TSTP Solution File: CAT006-1 by Metis---2.4
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%------------------------------------------------------------------------------
% 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
%------------------------------------------------------------------------------