TSTP Solution File: SEU401+1 by SuperZenon---0.0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% 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 *)
%------------------------------------------------------------------------------