%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : CAT013-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %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  : 600s
% DateTime : Fri Jul 15 00:04:35 EDT 2022

% Result   : Unsatisfiable 19.74s 19.96s
% Output   : CNFRefutation 19.74s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   15 (   7 unt;   0 nHn;  13 RR)
%            Number of literals    :   24 (   9 equ;  10 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    3 (   2 avg)
%            Number of predicates  :    4 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   1 con; 0-2 aty)
%            Number of variables   :    9 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(codomain_has_elements,axiom,
    ( ~ there_exists(codomain(X))
    | there_exists(X) ) ).

cnf(domain_codomain_composition1,axiom,
    ( ~ there_exists(compose(X,Y))
    | domain(X) = codomain(Y) ) ).

cnf(compose_codomain,axiom,
    compose(codomain(X),X) = X ).

cnf(assume_codomain_exists,hypothesis,
    there_exists(codomain(a)) ).

cnf(prove_domain_of_codomain_is_codomain,negated_conjecture,
    domain(codomain(a)) != codomain(a) ).

cnf(refute_0_0,plain,
    ( ~ there_exists(codomain(a))
    | there_exists(a) ),
    inference(subst,[],[codomain_has_elements:[bind(X,$fot(a))]]) ).

cnf(refute_0_1,plain,
    there_exists(a),
    inference(resolve,[$cnf( there_exists(codomain(a)) )],[assume_codomain_exists,refute_0_0]) ).

cnf(refute_0_2,plain,
    ( ~ there_exists(compose(codomain(X_33),X_33))
    | domain(codomain(X_33)) = codomain(X_33) ),
    inference(subst,[],[domain_codomain_composition1:[bind(X,$fot(codomain(X_33))),bind(Y,$fot(X_33))]]) ).

cnf(refute_0_3,plain,
    compose(codomain(X_33),X_33) = X_33,
    inference(subst,[],[compose_codomain:[bind(X,$fot(X_33))]]) ).

cnf(refute_0_4,plain,
    ( compose(codomain(X_33),X_33) != X_33
    | ~ there_exists(X_33)
    | there_exists(compose(codomain(X_33),X_33)) ),
    introduced(tautology,[equality,[$cnf( ~ there_exists(compose(codomain(X_33),X_33)) ),[0],$fot(X_33)]]) ).

cnf(refute_0_5,plain,
    ( ~ there_exists(X_33)
    | there_exists(compose(codomain(X_33),X_33)) ),
    inference(resolve,[$cnf( $equal(compose(codomain(X_33),X_33),X_33) )],[refute_0_3,refute_0_4]) ).

cnf(refute_0_6,plain,
    ( ~ there_exists(X_33)
    | domain(codomain(X_33)) = codomain(X_33) ),
    inference(resolve,[$cnf( there_exists(compose(codomain(X_33),X_33)) )],[refute_0_5,refute_0_2]) ).

cnf(refute_0_7,plain,
    ( ~ there_exists(a)
    | domain(codomain(a)) = codomain(a) ),
    inference(subst,[],[refute_0_6:[bind(X_33,$fot(a))]]) ).

cnf(refute_0_8,plain,
    domain(codomain(a)) = codomain(a),
    inference(resolve,[$cnf( there_exists(a) )],[refute_0_1,refute_0_7]) ).

cnf(refute_0_9,plain,
    $false,
    inference(resolve,[$cnf( $equal(domain(codomain(a)),codomain(a)) )],[refute_0_8,prove_domain_of_codomain_is_codomain]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : CAT013-3 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.13  % Command  : metis --show proof --show saturation %s
% 0.12/0.34  % Computer : n021.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Sun May 29 23:31:28 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.19/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 19.74/19.96  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 19.74/19.96  
% 19.74/19.96  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 19.74/19.96  
%------------------------------------------------------------------------------