TSTP Solution File: CAT002-4 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : CAT002-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n028.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 00:04:31 EDT 2022
% Result : Unsatisfiable 1.23s 1.43s
% Output : CNFRefutation 1.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 64
% Number of leaves : 132
% Syntax : Number of clauses : 513 ( 217 unt; 0 nHn; 401 RR)
% Number of literals : 919 ( 835 equ; 407 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 338 ( 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_ab_exists,hypothesis,
there_exists(compose(a,b)) ).
cnf(cancellation_for_compose1,hypothesis,
( compose(a,X) != Y
| compose(a,Z) != Y
| X = Z ) ).
cnf(cancellation_for_compose2,hypothesis,
( compose(b,X) != Y
| compose(b,Z) != Y
| X = Z ) ).
cnf(assume_h_exists,hypothesis,
there_exists(h) ).
cnf(ab_h_equals_ab_g,hypothesis,
compose(compose(a,b),h) = compose(compose(a,b),g) ).
cnf(prove_g_equals_h,negated_conjecture,
g != h ).
cnf(refute_0_0,plain,
compose(X_9,compose(domain(X_9),X_11)) = compose(compose(X_9,domain(X_9)),X_11),
inference(subst,[],[associativity_of_compose:[bind(X,$fot(X_9)),bind(Y,$fot(domain(X_9))),bind(Z,$fot(X_11))]]) ).
cnf(refute_0_1,plain,
compose(X_9,domain(X_9)) = X_9,
inference(subst,[],[compose_domain:[bind(X,$fot(X_9))]]) ).
cnf(refute_0_2,plain,
( compose(X_9,compose(domain(X_9),X_11)) != compose(compose(X_9,domain(X_9)),X_11)
| compose(X_9,domain(X_9)) != X_9
| compose(X_9,compose(domain(X_9),X_11)) = compose(X_9,X_11) ),
introduced(tautology,[equality,[$cnf( $equal(compose(X_9,compose(domain(X_9),X_11)),compose(compose(X_9,domain(X_9)),X_11)) ),[1,0],$fot(X_9)]]) ).
cnf(refute_0_3,plain,
( compose(X_9,compose(domain(X_9),X_11)) != compose(compose(X_9,domain(X_9)),X_11)
| compose(X_9,compose(domain(X_9),X_11)) = compose(X_9,X_11) ),
inference(resolve,[$cnf( $equal(compose(X_9,domain(X_9)),X_9) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
compose(X_9,compose(domain(X_9),X_11)) = compose(X_9,X_11),
inference(resolve,[$cnf( $equal(compose(X_9,compose(domain(X_9),X_11)),compose(compose(X_9,domain(X_9)),X_11)) )],[refute_0_0,refute_0_3]) ).
cnf(refute_0_5,plain,
compose(X_9,compose(domain(X_9),compose(domain(domain(X_9)),X_18))) = compose(X_9,compose(domain(domain(X_9)),X_18)),
inference(subst,[],[refute_0_4:[bind(X_11,$fot(compose(domain(domain(X_9)),X_18)))]]) ).
cnf(refute_0_6,plain,
compose(domain(X_9),compose(domain(domain(X_9)),X_18)) = compose(domain(X_9),X_18),
inference(subst,[],[refute_0_4:[bind(X_11,$fot(X_18)),bind(X_9,$fot(domain(X_9)))]]) ).
cnf(refute_0_7,plain,
( compose(X_9,compose(domain(X_9),compose(domain(domain(X_9)),X_18))) != compose(X_9,compose(domain(domain(X_9)),X_18))
| compose(domain(X_9),compose(domain(domain(X_9)),X_18)) != compose(domain(X_9),X_18)
| compose(X_9,compose(domain(X_9),X_18)) = compose(X_9,compose(domain(domain(X_9)),X_18)) ),
introduced(tautology,[equality,[$cnf( $equal(compose(X_9,compose(domain(X_9),compose(domain(domain(X_9)),X_18))),compose(X_9,compose(domain(domain(X_9)),X_18))) ),[0,1],$fot(compose(domain(X_9),X_18))]]) ).
cnf(refute_0_8,plain,
( compose(X_9,compose(domain(X_9),compose(domain(domain(X_9)),X_18))) != compose(X_9,compose(domain(domain(X_9)),X_18))
| compose(X_9,compose(domain(X_9),X_18)) = compose(X_9,compose(domain(domain(X_9)),X_18)) ),
inference(resolve,[$cnf( $equal(compose(domain(X_9),compose(domain(domain(X_9)),X_18)),compose(domain(X_9),X_18)) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
compose(X_9,compose(domain(X_9),X_18)) = compose(X_9,compose(domain(domain(X_9)),X_18)),
inference(resolve,[$cnf( $equal(compose(X_9,compose(domain(X_9),compose(domain(domain(X_9)),X_18))),compose(X_9,compose(domain(domain(X_9)),X_18))) )],[refute_0_5,refute_0_8]) ).
cnf(refute_0_10,plain,
compose(X_9,compose(domain(X_9),X_18)) = compose(X_9,X_18),
inference(subst,[],[refute_0_4:[bind(X_11,$fot(X_18))]]) ).
cnf(refute_0_11,plain,
( compose(X_9,compose(domain(X_9),X_18)) != compose(X_9,X_18)
| compose(X_9,compose(domain(X_9),X_18)) != compose(X_9,compose(domain(domain(X_9)),X_18))
| compose(X_9,X_18) = compose(X_9,compose(domain(domain(X_9)),X_18)) ),
introduced(tautology,[equality,[$cnf( $equal(compose(X_9,compose(domain(X_9),X_18)),compose(X_9,compose(domain(domain(X_9)),X_18))) ),[0],$fot(compose(X_9,X_18))]]) ).
cnf(refute_0_12,plain,
( compose(X_9,compose(domain(X_9),X_18)) != compose(X_9,compose(domain(domain(X_9)),X_18))
| compose(X_9,X_18) = compose(X_9,compose(domain(domain(X_9)),X_18)) ),
inference(resolve,[$cnf( $equal(compose(X_9,compose(domain(X_9),X_18)),compose(X_9,X_18)) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
compose(X_9,X_18) = compose(X_9,compose(domain(domain(X_9)),X_18)),
inference(resolve,[$cnf( $equal(compose(X_9,compose(domain(X_9),X_18)),compose(X_9,compose(domain(domain(X_9)),X_18))) )],[refute_0_9,refute_0_12]) ).
cnf(refute_0_14,plain,
compose(X_9,domain(compose(a,domain(domain(domain(domain(X_9))))))) = compose(X_9,compose(domain(domain(X_9)),domain(compose(a,domain(domain(domain(domain(X_9)))))))),
inference(subst,[],[refute_0_13:[bind(X_18,$fot(domain(compose(a,domain(domain(domain(domain(X_9))))))))]]) ).
cnf(refute_0_15,plain,
compose(X_9,domain(compose(a,domain(domain(X_9))))) = compose(X_9,compose(domain(domain(X_9)),domain(compose(a,domain(domain(X_9)))))),
inference(subst,[],[refute_0_13:[bind(X_18,$fot(domain(compose(a,domain(domain(X_9))))))]]) ).
cnf(refute_0_16,plain,
( compose(a,X) != compose(a,X)
| compose(a,Z) != compose(a,X)
| X = Z ),
inference(subst,[],[cancellation_for_compose1:[bind(Y,$fot(compose(a,X)))]]) ).
cnf(refute_0_17,plain,
compose(a,X) = compose(a,X),
introduced(tautology,[refl,[$fot(compose(a,X))]]) ).
cnf(refute_0_18,plain,
( compose(a,Z) != compose(a,X)
| X = Z ),
inference(resolve,[$cnf( $equal(compose(a,X),compose(a,X)) )],[refute_0_17,refute_0_16]) ).
cnf(refute_0_19,plain,
( compose(a,compose(X_10,domain(compose(a,X_10)))) != compose(a,X_63)
| X_63 = compose(X_10,domain(compose(a,X_10))) ),
inference(subst,[],[refute_0_18:[bind(X,$fot(X_63)),bind(Z,$fot(compose(X_10,domain(compose(a,X_10)))))]]) ).
cnf(refute_0_20,plain,
compose(compose(X_9,X_10),domain(compose(X_9,X_10))) = compose(X_9,X_10),
inference(subst,[],[compose_domain:[bind(X,$fot(compose(X_9,X_10)))]]) ).
cnf(refute_0_21,plain,
compose(X_9,compose(X_10,domain(compose(X_9,X_10)))) = compose(compose(X_9,X_10),domain(compose(X_9,X_10))),
inference(subst,[],[associativity_of_compose:[bind(X,$fot(X_9)),bind(Y,$fot(X_10)),bind(Z,$fot(domain(compose(X_9,X_10))))]]) ).
cnf(refute_0_22,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_23,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_24,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
( compose(X_9,compose(X_10,domain(compose(X_9,X_10)))) != compose(compose(X_9,X_10),domain(compose(X_9,X_10)))
| compose(compose(X_9,X_10),domain(compose(X_9,X_10))) = compose(X_9,compose(X_10,domain(compose(X_9,X_10)))) ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(compose(X_9,compose(X_10,domain(compose(X_9,X_10)))))),bind(Y0,$fot(compose(compose(X_9,X_10),domain(compose(X_9,X_10)))))]]) ).
cnf(refute_0_26,plain,
compose(compose(X_9,X_10),domain(compose(X_9,X_10))) = compose(X_9,compose(X_10,domain(compose(X_9,X_10)))),
inference(resolve,[$cnf( $equal(compose(X_9,compose(X_10,domain(compose(X_9,X_10)))),compose(compose(X_9,X_10),domain(compose(X_9,X_10)))) )],[refute_0_21,refute_0_25]) ).
cnf(refute_0_27,plain,
( compose(compose(X_9,X_10),domain(compose(X_9,X_10))) != compose(X_9,X_10)
| compose(compose(X_9,X_10),domain(compose(X_9,X_10))) != compose(X_9,compose(X_10,domain(compose(X_9,X_10))))
| compose(X_9,compose(X_10,domain(compose(X_9,X_10)))) = compose(X_9,X_10) ),
introduced(tautology,[equality,[$cnf( $equal(compose(compose(X_9,X_10),domain(compose(X_9,X_10))),compose(X_9,X_10)) ),[0],$fot(compose(X_9,compose(X_10,domain(compose(X_9,X_10)))))]]) ).
cnf(refute_0_28,plain,
( compose(compose(X_9,X_10),domain(compose(X_9,X_10))) != compose(X_9,X_10)
| compose(X_9,compose(X_10,domain(compose(X_9,X_10)))) = compose(X_9,X_10) ),
inference(resolve,[$cnf( $equal(compose(compose(X_9,X_10),domain(compose(X_9,X_10))),compose(X_9,compose(X_10,domain(compose(X_9,X_10))))) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
compose(X_9,compose(X_10,domain(compose(X_9,X_10)))) = compose(X_9,X_10),
inference(resolve,[$cnf( $equal(compose(compose(X_9,X_10),domain(compose(X_9,X_10))),compose(X_9,X_10)) )],[refute_0_20,refute_0_28]) ).
cnf(refute_0_30,plain,
compose(a,compose(X_10,domain(compose(a,X_10)))) = compose(a,X_10),
inference(subst,[],[refute_0_29:[bind(X_9,$fot(a))]]) ).
cnf(refute_0_31,plain,
( compose(a,X_10) != compose(a,X_63)
| compose(a,compose(X_10,domain(compose(a,X_10)))) != compose(a,X_10)
| compose(a,compose(X_10,domain(compose(a,X_10)))) = compose(a,X_63) ),
introduced(tautology,[equality,[$cnf( $equal(compose(a,compose(X_10,domain(compose(a,X_10)))),compose(a,X_10)) ),[1],$fot(compose(a,X_63))]]) ).
cnf(refute_0_32,plain,
( compose(a,X_10) != compose(a,X_63)
| compose(a,compose(X_10,domain(compose(a,X_10)))) = compose(a,X_63) ),
inference(resolve,[$cnf( $equal(compose(a,compose(X_10,domain(compose(a,X_10)))),compose(a,X_10)) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
( compose(a,X_10) != compose(a,X_63)
| X_63 = compose(X_10,domain(compose(a,X_10))) ),
inference(resolve,[$cnf( $equal(compose(a,compose(X_10,domain(compose(a,X_10)))),compose(a,X_63)) )],[refute_0_32,refute_0_19]) ).
cnf(refute_0_34,plain,
( compose(a,X_63) != compose(a,X_63)
| X_63 = compose(X_63,domain(compose(a,X_63))) ),
inference(subst,[],[refute_0_33:[bind(X_10,$fot(X_63))]]) ).
cnf(refute_0_35,plain,
compose(a,X_63) = compose(a,X_63),
introduced(tautology,[refl,[$fot(compose(a,X_63))]]) ).
cnf(refute_0_36,plain,
X_63 = compose(X_63,domain(compose(a,X_63))),
inference(resolve,[$cnf( $equal(compose(a,X_63),compose(a,X_63)) )],[refute_0_35,refute_0_34]) ).
cnf(refute_0_37,plain,
domain(domain(X_9)) = compose(domain(domain(X_9)),domain(compose(a,domain(domain(X_9))))),
inference(subst,[],[refute_0_36:[bind(X_63,$fot(domain(domain(X_9))))]]) ).
cnf(refute_0_38,plain,
( domain(domain(X_9)) != compose(domain(domain(X_9)),domain(compose(a,domain(domain(X_9)))))
| compose(domain(domain(X_9)),domain(compose(a,domain(domain(X_9))))) = domain(domain(X_9)) ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(domain(domain(X_9)))),bind(Y0,$fot(compose(domain(domain(X_9)),domain(compose(a,domain(domain(X_9)))))))]]) ).
cnf(refute_0_39,plain,
compose(domain(domain(X_9)),domain(compose(a,domain(domain(X_9))))) = domain(domain(X_9)),
inference(resolve,[$cnf( $equal(domain(domain(X_9)),compose(domain(domain(X_9)),domain(compose(a,domain(domain(X_9)))))) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
( compose(X_9,domain(compose(a,domain(domain(X_9))))) != compose(X_9,compose(domain(domain(X_9)),domain(compose(a,domain(domain(X_9))))))
| compose(domain(domain(X_9)),domain(compose(a,domain(domain(X_9))))) != domain(domain(X_9))
| compose(X_9,domain(compose(a,domain(domain(X_9))))) = compose(X_9,domain(domain(X_9))) ),
introduced(tautology,[equality,[$cnf( $equal(compose(X_9,domain(compose(a,domain(domain(X_9))))),compose(X_9,compose(domain(domain(X_9)),domain(compose(a,domain(domain(X_9))))))) ),[1,1],$fot(domain(domain(X_9)))]]) ).
cnf(refute_0_41,plain,
( compose(X_9,domain(compose(a,domain(domain(X_9))))) != compose(X_9,compose(domain(domain(X_9)),domain(compose(a,domain(domain(X_9))))))
| compose(X_9,domain(compose(a,domain(domain(X_9))))) = compose(X_9,domain(domain(X_9))) ),
inference(resolve,[$cnf( $equal(compose(domain(domain(X_9)),domain(compose(a,domain(domain(X_9))))),domain(domain(X_9))) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
compose(X_9,domain(compose(a,domain(domain(X_9))))) = compose(X_9,domain(domain(X_9))),
inference(resolve,[$cnf( $equal(compose(X_9,domain(compose(a,domain(domain(X_9))))),compose(X_9,compose(domain(domain(X_9)),domain(compose(a,domain(domain(X_9))))))) )],[refute_0_15,refute_0_41]) ).
cnf(refute_0_43,plain,
compose(X_19,compose(domain(X_19),domain(domain(X_19)))) = compose(X_19,domain(domain(X_19))),
inference(subst,[],[refute_0_4:[bind(X_11,$fot(domain(domain(X_19)))),bind(X_9,$fot(X_19))]]) ).
cnf(refute_0_44,plain,
compose(domain(X_19),domain(domain(X_19))) = domain(X_19),
inference(subst,[],[compose_domain:[bind(X,$fot(domain(X_19)))]]) ).
cnf(refute_0_45,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_46,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( $equal(compose(domain(X_19),domain(domain(X_19))),domain(X_19)) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
compose(X_19,domain(X_19)) = compose(X_19,domain(domain(X_19))),
inference(resolve,[$cnf( $equal(compose(X_19,compose(domain(X_19),domain(domain(X_19)))),compose(X_19,domain(domain(X_19)))) )],[refute_0_43,refute_0_46]) ).
cnf(refute_0_48,plain,
compose(X_19,domain(X_19)) = X_19,
inference(subst,[],[compose_domain:[bind(X,$fot(X_19))]]) ).
cnf(refute_0_49,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_50,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( $equal(compose(X_19,domain(X_19)),X_19) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
X_19 = compose(X_19,domain(domain(X_19))),
inference(resolve,[$cnf( $equal(compose(X_19,domain(X_19)),compose(X_19,domain(domain(X_19)))) )],[refute_0_47,refute_0_50]) ).
cnf(refute_0_52,plain,
( X_19 != compose(X_19,domain(domain(X_19)))
| compose(X_19,domain(domain(X_19))) = X_19 ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(X_19)),bind(Y0,$fot(compose(X_19,domain(domain(X_19)))))]]) ).
cnf(refute_0_53,plain,
compose(X_19,domain(domain(X_19))) = X_19,
inference(resolve,[$cnf( $equal(X_19,compose(X_19,domain(domain(X_19)))) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
compose(X_9,domain(domain(X_9))) = X_9,
inference(subst,[],[refute_0_53:[bind(X_19,$fot(X_9))]]) ).
cnf(refute_0_55,plain,
( compose(X_9,domain(compose(a,domain(domain(X_9))))) != compose(X_9,domain(domain(X_9)))
| compose(X_9,domain(domain(X_9))) != X_9
| compose(X_9,domain(compose(a,domain(domain(X_9))))) = X_9 ),
introduced(tautology,[equality,[$cnf( ~ $equal(compose(X_9,domain(compose(a,domain(domain(X_9))))),X_9) ),[0],$fot(compose(X_9,domain(domain(X_9))))]]) ).
cnf(refute_0_56,plain,
( compose(X_9,domain(compose(a,domain(domain(X_9))))) != compose(X_9,domain(domain(X_9)))
| compose(X_9,domain(compose(a,domain(domain(X_9))))) = X_9 ),
inference(resolve,[$cnf( $equal(compose(X_9,domain(domain(X_9))),X_9) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
compose(X_9,domain(compose(a,domain(domain(X_9))))) = X_9,
inference(resolve,[$cnf( $equal(compose(X_9,domain(compose(a,domain(domain(X_9))))),compose(X_9,domain(domain(X_9)))) )],[refute_0_42,refute_0_56]) ).
cnf(refute_0_58,plain,
compose(domain(domain(X_9)),domain(compose(a,domain(domain(domain(domain(X_9))))))) = domain(domain(X_9)),
inference(subst,[],[refute_0_57:[bind(X_9,$fot(domain(domain(X_9))))]]) ).
cnf(refute_0_59,plain,
( compose(X_9,domain(compose(a,domain(domain(domain(domain(X_9))))))) != compose(X_9,compose(domain(domain(X_9)),domain(compose(a,domain(domain(domain(domain(X_9))))))))
| compose(domain(domain(X_9)),domain(compose(a,domain(domain(domain(domain(X_9))))))) != domain(domain(X_9))
| compose(X_9,domain(compose(a,domain(domain(domain(domain(X_9))))))) = compose(X_9,domain(domain(X_9))) ),
introduced(tautology,[equality,[$cnf( $equal(compose(X_9,domain(compose(a,domain(domain(domain(domain(X_9))))))),compose(X_9,compose(domain(domain(X_9)),domain(compose(a,domain(domain(domain(domain(X_9))))))))) ),[1,1],$fot(domain(domain(X_9)))]]) ).
cnf(refute_0_60,plain,
( compose(X_9,domain(compose(a,domain(domain(domain(domain(X_9))))))) != compose(X_9,compose(domain(domain(X_9)),domain(compose(a,domain(domain(domain(domain(X_9))))))))
| compose(X_9,domain(compose(a,domain(domain(domain(domain(X_9))))))) = compose(X_9,domain(domain(X_9))) ),
inference(resolve,[$cnf( $equal(compose(domain(domain(X_9)),domain(compose(a,domain(domain(domain(domain(X_9))))))),domain(domain(X_9))) )],[refute_0_58,refute_0_59]) ).
cnf(refute_0_61,plain,
compose(X_9,domain(compose(a,domain(domain(domain(domain(X_9))))))) = compose(X_9,domain(domain(X_9))),
inference(resolve,[$cnf( $equal(compose(X_9,domain(compose(a,domain(domain(domain(domain(X_9))))))),compose(X_9,compose(domain(domain(X_9)),domain(compose(a,domain(domain(domain(domain(X_9))))))))) )],[refute_0_14,refute_0_60]) ).
cnf(refute_0_62,plain,
( compose(X_9,domain(compose(a,domain(domain(domain(domain(X_9))))))) != compose(X_9,domain(domain(X_9)))
| compose(X_9,domain(domain(X_9))) != X_9
| compose(X_9,domain(compose(a,domain(domain(domain(domain(X_9))))))) = X_9 ),
introduced(tautology,[equality,[$cnf( ~ $equal(compose(X_9,domain(compose(a,domain(domain(domain(domain(X_9))))))),X_9) ),[0],$fot(compose(X_9,domain(domain(X_9))))]]) ).
cnf(refute_0_63,plain,
( compose(X_9,domain(compose(a,domain(domain(domain(domain(X_9))))))) != compose(X_9,domain(domain(X_9)))
| compose(X_9,domain(compose(a,domain(domain(domain(domain(X_9))))))) = X_9 ),
inference(resolve,[$cnf( $equal(compose(X_9,domain(domain(X_9))),X_9) )],[refute_0_54,refute_0_62]) ).
cnf(refute_0_64,plain,
compose(X_9,domain(compose(a,domain(domain(domain(domain(X_9))))))) = X_9,
inference(resolve,[$cnf( $equal(compose(X_9,domain(compose(a,domain(domain(domain(domain(X_9))))))),compose(X_9,domain(domain(X_9)))) )],[refute_0_61,refute_0_63]) ).
cnf(refute_0_65,plain,
compose(h,domain(compose(a,domain(domain(domain(domain(h))))))) = h,
inference(subst,[],[refute_0_64:[bind(X_9,$fot(h))]]) ).
cnf(refute_0_66,plain,
( ~ there_exists(compose(X_30,domain(domain(domain(domain(domain(X_30)))))))
| there_exists(domain(X_30)) ),
inference(subst,[],[composition_implies_domain:[bind(X,$fot(X_30)),bind(Y,$fot(domain(domain(domain(domain(domain(X_30)))))))]]) ).
cnf(refute_0_67,plain,
compose(X_9,compose(domain(X_9),domain(domain(domain(domain(domain(X_9))))))) = compose(X_9,domain(domain(domain(domain(domain(X_9)))))),
inference(subst,[],[refute_0_4:[bind(X_11,$fot(domain(domain(domain(domain(domain(X_9)))))))]]) ).
cnf(refute_0_68,plain,
compose(X_9,compose(domain(X_9),domain(domain(domain(domain(X_9)))))) = compose(X_9,domain(domain(domain(domain(X_9))))),
inference(subst,[],[refute_0_4:[bind(X_11,$fot(domain(domain(domain(domain(X_9))))))]]) ).
cnf(refute_0_69,plain,
compose(X_9,compose(domain(X_9),domain(domain(domain(X_9))))) = compose(X_9,domain(domain(domain(X_9)))),
inference(subst,[],[refute_0_4:[bind(X_11,$fot(domain(domain(domain(X_9)))))]]) ).
cnf(refute_0_70,plain,
domain(X_9) = compose(domain(X_9),domain(domain(domain(X_9)))),
inference(subst,[],[refute_0_51:[bind(X_19,$fot(domain(X_9)))]]) ).
cnf(refute_0_71,plain,
( domain(X_9) != compose(domain(X_9),domain(domain(domain(X_9))))
| compose(domain(X_9),domain(domain(domain(X_9)))) = domain(X_9) ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(domain(X_9))),bind(Y0,$fot(compose(domain(X_9),domain(domain(domain(X_9))))))]]) ).
cnf(refute_0_72,plain,
compose(domain(X_9),domain(domain(domain(X_9)))) = domain(X_9),
inference(resolve,[$cnf( $equal(domain(X_9),compose(domain(X_9),domain(domain(domain(X_9))))) )],[refute_0_70,refute_0_71]) ).
cnf(refute_0_73,plain,
( compose(X_9,compose(domain(X_9),domain(domain(domain(X_9))))) != compose(X_9,domain(domain(domain(X_9))))
| compose(domain(X_9),domain(domain(domain(X_9)))) != domain(X_9)
| compose(X_9,domain(X_9)) = compose(X_9,domain(domain(domain(X_9)))) ),
introduced(tautology,[equality,[$cnf( $equal(compose(X_9,compose(domain(X_9),domain(domain(domain(X_9))))),compose(X_9,domain(domain(domain(X_9))))) ),[0,1],$fot(domain(X_9))]]) ).
cnf(refute_0_74,plain,
( compose(X_9,compose(domain(X_9),domain(domain(domain(X_9))))) != compose(X_9,domain(domain(domain(X_9))))
| compose(X_9,domain(X_9)) = compose(X_9,domain(domain(domain(X_9)))) ),
inference(resolve,[$cnf( $equal(compose(domain(X_9),domain(domain(domain(X_9)))),domain(X_9)) )],[refute_0_72,refute_0_73]) ).
cnf(refute_0_75,plain,
compose(X_9,domain(X_9)) = compose(X_9,domain(domain(domain(X_9)))),
inference(resolve,[$cnf( $equal(compose(X_9,compose(domain(X_9),domain(domain(domain(X_9))))),compose(X_9,domain(domain(domain(X_9))))) )],[refute_0_69,refute_0_74]) ).
cnf(refute_0_76,plain,
( compose(X_9,domain(X_9)) != X_9
| compose(X_9,domain(X_9)) != compose(X_9,domain(domain(domain(X_9))))
| X_9 = compose(X_9,domain(domain(domain(X_9)))) ),
introduced(tautology,[equality,[$cnf( $equal(compose(X_9,domain(X_9)),compose(X_9,domain(domain(domain(X_9))))) ),[0],$fot(X_9)]]) ).
cnf(refute_0_77,plain,
( compose(X_9,domain(X_9)) != compose(X_9,domain(domain(domain(X_9))))
| X_9 = compose(X_9,domain(domain(domain(X_9)))) ),
inference(resolve,[$cnf( $equal(compose(X_9,domain(X_9)),X_9) )],[refute_0_1,refute_0_76]) ).
cnf(refute_0_78,plain,
X_9 = compose(X_9,domain(domain(domain(X_9)))),
inference(resolve,[$cnf( $equal(compose(X_9,domain(X_9)),compose(X_9,domain(domain(domain(X_9))))) )],[refute_0_75,refute_0_77]) ).
cnf(refute_0_79,plain,
domain(X_9) = compose(domain(X_9),domain(domain(domain(domain(X_9))))),
inference(subst,[],[refute_0_78:[bind(X_9,$fot(domain(X_9)))]]) ).
cnf(refute_0_80,plain,
( domain(X_9) != compose(domain(X_9),domain(domain(domain(domain(X_9)))))
| compose(domain(X_9),domain(domain(domain(domain(X_9))))) = domain(X_9) ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(domain(X_9))),bind(Y0,$fot(compose(domain(X_9),domain(domain(domain(domain(X_9)))))))]]) ).
cnf(refute_0_81,plain,
compose(domain(X_9),domain(domain(domain(domain(X_9))))) = domain(X_9),
inference(resolve,[$cnf( $equal(domain(X_9),compose(domain(X_9),domain(domain(domain(domain(X_9)))))) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
( compose(X_9,compose(domain(X_9),domain(domain(domain(domain(X_9)))))) != compose(X_9,domain(domain(domain(domain(X_9)))))
| compose(domain(X_9),domain(domain(domain(domain(X_9))))) != domain(X_9)
| compose(X_9,domain(X_9)) = compose(X_9,domain(domain(domain(domain(X_9))))) ),
introduced(tautology,[equality,[$cnf( $equal(compose(X_9,compose(domain(X_9),domain(domain(domain(domain(X_9)))))),compose(X_9,domain(domain(domain(domain(X_9)))))) ),[0,1],$fot(domain(X_9))]]) ).
cnf(refute_0_83,plain,
( compose(X_9,compose(domain(X_9),domain(domain(domain(domain(X_9)))))) != compose(X_9,domain(domain(domain(domain(X_9)))))
| compose(X_9,domain(X_9)) = compose(X_9,domain(domain(domain(domain(X_9))))) ),
inference(resolve,[$cnf( $equal(compose(domain(X_9),domain(domain(domain(domain(X_9))))),domain(X_9)) )],[refute_0_81,refute_0_82]) ).
cnf(refute_0_84,plain,
compose(X_9,domain(X_9)) = compose(X_9,domain(domain(domain(domain(X_9))))),
inference(resolve,[$cnf( $equal(compose(X_9,compose(domain(X_9),domain(domain(domain(domain(X_9)))))),compose(X_9,domain(domain(domain(domain(X_9)))))) )],[refute_0_68,refute_0_83]) ).
cnf(refute_0_85,plain,
( compose(X_9,domain(X_9)) != X_9
| compose(X_9,domain(X_9)) != compose(X_9,domain(domain(domain(domain(X_9)))))
| X_9 = compose(X_9,domain(domain(domain(domain(X_9))))) ),
introduced(tautology,[equality,[$cnf( $equal(compose(X_9,domain(X_9)),compose(X_9,domain(domain(domain(domain(X_9)))))) ),[0],$fot(X_9)]]) ).
cnf(refute_0_86,plain,
( compose(X_9,domain(X_9)) != compose(X_9,domain(domain(domain(domain(X_9)))))
| X_9 = compose(X_9,domain(domain(domain(domain(X_9))))) ),
inference(resolve,[$cnf( $equal(compose(X_9,domain(X_9)),X_9) )],[refute_0_1,refute_0_85]) ).
cnf(refute_0_87,plain,
X_9 = compose(X_9,domain(domain(domain(domain(X_9))))),
inference(resolve,[$cnf( $equal(compose(X_9,domain(X_9)),compose(X_9,domain(domain(domain(domain(X_9)))))) )],[refute_0_84,refute_0_86]) ).
cnf(refute_0_88,plain,
domain(X_9) = compose(domain(X_9),domain(domain(domain(domain(domain(X_9)))))),
inference(subst,[],[refute_0_87:[bind(X_9,$fot(domain(X_9)))]]) ).
cnf(refute_0_89,plain,
( domain(X_9) != compose(domain(X_9),domain(domain(domain(domain(domain(X_9))))))
| compose(domain(X_9),domain(domain(domain(domain(domain(X_9)))))) = domain(X_9) ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(domain(X_9))),bind(Y0,$fot(compose(domain(X_9),domain(domain(domain(domain(domain(X_9))))))))]]) ).
cnf(refute_0_90,plain,
compose(domain(X_9),domain(domain(domain(domain(domain(X_9)))))) = domain(X_9),
inference(resolve,[$cnf( $equal(domain(X_9),compose(domain(X_9),domain(domain(domain(domain(domain(X_9))))))) )],[refute_0_88,refute_0_89]) ).
cnf(refute_0_91,plain,
( compose(X_9,compose(domain(X_9),domain(domain(domain(domain(domain(X_9))))))) != compose(X_9,domain(domain(domain(domain(domain(X_9))))))
| compose(domain(X_9),domain(domain(domain(domain(domain(X_9)))))) != domain(X_9)
| compose(X_9,domain(X_9)) = compose(X_9,domain(domain(domain(domain(domain(X_9)))))) ),
introduced(tautology,[equality,[$cnf( $equal(compose(X_9,compose(domain(X_9),domain(domain(domain(domain(domain(X_9))))))),compose(X_9,domain(domain(domain(domain(domain(X_9))))))) ),[0,1],$fot(domain(X_9))]]) ).
cnf(refute_0_92,plain,
( compose(X_9,compose(domain(X_9),domain(domain(domain(domain(domain(X_9))))))) != compose(X_9,domain(domain(domain(domain(domain(X_9))))))
| compose(X_9,domain(X_9)) = compose(X_9,domain(domain(domain(domain(domain(X_9)))))) ),
inference(resolve,[$cnf( $equal(compose(domain(X_9),domain(domain(domain(domain(domain(X_9)))))),domain(X_9)) )],[refute_0_90,refute_0_91]) ).
cnf(refute_0_93,plain,
compose(X_9,domain(X_9)) = compose(X_9,domain(domain(domain(domain(domain(X_9)))))),
inference(resolve,[$cnf( $equal(compose(X_9,compose(domain(X_9),domain(domain(domain(domain(domain(X_9))))))),compose(X_9,domain(domain(domain(domain(domain(X_9))))))) )],[refute_0_67,refute_0_92]) ).
cnf(refute_0_94,plain,
( compose(X_9,domain(X_9)) != X_9
| compose(X_9,domain(X_9)) != compose(X_9,domain(domain(domain(domain(domain(X_9))))))
| X_9 = compose(X_9,domain(domain(domain(domain(domain(X_9)))))) ),
introduced(tautology,[equality,[$cnf( $equal(compose(X_9,domain(X_9)),compose(X_9,domain(domain(domain(domain(domain(X_9))))))) ),[0],$fot(X_9)]]) ).
cnf(refute_0_95,plain,
( compose(X_9,domain(X_9)) != compose(X_9,domain(domain(domain(domain(domain(X_9))))))
| X_9 = compose(X_9,domain(domain(domain(domain(domain(X_9)))))) ),
inference(resolve,[$cnf( $equal(compose(X_9,domain(X_9)),X_9) )],[refute_0_1,refute_0_94]) ).
cnf(refute_0_96,plain,
X_9 = compose(X_9,domain(domain(domain(domain(domain(X_9)))))),
inference(resolve,[$cnf( $equal(compose(X_9,domain(X_9)),compose(X_9,domain(domain(domain(domain(domain(X_9))))))) )],[refute_0_93,refute_0_95]) ).
cnf(refute_0_97,plain,
X_30 = compose(X_30,domain(domain(domain(domain(domain(X_30)))))),
inference(subst,[],[refute_0_96:[bind(X_9,$fot(X_30))]]) ).
cnf(refute_0_98,plain,
( X_30 != compose(X_30,domain(domain(domain(domain(domain(X_30))))))
| compose(X_30,domain(domain(domain(domain(domain(X_30)))))) = X_30 ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(X_30)),bind(Y0,$fot(compose(X_30,domain(domain(domain(domain(domain(X_30))))))))]]) ).
cnf(refute_0_99,plain,
compose(X_30,domain(domain(domain(domain(domain(X_30)))))) = X_30,
inference(resolve,[$cnf( $equal(X_30,compose(X_30,domain(domain(domain(domain(domain(X_30))))))) )],[refute_0_97,refute_0_98]) ).
cnf(refute_0_100,plain,
( compose(X_30,domain(domain(domain(domain(domain(X_30)))))) != X_30
| ~ there_exists(X_30)
| there_exists(compose(X_30,domain(domain(domain(domain(domain(X_30))))))) ),
introduced(tautology,[equality,[$cnf( ~ there_exists(compose(X_30,domain(domain(domain(domain(domain(X_30))))))) ),[0],$fot(X_30)]]) ).
cnf(refute_0_101,plain,
( ~ there_exists(X_30)
| there_exists(compose(X_30,domain(domain(domain(domain(domain(X_30))))))) ),
inference(resolve,[$cnf( $equal(compose(X_30,domain(domain(domain(domain(domain(X_30)))))),X_30) )],[refute_0_99,refute_0_100]) ).
cnf(refute_0_102,plain,
( ~ there_exists(X_30)
| there_exists(domain(X_30)) ),
inference(resolve,[$cnf( there_exists(compose(X_30,domain(domain(domain(domain(domain(X_30))))))) )],[refute_0_101,refute_0_66]) ).
cnf(refute_0_103,plain,
( ~ there_exists(h)
| there_exists(domain(h)) ),
inference(subst,[],[refute_0_102:[bind(X_30,$fot(h))]]) ).
cnf(refute_0_104,plain,
there_exists(domain(h)),
inference(resolve,[$cnf( there_exists(h) )],[assume_h_exists,refute_0_103]) ).
cnf(refute_0_105,plain,
( ~ there_exists(compose(codomain(b),Y))
| domain(codomain(b)) = codomain(Y) ),
inference(subst,[],[domain_codomain_composition1:[bind(X,$fot(codomain(b)))]]) ).
cnf(refute_0_106,plain,
( compose(a,compose(domain(domain(a)),X_18)) != compose(a,X_63)
| X_63 = compose(domain(domain(a)),X_18) ),
inference(subst,[],[refute_0_18:[bind(X,$fot(X_63)),bind(Z,$fot(compose(domain(domain(a)),X_18)))]]) ).
cnf(refute_0_107,plain,
compose(a,X_18) = compose(a,compose(domain(domain(a)),X_18)),
inference(subst,[],[refute_0_13:[bind(X_9,$fot(a))]]) ).
cnf(refute_0_108,plain,
( compose(a,X_18) != compose(a,compose(domain(domain(a)),X_18))
| compose(a,compose(domain(domain(a)),X_18)) = compose(a,X_18) ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(compose(a,X_18))),bind(Y0,$fot(compose(a,compose(domain(domain(a)),X_18))))]]) ).
cnf(refute_0_109,plain,
compose(a,compose(domain(domain(a)),X_18)) = compose(a,X_18),
inference(resolve,[$cnf( $equal(compose(a,X_18),compose(a,compose(domain(domain(a)),X_18))) )],[refute_0_107,refute_0_108]) ).
cnf(refute_0_110,plain,
( compose(a,X_18) != compose(a,X_63)
| compose(a,compose(domain(domain(a)),X_18)) != compose(a,X_18)
| compose(a,compose(domain(domain(a)),X_18)) = compose(a,X_63) ),
introduced(tautology,[equality,[$cnf( $equal(compose(a,compose(domain(domain(a)),X_18)),compose(a,X_18)) ),[1],$fot(compose(a,X_63))]]) ).
cnf(refute_0_111,plain,
( compose(a,X_18) != compose(a,X_63)
| compose(a,compose(domain(domain(a)),X_18)) = compose(a,X_63) ),
inference(resolve,[$cnf( $equal(compose(a,compose(domain(domain(a)),X_18)),compose(a,X_18)) )],[refute_0_109,refute_0_110]) ).
cnf(refute_0_112,plain,
( compose(a,X_18) != compose(a,X_63)
| X_63 = compose(domain(domain(a)),X_18) ),
inference(resolve,[$cnf( $equal(compose(a,compose(domain(domain(a)),X_18)),compose(a,X_63)) )],[refute_0_111,refute_0_106]) ).
cnf(refute_0_113,plain,
compose(codomain(X_10),compose(X_10,X_11)) = compose(compose(codomain(X_10),X_10),X_11),
inference(subst,[],[associativity_of_compose:[bind(X,$fot(codomain(X_10))),bind(Y,$fot(X_10)),bind(Z,$fot(X_11))]]) ).
cnf(refute_0_114,plain,
compose(codomain(X_10),X_10) = X_10,
inference(subst,[],[compose_codomain:[bind(X,$fot(X_10))]]) ).
cnf(refute_0_115,plain,
( compose(codomain(X_10),X_10) != X_10
| compose(codomain(X_10),compose(X_10,X_11)) != compose(compose(codomain(X_10),X_10),X_11)
| compose(codomain(X_10),compose(X_10,X_11)) = compose(X_10,X_11) ),
introduced(tautology,[equality,[$cnf( $equal(compose(codomain(X_10),compose(X_10,X_11)),compose(compose(codomain(X_10),X_10),X_11)) ),[1,0],$fot(X_10)]]) ).
cnf(refute_0_116,plain,
( compose(codomain(X_10),compose(X_10,X_11)) != compose(compose(codomain(X_10),X_10),X_11)
| compose(codomain(X_10),compose(X_10,X_11)) = compose(X_10,X_11) ),
inference(resolve,[$cnf( $equal(compose(codomain(X_10),X_10),X_10) )],[refute_0_114,refute_0_115]) ).
cnf(refute_0_117,plain,
compose(codomain(X_10),compose(X_10,X_11)) = compose(X_10,X_11),
inference(resolve,[$cnf( $equal(compose(codomain(X_10),compose(X_10,X_11)),compose(compose(codomain(X_10),X_10),X_11)) )],[refute_0_113,refute_0_116]) ).
cnf(refute_0_118,plain,
compose(codomain(codomain(codomain(codomain(codomain(codomain(X_11)))))),compose(codomain(codomain(codomain(codomain(codomain(X_11))))),X_11)) = compose(codomain(codomain(codomain(codomain(codomain(X_11))))),X_11),
inference(subst,[],[refute_0_117:[bind(X_10,$fot(codomain(codomain(codomain(codomain(codomain(X_11)))))))]]) ).
cnf(refute_0_119,plain,
compose(codomain(codomain(codomain(codomain(codomain(X_11))))),compose(codomain(codomain(codomain(codomain(X_11)))),X_11)) = compose(codomain(codomain(codomain(codomain(X_11)))),X_11),
inference(subst,[],[refute_0_117:[bind(X_10,$fot(codomain(codomain(codomain(codomain(X_11))))))]]) ).
cnf(refute_0_120,plain,
compose(codomain(codomain(codomain(codomain(X_11)))),compose(codomain(codomain(codomain(X_11))),X_11)) = compose(codomain(codomain(codomain(X_11))),X_11),
inference(subst,[],[refute_0_117:[bind(X_10,$fot(codomain(codomain(codomain(X_11)))))]]) ).
cnf(refute_0_121,plain,
compose(codomain(codomain(codomain(X_11))),compose(codomain(codomain(X_11)),X_11)) = compose(codomain(codomain(X_11)),X_11),
inference(subst,[],[refute_0_117:[bind(X_10,$fot(codomain(codomain(X_11))))]]) ).
cnf(refute_0_122,plain,
compose(codomain(codomain(X_13)),compose(codomain(X_13),X_13)) = compose(codomain(X_13),X_13),
inference(subst,[],[refute_0_117:[bind(X_10,$fot(codomain(X_13))),bind(X_11,$fot(X_13))]]) ).
cnf(refute_0_123,plain,
compose(codomain(X_13),X_13) = X_13,
inference(subst,[],[compose_codomain:[bind(X,$fot(X_13))]]) ).
cnf(refute_0_124,plain,
( compose(codomain(X_13),X_13) != X_13
| compose(codomain(codomain(X_13)),compose(codomain(X_13),X_13)) != compose(codomain(X_13),X_13)
| compose(codomain(codomain(X_13)),X_13) = compose(codomain(X_13),X_13) ),
introduced(tautology,[equality,[$cnf( $equal(compose(codomain(codomain(X_13)),compose(codomain(X_13),X_13)),compose(codomain(X_13),X_13)) ),[0,1],$fot(X_13)]]) ).
cnf(refute_0_125,plain,
( compose(codomain(codomain(X_13)),compose(codomain(X_13),X_13)) != compose(codomain(X_13),X_13)
| compose(codomain(codomain(X_13)),X_13) = compose(codomain(X_13),X_13) ),
inference(resolve,[$cnf( $equal(compose(codomain(X_13),X_13),X_13) )],[refute_0_123,refute_0_124]) ).
cnf(refute_0_126,plain,
compose(codomain(codomain(X_13)),X_13) = compose(codomain(X_13),X_13),
inference(resolve,[$cnf( $equal(compose(codomain(codomain(X_13)),compose(codomain(X_13),X_13)),compose(codomain(X_13),X_13)) )],[refute_0_122,refute_0_125]) ).
cnf(refute_0_127,plain,
( compose(codomain(X_13),X_13) != X_13
| compose(codomain(codomain(X_13)),X_13) != compose(codomain(X_13),X_13)
| compose(codomain(codomain(X_13)),X_13) = X_13 ),
introduced(tautology,[equality,[$cnf( $equal(compose(codomain(codomain(X_13)),X_13),compose(codomain(X_13),X_13)) ),[1],$fot(X_13)]]) ).
cnf(refute_0_128,plain,
( compose(codomain(codomain(X_13)),X_13) != compose(codomain(X_13),X_13)
| compose(codomain(codomain(X_13)),X_13) = X_13 ),
inference(resolve,[$cnf( $equal(compose(codomain(X_13),X_13),X_13) )],[refute_0_123,refute_0_127]) ).
cnf(refute_0_129,plain,
compose(codomain(codomain(X_13)),X_13) = X_13,
inference(resolve,[$cnf( $equal(compose(codomain(codomain(X_13)),X_13),compose(codomain(X_13),X_13)) )],[refute_0_126,refute_0_128]) ).
cnf(refute_0_130,plain,
compose(codomain(codomain(X_11)),X_11) = X_11,
inference(subst,[],[refute_0_129:[bind(X_13,$fot(X_11))]]) ).
cnf(refute_0_131,plain,
( compose(codomain(codomain(X_11)),X_11) != X_11
| compose(codomain(codomain(codomain(X_11))),compose(codomain(codomain(X_11)),X_11)) != compose(codomain(codomain(X_11)),X_11)
| compose(codomain(codomain(codomain(X_11))),X_11) = compose(codomain(codomain(X_11)),X_11) ),
introduced(tautology,[equality,[$cnf( $equal(compose(codomain(codomain(codomain(X_11))),compose(codomain(codomain(X_11)),X_11)),compose(codomain(codomain(X_11)),X_11)) ),[0,1],$fot(X_11)]]) ).
cnf(refute_0_132,plain,
( compose(codomain(codomain(codomain(X_11))),compose(codomain(codomain(X_11)),X_11)) != compose(codomain(codomain(X_11)),X_11)
| compose(codomain(codomain(codomain(X_11))),X_11) = compose(codomain(codomain(X_11)),X_11) ),
inference(resolve,[$cnf( $equal(compose(codomain(codomain(X_11)),X_11),X_11) )],[refute_0_130,refute_0_131]) ).
cnf(refute_0_133,plain,
compose(codomain(codomain(codomain(X_11))),X_11) = compose(codomain(codomain(X_11)),X_11),
inference(resolve,[$cnf( $equal(compose(codomain(codomain(codomain(X_11))),compose(codomain(codomain(X_11)),X_11)),compose(codomain(codomain(X_11)),X_11)) )],[refute_0_121,refute_0_132]) ).
cnf(refute_0_134,plain,
( compose(codomain(codomain(X_11)),X_11) != X_11
| compose(codomain(codomain(codomain(X_11))),X_11) != compose(codomain(codomain(X_11)),X_11)
| compose(codomain(codomain(codomain(X_11))),X_11) = X_11 ),
introduced(tautology,[equality,[$cnf( $equal(compose(codomain(codomain(codomain(X_11))),X_11),compose(codomain(codomain(X_11)),X_11)) ),[1],$fot(X_11)]]) ).
cnf(refute_0_135,plain,
( compose(codomain(codomain(codomain(X_11))),X_11) != compose(codomain(codomain(X_11)),X_11)
| compose(codomain(codomain(codomain(X_11))),X_11) = X_11 ),
inference(resolve,[$cnf( $equal(compose(codomain(codomain(X_11)),X_11),X_11) )],[refute_0_130,refute_0_134]) ).
cnf(refute_0_136,plain,
compose(codomain(codomain(codomain(X_11))),X_11) = X_11,
inference(resolve,[$cnf( $equal(compose(codomain(codomain(codomain(X_11))),X_11),compose(codomain(codomain(X_11)),X_11)) )],[refute_0_133,refute_0_135]) ).
cnf(refute_0_137,plain,
( compose(codomain(codomain(codomain(X_11))),X_11) != X_11
| compose(codomain(codomain(codomain(codomain(X_11)))),compose(codomain(codomain(codomain(X_11))),X_11)) != compose(codomain(codomain(codomain(X_11))),X_11)
| compose(codomain(codomain(codomain(codomain(X_11)))),X_11) = compose(codomain(codomain(codomain(X_11))),X_11) ),
introduced(tautology,[equality,[$cnf( $equal(compose(codomain(codomain(codomain(codomain(X_11)))),compose(codomain(codomain(codomain(X_11))),X_11)),compose(codomain(codomain(codomain(X_11))),X_11)) ),[0,1],$fot(X_11)]]) ).
cnf(refute_0_138,plain,
( compose(codomain(codomain(codomain(codomain(X_11)))),compose(codomain(codomain(codomain(X_11))),X_11)) != compose(codomain(codomain(codomain(X_11))),X_11)
| compose(codomain(codomain(codomain(codomain(X_11)))),X_11) = compose(codomain(codomain(codomain(X_11))),X_11) ),
inference(resolve,[$cnf( $equal(compose(codomain(codomain(codomain(X_11))),X_11),X_11) )],[refute_0_136,refute_0_137]) ).
cnf(refute_0_139,plain,
compose(codomain(codomain(codomain(codomain(X_11)))),X_11) = compose(codomain(codomain(codomain(X_11))),X_11),
inference(resolve,[$cnf( $equal(compose(codomain(codomain(codomain(codomain(X_11)))),compose(codomain(codomain(codomain(X_11))),X_11)),compose(codomain(codomain(codomain(X_11))),X_11)) )],[refute_0_120,refute_0_138]) ).
cnf(refute_0_140,plain,
( compose(codomain(codomain(codomain(X_11))),X_11) != X_11
| compose(codomain(codomain(codomain(codomain(X_11)))),X_11) != compose(codomain(codomain(codomain(X_11))),X_11)
| compose(codomain(codomain(codomain(codomain(X_11)))),X_11) = X_11 ),
introduced(tautology,[equality,[$cnf( $equal(compose(codomain(codomain(codomain(codomain(X_11)))),X_11),compose(codomain(codomain(codomain(X_11))),X_11)) ),[1],$fot(X_11)]]) ).
cnf(refute_0_141,plain,
( compose(codomain(codomain(codomain(codomain(X_11)))),X_11) != compose(codomain(codomain(codomain(X_11))),X_11)
| compose(codomain(codomain(codomain(codomain(X_11)))),X_11) = X_11 ),
inference(resolve,[$cnf( $equal(compose(codomain(codomain(codomain(X_11))),X_11),X_11) )],[refute_0_136,refute_0_140]) ).
cnf(refute_0_142,plain,
compose(codomain(codomain(codomain(codomain(X_11)))),X_11) = X_11,
inference(resolve,[$cnf( $equal(compose(codomain(codomain(codomain(codomain(X_11)))),X_11),compose(codomain(codomain(codomain(X_11))),X_11)) )],[refute_0_139,refute_0_141]) ).
cnf(refute_0_143,plain,
( compose(codomain(codomain(codomain(codomain(X_11)))),X_11) != X_11
| compose(codomain(codomain(codomain(codomain(codomain(X_11))))),compose(codomain(codomain(codomain(codomain(X_11)))),X_11)) != compose(codomain(codomain(codomain(codomain(X_11)))),X_11)
| compose(codomain(codomain(codomain(codomain(codomain(X_11))))),X_11) = compose(codomain(codomain(codomain(codomain(X_11)))),X_11) ),
introduced(tautology,[equality,[$cnf( $equal(compose(codomain(codomain(codomain(codomain(codomain(X_11))))),compose(codomain(codomain(codomain(codomain(X_11)))),X_11)),compose(codomain(codomain(codomain(codomain(X_11)))),X_11)) ),[0,1],$fot(X_11)]]) ).
cnf(refute_0_144,plain,
( compose(codomain(codomain(codomain(codomain(codomain(X_11))))),compose(codomain(codomain(codomain(codomain(X_11)))),X_11)) != compose(codomain(codomain(codomain(codomain(X_11)))),X_11)
| compose(codomain(codomain(codomain(codomain(codomain(X_11))))),X_11) = compose(codomain(codomain(codomain(codomain(X_11)))),X_11) ),
inference(resolve,[$cnf( $equal(compose(codomain(codomain(codomain(codomain(X_11)))),X_11),X_11) )],[refute_0_142,refute_0_143]) ).
cnf(refute_0_145,plain,
compose(codomain(codomain(codomain(codomain(codomain(X_11))))),X_11) = compose(codomain(codomain(codomain(codomain(X_11)))),X_11),
inference(resolve,[$cnf( $equal(compose(codomain(codomain(codomain(codomain(codomain(X_11))))),compose(codomain(codomain(codomain(codomain(X_11)))),X_11)),compose(codomain(codomain(codomain(codomain(X_11)))),X_11)) )],[refute_0_119,refute_0_144]) ).
cnf(refute_0_146,plain,
( compose(codomain(codomain(codomain(codomain(X_11)))),X_11) != X_11
| compose(codomain(codomain(codomain(codomain(codomain(X_11))))),X_11) != compose(codomain(codomain(codomain(codomain(X_11)))),X_11)
| compose(codomain(codomain(codomain(codomain(codomain(X_11))))),X_11) = X_11 ),
introduced(tautology,[equality,[$cnf( $equal(compose(codomain(codomain(codomain(codomain(codomain(X_11))))),X_11),compose(codomain(codomain(codomain(codomain(X_11)))),X_11)) ),[1],$fot(X_11)]]) ).
cnf(refute_0_147,plain,
( compose(codomain(codomain(codomain(codomain(codomain(X_11))))),X_11) != compose(codomain(codomain(codomain(codomain(X_11)))),X_11)
| compose(codomain(codomain(codomain(codomain(codomain(X_11))))),X_11) = X_11 ),
inference(resolve,[$cnf( $equal(compose(codomain(codomain(codomain(codomain(X_11)))),X_11),X_11) )],[refute_0_142,refute_0_146]) ).
cnf(refute_0_148,plain,
compose(codomain(codomain(codomain(codomain(codomain(X_11))))),X_11) = X_11,
inference(resolve,[$cnf( $equal(compose(codomain(codomain(codomain(codomain(codomain(X_11))))),X_11),compose(codomain(codomain(codomain(codomain(X_11)))),X_11)) )],[refute_0_145,refute_0_147]) ).
cnf(refute_0_149,plain,
( compose(codomain(codomain(codomain(codomain(codomain(X_11))))),X_11) != X_11
| compose(codomain(codomain(codomain(codomain(codomain(codomain(X_11)))))),compose(codomain(codomain(codomain(codomain(codomain(X_11))))),X_11)) != compose(codomain(codomain(codomain(codomain(codomain(X_11))))),X_11)
| compose(codomain(codomain(codomain(codomain(codomain(codomain(X_11)))))),X_11) = compose(codomain(codomain(codomain(codomain(codomain(X_11))))),X_11) ),
introduced(tautology,[equality,[$cnf( $equal(compose(codomain(codomain(codomain(codomain(codomain(codomain(X_11)))))),compose(codomain(codomain(codomain(codomain(codomain(X_11))))),X_11)),compose(codomain(codomain(codomain(codomain(codomain(X_11))))),X_11)) ),[0,1],$fot(X_11)]]) ).
cnf(refute_0_150,plain,
( compose(codomain(codomain(codomain(codomain(codomain(codomain(X_11)))))),compose(codomain(codomain(codomain(codomain(codomain(X_11))))),X_11)) != compose(codomain(codomain(codomain(codomain(codomain(X_11))))),X_11)
| compose(codomain(codomain(codomain(codomain(codomain(codomain(X_11)))))),X_11) = compose(codomain(codomain(codomain(codomain(codomain(X_11))))),X_11) ),
inference(resolve,[$cnf( $equal(compose(codomain(codomain(codomain(codomain(codomain(X_11))))),X_11),X_11) )],[refute_0_148,refute_0_149]) ).
cnf(refute_0_151,plain,
compose(codomain(codomain(codomain(codomain(codomain(codomain(X_11)))))),X_11) = compose(codomain(codomain(codomain(codomain(codomain(X_11))))),X_11),
inference(resolve,[$cnf( $equal(compose(codomain(codomain(codomain(codomain(codomain(codomain(X_11)))))),compose(codomain(codomain(codomain(codomain(codomain(X_11))))),X_11)),compose(codomain(codomain(codomain(codomain(codomain(X_11))))),X_11)) )],[refute_0_118,refute_0_150]) ).
cnf(refute_0_152,plain,
( compose(codomain(codomain(codomain(codomain(codomain(X_11))))),X_11) != X_11
| compose(codomain(codomain(codomain(codomain(codomain(codomain(X_11)))))),X_11) != compose(codomain(codomain(codomain(codomain(codomain(X_11))))),X_11)
| compose(codomain(codomain(codomain(codomain(codomain(codomain(X_11)))))),X_11) = X_11 ),
introduced(tautology,[equality,[$cnf( $equal(compose(codomain(codomain(codomain(codomain(codomain(codomain(X_11)))))),X_11),compose(codomain(codomain(codomain(codomain(codomain(X_11))))),X_11)) ),[1],$fot(X_11)]]) ).
cnf(refute_0_153,plain,
( compose(codomain(codomain(codomain(codomain(codomain(codomain(X_11)))))),X_11) != compose(codomain(codomain(codomain(codomain(codomain(X_11))))),X_11)
| compose(codomain(codomain(codomain(codomain(codomain(codomain(X_11)))))),X_11) = X_11 ),
inference(resolve,[$cnf( $equal(compose(codomain(codomain(codomain(codomain(codomain(X_11))))),X_11),X_11) )],[refute_0_148,refute_0_152]) ).
cnf(refute_0_154,plain,
compose(codomain(codomain(codomain(codomain(codomain(codomain(X_11)))))),X_11) = X_11,
inference(resolve,[$cnf( $equal(compose(codomain(codomain(codomain(codomain(codomain(codomain(X_11)))))),X_11),compose(codomain(codomain(codomain(codomain(codomain(X_11))))),X_11)) )],[refute_0_151,refute_0_153]) ).
cnf(refute_0_155,plain,
compose(codomain(codomain(codomain(codomain(codomain(codomain(domain(codomain(b)))))))),domain(codomain(b))) = domain(codomain(b)),
inference(subst,[],[refute_0_154:[bind(X_11,$fot(domain(codomain(b))))]]) ).
cnf(refute_0_156,plain,
( ~ there_exists(compose(a,domain(codomain(b))))
| domain(a) = codomain(domain(codomain(b))) ),
inference(subst,[],[domain_codomain_composition1:[bind(X,$fot(a)),bind(Y,$fot(domain(codomain(b))))]]) ).
cnf(refute_0_157,plain,
a = compose(a,domain(domain(a))),
inference(subst,[],[refute_0_51:[bind(X_19,$fot(a))]]) ).
cnf(refute_0_158,plain,
( ~ there_exists(compose(a,b))
| domain(a) = codomain(b) ),
inference(subst,[],[domain_codomain_composition1:[bind(X,$fot(a)),bind(Y,$fot(b))]]) ).
cnf(refute_0_159,plain,
domain(a) = codomain(b),
inference(resolve,[$cnf( there_exists(compose(a,b)) )],[assume_ab_exists,refute_0_158]) ).
cnf(refute_0_160,plain,
( a != compose(a,domain(domain(a)))
| domain(a) != codomain(b)
| a = compose(a,domain(codomain(b))) ),
introduced(tautology,[equality,[$cnf( $equal(a,compose(a,domain(domain(a)))) ),[1,1,0],$fot(codomain(b))]]) ).
cnf(refute_0_161,plain,
( a != compose(a,domain(domain(a)))
| a = compose(a,domain(codomain(b))) ),
inference(resolve,[$cnf( $equal(domain(a),codomain(b)) )],[refute_0_159,refute_0_160]) ).
cnf(refute_0_162,plain,
a = compose(a,domain(codomain(b))),
inference(resolve,[$cnf( $equal(a,compose(a,domain(domain(a)))) )],[refute_0_157,refute_0_161]) ).
cnf(refute_0_163,plain,
( a != compose(a,domain(codomain(b)))
| compose(a,domain(codomain(b))) = a ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(a)),bind(Y0,$fot(compose(a,domain(codomain(b)))))]]) ).
cnf(refute_0_164,plain,
compose(a,domain(codomain(b))) = a,
inference(resolve,[$cnf( $equal(a,compose(a,domain(codomain(b)))) )],[refute_0_162,refute_0_163]) ).
cnf(refute_0_165,plain,
( compose(a,domain(codomain(b))) != a
| ~ there_exists(a)
| there_exists(compose(a,domain(codomain(b)))) ),
introduced(tautology,[equality,[$cnf( ~ there_exists(compose(a,domain(codomain(b)))) ),[0],$fot(a)]]) ).
cnf(refute_0_166,plain,
( ~ there_exists(a)
| there_exists(compose(a,domain(codomain(b)))) ),
inference(resolve,[$cnf( $equal(compose(a,domain(codomain(b))),a) )],[refute_0_164,refute_0_165]) ).
cnf(refute_0_167,plain,
( ~ there_exists(a)
| domain(a) = codomain(domain(codomain(b))) ),
inference(resolve,[$cnf( there_exists(compose(a,domain(codomain(b)))) )],[refute_0_166,refute_0_156]) ).
cnf(refute_0_168,plain,
( domain(a) != codomain(b)
| domain(a) != codomain(domain(codomain(b)))
| codomain(b) = codomain(domain(codomain(b))) ),
introduced(tautology,[equality,[$cnf( $equal(domain(a),codomain(domain(codomain(b)))) ),[0],$fot(codomain(b))]]) ).
cnf(refute_0_169,plain,
( domain(a) != codomain(domain(codomain(b)))
| codomain(b) = codomain(domain(codomain(b))) ),
inference(resolve,[$cnf( $equal(domain(a),codomain(b)) )],[refute_0_159,refute_0_168]) ).
cnf(refute_0_170,plain,
( ~ there_exists(a)
| codomain(b) = codomain(domain(codomain(b))) ),
inference(resolve,[$cnf( $equal(domain(a),codomain(domain(codomain(b)))) )],[refute_0_167,refute_0_169]) ).
cnf(refute_0_171,plain,
( ~ there_exists(domain(a))
| there_exists(a) ),
inference(subst,[],[domain_has_elements:[bind(X,$fot(a))]]) ).
cnf(refute_0_172,plain,
( domain(a) != codomain(b)
| ~ there_exists(codomain(b))
| there_exists(domain(a)) ),
introduced(tautology,[equality,[$cnf( ~ there_exists(domain(a)) ),[0],$fot(codomain(b))]]) ).
cnf(refute_0_173,plain,
( ~ there_exists(codomain(b))
| there_exists(domain(a)) ),
inference(resolve,[$cnf( $equal(domain(a),codomain(b)) )],[refute_0_159,refute_0_172]) ).
cnf(refute_0_174,plain,
( ~ there_exists(codomain(b))
| there_exists(a) ),
inference(resolve,[$cnf( there_exists(domain(a)) )],[refute_0_173,refute_0_171]) ).
cnf(refute_0_175,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_176,plain,
there_exists(domain(a)),
inference(resolve,[$cnf( there_exists(compose(a,b)) )],[assume_ab_exists,refute_0_175]) ).
cnf(refute_0_177,plain,
( domain(a) != codomain(b)
| ~ there_exists(domain(a))
| there_exists(codomain(b)) ),
introduced(tautology,[equality,[$cnf( there_exists(domain(a)) ),[0],$fot(codomain(b))]]) ).
cnf(refute_0_178,plain,
( ~ there_exists(domain(a))
| there_exists(codomain(b)) ),
inference(resolve,[$cnf( $equal(domain(a),codomain(b)) )],[refute_0_159,refute_0_177]) ).
cnf(refute_0_179,plain,
there_exists(codomain(b)),
inference(resolve,[$cnf( there_exists(domain(a)) )],[refute_0_176,refute_0_178]) ).
cnf(refute_0_180,plain,
there_exists(a),
inference(resolve,[$cnf( there_exists(codomain(b)) )],[refute_0_179,refute_0_174]) ).
cnf(refute_0_181,plain,
codomain(b) = codomain(domain(codomain(b))),
inference(resolve,[$cnf( there_exists(a) )],[refute_0_180,refute_0_170]) ).
cnf(refute_0_182,plain,
( codomain(b) != codomain(domain(codomain(b)))
| codomain(domain(codomain(b))) = codomain(b) ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(codomain(b))),bind(Y0,$fot(codomain(domain(codomain(b)))))]]) ).
cnf(refute_0_183,plain,
codomain(domain(codomain(b))) = codomain(b),
inference(resolve,[$cnf( $equal(codomain(b),codomain(domain(codomain(b)))) )],[refute_0_181,refute_0_182]) ).
cnf(refute_0_184,plain,
( codomain(domain(codomain(b))) != codomain(b)
| compose(codomain(codomain(codomain(codomain(codomain(codomain(domain(codomain(b)))))))),domain(codomain(b))) != domain(codomain(b))
| compose(codomain(codomain(codomain(codomain(codomain(codomain(b)))))),domain(codomain(b))) = domain(codomain(b)) ),
introduced(tautology,[equality,[$cnf( $equal(compose(codomain(codomain(codomain(codomain(codomain(codomain(domain(codomain(b)))))))),domain(codomain(b))),domain(codomain(b))) ),[0,0,0,0,0,0,0],$fot(codomain(b))]]) ).
cnf(refute_0_185,plain,
( compose(codomain(codomain(codomain(codomain(codomain(codomain(domain(codomain(b)))))))),domain(codomain(b))) != domain(codomain(b))
| compose(codomain(codomain(codomain(codomain(codomain(codomain(b)))))),domain(codomain(b))) = domain(codomain(b)) ),
inference(resolve,[$cnf( $equal(codomain(domain(codomain(b))),codomain(b)) )],[refute_0_183,refute_0_184]) ).
cnf(refute_0_186,plain,
compose(codomain(codomain(codomain(codomain(codomain(codomain(b)))))),domain(codomain(b))) = domain(codomain(b)),
inference(resolve,[$cnf( $equal(compose(codomain(codomain(codomain(codomain(codomain(codomain(domain(codomain(b)))))))),domain(codomain(b))),domain(codomain(b))) )],[refute_0_155,refute_0_185]) ).
cnf(refute_0_187,plain,
compose(codomain(b),domain(codomain(b))) = codomain(b),
inference(subst,[],[compose_domain:[bind(X,$fot(codomain(b)))]]) ).
cnf(refute_0_188,plain,
( ~ there_exists(compose(a,codomain(b)))
| domain(a) = codomain(codomain(b)) ),
inference(subst,[],[domain_codomain_composition1:[bind(X,$fot(a)),bind(Y,$fot(codomain(b)))]]) ).
cnf(refute_0_189,plain,
compose(a,domain(a)) = a,
inference(subst,[],[compose_domain:[bind(X,$fot(a))]]) ).
cnf(refute_0_190,plain,
( compose(a,domain(a)) != a
| domain(a) != codomain(b)
| compose(a,codomain(b)) = a ),
introduced(tautology,[equality,[$cnf( $equal(compose(a,domain(a)),a) ),[0,1],$fot(codomain(b))]]) ).
cnf(refute_0_191,plain,
( compose(a,domain(a)) != a
| compose(a,codomain(b)) = a ),
inference(resolve,[$cnf( $equal(domain(a),codomain(b)) )],[refute_0_159,refute_0_190]) ).
cnf(refute_0_192,plain,
compose(a,codomain(b)) = a,
inference(resolve,[$cnf( $equal(compose(a,domain(a)),a) )],[refute_0_189,refute_0_191]) ).
cnf(refute_0_193,plain,
( compose(a,codomain(b)) != a
| ~ there_exists(a)
| there_exists(compose(a,codomain(b))) ),
introduced(tautology,[equality,[$cnf( ~ there_exists(compose(a,codomain(b))) ),[0],$fot(a)]]) ).
cnf(refute_0_194,plain,
( ~ there_exists(a)
| there_exists(compose(a,codomain(b))) ),
inference(resolve,[$cnf( $equal(compose(a,codomain(b)),a) )],[refute_0_192,refute_0_193]) ).
cnf(refute_0_195,plain,
( ~ there_exists(a)
| domain(a) = codomain(codomain(b)) ),
inference(resolve,[$cnf( there_exists(compose(a,codomain(b))) )],[refute_0_194,refute_0_188]) ).
cnf(refute_0_196,plain,
( domain(a) != codomain(b)
| domain(a) != codomain(codomain(b))
| codomain(b) = codomain(codomain(b)) ),
introduced(tautology,[equality,[$cnf( $equal(domain(a),codomain(codomain(b))) ),[0],$fot(codomain(b))]]) ).
cnf(refute_0_197,plain,
( domain(a) != codomain(codomain(b))
| codomain(b) = codomain(codomain(b)) ),
inference(resolve,[$cnf( $equal(domain(a),codomain(b)) )],[refute_0_159,refute_0_196]) ).
cnf(refute_0_198,plain,
( ~ there_exists(a)
| codomain(b) = codomain(codomain(b)) ),
inference(resolve,[$cnf( $equal(domain(a),codomain(codomain(b))) )],[refute_0_195,refute_0_197]) ).
cnf(refute_0_199,plain,
codomain(b) = codomain(codomain(b)),
inference(resolve,[$cnf( there_exists(a) )],[refute_0_180,refute_0_198]) ).
cnf(refute_0_200,plain,
( codomain(b) != codomain(codomain(b))
| codomain(codomain(b)) = codomain(b) ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(codomain(b))),bind(Y0,$fot(codomain(codomain(b))))]]) ).
cnf(refute_0_201,plain,
codomain(codomain(b)) = codomain(b),
inference(resolve,[$cnf( $equal(codomain(b),codomain(codomain(b))) )],[refute_0_199,refute_0_200]) ).
cnf(refute_0_202,plain,
codomain(codomain(codomain(b))) = codomain(codomain(codomain(b))),
introduced(tautology,[refl,[$fot(codomain(codomain(codomain(b))))]]) ).
cnf(refute_0_203,plain,
( codomain(codomain(b)) != codomain(b)
| codomain(codomain(codomain(b))) != codomain(codomain(codomain(b)))
| codomain(codomain(codomain(b))) = codomain(codomain(b)) ),
introduced(tautology,[equality,[$cnf( $equal(codomain(codomain(codomain(b))),codomain(codomain(codomain(b)))) ),[1,0],$fot(codomain(b))]]) ).
cnf(refute_0_204,plain,
( codomain(codomain(b)) != codomain(b)
| codomain(codomain(codomain(b))) = codomain(codomain(b)) ),
inference(resolve,[$cnf( $equal(codomain(codomain(codomain(b))),codomain(codomain(codomain(b)))) )],[refute_0_202,refute_0_203]) ).
cnf(refute_0_205,plain,
codomain(codomain(codomain(b))) = codomain(codomain(b)),
inference(resolve,[$cnf( $equal(codomain(codomain(b)),codomain(b)) )],[refute_0_201,refute_0_204]) ).
cnf(refute_0_206,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_207,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_24,refute_0_206]) ).
cnf(refute_0_208,plain,
( codomain(codomain(b)) != codomain(b)
| codomain(codomain(codomain(b))) != codomain(codomain(b))
| codomain(codomain(codomain(b))) = codomain(b) ),
inference(subst,[],[refute_0_207:[bind(X0,$fot(codomain(codomain(codomain(b))))),bind(Y0,$fot(codomain(codomain(b)))),bind(Z0,$fot(codomain(b)))]]) ).
cnf(refute_0_209,plain,
( codomain(codomain(b)) != codomain(b)
| codomain(codomain(codomain(b))) = codomain(b) ),
inference(resolve,[$cnf( $equal(codomain(codomain(codomain(b))),codomain(codomain(b))) )],[refute_0_205,refute_0_208]) ).
cnf(refute_0_210,plain,
codomain(codomain(codomain(b))) = codomain(b),
inference(resolve,[$cnf( $equal(codomain(codomain(b)),codomain(b)) )],[refute_0_201,refute_0_209]) ).
cnf(refute_0_211,plain,
codomain(codomain(codomain(codomain(b)))) = codomain(codomain(codomain(codomain(b)))),
introduced(tautology,[refl,[$fot(codomain(codomain(codomain(codomain(b)))))]]) ).
cnf(refute_0_212,plain,
( codomain(codomain(codomain(b))) != codomain(b)
| codomain(codomain(codomain(codomain(b)))) != codomain(codomain(codomain(codomain(b))))
| codomain(codomain(codomain(codomain(b)))) = codomain(codomain(b)) ),
introduced(tautology,[equality,[$cnf( $equal(codomain(codomain(codomain(codomain(b)))),codomain(codomain(codomain(codomain(b))))) ),[1,0],$fot(codomain(b))]]) ).
cnf(refute_0_213,plain,
( codomain(codomain(codomain(b))) != codomain(b)
| codomain(codomain(codomain(codomain(b)))) = codomain(codomain(b)) ),
inference(resolve,[$cnf( $equal(codomain(codomain(codomain(codomain(b)))),codomain(codomain(codomain(codomain(b))))) )],[refute_0_211,refute_0_212]) ).
cnf(refute_0_214,plain,
codomain(codomain(codomain(codomain(b)))) = codomain(codomain(b)),
inference(resolve,[$cnf( $equal(codomain(codomain(codomain(b))),codomain(b)) )],[refute_0_210,refute_0_213]) ).
cnf(refute_0_215,plain,
( codomain(codomain(b)) != codomain(b)
| codomain(codomain(codomain(codomain(b)))) != codomain(codomain(b))
| codomain(codomain(codomain(codomain(b)))) = codomain(b) ),
inference(subst,[],[refute_0_207:[bind(X0,$fot(codomain(codomain(codomain(codomain(b)))))),bind(Y0,$fot(codomain(codomain(b)))),bind(Z0,$fot(codomain(b)))]]) ).
cnf(refute_0_216,plain,
( codomain(codomain(b)) != codomain(b)
| codomain(codomain(codomain(codomain(b)))) = codomain(b) ),
inference(resolve,[$cnf( $equal(codomain(codomain(codomain(codomain(b)))),codomain(codomain(b))) )],[refute_0_214,refute_0_215]) ).
cnf(refute_0_217,plain,
codomain(codomain(codomain(codomain(b)))) = codomain(b),
inference(resolve,[$cnf( $equal(codomain(codomain(b)),codomain(b)) )],[refute_0_201,refute_0_216]) ).
cnf(refute_0_218,plain,
codomain(codomain(codomain(codomain(codomain(b))))) = codomain(codomain(codomain(codomain(codomain(b))))),
introduced(tautology,[refl,[$fot(codomain(codomain(codomain(codomain(codomain(b))))))]]) ).
cnf(refute_0_219,plain,
( codomain(codomain(codomain(codomain(b)))) != codomain(b)
| codomain(codomain(codomain(codomain(codomain(b))))) != codomain(codomain(codomain(codomain(codomain(b)))))
| codomain(codomain(codomain(codomain(codomain(b))))) = codomain(codomain(b)) ),
introduced(tautology,[equality,[$cnf( $equal(codomain(codomain(codomain(codomain(codomain(b))))),codomain(codomain(codomain(codomain(codomain(b)))))) ),[1,0],$fot(codomain(b))]]) ).
cnf(refute_0_220,plain,
( codomain(codomain(codomain(codomain(b)))) != codomain(b)
| codomain(codomain(codomain(codomain(codomain(b))))) = codomain(codomain(b)) ),
inference(resolve,[$cnf( $equal(codomain(codomain(codomain(codomain(codomain(b))))),codomain(codomain(codomain(codomain(codomain(b)))))) )],[refute_0_218,refute_0_219]) ).
cnf(refute_0_221,plain,
codomain(codomain(codomain(codomain(codomain(b))))) = codomain(codomain(b)),
inference(resolve,[$cnf( $equal(codomain(codomain(codomain(codomain(b)))),codomain(b)) )],[refute_0_217,refute_0_220]) ).
cnf(refute_0_222,plain,
( codomain(codomain(b)) != codomain(b)
| codomain(codomain(codomain(codomain(codomain(b))))) != codomain(codomain(b))
| codomain(codomain(codomain(codomain(codomain(b))))) = codomain(b) ),
inference(subst,[],[refute_0_207:[bind(X0,$fot(codomain(codomain(codomain(codomain(codomain(b))))))),bind(Y0,$fot(codomain(codomain(b)))),bind(Z0,$fot(codomain(b)))]]) ).
cnf(refute_0_223,plain,
( codomain(codomain(b)) != codomain(b)
| codomain(codomain(codomain(codomain(codomain(b))))) = codomain(b) ),
inference(resolve,[$cnf( $equal(codomain(codomain(codomain(codomain(codomain(b))))),codomain(codomain(b))) )],[refute_0_221,refute_0_222]) ).
cnf(refute_0_224,plain,
codomain(codomain(codomain(codomain(codomain(b))))) = codomain(b),
inference(resolve,[$cnf( $equal(codomain(codomain(b)),codomain(b)) )],[refute_0_201,refute_0_223]) ).
cnf(refute_0_225,plain,
codomain(codomain(codomain(codomain(codomain(codomain(b)))))) = codomain(codomain(codomain(codomain(codomain(codomain(b)))))),
introduced(tautology,[refl,[$fot(codomain(codomain(codomain(codomain(codomain(codomain(b)))))))]]) ).
cnf(refute_0_226,plain,
( codomain(codomain(codomain(codomain(codomain(b))))) != codomain(b)
| codomain(codomain(codomain(codomain(codomain(codomain(b)))))) != codomain(codomain(codomain(codomain(codomain(codomain(b))))))
| codomain(codomain(codomain(codomain(codomain(codomain(b)))))) = codomain(codomain(b)) ),
introduced(tautology,[equality,[$cnf( $equal(codomain(codomain(codomain(codomain(codomain(codomain(b)))))),codomain(codomain(codomain(codomain(codomain(codomain(b))))))) ),[1,0],$fot(codomain(b))]]) ).
cnf(refute_0_227,plain,
( codomain(codomain(codomain(codomain(codomain(b))))) != codomain(b)
| codomain(codomain(codomain(codomain(codomain(codomain(b)))))) = codomain(codomain(b)) ),
inference(resolve,[$cnf( $equal(codomain(codomain(codomain(codomain(codomain(codomain(b)))))),codomain(codomain(codomain(codomain(codomain(codomain(b))))))) )],[refute_0_225,refute_0_226]) ).
cnf(refute_0_228,plain,
codomain(codomain(codomain(codomain(codomain(codomain(b)))))) = codomain(codomain(b)),
inference(resolve,[$cnf( $equal(codomain(codomain(codomain(codomain(codomain(b))))),codomain(b)) )],[refute_0_224,refute_0_227]) ).
cnf(refute_0_229,plain,
( codomain(codomain(b)) != codomain(b)
| codomain(codomain(codomain(codomain(codomain(codomain(b)))))) != codomain(codomain(b))
| codomain(codomain(codomain(codomain(codomain(codomain(b)))))) = codomain(b) ),
inference(subst,[],[refute_0_207:[bind(X0,$fot(codomain(codomain(codomain(codomain(codomain(codomain(b)))))))),bind(Y0,$fot(codomain(codomain(b)))),bind(Z0,$fot(codomain(b)))]]) ).
cnf(refute_0_230,plain,
( codomain(codomain(b)) != codomain(b)
| codomain(codomain(codomain(codomain(codomain(codomain(b)))))) = codomain(b) ),
inference(resolve,[$cnf( $equal(codomain(codomain(codomain(codomain(codomain(codomain(b)))))),codomain(codomain(b))) )],[refute_0_228,refute_0_229]) ).
cnf(refute_0_231,plain,
codomain(codomain(codomain(codomain(codomain(codomain(b)))))) = codomain(b),
inference(resolve,[$cnf( $equal(codomain(codomain(b)),codomain(b)) )],[refute_0_201,refute_0_230]) ).
cnf(refute_0_232,plain,
compose(codomain(codomain(codomain(codomain(codomain(codomain(b)))))),domain(codomain(b))) = compose(codomain(codomain(codomain(codomain(codomain(codomain(b)))))),domain(codomain(b))),
introduced(tautology,[refl,[$fot(compose(codomain(codomain(codomain(codomain(codomain(codomain(b)))))),domain(codomain(b))))]]) ).
cnf(refute_0_233,plain,
( codomain(codomain(codomain(codomain(codomain(codomain(b)))))) != codomain(b)
| compose(codomain(codomain(codomain(codomain(codomain(codomain(b)))))),domain(codomain(b))) != compose(codomain(codomain(codomain(codomain(codomain(codomain(b)))))),domain(codomain(b)))
| compose(codomain(codomain(codomain(codomain(codomain(codomain(b)))))),domain(codomain(b))) = compose(codomain(b),domain(codomain(b))) ),
introduced(tautology,[equality,[$cnf( $equal(compose(codomain(codomain(codomain(codomain(codomain(codomain(b)))))),domain(codomain(b))),compose(codomain(codomain(codomain(codomain(codomain(codomain(b)))))),domain(codomain(b)))) ),[1,0],$fot(codomain(b))]]) ).
cnf(refute_0_234,plain,
( codomain(codomain(codomain(codomain(codomain(codomain(b)))))) != codomain(b)
| compose(codomain(codomain(codomain(codomain(codomain(codomain(b)))))),domain(codomain(b))) = compose(codomain(b),domain(codomain(b))) ),
inference(resolve,[$cnf( $equal(compose(codomain(codomain(codomain(codomain(codomain(codomain(b)))))),domain(codomain(b))),compose(codomain(codomain(codomain(codomain(codomain(codomain(b)))))),domain(codomain(b)))) )],[refute_0_232,refute_0_233]) ).
cnf(refute_0_235,plain,
compose(codomain(codomain(codomain(codomain(codomain(codomain(b)))))),domain(codomain(b))) = compose(codomain(b),domain(codomain(b))),
inference(resolve,[$cnf( $equal(codomain(codomain(codomain(codomain(codomain(codomain(b)))))),codomain(b)) )],[refute_0_231,refute_0_234]) ).
cnf(refute_0_236,plain,
( compose(codomain(b),domain(codomain(b))) != codomain(b)
| compose(codomain(codomain(codomain(codomain(codomain(codomain(b)))))),domain(codomain(b))) != compose(codomain(b),domain(codomain(b)))
| compose(codomain(codomain(codomain(codomain(codomain(codomain(b)))))),domain(codomain(b))) = codomain(b) ),
inference(subst,[],[refute_0_207:[bind(X0,$fot(compose(codomain(codomain(codomain(codomain(codomain(codomain(b)))))),domain(codomain(b))))),bind(Y0,$fot(compose(codomain(b),domain(codomain(b))))),bind(Z0,$fot(codomain(b)))]]) ).
cnf(refute_0_237,plain,
( compose(codomain(b),domain(codomain(b))) != codomain(b)
| compose(codomain(codomain(codomain(codomain(codomain(codomain(b)))))),domain(codomain(b))) = codomain(b) ),
inference(resolve,[$cnf( $equal(compose(codomain(codomain(codomain(codomain(codomain(codomain(b)))))),domain(codomain(b))),compose(codomain(b),domain(codomain(b)))) )],[refute_0_235,refute_0_236]) ).
cnf(refute_0_238,plain,
compose(codomain(codomain(codomain(codomain(codomain(codomain(b)))))),domain(codomain(b))) = codomain(b),
inference(resolve,[$cnf( $equal(compose(codomain(b),domain(codomain(b))),codomain(b)) )],[refute_0_187,refute_0_237]) ).
cnf(refute_0_239,plain,
( compose(codomain(codomain(codomain(codomain(codomain(codomain(b)))))),domain(codomain(b))) != codomain(b)
| compose(codomain(codomain(codomain(codomain(codomain(codomain(b)))))),domain(codomain(b))) != domain(codomain(b))
| codomain(b) = domain(codomain(b)) ),
introduced(tautology,[equality,[$cnf( $equal(compose(codomain(codomain(codomain(codomain(codomain(codomain(b)))))),domain(codomain(b))),domain(codomain(b))) ),[0],$fot(codomain(b))]]) ).
cnf(refute_0_240,plain,
( compose(codomain(codomain(codomain(codomain(codomain(codomain(b)))))),domain(codomain(b))) != domain(codomain(b))
| codomain(b) = domain(codomain(b)) ),
inference(resolve,[$cnf( $equal(compose(codomain(codomain(codomain(codomain(codomain(codomain(b)))))),domain(codomain(b))),codomain(b)) )],[refute_0_238,refute_0_239]) ).
cnf(refute_0_241,plain,
codomain(b) = domain(codomain(b)),
inference(resolve,[$cnf( $equal(compose(codomain(codomain(codomain(codomain(codomain(codomain(b)))))),domain(codomain(b))),domain(codomain(b))) )],[refute_0_186,refute_0_240]) ).
cnf(refute_0_242,plain,
( codomain(b) != domain(codomain(b))
| domain(codomain(b)) = codomain(b) ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(codomain(b))),bind(Y0,$fot(domain(codomain(b))))]]) ).
cnf(refute_0_243,plain,
domain(codomain(b)) = codomain(b),
inference(resolve,[$cnf( $equal(codomain(b),domain(codomain(b))) )],[refute_0_241,refute_0_242]) ).
cnf(refute_0_244,plain,
domain(domain(a)) = domain(domain(a)),
introduced(tautology,[refl,[$fot(domain(domain(a)))]]) ).
cnf(refute_0_245,plain,
( domain(a) != codomain(b)
| domain(domain(a)) != domain(domain(a))
| domain(domain(a)) = domain(codomain(b)) ),
introduced(tautology,[equality,[$cnf( $equal(domain(domain(a)),domain(domain(a))) ),[1,0],$fot(codomain(b))]]) ).
cnf(refute_0_246,plain,
( domain(a) != codomain(b)
| domain(domain(a)) = domain(codomain(b)) ),
inference(resolve,[$cnf( $equal(domain(domain(a)),domain(domain(a))) )],[refute_0_244,refute_0_245]) ).
cnf(refute_0_247,plain,
domain(domain(a)) = domain(codomain(b)),
inference(resolve,[$cnf( $equal(domain(a),codomain(b)) )],[refute_0_159,refute_0_246]) ).
cnf(refute_0_248,plain,
( domain(codomain(b)) != codomain(b)
| domain(domain(a)) != domain(codomain(b))
| domain(domain(a)) = codomain(b) ),
inference(subst,[],[refute_0_207:[bind(X0,$fot(domain(domain(a)))),bind(Y0,$fot(domain(codomain(b)))),bind(Z0,$fot(codomain(b)))]]) ).
cnf(refute_0_249,plain,
( domain(codomain(b)) != codomain(b)
| domain(domain(a)) = codomain(b) ),
inference(resolve,[$cnf( $equal(domain(domain(a)),domain(codomain(b))) )],[refute_0_247,refute_0_248]) ).
cnf(refute_0_250,plain,
domain(domain(a)) = codomain(b),
inference(resolve,[$cnf( $equal(domain(codomain(b)),codomain(b)) )],[refute_0_243,refute_0_249]) ).
cnf(refute_0_251,plain,
compose(domain(domain(a)),X_18) = compose(domain(domain(a)),X_18),
introduced(tautology,[refl,[$fot(compose(domain(domain(a)),X_18))]]) ).
cnf(refute_0_252,plain,
( compose(domain(domain(a)),X_18) != compose(domain(domain(a)),X_18)
| domain(domain(a)) != codomain(b)
| compose(domain(domain(a)),X_18) = compose(codomain(b),X_18) ),
introduced(tautology,[equality,[$cnf( $equal(compose(domain(domain(a)),X_18),compose(domain(domain(a)),X_18)) ),[1,0],$fot(codomain(b))]]) ).
cnf(refute_0_253,plain,
( domain(domain(a)) != codomain(b)
| compose(domain(domain(a)),X_18) = compose(codomain(b),X_18) ),
inference(resolve,[$cnf( $equal(compose(domain(domain(a)),X_18),compose(domain(domain(a)),X_18)) )],[refute_0_251,refute_0_252]) ).
cnf(refute_0_254,plain,
compose(domain(domain(a)),X_18) = compose(codomain(b),X_18),
inference(resolve,[$cnf( $equal(domain(domain(a)),codomain(b)) )],[refute_0_250,refute_0_253]) ).
cnf(refute_0_255,plain,
( X_63 != compose(domain(domain(a)),X_18)
| compose(domain(domain(a)),X_18) != compose(codomain(b),X_18)
| X_63 = compose(codomain(b),X_18) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_63,compose(codomain(b),X_18)) ),[0],$fot(compose(domain(domain(a)),X_18))]]) ).
cnf(refute_0_256,plain,
( X_63 != compose(domain(domain(a)),X_18)
| X_63 = compose(codomain(b),X_18) ),
inference(resolve,[$cnf( $equal(compose(domain(domain(a)),X_18),compose(codomain(b),X_18)) )],[refute_0_254,refute_0_255]) ).
cnf(refute_0_257,plain,
( compose(a,X_18) != compose(a,X_63)
| X_63 = compose(codomain(b),X_18) ),
inference(resolve,[$cnf( $equal(X_63,compose(domain(domain(a)),X_18)) )],[refute_0_112,refute_0_256]) ).
cnf(refute_0_258,plain,
( compose(a,X_63) != compose(a,X_63)
| X_63 = compose(codomain(b),X_63) ),
inference(subst,[],[refute_0_257:[bind(X_18,$fot(X_63))]]) ).
cnf(refute_0_259,plain,
X_63 = compose(codomain(b),X_63),
inference(resolve,[$cnf( $equal(compose(a,X_63),compose(a,X_63)) )],[refute_0_35,refute_0_258]) ).
cnf(refute_0_260,plain,
Y = compose(codomain(b),Y),
inference(subst,[],[refute_0_259:[bind(X_63,$fot(Y))]]) ).
cnf(refute_0_261,plain,
( Y != compose(codomain(b),Y)
| compose(codomain(b),Y) = Y ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(Y)),bind(Y0,$fot(compose(codomain(b),Y)))]]) ).
cnf(refute_0_262,plain,
compose(codomain(b),Y) = Y,
inference(resolve,[$cnf( $equal(Y,compose(codomain(b),Y)) )],[refute_0_260,refute_0_261]) ).
cnf(refute_0_263,plain,
( compose(codomain(b),Y) != Y
| ~ there_exists(Y)
| there_exists(compose(codomain(b),Y)) ),
introduced(tautology,[equality,[$cnf( ~ there_exists(compose(codomain(b),Y)) ),[0],$fot(Y)]]) ).
cnf(refute_0_264,plain,
( ~ there_exists(Y)
| there_exists(compose(codomain(b),Y)) ),
inference(resolve,[$cnf( $equal(compose(codomain(b),Y),Y) )],[refute_0_262,refute_0_263]) ).
cnf(refute_0_265,plain,
( ~ there_exists(Y)
| domain(codomain(b)) = codomain(Y) ),
inference(resolve,[$cnf( there_exists(compose(codomain(b),Y)) )],[refute_0_264,refute_0_105]) ).
cnf(refute_0_266,plain,
( domain(codomain(b)) != codomain(Y)
| domain(codomain(b)) != codomain(b)
| codomain(b) = codomain(Y) ),
introduced(tautology,[equality,[$cnf( $equal(domain(codomain(b)),codomain(Y)) ),[0],$fot(codomain(b))]]) ).
cnf(refute_0_267,plain,
( domain(codomain(b)) != codomain(Y)
| codomain(b) = codomain(Y) ),
inference(resolve,[$cnf( $equal(domain(codomain(b)),codomain(b)) )],[refute_0_243,refute_0_266]) ).
cnf(refute_0_268,plain,
( ~ there_exists(Y)
| codomain(b) = codomain(Y) ),
inference(resolve,[$cnf( $equal(domain(codomain(b)),codomain(Y)) )],[refute_0_265,refute_0_267]) ).
cnf(refute_0_269,plain,
( ~ there_exists(domain(h))
| codomain(b) = codomain(domain(h)) ),
inference(subst,[],[refute_0_268:[bind(Y,$fot(domain(h)))]]) ).
cnf(refute_0_270,plain,
codomain(b) = codomain(domain(h)),
inference(resolve,[$cnf( there_exists(domain(h)) )],[refute_0_104,refute_0_269]) ).
cnf(refute_0_271,plain,
( ~ there_exists(a)
| codomain(b) = codomain(a) ),
inference(subst,[],[refute_0_268:[bind(Y,$fot(a))]]) ).
cnf(refute_0_272,plain,
codomain(b) = codomain(a),
inference(resolve,[$cnf( there_exists(a) )],[refute_0_180,refute_0_271]) ).
cnf(refute_0_273,plain,
( codomain(b) != codomain(a)
| codomain(b) != codomain(domain(h))
| codomain(a) = codomain(domain(h)) ),
introduced(tautology,[equality,[$cnf( $equal(codomain(b),codomain(domain(h))) ),[0],$fot(codomain(a))]]) ).
cnf(refute_0_274,plain,
( codomain(b) != codomain(domain(h))
| codomain(a) = codomain(domain(h)) ),
inference(resolve,[$cnf( $equal(codomain(b),codomain(a)) )],[refute_0_272,refute_0_273]) ).
cnf(refute_0_275,plain,
( ~ there_exists(compose(X_27,domain(X_27)))
| domain(X_27) = codomain(domain(X_27)) ),
inference(subst,[],[domain_codomain_composition1:[bind(X,$fot(X_27)),bind(Y,$fot(domain(X_27)))]]) ).
cnf(refute_0_276,plain,
compose(X_27,domain(X_27)) = X_27,
inference(subst,[],[compose_domain:[bind(X,$fot(X_27))]]) ).
cnf(refute_0_277,plain,
( compose(X_27,domain(X_27)) != X_27
| ~ there_exists(X_27)
| there_exists(compose(X_27,domain(X_27))) ),
introduced(tautology,[equality,[$cnf( ~ there_exists(compose(X_27,domain(X_27))) ),[0],$fot(X_27)]]) ).
cnf(refute_0_278,plain,
( ~ there_exists(X_27)
| there_exists(compose(X_27,domain(X_27))) ),
inference(resolve,[$cnf( $equal(compose(X_27,domain(X_27)),X_27) )],[refute_0_276,refute_0_277]) ).
cnf(refute_0_279,plain,
( ~ there_exists(X_27)
| domain(X_27) = codomain(domain(X_27)) ),
inference(resolve,[$cnf( there_exists(compose(X_27,domain(X_27))) )],[refute_0_278,refute_0_275]) ).
cnf(refute_0_280,plain,
( ~ there_exists(h)
| domain(h) = codomain(domain(h)) ),
inference(subst,[],[refute_0_279:[bind(X_27,$fot(h))]]) ).
cnf(refute_0_281,plain,
domain(h) = codomain(domain(h)),
inference(resolve,[$cnf( there_exists(h) )],[assume_h_exists,refute_0_280]) ).
cnf(refute_0_282,plain,
( domain(h) != codomain(domain(h))
| codomain(domain(h)) = domain(h) ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(domain(h))),bind(Y0,$fot(codomain(domain(h))))]]) ).
cnf(refute_0_283,plain,
codomain(domain(h)) = domain(h),
inference(resolve,[$cnf( $equal(domain(h),codomain(domain(h))) )],[refute_0_281,refute_0_282]) ).
cnf(refute_0_284,plain,
( codomain(a) != codomain(domain(h))
| codomain(domain(h)) != domain(h)
| codomain(a) = domain(h) ),
introduced(tautology,[equality,[$cnf( ~ $equal(codomain(a),domain(h)) ),[0],$fot(codomain(domain(h)))]]) ).
cnf(refute_0_285,plain,
( codomain(a) != codomain(domain(h))
| codomain(a) = domain(h) ),
inference(resolve,[$cnf( $equal(codomain(domain(h)),domain(h)) )],[refute_0_283,refute_0_284]) ).
cnf(refute_0_286,plain,
( codomain(b) != codomain(domain(h))
| codomain(a) = domain(h) ),
inference(resolve,[$cnf( $equal(codomain(a),codomain(domain(h))) )],[refute_0_274,refute_0_285]) ).
cnf(refute_0_287,plain,
codomain(a) = domain(h),
inference(resolve,[$cnf( $equal(codomain(b),codomain(domain(h))) )],[refute_0_270,refute_0_286]) ).
cnf(refute_0_288,plain,
( codomain(a) != domain(h)
| domain(h) = codomain(a) ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(codomain(a))),bind(Y0,$fot(domain(h)))]]) ).
cnf(refute_0_289,plain,
domain(h) = codomain(a),
inference(resolve,[$cnf( $equal(codomain(a),domain(h)) )],[refute_0_287,refute_0_288]) ).
cnf(refute_0_290,plain,
( compose(h,domain(compose(a,domain(domain(domain(domain(h))))))) != h
| domain(h) != codomain(a)
| compose(h,domain(compose(a,domain(domain(domain(codomain(a))))))) = h ),
introduced(tautology,[equality,[$cnf( $equal(compose(h,domain(compose(a,domain(domain(domain(domain(h))))))),h) ),[0,1,0,1,0,0,0],$fot(codomain(a))]]) ).
cnf(refute_0_291,plain,
( compose(h,domain(compose(a,domain(domain(domain(domain(h))))))) != h
| compose(h,domain(compose(a,domain(domain(domain(codomain(a))))))) = h ),
inference(resolve,[$cnf( $equal(domain(h),codomain(a)) )],[refute_0_289,refute_0_290]) ).
cnf(refute_0_292,plain,
compose(h,domain(compose(a,domain(domain(domain(codomain(a))))))) = h,
inference(resolve,[$cnf( $equal(compose(h,domain(compose(a,domain(domain(domain(domain(h))))))),h) )],[refute_0_65,refute_0_291]) ).
cnf(refute_0_293,plain,
( codomain(b) != codomain(a)
| domain(a) != codomain(b)
| domain(a) = codomain(a) ),
introduced(tautology,[equality,[$cnf( $equal(domain(a),codomain(b)) ),[1],$fot(codomain(a))]]) ).
cnf(refute_0_294,plain,
( domain(a) != codomain(b)
| domain(a) = codomain(a) ),
inference(resolve,[$cnf( $equal(codomain(b),codomain(a)) )],[refute_0_272,refute_0_293]) ).
cnf(refute_0_295,plain,
domain(a) = codomain(a),
inference(resolve,[$cnf( $equal(domain(a),codomain(b)) )],[refute_0_159,refute_0_294]) ).
cnf(refute_0_296,plain,
compose(a,codomain(b)) = compose(a,codomain(b)),
introduced(tautology,[refl,[$fot(compose(a,codomain(b)))]]) ).
cnf(refute_0_297,plain,
( codomain(b) != codomain(a)
| compose(a,codomain(b)) != compose(a,codomain(b))
| compose(a,codomain(b)) = compose(a,codomain(a)) ),
introduced(tautology,[equality,[$cnf( $equal(compose(a,codomain(b)),compose(a,codomain(b))) ),[1,1],$fot(codomain(a))]]) ).
cnf(refute_0_298,plain,
( codomain(b) != codomain(a)
| compose(a,codomain(b)) = compose(a,codomain(a)) ),
inference(resolve,[$cnf( $equal(compose(a,codomain(b)),compose(a,codomain(b))) )],[refute_0_296,refute_0_297]) ).
cnf(refute_0_299,plain,
compose(a,codomain(b)) = compose(a,codomain(a)),
inference(resolve,[$cnf( $equal(codomain(b),codomain(a)) )],[refute_0_272,refute_0_298]) ).
cnf(refute_0_300,plain,
( compose(a,codomain(b)) != a
| compose(a,codomain(b)) != compose(a,codomain(a))
| compose(a,codomain(a)) = a ),
introduced(tautology,[equality,[$cnf( $equal(compose(a,codomain(b)),a) ),[0],$fot(compose(a,codomain(a)))]]) ).
cnf(refute_0_301,plain,
( compose(a,codomain(b)) != a
| compose(a,codomain(a)) = a ),
inference(resolve,[$cnf( $equal(compose(a,codomain(b)),compose(a,codomain(a))) )],[refute_0_299,refute_0_300]) ).
cnf(refute_0_302,plain,
compose(a,codomain(a)) = a,
inference(resolve,[$cnf( $equal(compose(a,codomain(b)),a) )],[refute_0_192,refute_0_301]) ).
cnf(refute_0_303,plain,
( ~ there_exists(compose(codomain(X_28),X_28))
| domain(codomain(X_28)) = codomain(X_28) ),
inference(subst,[],[domain_codomain_composition1:[bind(X,$fot(codomain(X_28))),bind(Y,$fot(X_28))]]) ).
cnf(refute_0_304,plain,
compose(codomain(X_28),X_28) = X_28,
inference(subst,[],[compose_codomain:[bind(X,$fot(X_28))]]) ).
cnf(refute_0_305,plain,
( compose(codomain(X_28),X_28) != X_28
| ~ there_exists(X_28)
| there_exists(compose(codomain(X_28),X_28)) ),
introduced(tautology,[equality,[$cnf( ~ there_exists(compose(codomain(X_28),X_28)) ),[0],$fot(X_28)]]) ).
cnf(refute_0_306,plain,
( ~ there_exists(X_28)
| there_exists(compose(codomain(X_28),X_28)) ),
inference(resolve,[$cnf( $equal(compose(codomain(X_28),X_28),X_28) )],[refute_0_304,refute_0_305]) ).
cnf(refute_0_307,plain,
( ~ there_exists(X_28)
| domain(codomain(X_28)) = codomain(X_28) ),
inference(resolve,[$cnf( there_exists(compose(codomain(X_28),X_28)) )],[refute_0_306,refute_0_303]) ).
cnf(refute_0_308,plain,
( ~ there_exists(a)
| domain(codomain(a)) = codomain(a) ),
inference(subst,[],[refute_0_307:[bind(X_28,$fot(a))]]) ).
cnf(refute_0_309,plain,
domain(codomain(a)) = codomain(a),
inference(resolve,[$cnf( there_exists(a) )],[refute_0_180,refute_0_308]) ).
cnf(refute_0_310,plain,
domain(domain(codomain(a))) = domain(domain(codomain(a))),
introduced(tautology,[refl,[$fot(domain(domain(codomain(a))))]]) ).
cnf(refute_0_311,plain,
( domain(codomain(a)) != codomain(a)
| domain(domain(codomain(a))) != domain(domain(codomain(a)))
| domain(domain(codomain(a))) = domain(codomain(a)) ),
introduced(tautology,[equality,[$cnf( $equal(domain(domain(codomain(a))),domain(domain(codomain(a)))) ),[1,0],$fot(codomain(a))]]) ).
cnf(refute_0_312,plain,
( domain(codomain(a)) != codomain(a)
| domain(domain(codomain(a))) = domain(codomain(a)) ),
inference(resolve,[$cnf( $equal(domain(domain(codomain(a))),domain(domain(codomain(a)))) )],[refute_0_310,refute_0_311]) ).
cnf(refute_0_313,plain,
domain(domain(codomain(a))) = domain(codomain(a)),
inference(resolve,[$cnf( $equal(domain(codomain(a)),codomain(a)) )],[refute_0_309,refute_0_312]) ).
cnf(refute_0_314,plain,
( domain(codomain(a)) != codomain(a)
| domain(domain(codomain(a))) != domain(codomain(a))
| domain(domain(codomain(a))) = codomain(a) ),
inference(subst,[],[refute_0_207:[bind(X0,$fot(domain(domain(codomain(a))))),bind(Y0,$fot(domain(codomain(a)))),bind(Z0,$fot(codomain(a)))]]) ).
cnf(refute_0_315,plain,
( domain(codomain(a)) != codomain(a)
| domain(domain(codomain(a))) = codomain(a) ),
inference(resolve,[$cnf( $equal(domain(domain(codomain(a))),domain(codomain(a))) )],[refute_0_313,refute_0_314]) ).
cnf(refute_0_316,plain,
domain(domain(codomain(a))) = codomain(a),
inference(resolve,[$cnf( $equal(domain(codomain(a)),codomain(a)) )],[refute_0_309,refute_0_315]) ).
cnf(refute_0_317,plain,
domain(domain(domain(codomain(a)))) = domain(domain(domain(codomain(a)))),
introduced(tautology,[refl,[$fot(domain(domain(domain(codomain(a)))))]]) ).
cnf(refute_0_318,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_319,plain,
( domain(domain(codomain(a))) != codomain(a)
| domain(domain(domain(codomain(a)))) = domain(codomain(a)) ),
inference(resolve,[$cnf( $equal(domain(domain(domain(codomain(a)))),domain(domain(domain(codomain(a))))) )],[refute_0_317,refute_0_318]) ).
cnf(refute_0_320,plain,
domain(domain(domain(codomain(a)))) = domain(codomain(a)),
inference(resolve,[$cnf( $equal(domain(domain(codomain(a))),codomain(a)) )],[refute_0_316,refute_0_319]) ).
cnf(refute_0_321,plain,
( domain(codomain(a)) != codomain(a)
| domain(domain(domain(codomain(a)))) != domain(codomain(a))
| domain(domain(domain(codomain(a)))) = codomain(a) ),
inference(subst,[],[refute_0_207:[bind(X0,$fot(domain(domain(domain(codomain(a)))))),bind(Y0,$fot(domain(codomain(a)))),bind(Z0,$fot(codomain(a)))]]) ).
cnf(refute_0_322,plain,
( domain(codomain(a)) != codomain(a)
| domain(domain(domain(codomain(a)))) = codomain(a) ),
inference(resolve,[$cnf( $equal(domain(domain(domain(codomain(a)))),domain(codomain(a))) )],[refute_0_320,refute_0_321]) ).
cnf(refute_0_323,plain,
domain(domain(domain(codomain(a)))) = codomain(a),
inference(resolve,[$cnf( $equal(domain(codomain(a)),codomain(a)) )],[refute_0_309,refute_0_322]) ).
cnf(refute_0_324,plain,
compose(a,domain(domain(domain(codomain(a))))) = compose(a,domain(domain(domain(codomain(a))))),
introduced(tautology,[refl,[$fot(compose(a,domain(domain(domain(codomain(a))))))]]) ).
cnf(refute_0_325,plain,
( compose(a,domain(domain(domain(codomain(a))))) != compose(a,domain(domain(domain(codomain(a)))))
| domain(domain(domain(codomain(a)))) != codomain(a)
| compose(a,domain(domain(domain(codomain(a))))) = compose(a,codomain(a)) ),
introduced(tautology,[equality,[$cnf( $equal(compose(a,domain(domain(domain(codomain(a))))),compose(a,domain(domain(domain(codomain(a)))))) ),[1,1],$fot(codomain(a))]]) ).
cnf(refute_0_326,plain,
( domain(domain(domain(codomain(a)))) != codomain(a)
| compose(a,domain(domain(domain(codomain(a))))) = compose(a,codomain(a)) ),
inference(resolve,[$cnf( $equal(compose(a,domain(domain(domain(codomain(a))))),compose(a,domain(domain(domain(codomain(a)))))) )],[refute_0_324,refute_0_325]) ).
cnf(refute_0_327,plain,
compose(a,domain(domain(domain(codomain(a))))) = compose(a,codomain(a)),
inference(resolve,[$cnf( $equal(domain(domain(domain(codomain(a)))),codomain(a)) )],[refute_0_323,refute_0_326]) ).
cnf(refute_0_328,plain,
( compose(a,codomain(a)) != a
| compose(a,domain(domain(domain(codomain(a))))) != compose(a,codomain(a))
| compose(a,domain(domain(domain(codomain(a))))) = a ),
inference(subst,[],[refute_0_207:[bind(X0,$fot(compose(a,domain(domain(domain(codomain(a))))))),bind(Y0,$fot(compose(a,codomain(a)))),bind(Z0,$fot(a))]]) ).
cnf(refute_0_329,plain,
( compose(a,codomain(a)) != a
| compose(a,domain(domain(domain(codomain(a))))) = a ),
inference(resolve,[$cnf( $equal(compose(a,domain(domain(domain(codomain(a))))),compose(a,codomain(a))) )],[refute_0_327,refute_0_328]) ).
cnf(refute_0_330,plain,
compose(a,domain(domain(domain(codomain(a))))) = a,
inference(resolve,[$cnf( $equal(compose(a,codomain(a)),a) )],[refute_0_302,refute_0_329]) ).
cnf(refute_0_331,plain,
domain(compose(a,domain(domain(domain(codomain(a)))))) = domain(compose(a,domain(domain(domain(codomain(a)))))),
introduced(tautology,[refl,[$fot(domain(compose(a,domain(domain(domain(codomain(a)))))))]]) ).
cnf(refute_0_332,plain,
( compose(a,domain(domain(domain(codomain(a))))) != a
| domain(compose(a,domain(domain(domain(codomain(a)))))) != domain(compose(a,domain(domain(domain(codomain(a))))))
| domain(compose(a,domain(domain(domain(codomain(a)))))) = domain(a) ),
introduced(tautology,[equality,[$cnf( $equal(domain(compose(a,domain(domain(domain(codomain(a)))))),domain(compose(a,domain(domain(domain(codomain(a))))))) ),[1,0],$fot(a)]]) ).
cnf(refute_0_333,plain,
( compose(a,domain(domain(domain(codomain(a))))) != a
| domain(compose(a,domain(domain(domain(codomain(a)))))) = domain(a) ),
inference(resolve,[$cnf( $equal(domain(compose(a,domain(domain(domain(codomain(a)))))),domain(compose(a,domain(domain(domain(codomain(a))))))) )],[refute_0_331,refute_0_332]) ).
cnf(refute_0_334,plain,
domain(compose(a,domain(domain(domain(codomain(a)))))) = domain(a),
inference(resolve,[$cnf( $equal(compose(a,domain(domain(domain(codomain(a))))),a) )],[refute_0_330,refute_0_333]) ).
cnf(refute_0_335,plain,
( domain(a) != codomain(a)
| domain(compose(a,domain(domain(domain(codomain(a)))))) != domain(a)
| domain(compose(a,domain(domain(domain(codomain(a)))))) = codomain(a) ),
inference(subst,[],[refute_0_207:[bind(X0,$fot(domain(compose(a,domain(domain(domain(codomain(a)))))))),bind(Y0,$fot(domain(a))),bind(Z0,$fot(codomain(a)))]]) ).
cnf(refute_0_336,plain,
( domain(a) != codomain(a)
| domain(compose(a,domain(domain(domain(codomain(a)))))) = codomain(a) ),
inference(resolve,[$cnf( $equal(domain(compose(a,domain(domain(domain(codomain(a)))))),domain(a)) )],[refute_0_334,refute_0_335]) ).
cnf(refute_0_337,plain,
domain(compose(a,domain(domain(domain(codomain(a)))))) = codomain(a),
inference(resolve,[$cnf( $equal(domain(a),codomain(a)) )],[refute_0_295,refute_0_336]) ).
cnf(refute_0_338,plain,
compose(h,domain(compose(a,domain(domain(domain(codomain(a))))))) = compose(h,domain(compose(a,domain(domain(domain(codomain(a))))))),
introduced(tautology,[refl,[$fot(compose(h,domain(compose(a,domain(domain(domain(codomain(a))))))))]]) ).
cnf(refute_0_339,plain,
( compose(h,domain(compose(a,domain(domain(domain(codomain(a))))))) != compose(h,domain(compose(a,domain(domain(domain(codomain(a)))))))
| domain(compose(a,domain(domain(domain(codomain(a)))))) != codomain(a)
| compose(h,domain(compose(a,domain(domain(domain(codomain(a))))))) = compose(h,codomain(a)) ),
introduced(tautology,[equality,[$cnf( $equal(compose(h,domain(compose(a,domain(domain(domain(codomain(a))))))),compose(h,domain(compose(a,domain(domain(domain(codomain(a)))))))) ),[1,1],$fot(codomain(a))]]) ).
cnf(refute_0_340,plain,
( domain(compose(a,domain(domain(domain(codomain(a)))))) != codomain(a)
| compose(h,domain(compose(a,domain(domain(domain(codomain(a))))))) = compose(h,codomain(a)) ),
inference(resolve,[$cnf( $equal(compose(h,domain(compose(a,domain(domain(domain(codomain(a))))))),compose(h,domain(compose(a,domain(domain(domain(codomain(a)))))))) )],[refute_0_338,refute_0_339]) ).
cnf(refute_0_341,plain,
compose(h,domain(compose(a,domain(domain(domain(codomain(a))))))) = compose(h,codomain(a)),
inference(resolve,[$cnf( $equal(domain(compose(a,domain(domain(domain(codomain(a)))))),codomain(a)) )],[refute_0_337,refute_0_340]) ).
cnf(refute_0_342,plain,
( compose(h,domain(compose(a,domain(domain(domain(codomain(a))))))) != compose(h,codomain(a))
| compose(h,domain(compose(a,domain(domain(domain(codomain(a))))))) != h
| compose(h,codomain(a)) = h ),
introduced(tautology,[equality,[$cnf( $equal(compose(h,domain(compose(a,domain(domain(domain(codomain(a))))))),h) ),[0],$fot(compose(h,codomain(a)))]]) ).
cnf(refute_0_343,plain,
( compose(h,domain(compose(a,domain(domain(domain(codomain(a))))))) != h
| compose(h,codomain(a)) = h ),
inference(resolve,[$cnf( $equal(compose(h,domain(compose(a,domain(domain(domain(codomain(a))))))),compose(h,codomain(a))) )],[refute_0_341,refute_0_342]) ).
cnf(refute_0_344,plain,
compose(h,codomain(a)) = h,
inference(resolve,[$cnf( $equal(compose(h,domain(compose(a,domain(domain(domain(codomain(a))))))),h) )],[refute_0_292,refute_0_343]) ).
cnf(refute_0_345,plain,
( compose(b,X) != compose(b,X)
| compose(b,Z) != compose(b,X)
| X = Z ),
inference(subst,[],[cancellation_for_compose2:[bind(Y,$fot(compose(b,X)))]]) ).
cnf(refute_0_346,plain,
compose(b,X) = compose(b,X),
introduced(tautology,[refl,[$fot(compose(b,X))]]) ).
cnf(refute_0_347,plain,
( compose(b,Z) != compose(b,X)
| X = Z ),
inference(resolve,[$cnf( $equal(compose(b,X),compose(b,X)) )],[refute_0_346,refute_0_345]) ).
cnf(refute_0_348,plain,
( compose(b,compose(g,codomain(a))) != compose(b,X_83)
| X_83 = compose(g,codomain(a)) ),
inference(subst,[],[refute_0_347:[bind(X,$fot(X_83)),bind(Z,$fot(compose(g,codomain(a))))]]) ).
cnf(refute_0_349,plain,
( compose(a,compose(b,compose(g,domain(compose(domain(b),h))))) != compose(a,X_63)
| X_63 = compose(b,compose(g,domain(compose(domain(b),h)))) ),
inference(subst,[],[refute_0_18:[bind(X,$fot(X_63)),bind(Z,$fot(compose(b,compose(g,domain(compose(domain(b),h))))))]]) ).
cnf(refute_0_350,plain,
compose(a,compose(compose(b,h),X_11)) = compose(compose(a,compose(b,h)),X_11),
inference(subst,[],[associativity_of_compose:[bind(X,$fot(a)),bind(Y,$fot(compose(b,h))),bind(Z,$fot(X_11))]]) ).
cnf(refute_0_351,plain,
( compose(X,compose(Y,Z)) != compose(compose(X,Y),Z)
| compose(compose(X,Y),Z) = compose(X,compose(Y,Z)) ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(compose(X,compose(Y,Z)))),bind(Y0,$fot(compose(compose(X,Y),Z)))]]) ).
cnf(refute_0_352,plain,
compose(compose(X,Y),Z) = compose(X,compose(Y,Z)),
inference(resolve,[$cnf( $equal(compose(X,compose(Y,Z)),compose(compose(X,Y),Z)) )],[associativity_of_compose,refute_0_351]) ).
cnf(refute_0_353,plain,
compose(compose(a,b),h) = compose(a,compose(b,h)),
inference(subst,[],[refute_0_352:[bind(X,$fot(a)),bind(Y,$fot(b)),bind(Z,$fot(h))]]) ).
cnf(refute_0_354,plain,
( compose(compose(a,b),h) != compose(a,compose(b,h))
| compose(compose(a,b),h) != compose(compose(a,b),g)
| compose(a,compose(b,h)) = compose(compose(a,b),g) ),
introduced(tautology,[equality,[$cnf( $equal(compose(compose(a,b),h),compose(compose(a,b),g)) ),[0],$fot(compose(a,compose(b,h)))]]) ).
cnf(refute_0_355,plain,
( compose(compose(a,b),h) != compose(compose(a,b),g)
| compose(a,compose(b,h)) = compose(compose(a,b),g) ),
inference(resolve,[$cnf( $equal(compose(compose(a,b),h),compose(a,compose(b,h))) )],[refute_0_353,refute_0_354]) ).
cnf(refute_0_356,plain,
compose(compose(a,b),g) = compose(a,compose(b,g)),
inference(subst,[],[refute_0_352:[bind(X,$fot(a)),bind(Y,$fot(b)),bind(Z,$fot(g))]]) ).
cnf(refute_0_357,plain,
( compose(a,compose(b,h)) != compose(compose(a,b),g)
| compose(compose(a,b),g) != compose(a,compose(b,g))
| compose(a,compose(b,h)) = compose(a,compose(b,g)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(compose(a,compose(b,h)),compose(a,compose(b,g))) ),[0],$fot(compose(compose(a,b),g))]]) ).
cnf(refute_0_358,plain,
( compose(a,compose(b,h)) != compose(compose(a,b),g)
| compose(a,compose(b,h)) = compose(a,compose(b,g)) ),
inference(resolve,[$cnf( $equal(compose(compose(a,b),g),compose(a,compose(b,g))) )],[refute_0_356,refute_0_357]) ).
cnf(refute_0_359,plain,
( compose(compose(a,b),h) != compose(compose(a,b),g)
| compose(a,compose(b,h)) = compose(a,compose(b,g)) ),
inference(resolve,[$cnf( $equal(compose(a,compose(b,h)),compose(compose(a,b),g)) )],[refute_0_355,refute_0_358]) ).
cnf(refute_0_360,plain,
compose(a,compose(b,h)) = compose(a,compose(b,g)),
inference(resolve,[$cnf( $equal(compose(compose(a,b),h),compose(compose(a,b),g)) )],[ab_h_equals_ab_g,refute_0_359]) ).
cnf(refute_0_361,plain,
( compose(a,compose(b,h)) != compose(a,compose(b,g))
| compose(a,compose(compose(b,h),X_11)) != compose(compose(a,compose(b,h)),X_11)
| compose(a,compose(compose(b,h),X_11)) = compose(compose(a,compose(b,g)),X_11) ),
introduced(tautology,[equality,[$cnf( $equal(compose(a,compose(compose(b,h),X_11)),compose(compose(a,compose(b,h)),X_11)) ),[1,0],$fot(compose(a,compose(b,g)))]]) ).
cnf(refute_0_362,plain,
( compose(a,compose(compose(b,h),X_11)) != compose(compose(a,compose(b,h)),X_11)
| compose(a,compose(compose(b,h),X_11)) = compose(compose(a,compose(b,g)),X_11) ),
inference(resolve,[$cnf( $equal(compose(a,compose(b,h)),compose(a,compose(b,g))) )],[refute_0_360,refute_0_361]) ).
cnf(refute_0_363,plain,
compose(a,compose(compose(b,h),X_11)) = compose(compose(a,compose(b,g)),X_11),
inference(resolve,[$cnf( $equal(compose(a,compose(compose(b,h),X_11)),compose(compose(a,compose(b,h)),X_11)) )],[refute_0_350,refute_0_362]) ).
cnf(refute_0_364,plain,
compose(compose(b,h),X_11) = compose(b,compose(h,X_11)),
inference(subst,[],[refute_0_352:[bind(X,$fot(b)),bind(Y,$fot(h)),bind(Z,$fot(X_11))]]) ).
cnf(refute_0_365,plain,
compose(a,compose(compose(b,h),X_11)) = compose(a,compose(compose(b,h),X_11)),
introduced(tautology,[refl,[$fot(compose(a,compose(compose(b,h),X_11)))]]) ).
cnf(refute_0_366,plain,
( compose(a,compose(compose(b,h),X_11)) != compose(a,compose(compose(b,h),X_11))
| compose(compose(b,h),X_11) != compose(b,compose(h,X_11))
| compose(a,compose(compose(b,h),X_11)) = compose(a,compose(b,compose(h,X_11))) ),
introduced(tautology,[equality,[$cnf( $equal(compose(a,compose(compose(b,h),X_11)),compose(a,compose(compose(b,h),X_11))) ),[1,1],$fot(compose(b,compose(h,X_11)))]]) ).
cnf(refute_0_367,plain,
( compose(compose(b,h),X_11) != compose(b,compose(h,X_11))
| compose(a,compose(compose(b,h),X_11)) = compose(a,compose(b,compose(h,X_11))) ),
inference(resolve,[$cnf( $equal(compose(a,compose(compose(b,h),X_11)),compose(a,compose(compose(b,h),X_11))) )],[refute_0_365,refute_0_366]) ).
cnf(refute_0_368,plain,
compose(a,compose(compose(b,h),X_11)) = compose(a,compose(b,compose(h,X_11))),
inference(resolve,[$cnf( $equal(compose(compose(b,h),X_11),compose(b,compose(h,X_11))) )],[refute_0_364,refute_0_367]) ).
cnf(refute_0_369,plain,
( compose(a,compose(compose(b,h),X_11)) != compose(a,compose(b,compose(h,X_11)))
| compose(a,compose(compose(b,h),X_11)) != compose(compose(a,compose(b,g)),X_11)
| compose(a,compose(b,compose(h,X_11))) = compose(compose(a,compose(b,g)),X_11) ),
introduced(tautology,[equality,[$cnf( $equal(compose(a,compose(compose(b,h),X_11)),compose(compose(a,compose(b,g)),X_11)) ),[0],$fot(compose(a,compose(b,compose(h,X_11))))]]) ).
cnf(refute_0_370,plain,
( compose(a,compose(compose(b,h),X_11)) != compose(compose(a,compose(b,g)),X_11)
| compose(a,compose(b,compose(h,X_11))) = compose(compose(a,compose(b,g)),X_11) ),
inference(resolve,[$cnf( $equal(compose(a,compose(compose(b,h),X_11)),compose(a,compose(b,compose(h,X_11)))) )],[refute_0_368,refute_0_369]) ).
cnf(refute_0_371,plain,
compose(compose(b,g),X_11) = compose(b,compose(g,X_11)),
inference(subst,[],[refute_0_352:[bind(X,$fot(b)),bind(Y,$fot(g)),bind(Z,$fot(X_11))]]) ).
cnf(refute_0_372,plain,
compose(a,compose(compose(b,g),X_11)) = compose(a,compose(compose(b,g),X_11)),
introduced(tautology,[refl,[$fot(compose(a,compose(compose(b,g),X_11)))]]) ).
cnf(refute_0_373,plain,
( compose(a,compose(compose(b,g),X_11)) != compose(a,compose(compose(b,g),X_11))
| compose(compose(b,g),X_11) != compose(b,compose(g,X_11))
| compose(a,compose(compose(b,g),X_11)) = compose(a,compose(b,compose(g,X_11))) ),
introduced(tautology,[equality,[$cnf( $equal(compose(a,compose(compose(b,g),X_11)),compose(a,compose(compose(b,g),X_11))) ),[1,1],$fot(compose(b,compose(g,X_11)))]]) ).
cnf(refute_0_374,plain,
( compose(compose(b,g),X_11) != compose(b,compose(g,X_11))
| compose(a,compose(compose(b,g),X_11)) = compose(a,compose(b,compose(g,X_11))) ),
inference(resolve,[$cnf( $equal(compose(a,compose(compose(b,g),X_11)),compose(a,compose(compose(b,g),X_11))) )],[refute_0_372,refute_0_373]) ).
cnf(refute_0_375,plain,
compose(a,compose(compose(b,g),X_11)) = compose(a,compose(b,compose(g,X_11))),
inference(resolve,[$cnf( $equal(compose(compose(b,g),X_11),compose(b,compose(g,X_11))) )],[refute_0_371,refute_0_374]) ).
cnf(refute_0_376,plain,
compose(compose(a,compose(b,g)),X_11) = compose(a,compose(compose(b,g),X_11)),
inference(subst,[],[refute_0_352:[bind(X,$fot(a)),bind(Y,$fot(compose(b,g))),bind(Z,$fot(X_11))]]) ).
cnf(refute_0_377,plain,
( compose(a,compose(compose(b,g),X_11)) != compose(a,compose(b,compose(g,X_11)))
| compose(compose(a,compose(b,g)),X_11) != compose(a,compose(compose(b,g),X_11))
| compose(compose(a,compose(b,g)),X_11) = compose(a,compose(b,compose(g,X_11))) ),
inference(subst,[],[refute_0_207:[bind(X0,$fot(compose(compose(a,compose(b,g)),X_11))),bind(Y0,$fot(compose(a,compose(compose(b,g),X_11)))),bind(Z0,$fot(compose(a,compose(b,compose(g,X_11)))))]]) ).
cnf(refute_0_378,plain,
( compose(a,compose(compose(b,g),X_11)) != compose(a,compose(b,compose(g,X_11)))
| compose(compose(a,compose(b,g)),X_11) = compose(a,compose(b,compose(g,X_11))) ),
inference(resolve,[$cnf( $equal(compose(compose(a,compose(b,g)),X_11),compose(a,compose(compose(b,g),X_11))) )],[refute_0_376,refute_0_377]) ).
cnf(refute_0_379,plain,
compose(compose(a,compose(b,g)),X_11) = compose(a,compose(b,compose(g,X_11))),
inference(resolve,[$cnf( $equal(compose(a,compose(compose(b,g),X_11)),compose(a,compose(b,compose(g,X_11)))) )],[refute_0_375,refute_0_378]) ).
cnf(refute_0_380,plain,
( compose(a,compose(b,compose(h,X_11))) != compose(compose(a,compose(b,g)),X_11)
| compose(compose(a,compose(b,g)),X_11) != compose(a,compose(b,compose(g,X_11)))
| compose(a,compose(b,compose(h,X_11))) = compose(a,compose(b,compose(g,X_11))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(compose(a,compose(b,compose(h,X_11))),compose(a,compose(b,compose(g,X_11)))) ),[0],$fot(compose(compose(a,compose(b,g)),X_11))]]) ).
cnf(refute_0_381,plain,
( compose(a,compose(b,compose(h,X_11))) != compose(compose(a,compose(b,g)),X_11)
| compose(a,compose(b,compose(h,X_11))) = compose(a,compose(b,compose(g,X_11))) ),
inference(resolve,[$cnf( $equal(compose(compose(a,compose(b,g)),X_11),compose(a,compose(b,compose(g,X_11)))) )],[refute_0_379,refute_0_380]) ).
cnf(refute_0_382,plain,
( compose(a,compose(compose(b,h),X_11)) != compose(compose(a,compose(b,g)),X_11)
| compose(a,compose(b,compose(h,X_11))) = compose(a,compose(b,compose(g,X_11))) ),
inference(resolve,[$cnf( $equal(compose(a,compose(b,compose(h,X_11))),compose(compose(a,compose(b,g)),X_11)) )],[refute_0_370,refute_0_381]) ).
cnf(refute_0_383,plain,
compose(a,compose(b,compose(h,X_11))) = compose(a,compose(b,compose(g,X_11))),
inference(resolve,[$cnf( $equal(compose(a,compose(compose(b,h),X_11)),compose(compose(a,compose(b,g)),X_11)) )],[refute_0_363,refute_0_382]) ).
cnf(refute_0_384,plain,
compose(a,compose(b,compose(h,domain(compose(domain(b),h))))) = compose(a,compose(b,compose(g,domain(compose(domain(b),h))))),
inference(subst,[],[refute_0_383:[bind(X_11,$fot(domain(compose(domain(b),h))))]]) ).
cnf(refute_0_385,plain,
compose(X_9,compose(domain(X_9),compose(X_25,domain(compose(domain(X_9),X_25))))) = compose(X_9,compose(X_25,domain(compose(domain(X_9),X_25)))),
inference(subst,[],[refute_0_4:[bind(X_11,$fot(compose(X_25,domain(compose(domain(X_9),X_25)))))]]) ).
cnf(refute_0_386,plain,
compose(domain(X_9),compose(X_25,domain(compose(domain(X_9),X_25)))) = compose(domain(X_9),X_25),
inference(subst,[],[refute_0_29:[bind(X_10,$fot(X_25)),bind(X_9,$fot(domain(X_9)))]]) ).
cnf(refute_0_387,plain,
( compose(X_9,compose(domain(X_9),compose(X_25,domain(compose(domain(X_9),X_25))))) != compose(X_9,compose(X_25,domain(compose(domain(X_9),X_25))))
| compose(domain(X_9),compose(X_25,domain(compose(domain(X_9),X_25)))) != compose(domain(X_9),X_25)
| compose(X_9,compose(domain(X_9),X_25)) = compose(X_9,compose(X_25,domain(compose(domain(X_9),X_25)))) ),
introduced(tautology,[equality,[$cnf( $equal(compose(X_9,compose(domain(X_9),compose(X_25,domain(compose(domain(X_9),X_25))))),compose(X_9,compose(X_25,domain(compose(domain(X_9),X_25))))) ),[0,1],$fot(compose(domain(X_9),X_25))]]) ).
cnf(refute_0_388,plain,
( compose(X_9,compose(domain(X_9),compose(X_25,domain(compose(domain(X_9),X_25))))) != compose(X_9,compose(X_25,domain(compose(domain(X_9),X_25))))
| compose(X_9,compose(domain(X_9),X_25)) = compose(X_9,compose(X_25,domain(compose(domain(X_9),X_25)))) ),
inference(resolve,[$cnf( $equal(compose(domain(X_9),compose(X_25,domain(compose(domain(X_9),X_25)))),compose(domain(X_9),X_25)) )],[refute_0_386,refute_0_387]) ).
cnf(refute_0_389,plain,
compose(X_9,compose(domain(X_9),X_25)) = compose(X_9,compose(X_25,domain(compose(domain(X_9),X_25)))),
inference(resolve,[$cnf( $equal(compose(X_9,compose(domain(X_9),compose(X_25,domain(compose(domain(X_9),X_25))))),compose(X_9,compose(X_25,domain(compose(domain(X_9),X_25))))) )],[refute_0_385,refute_0_388]) ).
cnf(refute_0_390,plain,
compose(X_9,compose(domain(X_9),X_25)) = compose(X_9,X_25),
inference(subst,[],[refute_0_4:[bind(X_11,$fot(X_25))]]) ).
cnf(refute_0_391,plain,
( compose(X_9,compose(domain(X_9),X_25)) != compose(X_9,X_25)
| compose(X_9,compose(domain(X_9),X_25)) != compose(X_9,compose(X_25,domain(compose(domain(X_9),X_25))))
| compose(X_9,X_25) = compose(X_9,compose(X_25,domain(compose(domain(X_9),X_25)))) ),
introduced(tautology,[equality,[$cnf( $equal(compose(X_9,compose(domain(X_9),X_25)),compose(X_9,compose(X_25,domain(compose(domain(X_9),X_25))))) ),[0],$fot(compose(X_9,X_25))]]) ).
cnf(refute_0_392,plain,
( compose(X_9,compose(domain(X_9),X_25)) != compose(X_9,compose(X_25,domain(compose(domain(X_9),X_25))))
| compose(X_9,X_25) = compose(X_9,compose(X_25,domain(compose(domain(X_9),X_25)))) ),
inference(resolve,[$cnf( $equal(compose(X_9,compose(domain(X_9),X_25)),compose(X_9,X_25)) )],[refute_0_390,refute_0_391]) ).
cnf(refute_0_393,plain,
compose(X_9,X_25) = compose(X_9,compose(X_25,domain(compose(domain(X_9),X_25)))),
inference(resolve,[$cnf( $equal(compose(X_9,compose(domain(X_9),X_25)),compose(X_9,compose(X_25,domain(compose(domain(X_9),X_25))))) )],[refute_0_389,refute_0_392]) ).
cnf(refute_0_394,plain,
compose(b,h) = compose(b,compose(h,domain(compose(domain(b),h)))),
inference(subst,[],[refute_0_393:[bind(X_25,$fot(h)),bind(X_9,$fot(b))]]) ).
cnf(refute_0_395,plain,
( compose(b,h) != compose(b,compose(h,domain(compose(domain(b),h))))
| compose(b,compose(h,domain(compose(domain(b),h)))) = compose(b,h) ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(compose(b,h))),bind(Y0,$fot(compose(b,compose(h,domain(compose(domain(b),h))))))]]) ).
cnf(refute_0_396,plain,
compose(b,compose(h,domain(compose(domain(b),h)))) = compose(b,h),
inference(resolve,[$cnf( $equal(compose(b,h),compose(b,compose(h,domain(compose(domain(b),h))))) )],[refute_0_394,refute_0_395]) ).
cnf(refute_0_397,plain,
( compose(a,compose(b,compose(h,domain(compose(domain(b),h))))) != compose(a,compose(b,compose(g,domain(compose(domain(b),h)))))
| compose(b,compose(h,domain(compose(domain(b),h)))) != compose(b,h)
| compose(a,compose(b,h)) = compose(a,compose(b,compose(g,domain(compose(domain(b),h))))) ),
introduced(tautology,[equality,[$cnf( $equal(compose(a,compose(b,compose(h,domain(compose(domain(b),h))))),compose(a,compose(b,compose(g,domain(compose(domain(b),h)))))) ),[0,1],$fot(compose(b,h))]]) ).
cnf(refute_0_398,plain,
( compose(a,compose(b,compose(h,domain(compose(domain(b),h))))) != compose(a,compose(b,compose(g,domain(compose(domain(b),h)))))
| compose(a,compose(b,h)) = compose(a,compose(b,compose(g,domain(compose(domain(b),h))))) ),
inference(resolve,[$cnf( $equal(compose(b,compose(h,domain(compose(domain(b),h)))),compose(b,h)) )],[refute_0_396,refute_0_397]) ).
cnf(refute_0_399,plain,
compose(a,compose(b,h)) = compose(a,compose(b,compose(g,domain(compose(domain(b),h))))),
inference(resolve,[$cnf( $equal(compose(a,compose(b,compose(h,domain(compose(domain(b),h))))),compose(a,compose(b,compose(g,domain(compose(domain(b),h)))))) )],[refute_0_384,refute_0_398]) ).
cnf(refute_0_400,plain,
( compose(a,compose(b,h)) != compose(a,compose(b,compose(g,domain(compose(domain(b),h)))))
| compose(a,compose(b,h)) != compose(a,compose(b,g))
| compose(a,compose(b,g)) = compose(a,compose(b,compose(g,domain(compose(domain(b),h))))) ),
introduced(tautology,[equality,[$cnf( $equal(compose(a,compose(b,h)),compose(a,compose(b,compose(g,domain(compose(domain(b),h)))))) ),[0],$fot(compose(a,compose(b,g)))]]) ).
cnf(refute_0_401,plain,
( compose(a,compose(b,h)) != compose(a,compose(b,compose(g,domain(compose(domain(b),h)))))
| compose(a,compose(b,g)) = compose(a,compose(b,compose(g,domain(compose(domain(b),h))))) ),
inference(resolve,[$cnf( $equal(compose(a,compose(b,h)),compose(a,compose(b,g))) )],[refute_0_360,refute_0_400]) ).
cnf(refute_0_402,plain,
compose(a,compose(b,g)) = compose(a,compose(b,compose(g,domain(compose(domain(b),h))))),
inference(resolve,[$cnf( $equal(compose(a,compose(b,h)),compose(a,compose(b,compose(g,domain(compose(domain(b),h)))))) )],[refute_0_399,refute_0_401]) ).
cnf(refute_0_403,plain,
( compose(a,compose(b,g)) != compose(a,compose(b,compose(g,domain(compose(domain(b),h)))))
| compose(a,compose(b,compose(g,domain(compose(domain(b),h))))) = compose(a,compose(b,g)) ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(compose(a,compose(b,g)))),bind(Y0,$fot(compose(a,compose(b,compose(g,domain(compose(domain(b),h)))))))]]) ).
cnf(refute_0_404,plain,
compose(a,compose(b,compose(g,domain(compose(domain(b),h))))) = compose(a,compose(b,g)),
inference(resolve,[$cnf( $equal(compose(a,compose(b,g)),compose(a,compose(b,compose(g,domain(compose(domain(b),h)))))) )],[refute_0_402,refute_0_403]) ).
cnf(refute_0_405,plain,
( compose(a,compose(b,compose(g,domain(compose(domain(b),h))))) != compose(a,compose(b,g))
| compose(a,compose(b,g)) != compose(a,X_63)
| compose(a,compose(b,compose(g,domain(compose(domain(b),h))))) = compose(a,X_63) ),
introduced(tautology,[equality,[$cnf( ~ $equal(compose(a,compose(b,compose(g,domain(compose(domain(b),h))))),compose(a,X_63)) ),[0],$fot(compose(a,compose(b,g)))]]) ).
cnf(refute_0_406,plain,
( compose(a,compose(b,g)) != compose(a,X_63)
| compose(a,compose(b,compose(g,domain(compose(domain(b),h))))) = compose(a,X_63) ),
inference(resolve,[$cnf( $equal(compose(a,compose(b,compose(g,domain(compose(domain(b),h))))),compose(a,compose(b,g))) )],[refute_0_404,refute_0_405]) ).
cnf(refute_0_407,plain,
( compose(a,compose(b,g)) != compose(a,X_63)
| X_63 = compose(b,compose(g,domain(compose(domain(b),h)))) ),
inference(resolve,[$cnf( $equal(compose(a,compose(b,compose(g,domain(compose(domain(b),h))))),compose(a,X_63)) )],[refute_0_406,refute_0_349]) ).
cnf(refute_0_408,plain,
( compose(a,compose(b,g)) != compose(a,compose(b,g))
| compose(b,g) = compose(b,compose(g,domain(compose(domain(b),h)))) ),
inference(subst,[],[refute_0_407:[bind(X_63,$fot(compose(b,g)))]]) ).
cnf(refute_0_409,plain,
compose(a,compose(b,g)) = compose(a,compose(b,g)),
introduced(tautology,[refl,[$fot(compose(a,compose(b,g)))]]) ).
cnf(refute_0_410,plain,
compose(b,g) = compose(b,compose(g,domain(compose(domain(b),h)))),
inference(resolve,[$cnf( $equal(compose(a,compose(b,g)),compose(a,compose(b,g))) )],[refute_0_409,refute_0_408]) ).
cnf(refute_0_411,plain,
compose(codomain(b),X_63) = compose(codomain(b),X_63),
introduced(tautology,[refl,[$fot(compose(codomain(b),X_63))]]) ).
cnf(refute_0_412,plain,
( codomain(b) != codomain(a)
| compose(codomain(b),X_63) != compose(codomain(b),X_63)
| compose(codomain(b),X_63) = compose(codomain(a),X_63) ),
introduced(tautology,[equality,[$cnf( $equal(compose(codomain(b),X_63),compose(codomain(b),X_63)) ),[1,0],$fot(codomain(a))]]) ).
cnf(refute_0_413,plain,
( codomain(b) != codomain(a)
| compose(codomain(b),X_63) = compose(codomain(a),X_63) ),
inference(resolve,[$cnf( $equal(compose(codomain(b),X_63),compose(codomain(b),X_63)) )],[refute_0_411,refute_0_412]) ).
cnf(refute_0_414,plain,
compose(codomain(b),X_63) = compose(codomain(a),X_63),
inference(resolve,[$cnf( $equal(codomain(b),codomain(a)) )],[refute_0_272,refute_0_413]) ).
cnf(refute_0_415,plain,
( X_63 != compose(codomain(b),X_63)
| compose(codomain(b),X_63) != compose(codomain(a),X_63)
| X_63 = compose(codomain(a),X_63) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_63,compose(codomain(a),X_63)) ),[0],$fot(compose(codomain(b),X_63))]]) ).
cnf(refute_0_416,plain,
( X_63 != compose(codomain(b),X_63)
| X_63 = compose(codomain(a),X_63) ),
inference(resolve,[$cnf( $equal(compose(codomain(b),X_63),compose(codomain(a),X_63)) )],[refute_0_414,refute_0_415]) ).
cnf(refute_0_417,plain,
X_63 = compose(codomain(a),X_63),
inference(resolve,[$cnf( $equal(X_63,compose(codomain(b),X_63)) )],[refute_0_259,refute_0_416]) ).
cnf(refute_0_418,plain,
( X_63 != compose(codomain(a),X_63)
| compose(codomain(a),X_63) = X_63 ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(X_63)),bind(Y0,$fot(compose(codomain(a),X_63)))]]) ).
cnf(refute_0_419,plain,
compose(codomain(a),X_63) = X_63,
inference(resolve,[$cnf( $equal(X_63,compose(codomain(a),X_63)) )],[refute_0_417,refute_0_418]) ).
cnf(refute_0_420,plain,
compose(codomain(a),h) = h,
inference(subst,[],[refute_0_419:[bind(X_63,$fot(h))]]) ).
cnf(refute_0_421,plain,
( ~ there_exists(codomain(b))
| there_exists(b) ),
inference(subst,[],[codomain_has_elements:[bind(X,$fot(b))]]) ).
cnf(refute_0_422,plain,
there_exists(b),
inference(resolve,[$cnf( there_exists(codomain(b)) )],[refute_0_179,refute_0_421]) ).
cnf(refute_0_423,plain,
( ~ there_exists(b)
| there_exists(domain(b)) ),
inference(subst,[],[refute_0_102:[bind(X_30,$fot(b))]]) ).
cnf(refute_0_424,plain,
there_exists(domain(b)),
inference(resolve,[$cnf( there_exists(b) )],[refute_0_422,refute_0_423]) ).
cnf(refute_0_425,plain,
( ~ there_exists(domain(b))
| codomain(b) = codomain(domain(b)) ),
inference(subst,[],[refute_0_268:[bind(Y,$fot(domain(b)))]]) ).
cnf(refute_0_426,plain,
codomain(b) = codomain(domain(b)),
inference(resolve,[$cnf( there_exists(domain(b)) )],[refute_0_424,refute_0_425]) ).
cnf(refute_0_427,plain,
( codomain(b) != codomain(a)
| codomain(b) != codomain(domain(b))
| codomain(a) = codomain(domain(b)) ),
introduced(tautology,[equality,[$cnf( $equal(codomain(b),codomain(domain(b))) ),[0],$fot(codomain(a))]]) ).
cnf(refute_0_428,plain,
( codomain(b) != codomain(domain(b))
| codomain(a) = codomain(domain(b)) ),
inference(resolve,[$cnf( $equal(codomain(b),codomain(a)) )],[refute_0_272,refute_0_427]) ).
cnf(refute_0_429,plain,
( ~ there_exists(b)
| domain(b) = codomain(domain(b)) ),
inference(subst,[],[refute_0_279:[bind(X_27,$fot(b))]]) ).
cnf(refute_0_430,plain,
domain(b) = codomain(domain(b)),
inference(resolve,[$cnf( there_exists(b) )],[refute_0_422,refute_0_429]) ).
cnf(refute_0_431,plain,
( domain(b) != codomain(domain(b))
| codomain(domain(b)) = domain(b) ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(domain(b))),bind(Y0,$fot(codomain(domain(b))))]]) ).
cnf(refute_0_432,plain,
codomain(domain(b)) = domain(b),
inference(resolve,[$cnf( $equal(domain(b),codomain(domain(b))) )],[refute_0_430,refute_0_431]) ).
cnf(refute_0_433,plain,
( codomain(a) != codomain(domain(b))
| codomain(domain(b)) != domain(b)
| codomain(a) = domain(b) ),
introduced(tautology,[equality,[$cnf( ~ $equal(codomain(a),domain(b)) ),[0],$fot(codomain(domain(b)))]]) ).
cnf(refute_0_434,plain,
( codomain(a) != codomain(domain(b))
| codomain(a) = domain(b) ),
inference(resolve,[$cnf( $equal(codomain(domain(b)),domain(b)) )],[refute_0_432,refute_0_433]) ).
cnf(refute_0_435,plain,
( codomain(b) != codomain(domain(b))
| codomain(a) = domain(b) ),
inference(resolve,[$cnf( $equal(codomain(a),codomain(domain(b))) )],[refute_0_428,refute_0_434]) ).
cnf(refute_0_436,plain,
codomain(a) = domain(b),
inference(resolve,[$cnf( $equal(codomain(b),codomain(domain(b))) )],[refute_0_426,refute_0_435]) ).
cnf(refute_0_437,plain,
( codomain(a) != domain(b)
| domain(b) = codomain(a) ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(codomain(a))),bind(Y0,$fot(domain(b)))]]) ).
cnf(refute_0_438,plain,
domain(b) = codomain(a),
inference(resolve,[$cnf( $equal(codomain(a),domain(b)) )],[refute_0_436,refute_0_437]) ).
cnf(refute_0_439,plain,
compose(domain(b),h) = compose(domain(b),h),
introduced(tautology,[refl,[$fot(compose(domain(b),h))]]) ).
cnf(refute_0_440,plain,
( compose(domain(b),h) != compose(domain(b),h)
| domain(b) != codomain(a)
| compose(domain(b),h) = compose(codomain(a),h) ),
introduced(tautology,[equality,[$cnf( $equal(compose(domain(b),h),compose(domain(b),h)) ),[1,0],$fot(codomain(a))]]) ).
cnf(refute_0_441,plain,
( domain(b) != codomain(a)
| compose(domain(b),h) = compose(codomain(a),h) ),
inference(resolve,[$cnf( $equal(compose(domain(b),h),compose(domain(b),h)) )],[refute_0_439,refute_0_440]) ).
cnf(refute_0_442,plain,
compose(domain(b),h) = compose(codomain(a),h),
inference(resolve,[$cnf( $equal(domain(b),codomain(a)) )],[refute_0_438,refute_0_441]) ).
cnf(refute_0_443,plain,
( compose(codomain(a),h) != h
| compose(domain(b),h) != compose(codomain(a),h)
| compose(domain(b),h) = h ),
inference(subst,[],[refute_0_207:[bind(X0,$fot(compose(domain(b),h))),bind(Y0,$fot(compose(codomain(a),h))),bind(Z0,$fot(h))]]) ).
cnf(refute_0_444,plain,
( compose(codomain(a),h) != h
| compose(domain(b),h) = h ),
inference(resolve,[$cnf( $equal(compose(domain(b),h),compose(codomain(a),h)) )],[refute_0_442,refute_0_443]) ).
cnf(refute_0_445,plain,
compose(domain(b),h) = h,
inference(resolve,[$cnf( $equal(compose(codomain(a),h),h) )],[refute_0_420,refute_0_444]) ).
cnf(refute_0_446,plain,
domain(compose(domain(b),h)) = domain(compose(domain(b),h)),
introduced(tautology,[refl,[$fot(domain(compose(domain(b),h)))]]) ).
cnf(refute_0_447,plain,
( compose(domain(b),h) != h
| domain(compose(domain(b),h)) != domain(compose(domain(b),h))
| domain(compose(domain(b),h)) = domain(h) ),
introduced(tautology,[equality,[$cnf( $equal(domain(compose(domain(b),h)),domain(compose(domain(b),h))) ),[1,0],$fot(h)]]) ).
cnf(refute_0_448,plain,
( compose(domain(b),h) != h
| domain(compose(domain(b),h)) = domain(h) ),
inference(resolve,[$cnf( $equal(domain(compose(domain(b),h)),domain(compose(domain(b),h))) )],[refute_0_446,refute_0_447]) ).
cnf(refute_0_449,plain,
domain(compose(domain(b),h)) = domain(h),
inference(resolve,[$cnf( $equal(compose(domain(b),h),h) )],[refute_0_445,refute_0_448]) ).
cnf(refute_0_450,plain,
( domain(compose(domain(b),h)) != domain(h)
| domain(h) != codomain(a)
| domain(compose(domain(b),h)) = codomain(a) ),
inference(subst,[],[refute_0_207:[bind(X0,$fot(domain(compose(domain(b),h)))),bind(Y0,$fot(domain(h))),bind(Z0,$fot(codomain(a)))]]) ).
cnf(refute_0_451,plain,
( domain(h) != codomain(a)
| domain(compose(domain(b),h)) = codomain(a) ),
inference(resolve,[$cnf( $equal(domain(compose(domain(b),h)),domain(h)) )],[refute_0_449,refute_0_450]) ).
cnf(refute_0_452,plain,
domain(compose(domain(b),h)) = codomain(a),
inference(resolve,[$cnf( $equal(domain(h),codomain(a)) )],[refute_0_289,refute_0_451]) ).
cnf(refute_0_453,plain,
compose(g,domain(compose(domain(b),h))) = compose(g,domain(compose(domain(b),h))),
introduced(tautology,[refl,[$fot(compose(g,domain(compose(domain(b),h))))]]) ).
cnf(refute_0_454,plain,
( compose(g,domain(compose(domain(b),h))) != compose(g,domain(compose(domain(b),h)))
| domain(compose(domain(b),h)) != codomain(a)
| compose(g,domain(compose(domain(b),h))) = compose(g,codomain(a)) ),
introduced(tautology,[equality,[$cnf( $equal(compose(g,domain(compose(domain(b),h))),compose(g,domain(compose(domain(b),h)))) ),[1,1],$fot(codomain(a))]]) ).
cnf(refute_0_455,plain,
( domain(compose(domain(b),h)) != codomain(a)
| compose(g,domain(compose(domain(b),h))) = compose(g,codomain(a)) ),
inference(resolve,[$cnf( $equal(compose(g,domain(compose(domain(b),h))),compose(g,domain(compose(domain(b),h)))) )],[refute_0_453,refute_0_454]) ).
cnf(refute_0_456,plain,
compose(g,domain(compose(domain(b),h))) = compose(g,codomain(a)),
inference(resolve,[$cnf( $equal(domain(compose(domain(b),h)),codomain(a)) )],[refute_0_452,refute_0_455]) ).
cnf(refute_0_457,plain,
compose(b,compose(g,domain(compose(domain(b),h)))) = compose(b,compose(g,domain(compose(domain(b),h)))),
introduced(tautology,[refl,[$fot(compose(b,compose(g,domain(compose(domain(b),h)))))]]) ).
cnf(refute_0_458,plain,
( compose(b,compose(g,domain(compose(domain(b),h)))) != compose(b,compose(g,domain(compose(domain(b),h))))
| compose(g,domain(compose(domain(b),h))) != compose(g,codomain(a))
| compose(b,compose(g,domain(compose(domain(b),h)))) = compose(b,compose(g,codomain(a))) ),
introduced(tautology,[equality,[$cnf( $equal(compose(b,compose(g,domain(compose(domain(b),h)))),compose(b,compose(g,domain(compose(domain(b),h))))) ),[1,1],$fot(compose(g,codomain(a)))]]) ).
cnf(refute_0_459,plain,
( compose(g,domain(compose(domain(b),h))) != compose(g,codomain(a))
| compose(b,compose(g,domain(compose(domain(b),h)))) = compose(b,compose(g,codomain(a))) ),
inference(resolve,[$cnf( $equal(compose(b,compose(g,domain(compose(domain(b),h)))),compose(b,compose(g,domain(compose(domain(b),h))))) )],[refute_0_457,refute_0_458]) ).
cnf(refute_0_460,plain,
compose(b,compose(g,domain(compose(domain(b),h)))) = compose(b,compose(g,codomain(a))),
inference(resolve,[$cnf( $equal(compose(g,domain(compose(domain(b),h))),compose(g,codomain(a))) )],[refute_0_456,refute_0_459]) ).
cnf(refute_0_461,plain,
( compose(b,compose(g,domain(compose(domain(b),h)))) != compose(b,compose(g,codomain(a)))
| compose(b,g) != compose(b,compose(g,domain(compose(domain(b),h))))
| compose(b,g) = compose(b,compose(g,codomain(a))) ),
introduced(tautology,[equality,[$cnf( $equal(compose(b,g),compose(b,compose(g,domain(compose(domain(b),h))))) ),[1],$fot(compose(b,compose(g,codomain(a))))]]) ).
cnf(refute_0_462,plain,
( compose(b,g) != compose(b,compose(g,domain(compose(domain(b),h))))
| compose(b,g) = compose(b,compose(g,codomain(a))) ),
inference(resolve,[$cnf( $equal(compose(b,compose(g,domain(compose(domain(b),h)))),compose(b,compose(g,codomain(a)))) )],[refute_0_460,refute_0_461]) ).
cnf(refute_0_463,plain,
compose(b,g) = compose(b,compose(g,codomain(a))),
inference(resolve,[$cnf( $equal(compose(b,g),compose(b,compose(g,domain(compose(domain(b),h))))) )],[refute_0_410,refute_0_462]) ).
cnf(refute_0_464,plain,
( compose(b,g) != compose(b,compose(g,codomain(a)))
| compose(b,compose(g,codomain(a))) = compose(b,g) ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(compose(b,g))),bind(Y0,$fot(compose(b,compose(g,codomain(a)))))]]) ).
cnf(refute_0_465,plain,
compose(b,compose(g,codomain(a))) = compose(b,g),
inference(resolve,[$cnf( $equal(compose(b,g),compose(b,compose(g,codomain(a)))) )],[refute_0_463,refute_0_464]) ).
cnf(refute_0_466,plain,
( compose(b,compose(g,codomain(a))) != compose(b,g)
| compose(b,g) != compose(b,X_83)
| compose(b,compose(g,codomain(a))) = compose(b,X_83) ),
introduced(tautology,[equality,[$cnf( ~ $equal(compose(b,compose(g,codomain(a))),compose(b,X_83)) ),[0],$fot(compose(b,g))]]) ).
cnf(refute_0_467,plain,
( compose(b,g) != compose(b,X_83)
| compose(b,compose(g,codomain(a))) = compose(b,X_83) ),
inference(resolve,[$cnf( $equal(compose(b,compose(g,codomain(a))),compose(b,g)) )],[refute_0_465,refute_0_466]) ).
cnf(refute_0_468,plain,
( compose(b,g) != compose(b,X_83)
| X_83 = compose(g,codomain(a)) ),
inference(resolve,[$cnf( $equal(compose(b,compose(g,codomain(a))),compose(b,X_83)) )],[refute_0_467,refute_0_348]) ).
cnf(refute_0_469,plain,
( compose(b,g) != compose(b,g)
| g = compose(g,codomain(a)) ),
inference(subst,[],[refute_0_468:[bind(X_83,$fot(g))]]) ).
cnf(refute_0_470,plain,
compose(b,g) = compose(b,g),
introduced(tautology,[refl,[$fot(compose(b,g))]]) ).
cnf(refute_0_471,plain,
g = compose(g,codomain(a)),
inference(resolve,[$cnf( $equal(compose(b,g),compose(b,g)) )],[refute_0_470,refute_0_469]) ).
cnf(refute_0_472,plain,
( g != compose(g,codomain(a))
| compose(g,codomain(a)) = g ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(g)),bind(Y0,$fot(compose(g,codomain(a))))]]) ).
cnf(refute_0_473,plain,
compose(g,codomain(a)) = g,
inference(resolve,[$cnf( $equal(g,compose(g,codomain(a))) )],[refute_0_471,refute_0_472]) ).
cnf(refute_0_474,plain,
( compose(b,compose(h,X_11)) != compose(b,X_83)
| X_83 = compose(h,X_11) ),
inference(subst,[],[refute_0_347:[bind(X,$fot(X_83)),bind(Z,$fot(compose(h,X_11)))]]) ).
cnf(refute_0_475,plain,
( compose(a,compose(b,compose(h,X_11))) != compose(a,X_63)
| X_63 = compose(b,compose(h,X_11)) ),
inference(subst,[],[refute_0_18:[bind(X,$fot(X_63)),bind(Z,$fot(compose(b,compose(h,X_11))))]]) ).
cnf(refute_0_476,plain,
( compose(a,compose(b,compose(g,X_11))) != compose(a,X_63)
| compose(a,compose(b,compose(h,X_11))) != compose(a,compose(b,compose(g,X_11)))
| compose(a,compose(b,compose(h,X_11))) = compose(a,X_63) ),
introduced(tautology,[equality,[$cnf( $equal(compose(a,compose(b,compose(h,X_11))),compose(a,compose(b,compose(g,X_11)))) ),[1],$fot(compose(a,X_63))]]) ).
cnf(refute_0_477,plain,
( compose(a,compose(b,compose(g,X_11))) != compose(a,X_63)
| compose(a,compose(b,compose(h,X_11))) = compose(a,X_63) ),
inference(resolve,[$cnf( $equal(compose(a,compose(b,compose(h,X_11))),compose(a,compose(b,compose(g,X_11)))) )],[refute_0_383,refute_0_476]) ).
cnf(refute_0_478,plain,
( compose(a,compose(b,compose(g,X_11))) != compose(a,X_63)
| X_63 = compose(b,compose(h,X_11)) ),
inference(resolve,[$cnf( $equal(compose(a,compose(b,compose(h,X_11))),compose(a,X_63)) )],[refute_0_477,refute_0_475]) ).
cnf(refute_0_479,plain,
( compose(a,compose(b,compose(g,X_11))) != compose(a,compose(b,compose(g,X_11)))
| compose(b,compose(g,X_11)) = compose(b,compose(h,X_11)) ),
inference(subst,[],[refute_0_478:[bind(X_63,$fot(compose(b,compose(g,X_11))))]]) ).
cnf(refute_0_480,plain,
compose(a,compose(b,compose(g,X_11))) = compose(a,compose(b,compose(g,X_11))),
introduced(tautology,[refl,[$fot(compose(a,compose(b,compose(g,X_11))))]]) ).
cnf(refute_0_481,plain,
compose(b,compose(g,X_11)) = compose(b,compose(h,X_11)),
inference(resolve,[$cnf( $equal(compose(a,compose(b,compose(g,X_11))),compose(a,compose(b,compose(g,X_11)))) )],[refute_0_480,refute_0_479]) ).
cnf(refute_0_482,plain,
( compose(b,compose(g,X_11)) != compose(b,compose(h,X_11))
| compose(b,compose(h,X_11)) = compose(b,compose(g,X_11)) ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(compose(b,compose(g,X_11)))),bind(Y0,$fot(compose(b,compose(h,X_11))))]]) ).
cnf(refute_0_483,plain,
compose(b,compose(h,X_11)) = compose(b,compose(g,X_11)),
inference(resolve,[$cnf( $equal(compose(b,compose(g,X_11)),compose(b,compose(h,X_11))) )],[refute_0_481,refute_0_482]) ).
cnf(refute_0_484,plain,
( compose(b,compose(g,X_11)) != compose(b,X_83)
| compose(b,compose(h,X_11)) != compose(b,compose(g,X_11))
| compose(b,compose(h,X_11)) = compose(b,X_83) ),
introduced(tautology,[equality,[$cnf( $equal(compose(b,compose(h,X_11)),compose(b,compose(g,X_11))) ),[1],$fot(compose(b,X_83))]]) ).
cnf(refute_0_485,plain,
( compose(b,compose(g,X_11)) != compose(b,X_83)
| compose(b,compose(h,X_11)) = compose(b,X_83) ),
inference(resolve,[$cnf( $equal(compose(b,compose(h,X_11)),compose(b,compose(g,X_11))) )],[refute_0_483,refute_0_484]) ).
cnf(refute_0_486,plain,
( compose(b,compose(g,X_11)) != compose(b,X_83)
| X_83 = compose(h,X_11) ),
inference(resolve,[$cnf( $equal(compose(b,compose(h,X_11)),compose(b,X_83)) )],[refute_0_485,refute_0_474]) ).
cnf(refute_0_487,plain,
( compose(b,compose(g,X_11)) != compose(b,compose(g,X_11))
| compose(g,X_11) = compose(h,X_11) ),
inference(subst,[],[refute_0_486:[bind(X_83,$fot(compose(g,X_11)))]]) ).
cnf(refute_0_488,plain,
compose(b,compose(g,X_11)) = compose(b,compose(g,X_11)),
introduced(tautology,[refl,[$fot(compose(b,compose(g,X_11)))]]) ).
cnf(refute_0_489,plain,
compose(g,X_11) = compose(h,X_11),
inference(resolve,[$cnf( $equal(compose(b,compose(g,X_11)),compose(b,compose(g,X_11))) )],[refute_0_488,refute_0_487]) ).
cnf(refute_0_490,plain,
( compose(g,X_11) != compose(h,X_11)
| compose(h,X_11) = compose(g,X_11) ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(compose(g,X_11))),bind(Y0,$fot(compose(h,X_11)))]]) ).
cnf(refute_0_491,plain,
compose(h,X_11) = compose(g,X_11),
inference(resolve,[$cnf( $equal(compose(g,X_11),compose(h,X_11)) )],[refute_0_489,refute_0_490]) ).
cnf(refute_0_492,plain,
compose(h,codomain(a)) = compose(g,codomain(a)),
inference(subst,[],[refute_0_491:[bind(X_11,$fot(codomain(a)))]]) ).
cnf(refute_0_493,plain,
( compose(g,codomain(a)) != g
| compose(h,codomain(a)) != compose(g,codomain(a))
| compose(h,codomain(a)) = g ),
inference(subst,[],[refute_0_207:[bind(X0,$fot(compose(h,codomain(a)))),bind(Y0,$fot(compose(g,codomain(a)))),bind(Z0,$fot(g))]]) ).
cnf(refute_0_494,plain,
( compose(g,codomain(a)) != g
| compose(h,codomain(a)) = g ),
inference(resolve,[$cnf( $equal(compose(h,codomain(a)),compose(g,codomain(a))) )],[refute_0_492,refute_0_493]) ).
cnf(refute_0_495,plain,
compose(h,codomain(a)) = g,
inference(resolve,[$cnf( $equal(compose(g,codomain(a)),g) )],[refute_0_473,refute_0_494]) ).
cnf(refute_0_496,plain,
( compose(h,codomain(a)) != g
| compose(h,codomain(a)) != h
| g = h ),
introduced(tautology,[equality,[$cnf( $equal(compose(h,codomain(a)),h) ),[0],$fot(g)]]) ).
cnf(refute_0_497,plain,
( compose(h,codomain(a)) != h
| g = h ),
inference(resolve,[$cnf( $equal(compose(h,codomain(a)),g) )],[refute_0_495,refute_0_496]) ).
cnf(refute_0_498,plain,
g = h,
inference(resolve,[$cnf( $equal(compose(h,codomain(a)),h) )],[refute_0_344,refute_0_497]) ).
cnf(refute_0_499,plain,
$false,
inference(resolve,[$cnf( $equal(g,h) )],[refute_0_498,prove_g_equals_h]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : CAT002-4 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n028.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 17:28:18 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.23/1.43 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.23/1.43
% 1.23/1.43 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 1.31/1.47
%------------------------------------------------------------------------------