TSTP Solution File: CAT013-1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : CAT013-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n023.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 00:04:35 EDT 2022
% Result : Unsatisfiable 159.92s 160.10s
% Output : CNFRefutation 159.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 24
% Syntax : Number of clauses : 101 ( 48 unt; 0 nHn; 58 RR)
% Number of literals : 178 ( 88 equ; 79 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 6 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 118 ( 7 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associative_property2,axiom,
( ~ product(X,Y,Xy)
| ~ defined(Xy,Z)
| defined(Y,Z) ) ).
cnf(domain_is_an_identity_map,axiom,
identity_map(domain(X)) ).
cnf(codomain_is_an_identity_map,axiom,
identity_map(codomain(X)) ).
cnf(mapping_from_x_to_its_domain,axiom,
defined(X,domain(X)) ).
cnf(mapping_from_codomain_of_x_to_x,axiom,
defined(codomain(X),X) ).
cnf(product_on_codomain,axiom,
product(codomain(X),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(prove_domain_of_codomain_is_codomain,negated_conjecture,
domain(codomain(a)) != codomain(a) ).
cnf(refute_0_0,plain,
( ~ defined(domain(codomain(codomain(codomain(X_474)))),X_474)
| ~ identity_map(X_474)
| product(domain(codomain(codomain(codomain(X_474)))),X_474,domain(codomain(codomain(codomain(X_474))))) ),
inference(subst,[],[identity2:[bind(X,$fot(domain(codomain(codomain(codomain(X_474)))))),bind(Y,$fot(X_474))]]) ).
cnf(refute_0_1,plain,
( ~ defined(codomain(X_163),domain(codomain(codomain(codomain(X_163)))))
| ~ identity_map(domain(codomain(codomain(codomain(X_163)))))
| product(codomain(X_163),domain(codomain(codomain(codomain(X_163)))),codomain(X_163)) ),
inference(subst,[],[identity2:[bind(X,$fot(codomain(X_163))),bind(Y,$fot(domain(codomain(codomain(codomain(X_163))))))]]) ).
cnf(refute_0_2,plain,
defined(codomain(X_19),X_19),
inference(subst,[],[mapping_from_codomain_of_x_to_x:[bind(X,$fot(X_19))]]) ).
cnf(refute_0_3,plain,
( ~ defined(codomain(X_19),X_19)
| ~ identity_map(X_19)
| product(codomain(X_19),X_19,codomain(X_19)) ),
inference(subst,[],[identity2:[bind(X,$fot(codomain(X_19))),bind(Y,$fot(X_19))]]) ).
cnf(refute_0_4,plain,
( ~ identity_map(X_19)
| product(codomain(X_19),X_19,codomain(X_19)) ),
inference(resolve,[$cnf( defined(codomain(X_19),X_19) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( ~ identity_map(codomain(X))
| product(codomain(codomain(X)),codomain(X),codomain(codomain(X))) ),
inference(subst,[],[refute_0_4:[bind(X_19,$fot(codomain(X)))]]) ).
cnf(refute_0_6,plain,
product(codomain(codomain(X)),codomain(X),codomain(codomain(X))),
inference(resolve,[$cnf( identity_map(codomain(X)) )],[codomain_is_an_identity_map,refute_0_5]) ).
cnf(refute_0_7,plain,
( ~ defined(codomain(codomain(X)),X_64)
| ~ product(codomain(codomain(X)),codomain(X),codomain(codomain(X)))
| defined(codomain(X),X_64) ),
inference(subst,[],[associative_property2:[bind(X,$fot(codomain(codomain(X)))),bind(Xy,$fot(codomain(codomain(X)))),bind(Y,$fot(codomain(X))),bind(Z,$fot(X_64))]]) ).
cnf(refute_0_8,plain,
( ~ defined(codomain(codomain(X)),X_64)
| defined(codomain(X),X_64) ),
inference(resolve,[$cnf( product(codomain(codomain(X)),codomain(X),codomain(codomain(X))) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
( ~ defined(codomain(codomain(X)),domain(codomain(codomain(codomain(X)))))
| defined(codomain(X),domain(codomain(codomain(codomain(X))))) ),
inference(subst,[],[refute_0_8:[bind(X_64,$fot(domain(codomain(codomain(codomain(X))))))]]) ).
cnf(refute_0_10,plain,
defined(codomain(codomain(X_145)),domain(codomain(codomain(X_145)))),
inference(subst,[],[mapping_from_x_to_its_domain:[bind(X,$fot(codomain(codomain(X_145))))]]) ).
cnf(refute_0_11,plain,
( ~ defined(codomain(codomain(X_145)),domain(codomain(codomain(X_145))))
| defined(codomain(X_145),domain(codomain(codomain(X_145)))) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(X_145)),bind(X_64,$fot(domain(codomain(codomain(X_145)))))]]) ).
cnf(refute_0_12,plain,
defined(codomain(X_145),domain(codomain(codomain(X_145)))),
inference(resolve,[$cnf( defined(codomain(codomain(X_145)),domain(codomain(codomain(X_145)))) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
defined(codomain(codomain(X)),domain(codomain(codomain(codomain(X))))),
inference(subst,[],[refute_0_12:[bind(X_145,$fot(codomain(X)))]]) ).
cnf(refute_0_14,plain,
defined(codomain(X),domain(codomain(codomain(codomain(X))))),
inference(resolve,[$cnf( defined(codomain(codomain(X)),domain(codomain(codomain(codomain(X))))) )],[refute_0_13,refute_0_9]) ).
cnf(refute_0_15,plain,
defined(codomain(X_163),domain(codomain(codomain(codomain(X_163))))),
inference(subst,[],[refute_0_14:[bind(X,$fot(X_163))]]) ).
cnf(refute_0_16,plain,
( ~ identity_map(domain(codomain(codomain(codomain(X_163)))))
| product(codomain(X_163),domain(codomain(codomain(codomain(X_163)))),codomain(X_163)) ),
inference(resolve,[$cnf( defined(codomain(X_163),domain(codomain(codomain(codomain(X_163))))) )],[refute_0_15,refute_0_1]) ).
cnf(refute_0_17,plain,
identity_map(domain(codomain(codomain(codomain(X_163))))),
inference(subst,[],[domain_is_an_identity_map:[bind(X,$fot(codomain(codomain(codomain(X_163)))))]]) ).
cnf(refute_0_18,plain,
product(codomain(X_163),domain(codomain(codomain(codomain(X_163)))),codomain(X_163)),
inference(resolve,[$cnf( identity_map(domain(codomain(codomain(codomain(X_163))))) )],[refute_0_17,refute_0_16]) ).
cnf(refute_0_19,plain,
product(codomain(X_462),domain(codomain(codomain(codomain(X_462)))),codomain(X_462)),
inference(subst,[],[refute_0_18:[bind(X_163,$fot(X_462))]]) ).
cnf(refute_0_20,plain,
defined(codomain(X_64),X_64),
inference(subst,[],[mapping_from_codomain_of_x_to_x:[bind(X,$fot(X_64))]]) ).
cnf(refute_0_21,plain,
( ~ defined(codomain(X_64),X_64)
| ~ product(X_61,X_63,codomain(X_64))
| defined(X_63,X_64) ),
inference(subst,[],[associative_property2:[bind(X,$fot(X_61)),bind(Xy,$fot(codomain(X_64))),bind(Y,$fot(X_63)),bind(Z,$fot(X_64))]]) ).
cnf(refute_0_22,plain,
( ~ product(X_61,X_63,codomain(X_64))
| defined(X_63,X_64) ),
inference(resolve,[$cnf( defined(codomain(X_64),X_64) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
( ~ product(codomain(X_462),domain(codomain(codomain(codomain(X_462)))),codomain(X_462))
| defined(domain(codomain(codomain(codomain(X_462)))),X_462) ),
inference(subst,[],[refute_0_22:[bind(X_61,$fot(codomain(X_462))),bind(X_63,$fot(domain(codomain(codomain(codomain(X_462)))))),bind(X_64,$fot(X_462))]]) ).
cnf(refute_0_24,plain,
defined(domain(codomain(codomain(codomain(X_462)))),X_462),
inference(resolve,[$cnf( product(codomain(X_462),domain(codomain(codomain(codomain(X_462)))),codomain(X_462)) )],[refute_0_19,refute_0_23]) ).
cnf(refute_0_25,plain,
defined(domain(codomain(codomain(codomain(X_474)))),X_474),
inference(subst,[],[refute_0_24:[bind(X_462,$fot(X_474))]]) ).
cnf(refute_0_26,plain,
( ~ identity_map(X_474)
| product(domain(codomain(codomain(codomain(X_474)))),X_474,domain(codomain(codomain(codomain(X_474))))) ),
inference(resolve,[$cnf( defined(domain(codomain(codomain(codomain(X_474)))),X_474) )],[refute_0_25,refute_0_0]) ).
cnf(refute_0_27,plain,
( ~ identity_map(domain(X))
| product(domain(codomain(codomain(codomain(domain(X))))),domain(X),domain(codomain(codomain(codomain(domain(X)))))) ),
inference(subst,[],[refute_0_26:[bind(X_474,$fot(domain(X)))]]) ).
cnf(refute_0_28,plain,
product(domain(codomain(codomain(codomain(domain(X))))),domain(X),domain(codomain(codomain(codomain(domain(X)))))),
inference(resolve,[$cnf( identity_map(domain(X)) )],[domain_is_an_identity_map,refute_0_27]) ).
cnf(refute_0_29,plain,
( ~ defined(domain(codomain(codomain(codomain(X_474)))),X_474)
| ~ identity_map(domain(codomain(codomain(codomain(X_474)))))
| product(domain(codomain(codomain(codomain(X_474)))),X_474,X_474) ),
inference(subst,[],[identity1:[bind(X,$fot(domain(codomain(codomain(codomain(X_474)))))),bind(Y,$fot(X_474))]]) ).
cnf(refute_0_30,plain,
( ~ identity_map(domain(codomain(codomain(codomain(X_474)))))
| product(domain(codomain(codomain(codomain(X_474)))),X_474,X_474) ),
inference(resolve,[$cnf( defined(domain(codomain(codomain(codomain(X_474)))),X_474) )],[refute_0_25,refute_0_29]) ).
cnf(refute_0_31,plain,
identity_map(domain(codomain(codomain(codomain(X_474))))),
inference(subst,[],[domain_is_an_identity_map:[bind(X,$fot(codomain(codomain(codomain(X_474)))))]]) ).
cnf(refute_0_32,plain,
product(domain(codomain(codomain(codomain(X_474)))),X_474,X_474),
inference(resolve,[$cnf( identity_map(domain(codomain(codomain(codomain(X_474))))) )],[refute_0_31,refute_0_30]) ).
cnf(refute_0_33,plain,
product(domain(codomain(codomain(codomain(X_47695)))),X_47695,X_47695),
inference(subst,[],[refute_0_32:[bind(X_474,$fot(X_47695))]]) ).
cnf(refute_0_34,plain,
( ~ product(domain(codomain(codomain(codomain(X_47695)))),X_47695,X_47695)
| ~ product(domain(codomain(codomain(codomain(X_47695)))),X_47695,X_47698)
| X_47698 = X_47695 ),
inference(subst,[],[composition_is_well_defined:[bind(W,$fot(X_47695)),bind(X,$fot(domain(codomain(codomain(codomain(X_47695)))))),bind(Y,$fot(X_47695)),bind(Z,$fot(X_47698))]]) ).
cnf(refute_0_35,plain,
( ~ product(domain(codomain(codomain(codomain(X_47695)))),X_47695,X_47698)
| X_47698 = X_47695 ),
inference(resolve,[$cnf( product(domain(codomain(codomain(codomain(X_47695)))),X_47695,X_47695) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
( ~ product(domain(codomain(codomain(codomain(domain(X))))),domain(X),domain(codomain(codomain(codomain(domain(X))))))
| domain(codomain(codomain(codomain(domain(X))))) = domain(X) ),
inference(subst,[],[refute_0_35:[bind(X_47695,$fot(domain(X))),bind(X_47698,$fot(domain(codomain(codomain(codomain(domain(X)))))))]]) ).
cnf(refute_0_37,plain,
domain(codomain(codomain(codomain(domain(X))))) = domain(X),
inference(resolve,[$cnf( product(domain(codomain(codomain(codomain(domain(X))))),domain(X),domain(codomain(codomain(codomain(domain(X)))))) )],[refute_0_28,refute_0_36]) ).
cnf(refute_0_38,plain,
product(codomain(domain(X_48005)),domain(X_48005),domain(X_48005)),
inference(subst,[],[product_on_codomain:[bind(X,$fot(domain(X_48005)))]]) ).
cnf(refute_0_39,plain,
( ~ identity_map(domain(X))
| product(codomain(domain(X)),domain(X),codomain(domain(X))) ),
inference(subst,[],[refute_0_4:[bind(X_19,$fot(domain(X)))]]) ).
cnf(refute_0_40,plain,
product(codomain(domain(X)),domain(X),codomain(domain(X))),
inference(resolve,[$cnf( identity_map(domain(X)) )],[domain_is_an_identity_map,refute_0_39]) ).
cnf(refute_0_41,plain,
( ~ product(codomain(domain(X)),domain(X),X_47698)
| ~ product(codomain(domain(X)),domain(X),codomain(domain(X)))
| X_47698 = codomain(domain(X)) ),
inference(subst,[],[composition_is_well_defined:[bind(W,$fot(codomain(domain(X)))),bind(X,$fot(codomain(domain(X)))),bind(Y,$fot(domain(X))),bind(Z,$fot(X_47698))]]) ).
cnf(refute_0_42,plain,
( ~ product(codomain(domain(X)),domain(X),X_47698)
| X_47698 = codomain(domain(X)) ),
inference(resolve,[$cnf( product(codomain(domain(X)),domain(X),codomain(domain(X))) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
( ~ product(codomain(domain(X_48005)),domain(X_48005),domain(X_48005))
| domain(X_48005) = codomain(domain(X_48005)) ),
inference(subst,[],[refute_0_42:[bind(X,$fot(X_48005)),bind(X_47698,$fot(domain(X_48005)))]]) ).
cnf(refute_0_44,plain,
domain(X_48005) = codomain(domain(X_48005)),
inference(resolve,[$cnf( product(codomain(domain(X_48005)),domain(X_48005),domain(X_48005)) )],[refute_0_38,refute_0_43]) ).
cnf(refute_0_45,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_46,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_47,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
( domain(X_48005) != codomain(domain(X_48005))
| codomain(domain(X_48005)) = domain(X_48005) ),
inference(subst,[],[refute_0_47:[bind(X0,$fot(domain(X_48005))),bind(Y0,$fot(codomain(domain(X_48005))))]]) ).
cnf(refute_0_49,plain,
codomain(domain(X_48005)) = domain(X_48005),
inference(resolve,[$cnf( $equal(domain(X_48005),codomain(domain(X_48005))) )],[refute_0_44,refute_0_48]) ).
cnf(refute_0_50,plain,
codomain(domain(X)) = domain(X),
inference(subst,[],[refute_0_49:[bind(X_48005,$fot(X))]]) ).
cnf(refute_0_51,plain,
codomain(codomain(domain(X))) = codomain(codomain(domain(X))),
introduced(tautology,[refl,[$fot(codomain(codomain(domain(X))))]]) ).
cnf(refute_0_52,plain,
( codomain(codomain(domain(X))) != codomain(codomain(domain(X)))
| codomain(domain(X)) != domain(X)
| codomain(codomain(domain(X))) = codomain(domain(X)) ),
introduced(tautology,[equality,[$cnf( $equal(codomain(codomain(domain(X))),codomain(codomain(domain(X)))) ),[1,0],$fot(domain(X))]]) ).
cnf(refute_0_53,plain,
( codomain(domain(X)) != domain(X)
| codomain(codomain(domain(X))) = codomain(domain(X)) ),
inference(resolve,[$cnf( $equal(codomain(codomain(domain(X))),codomain(codomain(domain(X)))) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
codomain(codomain(domain(X))) = codomain(domain(X)),
inference(resolve,[$cnf( $equal(codomain(domain(X)),domain(X)) )],[refute_0_50,refute_0_53]) ).
cnf(refute_0_55,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_56,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_47,refute_0_55]) ).
cnf(refute_0_57,plain,
( codomain(codomain(domain(X))) != codomain(domain(X))
| codomain(domain(X)) != domain(X)
| codomain(codomain(domain(X))) = domain(X) ),
inference(subst,[],[refute_0_56:[bind(X0,$fot(codomain(codomain(domain(X))))),bind(Y0,$fot(codomain(domain(X)))),bind(Z0,$fot(domain(X)))]]) ).
cnf(refute_0_58,plain,
( codomain(domain(X)) != domain(X)
| codomain(codomain(domain(X))) = domain(X) ),
inference(resolve,[$cnf( $equal(codomain(codomain(domain(X))),codomain(domain(X))) )],[refute_0_54,refute_0_57]) ).
cnf(refute_0_59,plain,
codomain(codomain(domain(X))) = domain(X),
inference(resolve,[$cnf( $equal(codomain(domain(X)),domain(X)) )],[refute_0_50,refute_0_58]) ).
cnf(refute_0_60,plain,
codomain(codomain(codomain(domain(X)))) = codomain(codomain(codomain(domain(X)))),
introduced(tautology,[refl,[$fot(codomain(codomain(codomain(domain(X)))))]]) ).
cnf(refute_0_61,plain,
( codomain(codomain(codomain(domain(X)))) != codomain(codomain(codomain(domain(X))))
| codomain(codomain(domain(X))) != domain(X)
| codomain(codomain(codomain(domain(X)))) = codomain(domain(X)) ),
introduced(tautology,[equality,[$cnf( $equal(codomain(codomain(codomain(domain(X)))),codomain(codomain(codomain(domain(X))))) ),[1,0],$fot(domain(X))]]) ).
cnf(refute_0_62,plain,
( codomain(codomain(domain(X))) != domain(X)
| codomain(codomain(codomain(domain(X)))) = codomain(domain(X)) ),
inference(resolve,[$cnf( $equal(codomain(codomain(codomain(domain(X)))),codomain(codomain(codomain(domain(X))))) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
codomain(codomain(codomain(domain(X)))) = codomain(domain(X)),
inference(resolve,[$cnf( $equal(codomain(codomain(domain(X))),domain(X)) )],[refute_0_59,refute_0_62]) ).
cnf(refute_0_64,plain,
( codomain(codomain(codomain(domain(X)))) != codomain(domain(X))
| codomain(domain(X)) != domain(X)
| codomain(codomain(codomain(domain(X)))) = domain(X) ),
inference(subst,[],[refute_0_56:[bind(X0,$fot(codomain(codomain(codomain(domain(X)))))),bind(Y0,$fot(codomain(domain(X)))),bind(Z0,$fot(domain(X)))]]) ).
cnf(refute_0_65,plain,
( codomain(domain(X)) != domain(X)
| codomain(codomain(codomain(domain(X)))) = domain(X) ),
inference(resolve,[$cnf( $equal(codomain(codomain(codomain(domain(X)))),codomain(domain(X))) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
codomain(codomain(codomain(domain(X)))) = domain(X),
inference(resolve,[$cnf( $equal(codomain(domain(X)),domain(X)) )],[refute_0_50,refute_0_65]) ).
cnf(refute_0_67,plain,
domain(codomain(codomain(codomain(domain(X))))) = domain(codomain(codomain(codomain(domain(X))))),
introduced(tautology,[refl,[$fot(domain(codomain(codomain(codomain(domain(X))))))]]) ).
cnf(refute_0_68,plain,
( codomain(codomain(codomain(domain(X)))) != domain(X)
| domain(codomain(codomain(codomain(domain(X))))) != domain(codomain(codomain(codomain(domain(X)))))
| domain(codomain(codomain(codomain(domain(X))))) = domain(domain(X)) ),
introduced(tautology,[equality,[$cnf( $equal(domain(codomain(codomain(codomain(domain(X))))),domain(codomain(codomain(codomain(domain(X)))))) ),[1,0],$fot(domain(X))]]) ).
cnf(refute_0_69,plain,
( codomain(codomain(codomain(domain(X)))) != domain(X)
| domain(codomain(codomain(codomain(domain(X))))) = domain(domain(X)) ),
inference(resolve,[$cnf( $equal(domain(codomain(codomain(codomain(domain(X))))),domain(codomain(codomain(codomain(domain(X)))))) )],[refute_0_67,refute_0_68]) ).
cnf(refute_0_70,plain,
domain(codomain(codomain(codomain(domain(X))))) = domain(domain(X)),
inference(resolve,[$cnf( $equal(codomain(codomain(codomain(domain(X)))),domain(X)) )],[refute_0_66,refute_0_69]) ).
cnf(refute_0_71,plain,
( domain(codomain(codomain(codomain(domain(X))))) != domain(X)
| domain(codomain(codomain(codomain(domain(X))))) != domain(domain(X))
| domain(domain(X)) = domain(X) ),
introduced(tautology,[equality,[$cnf( $equal(domain(codomain(codomain(codomain(domain(X))))),domain(X)) ),[0],$fot(domain(domain(X)))]]) ).
cnf(refute_0_72,plain,
( domain(codomain(codomain(codomain(domain(X))))) != domain(X)
| domain(domain(X)) = domain(X) ),
inference(resolve,[$cnf( $equal(domain(codomain(codomain(codomain(domain(X))))),domain(domain(X))) )],[refute_0_70,refute_0_71]) ).
cnf(refute_0_73,plain,
domain(domain(X)) = domain(X),
inference(resolve,[$cnf( $equal(domain(codomain(codomain(codomain(domain(X))))),domain(X)) )],[refute_0_37,refute_0_72]) ).
cnf(refute_0_74,plain,
domain(domain(codomain(codomain(codomain(codomain(X)))))) = domain(codomain(codomain(codomain(codomain(X))))),
inference(subst,[],[refute_0_73:[bind(X,$fot(codomain(codomain(codomain(codomain(X))))))]]) ).
cnf(refute_0_75,plain,
( ~ identity_map(codomain(X))
| product(domain(codomain(codomain(codomain(codomain(X))))),codomain(X),domain(codomain(codomain(codomain(codomain(X)))))) ),
inference(subst,[],[refute_0_26:[bind(X_474,$fot(codomain(X)))]]) ).
cnf(refute_0_76,plain,
product(domain(codomain(codomain(codomain(codomain(X))))),codomain(X),domain(codomain(codomain(codomain(codomain(X)))))),
inference(resolve,[$cnf( identity_map(codomain(X)) )],[codomain_is_an_identity_map,refute_0_75]) ).
cnf(refute_0_77,plain,
( ~ product(domain(codomain(codomain(codomain(codomain(X))))),codomain(X),domain(codomain(codomain(codomain(codomain(X))))))
| domain(codomain(codomain(codomain(codomain(X))))) = codomain(X) ),
inference(subst,[],[refute_0_35:[bind(X_47695,$fot(codomain(X))),bind(X_47698,$fot(domain(codomain(codomain(codomain(codomain(X)))))))]]) ).
cnf(refute_0_78,plain,
domain(codomain(codomain(codomain(codomain(X))))) = codomain(X),
inference(resolve,[$cnf( product(domain(codomain(codomain(codomain(codomain(X))))),codomain(X),domain(codomain(codomain(codomain(codomain(X)))))) )],[refute_0_76,refute_0_77]) ).
cnf(refute_0_79,plain,
( domain(codomain(codomain(codomain(codomain(X))))) != codomain(X)
| domain(domain(codomain(codomain(codomain(codomain(X)))))) != domain(codomain(codomain(codomain(codomain(X)))))
| domain(codomain(X)) = domain(codomain(codomain(codomain(codomain(X))))) ),
introduced(tautology,[equality,[$cnf( $equal(domain(domain(codomain(codomain(codomain(codomain(X)))))),domain(codomain(codomain(codomain(codomain(X)))))) ),[0,0],$fot(codomain(X))]]) ).
cnf(refute_0_80,plain,
( domain(domain(codomain(codomain(codomain(codomain(X)))))) != domain(codomain(codomain(codomain(codomain(X)))))
| domain(codomain(X)) = domain(codomain(codomain(codomain(codomain(X))))) ),
inference(resolve,[$cnf( $equal(domain(codomain(codomain(codomain(codomain(X))))),codomain(X)) )],[refute_0_78,refute_0_79]) ).
cnf(refute_0_81,plain,
domain(codomain(X)) = domain(codomain(codomain(codomain(codomain(X))))),
inference(resolve,[$cnf( $equal(domain(domain(codomain(codomain(codomain(codomain(X)))))),domain(codomain(codomain(codomain(codomain(X)))))) )],[refute_0_74,refute_0_80]) ).
cnf(refute_0_82,plain,
( domain(codomain(X)) != domain(codomain(codomain(codomain(codomain(X)))))
| domain(codomain(codomain(codomain(codomain(X))))) != codomain(X)
| domain(codomain(X)) = codomain(X) ),
introduced(tautology,[equality,[$cnf( ~ $equal(domain(codomain(X)),codomain(X)) ),[0],$fot(domain(codomain(codomain(codomain(codomain(X))))))]]) ).
cnf(refute_0_83,plain,
( domain(codomain(X)) != domain(codomain(codomain(codomain(codomain(X)))))
| domain(codomain(X)) = codomain(X) ),
inference(resolve,[$cnf( $equal(domain(codomain(codomain(codomain(codomain(X))))),codomain(X)) )],[refute_0_78,refute_0_82]) ).
cnf(refute_0_84,plain,
domain(codomain(X)) = codomain(X),
inference(resolve,[$cnf( $equal(domain(codomain(X)),domain(codomain(codomain(codomain(codomain(X)))))) )],[refute_0_81,refute_0_83]) ).
cnf(refute_0_85,plain,
domain(codomain(a)) = codomain(a),
inference(subst,[],[refute_0_84:[bind(X,$fot(a))]]) ).
cnf(refute_0_86,plain,
( codomain(a) != codomain(a)
| domain(codomain(a)) != codomain(a)
| domain(codomain(a)) = codomain(a) ),
introduced(tautology,[equality,[$cnf( $equal(domain(codomain(a)),codomain(a)) ),[0,0],$fot(codomain(a))]]) ).
cnf(refute_0_87,plain,
( codomain(a) != codomain(a)
| domain(codomain(a)) = codomain(a) ),
inference(resolve,[$cnf( $equal(domain(codomain(a)),codomain(a)) )],[refute_0_85,refute_0_86]) ).
cnf(refute_0_88,plain,
codomain(a) != codomain(a),
inference(resolve,[$cnf( $equal(domain(codomain(a)),codomain(a)) )],[refute_0_87,prove_domain_of_codomain_is_codomain]) ).
cnf(refute_0_89,plain,
codomain(a) = codomain(a),
introduced(tautology,[refl,[$fot(codomain(a))]]) ).
cnf(refute_0_90,plain,
$false,
inference(resolve,[$cnf( $equal(codomain(a),codomain(a)) )],[refute_0_89,refute_0_88]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : CAT013-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n023.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 22:21:27 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 159.92/160.10 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 159.92/160.10
% 159.92/160.10 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 159.92/160.10
%------------------------------------------------------------------------------