%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : CAT012-4 : 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 00:04:35 EDT 2022

% Result   : Unsatisfiable 57.33s 57.50s
% Output   : CNFRefutation 57.33s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    8
% Syntax   : Number of clauses     :   20 (   9 unt;   0 nHn;  17 RR)
%            Number of literals    :   33 (  18 equ;  15 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   :   14 (   0 sgn)

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

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

cnf(compose_domain,axiom,
    compose(X,domain(X)) = X ).

cnf(assume_domain_exists,hypothesis,
    there_exists(domain(a)) ).

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

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

cnf(refute_0_1,plain,
    there_exists(a),
    inference(resolve,[$cnf( there_exists(domain(a)) )],[assume_domain_exists,refute_0_0]) ).

cnf(refute_0_2,plain,
    ( ~ there_exists(compose(X_48,domain(X_48)))
    | domain(X_48) = codomain(domain(X_48)) ),
    inference(subst,[],[domain_codomain_composition1:[bind(X,$fot(X_48)),bind(Y,$fot(domain(X_48)))]]) ).

cnf(refute_0_3,plain,
    compose(X_48,domain(X_48)) = X_48,
    inference(subst,[],[compose_domain:[bind(X,$fot(X_48))]]) ).

cnf(refute_0_4,plain,
    ( compose(X_48,domain(X_48)) != X_48
    | ~ there_exists(X_48)
    | there_exists(compose(X_48,domain(X_48))) ),
    introduced(tautology,[equality,[$cnf( ~ there_exists(compose(X_48,domain(X_48))) ),[0],$fot(X_48)]]) ).

cnf(refute_0_5,plain,
    ( ~ there_exists(X_48)
    | there_exists(compose(X_48,domain(X_48))) ),
    inference(resolve,[$cnf( $equal(compose(X_48,domain(X_48)),X_48) )],[refute_0_3,refute_0_4]) ).

cnf(refute_0_6,plain,
    ( ~ there_exists(X_48)
    | domain(X_48) = codomain(domain(X_48)) ),
    inference(resolve,[$cnf( there_exists(compose(X_48,domain(X_48))) )],[refute_0_5,refute_0_2]) ).

cnf(refute_0_7,plain,
    ( ~ there_exists(a)
    | domain(a) = codomain(domain(a)) ),
    inference(subst,[],[refute_0_6:[bind(X_48,$fot(a))]]) ).

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

cnf(refute_0_9,plain,
    X0 = X0,
    introduced(tautology,[refl,[$fot(X0)]]) ).

cnf(refute_0_10,plain,
    ( X0 != X0
    | X0 != Y0
    | Y0 = X0 ),
    introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).

cnf(refute_0_11,plain,
    ( X0 != Y0
    | Y0 = X0 ),
    inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_9,refute_0_10]) ).

cnf(refute_0_12,plain,
    ( domain(a) != codomain(domain(a))
    | codomain(domain(a)) = domain(a) ),
    inference(subst,[],[refute_0_11:[bind(X0,$fot(domain(a))),bind(Y0,$fot(codomain(domain(a))))]]) ).

cnf(refute_0_13,plain,
    domain(a) != codomain(domain(a)),
    inference(resolve,[$cnf( $equal(codomain(domain(a)),domain(a)) )],[refute_0_12,prove_codomain_of_domain_is_domain]) ).

cnf(refute_0_14,plain,
    $false,
    inference(resolve,[$cnf( $equal(domain(a),codomain(domain(a))) )],[refute_0_8,refute_0_13]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : CAT012-4 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.12  % Command  : metis --show proof --show saturation %s
% 0.13/0.33  % Computer : n017.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Sun May 29 19:54:39 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 57.33/57.50  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 57.33/57.50  
% 57.33/57.50  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 57.33/57.50  
%------------------------------------------------------------------------------