain(codomain(X_2))) = domain(codomain(X_2)),
    inference(subst,[],[codomain_of_domain_is_domain:[bind(X,$fot(codomain(X_2)))]]) ).

cnf(refute_0_1,plain,
    domain(codomain(X_2)) = codomain(X_2),
    inference(subst,[],[domain_of_codomain_is_codomain:[bind(X,$fot(X_2))]]) ).

cnf(refute_0_2,plain,
    ( codomain(domain(codomain(X_2))) != domain(codomain(X_2))
    | domain(codomain(X_2)) != codomain(X_2)
    | codomain(codomain(X_2)) = domain(codomain(X_2)) ),
    introduced(tautology,[equality,[$cnf( $equal(codomain(domain(codomain(X_2))),domain(codomain(X_2))) ),[0,0],$fot(codomain(X_2))]]) ).

cnf(refute_0_3,plain,
    ( codomain(domain(codomain(X_2))) != domain(codomain(X_2))
    | codomain(codomain(X_2)) = domain(codomain(X_2)) ),
    inference(resolve,[$cnf( $equal(domain(codomain(X_2)),codomain(X_2)) )],[refute_0_1,refute_0_2]) ).

cnf(refute_0_4,plain,
    codomain(codomain(X_2)) = domain(codomain(X_2)),
    inference(resolve,[$cnf( $equal(codomain(domain(codomain(X_2))),domain(codomain(X_2))) )],[refute_0_0,refute_0_3]) ).

cnf(refute_0_5,plain,
    ( codomain(codomain(X_2)) != domain(codomain(X_2))
    | domain(codomain(X_2)) != codomain(X_2)
    | codomain(codomain(X_2)) = codomain(X_2) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(codomain(codomain(X_2)),codomain(X_2)) ),[0],$fot(domain(codomain(X_2)))]]) ).

cnf(refute_0_6,plain,
    ( codomain(codomain(X_2)) != domain(codomain(X_2))
    | codomain(codomain(X_2)) = codomain(X_2) ),
    inference(resolve,[$cnf( $equal(domain(codomain(X_2)),codomain(X_2)) )],[refute_0_1,refute_0_5]) ).

cnf(refute_0_7,plain,
    codomain(codomain(X_2)) = codomain(X_2),
    inference(resolve,[$cnf( $equal(codomain(codomain(X_2)),domain(codomain(X_2))) )],[refute_0_4,refute_0_6]) ).

cnf(refute_0_8,plain,
    codomain(codomain(a)) = codomain(a),
    inference(subst,[],[refute_0_7:[bind(X_2,$fot(a))]]) ).

cnf(refute_0_9,plain,
    ( codomain(a) != codomain(a)
    | codomain(codomain(a)) != codomain(a)
    | codomain(codomain(a)) = codomain(a) ),
    introduced(tautology,[equality,[$cnf( $equal(codomain(codomain(a)),codomain(a)) ),[0,0],$fot(codomain(a))]]) ).

cnf(refute_0_10,plain,
    ( codomain(a) != codomain(a)
    | codomain(codomain(a)) = codomain(a) ),
    inference(resolve,[$cnf( $equal(codomain(codomain(a)),codomain(a)) )],[refute_0_8,refute_0_9]) ).

cnf(refute_0_11,plain,
    codomain(a) != codomain(a),
    inference(resolve,[$cnf( $equal(codomain(codomain(a)),codomain(a)) )],[refute_0_10,prove_codomain_is_idempotent]) ).

cnf(refute_0_12,plain,
    codomain(a) = codomain(a),
    introduced(tautology,[refl,[$fot(codomain(a))]]) ).

cnf(refute_0_13,plain,
    $false,
    inference(resolve,[$cnf( $equal(codomain(a),codomain(a)) )],[refute_0_12,refute_0_11]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.11  % Problem  : CAT014-2 : TPTP v8.1.0. Released v1.0.0.
% 0.04/0.12  % Command  : metis --show proof --show saturation %s
% 0.11/0.32  % Computer : n026.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit : 300
% 0.11/0.32  % WCLimit  : 600
% 0.11/0.32  % DateTime : Sun May 29 15:44:24 EDT 2022
% 0.11/0.32  % CPUTime  : 
% 0.11/0.33  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.11/0.33  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.33  
% 0.11/0.33  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.11/0.33  
%------------------------------------------------------------------------------