TSTP Solution File: CAT014-3 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : CAT014-3 : 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 8.78s 8.99s
% Output : CNFRefutation 8.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 36
% Syntax : Number of clauses : 140 ( 67 unt; 0 nHn; 97 RR)
% Number of literals : 242 ( 220 equ; 104 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 9 ( 3 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 : 118 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(codomain_has_elements,axiom,
( ~ there_exists(codomain(X))
| there_exists(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(compose(codomain(a),codomain(a)))
| domain(codomain(a)) = codomain(codomain(a)) ),
inference(subst,[],[domain_codomain_composition1:[bind(X,$fot(codomain(a))),bind(Y,$fot(codomain(a)))]]) ).
cnf(refute_0_1,plain,
compose(X,compose(domain(domain(domain(X))),Z)) = compose(compose(X,domain(domain(domain(X)))),Z),
inference(subst,[],[associativity_of_compose:[bind(Y,$fot(domain(domain(domain(X)))))]]) ).
cnf(refute_0_2,plain,
compose(X_11,compose(domain(X_11),X_13)) = compose(compose(X_11,domain(X_11)),X_13),
inference(subst,[],[associativity_of_compose:[bind(X,$fot(X_11)),bind(Y,$fot(domain(X_11))),bind(Z,$fot(X_13))]]) ).
cnf(refute_0_3,plain,
compose(X_11,domain(X_11)) = X_11,
inference(subst,[],[compose_domain:[bind(X,$fot(X_11))]]) ).
cnf(refute_0_4,plain,
( compose(X_11,compose(domain(X_11),X_13)) != compose(compose(X_11,domain(X_11)),X_13)
| compose(X_11,domain(X_11)) != X_11
| compose(X_11,compose(domain(X_11),X_13)) = compose(X_11,X_13) ),
introduced(tautology,[equality,[$cnf( $equal(compose(X_11,compose(domain(X_11),X_13)),compose(compose(X_11,domain(X_11)),X_13)) ),[1,0],$fot(X_11)]]) ).
cnf(refute_0_5,plain,
( compose(X_11,compose(domain(X_11),X_13)) != compose(compose(X_11,domain(X_11)),X_13)
| compose(X_11,compose(domain(X_11),X_13)) = compose(X_11,X_13) ),
inference(resolve,[$cnf( $equal(compose(X_11,domain(X_11)),X_11) )],[refute_0_3,refute_0_4]) ).
cnf(refute_0_6,plain,
compose(X_11,compose(domain(X_11),X_13)) = compose(X_11,X_13),
inference(resolve,[$cnf( $equal(compose(X_11,compose(domain(X_11),X_13)),compose(compose(X_11,domain(X_11)),X_13)) )],[refute_0_2,refute_0_5]) ).
cnf(refute_0_7,plain,
compose(X_11,compose(domain(X_11),domain(domain(domain(X_11))))) = compose(X_11,domain(domain(domain(X_11)))),
inference(subst,[],[refute_0_6:[bind(X_13,$fot(domain(domain(domain(X_11)))))]]) ).
cnf(refute_0_8,plain,
compose(X_19,compose(domain(X_19),domain(domain(X_19)))) = compose(X_19,domain(domain(X_19))),
inference(subst,[],[refute_0_6:[bind(X_11,$fot(X_19)),bind(X_13,$fot(domain(domain(X_19))))]]) ).
cnf(refute_0_9,plain,
compose(domain(X_19),domain(domain(X_19))) = domain(X_19),
inference(subst,[],[compose_domain:[bind(X,$fot(domain(X_19)))]]) ).
cnf(refute_0_10,plain,
( compose(X_19,compose(domain(X_19),domain(domain(X_19)))) != compose(X_19,domain(domain(X_19)))
| compose(domain(X_19),domain(domain(X_19))) != domain(X_19)
| compose(X_19,domain(X_19)) = compose(X_19,domain(domain(X_19))) ),
introduced(tautology,[equality,[$cnf( $equal(compose(X_19,compose(domain(X_19),domain(domain(X_19)))),compose(X_19,domain(domain(X_19)))) ),[0,1],$fot(domain(X_19))]]) ).
cnf(refute_0_11,plain,
( compose(X_19,compose(domain(X_19),domain(domain(X_19)))) != compose(X_19,domain(domain(X_19)))
| compose(X_19,domain(X_19)) = compose(X_19,domain(domain(X_19))) ),
inference(resolve,[$cnf( $equal(compose(domain(X_19),domain(domain(X_19))),domain(X_19)) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
compose(X_19,domain(X_19)) = compose(X_19,domain(domain(X_19))),
inference(resolve,[$cnf( $equal(compose(X_19,compose(domain(X_19),domain(domain(X_19)))),compose(X_19,domain(domain(X_19)))) )],[refute_0_8,refute_0_11]) ).
cnf(refute_0_13,plain,
compose(X_19,domain(X_19)) = X_19,
inference(subst,[],[compose_domain:[bind(X,$fot(X_19))]]) ).
cnf(refute_0_14,plain,
( compose(X_19,domain(X_19)) != X_19
| compose(X_19,domain(X_19)) != compose(X_19,domain(domain(X_19)))
| X_19 = compose(X_19,domain(domain(X_19))) ),
introduced(tautology,[equality,[$cnf( $equal(compose(X_19,domain(X_19)),compose(X_19,domain(domain(X_19)))) ),[0],$fot(X_19)]]) ).
cnf(refute_0_15,plain,
( compose(X_19,domain(X_19)) != compose(X_19,domain(domain(X_19)))
| X_19 = compose(X_19,domain(domain(X_19))) ),
inference(resolve,[$cnf( $equal(compose(X_19,domain(X_19)),X_19) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
X_19 = compose(X_19,domain(domain(X_19))),
inference(resolve,[$cnf( $equal(compose(X_19,domain(X_19)),compose(X_19,domain(domain(X_19)))) )],[refute_0_12,refute_0_15]) ).
cnf(refute_0_17,plain,
domain(X_11) = compose(domain(X_11),domain(domain(domain(X_11)))),
inference(subst,[],[refute_0_16:[bind(X_19,$fot(domain(X_11)))]]) ).
cnf(refute_0_18,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_19,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_20,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
( domain(X_11) != compose(domain(X_11),domain(domain(domain(X_11))))
| compose(domain(X_11),domain(domain(domain(X_11)))) = domain(X_11) ),
inference(subst,[],[refute_0_20:[bind(X0,$fot(domain(X_11))),bind(Y0,$fot(compose(domain(X_11),domain(domain(domain(X_11))))))]]) ).
cnf(refute_0_22,plain,
compose(domain(X_11),domain(domain(domain(X_11)))) = domain(X_11),
inference(resolve,[$cnf( $equal(domain(X_11),compose(domain(X_11),domain(domain(domain(X_11))))) )],[refute_0_17,refute_0_21]) ).
cnf(refute_0_23,plain,
( compose(X_11,compose(domain(X_11),domain(domain(domain(X_11))))) != compose(X_11,domain(domain(domain(X_11))))
| compose(domain(X_11),domain(domain(domain(X_11)))) != domain(X_11)
| compose(X_11,domain(X_11)) = compose(X_11,domain(domain(domain(X_11)))) ),
introduced(tautology,[equality,[$cnf( $equal(compose(X_11,compose(domain(X_11),domain(domain(domain(X_11))))),compose(X_11,domain(domain(domain(X_11))))) ),[0,1],$fot(domain(X_11))]]) ).
cnf(refute_0_24,plain,
( compose(X_11,compose(domain(X_11),domain(domain(domain(X_11))))) != compose(X_11,domain(domain(domain(X_11))))
| compose(X_11,domain(X_11)) = compose(X_11,domain(domain(domain(X_11)))) ),
inference(resolve,[$cnf( $equal(compose(domain(X_11),domain(domain(domain(X_11)))),domain(X_11)) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
compose(X_11,domain(X_11)) = compose(X_11,domain(domain(domain(X_11)))),
inference(resolve,[$cnf( $equal(compose(X_11,compose(domain(X_11),domain(domain(domain(X_11))))),compose(X_11,domain(domain(domain(X_11))))) )],[refute_0_7,refute_0_24]) ).
cnf(refute_0_26,plain,
( compose(X_11,domain(X_11)) != X_11
| compose(X_11,domain(X_11)) != compose(X_11,domain(domain(domain(X_11))))
| X_11 = compose(X_11,domain(domain(domain(X_11)))) ),
introduced(tautology,[equality,[$cnf( $equal(compose(X_11,domain(X_11)),compose(X_11,domain(domain(domain(X_11))))) ),[0],$fot(X_11)]]) ).
cnf(refute_0_27,plain,
( compose(X_11,domain(X_11)) != compose(X_11,domain(domain(domain(X_11))))
| X_11 = compose(X_11,domain(domain(domain(X_11)))) ),
inference(resolve,[$cnf( $equal(compose(X_11,domain(X_11)),X_11) )],[refute_0_3,refute_0_26]) ).
cnf(refute_0_28,plain,
X_11 = compose(X_11,domain(domain(domain(X_11)))),
inference(resolve,[$cnf( $equal(compose(X_11,domain(X_11)),compose(X_11,domain(domain(domain(X_11))))) )],[refute_0_25,refute_0_27]) ).
cnf(refute_0_29,plain,
X = compose(X,domain(domain(domain(X)))),
inference(subst,[],[refute_0_28:[bind(X_11,$fot(X))]]) ).
cnf(refute_0_30,plain,
( X != compose(X,domain(domain(domain(X))))
| compose(X,domain(domain(domain(X)))) = X ),
inference(subst,[],[refute_0_20:[bind(X0,$fot(X)),bind(Y0,$fot(compose(X,domain(domain(domain(X))))))]]) ).
cnf(refute_0_31,plain,
compose(X,domain(domain(domain(X)))) = X,
inference(resolve,[$cnf( $equal(X,compose(X,domain(domain(domain(X))))) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
( compose(X,compose(domain(domain(domain(X))),Z)) != compose(compose(X,domain(domain(domain(X)))),Z)
| compose(X,domain(domain(domain(X)))) != X
| compose(X,compose(domain(domain(domain(X))),Z)) = compose(X,Z) ),
introduced(tautology,[equality,[$cnf( $equal(compose(X,compose(domain(domain(domain(X))),Z)),compose(compose(X,domain(domain(domain(X)))),Z)) ),[1,0],$fot(X)]]) ).
cnf(refute_0_33,plain,
( compose(X,compose(domain(domain(domain(X))),Z)) != compose(compose(X,domain(domain(domain(X)))),Z)
| compose(X,compose(domain(domain(domain(X))),Z)) = compose(X,Z) ),
inference(resolve,[$cnf( $equal(compose(X,domain(domain(domain(X)))),X) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
compose(X,compose(domain(domain(domain(X))),Z)) = compose(X,Z),
inference(resolve,[$cnf( $equal(compose(X,compose(domain(domain(domain(X))),Z)),compose(compose(X,domain(domain(domain(X)))),Z)) )],[refute_0_1,refute_0_33]) ).
cnf(refute_0_35,plain,
compose(X_60,compose(domain(domain(domain(X_60))),domain(compose(domain(domain(domain(domain(X_60)))),domain(domain(domain(domain(X_60)))))))) = compose(X_60,domain(compose(domain(domain(domain(domain(X_60)))),domain(domain(domain(domain(X_60))))))),
inference(subst,[],[refute_0_34:[bind(X,$fot(X_60)),bind(Z,$fot(domain(compose(domain(domain(domain(domain(X_60)))),domain(domain(domain(domain(X_60))))))))]]) ).
cnf(refute_0_36,plain,
compose(X_11,compose(domain(X_11),domain(compose(domain(X_11),domain(X_11))))) = compose(X_11,domain(compose(domain(X_11),domain(X_11)))),
inference(subst,[],[refute_0_6:[bind(X_13,$fot(domain(compose(domain(X_11),domain(X_11)))))]]) ).
cnf(refute_0_37,plain,
compose(X_11,compose(domain(X_11),compose(X_34,domain(compose(domain(X_11),X_34))))) = compose(X_11,compose(X_34,domain(compose(domain(X_11),X_34)))),
inference(subst,[],[refute_0_6:[bind(X_13,$fot(compose(X_34,domain(compose(domain(X_11),X_34)))))]]) ).
cnf(refute_0_38,plain,
compose(compose(X_11,X_12),domain(compose(X_11,X_12))) = compose(X_11,X_12),
inference(subst,[],[compose_domain:[bind(X,$fot(compose(X_11,X_12)))]]) ).
cnf(refute_0_39,plain,
compose(X_11,compose(X_12,domain(compose(X_11,X_12)))) = compose(compose(X_11,X_12),domain(compose(X_11,X_12))),
inference(subst,[],[associativity_of_compose:[bind(X,$fot(X_11)),bind(Y,$fot(X_12)),bind(Z,$fot(domain(compose(X_11,X_12))))]]) ).
cnf(refute_0_40,plain,
( compose(X_11,compose(X_12,domain(compose(X_11,X_12)))) != compose(compose(X_11,X_12),domain(compose(X_11,X_12)))
| compose(compose(X_11,X_12),domain(compose(X_11,X_12))) = compose(X_11,compose(X_12,domain(compose(X_11,X_12)))) ),
inference(subst,[],[refute_0_20:[bind(X0,$fot(compose(X_11,compose(X_12,domain(compose(X_11,X_12)))))),bind(Y0,$fot(compose(compose(X_11,X_12),domain(compose(X_11,X_12)))))]]) ).
cnf(refute_0_41,plain,
compose(compose(X_11,X_12),domain(compose(X_11,X_12))) = compose(X_11,compose(X_12,domain(compose(X_11,X_12)))),
inference(resolve,[$cnf( $equal(compose(X_11,compose(X_12,domain(compose(X_11,X_12)))),compose(compose(X_11,X_12),domain(compose(X_11,X_12)))) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
( compose(compose(X_11,X_12),domain(compose(X_11,X_12))) != compose(X_11,X_12)
| compose(compose(X_11,X_12),domain(compose(X_11,X_12))) != compose(X_11,compose(X_12,domain(compose(X_11,X_12))))
| compose(X_11,compose(X_12,domain(compose(X_11,X_12)))) = compose(X_11,X_12) ),
introduced(tautology,[equality,[$cnf( $equal(compose(compose(X_11,X_12),domain(compose(X_11,X_12))),compose(X_11,X_12)) ),[0],$fot(compose(X_11,compose(X_12,domain(compose(X_11,X_12)))))]]) ).
cnf(refute_0_43,plain,
( compose(compose(X_11,X_12),domain(compose(X_11,X_12))) != compose(X_11,X_12)
| compose(X_11,compose(X_12,domain(compose(X_11,X_12)))) = compose(X_11,X_12) ),
inference(resolve,[$cnf( $equal(compose(compose(X_11,X_12),domain(compose(X_11,X_12))),compose(X_11,compose(X_12,domain(compose(X_11,X_12))))) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
compose(X_11,compose(X_12,domain(compose(X_11,X_12)))) = compose(X_11,X_12),
inference(resolve,[$cnf( $equal(compose(compose(X_11,X_12),domain(compose(X_11,X_12))),compose(X_11,X_12)) )],[refute_0_38,refute_0_43]) ).
cnf(refute_0_45,plain,
compose(domain(X_11),compose(X_34,domain(compose(domain(X_11),X_34)))) = compose(domain(X_11),X_34),
inference(subst,[],[refute_0_44:[bind(X_11,$fot(domain(X_11))),bind(X_12,$fot(X_34))]]) ).
cnf(refute_0_46,plain,
( compose(X_11,compose(domain(X_11),compose(X_34,domain(compose(domain(X_11),X_34))))) != compose(X_11,compose(X_34,domain(compose(domain(X_11),X_34))))
| compose(domain(X_11),compose(X_34,domain(compose(domain(X_11),X_34)))) != compose(domain(X_11),X_34)
| compose(X_11,compose(domain(X_11),X_34)) = compose(X_11,compose(X_34,domain(compose(domain(X_11),X_34)))) ),
introduced(tautology,[equality,[$cnf( $equal(compose(X_11,compose(domain(X_11),compose(X_34,domain(compose(domain(X_11),X_34))))),compose(X_11,compose(X_34,domain(compose(domain(X_11),X_34))))) ),[0,1],$fot(compose(domain(X_11),X_34))]]) ).
cnf(refute_0_47,plain,
( compose(X_11,compose(domain(X_11),compose(X_34,domain(compose(domain(X_11),X_34))))) != compose(X_11,compose(X_34,domain(compose(domain(X_11),X_34))))
| compose(X_11,compose(domain(X_11),X_34)) = compose(X_11,compose(X_34,domain(compose(domain(X_11),X_34)))) ),
inference(resolve,[$cnf( $equal(compose(domain(X_11),compose(X_34,domain(compose(domain(X_11),X_34)))),compose(domain(X_11),X_34)) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
compose(X_11,compose(domain(X_11),X_34)) = compose(X_11,compose(X_34,domain(compose(domain(X_11),X_34)))),
inference(resolve,[$cnf( $equal(compose(X_11,compose(domain(X_11),compose(X_34,domain(compose(domain(X_11),X_34))))),compose(X_11,compose(X_34,domain(compose(domain(X_11),X_34))))) )],[refute_0_37,refute_0_47]) ).
cnf(refute_0_49,plain,
compose(X_11,compose(domain(X_11),X_34)) = compose(X_11,X_34),
inference(subst,[],[refute_0_6:[bind(X_13,$fot(X_34))]]) ).
cnf(refute_0_50,plain,
( compose(X_11,compose(domain(X_11),X_34)) != compose(X_11,X_34)
| compose(X_11,compose(domain(X_11),X_34)) != compose(X_11,compose(X_34,domain(compose(domain(X_11),X_34))))
| compose(X_11,X_34) = compose(X_11,compose(X_34,domain(compose(domain(X_11),X_34)))) ),
introduced(tautology,[equality,[$cnf( $equal(compose(X_11,compose(domain(X_11),X_34)),compose(X_11,compose(X_34,domain(compose(domain(X_11),X_34))))) ),[0],$fot(compose(X_11,X_34))]]) ).
cnf(refute_0_51,plain,
( compose(X_11,compose(domain(X_11),X_34)) != compose(X_11,compose(X_34,domain(compose(domain(X_11),X_34))))
| compose(X_11,X_34) = compose(X_11,compose(X_34,domain(compose(domain(X_11),X_34)))) ),
inference(resolve,[$cnf( $equal(compose(X_11,compose(domain(X_11),X_34)),compose(X_11,X_34)) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
compose(X_11,X_34) = compose(X_11,compose(X_34,domain(compose(domain(X_11),X_34)))),
inference(resolve,[$cnf( $equal(compose(X_11,compose(domain(X_11),X_34)),compose(X_11,compose(X_34,domain(compose(domain(X_11),X_34))))) )],[refute_0_48,refute_0_51]) ).
cnf(refute_0_53,plain,
compose(X_11,domain(X_11)) = compose(X_11,compose(domain(X_11),domain(compose(domain(X_11),domain(X_11))))),
inference(subst,[],[refute_0_52:[bind(X_34,$fot(domain(X_11)))]]) ).
cnf(refute_0_54,plain,
( compose(X_11,domain(X_11)) != compose(X_11,compose(domain(X_11),domain(compose(domain(X_11),domain(X_11)))))
| compose(X_11,compose(domain(X_11),domain(compose(domain(X_11),domain(X_11))))) = compose(X_11,domain(X_11)) ),
inference(subst,[],[refute_0_20:[bind(X0,$fot(compose(X_11,domain(X_11)))),bind(Y0,$fot(compose(X_11,compose(domain(X_11),domain(compose(domain(X_11),domain(X_11)))))))]]) ).
cnf(refute_0_55,plain,
compose(X_11,compose(domain(X_11),domain(compose(domain(X_11),domain(X_11))))) = compose(X_11,domain(X_11)),
inference(resolve,[$cnf( $equal(compose(X_11,domain(X_11)),compose(X_11,compose(domain(X_11),domain(compose(domain(X_11),domain(X_11)))))) )],[refute_0_53,refute_0_54]) ).
cnf(refute_0_56,plain,
( compose(X_11,compose(domain(X_11),domain(compose(domain(X_11),domain(X_11))))) != compose(X_11,domain(X_11))
| compose(X_11,compose(domain(X_11),domain(compose(domain(X_11),domain(X_11))))) != compose(X_11,domain(compose(domain(X_11),domain(X_11))))
| compose(X_11,domain(X_11)) = compose(X_11,domain(compose(domain(X_11),domain(X_11)))) ),
introduced(tautology,[equality,[$cnf( $equal(compose(X_11,compose(domain(X_11),domain(compose(domain(X_11),domain(X_11))))),compose(X_11,domain(compose(domain(X_11),domain(X_11))))) ),[0],$fot(compose(X_11,domain(X_11)))]]) ).
cnf(refute_0_57,plain,
( compose(X_11,compose(domain(X_11),domain(compose(domain(X_11),domain(X_11))))) != compose(X_11,domain(compose(domain(X_11),domain(X_11))))
| compose(X_11,domain(X_11)) = compose(X_11,domain(compose(domain(X_11),domain(X_11)))) ),
inference(resolve,[$cnf( $equal(compose(X_11,compose(domain(X_11),domain(compose(domain(X_11),domain(X_11))))),compose(X_11,domain(X_11))) )],[refute_0_55,refute_0_56]) ).
cnf(refute_0_58,plain,
compose(X_11,domain(X_11)) = compose(X_11,domain(compose(domain(X_11),domain(X_11)))),
inference(resolve,[$cnf( $equal(compose(X_11,compose(domain(X_11),domain(compose(domain(X_11),domain(X_11))))),compose(X_11,domain(compose(domain(X_11),domain(X_11))))) )],[refute_0_36,refute_0_57]) ).
cnf(refute_0_59,plain,
( compose(X_11,domain(X_11)) != X_11
| compose(X_11,domain(X_11)) != compose(X_11,domain(compose(domain(X_11),domain(X_11))))
| X_11 = compose(X_11,domain(compose(domain(X_11),domain(X_11)))) ),
introduced(tautology,[equality,[$cnf( $equal(compose(X_11,domain(X_11)),compose(X_11,domain(compose(domain(X_11),domain(X_11))))) ),[0],$fot(X_11)]]) ).
cnf(refute_0_60,plain,
( compose(X_11,domain(X_11)) != compose(X_11,domain(compose(domain(X_11),domain(X_11))))
| X_11 = compose(X_11,domain(compose(domain(X_11),domain(X_11)))) ),
inference(resolve,[$cnf( $equal(compose(X_11,domain(X_11)),X_11) )],[refute_0_3,refute_0_59]) ).
cnf(refute_0_61,plain,
X_11 = compose(X_11,domain(compose(domain(X_11),domain(X_11)))),
inference(resolve,[$cnf( $equal(compose(X_11,domain(X_11)),compose(X_11,domain(compose(domain(X_11),domain(X_11))))) )],[refute_0_58,refute_0_60]) ).
cnf(refute_0_62,plain,
domain(domain(domain(X_60))) = compose(domain(domain(domain(X_60))),domain(compose(domain(domain(domain(domain(X_60)))),domain(domain(domain(domain(X_60))))))),
inference(subst,[],[refute_0_61:[bind(X_11,$fot(domain(domain(domain(X_60)))))]]) ).
cnf(refute_0_63,plain,
( domain(domain(domain(X_60))) != compose(domain(domain(domain(X_60))),domain(compose(domain(domain(domain(domain(X_60)))),domain(domain(domain(domain(X_60)))))))
| compose(domain(domain(domain(X_60))),domain(compose(domain(domain(domain(domain(X_60)))),domain(domain(domain(domain(X_60))))))) = domain(domain(domain(X_60))) ),
inference(subst,[],[refute_0_20:[bind(X0,$fot(domain(domain(domain(X_60))))),bind(Y0,$fot(compose(domain(domain(domain(X_60))),domain(compose(domain(domain(domain(domain(X_60)))),domain(domain(domain(domain(X_60)))))))))]]) ).
cnf(refute_0_64,plain,
compose(domain(domain(domain(X_60))),domain(compose(domain(domain(domain(domain(X_60)))),domain(domain(domain(domain(X_60))))))) = domain(domain(domain(X_60))),
inference(resolve,[$cnf( $equal(domain(domain(domain(X_60))),compose(domain(domain(domain(X_60))),domain(compose(domain(domain(domain(domain(X_60)))),domain(domain(domain(domain(X_60)))))))) )],[refute_0_62,refute_0_63]) ).
cnf(refute_0_65,plain,
( compose(X_60,compose(domain(domain(domain(X_60))),domain(compose(domain(domain(domain(domain(X_60)))),domain(domain(domain(domain(X_60)))))))) != compose(X_60,domain(compose(domain(domain(domain(domain(X_60)))),domain(domain(domain(domain(X_60)))))))
| compose(domain(domain(domain(X_60))),domain(compose(domain(domain(domain(domain(X_60)))),domain(domain(domain(domain(X_60))))))) != domain(domain(domain(X_60)))
| compose(X_60,domain(domain(domain(X_60)))) = compose(X_60,domain(compose(domain(domain(domain(domain(X_60)))),domain(domain(domain(domain(X_60))))))) ),
introduced(tautology,[equality,[$cnf( $equal(compose(X_60,compose(domain(domain(domain(X_60))),domain(compose(domain(domain(domain(domain(X_60)))),domain(domain(domain(domain(X_60)))))))),compose(X_60,domain(compose(domain(domain(domain(domain(X_60)))),domain(domain(domain(domain(X_60)))))))) ),[0,1],$fot(domain(domain(domain(X_60))))]]) ).
cnf(refute_0_66,plain,
( compose(X_60,compose(domain(domain(domain(X_60))),domain(compose(domain(domain(domain(domain(X_60)))),domain(domain(domain(domain(X_60)))))))) != compose(X_60,domain(compose(domain(domain(domain(domain(X_60)))),domain(domain(domain(domain(X_60)))))))
| compose(X_60,domain(domain(domain(X_60)))) = compose(X_60,domain(compose(domain(domain(domain(domain(X_60)))),domain(domain(domain(domain(X_60))))))) ),
inference(resolve,[$cnf( $equal(compose(domain(domain(domain(X_60))),domain(compose(domain(domain(domain(domain(X_60)))),domain(domain(domain(domain(X_60))))))),domain(domain(domain(X_60)))) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
compose(X_60,domain(domain(domain(X_60)))) = compose(X_60,domain(compose(domain(domain(domain(domain(X_60)))),domain(domain(domain(domain(X_60))))))),
inference(resolve,[$cnf( $equal(compose(X_60,compose(domain(domain(domain(X_60))),domain(compose(domain(domain(domain(domain(X_60)))),domain(domain(domain(domain(X_60)))))))),compose(X_60,domain(compose(domain(domain(domain(domain(X_60)))),domain(domain(domain(domain(X_60)))))))) )],[refute_0_35,refute_0_66]) ).
cnf(refute_0_68,plain,
( X_11 != compose(X_11,domain(domain(domain(X_11))))
| compose(X_11,domain(domain(domain(X_11)))) = X_11 ),
inference(subst,[],[refute_0_20:[bind(X0,$fot(X_11)),bind(Y0,$fot(compose(X_11,domain(domain(domain(X_11))))))]]) ).
cnf(refute_0_69,plain,
compose(X_11,domain(domain(domain(X_11)))) = X_11,
inference(resolve,[$cnf( $equal(X_11,compose(X_11,domain(domain(domain(X_11))))) )],[refute_0_28,refute_0_68]) ).
cnf(refute_0_70,plain,
compose(X_60,domain(domain(domain(X_60)))) = X_60,
inference(subst,[],[refute_0_69:[bind(X_11,$fot(X_60))]]) ).
cnf(refute_0_71,plain,
( compose(X_60,domain(domain(domain(X_60)))) != X_60
| compose(X_60,domain(domain(domain(X_60)))) != compose(X_60,domain(compose(domain(domain(domain(domain(X_60)))),domain(domain(domain(domain(X_60)))))))
| X_60 = compose(X_60,domain(compose(domain(domain(domain(domain(X_60)))),domain(domain(domain(domain(X_60))))))) ),
introduced(tautology,[equality,[$cnf( $equal(compose(X_60,domain(domain(domain(X_60)))),compose(X_60,domain(compose(domain(domain(domain(domain(X_60)))),domain(domain(domain(domain(X_60)))))))) ),[0],$fot(X_60)]]) ).
cnf(refute_0_72,plain,
( compose(X_60,domain(domain(domain(X_60)))) != compose(X_60,domain(compose(domain(domain(domain(domain(X_60)))),domain(domain(domain(domain(X_60)))))))
| X_60 = compose(X_60,domain(compose(domain(domain(domain(domain(X_60)))),domain(domain(domain(domain(X_60))))))) ),
inference(resolve,[$cnf( $equal(compose(X_60,domain(domain(domain(X_60)))),X_60) )],[refute_0_70,refute_0_71]) ).
cnf(refute_0_73,plain,
X_60 = compose(X_60,domain(compose(domain(domain(domain(domain(X_60)))),domain(domain(domain(domain(X_60))))))),
inference(resolve,[$cnf( $equal(compose(X_60,domain(domain(domain(X_60)))),compose(X_60,domain(compose(domain(domain(domain(domain(X_60)))),domain(domain(domain(domain(X_60)))))))) )],[refute_0_67,refute_0_72]) ).
cnf(refute_0_74,plain,
codomain(a) = compose(codomain(a),domain(compose(domain(domain(domain(domain(codomain(a))))),domain(domain(domain(domain(codomain(a)))))))),
inference(subst,[],[refute_0_73:[bind(X_60,$fot(codomain(a)))]]) ).
cnf(refute_0_75,plain,
( ~ there_exists(codomain(a))
| there_exists(a) ),
inference(subst,[],[codomain_has_elements:[bind(X,$fot(a))]]) ).
cnf(refute_0_76,plain,
there_exists(a),
inference(resolve,[$cnf( there_exists(codomain(a)) )],[assume_codomain_exists,refute_0_75]) ).
cnf(refute_0_77,plain,
( ~ there_exists(compose(codomain(X_41),X_41))
| domain(codomain(X_41)) = codomain(X_41) ),
inference(subst,[],[domain_codomain_composition1:[bind(X,$fot(codomain(X_41))),bind(Y,$fot(X_41))]]) ).
cnf(refute_0_78,plain,
compose(codomain(X_41),X_41) = X_41,
inference(subst,[],[compose_codomain:[bind(X,$fot(X_41))]]) ).
cnf(refute_0_79,plain,
( compose(codomain(X_41),X_41) != X_41
| ~ there_exists(X_41)
| there_exists(compose(codomain(X_41),X_41)) ),
introduced(tautology,[equality,[$cnf( ~ there_exists(compose(codomain(X_41),X_41)) ),[0],$fot(X_41)]]) ).
cnf(refute_0_80,plain,
( ~ there_exists(X_41)
| there_exists(compose(codomain(X_41),X_41)) ),
inference(resolve,[$cnf( $equal(compose(codomain(X_41),X_41),X_41) )],[refute_0_78,refute_0_79]) ).
cnf(refute_0_81,plain,
( ~ there_exists(X_41)
| domain(codomain(X_41)) = codomain(X_41) ),
inference(resolve,[$cnf( there_exists(compose(codomain(X_41),X_41)) )],[refute_0_80,refute_0_77]) ).
cnf(refute_0_82,plain,
( ~ there_exists(a)
| domain(codomain(a)) = codomain(a) ),
inference(subst,[],[refute_0_81:[bind(X_41,$fot(a))]]) ).
cnf(refute_0_83,plain,
domain(codomain(a)) = codomain(a),
inference(resolve,[$cnf( there_exists(a) )],[refute_0_76,refute_0_82]) ).
cnf(refute_0_84,plain,
( codomain(a) != compose(codomain(a),domain(compose(domain(domain(domain(domain(codomain(a))))),domain(domain(domain(domain(codomain(a))))))))
| domain(codomain(a)) != codomain(a)
| codomain(a) = compose(codomain(a),domain(compose(domain(domain(domain(codomain(a)))),domain(domain(domain(domain(codomain(a)))))))) ),
introduced(tautology,[equality,[$cnf( $equal(codomain(a),compose(codomain(a),domain(compose(domain(domain(domain(domain(codomain(a))))),domain(domain(domain(domain(codomain(a))))))))) ),[1,1,0,0,0,0,0],$fot(codomain(a))]]) ).
cnf(refute_0_85,plain,
( codomain(a) != compose(codomain(a),domain(compose(domain(domain(domain(domain(codomain(a))))),domain(domain(domain(domain(codomain(a))))))))
| codomain(a) = compose(codomain(a),domain(compose(domain(domain(domain(codomain(a)))),domain(domain(domain(domain(codomain(a)))))))) ),
inference(resolve,[$cnf( $equal(domain(codomain(a)),codomain(a)) )],[refute_0_83,refute_0_84]) ).
cnf(refute_0_86,plain,
codomain(a) = compose(codomain(a),domain(compose(domain(domain(domain(codomain(a)))),domain(domain(domain(domain(codomain(a)))))))),
inference(resolve,[$cnf( $equal(codomain(a),compose(codomain(a),domain(compose(domain(domain(domain(domain(codomain(a))))),domain(domain(domain(domain(codomain(a))))))))) )],[refute_0_74,refute_0_85]) ).
cnf(refute_0_87,plain,
domain(domain(codomain(a))) = domain(domain(codomain(a))),
introduced(tautology,[refl,[$fot(domain(domain(codomain(a))))]]) ).
cnf(refute_0_88,plain,
( domain(codomain(a)) != codomain(a)
| domain(domain(codomain(a))) != domain(domain(codomain(a)))
| domain(domain(codomain(a))) = domain(codomain(a)) ),
introduced(tautology,[equality,[$cnf( $equal(domain(domain(codomain(a))),domain(domain(codomain(a)))) ),[1,0],$fot(codomain(a))]]) ).
cnf(refute_0_89,plain,
( domain(codomain(a)) != codomain(a)
| domain(domain(codomain(a))) = domain(codomain(a)) ),
inference(resolve,[$cnf( $equal(domain(domain(codomain(a))),domain(domain(codomain(a)))) )],[refute_0_87,refute_0_88]) ).
cnf(refute_0_90,plain,
domain(domain(codomain(a))) = domain(codomain(a)),
inference(resolve,[$cnf( $equal(domain(codomain(a)),codomain(a)) )],[refute_0_83,refute_0_89]) ).
cnf(refute_0_91,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_92,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_20,refute_0_91]) ).
cnf(refute_0_93,plain,
( domain(codomain(a)) != codomain(a)
| domain(domain(codomain(a))) != domain(codomain(a))
| domain(domain(codomain(a))) = codomain(a) ),
inference(subst,[],[refute_0_92:[bind(X0,$fot(domain(domain(codomain(a))))),bind(Y0,$fot(domain(codomain(a)))),bind(Z0,$fot(codomain(a)))]]) ).
cnf(refute_0_94,plain,
( domain(codomain(a)) != codomain(a)
| domain(domain(codomain(a))) = codomain(a) ),
inference(resolve,[$cnf( $equal(domain(domain(codomain(a))),domain(codomain(a))) )],[refute_0_90,refute_0_93]) ).
cnf(refute_0_95,plain,
domain(domain(codomain(a))) = codomain(a),
inference(resolve,[$cnf( $equal(domain(codomain(a)),codomain(a)) )],[refute_0_83,refute_0_94]) ).
cnf(refute_0_96,plain,
domain(domain(domain(codomain(a)))) = domain(domain(domain(codomain(a)))),
introduced(tautology,[refl,[$fot(domain(domain(domain(codomain(a)))))]]) ).
cnf(refute_0_97,plain,
( domain(domain(codomain(a))) != codomain(a)
| domain(domain(domain(codomain(a)))) != domain(domain(domain(codomain(a))))
| domain(domain(domain(codomain(a)))) = domain(codomain(a)) ),
introduced(tautology,[equality,[$cnf( $equal(domain(domain(domain(codomain(a)))),domain(domain(domain(codomain(a))))) ),[1,0],$fot(codomain(a))]]) ).
cnf(refute_0_98,plain,
( domain(domain(codomain(a))) != codomain(a)
| domain(domain(domain(codomain(a)))) = domain(codomain(a)) ),
inference(resolve,[$cnf( $equal(domain(domain(domain(codomain(a)))),domain(domain(domain(codomain(a))))) )],[refute_0_96,refute_0_97]) ).
cnf(refute_0_99,plain,
domain(domain(domain(codomain(a)))) = domain(codomain(a)),
inference(resolve,[$cnf( $equal(domain(domain(codomain(a))),codomain(a)) )],[refute_0_95,refute_0_98]) ).
cnf(refute_0_100,plain,
( domain(codomain(a)) != codomain(a)
| domain(domain(domain(codomain(a)))) != domain(codomain(a))
| domain(domain(domain(codomain(a)))) = codomain(a) ),
inference(subst,[],[refute_0_92:[bind(X0,$fot(domain(domain(domain(codomain(a)))))),bind(Y0,$fot(domain(codomain(a)))),bind(Z0,$fot(codomain(a)))]]) ).
cnf(refute_0_101,plain,
( domain(codomain(a)) != codomain(a)
| domain(domain(domain(codomain(a)))) = codomain(a) ),
inference(resolve,[$cnf( $equal(domain(domain(domain(codomain(a)))),domain(codomain(a))) )],[refute_0_99,refute_0_100]) ).
cnf(refute_0_102,plain,
domain(domain(domain(codomain(a)))) = codomain(a),
inference(resolve,[$cnf( $equal(domain(codomain(a)),codomain(a)) )],[refute_0_83,refute_0_101]) ).
cnf(refute_0_103,plain,
compose(domain(domain(domain(codomain(a)))),domain(domain(domain(domain(codomain(a)))))) = domain(domain(domain(codomain(a)))),
inference(subst,[],[compose_domain:[bind(X,$fot(domain(domain(domain(codomain(a))))))]]) ).
cnf(refute_0_104,plain,
( compose(domain(domain(domain(codomain(a)))),domain(domain(domain(domain(codomain(a)))))) != domain(domain(domain(codomain(a))))
| domain(domain(domain(codomain(a)))) != codomain(a)
| compose(domain(domain(domain(codomain(a)))),domain(domain(domain(domain(codomain(a)))))) = codomain(a) ),
inference(subst,[],[refute_0_92:[bind(X0,$fot(compose(domain(domain(domain(codomain(a)))),domain(domain(domain(domain(codomain(a)))))))),bind(Y0,$fot(domain(domain(domain(codomain(a)))))),bind(Z0,$fot(codomain(a)))]]) ).
cnf(refute_0_105,plain,
( domain(domain(domain(codomain(a)))) != codomain(a)
| compose(domain(domain(domain(codomain(a)))),domain(domain(domain(domain(codomain(a)))))) = codomain(a) ),
inference(resolve,[$cnf( $equal(compose(domain(domain(domain(codomain(a)))),domain(domain(domain(domain(codomain(a)))))),domain(domain(domain(codomain(a))))) )],[refute_0_103,refute_0_104]) ).
cnf(refute_0_106,plain,
compose(domain(domain(domain(codomain(a)))),domain(domain(domain(domain(codomain(a)))))) = codomain(a),
inference(resolve,[$cnf( $equal(domain(domain(domain(codomain(a)))),codomain(a)) )],[refute_0_102,refute_0_105]) ).
cnf(refute_0_107,plain,
domain(compose(domain(domain(domain(codomain(a)))),domain(domain(domain(domain(codomain(a))))))) = domain(compose(domain(domain(domain(codomain(a)))),domain(domain(domain(domain(codomain(a))))))),
introduced(tautology,[refl,[$fot(domain(compose(domain(domain(domain(codomain(a)))),domain(domain(domain(domain(codomain(a))))))))]]) ).
cnf(refute_0_108,plain,
( compose(domain(domain(domain(codomain(a)))),domain(domain(domain(domain(codomain(a)))))) != codomain(a)
| domain(compose(domain(domain(domain(codomain(a)))),domain(domain(domain(domain(codomain(a))))))) != domain(compose(domain(domain(domain(codomain(a)))),domain(domain(domain(domain(codomain(a)))))))
| domain(compose(domain(domain(domain(codomain(a)))),domain(domain(domain(domain(codomain(a))))))) = domain(codomain(a)) ),
introduced(tautology,[equality,[$cnf( $equal(domain(compose(domain(domain(domain(codomain(a)))),domain(domain(domain(domain(codomain(a))))))),domain(compose(domain(domain(domain(codomain(a)))),domain(domain(domain(domain(codomain(a)))))))) ),[1,0],$fot(codomain(a))]]) ).
cnf(refute_0_109,plain,
( compose(domain(domain(domain(codomain(a)))),domain(domain(domain(domain(codomain(a)))))) != codomain(a)
| domain(compose(domain(domain(domain(codomain(a)))),domain(domain(domain(domain(codomain(a))))))) = domain(codomain(a)) ),
inference(resolve,[$cnf( $equal(domain(compose(domain(domain(domain(codomain(a)))),domain(domain(domain(domain(codomain(a))))))),domain(compose(domain(domain(domain(codomain(a)))),domain(domain(domain(domain(codomain(a)))))))) )],[refute_0_107,refute_0_108]) ).
cnf(refute_0_110,plain,
domain(compose(domain(domain(domain(codomain(a)))),domain(domain(domain(domain(codomain(a))))))) = domain(codomain(a)),
inference(resolve,[$cnf( $equal(compose(domain(domain(domain(codomain(a)))),domain(domain(domain(domain(codomain(a)))))),codomain(a)) )],[refute_0_106,refute_0_109]) ).
cnf(refute_0_111,plain,
( domain(codomain(a)) != codomain(a)
| domain(compose(domain(domain(domain(codomain(a)))),domain(domain(domain(domain(codomain(a))))))) != domain(codomain(a))
| domain(compose(domain(domain(domain(codomain(a)))),domain(domain(domain(domain(codomain(a))))))) = codomain(a) ),
inference(subst,[],[refute_0_92:[bind(X0,$fot(domain(compose(domain(domain(domain(codomain(a)))),domain(domain(domain(domain(codomain(a))))))))),bind(Y0,$fot(domain(codomain(a)))),bind(Z0,$fot(codomain(a)))]]) ).
cnf(refute_0_112,plain,
( domain(codomain(a)) != codomain(a)
| domain(compose(domain(domain(domain(codomain(a)))),domain(domain(domain(domain(codomain(a))))))) = codomain(a) ),
inference(resolve,[$cnf( $equal(domain(compose(domain(domain(domain(codomain(a)))),domain(domain(domain(domain(codomain(a))))))),domain(codomain(a))) )],[refute_0_110,refute_0_111]) ).
cnf(refute_0_113,plain,
domain(compose(domain(domain(domain(codomain(a)))),domain(domain(domain(domain(codomain(a))))))) = codomain(a),
inference(resolve,[$cnf( $equal(domain(codomain(a)),codomain(a)) )],[refute_0_83,refute_0_112]) ).
cnf(refute_0_114,plain,
compose(codomain(a),domain(compose(domain(domain(domain(codomain(a)))),domain(domain(domain(domain(codomain(a)))))))) = compose(codomain(a),domain(compose(domain(domain(domain(codomain(a)))),domain(domain(domain(domain(codomain(a)))))))),
introduced(tautology,[refl,[$fot(compose(codomain(a),domain(compose(domain(domain(domain(codomain(a)))),domain(domain(domain(domain(codomain(a)))))))))]]) ).
cnf(refute_0_115,plain,
( compose(codomain(a),domain(compose(domain(domain(domain(codomain(a)))),domain(domain(domain(domain(codomain(a)))))))) != compose(codomain(a),domain(compose(domain(domain(domain(codomain(a)))),domain(domain(domain(domain(codomain(a))))))))
| domain(compose(domain(domain(domain(codomain(a)))),domain(domain(domain(domain(codomain(a))))))) != codomain(a)
| compose(codomain(a),domain(compose(domain(domain(domain(codomain(a)))),domain(domain(domain(domain(codomain(a)))))))) = compose(codomain(a),codomain(a)) ),
introduced(tautology,[equality,[$cnf( $equal(compose(codomain(a),domain(compose(domain(domain(domain(codomain(a)))),domain(domain(domain(domain(codomain(a)))))))),compose(codomain(a),domain(compose(domain(domain(domain(codomain(a)))),domain(domain(domain(domain(codomain(a))))))))) ),[1,1],$fot(codomain(a))]]) ).
cnf(refute_0_116,plain,
( domain(compose(domain(domain(domain(codomain(a)))),domain(domain(domain(domain(codomain(a))))))) != codomain(a)
| compose(codomain(a),domain(compose(domain(domain(domain(codomain(a)))),domain(domain(domain(domain(codomain(a)))))))) = compose(codomain(a),codomain(a)) ),
inference(resolve,[$cnf( $equal(compose(codomain(a),domain(compose(domain(domain(domain(codomain(a)))),domain(domain(domain(domain(codomain(a)))))))),compose(codomain(a),domain(compose(domain(domain(domain(codomain(a)))),domain(domain(domain(domain(codomain(a))))))))) )],[refute_0_114,refute_0_115]) ).
cnf(refute_0_117,plain,
compose(codomain(a),domain(compose(domain(domain(domain(codomain(a)))),domain(domain(domain(domain(codomain(a)))))))) = compose(codomain(a),codomain(a)),
inference(resolve,[$cnf( $equal(domain(compose(domain(domain(domain(codomain(a)))),domain(domain(domain(domain(codomain(a))))))),codomain(a)) )],[refute_0_113,refute_0_116]) ).
cnf(refute_0_118,plain,
( codomain(a) != compose(codomain(a),domain(compose(domain(domain(domain(codomain(a)))),domain(domain(domain(domain(codomain(a))))))))
| compose(codomain(a),domain(compose(domain(domain(domain(codomain(a)))),domain(domain(domain(domain(codomain(a)))))))) != compose(codomain(a),codomain(a))
| codomain(a) = compose(codomain(a),codomain(a)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(codomain(a),compose(codomain(a),codomain(a))) ),[0],$fot(compose(codomain(a),domain(compose(domain(domain(domain(codomain(a)))),domain(domain(domain(domain(codomain(a)))))))))]]) ).
cnf(refute_0_119,plain,
( codomain(a) != compose(codomain(a),domain(compose(domain(domain(domain(codomain(a)))),domain(domain(domain(domain(codomain(a))))))))
| codomain(a) = compose(codomain(a),codomain(a)) ),
inference(resolve,[$cnf( $equal(compose(codomain(a),domain(compose(domain(domain(domain(codomain(a)))),domain(domain(domain(domain(codomain(a)))))))),compose(codomain(a),codomain(a))) )],[refute_0_117,refute_0_118]) ).
cnf(refute_0_120,plain,
codomain(a) = compose(codomain(a),codomain(a)),
inference(resolve,[$cnf( $equal(codomain(a),compose(codomain(a),domain(compose(domain(domain(domain(codomain(a)))),domain(domain(domain(domain(codomain(a))))))))) )],[refute_0_86,refute_0_119]) ).
cnf(refute_0_121,plain,
( codomain(a) != compose(codomain(a),codomain(a))
| compose(codomain(a),codomain(a)) = codomain(a) ),
inference(subst,[],[refute_0_20:[bind(X0,$fot(codomain(a))),bind(Y0,$fot(compose(codomain(a),codomain(a))))]]) ).
cnf(refute_0_122,plain,
compose(codomain(a),codomain(a)) = codomain(a),
inference(resolve,[$cnf( $equal(codomain(a),compose(codomain(a),codomain(a))) )],[refute_0_120,refute_0_121]) ).
cnf(refute_0_123,plain,
( compose(codomain(a),codomain(a)) != codomain(a)
| ~ there_exists(codomain(a))
| there_exists(compose(codomain(a),codomain(a))) ),
introduced(tautology,[equality,[$cnf( ~ there_exists(compose(codomain(a),codomain(a))) ),[0],$fot(codomain(a))]]) ).
cnf(refute_0_124,plain,
( ~ there_exists(codomain(a))
| there_exists(compose(codomain(a),codomain(a))) ),
inference(resolve,[$cnf( $equal(compose(codomain(a),codomain(a)),codomain(a)) )],[refute_0_122,refute_0_123]) ).
cnf(refute_0_125,plain,
( ~ there_exists(codomain(a))
| domain(codomain(a)) = codomain(codomain(a)) ),
inference(resolve,[$cnf( there_exists(compose(codomain(a),codomain(a))) )],[refute_0_124,refute_0_0]) ).
cnf(refute_0_126,plain,
( domain(codomain(a)) != codomain(a)
| domain(codomain(a)) != codomain(codomain(a))
| codomain(a) = codomain(codomain(a)) ),
introduced(tautology,[equality,[$cnf( $equal(domain(codomain(a)),codomain(codomain(a))) ),[0],$fot(codomain(a))]]) ).
cnf(refute_0_127,plain,
( domain(codomain(a)) != codomain(codomain(a))
| codomain(a) = codomain(codomain(a)) ),
inference(resolve,[$cnf( $equal(domain(codomain(a)),codomain(a)) )],[refute_0_83,refute_0_126]) ).
cnf(refute_0_128,plain,
( ~ there_exists(codomain(a))
| codomain(a) = codomain(codomain(a)) ),
inference(resolve,[$cnf( $equal(domain(codomain(a)),codomain(codomain(a))) )],[refute_0_125,refute_0_127]) ).
cnf(refute_0_129,plain,
codomain(a) = codomain(codomain(a)),
inference(resolve,[$cnf( there_exists(codomain(a)) )],[assume_codomain_exists,refute_0_128]) ).
cnf(refute_0_130,plain,
( codomain(a) != codomain(codomain(a))
| codomain(codomain(a)) = codomain(a) ),
inference(subst,[],[refute_0_20:[bind(X0,$fot(codomain(a))),bind(Y0,$fot(codomain(codomain(a))))]]) ).
cnf(refute_0_131,plain,
codomain(a) != codomain(codomain(a)),
inference(resolve,[$cnf( $equal(codomain(codomain(a)),codomain(a)) )],[refute_0_130,prove_codomain_is_idempotent]) ).
cnf(refute_0_132,plain,
$false,
inference(resolve,[$cnf( $equal(codomain(a),codomain(codomain(a))) )],[refute_0_129,refute_0_131]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : CAT014-3 : 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 21:00:12 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 8.78/8.99 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.78/8.99
% 8.78/8.99 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 8.78/9.01
%------------------------------------------------------------------------------