%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : SEU401+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % Computer : n022.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 : Tue Jul 19 14:50:52 EDT 2022 % Result : Theorem 10.55s 10.74s % Output : Proof 10.55s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SEU401+1 : TPTP v8.1.0. Released v3.3.0. % 0.11/0.12 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 0.12/0.33 % Computer : n022.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 : Mon Jun 20 09:46:01 EDT 2022 % 0.12/0.33 % CPUTime : % 10.55/10.74 % SZS status Theorem % 10.55/10.74 (* PROOF-FOUND *) % 10.55/10.74 (* BEGIN-PROOF *) % 10.55/10.74 % SZS output start Proof % 10.55/10.74 1. (in T_0 T_1) (-. (in T_0 T_1)) ### Axiom % 10.55/10.74 2. (-. (in T_0 (the_carrier T_2))) (in T_0 (the_carrier T_2)) ### Axiom % 10.55/10.74 3. ((in T_0 (the_carrier T_2)) /\ (Ex H, ((netstr_induced_subset H T_3 T_2) /\ (Ex I, ((element I (the_carrier T_2)) /\ ((T_4 = (topstr_closure T_3 H)) /\ ((T_0 = I) /\ (H = (relation_rng_as_subset (the_carrier (subnetstr_of_element T_3 T_2 I)) (the_carrier T_3) (the_mapping T_3 (subnetstr_of_element T_3 T_2 I))))))))))) (-. (in T_0 (the_carrier T_2))) ### And 2 % 10.55/10.74 4. ((in T_0 T_1) <=> ((in T_0 (the_carrier T_2)) /\ (Ex H, ((netstr_induced_subset H T_3 T_2) /\ (Ex I, ((element I (the_carrier T_2)) /\ ((T_4 = (topstr_closure T_3 H)) /\ ((T_0 = I) /\ (H = (relation_rng_as_subset (the_carrier (subnetstr_of_element T_3 T_2 I)) (the_carrier T_3) (the_mapping T_3 (subnetstr_of_element T_3 T_2 I)))))))))))) (-. (in T_0 (the_carrier T_2))) (in T_0 T_1) ### Equiv 1 3 % 10.55/10.74 5. (All G, ((in G T_1) <=> ((in G (the_carrier T_2)) /\ (Ex H, ((netstr_induced_subset H T_3 T_2) /\ (Ex I, ((element I (the_carrier T_2)) /\ ((T_4 = (topstr_closure T_3 H)) /\ ((G = I) /\ (H = (relation_rng_as_subset (the_carrier (subnetstr_of_element T_3 T_2 I)) (the_carrier T_3) (the_mapping T_3 (subnetstr_of_element T_3 T_2 I))))))))))))) (in T_0 T_1) (-. (in T_0 (the_carrier T_2))) ### All 4 % 10.55/10.74 6. (in T_0 T_1) (-. (in T_0 T_1)) ### Axiom % 10.55/10.74 7. (-. (Ex H, ((netstr_induced_subset H T_3 T_2) /\ (Ex I, ((element I (the_carrier T_2)) /\ ((T_4 = (topstr_closure T_3 H)) /\ ((T_0 = I) /\ (H = (relation_rng_as_subset (the_carrier (subnetstr_of_element T_3 T_2 I)) (the_carrier T_3) (the_mapping T_3 (subnetstr_of_element T_3 T_2 I))))))))))) (Ex H, ((netstr_induced_subset H T_3 T_2) /\ (Ex I, ((element I (the_carrier T_2)) /\ ((T_4 = (topstr_closure T_3 H)) /\ ((T_0 = I) /\ (H = (relation_rng_as_subset (the_carrier (subnetstr_of_element T_3 T_2 I)) (the_carrier T_3) (the_mapping T_3 (subnetstr_of_element T_3 T_2 I)))))))))) ### Axiom % 10.55/10.74 8. ((in T_0 (the_carrier T_2)) /\ (Ex H, ((netstr_induced_subset H T_3 T_2) /\ (Ex I, ((element I (the_carrier T_2)) /\ ((T_4 = (topstr_closure T_3 H)) /\ ((T_0 = I) /\ (H = (relation_rng_as_subset (the_carrier (subnetstr_of_element T_3 T_2 I)) (the_carrier T_3) (the_mapping T_3 (subnetstr_of_element T_3 T_2 I))))))))))) (-. (Ex H, ((netstr_induced_subset H T_3 T_2) /\ (Ex I, ((element I (the_carrier T_2)) /\ ((T_4 = (topstr_closure T_3 H)) /\ ((T_0 = I) /\ (H = (relation_rng_as_subset (the_carrier (subnetstr_of_element T_3 T_2 I)) (the_carrier T_3) (the_mapping T_3 (subnetstr_of_element T_3 T_2 I))))))))))) ### And 7 % 10.55/10.74 9. ((in T_0 T_1) <=> ((in T_0 (the_carrier T_2)) /\ (Ex H, ((netstr_induced_subset H T_3 T_2) /\ (Ex I, ((element I (the_carrier T_2)) /\ ((T_4 = (topstr_closure T_3 H)) /\ ((T_0 = I) /\ (H = (relation_rng_as_subset (the_carrier (subnetstr_of_element T_3 T_2 I)) (the_carrier T_3) (the_mapping T_3 (subnetstr_of_element T_3 T_2 I)))))))))))) (-. (Ex H, ((netstr_induced_subset H T_3 T_2) /\ (Ex I, ((element I (the_carrier T_2)) /\ ((T_4 = (topstr_closure T_3 H)) /\ ((T_0 = I) /\ (H = (relation_rng_as_subset (the_carrier (subnetstr_of_element T_3 T_2 I)) (the_carrier T_3) (the_mapping T_3 (subnetstr_of_element T_3 T_2 I))))))))))) (in T_0 T_1) ### Equiv 6 8 % 10.55/10.74 10. (All G, ((in G T_1) <=> ((in G (the_carrier T_2)) /\ (Ex H, ((netstr_induced_subset H T_3 T_2) /\ (Ex I, ((element I (the_carrier T_2)) /\ ((T_4 = (topstr_closure T_3 H)) /\ ((G = I) /\ (H = (relation_rng_as_subset (the_carrier (subnetstr_of_element T_3 T_2 I)) (the_carrier T_3) (the_mapping T_3 (subnetstr_of_element T_3 T_2 I))))))))))))) (in T_0 T_1) (-. (Ex H, ((netstr_induced_subset H T_3 T_2) /\ (Ex I, ((element I (the_carrier T_2)) /\ ((T_4 = (topstr_closure T_3 H)) /\ ((T_0 = I) /\ (H = (relation_rng_as_subset (the_carrier (subnetstr_of_element T_3 T_2 I)) (the_carrier T_3) (the_mapping T_3 (subnetstr_of_element T_3 T_2 I))))))))))) ### All 9 % 10.55/10.74 11. (-. ((in T_0 (the_carrier T_2)) /\ (Ex H, ((netstr_induced_subset H T_3 T_2) /\ (Ex I, ((element I (the_carrier T_2)) /\ ((T_4 = (topstr_closure T_3 H)) /\ ((T_0 = I) /\ (H = (relation_rng_as_subset (the_carrier (subnetstr_of_element T_3 T_2 I)) (the_carrier T_3) (the_mapping T_3 (subnetstr_of_element T_3 T_2 I)))))))))))) (in T_0 T_1) (All G, ((in G T_1) <=> ((in G (the_carrier T_2)) /\ (Ex H, ((netstr_induced_subset H T_3 T_2) /\ (Ex I, ((element I (the_carrier T_2)) /\ ((T_4 = (topstr_closure T_3 H)) /\ ((G = I) /\ (H = (relation_rng_as_subset (the_carrier (subnetstr_of_element T_3 T_2 I)) (the_carrier T_3) (the_mapping T_3 (subnetstr_of_element T_3 T_2 I))))))))))))) ### NotAnd 5 10 % 10.55/10.74 12. (-. (in T_0 T_5)) (in T_0 T_5) ### Axiom % 10.55/10.74 13. ((in T_0 T_5) <=> ((in T_0 (the_carrier T_2)) /\ (Ex H, ((netstr_induced_subset H T_3 T_2) /\ (Ex I, ((element I (the_carrier T_2)) /\ ((T_4 = (topstr_closure T_3 H)) /\ ((T_0 = I) /\ (H = (relation_rng_as_subset (the_carrier (subnetstr_of_element T_3 T_2 I)) (the_carrier T_3) (the_mapping T_3 (subnetstr_of_element T_3 T_2 I)))))))))))) (-. (in T_0 T_5)) (All G, ((in G T_1) <=> ((in G (the_carrier T_2)) /\ (Ex H, ((netstr_induced_subset H T_3 T_2) /\ (Ex I, ((element I (the_carrier T_2)) /\ ((T_4 = (topstr_closure T_3 H)) /\ ((G = I) /\ (H = (relation_rng_as_subset (the_carrier (subnetstr_of_element T_3 T_2 I)) (the_carrier T_3) (the_mapping T_3 (subnetstr_of_element T_3 T_2 I))))))))))))) (in T_0 T_1) ### Equiv 11 12 % 10.55/10.74 14. (All G, ((in G T_5) <=> ((in G (the_carrier T_2)) /\ (Ex H, ((netstr_induced_subset H T_3 T_2) /\ (Ex I, ((element I (the_carrier T_2)) /\ ((T_4 = (topstr_closure T_3 H)) /\ ((G = I) /\ (H = (relation_rng_as_subset (the_carrier (subnetstr_of_element T_3 T_2 I)) (the_carrier T_3) (the_mapping T_3 (subnetstr_of_element T_3 T_2 I))))))))))))) (in T_0 T_1) (All G, ((in G T_1) <=> ((in G (the_carrier T_2)) /\ (Ex H, ((netstr_induced_subset H T_3 T_2) /\ (Ex I, ((element I (the_carrier T_2)) /\ ((T_4 = (topstr_closure T_3 H)) /\ ((G = I) /\ (H = (relation_rng_as_subset (the_carrier (subnetstr_of_element T_3 T_2 I)) (the_carrier T_3) (the_mapping T_3 (subnetstr_of_element T_3 T_2 I))))))))))))) (-. (in T_0 T_5)) ### All 13 % 10.55/10.74 15. (in T_0 T_5) (-. (in T_0 T_5)) ### Axiom % 10.55/10.74 16. ((in T_0 T_5) <=> ((in T_0 (the_carrier T_2)) /\ (Ex H, ((netstr_induced_subset H T_3 T_2) /\ (Ex I, ((element I (the_carrier T_2)) /\ ((T_4 = (topstr_closure T_3 H)) /\ ((T_0 = I) /\ (H = (relation_rng_as_subset (the_carrier (subnetstr_of_element T_3 T_2 I)) (the_carrier T_3) (the_mapping T_3 (subnetstr_of_element T_3 T_2 I)))))))))))) (-. (in T_0 (the_carrier T_2))) (in T_0 T_5) ### Equiv 15 3 % 10.55/10.74 17. (All G, ((in G T_5) <=> ((in G (the_carrier T_2)) /\ (Ex H, ((netstr_induced_subset H T_3 T_2) /\ (Ex I, ((element I (the_carrier T_2)) /\ ((T_4 = (topstr_closure T_3 H)) /\ ((G = I) /\ (H = (relation_rng_as_subset (the_carrier (subnetstr_of_element T_3 T_2 I)) (the_carrier T_3) (the_mapping T_3 (subnetstr_of_element T_3 T_2 I))))))))))))) (in T_0 T_5) (-. (in T_0 (the_carrier T_2))) ### All 16 % 10.55/10.74 18. (in T_0 T_5) (-. (in T_0 T_5)) ### Axiom % 10.55/10.74 19. ((in T_0 T_5) <=> ((in T_0 (the_carrier T_2)) /\ (Ex H, ((netstr_induced_subset H T_3 T_2) /\ (Ex I, ((element I (the_carrier T_2)) /\ ((T_4 = (topstr_closure T_3 H)) /\ ((T_0 = I) /\ (H = (relation_rng_as_subset (the_carrier (subnetstr_of_element T_3 T_2 I)) (the_carrier T_3) (the_mapping T_3 (subnetstr_of_element T_3 T_2 I)))))))))))) (-. (Ex H, ((netstr_induced_subset H T_3 T_2) /\ (Ex I, ((element I (the_carrier T_2)) /\ ((T_4 = (topstr_closure T_3 H)) /\ ((T_0 = I) /\ (H = (relation_rng_as_subset (the_carrier (subnetstr_of_element T_3 T_2 I)) (the_carrier T_3) (the_mapping T_3 (subnetstr_of_element T_3 T_2 I))))))))))) (in T_0 T_5) ### Equiv 18 8 % 10.55/10.74 20. (All G, ((in G T_5) <=> ((in G (the_carrier T_2)) /\ (Ex H, ((netstr_induced_subset H T_3 T_2) /\ (Ex I, ((element I (the_carrier T_2)) /\ ((T_4 = (topstr_closure T_3 H)) /\ ((G = I) /\ (H = (relation_rng_as_subset (the_carrier (subnetstr_of_element T_3 T_2 I)) (the_carrier T_3) (the_mapping T_3 (subnetstr_of_element T_3 T_2 I))))))))))))) (in T_0 T_5) (-. (Ex H, ((netstr_induced_subset H T_3 T_2) /\ (Ex I, ((element I (the_carrier T_2)) /\ ((T_4 = (topstr_closure T_3 H)) /\ ((T_0 = I) /\ (H = (relation_rng_as_subset (the_carrier (subnetstr_of_element T_3 T_2 I)) (the_carrier T_3) (the_mapping T_3 (subnetstr_of_element T_3 T_2 I))))))))))) ### All 19 % 10.55/10.75 21. (-. ((in T_0 (the_carrier T_2)) /\ (Ex H, ((netstr_induced_subset H T_3 T_2) /\ (Ex I, ((element I (the_carrier T_2)) /\ ((T_4 = (topstr_closure T_3 H)) /\ ((T_0 = I) /\ (H = (relation_rng_as_subset (the_carrier (subnetstr_of_element T_3 T_2 I)) (the_carrier T_3) (the_mapping T_3 (subnetstr_of_element T_3 T_2 I)))))))))))) (in T_0 T_5) (All G, ((in G T_5) <=> ((in G (the_carrier T_2)) /\ (Ex H, ((netstr_induced_subset H T_3 T_2) /\ (Ex I, ((element I (the_carrier T_2)) /\ ((T_4 = (topstr_closure T_3 H)) /\ ((G = I) /\ (H = (relation_rng_as_subset (the_carrier (subnetstr_of_element T_3 T_2 I)) (the_carrier T_3) (the_mapping T_3 (subnetstr_of_element T_3 T_2 I))))))))))))) ### NotAnd 17 20 % 10.55/10.75 22. (-. (in T_0 T_1)) (in T_0 T_1) ### Axiom % 10.55/10.75 23. ((in T_0 T_1) <=> ((in T_0 (the_carrier T_2)) /\ (Ex H, ((netstr_induced_subset H T_3 T_2) /\ (Ex I, ((element I (the_carrier T_2)) /\ ((T_4 = (topstr_closure T_3 H)) /\ ((T_0 = I) /\ (H = (relation_rng_as_subset (the_carrier (subnetstr_of_element T_3 T_2 I)) (the_carrier T_3) (the_mapping T_3 (subnetstr_of_element T_3 T_2 I)))))))))))) (-. (in T_0 T_1)) (All G, ((in G T_5) <=> ((in G (the_carrier T_2)) /\ (Ex H, ((netstr_induced_subset H T_3 T_2) /\ (Ex I, ((element I (the_carrier T_2)) /\ ((T_4 = (topstr_closure T_3 H)) /\ ((G = I) /\ (H = (relation_rng_as_subset (the_carrier (subnetstr_of_element T_3 T_2 I)) (the_carrier T_3) (the_mapping T_3 (subnetstr_of_element T_3 T_2 I))))))))))))) (in T_0 T_5) ### Equiv 21 22 % 10.55/10.75 24. (All G, ((in G T_1) <=> ((in G (the_carrier T_2)) /\ (Ex H, ((netstr_induced_subset H T_3 T_2) /\ (Ex I, ((element I (the_carrier T_2)) /\ ((T_4 = (topstr_closure T_3 H)) /\ ((G = I) /\ (H = (relation_rng_as_subset (the_carrier (subnetstr_of_element T_3 T_2 I)) (the_carrier T_3) (the_mapping T_3 (subnetstr_of_element T_3 T_2 I))))))))))))) (in T_0 T_5) (All G, ((in G T_5) <=> ((in G (the_carrier T_2)) /\ (Ex H, ((netstr_induced_subset H T_3 T_2) /\ (Ex I, ((element I (the_carrier T_2)) /\ ((T_4 = (topstr_closure T_3 H)) /\ ((G = I) /\ (H = (relation_rng_as_subset (the_carrier (subnetstr_of_element T_3 T_2 I)) (the_carrier T_3) (the_mapping T_3 (subnetstr_of_element T_3 T_2 I))))))))))))) (-. (in T_0 T_1)) ### All 23 % 10.55/10.75 25. (-. ((in T_0 T_5) <=> (in T_0 T_1))) (All G, ((in G T_1) <=> ((in G (the_carrier T_2)) /\ (Ex H, ((netstr_induced_subset H T_3 T_2) /\ (Ex I, ((element I (the_carrier T_2)) /\ ((T_4 = (topstr_closure T_3 H)) /\ ((G = I) /\ (H = (relation_rng_as_subset (the_carrier (subnetstr_of_element T_3 T_2 I)) (the_carrier T_3) (the_mapping T_3 (subnetstr_of_element T_3 T_2 I))))))))))))) (All G, ((in G T_5) <=> ((in G (the_carrier T_2)) /\ (Ex H, ((netstr_induced_subset H T_3 T_2) /\ (Ex I, ((element I (the_carrier T_2)) /\ ((T_4 = (topstr_closure T_3 H)) /\ ((G = I) /\ (H = (relation_rng_as_subset (the_carrier (subnetstr_of_element T_3 T_2 I)) (the_carrier T_3) (the_mapping T_3 (subnetstr_of_element T_3 T_2 I))))))))))))) ### NotEquiv 14 24 % 10.55/10.75 26. (-. (All C, ((in C T_5) <=> (in C T_1)))) (All G, ((in G T_5) <=> ((in G (the_carrier T_2)) /\ (Ex H, ((netstr_induced_subset H T_3 T_2) /\ (Ex I, ((element I (the_carrier T_2)) /\ ((T_4 = (topstr_closure T_3 H)) /\ ((G = I) /\ (H = (relation_rng_as_subset (the_carrier (subnetstr_of_element T_3 T_2 I)) (the_carrier T_3) (the_mapping T_3 (subnetstr_of_element T_3 T_2 I))))))))))))) (All G, ((in G T_1) <=> ((in G (the_carrier T_2)) /\ (Ex H, ((netstr_induced_subset H T_3 T_2) /\ (Ex I, ((element I (the_carrier T_2)) /\ ((T_4 = (topstr_closure T_3 H)) /\ ((G = I) /\ (H = (relation_rng_as_subset (the_carrier (subnetstr_of_element T_3 T_2 I)) (the_carrier T_3) (the_mapping T_3 (subnetstr_of_element T_3 T_2 I))))))))))))) ### NotAllEx 25 % 10.55/10.75 27. (T_1 != T_5) (T_5 = T_1) ### Sym(=) % 10.55/10.75 28. ((All C, ((in C T_5) <=> (in C T_1))) => (T_5 = T_1)) (T_1 != T_5) (All G, ((in G T_1) <=> ((in G (the_carrier T_2)) /\ (Ex H, ((netstr_induced_subset H T_3 T_2) /\ (Ex I, ((element I (the_carrier T_2)) /\ ((T_4 = (topstr_closure T_3 H)) /\ ((G = I) /\ (H = (relation_rng_as_subset (the_carrier (subnetstr_of_element T_3 T_2 I)) (the_carrier T_3) (the_mapping T_3 (subnetstr_of_element T_3 T_2 I))))))))))))) (All G, ((in G T_5) <=> ((in G (the_carrier T_2)) /\ (Ex H, ((netstr_induced_subset H T_3 T_2) /\ (Ex I, ((element I (the_carrier T_2)) /\ ((T_4 = (topstr_closure T_3 H)) /\ ((G = I) /\ (H = (relation_rng_as_subset (the_carrier (subnetstr_of_element T_3 T_2 I)) (the_carrier T_3) (the_mapping T_3 (subnetstr_of_element T_3 T_2 I))))))))))))) ### Imply 26 27 % 10.55/10.75 29. (All B, ((All C, ((in C T_5) <=> (in C B))) => (T_5 = B))) (All G, ((in G T_5) <=> ((in G (the_carrier T_2)) /\ (Ex H, ((netstr_induced_subset H T_3 T_2) /\ (Ex I, ((element I (the_carrier T_2)) /\ ((T_4 = (topstr_closure T_3 H)) /\ ((G = I) /\ (H = (relation_rng_as_subset (the_carrier (subnetstr_of_element T_3 T_2 I)) (the_carrier T_3) (the_mapping T_3 (subnetstr_of_element T_3 T_2 I))))))))))))) (All G, ((in G T_1) <=> ((in G (the_carrier T_2)) /\ (Ex H, ((netstr_induced_subset H T_3 T_2) /\ (Ex I, ((element I (the_carrier T_2)) /\ ((T_4 = (topstr_closure T_3 H)) /\ ((G = I) /\ (H = (relation_rng_as_subset (the_carrier (subnetstr_of_element T_3 T_2 I)) (the_carrier T_3) (the_mapping T_3 (subnetstr_of_element T_3 T_2 I))))))))))))) (T_1 != T_5) ### All 28 % 10.55/10.75 30. (All A, (All B, ((All C, ((in C A) <=> (in C B))) => (A = B)))) (T_1 != T_5) (All G, ((in G T_1) <=> ((in G (the_carrier T_2)) /\ (Ex H, ((netstr_induced_subset H T_3 T_2) /\ (Ex I, ((element I (the_carrier T_2)) /\ ((T_4 = (topstr_closure T_3 H)) /\ ((G = I) /\ (H = (relation_rng_as_subset (the_carrier (subnetstr_of_element T_3 T_2 I)) (the_carrier T_3) (the_mapping T_3 (subnetstr_of_element T_3 T_2 I))))))))))))) (All G, ((in G T_5) <=> ((in G (the_carrier T_2)) /\ (Ex H, ((netstr_induced_subset H T_3 T_2) /\ (Ex I, ((element I (the_carrier T_2)) /\ ((T_4 = (topstr_closure T_3 H)) /\ ((G = I) /\ (H = (relation_rng_as_subset (the_carrier (subnetstr_of_element T_3 T_2 I)) (the_carrier T_3) (the_mapping T_3 (subnetstr_of_element T_3 T_2 I))))))))))))) ### All 29 % 10.55/10.75 31. (-. (((All G, ((in G T_1) <=> ((in G (the_carrier T_2)) /\ (Ex H, ((netstr_induced_subset H T_3 T_2) /\ (Ex I, ((element I (the_carrier T_2)) /\ ((T_4 = (topstr_closure T_3 H)) /\ ((G = I) /\ (H = (relation_rng_as_subset (the_carrier (subnetstr_of_element T_3 T_2 I)) (the_carrier T_3) (the_mapping T_3 (subnetstr_of_element T_3 T_2 I))))))))))))) /\ (All G, ((in G T_5) <=> ((in G (the_carrier T_2)) /\ (Ex H, ((netstr_induced_subset H T_3 T_2) /\ (Ex I, ((element I (the_carrier T_2)) /\ ((T_4 = (topstr_closure T_3 H)) /\ ((G = I) /\ (H = (relation_rng_as_subset (the_carrier (subnetstr_of_element T_3 T_2 I)) (the_carrier T_3) (the_mapping T_3 (subnetstr_of_element T_3 T_2 I)))))))))))))) => (T_1 = T_5))) (All A, (All B, ((All C, ((in C A) <=> (in C B))) => (A = B)))) ### ConjTree 30 % 10.55/10.75 32. (-. (All F, (((All G, ((in G T_1) <=> ((in G (the_carrier T_2)) /\ (Ex H, ((netstr_induced_subset H T_3 T_2) /\ (Ex I, ((element I (the_carrier T_2)) /\ ((T_4 = (topstr_closure T_3 H)) /\ ((G = I) /\ (H = (relation_rng_as_subset (the_carrier (subnetstr_of_element T_3 T_2 I)) (the_carrier T_3) (the_mapping T_3 (subnetstr_of_element T_3 T_2 I))))))))))))) /\ (All G, ((in G F) <=> ((in G (the_carrier T_2)) /\ (Ex H, ((netstr_induced_subset H T_3 T_2) /\ (Ex I, ((element I (the_carrier T_2)) /\ ((T_4 = (topstr_closure T_3 H)) /\ ((G = I) /\ (H = (relation_rng_as_subset (the_carrier (subnetstr_of_element T_3 T_2 I)) (the_carrier T_3) (the_mapping T_3 (subnetstr_of_element T_3 T_2 I)))))))))))))) => (T_1 = F)))) (All A, (All B, ((All C, ((in C A) <=> (in C B))) => (A = B)))) ### NotAllEx 31 % 10.55/10.75 33. (-. (All E, (All F, (((All G, ((in G E) <=> ((in G (the_carrier T_2)) /\ (Ex H, ((netstr_induced_subset H T_3 T_2) /\ (Ex I, ((element I (the_carrier T_2)) /\ ((T_4 = (topstr_closure T_3 H)) /\ ((G = I) /\ (H = (relation_rng_as_subset (the_carrier (subnetstr_of_element T_3 T_2 I)) (the_carrier T_3) (the_mapping T_3 (subnetstr_of_element T_3 T_2 I))))))))))))) /\ (All G, ((in G F) <=> ((in G (the_carrier T_2)) /\ (Ex H, ((netstr_induced_subset H T_3 T_2) /\ (Ex I, ((element I (the_carrier T_2)) /\ ((T_4 = (topstr_closure T_3 H)) /\ ((G = I) /\ (H = (relation_rng_as_subset (the_carrier (subnetstr_of_element T_3 T_2 I)) (the_carrier T_3) (the_mapping T_3 (subnetstr_of_element T_3 T_2 I)))))))))))))) => (E = F))))) (All A, (All B, ((All C, ((in C A) <=> (in C B))) => (A = B)))) ### NotAllEx 32 % 10.55/10.77 34. (-. (All D, (All E, (All F, (((All G, ((in G E) <=> ((in G (the_carrier T_2)) /\ (Ex H, ((netstr_induced_subset H T_3 T_2) /\ (Ex I, ((element I (the_carrier T_2)) /\ ((D = (topstr_closure T_3 H)) /\ ((G = I) /\ (H = (relation_rng_as_subset (the_carrier (subnetstr_of_element T_3 T_2 I)) (the_carrier T_3) (the_mapping T_3 (subnetstr_of_element T_3 T_2 I))))))))))))) /\ (All G, ((in G F) <=> ((in G (the_carrier T_2)) /\ (Ex H, ((netstr_induced_subset H T_3 T_2) /\ (Ex I, ((element I (the_carrier T_2)) /\ ((D = (topstr_closure T_3 H)) /\ ((G = I) /\ (H = (relation_rng_as_subset (the_carrier (subnetstr_of_element T_3 T_2 I)) (the_carrier T_3) (the_mapping T_3 (subnetstr_of_element T_3 T_2 I)))))))))))))) => (E = F)))))) (All A, (All B, ((All C, ((in C A) <=> (in C B))) => (A = B)))) ### NotAllEx 33 % 10.55/10.77 35. (-. (((-. (empty_carrier T_3)) /\ ((topological_space T_3) /\ ((top_str T_3) /\ ((-. (empty_carrier T_2)) /\ ((transitive_relstr T_2) /\ ((directed_relstr T_2) /\ (net_str T_2 T_3))))))) => (All D, (All E, (All F, (((All G, ((in G E) <=> ((in G (the_carrier T_2)) /\ (Ex H, ((netstr_induced_subset H T_3 T_2) /\ (Ex I, ((element I (the_carrier T_2)) /\ ((D = (topstr_closure T_3 H)) /\ ((G = I) /\ (H = (relation_rng_as_subset (the_carrier (subnetstr_of_element T_3 T_2 I)) (the_carrier T_3) (the_mapping T_3 (subnetstr_of_element T_3 T_2 I))))))))))))) /\ (All G, ((in G F) <=> ((in G (the_carrier T_2)) /\ (Ex H, ((netstr_induced_subset H T_3 T_2) /\ (Ex I, ((element I (the_carrier T_2)) /\ ((D = (topstr_closure T_3 H)) /\ ((G = I) /\ (H = (relation_rng_as_subset (the_carrier (subnetstr_of_element T_3 T_2 I)) (the_carrier T_3) (the_mapping T_3 (subnetstr_of_element T_3 T_2 I)))))))))))))) => (E = F))))))) (All A, (All B, ((All C, ((in C A) <=> (in C B))) => (A = B)))) ### ConjTree 34 % 10.55/10.77 36. (-. (All C, (((-. (empty_carrier T_3)) /\ ((topological_space T_3) /\ ((top_str T_3) /\ ((-. (empty_carrier T_2)) /\ ((transitive_relstr T_2) /\ ((directed_relstr T_2) /\ (net_str T_2 T_3))))))) => (All D, (All E, (All F, (((All G, ((in G E) <=> ((in G (the_carrier T_2)) /\ (Ex H, ((netstr_induced_subset H T_3 T_2) /\ (Ex I, ((element I (the_carrier T_2)) /\ ((D = (topstr_closure T_3 H)) /\ ((G = I) /\ (H = (relation_rng_as_subset (the_carrier (subnetstr_of_element T_3 T_2 I)) (the_carrier T_3) (the_mapping T_3 (subnetstr_of_element T_3 T_2 I))))))))))))) /\ (All G, ((in G F) <=> ((in G (the_carrier T_2)) /\ (Ex H, ((netstr_induced_subset H T_3 T_2) /\ (Ex I, ((element I (the_carrier T_2)) /\ ((D = (topstr_closure T_3 H)) /\ ((G = I) /\ (H = (relation_rng_as_subset (the_carrier (subnetstr_of_element T_3 T_2 I)) (the_carrier T_3) (the_mapping T_3 (subnetstr_of_element T_3 T_2 I)))))))))))))) => (E = F)))))))) (All A, (All B, ((All C, ((in C A) <=> (in C B))) => (A = B)))) ### NotAllEx 35 % 10.55/10.77 37. (-. (All B, (All C, (((-. (empty_carrier T_3)) /\ ((topological_space T_3) /\ ((top_str T_3) /\ ((-. (empty_carrier B)) /\ ((transitive_relstr B) /\ ((directed_relstr B) /\ (net_str B T_3))))))) => (All D, (All E, (All F, (((All G, ((in G E) <=> ((in G (the_carrier B)) /\ (Ex H, ((netstr_induced_subset H T_3 B) /\ (Ex I, ((element I (the_carrier B)) /\ ((D = (topstr_closure T_3 H)) /\ ((G = I) /\ (H = (relation_rng_as_subset (the_carrier (subnetstr_of_element T_3 B I)) (the_carrier T_3) (the_mapping T_3 (subnetstr_of_element T_3 B I))))))))))))) /\ (All G, ((in G F) <=> ((in G (the_carrier B)) /\ (Ex H, ((netstr_induced_subset H T_3 B) /\ (Ex I, ((element I (the_carrier B)) /\ ((D = (topstr_closure T_3 H)) /\ ((G = I) /\ (H = (relation_rng_as_subset (the_carrier (subnetstr_of_element T_3 B I)) (the_carrier T_3) (the_mapping T_3 (subnetstr_of_element T_3 B I)))))))))))))) => (E = F))))))))) (All A, (All B, ((All C, ((in C A) <=> (in C B))) => (A = B)))) ### NotAllEx 36 % 10.55/10.77 38. (-. (All A, (All B, (All C, (((-. (empty_carrier A)) /\ ((topological_space A) /\ ((top_str A) /\ ((-. (empty_carrier B)) /\ ((transitive_relstr B) /\ ((directed_relstr B) /\ (net_str B A))))))) => (All D, (All E, (All F, (((All G, ((in G E) <=> ((in G (the_carrier B)) /\ (Ex H, ((netstr_induced_subset H A B) /\ (Ex I, ((element I (the_carrier B)) /\ ((D = (topstr_closure A H)) /\ ((G = I) /\ (H = (relation_rng_as_subset (the_carrier (subnetstr_of_element A B I)) (the_carrier A) (the_mapping A (subnetstr_of_element A B I))))))))))))) /\ (All G, ((in G F) <=> ((in G (the_carrier B)) /\ (Ex H, ((netstr_induced_subset H A B) /\ (Ex I, ((element I (the_carrier B)) /\ ((D = (topstr_closure A H)) /\ ((G = I) /\ (H = (relation_rng_as_subset (the_carrier (subnetstr_of_element A B I)) (the_carrier A) (the_mapping A (subnetstr_of_element A B I)))))))))))))) => (E = F)))))))))) (All A, (All B, ((All C, ((in C A) <=> (in C B))) => (A = B)))) ### NotAllEx 37 % 10.55/10.77 % SZS output end Proof % 10.55/10.77 (* END-PROOF *) %------------------------------------------------------------------------------