%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : CAT014-4 : 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 00:04:36 EDT 2022
% Result : Unsatisfiable 20.23s 20.46s
% Output : CNFRefutation 20.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 21
% Syntax : Number of clauses : 63 ( 26 unt; 0 nHn; 49 RR)
% Number of literals : 110 ( 70 equ; 49 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 48 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(domain_has_elements,axiom,
( ~ there_exists(domain(X))
| there_exists(X) ) ).
cnf(codomain_has_elements,axiom,
( ~ there_exists(codomain(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(associativity_of_compose,axiom,
compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) ).
cnf(compose_domain,axiom,
compose(X,domain(X)) = X ).
cnf(compose_codomain,axiom,
compose(codomain(X),X) = X ).
cnf(assume_codomain_exists,hypothesis,
there_exists(codomain(a)) ).
cnf(prove_codomain_is_idempotent,negated_conjecture,
codomain(codomain(a)) != codomain(a) ).
cnf(refute_0_0,plain,
( ~ there_exists(domain(codomain(codomain(a))))
| there_exists(codomain(codomain(a))) ),
inference(subst,[],[domain_has_elements:[bind(X,$fot(codomain(codomain(a))))]]) ).
cnf(refute_0_1,plain,
( ~ there_exists(compose(codomain(X_10),X_10))
| there_exists(domain(codomain(X_10))) ),
inference(subst,[],[composition_implies_domain:[bind(X,$fot(codomain(X_10))),bind(Y,$fot(X_10))]]) ).
cnf(refute_0_2,plain,
compose(codomain(X_10),X_10) = X_10,
inference(subst,[],[compose_codomain:[bind(X,$fot(X_10))]]) ).
cnf(refute_0_3,plain,
( compose(codomain(X_10),X_10) != X_10
| ~ there_exists(X_10)
| there_exists(compose(codomain(X_10),X_10)) ),
introduced(tautology,[equality,[$cnf( ~ there_exists(compose(codomain(X_10),X_10)) ),[0],$fot(X_10)]]) ).
cnf(refute_0_4,plain,
( ~ there_exists(X_10)
| there_exists(compose(codomain(X_10),X_10)) ),
inference(resolve,[$cnf( $equal(compose(codomain(X_10),X_10),X_10) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( ~ there_exists(X_10)
| there_exists(domain(codomain(X_10))) ),
inference(resolve,[$cnf( there_exists(compose(codomain(X_10),X_10)) )],[refute_0_4,refute_0_1]) ).
cnf(refute_0_6,plain,
( ~ there_exists(codomain(a))
| there_exists(domain(codomain(codomain(a)))) ),
inference(subst,[],[refute_0_5:[bind(X_10,$fot(codomain(a)))]]) ).
cnf(refute_0_7,plain,
there_exists(domain(codomain(codomain(a)))),
inference(resolve,[$cnf( there_exists(codomain(a)) )],[assume_codomain_exists,refute_0_6]) ).
cnf(refute_0_8,plain,
there_exists(codomain(codomain(a))),
inference(resolve,[$cnf( there_exists(domain(codomain(codomain(a)))) )],[refute_0_7,refute_0_0]) ).
cnf(refute_0_9,plain,
( ~ there_exists(compose(X_37,domain(X_37)))
| domain(X_37) = codomain(domain(X_37)) ),
inference(subst,[],[domain_codomain_composition1:[bind(X,$fot(X_37)),bind(Y,$fot(domain(X_37)))]]) ).
cnf(refute_0_10,plain,
compose(X_37,domain(X_37)) = X_37,
inference(subst,[],[compose_domain:[bind(X,$fot(X_37))]]) ).
cnf(refute_0_11,plain,
( compose(X_37,domain(X_37)) != X_37
| ~ there_exists(X_37)
| there_exists(compose(X_37,domain(X_37))) ),
introduced(tautology,[equality,[$cnf( ~ there_exists(compose(X_37,domain(X_37))) ),[0],$fot(X_37)]]) ).
cnf(refute_0_12,plain,
( ~ there_exists(X_37)
| there_exists(compose(X_37,domain(X_37))) ),
inference(resolve,[$cnf( $equal(compose(X_37,domain(X_37)),X_37) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
( ~ there_exists(X_37)
| domain(X_37) = codomain(domain(X_37)) ),
inference(resolve,[$cnf( there_exists(compose(X_37,domain(X_37))) )],[refute_0_12,refute_0_9]) ).
cnf(refute_0_14,plain,
( ~ there_exists(codomain(codomain(a)))
| domain(codomain(codomain(a))) = codomain(domain(codomain(codomain(a)))) ),
inference(subst,[],[refute_0_13:[bind(X_37,$fot(codomain(codomain(a))))]]) ).
cnf(refute_0_15,plain,
domain(codomain(codomain(a))) = codomain(domain(codomain(codomain(a)))),
inference(resolve,[$cnf( there_exists(codomain(codomain(a))) )],[refute_0_8,refute_0_14]) ).
cnf(refute_0_16,plain,
( ~ there_exists(codomain(a))
| there_exists(a) ),
inference(subst,[],[codomain_has_elements:[bind(X,$fot(a))]]) ).
cnf(refute_0_17,plain,
there_exists(a),
inference(resolve,[$cnf( there_exists(codomain(a)) )],[assume_codomain_exists,refute_0_16]) ).
cnf(refute_0_18,plain,
( ~ there_exists(compose(codomain(codomain(X_38)),X_38))
| domain(codomain(codomain(X_38))) = codomain(X_38) ),
inference(subst,[],[domain_codomain_composition1:[bind(X,$fot(codomain(codomain(X_38)))),bind(Y,$fot(X_38))]]) ).
cnf(refute_0_19,plain,
compose(codomain(X_14),compose(X_14,X_15)) = compose(compose(codomain(X_14),X_14),X_15),
inference(subst,[],[associativity_of_compose:[bind(X,$fot(codomain(X_14))),bind(Y,$fot(X_14)),bind(Z,$fot(X_15))]]) ).
cnf(refute_0_20,plain,
compose(codomain(X_14),X_14) = X_14,
inference(subst,[],[compose_codomain:[bind(X,$fot(X_14))]]) ).
cnf(refute_0_21,plain,
( compose(codomain(X_14),X_14) != X_14
| compose(codomain(X_14),compose(X_14,X_15)) != compose(compose(codomain(X_14),X_14),X_15)
| compose(codomain(X_14),compose(X_14,X_15)) = compose(X_14,X_15) ),
introduced(tautology,[equality,[$cnf( $equal(compose(codomain(X_14),compose(X_14,X_15)),compose(compose(codomain(X_14),X_14),X_15)) ),[1,0],$fot(X_14)]]) ).
cnf(refute_0_22,plain,
( compose(codomain(X_14),compose(X_14,X_15)) != compose(compose(codomain(X_14),X_14),X_15)
| compose(codomain(X_14),compose(X_14,X_15)) = compose(X_14,X_15) ),
inference(resolve,[$cnf( $equal(compose(codomain(X_14),X_14),X_14) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
compose(codomain(X_14),compose(X_14,X_15)) = compose(X_14,X_15),
inference(resolve,[$cnf( $equal(compose(codomain(X_14),compose(X_14,X_15)),compose(compose(codomain(X_14),X_14),X_15)) )],[refute_0_19,refute_0_22]) ).
cnf(refute_0_24,plain,
compose(codomain(codomain(X_17)),compose(codomain(X_17),X_17)) = compose(codomain(X_17),X_17),
inference(subst,[],[refute_0_23:[bind(X_14,$fot(codomain(X_17))),bind(X_15,$fot(X_17))]]) ).
cnf(refute_0_25,plain,
compose(codomain(X_17),X_17) = X_17,
inference(subst,[],[compose_codomain:[bind(X,$fot(X_17))]]) ).
cnf(refute_0_26,plain,
( compose(codomain(X_17),X_17) != X_17
| compose(codomain(codomain(X_17)),compose(codomain(X_17),X_17)) != compose(codomain(X_17),X_17)
| compose(codomain(codomain(X_17)),X_17) = compose(codomain(X_17),X_17) ),
introduced(tautology,[equality,[$cnf( $equal(compose(codomain(codomain(X_17)),compose(codomain(X_17),X_17)),compose(codomain(X_17),X_17)) ),[0,1],$fot(X_17)]]) ).
cnf(refute_0_27,plain,
( compose(codomain(codomain(X_17)),compose(codomain(X_17),X_17)) != compose(codomain(X_17),X_17)
| compose(codomain(codomain(X_17)),X_17) = compose(codomain(X_17),X_17) ),
inference(resolve,[$cnf( $equal(compose(codomain(X_17),X_17),X_17) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
compose(codomain(codomain(X_17)),X_17) = compose(codomain(X_17),X_17),
inference(resolve,[$cnf( $equal(compose(codomain(codomain(X_17)),compose(codomain(X_17),X_17)),compose(codomain(X_17),X_17)) )],[refute_0_24,refute_0_27]) ).
cnf(refute_0_29,plain,
( compose(codomain(X_17),X_17) != X_17
| compose(codomain(codomain(X_17)),X_17) != compose(codomain(X_17),X_17)
| compose(codomain(codomain(X_17)),X_17) = X_17 ),
introduced(tautology,[equality,[$cnf( $equal(compose(codomain(codomain(X_17)),X_17),compose(codomain(X_17),X_17)) ),[1],$fot(X_17)]]) ).
cnf(refute_0_30,plain,
( compose(codomain(codomain(X_17)),X_17) != compose(codomain(X_17),X_17)
| compose(codomain(codomain(X_17)),X_17) = X_17 ),
inference(resolve,[$cnf( $equal(compose(codomain(X_17),X_17),X_17) )],[refute_0_25,refute_0_29]) ).
cnf(refute_0_31,plain,
compose(codomain(codomain(X_17)),X_17) = X_17,
inference(resolve,[$cnf( $equal(compose(codomain(codomain(X_17)),X_17),compose(codomain(X_17),X_17)) )],[refute_0_28,refute_0_30]) ).
cnf(refute_0_32,plain,
compose(codomain(codomain(X_38)),X_38) = X_38,
inference(subst,[],[refute_0_31:[bind(X_17,$fot(X_38))]]) ).
cnf(refute_0_33,plain,
( compose(codomain(codomain(X_38)),X_38) != X_38
| ~ there_exists(X_38)
| there_exists(compose(codomain(codomain(X_38)),X_38)) ),
introduced(tautology,[equality,[$cnf( ~ there_exists(compose(codomain(codomain(X_38)),X_38)) ),[0],$fot(X_38)]]) ).
cnf(refute_0_34,plain,
( ~ there_exists(X_38)
| there_exists(compose(codomain(codomain(X_38)),X_38)) ),
inference(resolve,[$cnf( $equal(compose(codomain(codomain(X_38)),X_38),X_38) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
( ~ there_exists(X_38)
| domain(codomain(codomain(X_38))) = codomain(X_38) ),
inference(resolve,[$cnf( there_exists(compose(codomain(codomain(X_38)),X_38)) )],[refute_0_34,refute_0_18]) ).
cnf(refute_0_36,plain,
( ~ there_exists(a)
| domain(codomain(codomain(a))) = codomain(a) ),
inference(subst,[],[refute_0_35:[bind(X_38,$fot(a))]]) ).
cnf(refute_0_37,plain,
domain(codomain(codomain(a))) = codomain(a),
inference(resolve,[$cnf( there_exists(a) )],[refute_0_17,refute_0_36]) ).
cnf(refute_0_38,plain,
( domain(codomain(codomain(a))) != codomain(a)
| domain(codomain(codomain(a))) != codomain(domain(codomain(codomain(a))))
| codomain(a) = codomain(domain(codomain(codomain(a)))) ),
introduced(tautology,[equality,[$cnf( $equal(domain(codomain(codomain(a))),codomain(domain(codomain(codomain(a))))) ),[0],$fot(codomain(a))]]) ).
cnf(refute_0_39,plain,
( domain(codomain(codomain(a))) != codomain(domain(codomain(codomain(a))))
| codomain(a) = codomain(domain(codomain(codomain(a)))) ),
inference(resolve,[$cnf( $equal(domain(codomain(codomain(a))),codomain(a)) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
codomain(domain(codomain(codomain(a)))) = codomain(domain(codomain(codomain(a)))),
introduced(tautology,[refl,[$fot(codomain(domain(codomain(codomain(a)))))]]) ).
cnf(refute_0_41,plain,
( codomain(domain(codomain(codomain(a)))) != codomain(domain(codomain(codomain(a))))
| domain(codomain(codomain(a))) != codomain(a)
| codomain(domain(codomain(codomain(a)))) = codomain(codomain(a)) ),
introduced(tautology,[equality,[$cnf( $equal(codomain(domain(codomain(codomain(a)))),codomain(domain(codomain(codomain(a))))) ),[1,0],$fot(codomain(a))]]) ).
cnf(refute_0_42,plain,
( domain(codomain(codomain(a))) != codomain(a)
| codomain(domain(codomain(codomain(a)))) = codomain(codomain(a)) ),
inference(resolve,[$cnf( $equal(codomain(domain(codomain(codomain(a)))),codomain(domain(codomain(codomain(a))))) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
codomain(domain(codomain(codomain(a)))) = codomain(codomain(a)),
inference(resolve,[$cnf( $equal(domain(codomain(codomain(a))),codomain(a)) )],[refute_0_37,refute_0_42]) ).
cnf(refute_0_44,plain,
( codomain(a) != codomain(domain(codomain(codomain(a))))
| codomain(domain(codomain(codomain(a)))) != codomain(codomain(a))
| codomain(a) = codomain(codomain(a)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(codomain(a),codomain(codomain(a))) ),[0],$fot(codomain(domain(codomain(codomain(a)))))]]) ).
cnf(refute_0_45,plain,
( codomain(a) != codomain(domain(codomain(codomain(a))))
| codomain(a) = codomain(codomain(a)) ),
inference(resolve,[$cnf( $equal(codomain(domain(codomain(codomain(a)))),codomain(codomain(a))) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
( domain(codomain(codomain(a))) != codomain(domain(codomain(codomain(a))))
| codomain(a) = codomain(codomain(a)) ),
inference(resolve,[$cnf( $equal(codomain(a),codomain(domain(codomain(codomain(a))))) )],[refute_0_39,refute_0_45]) ).
cnf(refute_0_47,plain,
codomain(a) = codomain(codomain(a)),
inference(resolve,[$cnf( $equal(domain(codomain(codomain(a))),codomain(domain(codomain(codomain(a))))) )],[refute_0_15,refute_0_46]) ).
cnf(refute_0_48,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_49,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_50,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
( codomain(a) != codomain(codomain(a))
| codomain(codomain(a)) = codomain(a) ),
inference(subst,[],[refute_0_50:[bind(X0,$fot(codomain(a))),bind(Y0,$fot(codomain(codomain(a))))]]) ).
cnf(refute_0_52,plain,
codomain(a) != codomain(codomain(a)),
inference(resolve,[$cnf( $equal(codomain(codomain(a)),codomain(a)) )],[refute_0_51,prove_codomain_is_idempotent]) ).
cnf(refute_0_53,plain,
$false,
inference(resolve,[$cnf( $equal(codomain(a),codomain(codomain(a))) )],[refute_0_47,refute_0_52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : CAT014-4 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % 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
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sun May 29 17:48:41 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 20.23/20.46 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 20.23/20.46
% 20.23/20.46 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 20.23/20.47
%------------------------------------------------------------------------------