TSTP Solution File: CAT001-4 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : CAT001-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n026.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 00:04:30 EDT 2022
% Result : Unsatisfiable 162.07s 162.24s
% Output : CNFRefutation 162.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 74
% Syntax : Number of clauses : 321 ( 132 unt; 0 nHn; 257 RR)
% Number of literals : 573 ( 446 equ; 254 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 9 ( 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 : 195 ( 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(monomorphism,hypothesis,
( compose(compose(a,b),X) != Y
| compose(compose(a,b),Z) != Y
| X = Z ) ).
cnf(assume_bh_exists,hypothesis,
there_exists(compose(b,h)) ).
cnf(bh_equals_bg,hypothesis,
compose(b,h) = compose(b,g) ).
cnf(prove_h_equals_g,negated_conjecture,
h != g ).
cnf(refute_0_0,plain,
compose(X_15,compose(domain(X_15),X_17)) = compose(compose(X_15,domain(X_15)),X_17),
inference(subst,[],[associativity_of_compose:[bind(X,$fot(X_15)),bind(Y,$fot(domain(X_15))),bind(Z,$fot(X_17))]]) ).
cnf(refute_0_1,plain,
compose(X_15,domain(X_15)) = X_15,
inference(subst,[],[compose_domain:[bind(X,$fot(X_15))]]) ).
cnf(refute_0_2,plain,
( compose(X_15,compose(domain(X_15),X_17)) != compose(compose(X_15,domain(X_15)),X_17)
| compose(X_15,domain(X_15)) != X_15
| compose(X_15,compose(domain(X_15),X_17)) = compose(X_15,X_17) ),
introduced(tautology,[equality,[$cnf( $equal(compose(X_15,compose(domain(X_15),X_17)),compose(compose(X_15,domain(X_15)),X_17)) ),[1,0],$fot(X_15)]]) ).
cnf(refute_0_3,plain,
( compose(X_15,compose(domain(X_15),X_17)) != compose(compose(X_15,domain(X_15)),X_17)
| compose(X_15,compose(domain(X_15),X_17)) = compose(X_15,X_17) ),
inference(resolve,[$cnf( $equal(compose(X_15,domain(X_15)),X_15) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
compose(X_15,compose(domain(X_15),X_17)) = compose(X_15,X_17),
inference(resolve,[$cnf( $equal(compose(X_15,compose(domain(X_15),X_17)),compose(compose(X_15,domain(X_15)),X_17)) )],[refute_0_0,refute_0_3]) ).
cnf(refute_0_5,plain,
compose(X_15,compose(domain(X_15),compose(domain(domain(X_15)),X_25))) = compose(X_15,compose(domain(domain(X_15)),X_25)),
inference(subst,[],[refute_0_4:[bind(X_17,$fot(compose(domain(domain(X_15)),X_25)))]]) ).
cnf(refute_0_6,plain,
compose(domain(X_15),compose(domain(domain(X_15)),X_25)) = compose(domain(X_15),X_25),
inference(subst,[],[refute_0_4:[bind(X_15,$fot(domain(X_15))),bind(X_17,$fot(X_25))]]) ).
cnf(refute_0_7,plain,
( compose(X_15,compose(domain(X_15),compose(domain(domain(X_15)),X_25))) != compose(X_15,compose(domain(domain(X_15)),X_25))
| compose(domain(X_15),compose(domain(domain(X_15)),X_25)) != compose(domain(X_15),X_25)
| compose(X_15,compose(domain(X_15),X_25)) = compose(X_15,compose(domain(domain(X_15)),X_25)) ),
introduced(tautology,[equality,[$cnf( $equal(compose(X_15,compose(domain(X_15),compose(domain(domain(X_15)),X_25))),compose(X_15,compose(domain(domain(X_15)),X_25))) ),[0,1],$fot(compose(domain(X_15),X_25))]]) ).
cnf(refute_0_8,plain,
( compose(X_15,compose(domain(X_15),compose(domain(domain(X_15)),X_25))) != compose(X_15,compose(domain(domain(X_15)),X_25))
| compose(X_15,compose(domain(X_15),X_25)) = compose(X_15,compose(domain(domain(X_15)),X_25)) ),
inference(resolve,[$cnf( $equal(compose(domain(X_15),compose(domain(domain(X_15)),X_25)),compose(domain(X_15),X_25)) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
compose(X_15,compose(domain(X_15),X_25)) = compose(X_15,compose(domain(domain(X_15)),X_25)),
inference(resolve,[$cnf( $equal(compose(X_15,compose(domain(X_15),compose(domain(domain(X_15)),X_25))),compose(X_15,compose(domain(domain(X_15)),X_25))) )],[refute_0_5,refute_0_8]) ).
cnf(refute_0_10,plain,
compose(X_15,compose(domain(X_15),X_25)) = compose(X_15,X_25),
inference(subst,[],[refute_0_4:[bind(X_17,$fot(X_25))]]) ).
cnf(refute_0_11,plain,
( compose(X_15,compose(domain(X_15),X_25)) != compose(X_15,X_25)
| compose(X_15,compose(domain(X_15),X_25)) != compose(X_15,compose(domain(domain(X_15)),X_25))
| compose(X_15,X_25) = compose(X_15,compose(domain(domain(X_15)),X_25)) ),
introduced(tautology,[equality,[$cnf( $equal(compose(X_15,compose(domain(X_15),X_25)),compose(X_15,compose(domain(domain(X_15)),X_25))) ),[0],$fot(compose(X_15,X_25))]]) ).
cnf(refute_0_12,plain,
( compose(X_15,compose(domain(X_15),X_25)) != compose(X_15,compose(domain(domain(X_15)),X_25))
| compose(X_15,X_25) = compose(X_15,compose(domain(domain(X_15)),X_25)) ),
inference(resolve,[$cnf( $equal(compose(X_15,compose(domain(X_15),X_25)),compose(X_15,X_25)) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
compose(X_15,X_25) = compose(X_15,compose(domain(domain(X_15)),X_25)),
inference(resolve,[$cnf( $equal(compose(X_15,compose(domain(X_15),X_25)),compose(X_15,compose(domain(domain(X_15)),X_25))) )],[refute_0_9,refute_0_12]) ).
cnf(refute_0_14,plain,
compose(X_34,domain(domain(domain(domain(domain(domain(X_34))))))) = compose(X_34,compose(domain(domain(X_34)),domain(domain(domain(domain(domain(domain(X_34)))))))),
inference(subst,[],[refute_0_13:[bind(X_15,$fot(X_34)),bind(X_25,$fot(domain(domain(domain(domain(domain(domain(X_34))))))))]]) ).
cnf(refute_0_15,plain,
compose(X_15,compose(domain(X_15),domain(domain(domain(domain(X_15)))))) = compose(X_15,domain(domain(domain(domain(X_15))))),
inference(subst,[],[refute_0_4:[bind(X_17,$fot(domain(domain(domain(domain(X_15))))))]]) ).
cnf(refute_0_16,plain,
compose(X_15,compose(domain(X_15),domain(domain(domain(X_15))))) = compose(X_15,domain(domain(domain(X_15)))),
inference(subst,[],[refute_0_4:[bind(X_17,$fot(domain(domain(domain(X_15)))))]]) ).
cnf(refute_0_17,plain,
compose(X_24,compose(domain(X_24),domain(domain(X_24)))) = compose(X_24,domain(domain(X_24))),
inference(subst,[],[refute_0_4:[bind(X_15,$fot(X_24)),bind(X_17,$fot(domain(domain(X_24))))]]) ).
cnf(refute_0_18,plain,
compose(domain(X_24),domain(domain(X_24))) = domain(X_24),
inference(subst,[],[compose_domain:[bind(X,$fot(domain(X_24)))]]) ).
cnf(refute_0_19,plain,
( compose(X_24,compose(domain(X_24),domain(domain(X_24)))) != compose(X_24,domain(domain(X_24)))
| compose(domain(X_24),domain(domain(X_24))) != domain(X_24)
| compose(X_24,domain(X_24)) = compose(X_24,domain(domain(X_24))) ),
introduced(tautology,[equality,[$cnf( $equal(compose(X_24,compose(domain(X_24),domain(domain(X_24)))),compose(X_24,domain(domain(X_24)))) ),[0,1],$fot(domain(X_24))]]) ).
cnf(refute_0_20,plain,
( compose(X_24,compose(domain(X_24),domain(domain(X_24)))) != compose(X_24,domain(domain(X_24)))
| compose(X_24,domain(X_24)) = compose(X_24,domain(domain(X_24))) ),
inference(resolve,[$cnf( $equal(compose(domain(X_24),domain(domain(X_24))),domain(X_24)) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
compose(X_24,domain(X_24)) = compose(X_24,domain(domain(X_24))),
inference(resolve,[$cnf( $equal(compose(X_24,compose(domain(X_24),domain(domain(X_24)))),compose(X_24,domain(domain(X_24)))) )],[refute_0_17,refute_0_20]) ).
cnf(refute_0_22,plain,
compose(X_24,domain(X_24)) = X_24,
inference(subst,[],[compose_domain:[bind(X,$fot(X_24))]]) ).
cnf(refute_0_23,plain,
( compose(X_24,domain(X_24)) != X_24
| compose(X_24,domain(X_24)) != compose(X_24,domain(domain(X_24)))
| X_24 = compose(X_24,domain(domain(X_24))) ),
introduced(tautology,[equality,[$cnf( $equal(compose(X_24,domain(X_24)),compose(X_24,domain(domain(X_24)))) ),[0],$fot(X_24)]]) ).
cnf(refute_0_24,plain,
( compose(X_24,domain(X_24)) != compose(X_24,domain(domain(X_24)))
| X_24 = compose(X_24,domain(domain(X_24))) ),
inference(resolve,[$cnf( $equal(compose(X_24,domain(X_24)),X_24) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
X_24 = compose(X_24,domain(domain(X_24))),
inference(resolve,[$cnf( $equal(compose(X_24,domain(X_24)),compose(X_24,domain(domain(X_24)))) )],[refute_0_21,refute_0_24]) ).
cnf(refute_0_26,plain,
domain(X_15) = compose(domain(X_15),domain(domain(domain(X_15)))),
inference(subst,[],[refute_0_25:[bind(X_24,$fot(domain(X_15)))]]) ).
cnf(refute_0_27,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_28,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_29,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
( domain(X_15) != compose(domain(X_15),domain(domain(domain(X_15))))
| compose(domain(X_15),domain(domain(domain(X_15)))) = domain(X_15) ),
inference(subst,[],[refute_0_29:[bind(X0,$fot(domain(X_15))),bind(Y0,$fot(compose(domain(X_15),domain(domain(domain(X_15))))))]]) ).
cnf(refute_0_31,plain,
compose(domain(X_15),domain(domain(domain(X_15)))) = domain(X_15),
inference(resolve,[$cnf( $equal(domain(X_15),compose(domain(X_15),domain(domain(domain(X_15))))) )],[refute_0_26,refute_0_30]) ).
cnf(refute_0_32,plain,
( compose(X_15,compose(domain(X_15),domain(domain(domain(X_15))))) != compose(X_15,domain(domain(domain(X_15))))
| compose(domain(X_15),domain(domain(domain(X_15)))) != domain(X_15)
| compose(X_15,domain(X_15)) = compose(X_15,domain(domain(domain(X_15)))) ),
introduced(tautology,[equality,[$cnf( $equal(compose(X_15,compose(domain(X_15),domain(domain(domain(X_15))))),compose(X_15,domain(domain(domain(X_15))))) ),[0,1],$fot(domain(X_15))]]) ).
cnf(refute_0_33,plain,
( compose(X_15,compose(domain(X_15),domain(domain(domain(X_15))))) != compose(X_15,domain(domain(domain(X_15))))
| compose(X_15,domain(X_15)) = compose(X_15,domain(domain(domain(X_15)))) ),
inference(resolve,[$cnf( $equal(compose(domain(X_15),domain(domain(domain(X_15)))),domain(X_15)) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
compose(X_15,domain(X_15)) = compose(X_15,domain(domain(domain(X_15)))),
inference(resolve,[$cnf( $equal(compose(X_15,compose(domain(X_15),domain(domain(domain(X_15))))),compose(X_15,domain(domain(domain(X_15))))) )],[refute_0_16,refute_0_33]) ).
cnf(refute_0_35,plain,
( compose(X_15,domain(X_15)) != X_15
| compose(X_15,domain(X_15)) != compose(X_15,domain(domain(domain(X_15))))
| X_15 = compose(X_15,domain(domain(domain(X_15)))) ),
introduced(tautology,[equality,[$cnf( $equal(compose(X_15,domain(X_15)),compose(X_15,domain(domain(domain(X_15))))) ),[0],$fot(X_15)]]) ).
cnf(refute_0_36,plain,
( compose(X_15,domain(X_15)) != compose(X_15,domain(domain(domain(X_15))))
| X_15 = compose(X_15,domain(domain(domain(X_15)))) ),
inference(resolve,[$cnf( $equal(compose(X_15,domain(X_15)),X_15) )],[refute_0_1,refute_0_35]) ).
cnf(refute_0_37,plain,
X_15 = compose(X_15,domain(domain(domain(X_15)))),
inference(resolve,[$cnf( $equal(compose(X_15,domain(X_15)),compose(X_15,domain(domain(domain(X_15))))) )],[refute_0_34,refute_0_36]) ).
cnf(refute_0_38,plain,
domain(X_15) = compose(domain(X_15),domain(domain(domain(domain(X_15))))),
inference(subst,[],[refute_0_37:[bind(X_15,$fot(domain(X_15)))]]) ).
cnf(refute_0_39,plain,
( domain(X_15) != compose(domain(X_15),domain(domain(domain(domain(X_15)))))
| compose(domain(X_15),domain(domain(domain(domain(X_15))))) = domain(X_15) ),
inference(subst,[],[refute_0_29:[bind(X0,$fot(domain(X_15))),bind(Y0,$fot(compose(domain(X_15),domain(domain(domain(domain(X_15)))))))]]) ).
cnf(refute_0_40,plain,
compose(domain(X_15),domain(domain(domain(domain(X_15))))) = domain(X_15),
inference(resolve,[$cnf( $equal(domain(X_15),compose(domain(X_15),domain(domain(domain(domain(X_15)))))) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
( compose(X_15,compose(domain(X_15),domain(domain(domain(domain(X_15)))))) != compose(X_15,domain(domain(domain(domain(X_15)))))
| compose(domain(X_15),domain(domain(domain(domain(X_15))))) != domain(X_15)
| compose(X_15,domain(X_15)) = compose(X_15,domain(domain(domain(domain(X_15))))) ),
introduced(tautology,[equality,[$cnf( $equal(compose(X_15,compose(domain(X_15),domain(domain(domain(domain(X_15)))))),compose(X_15,domain(domain(domain(domain(X_15)))))) ),[0,1],$fot(domain(X_15))]]) ).
cnf(refute_0_42,plain,
( compose(X_15,compose(domain(X_15),domain(domain(domain(domain(X_15)))))) != compose(X_15,domain(domain(domain(domain(X_15)))))
| compose(X_15,domain(X_15)) = compose(X_15,domain(domain(domain(domain(X_15))))) ),
inference(resolve,[$cnf( $equal(compose(domain(X_15),domain(domain(domain(domain(X_15))))),domain(X_15)) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
compose(X_15,domain(X_15)) = compose(X_15,domain(domain(domain(domain(X_15))))),
inference(resolve,[$cnf( $equal(compose(X_15,compose(domain(X_15),domain(domain(domain(domain(X_15)))))),compose(X_15,domain(domain(domain(domain(X_15)))))) )],[refute_0_15,refute_0_42]) ).
cnf(refute_0_44,plain,
( compose(X_15,domain(X_15)) != X_15
| compose(X_15,domain(X_15)) != compose(X_15,domain(domain(domain(domain(X_15)))))
| X_15 = compose(X_15,domain(domain(domain(domain(X_15))))) ),
introduced(tautology,[equality,[$cnf( $equal(compose(X_15,domain(X_15)),compose(X_15,domain(domain(domain(domain(X_15)))))) ),[0],$fot(X_15)]]) ).
cnf(refute_0_45,plain,
( compose(X_15,domain(X_15)) != compose(X_15,domain(domain(domain(domain(X_15)))))
| X_15 = compose(X_15,domain(domain(domain(domain(X_15))))) ),
inference(resolve,[$cnf( $equal(compose(X_15,domain(X_15)),X_15) )],[refute_0_1,refute_0_44]) ).
cnf(refute_0_46,plain,
X_15 = compose(X_15,domain(domain(domain(domain(X_15))))),
inference(resolve,[$cnf( $equal(compose(X_15,domain(X_15)),compose(X_15,domain(domain(domain(domain(X_15)))))) )],[refute_0_43,refute_0_45]) ).
cnf(refute_0_47,plain,
domain(domain(X_34)) = compose(domain(domain(X_34)),domain(domain(domain(domain(domain(domain(X_34))))))),
inference(subst,[],[refute_0_46:[bind(X_15,$fot(domain(domain(X_34))))]]) ).
cnf(refute_0_48,plain,
( domain(domain(X_34)) != compose(domain(domain(X_34)),domain(domain(domain(domain(domain(domain(X_34)))))))
| compose(domain(domain(X_34)),domain(domain(domain(domain(domain(domain(X_34))))))) = domain(domain(X_34)) ),
inference(subst,[],[refute_0_29:[bind(X0,$fot(domain(domain(X_34)))),bind(Y0,$fot(compose(domain(domain(X_34)),domain(domain(domain(domain(domain(domain(X_34)))))))))]]) ).
cnf(refute_0_49,plain,
compose(domain(domain(X_34)),domain(domain(domain(domain(domain(domain(X_34))))))) = domain(domain(X_34)),
inference(resolve,[$cnf( $equal(domain(domain(X_34)),compose(domain(domain(X_34)),domain(domain(domain(domain(domain(domain(X_34)))))))) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
( compose(X_34,domain(domain(domain(domain(domain(domain(X_34))))))) != compose(X_34,compose(domain(domain(X_34)),domain(domain(domain(domain(domain(domain(X_34))))))))
| compose(domain(domain(X_34)),domain(domain(domain(domain(domain(domain(X_34))))))) != domain(domain(X_34))
| compose(X_34,domain(domain(domain(domain(domain(domain(X_34))))))) = compose(X_34,domain(domain(X_34))) ),
introduced(tautology,[equality,[$cnf( $equal(compose(X_34,domain(domain(domain(domain(domain(domain(X_34))))))),compose(X_34,compose(domain(domain(X_34)),domain(domain(domain(domain(domain(domain(X_34))))))))) ),[1,1],$fot(domain(domain(X_34)))]]) ).
cnf(refute_0_51,plain,
( compose(X_34,domain(domain(domain(domain(domain(domain(X_34))))))) != compose(X_34,compose(domain(domain(X_34)),domain(domain(domain(domain(domain(domain(X_34))))))))
| compose(X_34,domain(domain(domain(domain(domain(domain(X_34))))))) = compose(X_34,domain(domain(X_34))) ),
inference(resolve,[$cnf( $equal(compose(domain(domain(X_34)),domain(domain(domain(domain(domain(domain(X_34))))))),domain(domain(X_34))) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
compose(X_34,domain(domain(domain(domain(domain(domain(X_34))))))) = compose(X_34,domain(domain(X_34))),
inference(resolve,[$cnf( $equal(compose(X_34,domain(domain(domain(domain(domain(domain(X_34))))))),compose(X_34,compose(domain(domain(X_34)),domain(domain(domain(domain(domain(domain(X_34))))))))) )],[refute_0_14,refute_0_51]) ).
cnf(refute_0_53,plain,
( X_24 != compose(X_24,domain(domain(X_24)))
| compose(X_24,domain(domain(X_24))) = X_24 ),
inference(subst,[],[refute_0_29:[bind(X0,$fot(X_24)),bind(Y0,$fot(compose(X_24,domain(domain(X_24)))))]]) ).
cnf(refute_0_54,plain,
compose(X_24,domain(domain(X_24))) = X_24,
inference(resolve,[$cnf( $equal(X_24,compose(X_24,domain(domain(X_24)))) )],[refute_0_25,refute_0_53]) ).
cnf(refute_0_55,plain,
compose(X_34,domain(domain(X_34))) = X_34,
inference(subst,[],[refute_0_54:[bind(X_24,$fot(X_34))]]) ).
cnf(refute_0_56,plain,
( compose(X_34,domain(domain(X_34))) != X_34
| compose(X_34,domain(domain(domain(domain(domain(domain(X_34))))))) != compose(X_34,domain(domain(X_34)))
| compose(X_34,domain(domain(domain(domain(domain(domain(X_34))))))) = X_34 ),
introduced(tautology,[equality,[$cnf( $equal(compose(X_34,domain(domain(domain(domain(domain(domain(X_34))))))),compose(X_34,domain(domain(X_34)))) ),[1],$fot(X_34)]]) ).
cnf(refute_0_57,plain,
( compose(X_34,domain(domain(domain(domain(domain(domain(X_34))))))) != compose(X_34,domain(domain(X_34)))
| compose(X_34,domain(domain(domain(domain(domain(domain(X_34))))))) = X_34 ),
inference(resolve,[$cnf( $equal(compose(X_34,domain(domain(X_34))),X_34) )],[refute_0_55,refute_0_56]) ).
cnf(refute_0_58,plain,
compose(X_34,domain(domain(domain(domain(domain(domain(X_34))))))) = X_34,
inference(resolve,[$cnf( $equal(compose(X_34,domain(domain(domain(domain(domain(domain(X_34))))))),compose(X_34,domain(domain(X_34)))) )],[refute_0_52,refute_0_57]) ).
cnf(refute_0_59,plain,
compose(h,domain(domain(domain(domain(domain(domain(h))))))) = h,
inference(subst,[],[refute_0_58:[bind(X_34,$fot(h))]]) ).
cnf(refute_0_60,plain,
( ~ there_exists(compose(domain(domain(h)),domain(domain(h))))
| domain(domain(domain(h))) = codomain(domain(domain(h))) ),
inference(subst,[],[domain_codomain_composition1:[bind(X,$fot(domain(domain(h)))),bind(Y,$fot(domain(domain(h))))]]) ).
cnf(refute_0_61,plain,
( ~ there_exists(domain(compose(domain(domain(h)),domain(domain(h)))))
| there_exists(compose(domain(domain(h)),domain(domain(h)))) ),
inference(subst,[],[domain_has_elements:[bind(X,$fot(compose(domain(domain(h)),domain(domain(h)))))]]) ).
cnf(refute_0_62,plain,
( ~ there_exists(codomain(domain(compose(domain(domain(h)),domain(domain(h))))))
| there_exists(domain(compose(domain(domain(h)),domain(domain(h))))) ),
inference(subst,[],[codomain_has_elements:[bind(X,$fot(domain(compose(domain(domain(h)),domain(domain(h))))))]]) ).
cnf(refute_0_63,plain,
( ~ there_exists(compose(g,domain(compose(domain(domain(h)),domain(domain(h))))))
| domain(g) = codomain(domain(compose(domain(domain(h)),domain(domain(h))))) ),
inference(subst,[],[domain_codomain_composition1:[bind(X,$fot(g)),bind(Y,$fot(domain(compose(domain(domain(h)),domain(domain(h))))))]]) ).
cnf(refute_0_64,plain,
( ~ there_exists(codomain(compose(g,domain(compose(domain(domain(h)),domain(domain(h)))))))
| there_exists(compose(g,domain(compose(domain(domain(h)),domain(domain(h)))))) ),
inference(subst,[],[codomain_has_elements:[bind(X,$fot(compose(g,domain(compose(domain(domain(h)),domain(domain(h)))))))]]) ).
cnf(refute_0_65,plain,
( ~ there_exists(compose(b,compose(g,domain(compose(domain(domain(h)),domain(domain(h)))))))
| domain(b) = codomain(compose(g,domain(compose(domain(domain(h)),domain(domain(h)))))) ),
inference(subst,[],[domain_codomain_composition1:[bind(X,$fot(b)),bind(Y,$fot(compose(g,domain(compose(domain(domain(h)),domain(domain(h)))))))]]) ).
cnf(refute_0_66,plain,
compose(b,compose(h,X_17)) = compose(compose(b,h),X_17),
inference(subst,[],[associativity_of_compose:[bind(X,$fot(b)),bind(Y,$fot(h)),bind(Z,$fot(X_17))]]) ).
cnf(refute_0_67,plain,
( compose(b,compose(h,X_17)) != compose(compose(b,h),X_17)
| compose(b,h) != compose(b,g)
| compose(b,compose(h,X_17)) = compose(compose(b,g),X_17) ),
introduced(tautology,[equality,[$cnf( $equal(compose(b,compose(h,X_17)),compose(compose(b,h),X_17)) ),[1,0],$fot(compose(b,g))]]) ).
cnf(refute_0_68,plain,
( compose(b,compose(h,X_17)) != compose(compose(b,h),X_17)
| compose(b,compose(h,X_17)) = compose(compose(b,g),X_17) ),
inference(resolve,[$cnf( $equal(compose(b,h),compose(b,g)) )],[bh_equals_bg,refute_0_67]) ).
cnf(refute_0_69,plain,
compose(b,compose(h,X_17)) = compose(compose(b,g),X_17),
inference(resolve,[$cnf( $equal(compose(b,compose(h,X_17)),compose(compose(b,h),X_17)) )],[refute_0_66,refute_0_68]) ).
cnf(refute_0_70,plain,
( compose(X,compose(Y,Z)) != compose(compose(X,Y),Z)
| compose(compose(X,Y),Z) = compose(X,compose(Y,Z)) ),
inference(subst,[],[refute_0_29:[bind(X0,$fot(compose(X,compose(Y,Z)))),bind(Y0,$fot(compose(compose(X,Y),Z)))]]) ).
cnf(refute_0_71,plain,
compose(compose(X,Y),Z) = compose(X,compose(Y,Z)),
inference(resolve,[$cnf( $equal(compose(X,compose(Y,Z)),compose(compose(X,Y),Z)) )],[associativity_of_compose,refute_0_70]) ).
cnf(refute_0_72,plain,
compose(compose(b,g),X_17) = compose(b,compose(g,X_17)),
inference(subst,[],[refute_0_71:[bind(X,$fot(b)),bind(Y,$fot(g)),bind(Z,$fot(X_17))]]) ).
cnf(refute_0_73,plain,
( compose(b,compose(h,X_17)) != compose(compose(b,g),X_17)
| compose(compose(b,g),X_17) != compose(b,compose(g,X_17))
| compose(b,compose(h,X_17)) = compose(b,compose(g,X_17)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(compose(b,compose(h,X_17)),compose(b,compose(g,X_17))) ),[0],$fot(compose(compose(b,g),X_17))]]) ).
cnf(refute_0_74,plain,
( compose(b,compose(h,X_17)) != compose(compose(b,g),X_17)
| compose(b,compose(h,X_17)) = compose(b,compose(g,X_17)) ),
inference(resolve,[$cnf( $equal(compose(compose(b,g),X_17),compose(b,compose(g,X_17))) )],[refute_0_72,refute_0_73]) ).
cnf(refute_0_75,plain,
compose(b,compose(h,X_17)) = compose(b,compose(g,X_17)),
inference(resolve,[$cnf( $equal(compose(b,compose(h,X_17)),compose(compose(b,g),X_17)) )],[refute_0_69,refute_0_74]) ).
cnf(refute_0_76,plain,
compose(b,compose(h,compose(domain(h),X_17))) = compose(b,compose(g,compose(domain(h),X_17))),
inference(subst,[],[refute_0_75:[bind(X_17,$fot(compose(domain(h),X_17)))]]) ).
cnf(refute_0_77,plain,
compose(h,compose(domain(h),X_17)) = compose(h,X_17),
inference(subst,[],[refute_0_4:[bind(X_15,$fot(h))]]) ).
cnf(refute_0_78,plain,
( compose(b,compose(h,compose(domain(h),X_17))) != compose(b,compose(g,compose(domain(h),X_17)))
| compose(h,compose(domain(h),X_17)) != compose(h,X_17)
| compose(b,compose(h,X_17)) = compose(b,compose(g,compose(domain(h),X_17))) ),
introduced(tautology,[equality,[$cnf( $equal(compose(b,compose(h,compose(domain(h),X_17))),compose(b,compose(g,compose(domain(h),X_17)))) ),[0,1],$fot(compose(h,X_17))]]) ).
cnf(refute_0_79,plain,
( compose(b,compose(h,compose(domain(h),X_17))) != compose(b,compose(g,compose(domain(h),X_17)))
| compose(b,compose(h,X_17)) = compose(b,compose(g,compose(domain(h),X_17))) ),
inference(resolve,[$cnf( $equal(compose(h,compose(domain(h),X_17)),compose(h,X_17)) )],[refute_0_77,refute_0_78]) ).
cnf(refute_0_80,plain,
compose(b,compose(h,X_17)) = compose(b,compose(g,compose(domain(h),X_17))),
inference(resolve,[$cnf( $equal(compose(b,compose(h,compose(domain(h),X_17))),compose(b,compose(g,compose(domain(h),X_17)))) )],[refute_0_76,refute_0_79]) ).
cnf(refute_0_81,plain,
( compose(b,compose(h,X_17)) != compose(b,compose(g,X_17))
| compose(b,compose(h,X_17)) != compose(b,compose(g,compose(domain(h),X_17)))
| compose(b,compose(g,X_17)) = compose(b,compose(g,compose(domain(h),X_17))) ),
introduced(tautology,[equality,[$cnf( $equal(compose(b,compose(h,X_17)),compose(b,compose(g,compose(domain(h),X_17)))) ),[0],$fot(compose(b,compose(g,X_17)))]]) ).
cnf(refute_0_82,plain,
( compose(b,compose(h,X_17)) != compose(b,compose(g,compose(domain(h),X_17)))
| compose(b,compose(g,X_17)) = compose(b,compose(g,compose(domain(h),X_17))) ),
inference(resolve,[$cnf( $equal(compose(b,compose(h,X_17)),compose(b,compose(g,X_17))) )],[refute_0_75,refute_0_81]) ).
cnf(refute_0_83,plain,
compose(b,compose(g,X_17)) = compose(b,compose(g,compose(domain(h),X_17))),
inference(resolve,[$cnf( $equal(compose(b,compose(h,X_17)),compose(b,compose(g,compose(domain(h),X_17)))) )],[refute_0_80,refute_0_82]) ).
cnf(refute_0_84,plain,
compose(b,compose(g,domain(compose(domain(domain(h)),domain(domain(h)))))) = compose(b,compose(g,compose(domain(h),domain(compose(domain(domain(h)),domain(domain(h))))))),
inference(subst,[],[refute_0_83:[bind(X_17,$fot(domain(compose(domain(domain(h)),domain(domain(h))))))]]) ).
cnf(refute_0_85,plain,
compose(X_15,compose(domain(X_15),domain(compose(domain(X_15),domain(X_15))))) = compose(X_15,domain(compose(domain(X_15),domain(X_15)))),
inference(subst,[],[refute_0_4:[bind(X_17,$fot(domain(compose(domain(X_15),domain(X_15)))))]]) ).
cnf(refute_0_86,plain,
compose(X_15,compose(domain(X_15),compose(X_30,domain(compose(domain(X_15),X_30))))) = compose(X_15,compose(X_30,domain(compose(domain(X_15),X_30)))),
inference(subst,[],[refute_0_4:[bind(X_17,$fot(compose(X_30,domain(compose(domain(X_15),X_30)))))]]) ).
cnf(refute_0_87,plain,
compose(compose(X_15,X_16),domain(compose(X_15,X_16))) = compose(X_15,X_16),
inference(subst,[],[compose_domain:[bind(X,$fot(compose(X_15,X_16)))]]) ).
cnf(refute_0_88,plain,
compose(X_15,compose(X_16,domain(compose(X_15,X_16)))) = compose(compose(X_15,X_16),domain(compose(X_15,X_16))),
inference(subst,[],[associativity_of_compose:[bind(X,$fot(X_15)),bind(Y,$fot(X_16)),bind(Z,$fot(domain(compose(X_15,X_16))))]]) ).
cnf(refute_0_89,plain,
( compose(X_15,compose(X_16,domain(compose(X_15,X_16)))) != compose(compose(X_15,X_16),domain(compose(X_15,X_16)))
| compose(compose(X_15,X_16),domain(compose(X_15,X_16))) = compose(X_15,compose(X_16,domain(compose(X_15,X_16)))) ),
inference(subst,[],[refute_0_29:[bind(X0,$fot(compose(X_15,compose(X_16,domain(compose(X_15,X_16)))))),bind(Y0,$fot(compose(compose(X_15,X_16),domain(compose(X_15,X_16)))))]]) ).
cnf(refute_0_90,plain,
compose(compose(X_15,X_16),domain(compose(X_15,X_16))) = compose(X_15,compose(X_16,domain(compose(X_15,X_16)))),
inference(resolve,[$cnf( $equal(compose(X_15,compose(X_16,domain(compose(X_15,X_16)))),compose(compose(X_15,X_16),domain(compose(X_15,X_16)))) )],[refute_0_88,refute_0_89]) ).
cnf(refute_0_91,plain,
( compose(compose(X_15,X_16),domain(compose(X_15,X_16))) != compose(X_15,X_16)
| compose(compose(X_15,X_16),domain(compose(X_15,X_16))) != compose(X_15,compose(X_16,domain(compose(X_15,X_16))))
| compose(X_15,compose(X_16,domain(compose(X_15,X_16)))) = compose(X_15,X_16) ),
introduced(tautology,[equality,[$cnf( $equal(compose(compose(X_15,X_16),domain(compose(X_15,X_16))),compose(X_15,X_16)) ),[0],$fot(compose(X_15,compose(X_16,domain(compose(X_15,X_16)))))]]) ).
cnf(refute_0_92,plain,
( compose(compose(X_15,X_16),domain(compose(X_15,X_16))) != compose(X_15,X_16)
| compose(X_15,compose(X_16,domain(compose(X_15,X_16)))) = compose(X_15,X_16) ),
inference(resolve,[$cnf( $equal(compose(compose(X_15,X_16),domain(compose(X_15,X_16))),compose(X_15,compose(X_16,domain(compose(X_15,X_16))))) )],[refute_0_90,refute_0_91]) ).
cnf(refute_0_93,plain,
compose(X_15,compose(X_16,domain(compose(X_15,X_16)))) = compose(X_15,X_16),
inference(resolve,[$cnf( $equal(compose(compose(X_15,X_16),domain(compose(X_15,X_16))),compose(X_15,X_16)) )],[refute_0_87,refute_0_92]) ).
cnf(refute_0_94,plain,
compose(domain(X_15),compose(X_30,domain(compose(domain(X_15),X_30)))) = compose(domain(X_15),X_30),
inference(subst,[],[refute_0_93:[bind(X_15,$fot(domain(X_15))),bind(X_16,$fot(X_30))]]) ).
cnf(refute_0_95,plain,
( compose(X_15,compose(domain(X_15),compose(X_30,domain(compose(domain(X_15),X_30))))) != compose(X_15,compose(X_30,domain(compose(domain(X_15),X_30))))
| compose(domain(X_15),compose(X_30,domain(compose(domain(X_15),X_30)))) != compose(domain(X_15),X_30)
| compose(X_15,compose(domain(X_15),X_30)) = compose(X_15,compose(X_30,domain(compose(domain(X_15),X_30)))) ),
introduced(tautology,[equality,[$cnf( $equal(compose(X_15,compose(domain(X_15),compose(X_30,domain(compose(domain(X_15),X_30))))),compose(X_15,compose(X_30,domain(compose(domain(X_15),X_30))))) ),[0,1],$fot(compose(domain(X_15),X_30))]]) ).
cnf(refute_0_96,plain,
( compose(X_15,compose(domain(X_15),compose(X_30,domain(compose(domain(X_15),X_30))))) != compose(X_15,compose(X_30,domain(compose(domain(X_15),X_30))))
| compose(X_15,compose(domain(X_15),X_30)) = compose(X_15,compose(X_30,domain(compose(domain(X_15),X_30)))) ),
inference(resolve,[$cnf( $equal(compose(domain(X_15),compose(X_30,domain(compose(domain(X_15),X_30)))),compose(domain(X_15),X_30)) )],[refute_0_94,refute_0_95]) ).
cnf(refute_0_97,plain,
compose(X_15,compose(domain(X_15),X_30)) = compose(X_15,compose(X_30,domain(compose(domain(X_15),X_30)))),
inference(resolve,[$cnf( $equal(compose(X_15,compose(domain(X_15),compose(X_30,domain(compose(domain(X_15),X_30))))),compose(X_15,compose(X_30,domain(compose(domain(X_15),X_30))))) )],[refute_0_86,refute_0_96]) ).
cnf(refute_0_98,plain,
compose(X_15,compose(domain(X_15),X_30)) = compose(X_15,X_30),
inference(subst,[],[refute_0_4:[bind(X_17,$fot(X_30))]]) ).
cnf(refute_0_99,plain,
( compose(X_15,compose(domain(X_15),X_30)) != compose(X_15,X_30)
| compose(X_15,compose(domain(X_15),X_30)) != compose(X_15,compose(X_30,domain(compose(domain(X_15),X_30))))
| compose(X_15,X_30) = compose(X_15,compose(X_30,domain(compose(domain(X_15),X_30)))) ),
introduced(tautology,[equality,[$cnf( $equal(compose(X_15,compose(domain(X_15),X_30)),compose(X_15,compose(X_30,domain(compose(domain(X_15),X_30))))) ),[0],$fot(compose(X_15,X_30))]]) ).
cnf(refute_0_100,plain,
( compose(X_15,compose(domain(X_15),X_30)) != compose(X_15,compose(X_30,domain(compose(domain(X_15),X_30))))
| compose(X_15,X_30) = compose(X_15,compose(X_30,domain(compose(domain(X_15),X_30)))) ),
inference(resolve,[$cnf( $equal(compose(X_15,compose(domain(X_15),X_30)),compose(X_15,X_30)) )],[refute_0_98,refute_0_99]) ).
cnf(refute_0_101,plain,
compose(X_15,X_30) = compose(X_15,compose(X_30,domain(compose(domain(X_15),X_30)))),
inference(resolve,[$cnf( $equal(compose(X_15,compose(domain(X_15),X_30)),compose(X_15,compose(X_30,domain(compose(domain(X_15),X_30))))) )],[refute_0_97,refute_0_100]) ).
cnf(refute_0_102,plain,
compose(X_15,domain(X_15)) = compose(X_15,compose(domain(X_15),domain(compose(domain(X_15),domain(X_15))))),
inference(subst,[],[refute_0_101:[bind(X_30,$fot(domain(X_15)))]]) ).
cnf(refute_0_103,plain,
( compose(X_15,domain(X_15)) != compose(X_15,compose(domain(X_15),domain(compose(domain(X_15),domain(X_15)))))
| compose(X_15,compose(domain(X_15),domain(compose(domain(X_15),domain(X_15))))) = compose(X_15,domain(X_15)) ),
inference(subst,[],[refute_0_29:[bind(X0,$fot(compose(X_15,domain(X_15)))),bind(Y0,$fot(compose(X_15,compose(domain(X_15),domain(compose(domain(X_15),domain(X_15)))))))]]) ).
cnf(refute_0_104,plain,
compose(X_15,compose(domain(X_15),domain(compose(domain(X_15),domain(X_15))))) = compose(X_15,domain(X_15)),
inference(resolve,[$cnf( $equal(compose(X_15,domain(X_15)),compose(X_15,compose(domain(X_15),domain(compose(domain(X_15),domain(X_15)))))) )],[refute_0_102,refute_0_103]) ).
cnf(refute_0_105,plain,
( compose(X_15,compose(domain(X_15),domain(compose(domain(X_15),domain(X_15))))) != compose(X_15,domain(X_15))
| compose(X_15,compose(domain(X_15),domain(compose(domain(X_15),domain(X_15))))) != compose(X_15,domain(compose(domain(X_15),domain(X_15))))
| compose(X_15,domain(X_15)) = compose(X_15,domain(compose(domain(X_15),domain(X_15)))) ),
introduced(tautology,[equality,[$cnf( $equal(compose(X_15,compose(domain(X_15),domain(compose(domain(X_15),domain(X_15))))),compose(X_15,domain(compose(domain(X_15),domain(X_15))))) ),[0],$fot(compose(X_15,domain(X_15)))]]) ).
cnf(refute_0_106,plain,
( compose(X_15,compose(domain(X_15),domain(compose(domain(X_15),domain(X_15))))) != compose(X_15,domain(compose(domain(X_15),domain(X_15))))
| compose(X_15,domain(X_15)) = compose(X_15,domain(compose(domain(X_15),domain(X_15)))) ),
inference(resolve,[$cnf( $equal(compose(X_15,compose(domain(X_15),domain(compose(domain(X_15),domain(X_15))))),compose(X_15,domain(X_15))) )],[refute_0_104,refute_0_105]) ).
cnf(refute_0_107,plain,
compose(X_15,domain(X_15)) = compose(X_15,domain(compose(domain(X_15),domain(X_15)))),
inference(resolve,[$cnf( $equal(compose(X_15,compose(domain(X_15),domain(compose(domain(X_15),domain(X_15))))),compose(X_15,domain(compose(domain(X_15),domain(X_15))))) )],[refute_0_85,refute_0_106]) ).
cnf(refute_0_108,plain,
( compose(X_15,domain(X_15)) != X_15
| compose(X_15,domain(X_15)) != compose(X_15,domain(compose(domain(X_15),domain(X_15))))
| X_15 = compose(X_15,domain(compose(domain(X_15),domain(X_15)))) ),
introduced(tautology,[equality,[$cnf( $equal(compose(X_15,domain(X_15)),compose(X_15,domain(compose(domain(X_15),domain(X_15))))) ),[0],$fot(X_15)]]) ).
cnf(refute_0_109,plain,
( compose(X_15,domain(X_15)) != compose(X_15,domain(compose(domain(X_15),domain(X_15))))
| X_15 = compose(X_15,domain(compose(domain(X_15),domain(X_15)))) ),
inference(resolve,[$cnf( $equal(compose(X_15,domain(X_15)),X_15) )],[refute_0_1,refute_0_108]) ).
cnf(refute_0_110,plain,
X_15 = compose(X_15,domain(compose(domain(X_15),domain(X_15)))),
inference(resolve,[$cnf( $equal(compose(X_15,domain(X_15)),compose(X_15,domain(compose(domain(X_15),domain(X_15))))) )],[refute_0_107,refute_0_109]) ).
cnf(refute_0_111,plain,
domain(h) = compose(domain(h),domain(compose(domain(domain(h)),domain(domain(h))))),
inference(subst,[],[refute_0_110:[bind(X_15,$fot(domain(h)))]]) ).
cnf(refute_0_112,plain,
( domain(h) != compose(domain(h),domain(compose(domain(domain(h)),domain(domain(h)))))
| compose(domain(h),domain(compose(domain(domain(h)),domain(domain(h))))) = domain(h) ),
inference(subst,[],[refute_0_29:[bind(X0,$fot(domain(h))),bind(Y0,$fot(compose(domain(h),domain(compose(domain(domain(h)),domain(domain(h)))))))]]) ).
cnf(refute_0_113,plain,
compose(domain(h),domain(compose(domain(domain(h)),domain(domain(h))))) = domain(h),
inference(resolve,[$cnf( $equal(domain(h),compose(domain(h),domain(compose(domain(domain(h)),domain(domain(h)))))) )],[refute_0_111,refute_0_112]) ).
cnf(refute_0_114,plain,
( compose(b,compose(g,domain(compose(domain(domain(h)),domain(domain(h)))))) != compose(b,compose(g,compose(domain(h),domain(compose(domain(domain(h)),domain(domain(h)))))))
| compose(domain(h),domain(compose(domain(domain(h)),domain(domain(h))))) != domain(h)
| compose(b,compose(g,domain(compose(domain(domain(h)),domain(domain(h)))))) = compose(b,compose(g,domain(h))) ),
introduced(tautology,[equality,[$cnf( $equal(compose(b,compose(g,domain(compose(domain(domain(h)),domain(domain(h)))))),compose(b,compose(g,compose(domain(h),domain(compose(domain(domain(h)),domain(domain(h)))))))) ),[1,1,1],$fot(domain(h))]]) ).
cnf(refute_0_115,plain,
( compose(b,compose(g,domain(compose(domain(domain(h)),domain(domain(h)))))) != compose(b,compose(g,compose(domain(h),domain(compose(domain(domain(h)),domain(domain(h)))))))
| compose(b,compose(g,domain(compose(domain(domain(h)),domain(domain(h)))))) = compose(b,compose(g,domain(h))) ),
inference(resolve,[$cnf( $equal(compose(domain(h),domain(compose(domain(domain(h)),domain(domain(h))))),domain(h)) )],[refute_0_113,refute_0_114]) ).
cnf(refute_0_116,plain,
compose(b,compose(g,domain(compose(domain(domain(h)),domain(domain(h)))))) = compose(b,compose(g,domain(h))),
inference(resolve,[$cnf( $equal(compose(b,compose(g,domain(compose(domain(domain(h)),domain(domain(h)))))),compose(b,compose(g,compose(domain(h),domain(compose(domain(domain(h)),domain(domain(h)))))))) )],[refute_0_84,refute_0_115]) ).
cnf(refute_0_117,plain,
compose(b,compose(h,domain(h))) = compose(b,compose(g,domain(h))),
inference(subst,[],[refute_0_75:[bind(X_17,$fot(domain(h)))]]) ).
cnf(refute_0_118,plain,
compose(h,domain(h)) = h,
inference(subst,[],[compose_domain:[bind(X,$fot(h))]]) ).
cnf(refute_0_119,plain,
( compose(b,compose(h,domain(h))) != compose(b,compose(g,domain(h)))
| compose(h,domain(h)) != h
| compose(b,h) = compose(b,compose(g,domain(h))) ),
introduced(tautology,[equality,[$cnf( $equal(compose(b,compose(h,domain(h))),compose(b,compose(g,domain(h)))) ),[0,1],$fot(h)]]) ).
cnf(refute_0_120,plain,
( compose(b,compose(h,domain(h))) != compose(b,compose(g,domain(h)))
| compose(b,h) = compose(b,compose(g,domain(h))) ),
inference(resolve,[$cnf( $equal(compose(h,domain(h)),h) )],[refute_0_118,refute_0_119]) ).
cnf(refute_0_121,plain,
compose(b,h) = compose(b,compose(g,domain(h))),
inference(resolve,[$cnf( $equal(compose(b,compose(h,domain(h))),compose(b,compose(g,domain(h)))) )],[refute_0_117,refute_0_120]) ).
cnf(refute_0_122,plain,
( compose(b,h) != compose(b,compose(g,domain(h)))
| compose(b,h) != compose(b,g)
| compose(b,g) = compose(b,compose(g,domain(h))) ),
introduced(tautology,[equality,[$cnf( $equal(compose(b,h),compose(b,compose(g,domain(h)))) ),[0],$fot(compose(b,g))]]) ).
cnf(refute_0_123,plain,
( compose(b,h) != compose(b,compose(g,domain(h)))
| compose(b,g) = compose(b,compose(g,domain(h))) ),
inference(resolve,[$cnf( $equal(compose(b,h),compose(b,g)) )],[bh_equals_bg,refute_0_122]) ).
cnf(refute_0_124,plain,
compose(b,g) = compose(b,compose(g,domain(h))),
inference(resolve,[$cnf( $equal(compose(b,h),compose(b,compose(g,domain(h)))) )],[refute_0_121,refute_0_123]) ).
cnf(refute_0_125,plain,
( compose(b,g) != compose(b,compose(g,domain(h)))
| compose(b,compose(g,domain(h))) = compose(b,g) ),
inference(subst,[],[refute_0_29:[bind(X0,$fot(compose(b,g))),bind(Y0,$fot(compose(b,compose(g,domain(h)))))]]) ).
cnf(refute_0_126,plain,
compose(b,compose(g,domain(h))) = compose(b,g),
inference(resolve,[$cnf( $equal(compose(b,g),compose(b,compose(g,domain(h)))) )],[refute_0_124,refute_0_125]) ).
cnf(refute_0_127,plain,
( compose(b,compose(g,domain(compose(domain(domain(h)),domain(domain(h)))))) != compose(b,compose(g,domain(h)))
| compose(b,compose(g,domain(h))) != compose(b,g)
| compose(b,compose(g,domain(compose(domain(domain(h)),domain(domain(h)))))) = compose(b,g) ),
introduced(tautology,[equality,[$cnf( ~ $equal(compose(b,compose(g,domain(compose(domain(domain(h)),domain(domain(h)))))),compose(b,g)) ),[0],$fot(compose(b,compose(g,domain(h))))]]) ).
cnf(refute_0_128,plain,
( compose(b,compose(g,domain(compose(domain(domain(h)),domain(domain(h)))))) != compose(b,compose(g,domain(h)))
| compose(b,compose(g,domain(compose(domain(domain(h)),domain(domain(h)))))) = compose(b,g) ),
inference(resolve,[$cnf( $equal(compose(b,compose(g,domain(h))),compose(b,g)) )],[refute_0_126,refute_0_127]) ).
cnf(refute_0_129,plain,
compose(b,compose(g,domain(compose(domain(domain(h)),domain(domain(h)))))) = compose(b,g),
inference(resolve,[$cnf( $equal(compose(b,compose(g,domain(compose(domain(domain(h)),domain(domain(h)))))),compose(b,compose(g,domain(h)))) )],[refute_0_116,refute_0_128]) ).
cnf(refute_0_130,plain,
( compose(b,compose(g,domain(compose(domain(domain(h)),domain(domain(h)))))) != compose(b,g)
| ~ there_exists(compose(b,g))
| there_exists(compose(b,compose(g,domain(compose(domain(domain(h)),domain(domain(h))))))) ),
introduced(tautology,[equality,[$cnf( ~ there_exists(compose(b,compose(g,domain(compose(domain(domain(h)),domain(domain(h))))))) ),[0],$fot(compose(b,g))]]) ).
cnf(refute_0_131,plain,
( ~ there_exists(compose(b,g))
| there_exists(compose(b,compose(g,domain(compose(domain(domain(h)),domain(domain(h))))))) ),
inference(resolve,[$cnf( $equal(compose(b,compose(g,domain(compose(domain(domain(h)),domain(domain(h)))))),compose(b,g)) )],[refute_0_129,refute_0_130]) ).
cnf(refute_0_132,plain,
( ~ there_exists(compose(b,g))
| domain(b) = codomain(compose(g,domain(compose(domain(domain(h)),domain(domain(h)))))) ),
inference(resolve,[$cnf( there_exists(compose(b,compose(g,domain(compose(domain(domain(h)),domain(domain(h))))))) )],[refute_0_131,refute_0_65]) ).
cnf(refute_0_133,plain,
( compose(b,h) != compose(b,g)
| ~ there_exists(compose(b,h))
| there_exists(compose(b,g)) ),
introduced(tautology,[equality,[$cnf( there_exists(compose(b,h)) ),[0],$fot(compose(b,g))]]) ).
cnf(refute_0_134,plain,
( ~ there_exists(compose(b,h))
| there_exists(compose(b,g)) ),
inference(resolve,[$cnf( $equal(compose(b,h),compose(b,g)) )],[bh_equals_bg,refute_0_133]) ).
cnf(refute_0_135,plain,
there_exists(compose(b,g)),
inference(resolve,[$cnf( there_exists(compose(b,h)) )],[assume_bh_exists,refute_0_134]) ).
cnf(refute_0_136,plain,
( ~ there_exists(compose(b,g))
| domain(b) = codomain(g) ),
inference(subst,[],[domain_codomain_composition1:[bind(X,$fot(b)),bind(Y,$fot(g))]]) ).
cnf(refute_0_137,plain,
domain(b) = codomain(g),
inference(resolve,[$cnf( there_exists(compose(b,g)) )],[refute_0_135,refute_0_136]) ).
cnf(refute_0_138,plain,
( domain(b) != codomain(compose(g,domain(compose(domain(domain(h)),domain(domain(h))))))
| domain(b) != codomain(g)
| codomain(g) = codomain(compose(g,domain(compose(domain(domain(h)),domain(domain(h)))))) ),
introduced(tautology,[equality,[$cnf( $equal(domain(b),codomain(compose(g,domain(compose(domain(domain(h)),domain(domain(h))))))) ),[0],$fot(codomain(g))]]) ).
cnf(refute_0_139,plain,
( domain(b) != codomain(compose(g,domain(compose(domain(domain(h)),domain(domain(h))))))
| codomain(g) = codomain(compose(g,domain(compose(domain(domain(h)),domain(domain(h)))))) ),
inference(resolve,[$cnf( $equal(domain(b),codomain(g)) )],[refute_0_137,refute_0_138]) ).
cnf(refute_0_140,plain,
( ~ there_exists(compose(b,g))
| codomain(g) = codomain(compose(g,domain(compose(domain(domain(h)),domain(domain(h)))))) ),
inference(resolve,[$cnf( $equal(domain(b),codomain(compose(g,domain(compose(domain(domain(h)),domain(domain(h))))))) )],[refute_0_132,refute_0_139]) ).
cnf(refute_0_141,plain,
codomain(g) = codomain(compose(g,domain(compose(domain(domain(h)),domain(domain(h)))))),
inference(resolve,[$cnf( there_exists(compose(b,g)) )],[refute_0_135,refute_0_140]) ).
cnf(refute_0_142,plain,
( codomain(g) != codomain(compose(g,domain(compose(domain(domain(h)),domain(domain(h))))))
| codomain(compose(g,domain(compose(domain(domain(h)),domain(domain(h)))))) = codomain(g) ),
inference(subst,[],[refute_0_29:[bind(X0,$fot(codomain(g))),bind(Y0,$fot(codomain(compose(g,domain(compose(domain(domain(h)),domain(domain(h))))))))]]) ).
cnf(refute_0_143,plain,
codomain(compose(g,domain(compose(domain(domain(h)),domain(domain(h)))))) = codomain(g),
inference(resolve,[$cnf( $equal(codomain(g),codomain(compose(g,domain(compose(domain(domain(h)),domain(domain(h))))))) )],[refute_0_141,refute_0_142]) ).
cnf(refute_0_144,plain,
( codomain(compose(g,domain(compose(domain(domain(h)),domain(domain(h)))))) != codomain(g)
| ~ there_exists(codomain(g))
| there_exists(codomain(compose(g,domain(compose(domain(domain(h)),domain(domain(h))))))) ),
introduced(tautology,[equality,[$cnf( ~ there_exists(codomain(compose(g,domain(compose(domain(domain(h)),domain(domain(h))))))) ),[0],$fot(codomain(g))]]) ).
cnf(refute_0_145,plain,
( ~ there_exists(codomain(g))
| there_exists(codomain(compose(g,domain(compose(domain(domain(h)),domain(domain(h))))))) ),
inference(resolve,[$cnf( $equal(codomain(compose(g,domain(compose(domain(domain(h)),domain(domain(h)))))),codomain(g)) )],[refute_0_143,refute_0_144]) ).
cnf(refute_0_146,plain,
( ~ there_exists(codomain(g))
| there_exists(compose(g,domain(compose(domain(domain(h)),domain(domain(h)))))) ),
inference(resolve,[$cnf( there_exists(codomain(compose(g,domain(compose(domain(domain(h)),domain(domain(h))))))) )],[refute_0_145,refute_0_64]) ).
cnf(refute_0_147,plain,
( ~ there_exists(compose(b,g))
| there_exists(domain(b)) ),
inference(subst,[],[composition_implies_domain:[bind(X,$fot(b)),bind(Y,$fot(g))]]) ).
cnf(refute_0_148,plain,
there_exists(domain(b)),
inference(resolve,[$cnf( there_exists(compose(b,g)) )],[refute_0_135,refute_0_147]) ).
cnf(refute_0_149,plain,
( domain(b) != codomain(g)
| ~ there_exists(domain(b))
| there_exists(codomain(g)) ),
introduced(tautology,[equality,[$cnf( there_exists(domain(b)) ),[0],$fot(codomain(g))]]) ).
cnf(refute_0_150,plain,
( ~ there_exists(domain(b))
| there_exists(codomain(g)) ),
inference(resolve,[$cnf( $equal(domain(b),codomain(g)) )],[refute_0_137,refute_0_149]) ).
cnf(refute_0_151,plain,
there_exists(codomain(g)),
inference(resolve,[$cnf( there_exists(domain(b)) )],[refute_0_148,refute_0_150]) ).
cnf(refute_0_152,plain,
there_exists(compose(g,domain(compose(domain(domain(h)),domain(domain(h)))))),
inference(resolve,[$cnf( there_exists(codomain(g)) )],[refute_0_151,refute_0_146]) ).
cnf(refute_0_153,plain,
domain(g) = codomain(domain(compose(domain(domain(h)),domain(domain(h))))),
inference(resolve,[$cnf( there_exists(compose(g,domain(compose(domain(domain(h)),domain(domain(h)))))) )],[refute_0_152,refute_0_63]) ).
cnf(refute_0_154,plain,
( domain(g) != codomain(domain(compose(domain(domain(h)),domain(domain(h)))))
| codomain(domain(compose(domain(domain(h)),domain(domain(h))))) = domain(g) ),
inference(subst,[],[refute_0_29:[bind(X0,$fot(domain(g))),bind(Y0,$fot(codomain(domain(compose(domain(domain(h)),domain(domain(h)))))))]]) ).
cnf(refute_0_155,plain,
codomain(domain(compose(domain(domain(h)),domain(domain(h))))) = domain(g),
inference(resolve,[$cnf( $equal(domain(g),codomain(domain(compose(domain(domain(h)),domain(domain(h)))))) )],[refute_0_153,refute_0_154]) ).
cnf(refute_0_156,plain,
( codomain(domain(compose(domain(domain(h)),domain(domain(h))))) != domain(g)
| ~ there_exists(domain(g))
| there_exists(codomain(domain(compose(domain(domain(h)),domain(domain(h)))))) ),
introduced(tautology,[equality,[$cnf( ~ there_exists(codomain(domain(compose(domain(domain(h)),domain(domain(h)))))) ),[0],$fot(domain(g))]]) ).
cnf(refute_0_157,plain,
( ~ there_exists(domain(g))
| there_exists(codomain(domain(compose(domain(domain(h)),domain(domain(h)))))) ),
inference(resolve,[$cnf( $equal(codomain(domain(compose(domain(domain(h)),domain(domain(h))))),domain(g)) )],[refute_0_155,refute_0_156]) ).
cnf(refute_0_158,plain,
( ~ there_exists(domain(g))
| there_exists(domain(compose(domain(domain(h)),domain(domain(h))))) ),
inference(resolve,[$cnf( there_exists(codomain(domain(compose(domain(domain(h)),domain(domain(h)))))) )],[refute_0_157,refute_0_62]) ).
cnf(refute_0_159,plain,
( ~ there_exists(compose(X_7,domain(X_7)))
| there_exists(domain(X_7)) ),
inference(subst,[],[composition_implies_domain:[bind(X,$fot(X_7)),bind(Y,$fot(domain(X_7)))]]) ).
cnf(refute_0_160,plain,
compose(X_7,domain(X_7)) = X_7,
inference(subst,[],[compose_domain:[bind(X,$fot(X_7))]]) ).
cnf(refute_0_161,plain,
( compose(X_7,domain(X_7)) != X_7
| ~ there_exists(X_7)
| there_exists(compose(X_7,domain(X_7))) ),
introduced(tautology,[equality,[$cnf( ~ there_exists(compose(X_7,domain(X_7))) ),[0],$fot(X_7)]]) ).
cnf(refute_0_162,plain,
( ~ there_exists(X_7)
| there_exists(compose(X_7,domain(X_7))) ),
inference(resolve,[$cnf( $equal(compose(X_7,domain(X_7)),X_7) )],[refute_0_160,refute_0_161]) ).
cnf(refute_0_163,plain,
( ~ there_exists(X_7)
| there_exists(domain(X_7)) ),
inference(resolve,[$cnf( there_exists(compose(X_7,domain(X_7))) )],[refute_0_162,refute_0_159]) ).
cnf(refute_0_164,plain,
( ~ there_exists(g)
| there_exists(domain(g)) ),
inference(subst,[],[refute_0_163:[bind(X_7,$fot(g))]]) ).
cnf(refute_0_165,plain,
( ~ there_exists(codomain(g))
| there_exists(g) ),
inference(subst,[],[codomain_has_elements:[bind(X,$fot(g))]]) ).
cnf(refute_0_166,plain,
there_exists(g),
inference(resolve,[$cnf( there_exists(codomain(g)) )],[refute_0_151,refute_0_165]) ).
cnf(refute_0_167,plain,
there_exists(domain(g)),
inference(resolve,[$cnf( there_exists(g) )],[refute_0_166,refute_0_164]) ).
cnf(refute_0_168,plain,
there_exists(domain(compose(domain(domain(h)),domain(domain(h))))),
inference(resolve,[$cnf( there_exists(domain(g)) )],[refute_0_167,refute_0_158]) ).
cnf(refute_0_169,plain,
there_exists(compose(domain(domain(h)),domain(domain(h)))),
inference(resolve,[$cnf( there_exists(domain(compose(domain(domain(h)),domain(domain(h))))) )],[refute_0_168,refute_0_61]) ).
cnf(refute_0_170,plain,
domain(domain(domain(h))) = codomain(domain(domain(h))),
inference(resolve,[$cnf( there_exists(compose(domain(domain(h)),domain(domain(h)))) )],[refute_0_169,refute_0_60]) ).
cnf(refute_0_171,plain,
( ~ there_exists(compose(g,domain(domain(h))))
| domain(g) = codomain(domain(domain(h))) ),
inference(subst,[],[domain_codomain_composition1:[bind(X,$fot(g)),bind(Y,$fot(domain(domain(h))))]]) ).
cnf(refute_0_172,plain,
( ~ there_exists(codomain(compose(g,domain(domain(h)))))
| there_exists(compose(g,domain(domain(h)))) ),
inference(subst,[],[codomain_has_elements:[bind(X,$fot(compose(g,domain(domain(h)))))]]) ).
cnf(refute_0_173,plain,
( ~ there_exists(compose(b,compose(g,domain(domain(h)))))
| domain(b) = codomain(compose(g,domain(domain(h)))) ),
inference(subst,[],[domain_codomain_composition1:[bind(X,$fot(b)),bind(Y,$fot(compose(g,domain(domain(h)))))]]) ).
cnf(refute_0_174,plain,
compose(b,compose(h,domain(domain(h)))) = compose(b,compose(g,domain(domain(h)))),
inference(subst,[],[refute_0_75:[bind(X_17,$fot(domain(domain(h))))]]) ).
cnf(refute_0_175,plain,
h = compose(h,domain(domain(h))),
inference(subst,[],[refute_0_25:[bind(X_24,$fot(h))]]) ).
cnf(refute_0_176,plain,
( h != compose(h,domain(domain(h)))
| compose(h,domain(domain(h))) = h ),
inference(subst,[],[refute_0_29:[bind(X0,$fot(h)),bind(Y0,$fot(compose(h,domain(domain(h)))))]]) ).
cnf(refute_0_177,plain,
compose(h,domain(domain(h))) = h,
inference(resolve,[$cnf( $equal(h,compose(h,domain(domain(h)))) )],[refute_0_175,refute_0_176]) ).
cnf(refute_0_178,plain,
( compose(b,compose(h,domain(domain(h)))) != compose(b,compose(g,domain(domain(h))))
| compose(h,domain(domain(h))) != h
| compose(b,h) = compose(b,compose(g,domain(domain(h)))) ),
introduced(tautology,[equality,[$cnf( $equal(compose(b,compose(h,domain(domain(h)))),compose(b,compose(g,domain(domain(h))))) ),[0,1],$fot(h)]]) ).
cnf(refute_0_179,plain,
( compose(b,compose(h,domain(domain(h)))) != compose(b,compose(g,domain(domain(h))))
| compose(b,h) = compose(b,compose(g,domain(domain(h)))) ),
inference(resolve,[$cnf( $equal(compose(h,domain(domain(h))),h) )],[refute_0_177,refute_0_178]) ).
cnf(refute_0_180,plain,
compose(b,h) = compose(b,compose(g,domain(domain(h)))),
inference(resolve,[$cnf( $equal(compose(b,compose(h,domain(domain(h)))),compose(b,compose(g,domain(domain(h))))) )],[refute_0_174,refute_0_179]) ).
cnf(refute_0_181,plain,
( compose(b,h) != compose(b,compose(g,domain(domain(h))))
| compose(b,h) != compose(b,g)
| compose(b,g) = compose(b,compose(g,domain(domain(h)))) ),
introduced(tautology,[equality,[$cnf( $equal(compose(b,h),compose(b,compose(g,domain(domain(h))))) ),[0],$fot(compose(b,g))]]) ).
cnf(refute_0_182,plain,
( compose(b,h) != compose(b,compose(g,domain(domain(h))))
| compose(b,g) = compose(b,compose(g,domain(domain(h)))) ),
inference(resolve,[$cnf( $equal(compose(b,h),compose(b,g)) )],[bh_equals_bg,refute_0_181]) ).
cnf(refute_0_183,plain,
compose(b,g) = compose(b,compose(g,domain(domain(h)))),
inference(resolve,[$cnf( $equal(compose(b,h),compose(b,compose(g,domain(domain(h))))) )],[refute_0_180,refute_0_182]) ).
cnf(refute_0_184,plain,
( compose(b,g) != compose(b,compose(g,domain(domain(h))))
| compose(b,compose(g,domain(domain(h)))) = compose(b,g) ),
inference(subst,[],[refute_0_29:[bind(X0,$fot(compose(b,g))),bind(Y0,$fot(compose(b,compose(g,domain(domain(h))))))]]) ).
cnf(refute_0_185,plain,
compose(b,compose(g,domain(domain(h)))) = compose(b,g),
inference(resolve,[$cnf( $equal(compose(b,g),compose(b,compose(g,domain(domain(h))))) )],[refute_0_183,refute_0_184]) ).
cnf(refute_0_186,plain,
( compose(b,compose(g,domain(domain(h)))) != compose(b,g)
| ~ there_exists(compose(b,g))
| there_exists(compose(b,compose(g,domain(domain(h))))) ),
introduced(tautology,[equality,[$cnf( ~ there_exists(compose(b,compose(g,domain(domain(h))))) ),[0],$fot(compose(b,g))]]) ).
cnf(refute_0_187,plain,
( ~ there_exists(compose(b,g))
| there_exists(compose(b,compose(g,domain(domain(h))))) ),
inference(resolve,[$cnf( $equal(compose(b,compose(g,domain(domain(h)))),compose(b,g)) )],[refute_0_185,refute_0_186]) ).
cnf(refute_0_188,plain,
( ~ there_exists(compose(b,g))
| domain(b) = codomain(compose(g,domain(domain(h)))) ),
inference(resolve,[$cnf( there_exists(compose(b,compose(g,domain(domain(h))))) )],[refute_0_187,refute_0_173]) ).
cnf(refute_0_189,plain,
( domain(b) != codomain(compose(g,domain(domain(h))))
| domain(b) != codomain(g)
| codomain(g) = codomain(compose(g,domain(domain(h)))) ),
introduced(tautology,[equality,[$cnf( $equal(domain(b),codomain(compose(g,domain(domain(h))))) ),[0],$fot(codomain(g))]]) ).
cnf(refute_0_190,plain,
( domain(b) != codomain(compose(g,domain(domain(h))))
| codomain(g) = codomain(compose(g,domain(domain(h)))) ),
inference(resolve,[$cnf( $equal(domain(b),codomain(g)) )],[refute_0_137,refute_0_189]) ).
cnf(refute_0_191,plain,
( ~ there_exists(compose(b,g))
| codomain(g) = codomain(compose(g,domain(domain(h)))) ),
inference(resolve,[$cnf( $equal(domain(b),codomain(compose(g,domain(domain(h))))) )],[refute_0_188,refute_0_190]) ).
cnf(refute_0_192,plain,
codomain(g) = codomain(compose(g,domain(domain(h)))),
inference(resolve,[$cnf( there_exists(compose(b,g)) )],[refute_0_135,refute_0_191]) ).
cnf(refute_0_193,plain,
( codomain(g) != codomain(compose(g,domain(domain(h))))
| codomain(compose(g,domain(domain(h)))) = codomain(g) ),
inference(subst,[],[refute_0_29:[bind(X0,$fot(codomain(g))),bind(Y0,$fot(codomain(compose(g,domain(domain(h))))))]]) ).
cnf(refute_0_194,plain,
codomain(compose(g,domain(domain(h)))) = codomain(g),
inference(resolve,[$cnf( $equal(codomain(g),codomain(compose(g,domain(domain(h))))) )],[refute_0_192,refute_0_193]) ).
cnf(refute_0_195,plain,
( codomain(compose(g,domain(domain(h)))) != codomain(g)
| ~ there_exists(codomain(g))
| there_exists(codomain(compose(g,domain(domain(h))))) ),
introduced(tautology,[equality,[$cnf( ~ there_exists(codomain(compose(g,domain(domain(h))))) ),[0],$fot(codomain(g))]]) ).
cnf(refute_0_196,plain,
( ~ there_exists(codomain(g))
| there_exists(codomain(compose(g,domain(domain(h))))) ),
inference(resolve,[$cnf( $equal(codomain(compose(g,domain(domain(h)))),codomain(g)) )],[refute_0_194,refute_0_195]) ).
cnf(refute_0_197,plain,
( ~ there_exists(codomain(g))
| there_exists(compose(g,domain(domain(h)))) ),
inference(resolve,[$cnf( there_exists(codomain(compose(g,domain(domain(h))))) )],[refute_0_196,refute_0_172]) ).
cnf(refute_0_198,plain,
there_exists(compose(g,domain(domain(h)))),
inference(resolve,[$cnf( there_exists(codomain(g)) )],[refute_0_151,refute_0_197]) ).
cnf(refute_0_199,plain,
domain(g) = codomain(domain(domain(h))),
inference(resolve,[$cnf( there_exists(compose(g,domain(domain(h)))) )],[refute_0_198,refute_0_171]) ).
cnf(refute_0_200,plain,
( domain(g) != codomain(domain(domain(h)))
| codomain(domain(domain(h))) = domain(g) ),
inference(subst,[],[refute_0_29:[bind(X0,$fot(domain(g))),bind(Y0,$fot(codomain(domain(domain(h)))))]]) ).
cnf(refute_0_201,plain,
codomain(domain(domain(h))) = domain(g),
inference(resolve,[$cnf( $equal(domain(g),codomain(domain(domain(h)))) )],[refute_0_199,refute_0_200]) ).
cnf(refute_0_202,plain,
( codomain(domain(domain(h))) != domain(g)
| domain(domain(domain(h))) != codomain(domain(domain(h)))
| domain(domain(domain(h))) = domain(g) ),
introduced(tautology,[equality,[$cnf( $equal(domain(domain(domain(h))),codomain(domain(domain(h)))) ),[1],$fot(domain(g))]]) ).
cnf(refute_0_203,plain,
( domain(domain(domain(h))) != codomain(domain(domain(h)))
| domain(domain(domain(h))) = domain(g) ),
inference(resolve,[$cnf( $equal(codomain(domain(domain(h))),domain(g)) )],[refute_0_201,refute_0_202]) ).
cnf(refute_0_204,plain,
domain(domain(domain(h))) = domain(g),
inference(resolve,[$cnf( $equal(domain(domain(domain(h))),codomain(domain(domain(h)))) )],[refute_0_170,refute_0_203]) ).
cnf(refute_0_205,plain,
( compose(h,domain(domain(domain(domain(domain(domain(h))))))) != h
| domain(domain(domain(h))) != domain(g)
| compose(h,domain(domain(domain(domain(g))))) = h ),
introduced(tautology,[equality,[$cnf( $equal(compose(h,domain(domain(domain(domain(domain(domain(h))))))),h) ),[0,1,0,0,0],$fot(domain(g))]]) ).
cnf(refute_0_206,plain,
( compose(h,domain(domain(domain(domain(domain(domain(h))))))) != h
| compose(h,domain(domain(domain(domain(g))))) = h ),
inference(resolve,[$cnf( $equal(domain(domain(domain(h))),domain(g)) )],[refute_0_204,refute_0_205]) ).
cnf(refute_0_207,plain,
compose(h,domain(domain(domain(domain(g))))) = h,
inference(resolve,[$cnf( $equal(compose(h,domain(domain(domain(domain(domain(domain(h))))))),h) )],[refute_0_59,refute_0_206]) ).
cnf(refute_0_208,plain,
( ~ there_exists(compose(domain(g),domain(h)))
| domain(domain(g)) = codomain(domain(h)) ),
inference(subst,[],[domain_codomain_composition1:[bind(X,$fot(domain(g))),bind(Y,$fot(domain(h)))]]) ).
cnf(refute_0_209,plain,
compose(codomain(domain(h)),domain(h)) = domain(h),
inference(subst,[],[compose_codomain:[bind(X,$fot(domain(h)))]]) ).
cnf(refute_0_210,plain,
( ~ there_exists(compose(g,domain(h)))
| domain(g) = codomain(domain(h)) ),
inference(subst,[],[domain_codomain_composition1:[bind(X,$fot(g)),bind(Y,$fot(domain(h)))]]) ).
cnf(refute_0_211,plain,
( ~ there_exists(codomain(compose(g,domain(h))))
| there_exists(compose(g,domain(h))) ),
inference(subst,[],[codomain_has_elements:[bind(X,$fot(compose(g,domain(h))))]]) ).
cnf(refute_0_212,plain,
( ~ there_exists(compose(b,compose(g,domain(h))))
| domain(b) = codomain(compose(g,domain(h))) ),
inference(subst,[],[domain_codomain_composition1:[bind(X,$fot(b)),bind(Y,$fot(compose(g,domain(h))))]]) ).
cnf(refute_0_213,plain,
( compose(b,compose(g,domain(h))) != compose(b,g)
| ~ there_exists(compose(b,g))
| there_exists(compose(b,compose(g,domain(h)))) ),
introduced(tautology,[equality,[$cnf( ~ there_exists(compose(b,compose(g,domain(h)))) ),[0],$fot(compose(b,g))]]) ).
cnf(refute_0_214,plain,
( ~ there_exists(compose(b,g))
| there_exists(compose(b,compose(g,domain(h)))) ),
inference(resolve,[$cnf( $equal(compose(b,compose(g,domain(h))),compose(b,g)) )],[refute_0_126,refute_0_213]) ).
cnf(refute_0_215,plain,
( ~ there_exists(compose(b,g))
| domain(b) = codomain(compose(g,domain(h))) ),
inference(resolve,[$cnf( there_exists(compose(b,compose(g,domain(h)))) )],[refute_0_214,refute_0_212]) ).
cnf(refute_0_216,plain,
( domain(b) != codomain(compose(g,domain(h)))
| domain(b) != codomain(g)
| codomain(g) = codomain(compose(g,domain(h))) ),
introduced(tautology,[equality,[$cnf( $equal(domain(b),codomain(compose(g,domain(h)))) ),[0],$fot(codomain(g))]]) ).
cnf(refute_0_217,plain,
( domain(b) != codomain(compose(g,domain(h)))
| codomain(g) = codomain(compose(g,domain(h))) ),
inference(resolve,[$cnf( $equal(domain(b),codomain(g)) )],[refute_0_137,refute_0_216]) ).
cnf(refute_0_218,plain,
( ~ there_exists(compose(b,g))
| codomain(g) = codomain(compose(g,domain(h))) ),
inference(resolve,[$cnf( $equal(domain(b),codomain(compose(g,domain(h)))) )],[refute_0_215,refute_0_217]) ).
cnf(refute_0_219,plain,
codomain(g) = codomain(compose(g,domain(h))),
inference(resolve,[$cnf( there_exists(compose(b,g)) )],[refute_0_135,refute_0_218]) ).
cnf(refute_0_220,plain,
( codomain(g) != codomain(compose(g,domain(h)))
| codomain(compose(g,domain(h))) = codomain(g) ),
inference(subst,[],[refute_0_29:[bind(X0,$fot(codomain(g))),bind(Y0,$fot(codomain(compose(g,domain(h)))))]]) ).
cnf(refute_0_221,plain,
codomain(compose(g,domain(h))) = codomain(g),
inference(resolve,[$cnf( $equal(codomain(g),codomain(compose(g,domain(h)))) )],[refute_0_219,refute_0_220]) ).
cnf(refute_0_222,plain,
( codomain(compose(g,domain(h))) != codomain(g)
| ~ there_exists(codomain(g))
| there_exists(codomain(compose(g,domain(h)))) ),
introduced(tautology,[equality,[$cnf( ~ there_exists(codomain(compose(g,domain(h)))) ),[0],$fot(codomain(g))]]) ).
cnf(refute_0_223,plain,
( ~ there_exists(codomain(g))
| there_exists(codomain(compose(g,domain(h)))) ),
inference(resolve,[$cnf( $equal(codomain(compose(g,domain(h))),codomain(g)) )],[refute_0_221,refute_0_222]) ).
cnf(refute_0_224,plain,
( ~ there_exists(codomain(g))
| there_exists(compose(g,domain(h))) ),
inference(resolve,[$cnf( there_exists(codomain(compose(g,domain(h)))) )],[refute_0_223,refute_0_211]) ).
cnf(refute_0_225,plain,
there_exists(compose(g,domain(h))),
inference(resolve,[$cnf( there_exists(codomain(g)) )],[refute_0_151,refute_0_224]) ).
cnf(refute_0_226,plain,
domain(g) = codomain(domain(h)),
inference(resolve,[$cnf( there_exists(compose(g,domain(h))) )],[refute_0_225,refute_0_210]) ).
cnf(refute_0_227,plain,
( domain(g) != codomain(domain(h))
| codomain(domain(h)) = domain(g) ),
inference(subst,[],[refute_0_29:[bind(X0,$fot(domain(g))),bind(Y0,$fot(codomain(domain(h))))]]) ).
cnf(refute_0_228,plain,
codomain(domain(h)) = domain(g),
inference(resolve,[$cnf( $equal(domain(g),codomain(domain(h))) )],[refute_0_226,refute_0_227]) ).
cnf(refute_0_229,plain,
( codomain(domain(h)) != domain(g)
| compose(codomain(domain(h)),domain(h)) != domain(h)
| compose(domain(g),domain(h)) = domain(h) ),
introduced(tautology,[equality,[$cnf( $equal(compose(codomain(domain(h)),domain(h)),domain(h)) ),[0,0],$fot(domain(g))]]) ).
cnf(refute_0_230,plain,
( compose(codomain(domain(h)),domain(h)) != domain(h)
| compose(domain(g),domain(h)) = domain(h) ),
inference(resolve,[$cnf( $equal(codomain(domain(h)),domain(g)) )],[refute_0_228,refute_0_229]) ).
cnf(refute_0_231,plain,
compose(domain(g),domain(h)) = domain(h),
inference(resolve,[$cnf( $equal(compose(codomain(domain(h)),domain(h)),domain(h)) )],[refute_0_209,refute_0_230]) ).
cnf(refute_0_232,plain,
( compose(domain(g),domain(h)) != domain(h)
| ~ there_exists(domain(h))
| there_exists(compose(domain(g),domain(h))) ),
introduced(tautology,[equality,[$cnf( ~ there_exists(compose(domain(g),domain(h))) ),[0],$fot(domain(h))]]) ).
cnf(refute_0_233,plain,
( ~ there_exists(domain(h))
| there_exists(compose(domain(g),domain(h))) ),
inference(resolve,[$cnf( $equal(compose(domain(g),domain(h)),domain(h)) )],[refute_0_231,refute_0_232]) ).
cnf(refute_0_234,plain,
( ~ there_exists(domain(h))
| domain(domain(g)) = codomain(domain(h)) ),
inference(resolve,[$cnf( there_exists(compose(domain(g),domain(h))) )],[refute_0_233,refute_0_208]) ).
cnf(refute_0_235,plain,
( codomain(domain(h)) != domain(g)
| domain(domain(g)) != codomain(domain(h))
| domain(domain(g)) = domain(g) ),
introduced(tautology,[equality,[$cnf( $equal(domain(domain(g)),codomain(domain(h))) ),[1],$fot(domain(g))]]) ).
cnf(refute_0_236,plain,
( domain(domain(g)) != codomain(domain(h))
| domain(domain(g)) = domain(g) ),
inference(resolve,[$cnf( $equal(codomain(domain(h)),domain(g)) )],[refute_0_228,refute_0_235]) ).
cnf(refute_0_237,plain,
( ~ there_exists(domain(h))
| domain(domain(g)) = domain(g) ),
inference(resolve,[$cnf( $equal(domain(domain(g)),codomain(domain(h))) )],[refute_0_234,refute_0_236]) ).
cnf(refute_0_238,plain,
( ~ there_exists(h)
| there_exists(domain(h)) ),
inference(subst,[],[refute_0_163:[bind(X_7,$fot(h))]]) ).
cnf(refute_0_239,plain,
( ~ there_exists(codomain(h))
| there_exists(h) ),
inference(subst,[],[codomain_has_elements:[bind(X,$fot(h))]]) ).
cnf(refute_0_240,plain,
( ~ there_exists(compose(b,h))
| domain(b) = codomain(h) ),
inference(subst,[],[domain_codomain_composition1:[bind(X,$fot(b)),bind(Y,$fot(h))]]) ).
cnf(refute_0_241,plain,
( compose(b,h) != compose(b,g)
| ~ there_exists(compose(b,g))
| there_exists(compose(b,h)) ),
introduced(tautology,[equality,[$cnf( ~ there_exists(compose(b,h)) ),[0],$fot(compose(b,g))]]) ).
cnf(refute_0_242,plain,
( ~ there_exists(compose(b,g))
| there_exists(compose(b,h)) ),
inference(resolve,[$cnf( $equal(compose(b,h),compose(b,g)) )],[bh_equals_bg,refute_0_241]) ).
cnf(refute_0_243,plain,
( ~ there_exists(compose(b,g))
| domain(b) = codomain(h) ),
inference(resolve,[$cnf( there_exists(compose(b,h)) )],[refute_0_242,refute_0_240]) ).
cnf(refute_0_244,plain,
( domain(b) != codomain(g)
| domain(b) != codomain(h)
| codomain(g) = codomain(h) ),
introduced(tautology,[equality,[$cnf( $equal(domain(b),codomain(h)) ),[0],$fot(codomain(g))]]) ).
cnf(refute_0_245,plain,
( domain(b) != codomain(h)
| codomain(g) = codomain(h) ),
inference(resolve,[$cnf( $equal(domain(b),codomain(g)) )],[refute_0_137,refute_0_244]) ).
cnf(refute_0_246,plain,
( ~ there_exists(compose(b,g))
| codomain(g) = codomain(h) ),
inference(resolve,[$cnf( $equal(domain(b),codomain(h)) )],[refute_0_243,refute_0_245]) ).
cnf(refute_0_247,plain,
codomain(g) = codomain(h),
inference(resolve,[$cnf( there_exists(compose(b,g)) )],[refute_0_135,refute_0_246]) ).
cnf(refute_0_248,plain,
( codomain(g) != codomain(h)
| codomain(h) = codomain(g) ),
inference(subst,[],[refute_0_29:[bind(X0,$fot(codomain(g))),bind(Y0,$fot(codomain(h)))]]) ).
cnf(refute_0_249,plain,
codomain(h) = codomain(g),
inference(resolve,[$cnf( $equal(codomain(g),codomain(h)) )],[refute_0_247,refute_0_248]) ).
cnf(refute_0_250,plain,
( codomain(h) != codomain(g)
| ~ there_exists(codomain(g))
| there_exists(codomain(h)) ),
introduced(tautology,[equality,[$cnf( ~ there_exists(codomain(h)) ),[0],$fot(codomain(g))]]) ).
cnf(refute_0_251,plain,
( ~ there_exists(codomain(g))
| there_exists(codomain(h)) ),
inference(resolve,[$cnf( $equal(codomain(h),codomain(g)) )],[refute_0_249,refute_0_250]) ).
cnf(refute_0_252,plain,
( ~ there_exists(codomain(g))
| there_exists(h) ),
inference(resolve,[$cnf( there_exists(codomain(h)) )],[refute_0_251,refute_0_239]) ).
cnf(refute_0_253,plain,
there_exists(h),
inference(resolve,[$cnf( there_exists(codomain(g)) )],[refute_0_151,refute_0_252]) ).
cnf(refute_0_254,plain,
there_exists(domain(h)),
inference(resolve,[$cnf( there_exists(h) )],[refute_0_253,refute_0_238]) ).
cnf(refute_0_255,plain,
domain(domain(g)) = domain(g),
inference(resolve,[$cnf( there_exists(domain(h)) )],[refute_0_254,refute_0_237]) ).
cnf(refute_0_256,plain,
domain(domain(domain(g))) = domain(domain(domain(g))),
introduced(tautology,[refl,[$fot(domain(domain(domain(g))))]]) ).
cnf(refute_0_257,plain,
( domain(domain(domain(g))) != domain(domain(domain(g)))
| domain(domain(g)) != domain(g)
| domain(domain(domain(g))) = domain(domain(g)) ),
introduced(tautology,[equality,[$cnf( $equal(domain(domain(domain(g))),domain(domain(domain(g)))) ),[1,0],$fot(domain(g))]]) ).
cnf(refute_0_258,plain,
( domain(domain(g)) != domain(g)
| domain(domain(domain(g))) = domain(domain(g)) ),
inference(resolve,[$cnf( $equal(domain(domain(domain(g))),domain(domain(domain(g)))) )],[refute_0_256,refute_0_257]) ).
cnf(refute_0_259,plain,
domain(domain(domain(g))) = domain(domain(g)),
inference(resolve,[$cnf( $equal(domain(domain(g)),domain(g)) )],[refute_0_255,refute_0_258]) ).
cnf(refute_0_260,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_261,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_29,refute_0_260]) ).
cnf(refute_0_262,plain,
( domain(domain(domain(g))) != domain(domain(g))
| domain(domain(g)) != domain(g)
| domain(domain(domain(g))) = domain(g) ),
inference(subst,[],[refute_0_261:[bind(X0,$fot(domain(domain(domain(g))))),bind(Y0,$fot(domain(domain(g)))),bind(Z0,$fot(domain(g)))]]) ).
cnf(refute_0_263,plain,
( domain(domain(g)) != domain(g)
| domain(domain(domain(g))) = domain(g) ),
inference(resolve,[$cnf( $equal(domain(domain(domain(g))),domain(domain(g))) )],[refute_0_259,refute_0_262]) ).
cnf(refute_0_264,plain,
domain(domain(domain(g))) = domain(g),
inference(resolve,[$cnf( $equal(domain(domain(g)),domain(g)) )],[refute_0_255,refute_0_263]) ).
cnf(refute_0_265,plain,
domain(domain(domain(domain(g)))) = domain(domain(domain(domain(g)))),
introduced(tautology,[refl,[$fot(domain(domain(domain(domain(g)))))]]) ).
cnf(refute_0_266,plain,
( domain(domain(domain(domain(g)))) != domain(domain(domain(domain(g))))
| domain(domain(domain(g))) != domain(g)
| domain(domain(domain(domain(g)))) = domain(domain(g)) ),
introduced(tautology,[equality,[$cnf( $equal(domain(domain(domain(domain(g)))),domain(domain(domain(domain(g))))) ),[1,0],$fot(domain(g))]]) ).
cnf(refute_0_267,plain,
( domain(domain(domain(g))) != domain(g)
| domain(domain(domain(domain(g)))) = domain(domain(g)) ),
inference(resolve,[$cnf( $equal(domain(domain(domain(domain(g)))),domain(domain(domain(domain(g))))) )],[refute_0_265,refute_0_266]) ).
cnf(refute_0_268,plain,
domain(domain(domain(domain(g)))) = domain(domain(g)),
inference(resolve,[$cnf( $equal(domain(domain(domain(g))),domain(g)) )],[refute_0_264,refute_0_267]) ).
cnf(refute_0_269,plain,
( domain(domain(domain(domain(g)))) != domain(domain(g))
| domain(domain(g)) != domain(g)
| domain(domain(domain(domain(g)))) = domain(g) ),
inference(subst,[],[refute_0_261:[bind(X0,$fot(domain(domain(domain(domain(g)))))),bind(Y0,$fot(domain(domain(g)))),bind(Z0,$fot(domain(g)))]]) ).
cnf(refute_0_270,plain,
( domain(domain(g)) != domain(g)
| domain(domain(domain(domain(g)))) = domain(g) ),
inference(resolve,[$cnf( $equal(domain(domain(domain(domain(g)))),domain(domain(g))) )],[refute_0_268,refute_0_269]) ).
cnf(refute_0_271,plain,
domain(domain(domain(domain(g)))) = domain(g),
inference(resolve,[$cnf( $equal(domain(domain(g)),domain(g)) )],[refute_0_255,refute_0_270]) ).
cnf(refute_0_272,plain,
compose(h,domain(domain(domain(domain(g))))) = compose(h,domain(domain(domain(domain(g))))),
introduced(tautology,[refl,[$fot(compose(h,domain(domain(domain(domain(g))))))]]) ).
cnf(refute_0_273,plain,
( compose(h,domain(domain(domain(domain(g))))) != compose(h,domain(domain(domain(domain(g)))))
| domain(domain(domain(domain(g)))) != domain(g)
| compose(h,domain(domain(domain(domain(g))))) = compose(h,domain(g)) ),
introduced(tautology,[equality,[$cnf( $equal(compose(h,domain(domain(domain(domain(g))))),compose(h,domain(domain(domain(domain(g)))))) ),[1,1],$fot(domain(g))]]) ).
cnf(refute_0_274,plain,
( domain(domain(domain(domain(g)))) != domain(g)
| compose(h,domain(domain(domain(domain(g))))) = compose(h,domain(g)) ),
inference(resolve,[$cnf( $equal(compose(h,domain(domain(domain(domain(g))))),compose(h,domain(domain(domain(domain(g)))))) )],[refute_0_272,refute_0_273]) ).
cnf(refute_0_275,plain,
compose(h,domain(domain(domain(domain(g))))) = compose(h,domain(g)),
inference(resolve,[$cnf( $equal(domain(domain(domain(domain(g)))),domain(g)) )],[refute_0_271,refute_0_274]) ).
cnf(refute_0_276,plain,
( compose(h,domain(domain(domain(domain(g))))) != compose(h,domain(g))
| compose(h,domain(domain(domain(domain(g))))) != h
| compose(h,domain(g)) = h ),
introduced(tautology,[equality,[$cnf( $equal(compose(h,domain(domain(domain(domain(g))))),h) ),[0],$fot(compose(h,domain(g)))]]) ).
cnf(refute_0_277,plain,
( compose(h,domain(domain(domain(domain(g))))) != h
| compose(h,domain(g)) = h ),
inference(resolve,[$cnf( $equal(compose(h,domain(domain(domain(domain(g))))),compose(h,domain(g))) )],[refute_0_275,refute_0_276]) ).
cnf(refute_0_278,plain,
compose(h,domain(g)) = h,
inference(resolve,[$cnf( $equal(compose(h,domain(domain(domain(domain(g))))),h) )],[refute_0_207,refute_0_277]) ).
cnf(refute_0_279,plain,
compose(g,domain(g)) = g,
inference(subst,[],[compose_domain:[bind(X,$fot(g))]]) ).
cnf(refute_0_280,plain,
( compose(compose(a,b),X) != compose(compose(a,b),X)
| compose(compose(a,b),Z) != compose(compose(a,b),X)
| X = Z ),
inference(subst,[],[monomorphism:[bind(Y,$fot(compose(compose(a,b),X)))]]) ).
cnf(refute_0_281,plain,
compose(compose(a,b),X) = compose(compose(a,b),X),
introduced(tautology,[refl,[$fot(compose(compose(a,b),X))]]) ).
cnf(refute_0_282,plain,
( compose(compose(a,b),Z) != compose(compose(a,b),X)
| X = Z ),
inference(resolve,[$cnf( $equal(compose(compose(a,b),X),compose(compose(a,b),X)) )],[refute_0_281,refute_0_280]) ).
cnf(refute_0_283,plain,
compose(compose(a,b),Z) = compose(a,compose(b,Z)),
inference(subst,[],[refute_0_71:[bind(X,$fot(a)),bind(Y,$fot(b))]]) ).
cnf(refute_0_284,plain,
( compose(a,compose(b,Z)) != compose(compose(a,b),X)
| compose(compose(a,b),Z) != compose(a,compose(b,Z))
| compose(compose(a,b),Z) = compose(compose(a,b),X) ),
introduced(tautology,[equality,[$cnf( $equal(compose(compose(a,b),Z),compose(a,compose(b,Z))) ),[1],$fot(compose(compose(a,b),X))]]) ).
cnf(refute_0_285,plain,
( compose(a,compose(b,Z)) != compose(compose(a,b),X)
| compose(compose(a,b),Z) = compose(compose(a,b),X) ),
inference(resolve,[$cnf( $equal(compose(compose(a,b),Z),compose(a,compose(b,Z))) )],[refute_0_283,refute_0_284]) ).
cnf(refute_0_286,plain,
compose(compose(a,b),X) = compose(a,compose(b,X)),
inference(subst,[],[refute_0_71:[bind(X,$fot(a)),bind(Y,$fot(b)),bind(Z,$fot(X))]]) ).
cnf(refute_0_287,plain,
( compose(a,compose(b,Z)) != compose(a,compose(b,X))
| compose(compose(a,b),X) != compose(a,compose(b,X))
| compose(a,compose(b,Z)) = compose(compose(a,b),X) ),
introduced(tautology,[equality,[$cnf( ~ $equal(compose(a,compose(b,Z)),compose(compose(a,b),X)) ),[1],$fot(compose(a,compose(b,X)))]]) ).
cnf(refute_0_288,plain,
( compose(a,compose(b,Z)) != compose(a,compose(b,X))
| compose(a,compose(b,Z)) = compose(compose(a,b),X) ),
inference(resolve,[$cnf( $equal(compose(compose(a,b),X),compose(a,compose(b,X))) )],[refute_0_286,refute_0_287]) ).
cnf(refute_0_289,plain,
( compose(a,compose(b,Z)) != compose(a,compose(b,X))
| compose(compose(a,b),Z) = compose(compose(a,b),X) ),
inference(resolve,[$cnf( $equal(compose(a,compose(b,Z)),compose(compose(a,b),X)) )],[refute_0_288,refute_0_285]) ).
cnf(refute_0_290,plain,
( compose(a,compose(b,Z)) != compose(a,compose(b,X))
| X = Z ),
inference(resolve,[$cnf( $equal(compose(compose(a,b),Z),compose(compose(a,b),X)) )],[refute_0_289,refute_0_282]) ).
cnf(refute_0_291,plain,
( compose(a,compose(b,compose(h,X_17))) != compose(a,compose(b,X_100))
| X_100 = compose(h,X_17) ),
inference(subst,[],[refute_0_290:[bind(X,$fot(X_100)),bind(Z,$fot(compose(h,X_17)))]]) ).
cnf(refute_0_292,plain,
( compose(a,compose(b,compose(g,X_17))) != compose(a,compose(b,X_100))
| compose(b,compose(h,X_17)) != compose(b,compose(g,X_17))
| compose(a,compose(b,compose(h,X_17))) = compose(a,compose(b,X_100)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(compose(a,compose(b,compose(h,X_17))),compose(a,compose(b,X_100))) ),[0,1],$fot(compose(b,compose(g,X_17)))]]) ).
cnf(refute_0_293,plain,
( compose(a,compose(b,compose(g,X_17))) != compose(a,compose(b,X_100))
| compose(a,compose(b,compose(h,X_17))) = compose(a,compose(b,X_100)) ),
inference(resolve,[$cnf( $equal(compose(b,compose(h,X_17)),compose(b,compose(g,X_17))) )],[refute_0_75,refute_0_292]) ).
cnf(refute_0_294,plain,
( compose(a,compose(b,compose(g,X_17))) != compose(a,compose(b,X_100))
| X_100 = compose(h,X_17) ),
inference(resolve,[$cnf( $equal(compose(a,compose(b,compose(h,X_17))),compose(a,compose(b,X_100))) )],[refute_0_293,refute_0_291]) ).
cnf(refute_0_295,plain,
( compose(a,compose(b,compose(g,X_17))) != compose(a,compose(b,compose(g,X_17)))
| compose(g,X_17) = compose(h,X_17) ),
inference(subst,[],[refute_0_294:[bind(X_100,$fot(compose(g,X_17)))]]) ).
cnf(refute_0_296,plain,
compose(a,compose(b,compose(g,X_17))) = compose(a,compose(b,compose(g,X_17))),
introduced(tautology,[refl,[$fot(compose(a,compose(b,compose(g,X_17))))]]) ).
cnf(refute_0_297,plain,
compose(g,X_17) = compose(h,X_17),
inference(resolve,[$cnf( $equal(compose(a,compose(b,compose(g,X_17))),compose(a,compose(b,compose(g,X_17)))) )],[refute_0_296,refute_0_295]) ).
cnf(refute_0_298,plain,
( compose(g,X_17) != compose(h,X_17)
| compose(h,X_17) = compose(g,X_17) ),
inference(subst,[],[refute_0_29:[bind(X0,$fot(compose(g,X_17))),bind(Y0,$fot(compose(h,X_17)))]]) ).
cnf(refute_0_299,plain,
compose(h,X_17) = compose(g,X_17),
inference(resolve,[$cnf( $equal(compose(g,X_17),compose(h,X_17)) )],[refute_0_297,refute_0_298]) ).
cnf(refute_0_300,plain,
compose(h,domain(g)) = compose(g,domain(g)),
inference(subst,[],[refute_0_299:[bind(X_17,$fot(domain(g)))]]) ).
cnf(refute_0_301,plain,
( compose(g,domain(g)) != g
| compose(h,domain(g)) != compose(g,domain(g))
| compose(h,domain(g)) = g ),
inference(subst,[],[refute_0_261:[bind(X0,$fot(compose(h,domain(g)))),bind(Y0,$fot(compose(g,domain(g)))),bind(Z0,$fot(g))]]) ).
cnf(refute_0_302,plain,
( compose(g,domain(g)) != g
| compose(h,domain(g)) = g ),
inference(resolve,[$cnf( $equal(compose(h,domain(g)),compose(g,domain(g))) )],[refute_0_300,refute_0_301]) ).
cnf(refute_0_303,plain,
compose(h,domain(g)) = g,
inference(resolve,[$cnf( $equal(compose(g,domain(g)),g) )],[refute_0_279,refute_0_302]) ).
cnf(refute_0_304,plain,
( compose(h,domain(g)) != g
| compose(h,domain(g)) != h
| g = h ),
introduced(tautology,[equality,[$cnf( $equal(compose(h,domain(g)),h) ),[0],$fot(g)]]) ).
cnf(refute_0_305,plain,
( compose(h,domain(g)) != h
| g = h ),
inference(resolve,[$cnf( $equal(compose(h,domain(g)),g) )],[refute_0_303,refute_0_304]) ).
cnf(refute_0_306,plain,
g = h,
inference(resolve,[$cnf( $equal(compose(h,domain(g)),h) )],[refute_0_278,refute_0_305]) ).
cnf(refute_0_307,plain,
( g != h
| h = g ),
inference(subst,[],[refute_0_29:[bind(X0,$fot(g)),bind(Y0,$fot(h))]]) ).
cnf(refute_0_308,plain,
g != h,
inference(resolve,[$cnf( $equal(h,g) )],[refute_0_307,prove_h_equals_g]) ).
cnf(refute_0_309,plain,
$false,
inference(resolve,[$cnf( $equal(g,h) )],[refute_0_306,refute_0_308]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : CAT001-4 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n026.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun May 29 17:51:54 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 162.07/162.24 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 162.07/162.24
% 162.07/162.24 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 162.07/162.26
%------------------------------------------------------------------------------