%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : CAT009-3 : 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 33.16s 33.48s
% Output : CNFRefutation 33.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 30
% Syntax : Number of clauses : 107 ( 41 unt; 0 nHn; 90 RR)
% Number of literals : 195 ( 126 equ; 90 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 73 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
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(domain_codomain_composition2,axiom,
( ~ there_exists(domain(X))
| domain(X) != codomain(Y)
| there_exists(compose(X,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(ab_exists,hypothesis,
there_exists(compose(a,b)) ).
cnf(prove_domain_of_ab_equals_domain_of_b,negated_conjecture,
domain(compose(a,b)) != domain(b) ).
cnf(refute_0_0,plain,
( ~ there_exists(compose(b,domain(compose(a,b))))
| domain(b) = codomain(domain(compose(a,b))) ),
inference(subst,[],[domain_codomain_composition1:[bind(X,$fot(b)),bind(Y,$fot(domain(compose(a,b))))]]) ).
cnf(refute_0_1,plain,
( domain(codomain(b)) != codomain(X_232)
| ~ there_exists(domain(codomain(b)))
| there_exists(compose(codomain(b),X_232)) ),
inference(subst,[],[domain_codomain_composition2:[bind(X,$fot(codomain(b))),bind(Y,$fot(X_232))]]) ).
cnf(refute_0_2,plain,
( ~ there_exists(compose(codomain(X_6),X_6))
| domain(codomain(X_6)) = codomain(X_6) ),
inference(subst,[],[domain_codomain_composition1:[bind(X,$fot(codomain(X_6))),bind(Y,$fot(X_6))]]) ).
cnf(refute_0_3,plain,
compose(codomain(X_6),X_6) = X_6,
inference(subst,[],[compose_codomain:[bind(X,$fot(X_6))]]) ).
cnf(refute_0_4,plain,
( compose(codomain(X_6),X_6) != X_6
| ~ there_exists(X_6)
| there_exists(compose(codomain(X_6),X_6)) ),
introduced(tautology,[equality,[$cnf( ~ there_exists(compose(codomain(X_6),X_6)) ),[0],$fot(X_6)]]) ).
cnf(refute_0_5,plain,
( ~ there_exists(X_6)
| there_exists(compose(codomain(X_6),X_6)) ),
inference(resolve,[$cnf( $equal(compose(codomain(X_6),X_6),X_6) )],[refute_0_3,refute_0_4]) ).
cnf(refute_0_6,plain,
( ~ there_exists(X_6)
| domain(codomain(X_6)) = codomain(X_6) ),
inference(resolve,[$cnf( there_exists(compose(codomain(X_6),X_6)) )],[refute_0_5,refute_0_2]) ).
cnf(refute_0_7,plain,
( ~ there_exists(b)
| domain(codomain(b)) = codomain(b) ),
inference(subst,[],[refute_0_6:[bind(X_6,$fot(b))]]) ).
cnf(refute_0_8,plain,
( ~ there_exists(codomain(b))
| there_exists(b) ),
inference(subst,[],[codomain_has_elements:[bind(X,$fot(b))]]) ).
cnf(refute_0_9,plain,
( ~ there_exists(compose(a,b))
| there_exists(domain(a)) ),
inference(subst,[],[composition_implies_domain:[bind(X,$fot(a)),bind(Y,$fot(b))]]) ).
cnf(refute_0_10,plain,
there_exists(domain(a)),
inference(resolve,[$cnf( there_exists(compose(a,b)) )],[ab_exists,refute_0_9]) ).
cnf(refute_0_11,plain,
( ~ there_exists(compose(a,b))
| domain(a) = codomain(b) ),
inference(subst,[],[domain_codomain_composition1:[bind(X,$fot(a)),bind(Y,$fot(b))]]) ).
cnf(refute_0_12,plain,
domain(a) = codomain(b),
inference(resolve,[$cnf( there_exists(compose(a,b)) )],[ab_exists,refute_0_11]) ).
cnf(refute_0_13,plain,
( domain(a) != codomain(b)
| ~ there_exists(domain(a))
| there_exists(codomain(b)) ),
introduced(tautology,[equality,[$cnf( there_exists(domain(a)) ),[0],$fot(codomain(b))]]) ).
cnf(refute_0_14,plain,
( ~ there_exists(domain(a))
| there_exists(codomain(b)) ),
inference(resolve,[$cnf( $equal(domain(a),codomain(b)) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
there_exists(codomain(b)),
inference(resolve,[$cnf( there_exists(domain(a)) )],[refute_0_10,refute_0_14]) ).
cnf(refute_0_16,plain,
there_exists(b),
inference(resolve,[$cnf( there_exists(codomain(b)) )],[refute_0_15,refute_0_8]) ).
cnf(refute_0_17,plain,
domain(codomain(b)) = codomain(b),
inference(resolve,[$cnf( there_exists(b) )],[refute_0_16,refute_0_7]) ).
cnf(refute_0_18,plain,
( domain(codomain(b)) != codomain(b)
| ~ there_exists(codomain(b))
| there_exists(domain(codomain(b))) ),
introduced(tautology,[equality,[$cnf( ~ there_exists(domain(codomain(b))) ),[0],$fot(codomain(b))]]) ).
cnf(refute_0_19,plain,
( ~ there_exists(codomain(b))
| there_exists(domain(codomain(b))) ),
inference(resolve,[$cnf( $equal(domain(codomain(b)),codomain(b)) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
( domain(codomain(b)) != codomain(X_232)
| ~ there_exists(codomain(b))
| there_exists(compose(codomain(b),X_232)) ),
inference(resolve,[$cnf( there_exists(domain(codomain(b))) )],[refute_0_19,refute_0_1]) ).
cnf(refute_0_21,plain,
( codomain(b) != codomain(X_232)
| domain(codomain(b)) != codomain(b)
| domain(codomain(b)) = codomain(X_232) ),
introduced(tautology,[equality,[$cnf( $equal(domain(codomain(b)),codomain(b)) ),[1],$fot(codomain(X_232))]]) ).
cnf(refute_0_22,plain,
( codomain(b) != codomain(X_232)
| domain(codomain(b)) = codomain(X_232) ),
inference(resolve,[$cnf( $equal(domain(codomain(b)),codomain(b)) )],[refute_0_17,refute_0_21]) ).
cnf(refute_0_23,plain,
( codomain(b) != codomain(X_232)
| ~ there_exists(codomain(b))
| there_exists(compose(codomain(b),X_232)) ),
inference(resolve,[$cnf( $equal(domain(codomain(b)),codomain(X_232)) )],[refute_0_22,refute_0_20]) ).
cnf(refute_0_24,plain,
( codomain(b) != codomain(X_232)
| there_exists(compose(codomain(b),X_232)) ),
inference(resolve,[$cnf( there_exists(codomain(b)) )],[refute_0_15,refute_0_23]) ).
cnf(refute_0_25,plain,
( codomain(b) != codomain(compose(b,domain(compose(a,b))))
| there_exists(compose(codomain(b),compose(b,domain(compose(a,b))))) ),
inference(subst,[],[refute_0_24:[bind(X_232,$fot(compose(b,domain(compose(a,b)))))]]) ).
cnf(refute_0_26,plain,
( ~ there_exists(compose(a,compose(codomain(b),X_28)))
| domain(a) = codomain(compose(codomain(b),X_28)) ),
inference(subst,[],[domain_codomain_composition1:[bind(X,$fot(a)),bind(Y,$fot(compose(codomain(b),X_28)))]]) ).
cnf(refute_0_27,plain,
compose(a,compose(codomain(b),X_27)) = compose(compose(a,codomain(b)),X_27),
inference(subst,[],[associativity_of_compose:[bind(X,$fot(a)),bind(Y,$fot(codomain(b))),bind(Z,$fot(X_27))]]) ).
cnf(refute_0_28,plain,
compose(a,domain(a)) = a,
inference(subst,[],[compose_domain:[bind(X,$fot(a))]]) ).
cnf(refute_0_29,plain,
( compose(a,domain(a)) != a
| domain(a) != codomain(b)
| compose(a,codomain(b)) = a ),
introduced(tautology,[equality,[$cnf( $equal(compose(a,domain(a)),a) ),[0,1],$fot(codomain(b))]]) ).
cnf(refute_0_30,plain,
( compose(a,domain(a)) != a
| compose(a,codomain(b)) = a ),
inference(resolve,[$cnf( $equal(domain(a),codomain(b)) )],[refute_0_12,refute_0_29]) ).
cnf(refute_0_31,plain,
compose(a,codomain(b)) = a,
inference(resolve,[$cnf( $equal(compose(a,domain(a)),a) )],[refute_0_28,refute_0_30]) ).
cnf(refute_0_32,plain,
( compose(a,codomain(b)) != a
| compose(a,compose(codomain(b),X_27)) != compose(compose(a,codomain(b)),X_27)
| compose(a,compose(codomain(b),X_27)) = compose(a,X_27) ),
introduced(tautology,[equality,[$cnf( $equal(compose(a,compose(codomain(b),X_27)),compose(compose(a,codomain(b)),X_27)) ),[1,0],$fot(a)]]) ).
cnf(refute_0_33,plain,
( compose(a,compose(codomain(b),X_27)) != compose(compose(a,codomain(b)),X_27)
| compose(a,compose(codomain(b),X_27)) = compose(a,X_27) ),
inference(resolve,[$cnf( $equal(compose(a,codomain(b)),a) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
compose(a,compose(codomain(b),X_27)) = compose(a,X_27),
inference(resolve,[$cnf( $equal(compose(a,compose(codomain(b),X_27)),compose(compose(a,codomain(b)),X_27)) )],[refute_0_27,refute_0_33]) ).
cnf(refute_0_35,plain,
compose(a,compose(codomain(b),X_28)) = compose(a,X_28),
inference(subst,[],[refute_0_34:[bind(X_27,$fot(X_28))]]) ).
cnf(refute_0_36,plain,
( compose(a,compose(codomain(b),X_28)) != compose(a,X_28)
| ~ there_exists(compose(a,X_28))
| there_exists(compose(a,compose(codomain(b),X_28))) ),
introduced(tautology,[equality,[$cnf( ~ there_exists(compose(a,compose(codomain(b),X_28))) ),[0],$fot(compose(a,X_28))]]) ).
cnf(refute_0_37,plain,
( ~ there_exists(compose(a,X_28))
| there_exists(compose(a,compose(codomain(b),X_28))) ),
inference(resolve,[$cnf( $equal(compose(a,compose(codomain(b),X_28)),compose(a,X_28)) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
( ~ there_exists(compose(a,X_28))
| domain(a) = codomain(compose(codomain(b),X_28)) ),
inference(resolve,[$cnf( there_exists(compose(a,compose(codomain(b),X_28))) )],[refute_0_37,refute_0_26]) ).
cnf(refute_0_39,plain,
( domain(a) != codomain(b)
| domain(a) != codomain(compose(codomain(b),X_28))
| codomain(b) = codomain(compose(codomain(b),X_28)) ),
introduced(tautology,[equality,[$cnf( $equal(domain(a),codomain(compose(codomain(b),X_28))) ),[0],$fot(codomain(b))]]) ).
cnf(refute_0_40,plain,
( domain(a) != codomain(compose(codomain(b),X_28))
| codomain(b) = codomain(compose(codomain(b),X_28)) ),
inference(resolve,[$cnf( $equal(domain(a),codomain(b)) )],[refute_0_12,refute_0_39]) ).
cnf(refute_0_41,plain,
( ~ there_exists(compose(a,X_28))
| codomain(b) = codomain(compose(codomain(b),X_28)) ),
inference(resolve,[$cnf( $equal(domain(a),codomain(compose(codomain(b),X_28))) )],[refute_0_38,refute_0_40]) ).
cnf(refute_0_42,plain,
( ~ there_exists(compose(a,compose(X_26,domain(compose(a,X_26)))))
| codomain(b) = codomain(compose(codomain(b),compose(X_26,domain(compose(a,X_26))))) ),
inference(subst,[],[refute_0_41:[bind(X_28,$fot(compose(X_26,domain(compose(a,X_26)))))]]) ).
cnf(refute_0_43,plain,
compose(compose(X_25,X_26),domain(compose(X_25,X_26))) = compose(X_25,X_26),
inference(subst,[],[compose_domain:[bind(X,$fot(compose(X_25,X_26)))]]) ).
cnf(refute_0_44,plain,
compose(X_25,compose(X_26,domain(compose(X_25,X_26)))) = compose(compose(X_25,X_26),domain(compose(X_25,X_26))),
inference(subst,[],[associativity_of_compose:[bind(X,$fot(X_25)),bind(Y,$fot(X_26)),bind(Z,$fot(domain(compose(X_25,X_26))))]]) ).
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( $equal(X0,X0) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
( compose(X_25,compose(X_26,domain(compose(X_25,X_26)))) != compose(compose(X_25,X_26),domain(compose(X_25,X_26)))
| compose(compose(X_25,X_26),domain(compose(X_25,X_26))) = compose(X_25,compose(X_26,domain(compose(X_25,X_26)))) ),
inference(subst,[],[refute_0_47:[bind(X0,$fot(compose(X_25,compose(X_26,domain(compose(X_25,X_26)))))),bind(Y0,$fot(compose(compose(X_25,X_26),domain(compose(X_25,X_26)))))]]) ).
cnf(refute_0_49,plain,
compose(compose(X_25,X_26),domain(compose(X_25,X_26))) = compose(X_25,compose(X_26,domain(compose(X_25,X_26)))),
inference(resolve,[$cnf( $equal(compose(X_25,compose(X_26,domain(compose(X_25,X_26)))),compose(compose(X_25,X_26),domain(compose(X_25,X_26)))) )],[refute_0_44,refute_0_48]) ).
cnf(refute_0_50,plain,
( compose(compose(X_25,X_26),domain(compose(X_25,X_26))) != compose(X_25,X_26)
| compose(compose(X_25,X_26),domain(compose(X_25,X_26))) != compose(X_25,compose(X_26,domain(compose(X_25,X_26))))
| compose(X_25,compose(X_26,domain(compose(X_25,X_26)))) = compose(X_25,X_26) ),
introduced(tautology,[equality,[$cnf( $equal(compose(compose(X_25,X_26),domain(compose(X_25,X_26))),compose(X_25,X_26)) ),[0],$fot(compose(X_25,compose(X_26,domain(compose(X_25,X_26)))))]]) ).
cnf(refute_0_51,plain,
( compose(compose(X_25,X_26),domain(compose(X_25,X_26))) != compose(X_25,X_26)
| compose(X_25,compose(X_26,domain(compose(X_25,X_26)))) = compose(X_25,X_26) ),
inference(resolve,[$cnf( $equal(compose(compose(X_25,X_26),domain(compose(X_25,X_26))),compose(X_25,compose(X_26,domain(compose(X_25,X_26))))) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
compose(X_25,compose(X_26,domain(compose(X_25,X_26)))) = compose(X_25,X_26),
inference(resolve,[$cnf( $equal(compose(compose(X_25,X_26),domain(compose(X_25,X_26))),compose(X_25,X_26)) )],[refute_0_43,refute_0_51]) ).
cnf(refute_0_53,plain,
compose(a,compose(X_26,domain(compose(a,X_26)))) = compose(a,X_26),
inference(subst,[],[refute_0_52:[bind(X_25,$fot(a))]]) ).
cnf(refute_0_54,plain,
( compose(a,compose(X_26,domain(compose(a,X_26)))) != compose(a,X_26)
| ~ there_exists(compose(a,X_26))
| there_exists(compose(a,compose(X_26,domain(compose(a,X_26))))) ),
introduced(tautology,[equality,[$cnf( ~ there_exists(compose(a,compose(X_26,domain(compose(a,X_26))))) ),[0],$fot(compose(a,X_26))]]) ).
cnf(refute_0_55,plain,
( ~ there_exists(compose(a,X_26))
| there_exists(compose(a,compose(X_26,domain(compose(a,X_26))))) ),
inference(resolve,[$cnf( $equal(compose(a,compose(X_26,domain(compose(a,X_26)))),compose(a,X_26)) )],[refute_0_53,refute_0_54]) ).
cnf(refute_0_56,plain,
( ~ there_exists(compose(a,X_26))
| codomain(b) = codomain(compose(codomain(b),compose(X_26,domain(compose(a,X_26))))) ),
inference(resolve,[$cnf( there_exists(compose(a,compose(X_26,domain(compose(a,X_26))))) )],[refute_0_55,refute_0_42]) ).
cnf(refute_0_57,plain,
( ~ there_exists(compose(a,b))
| codomain(b) = codomain(compose(codomain(b),compose(b,domain(compose(a,b))))) ),
inference(subst,[],[refute_0_56:[bind(X_26,$fot(b))]]) ).
cnf(refute_0_58,plain,
codomain(b) = codomain(compose(codomain(b),compose(b,domain(compose(a,b))))),
inference(resolve,[$cnf( there_exists(compose(a,b)) )],[ab_exists,refute_0_57]) ).
cnf(refute_0_59,plain,
compose(codomain(X_26),compose(X_26,X_27)) = compose(compose(codomain(X_26),X_26),X_27),
inference(subst,[],[associativity_of_compose:[bind(X,$fot(codomain(X_26))),bind(Y,$fot(X_26)),bind(Z,$fot(X_27))]]) ).
cnf(refute_0_60,plain,
compose(codomain(X_26),X_26) = X_26,
inference(subst,[],[compose_codomain:[bind(X,$fot(X_26))]]) ).
cnf(refute_0_61,plain,
( compose(codomain(X_26),X_26) != X_26
| compose(codomain(X_26),compose(X_26,X_27)) != compose(compose(codomain(X_26),X_26),X_27)
| compose(codomain(X_26),compose(X_26,X_27)) = compose(X_26,X_27) ),
introduced(tautology,[equality,[$cnf( $equal(compose(codomain(X_26),compose(X_26,X_27)),compose(compose(codomain(X_26),X_26),X_27)) ),[1,0],$fot(X_26)]]) ).
cnf(refute_0_62,plain,
( compose(codomain(X_26),compose(X_26,X_27)) != compose(compose(codomain(X_26),X_26),X_27)
| compose(codomain(X_26),compose(X_26,X_27)) = compose(X_26,X_27) ),
inference(resolve,[$cnf( $equal(compose(codomain(X_26),X_26),X_26) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
compose(codomain(X_26),compose(X_26,X_27)) = compose(X_26,X_27),
inference(resolve,[$cnf( $equal(compose(codomain(X_26),compose(X_26,X_27)),compose(compose(codomain(X_26),X_26),X_27)) )],[refute_0_59,refute_0_62]) ).
cnf(refute_0_64,plain,
compose(codomain(b),compose(b,domain(compose(a,b)))) = compose(b,domain(compose(a,b))),
inference(subst,[],[refute_0_63:[bind(X_26,$fot(b)),bind(X_27,$fot(domain(compose(a,b))))]]) ).
cnf(refute_0_65,plain,
codomain(compose(codomain(b),compose(b,domain(compose(a,b))))) = codomain(compose(codomain(b),compose(b,domain(compose(a,b))))),
introduced(tautology,[refl,[$fot(codomain(compose(codomain(b),compose(b,domain(compose(a,b))))))]]) ).
cnf(refute_0_66,plain,
( codomain(compose(codomain(b),compose(b,domain(compose(a,b))))) != codomain(compose(codomain(b),compose(b,domain(compose(a,b)))))
| compose(codomain(b),compose(b,domain(compose(a,b)))) != compose(b,domain(compose(a,b)))
| codomain(compose(codomain(b),compose(b,domain(compose(a,b))))) = codomain(compose(b,domain(compose(a,b)))) ),
introduced(tautology,[equality,[$cnf( $equal(codomain(compose(codomain(b),compose(b,domain(compose(a,b))))),codomain(compose(codomain(b),compose(b,domain(compose(a,b)))))) ),[1,0],$fot(compose(b,domain(compose(a,b))))]]) ).
cnf(refute_0_67,plain,
( compose(codomain(b),compose(b,domain(compose(a,b)))) != compose(b,domain(compose(a,b)))
| codomain(compose(codomain(b),compose(b,domain(compose(a,b))))) = codomain(compose(b,domain(compose(a,b)))) ),
inference(resolve,[$cnf( $equal(codomain(compose(codomain(b),compose(b,domain(compose(a,b))))),codomain(compose(codomain(b),compose(b,domain(compose(a,b)))))) )],[refute_0_65,refute_0_66]) ).
cnf(refute_0_68,plain,
codomain(compose(codomain(b),compose(b,domain(compose(a,b))))) = codomain(compose(b,domain(compose(a,b)))),
inference(resolve,[$cnf( $equal(compose(codomain(b),compose(b,domain(compose(a,b)))),compose(b,domain(compose(a,b)))) )],[refute_0_64,refute_0_67]) ).
cnf(refute_0_69,plain,
( codomain(b) != codomain(compose(codomain(b),compose(b,domain(compose(a,b)))))
| codomain(compose(codomain(b),compose(b,domain(compose(a,b))))) != codomain(compose(b,domain(compose(a,b))))
| codomain(b) = codomain(compose(b,domain(compose(a,b)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(codomain(b),codomain(compose(b,domain(compose(a,b))))) ),[0],$fot(codomain(compose(codomain(b),compose(b,domain(compose(a,b))))))]]) ).
cnf(refute_0_70,plain,
( codomain(b) != codomain(compose(codomain(b),compose(b,domain(compose(a,b)))))
| codomain(b) = codomain(compose(b,domain(compose(a,b)))) ),
inference(resolve,[$cnf( $equal(codomain(compose(codomain(b),compose(b,domain(compose(a,b))))),codomain(compose(b,domain(compose(a,b))))) )],[refute_0_68,refute_0_69]) ).
cnf(refute_0_71,plain,
codomain(b) = codomain(compose(b,domain(compose(a,b)))),
inference(resolve,[$cnf( $equal(codomain(b),codomain(compose(codomain(b),compose(b,domain(compose(a,b)))))) )],[refute_0_58,refute_0_70]) ).
cnf(refute_0_72,plain,
( codomain(b) != codomain(compose(b,domain(compose(a,b))))
| codomain(compose(b,domain(compose(a,b)))) = codomain(b) ),
inference(subst,[],[refute_0_47:[bind(X0,$fot(codomain(b))),bind(Y0,$fot(codomain(compose(b,domain(compose(a,b))))))]]) ).
cnf(refute_0_73,plain,
codomain(compose(b,domain(compose(a,b)))) = codomain(b),
inference(resolve,[$cnf( $equal(codomain(b),codomain(compose(b,domain(compose(a,b))))) )],[refute_0_71,refute_0_72]) ).
cnf(refute_0_74,plain,
( codomain(b) != codomain(b)
| codomain(compose(b,domain(compose(a,b)))) != codomain(b)
| codomain(b) = codomain(compose(b,domain(compose(a,b)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(codomain(b),codomain(compose(b,domain(compose(a,b))))) ),[1],$fot(codomain(b))]]) ).
cnf(refute_0_75,plain,
( codomain(b) != codomain(b)
| codomain(b) = codomain(compose(b,domain(compose(a,b)))) ),
inference(resolve,[$cnf( $equal(codomain(compose(b,domain(compose(a,b)))),codomain(b)) )],[refute_0_73,refute_0_74]) ).
cnf(refute_0_76,plain,
( codomain(b) != codomain(b)
| there_exists(compose(codomain(b),compose(b,domain(compose(a,b))))) ),
inference(resolve,[$cnf( $equal(codomain(b),codomain(compose(b,domain(compose(a,b))))) )],[refute_0_75,refute_0_25]) ).
cnf(refute_0_77,plain,
codomain(b) = codomain(b),
introduced(tautology,[refl,[$fot(codomain(b))]]) ).
cnf(refute_0_78,plain,
there_exists(compose(codomain(b),compose(b,domain(compose(a,b))))),
inference(resolve,[$cnf( $equal(codomain(b),codomain(b)) )],[refute_0_77,refute_0_76]) ).
cnf(refute_0_79,plain,
( compose(codomain(b),compose(b,domain(compose(a,b)))) != compose(b,domain(compose(a,b)))
| ~ there_exists(compose(codomain(b),compose(b,domain(compose(a,b)))))
| there_exists(compose(b,domain(compose(a,b)))) ),
introduced(tautology,[equality,[$cnf( there_exists(compose(codomain(b),compose(b,domain(compose(a,b))))) ),[0],$fot(compose(b,domain(compose(a,b))))]]) ).
cnf(refute_0_80,plain,
( ~ there_exists(compose(codomain(b),compose(b,domain(compose(a,b)))))
| there_exists(compose(b,domain(compose(a,b)))) ),
inference(resolve,[$cnf( $equal(compose(codomain(b),compose(b,domain(compose(a,b)))),compose(b,domain(compose(a,b)))) )],[refute_0_64,refute_0_79]) ).
cnf(refute_0_81,plain,
there_exists(compose(b,domain(compose(a,b)))),
inference(resolve,[$cnf( there_exists(compose(codomain(b),compose(b,domain(compose(a,b))))) )],[refute_0_78,refute_0_80]) ).
cnf(refute_0_82,plain,
domain(b) = codomain(domain(compose(a,b))),
inference(resolve,[$cnf( there_exists(compose(b,domain(compose(a,b)))) )],[refute_0_81,refute_0_0]) ).
cnf(refute_0_83,plain,
( ~ there_exists(compose(X_5,domain(X_5)))
| domain(X_5) = codomain(domain(X_5)) ),
inference(subst,[],[domain_codomain_composition1:[bind(X,$fot(X_5)),bind(Y,$fot(domain(X_5)))]]) ).
cnf(refute_0_84,plain,
compose(X_5,domain(X_5)) = X_5,
inference(subst,[],[compose_domain:[bind(X,$fot(X_5))]]) ).
cnf(refute_0_85,plain,
( compose(X_5,domain(X_5)) != X_5
| ~ there_exists(X_5)
| there_exists(compose(X_5,domain(X_5))) ),
introduced(tautology,[equality,[$cnf( ~ there_exists(compose(X_5,domain(X_5))) ),[0],$fot(X_5)]]) ).
cnf(refute_0_86,plain,
( ~ there_exists(X_5)
| there_exists(compose(X_5,domain(X_5))) ),
inference(resolve,[$cnf( $equal(compose(X_5,domain(X_5)),X_5) )],[refute_0_84,refute_0_85]) ).
cnf(refute_0_87,plain,
( ~ there_exists(X_5)
| domain(X_5) = codomain(domain(X_5)) ),
inference(resolve,[$cnf( there_exists(compose(X_5,domain(X_5))) )],[refute_0_86,refute_0_83]) ).
cnf(refute_0_88,plain,
( ~ there_exists(compose(a,b))
| domain(compose(a,b)) = codomain(domain(compose(a,b))) ),
inference(subst,[],[refute_0_87:[bind(X_5,$fot(compose(a,b)))]]) ).
cnf(refute_0_89,plain,
domain(compose(a,b)) = codomain(domain(compose(a,b))),
inference(resolve,[$cnf( there_exists(compose(a,b)) )],[ab_exists,refute_0_88]) ).
cnf(refute_0_90,plain,
( domain(compose(a,b)) != codomain(domain(compose(a,b)))
| codomain(domain(compose(a,b))) = domain(compose(a,b)) ),
inference(subst,[],[refute_0_47:[bind(X0,$fot(domain(compose(a,b)))),bind(Y0,$fot(codomain(domain(compose(a,b)))))]]) ).
cnf(refute_0_91,plain,
codomain(domain(compose(a,b))) = domain(compose(a,b)),
inference(resolve,[$cnf( $equal(domain(compose(a,b)),codomain(domain(compose(a,b)))) )],[refute_0_89,refute_0_90]) ).
cnf(refute_0_92,plain,
( codomain(domain(compose(a,b))) != domain(compose(a,b))
| domain(b) != codomain(domain(compose(a,b)))
| domain(b) = domain(compose(a,b)) ),
introduced(tautology,[equality,[$cnf( $equal(domain(b),codomain(domain(compose(a,b)))) ),[1],$fot(domain(compose(a,b)))]]) ).
cnf(refute_0_93,plain,
( domain(b) != codomain(domain(compose(a,b)))
| domain(b) = domain(compose(a,b)) ),
inference(resolve,[$cnf( $equal(codomain(domain(compose(a,b))),domain(compose(a,b))) )],[refute_0_91,refute_0_92]) ).
cnf(refute_0_94,plain,
domain(b) = domain(compose(a,b)),
inference(resolve,[$cnf( $equal(domain(b),codomain(domain(compose(a,b)))) )],[refute_0_82,refute_0_93]) ).
cnf(refute_0_95,plain,
( domain(b) != domain(compose(a,b))
| domain(compose(a,b)) = domain(b) ),
inference(subst,[],[refute_0_47:[bind(X0,$fot(domain(b))),bind(Y0,$fot(domain(compose(a,b))))]]) ).
cnf(refute_0_96,plain,
domain(b) != domain(compose(a,b)),
inference(resolve,[$cnf( $equal(domain(compose(a,b)),domain(b)) )],[refute_0_95,prove_domain_of_ab_equals_domain_of_b]) ).
cnf(refute_0_97,plain,
$false,
inference(resolve,[$cnf( $equal(domain(b),domain(compose(a,b))) )],[refute_0_94,refute_0_96]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : CAT009-3 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n025.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
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun May 29 20:27:26 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 33.16/33.48 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 33.16/33.48
% 33.16/33.48 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 33.16/33.49
%------------------------------------------------------------------------------