%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : CAT005-4 : 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 00:04:33 EDT 2022

% Result   : Unsatisfiable 34.24s 34.47s
% Output   : CNFRefutation 34.24s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   15
% Syntax   : Number of clauses     :   43 (  15 unt;   0 nHn;  41 RR)
%            Number of literals    :   78 (  38 equ;  38 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   12 (   1 sgn)

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

cnf(composition_implies_domain,axiom,
    ( ~ there_exists(compose(X,Y))
    | there_exists(domain(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(ad_exists,hypothesis,
    there_exists(compose(a,d)) ).

cnf(xd_equals_x,hypothesis,
    ( ~ there_exists(compose(X,d))
    | compose(X,d) = X ) ).

cnf(prove_domain_of_a_is_d,negated_conjecture,
    domain(a) != d ).

cnf(refute_0_0,plain,
    ( ~ there_exists(compose(codomain(d),d))
    | compose(codomain(d),d) = codomain(d) ),
    inference(subst,[],[xd_equals_x:[bind(X,$fot(codomain(d)))]]) ).

cnf(refute_0_1,plain,
    compose(codomain(d),d) = d,
    inference(subst,[],[compose_codomain:[bind(X,$fot(d))]]) ).

cnf(refute_0_2,plain,
    ( compose(codomain(d),d) != d
    | ~ there_exists(d)
    | there_exists(compose(codomain(d),d)) ),
    introduced(tautology,[equality,[$cnf( ~ there_exists(compose(codomain(d),d)) ),[0],$fot(d)]]) ).

cnf(refute_0_3,plain,
    ( ~ there_exists(d)
    | there_exists(compose(codomain(d),d)) ),
    inference(resolve,[$cnf( $equal(compose(codomain(d),d),d) )],[refute_0_1,refute_0_2]) ).

cnf(refute_0_4,plain,
    ( ~ there_exists(d)
    | compose(codomain(d),d) = codomain(d) ),
    inference(resolve,[$cnf( there_exists(compose(codomain(d),d)) )],[refute_0_3,refute_0_0]) ).

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

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

cnf(refute_0_7,plain,
    ( ~ there_exists(d)
    | d = codomain(d) ),
    inference(resolve,[$cnf( $equal(compose(codomain(d),d),codomain(d)) )],[refute_0_4,refute_0_6]) ).

cnf(refute_0_8,plain,
    ( ~ there_exists(codomain(d))
    | there_exists(d) ),
    inference(subst,[],[codomain_has_elements:[bind(X,$fot(d))]]) ).

cnf(refute_0_9,plain,
    ( ~ there_exists(compose(a,d))
    | there_exists(domain(a)) ),
    inference(subst,[],[composition_implies_domain:[bind(X,$fot(a)),bind(Y,$fot(d))]]) ).

cnf(refute_0_10,plain,
    ( ~ there_exists(compose(a,d))
    | compose(a,d) = a ),
    inference(subst,[],[xd_equals_x:[bind(X,$fot(a))]]) ).

cnf(refute_0_11,plain,
    compose(a,d) = a,
    inference(resolve,[$cnf( there_exists(compose(a,d)) )],[ad_exists,refute_0_10]) ).

cnf(refute_0_12,plain,
    ( compose(a,d) != a
    | ~ there_exists(a)
    | there_exists(compose(a,d)) ),
    introduced(tautology,[equality,[$cnf( ~ there_exists(compose(a,d)) ),[0],$fot(a)]]) ).

cnf(refute_0_13,plain,
    ( ~ there_exists(a)
    | there_exists(compose(a,d)) ),
    inference(resolve,[$cnf( $equal(compose(a,d),a) )],[refute_0_11,refute_0_12]) ).

cnf(refute_0_14,plain,
    ( ~ there_exists(a)
    | there_exists(domain(a)) ),
    inference(resolve,[$cnf( there_exists(compose(a,d)) )],[refute_0_13,refute_0_9]) ).

cnf(refute_0_15,plain,
    ( compose(a,d) != a
    | ~ there_exists(compose(a,d))
    | there_exists(a) ),
    introduced(tautology,[equality,[$cnf( there_exists(compose(a,d)) ),[0],$fot(a)]]) ).

cnf(refute_0_16,plain,
    ( ~ there_exists(compose(a,d))
    | there_exists(a) ),
    inference(resolve,[$cnf( $equal(compose(a,d),a) )],[refute_0_11,refute_0_15]) ).

cnf(refute_0_17,plain,
    there_exists(a),
    inference(resolve,[$cnf( there_exists(compose(a,d)) )],[ad_exists,refute_0_16]) ).

cnf(refute_0_18,plain,
    there_exists(domain(a)),
    inference(resolve,[$cnf( there_exists(a) )],[refute_0_17,refute_0_14]) ).

cnf(refute_0_19,plain,
    ( ~ there_exists(compose(a,d))
    | domain(a) = codomain(d) ),
    inference(subst,[],[domain_codomain_composition1:[bind(X,$fot(a)),bind(Y,$fot(d))]]) ).

cnf(refute_0_20,plain,
    ( ~ there_exists(a)
    | domain(a) = codomain(d) ),
    inference(resolve,[$cnf( there_exists(compose(a,d)) )],[refute_0_13,refute_0_19]) ).

cnf(refute_0_21,plain,
    domain(a) = codomain(d),
    inference(resolve,[$cnf( there_exists(a) )],[refute_0_17,refute_0_20]) ).

cnf(refute_0_22,plain,
    ( domain(a) != codomain(d)
    | ~ there_exists(domain(a))
    | there_exists(codomain(d)) ),
    introduced(tautology,[equality,[$cnf( there_exists(domain(a)) ),[0],$fot(codomain(d))]]) ).

cnf(refute_0_23,plain,
    ( ~ there_exists(domain(a))
    | there_exists(codomain(d)) ),
    inference(resolve,[$cnf( $equal(domain(a),codomain(d)) )],[refute_0_21,refute_0_22]) ).

cnf(refute_0_24,plain,
    there_exists(codomain(d)),
    inference(resolve,[$cnf( there_exists(domain(a)) )],[refute_0_18,refute_0_23]) ).

cnf(refute_0_25,plain,
    there_exists(d),
    inference(resolve,[$cnf( there_exists(codomain(d)) )],[refute_0_24,refute_0_8]) ).

cnf(refute_0_26,plain,
    d = codomain(d),
    inference(resolve,[$cnf( there_exists(d) )],[refute_0_25,refute_0_7]) ).

cnf(refute_0_27,plain,
    ( codomain(d) != d
    | domain(a) != codomain(d)
    | domain(a) = d ),
    introduced(tautology,[equality,[$cnf( $equal(domain(a),codomain(d)) ),[1],$fot(d)]]) ).

cnf(refute_0_28,plain,
    ( codomain(d) != d
    | domain(a) = d ),
    inference(resolve,[$cnf( $equal(domain(a),codomain(d)) )],[refute_0_21,refute_0_27]) ).

cnf(refute_0_29,plain,
    codomain(d) != d,
    inference(resolve,[$cnf( $equal(domain(a),d) )],[refute_0_28,prove_domain_of_a_is_d]) ).

cnf(refute_0_30,plain,
    X0 = X0,
    introduced(tautology,[refl,[$fot(X0)]]) ).

cnf(refute_0_31,plain,
    ( X0 != X0
    | X0 != Y0
    | Y0 = X0 ),
    introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).

cnf(refute_0_32,plain,
    ( X0 != Y0
    | Y0 = X0 ),
    inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_30,refute_0_31]) ).

cnf(refute_0_33,plain,
    ( d != codomain(d)
    | codomain(d) = d ),
    inference(subst,[],[refute_0_32:[bind(X0,$fot(d)),bind(Y0,$fot(codomain(d)))]]) ).

cnf(refute_0_34,plain,
    d != codomain(d),
    inference(resolve,[$cnf( $equal(codomain(d),d) )],[refute_0_33,refute_0_29]) ).

cnf(refute_0_35,plain,
    $false,
    inference(resolve,[$cnf( $equal(d,codomain(d)) )],[refute_0_26,refute_0_34]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : CAT005-4 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12  % 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 17:15:09 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 0.13/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 34.24/34.47  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 34.24/34.47  
% 34.24/34.47  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 34.24/34.47  
%------------------------------------------------------------------------------