%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : CAT006-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n027.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 0.18s 0.41s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   11
% Syntax   : Number of clauses     :   34 (  15 unt;   0 nHn;  31 RR)
%            Number of literals    :   63 (  15 equ;  31 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    6 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :    3 (   3 usr;   2 con; 0-1 aty)
%            Number of variables   :   23 (   2 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(category_theory_axiom3,axiom,
    ( ~ product(Y,Z,Yz)
    | ~ defined(X,Yz)
    | defined(X,Y) ) ).

cnf(codomain_is_an_identity_map,axiom,
    identity_map(codomain(X)) ).

cnf(mapping_from_codomain_of_x_to_x,axiom,
    defined(codomain(X),X) ).

cnf(identity1,axiom,
    ( ~ defined(X,Y)
    | ~ identity_map(X)
    | product(X,Y,Y) ) ).

cnf(identity2,axiom,
    ( ~ defined(X,Y)
    | ~ identity_map(Y)
    | product(X,Y,X) ) ).

cnf(composition_is_well_defined,axiom,
    ( ~ product(X,Y,Z)
    | ~ product(X,Y,W)
    | Z = W ) ).

cnf(ha_defined,hypothesis,
    defined(h,a) ).

cnf(h_is_the_identity_map,hypothesis,
    identity_map(h) ).

cnf(prove_codomain_of_a_is_h,negated_conjecture,
    codomain(a) != h ).

cnf(refute_0_0,plain,
    ( ~ defined(codomain(a),h)
    | ~ identity_map(h)
    | product(codomain(a),h,codomain(a)) ),
    inference(subst,[],[identity2:[bind(X,$fot(codomain(a))),bind(Y,$fot(h))]]) ).

cnf(refute_0_1,plain,
    defined(codomain(a),a),
    inference(subst,[],[mapping_from_codomain_of_x_to_x:[bind(X,$fot(a))]]) ).

cnf(refute_0_2,plain,
    ( ~ defined(h,a)
    | ~ identity_map(h)
    | product(h,a,a) ),
    inference(subst,[],[identity1:[bind(X,$fot(h)),bind(Y,$fot(a))]]) ).

cnf(refute_0_3,plain,
    ( ~ identity_map(h)
    | product(h,a,a) ),
    inference(resolve,[$cnf( defined(h,a) )],[ha_defined,refute_0_2]) ).

cnf(refute_0_4,plain,
    product(h,a,a),
    inference(resolve,[$cnf( identity_map(h) )],[h_is_the_identity_map,refute_0_3]) ).

cnf(refute_0_5,plain,
    ( ~ defined(X_106,a)
    | ~ product(h,a,a)
    | defined(X_106,h) ),
    inference(subst,[],[category_theory_axiom3:[bind(X,$fot(X_106)),bind(Y,$fot(h)),bind(Yz,$fot(a)),bind(Z,$fot(a))]]) ).

cnf(refute_0_6,plain,
    ( ~ defined(X_106,a)
    | defined(X_106,h) ),
    inference(resolve,[$cnf( product(h,a,a) )],[refute_0_4,refute_0_5]) ).

cnf(refute_0_7,plain,
    ( ~ defined(codomain(a),a)
    | defined(codomain(a),h) ),
    inference(subst,[],[refute_0_6:[bind(X_106,$fot(codomain(a)))]]) ).

cnf(refute_0_8,plain,
    defined(codomain(a),h),
    inference(resolve,[$cnf( defined(codomain(a),a) )],[refute_0_1,refute_0_7]) ).

cnf(refute_0_9,plain,
    ( ~ identity_map(h)
    | product(codomain(a),h,codomain(a)) ),
    inference(resolve,[$cnf( defined(codomain(a),h) )],[refute_0_8,refute_0_0]) ).

cnf(refute_0_10,plain,
    product(codomain(a),h,codomain(a)),
    inference(resolve,[$cnf( identity_map(h) )],[h_is_the_identity_map,refute_0_9]) ).

cnf(refute_0_11,plain,
    ( ~ product(codomain(a),h,W)
    | ~ product(codomain(a),h,h)
    | h = W ),
    inference(subst,[],[composition_is_well_defined:[bind(X,$fot(codomain(a))),bind(Y,$fot(h)),bind(Z,$fot(h))]]) ).

cnf(refute_0_12,plain,
    ( ~ defined(codomain(a),h)
    | ~ identity_map(codomain(a))
    | product(codomain(a),h,h) ),
    inference(subst,[],[identity1:[bind(X,$fot(codomain(a))),bind(Y,$fot(h))]]) ).

cnf(refute_0_13,plain,
    ( ~ identity_map(codomain(a))
    | product(codomain(a),h,h) ),
    inference(resolve,[$cnf( defined(codomain(a),h) )],[refute_0_8,refute_0_12]) ).

cnf(refute_0_14,plain,
    identity_map(codomain(a)),
    inference(subst,[],[codomain_is_an_identity_map:[bind(X,$fot(a))]]) ).

cnf(refute_0_15,plain,
    product(codomain(a),h,h),
    inference(resolve,[$cnf( identity_map(codomain(a)) )],[refute_0_14,refute_0_13]) ).

cnf(refute_0_16,plain,
    ( ~ product(codomain(a),h,W)
    | h = W ),
    inference(resolve,[$cnf( product(codomain(a),h,h) )],[refute_0_15,refute_0_11]) ).

cnf(refute_0_17,plain,
    ( ~ product(codomain(a),h,codomain(a))
    | h = codomain(a) ),
    inference(subst,[],[refute_0_16:[bind(W,$fot(codomain(a)))]]) ).

cnf(refute_0_18,plain,
    h = codomain(a),
    inference(resolve,[$cnf( product(codomain(a),h,codomain(a)) )],[refute_0_10,refute_0_17]) ).

cnf(refute_0_19,plain,
    X0 = X0,
    introduced(tautology,[refl,[$fot(X0)]]) ).

cnf(refute_0_20,plain,
    ( X0 != X0
    | X0 != Y0
    | Y0 = X0 ),
    introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).

cnf(refute_0_21,plain,
    ( X0 != Y0
    | Y0 = X0 ),
    inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_19,refute_0_20]) ).

cnf(refute_0_22,plain,
    ( h != codomain(a)
    | codomain(a) = h ),
    inference(subst,[],[refute_0_21:[bind(X0,$fot(h)),bind(Y0,$fot(codomain(a)))]]) ).

cnf(refute_0_23,plain,
    h != codomain(a),
    inference(resolve,[$cnf( $equal(codomain(a),h) )],[refute_0_22,prove_codomain_of_a_is_h]) ).

cnf(refute_0_24,plain,
    $false,
    inference(resolve,[$cnf( $equal(h,codomain(a)) )],[refute_0_18,refute_0_23]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem  : CAT006-1 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.12  % Command  : metis --show proof --show saturation %s
% 0.12/0.33  % Computer : n027.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Sun May 29 19:09:30 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.33  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.18/0.41  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.41  
% 0.18/0.41  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.18/0.41  
%------------------------------------------------------------------------------