%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : CAT017-3 : 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 00:04:36 EDT 2022

% Result   : Unsatisfiable 0.14s 0.33s
% Output   : CNFRefutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   15 (   7 unt;   0 nHn;  13 RR)
%            Number of literals    :   24 (   3 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 (   1 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(domain_has_elements,axiom,
    ( ~ there_exists(domain(X))
    | there_exists(X) ) ).

cnf(composition_implies_domain,axiom,
    ( ~ there_exists(compose(X,Y))
    | there_exists(domain(X)) ) ).

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

cnf(assume_a_exists,hypothesis,
    there_exists(a) ).

cnf(prove_codomain_of_a_exists,negated_conjecture,
    ~ there_exists(codomain(a)) ).

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

cnf(refute_0_1,plain,
    ( ~ there_exists(compose(codomain(X_34),X_34))
    | there_exists(domain(codomain(X_34))) ),
    inference(subst,[],[composition_implies_domain:[bind(X,$fot(codomain(X_34))),bind(Y,$fot(X_34))]]) ).

cnf(refute_0_2,plain,
    compose(codomain(X_34),X_34) = X_34,
    inference(subst,[],[compose_codomain:[bind(X,$fot(X_34))]]) ).

cnf(refute_0_3,plain,
    ( compose(codomain(X_34),X_34) != X_34
    | ~ there_exists(X_34)
    | there_exists(compose(codomain(X_34),X_34)) ),
    introduced(tautology,[equality,[$cnf( ~ there_exists(compose(codomain(X_34),X_34)) ),[0],$fot(X_34)]]) ).

cnf(refute_0_4,plain,
    ( ~ there_exists(X_34)
    | there_exists(compose(codomain(X_34),X_34)) ),
    inference(resolve,[$cnf( $equal(compose(codomain(X_34),X_34),X_34) )],[refute_0_2,refute_0_3]) ).

cnf(refute_0_5,plain,
    ( ~ there_exists(X_34)
    | there_exists(domain(codomain(X_34))) ),
    inference(resolve,[$cnf( there_exists(compose(codomain(X_34),X_34)) )],[refute_0_4,refute_0_1]) ).

cnf(refute_0_6,plain,
    ( ~ there_exists(a)
    | there_exists(domain(codomain(a))) ),
    inference(subst,[],[refute_0_5:[bind(X_34,$fot(a))]]) ).

cnf(refute_0_7,plain,
    there_exists(domain(codomain(a))),
    inference(resolve,[$cnf( there_exists(a) )],[assume_a_exists,refute_0_6]) ).

cnf(refute_0_8,plain,
    there_exists(codomain(a)),
    inference(resolve,[$cnf( there_exists(domain(codomain(a))) )],[refute_0_7,refute_0_0]) ).

cnf(refute_0_9,plain,
    $false,
    inference(resolve,[$cnf( there_exists(codomain(a)) )],[refute_0_8,prove_codomain_of_a_exists]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09  % Problem  : CAT017-3 : TPTP v8.1.0. Released v1.0.0.
% 0.05/0.10  % Command  : metis --show proof --show saturation %s
% 0.09/0.30  % Computer : n017.cluster.edu
% 0.09/0.30  % Model    : x86_64 x86_64
% 0.09/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30  % Memory   : 8042.1875MB
% 0.09/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30  % CPULimit : 300
% 0.09/0.30  % WCLimit  : 600
% 0.09/0.30  % DateTime : Sun May 29 19:52:39 EDT 2022
% 0.09/0.30  % CPUTime  : 
% 0.09/0.30  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.14/0.33  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.33  
% 0.14/0.33  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.14/0.33  
%------------------------------------------------------------------------------