%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : CAT006-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n019.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 1.01s 1.18s
% Output   : CNFRefutation 1.01s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   14
% Syntax   : Number of clauses     :   42 (  14 unt;   0 nHn;  40 RR)
%            Number of literals    :   76 (  40 equ;  36 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(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(domain_codomain_composition1,axiom,
    ( ~ there_exists(compose(X,Y))
    | domain(X) = codomain(Y) ) ).

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

cnf(da_exists,hypothesis,
    there_exists(compose(d,a)) ).

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

cnf(prove_codomain_of_a_is_d,negated_conjecture,
    codomain(a) != d ).

cnf(refute_0_0,plain,
    ( ~ there_exists(compose(d,a))
    | domain(d) = codomain(a) ),
    inference(subst,[],[domain_codomain_composition1:[bind(X,$fot(d)),bind(Y,$fot(a))]]) ).

cnf(refute_0_1,plain,
    ( ~ there_exists(compose(d,a))
    | compose(d,a) = a ),
    inference(subst,[],[dx_equals_x:[bind(X,$fot(a))]]) ).

cnf(refute_0_2,plain,
    compose(d,a) = a,
    inference(resolve,[$cnf( there_exists(compose(d,a)) )],[da_exists,refute_0_1]) ).

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

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

cnf(refute_0_5,plain,
    ( ~ there_exists(a)
    | domain(d) = codomain(a) ),
    inference(resolve,[$cnf( there_exists(compose(d,a)) )],[refute_0_4,refute_0_0]) ).

cnf(refute_0_6,plain,
    ( ~ there_exists(compose(d,domain(d)))
    | compose(d,domain(d)) = domain(d) ),
    inference(subst,[],[dx_equals_x:[bind(X,$fot(domain(d)))]]) ).

cnf(refute_0_7,plain,
    compose(d,domain(d)) = d,
    inference(subst,[],[compose_domain:[bind(X,$fot(d))]]) ).

cnf(refute_0_8,plain,
    ( compose(d,domain(d)) != d
    | ~ there_exists(d)
    | there_exists(compose(d,domain(d))) ),
    introduced(tautology,[equality,[$cnf( ~ there_exists(compose(d,domain(d))) ),[0],$fot(d)]]) ).

cnf(refute_0_9,plain,
    ( ~ there_exists(d)
    | there_exists(compose(d,domain(d))) ),
    inference(resolve,[$cnf( $equal(compose(d,domain(d)),d) )],[refute_0_7,refute_0_8]) ).

cnf(refute_0_10,plain,
    ( ~ there_exists(d)
    | compose(d,domain(d)) = domain(d) ),
    inference(resolve,[$cnf( there_exists(compose(d,domain(d))) )],[refute_0_9,refute_0_6]) ).

cnf(refute_0_11,plain,
    ( compose(d,domain(d)) != d
    | compose(d,domain(d)) != domain(d)
    | d = domain(d) ),
    introduced(tautology,[equality,[$cnf( $equal(compose(d,domain(d)),domain(d)) ),[0],$fot(d)]]) ).

cnf(refute_0_12,plain,
    ( compose(d,domain(d)) != domain(d)
    | d = domain(d) ),
    inference(resolve,[$cnf( $equal(compose(d,domain(d)),d) )],[refute_0_7,refute_0_11]) ).

cnf(refute_0_13,plain,
    ( ~ there_exists(d)
    | d = domain(d) ),
    inference(resolve,[$cnf( $equal(compose(d,domain(d)),domain(d)) )],[refute_0_10,refute_0_12]) ).

cnf(refute_0_14,plain,
    ( ~ there_exists(domain(d))
    | there_exists(d) ),
    inference(subst,[],[domain_has_elements:[bind(X,$fot(d))]]) ).

cnf(refute_0_15,plain,
    ( ~ there_exists(compose(d,a))
    | there_exists(domain(d)) ),
    inference(subst,[],[composition_implies_domain:[bind(X,$fot(d)),bind(Y,$fot(a))]]) ).

cnf(refute_0_16,plain,
    ( ~ there_exists(a)
    | there_exists(domain(d)) ),
    inference(resolve,[$cnf( there_exists(compose(d,a)) )],[refute_0_4,refute_0_15]) ).

cnf(refute_0_17,plain,
    ( compose(d,a) != a
    | ~ there_exists(compose(d,a))
    | there_exists(a) ),
    introduced(tautology,[equality,[$cnf( there_exists(compose(d,a)) ),[0],$fot(a)]]) ).

cnf(refute_0_18,plain,
    ( ~ there_exists(compose(d,a))
    | there_exists(a) ),
    inference(resolve,[$cnf( $equal(compose(d,a),a) )],[refute_0_2,refute_0_17]) ).

cnf(refute_0_19,plain,
    there_exists(a),
    inference(resolve,[$cnf( there_exists(compose(d,a)) )],[da_exists,refute_0_18]) ).

cnf(refute_0_20,plain,
    there_exists(domain(d)),
    inference(resolve,[$cnf( there_exists(a) )],[refute_0_19,refute_0_16]) ).

cnf(refute_0_21,plain,
    there_exists(d),
    inference(resolve,[$cnf( there_exists(domain(d)) )],[refute_0_20,refute_0_14]) ).

cnf(refute_0_22,plain,
    d = domain(d),
    inference(resolve,[$cnf( there_exists(d) )],[refute_0_21,refute_0_13]) ).

cnf(refute_0_23,plain,
    X0 = X0,
    introduced(tautology,[refl,[$fot(X0)]]) ).

cnf(refute_0_24,plain,
    ( X0 != X0
    | X0 != Y0
    | Y0 = X0 ),
    introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).

cnf(refute_0_25,plain,
    ( X0 != Y0
    | Y0 = X0 ),
    inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_23,refute_0_24]) ).

cnf(refute_0_26,plain,
    ( d != domain(d)
    | domain(d) = d ),
    inference(subst,[],[refute_0_25:[bind(X0,$fot(d)),bind(Y0,$fot(domain(d)))]]) ).

cnf(refute_0_27,plain,
    domain(d) = d,
    inference(resolve,[$cnf( $equal(d,domain(d)) )],[refute_0_22,refute_0_26]) ).

cnf(refute_0_28,plain,
    ( domain(d) != codomain(a)
    | domain(d) != d
    | d = codomain(a) ),
    introduced(tautology,[equality,[$cnf( $equal(domain(d),codomain(a)) ),[0],$fot(d)]]) ).

cnf(refute_0_29,plain,
    ( domain(d) != codomain(a)
    | d = codomain(a) ),
    inference(resolve,[$cnf( $equal(domain(d),d) )],[refute_0_27,refute_0_28]) ).

cnf(refute_0_30,plain,
    ( ~ there_exists(a)
    | d = codomain(a) ),
    inference(resolve,[$cnf( $equal(domain(d),codomain(a)) )],[refute_0_5,refute_0_29]) ).

cnf(refute_0_31,plain,
    d = codomain(a),
    inference(resolve,[$cnf( there_exists(a) )],[refute_0_19,refute_0_30]) ).

cnf(refute_0_32,plain,
    ( d != codomain(a)
    | codomain(a) = d ),
    inference(subst,[],[refute_0_25:[bind(X0,$fot(d)),bind(Y0,$fot(codomain(a)))]]) ).

cnf(refute_0_33,plain,
    d != codomain(a),
    inference(resolve,[$cnf( $equal(codomain(a),d) )],[refute_0_32,prove_codomain_of_a_is_d]) ).

cnf(refute_0_34,plain,
    $false,
    inference(resolve,[$cnf( $equal(d,codomain(a)) )],[refute_0_31,refute_0_33]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : CAT006-4 : TPTP v8.1.0. Released v1.0.0.
% 0.04/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.34  % Computer : n019.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Sun May 29 17:53:41 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.13/0.35  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.01/1.18  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.01/1.18  
% 1.01/1.18  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 1.01/1.18  
%------------------------------------------------------------------------------