TSTP Solution File: CAT011-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : CAT011-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n025.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 00:04:34 EDT 2022
% Result : Unsatisfiable 275.70s 275.99s
% Output : CNFRefutation 275.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 12
% Syntax : Number of clauses : 38 ( 20 unt; 0 nHn; 23 RR)
% Number of literals : 63 ( 32 equ; 27 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 6 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 40 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(closure_of_composition,axiom,
( ~ defined(X,Y)
| product(X,Y,compose(X,Y)) ) ).
cnf(domain_is_an_identity_map,axiom,
identity_map(domain(X)) ).
cnf(mapping_from_x_to_its_domain,axiom,
defined(X,domain(X)) ).
cnf(product_on_domain,axiom,
product(X,domain(X),X) ).
cnf(identity1,axiom,
( ~ defined(X,Y)
| ~ identity_map(X)
| product(X,Y,Y) ) ).
cnf(composition_is_well_defined,axiom,
( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| Z = W ) ).
cnf(prove_domain_is_idempotent,negated_conjecture,
domain(domain(a)) != domain(a) ).
cnf(refute_0_0,plain,
defined(X_13,domain(X_13)),
inference(subst,[],[mapping_from_x_to_its_domain:[bind(X,$fot(X_13))]]) ).
cnf(refute_0_1,plain,
( ~ defined(X_13,domain(X_13))
| ~ identity_map(X_13)
| product(X_13,domain(X_13),domain(X_13)) ),
inference(subst,[],[identity1:[bind(X,$fot(X_13)),bind(Y,$fot(domain(X_13)))]]) ).
cnf(refute_0_2,plain,
( ~ identity_map(X_13)
| product(X_13,domain(X_13),domain(X_13)) ),
inference(resolve,[$cnf( defined(X_13,domain(X_13)) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( ~ identity_map(domain(X))
| product(domain(X),domain(domain(X)),domain(domain(X))) ),
inference(subst,[],[refute_0_2:[bind(X_13,$fot(domain(X)))]]) ).
cnf(refute_0_4,plain,
product(domain(X),domain(domain(X)),domain(domain(X))),
inference(resolve,[$cnf( identity_map(domain(X)) )],[domain_is_an_identity_map,refute_0_3]) ).
cnf(refute_0_5,plain,
defined(X_9,domain(X_9)),
inference(subst,[],[mapping_from_x_to_its_domain:[bind(X,$fot(X_9))]]) ).
cnf(refute_0_6,plain,
( ~ defined(X_9,domain(X_9))
| product(X_9,domain(X_9),compose(X_9,domain(X_9))) ),
inference(subst,[],[closure_of_composition:[bind(X,$fot(X_9)),bind(Y,$fot(domain(X_9)))]]) ).
cnf(refute_0_7,plain,
product(X_9,domain(X_9),compose(X_9,domain(X_9))),
inference(resolve,[$cnf( defined(X_9,domain(X_9)) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
product(X_105654,domain(X_105654),compose(X_105654,domain(X_105654))),
inference(subst,[],[refute_0_7:[bind(X_9,$fot(X_105654))]]) ).
cnf(refute_0_9,plain,
( ~ product(X_105654,domain(X_105654),X_105656)
| ~ product(X_105654,domain(X_105654),compose(X_105654,domain(X_105654)))
| X_105656 = compose(X_105654,domain(X_105654)) ),
inference(subst,[],[composition_is_well_defined:[bind(W,$fot(compose(X_105654,domain(X_105654)))),bind(X,$fot(X_105654)),bind(Y,$fot(domain(X_105654))),bind(Z,$fot(X_105656))]]) ).
cnf(refute_0_10,plain,
( ~ product(X_105654,domain(X_105654),X_105656)
| X_105656 = compose(X_105654,domain(X_105654)) ),
inference(resolve,[$cnf( product(X_105654,domain(X_105654),compose(X_105654,domain(X_105654))) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
( ~ product(domain(X),domain(domain(X)),domain(domain(X)))
| domain(domain(X)) = compose(domain(X),domain(domain(X))) ),
inference(subst,[],[refute_0_10:[bind(X_105654,$fot(domain(X))),bind(X_105656,$fot(domain(domain(X))))]]) ).
cnf(refute_0_12,plain,
domain(domain(X)) = compose(domain(X),domain(domain(X))),
inference(resolve,[$cnf( product(domain(X),domain(domain(X)),domain(domain(X))) )],[refute_0_4,refute_0_11]) ).
cnf(refute_0_13,plain,
product(X_105950,domain(X_105950),X_105950),
inference(subst,[],[product_on_domain:[bind(X,$fot(X_105950))]]) ).
cnf(refute_0_14,plain,
( ~ product(X_105950,domain(X_105950),X_105950)
| X_105950 = compose(X_105950,domain(X_105950)) ),
inference(subst,[],[refute_0_10:[bind(X_105654,$fot(X_105950)),bind(X_105656,$fot(X_105950))]]) ).
cnf(refute_0_15,plain,
X_105950 = compose(X_105950,domain(X_105950)),
inference(resolve,[$cnf( product(X_105950,domain(X_105950),X_105950) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_17,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_18,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
( X_105950 != compose(X_105950,domain(X_105950))
| compose(X_105950,domain(X_105950)) = X_105950 ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(X_105950)),bind(Y0,$fot(compose(X_105950,domain(X_105950))))]]) ).
cnf(refute_0_20,plain,
compose(X_105950,domain(X_105950)) = X_105950,
inference(resolve,[$cnf( $equal(X_105950,compose(X_105950,domain(X_105950))) )],[refute_0_15,refute_0_19]) ).
cnf(refute_0_21,plain,
compose(domain(X),domain(domain(X))) = domain(X),
inference(subst,[],[refute_0_20:[bind(X_105950,$fot(domain(X)))]]) ).
cnf(refute_0_22,plain,
( compose(domain(X),domain(domain(X))) != domain(X)
| domain(domain(X)) != compose(domain(X),domain(domain(X)))
| domain(domain(X)) = domain(X) ),
introduced(tautology,[equality,[$cnf( $equal(domain(domain(X)),compose(domain(X),domain(domain(X)))) ),[1],$fot(domain(X))]]) ).
cnf(refute_0_23,plain,
( domain(domain(X)) != compose(domain(X),domain(domain(X)))
| domain(domain(X)) = domain(X) ),
inference(resolve,[$cnf( $equal(compose(domain(X),domain(domain(X))),domain(X)) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
domain(domain(X)) = domain(X),
inference(resolve,[$cnf( $equal(domain(domain(X)),compose(domain(X),domain(domain(X)))) )],[refute_0_12,refute_0_23]) ).
cnf(refute_0_25,plain,
domain(domain(a)) = domain(a),
inference(subst,[],[refute_0_24:[bind(X,$fot(a))]]) ).
cnf(refute_0_26,plain,
( domain(a) != domain(a)
| domain(domain(a)) != domain(a)
| domain(domain(a)) = domain(a) ),
introduced(tautology,[equality,[$cnf( $equal(domain(domain(a)),domain(a)) ),[0,0],$fot(domain(a))]]) ).
cnf(refute_0_27,plain,
( domain(a) != domain(a)
| domain(domain(a)) = domain(a) ),
inference(resolve,[$cnf( $equal(domain(domain(a)),domain(a)) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
domain(a) != domain(a),
inference(resolve,[$cnf( $equal(domain(domain(a)),domain(a)) )],[refute_0_27,prove_domain_is_idempotent]) ).
cnf(refute_0_29,plain,
domain(a) = domain(a),
introduced(tautology,[refl,[$fot(domain(a))]]) ).
cnf(refute_0_30,plain,
$false,
inference(resolve,[$cnf( $equal(domain(a),domain(a)) )],[refute_0_29,refute_0_28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : CAT011-1 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n025.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 22:27:56 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 275.70/275.99 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 275.70/275.99
% 275.70/275.99 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 275.70/275.99
%------------------------------------------------------------------------------