%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : TOP022+1 : TPTP v8.1.0. Released v3.1.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n032.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 : Thu Jul 21 21:38:08 EDT 2022 % Result : Theorem 0.14s 0.40s % Output : Proof 0.14s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.09 % Problem : TOP022+1 : TPTP v8.1.0. Released v3.1.0. % 0.00/0.10 % Command : run_zenon %s %d % 0.09/0.29 % Computer : n032.cluster.edu % 0.09/0.29 % Model : x86_64 x86_64 % 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.29 % Memory : 8042.1875MB % 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64 % 0.09/0.29 % CPULimit : 300 % 0.09/0.29 % WCLimit : 600 % 0.09/0.29 % DateTime : Sun May 29 08:32:26 EDT 2022 % 0.09/0.29 % CPUTime : % 0.14/0.40 (* PROOF-FOUND *) % 0.14/0.40 % SZS status Theorem % 0.14/0.40 (* BEGIN-PROOF *) % 0.14/0.40 % SZS output start Proof % 0.14/0.40 Theorem m_8_2_2 : (forall X : zenon_U, (forall X0 : zenon_U, (forall X1 : zenon_U, (((path_connected X)/\((a_member_of X0 X)/\(a_member_of X1 X)))->(isomorphic_groups (first_homotop_grp X X0) (first_homotop_grp X X1)))))). % 0.14/0.40 Proof. % 0.14/0.40 apply NNPP. intro zenon_G. % 0.14/0.40 apply (zenon_notallex_s (fun X : zenon_U => (forall X0 : zenon_U, (forall X1 : zenon_U, (((path_connected X)/\((a_member_of X0 X)/\(a_member_of X1 X)))->(isomorphic_groups (first_homotop_grp X X0) (first_homotop_grp X X1)))))) zenon_G); [ zenon_intro zenon_H4; idtac ]. % 0.14/0.40 elim zenon_H4. zenon_intro zenon_TX_f. zenon_intro zenon_H6. % 0.14/0.40 apply (zenon_notallex_s (fun X0 : zenon_U => (forall X1 : zenon_U, (((path_connected zenon_TX_f)/\((a_member_of X0 zenon_TX_f)/\(a_member_of X1 zenon_TX_f)))->(isomorphic_groups (first_homotop_grp zenon_TX_f X0) (first_homotop_grp zenon_TX_f X1))))) zenon_H6); [ zenon_intro zenon_H7; idtac ]. % 0.14/0.40 elim zenon_H7. zenon_intro zenon_TX0_i. zenon_intro zenon_H9. % 0.14/0.40 apply (zenon_notallex_s (fun X1 : zenon_U => (((path_connected zenon_TX_f)/\((a_member_of zenon_TX0_i zenon_TX_f)/\(a_member_of X1 zenon_TX_f)))->(isomorphic_groups (first_homotop_grp zenon_TX_f zenon_TX0_i) (first_homotop_grp zenon_TX_f X1)))) zenon_H9); [ zenon_intro zenon_Ha; idtac ]. % 0.14/0.40 elim zenon_Ha. zenon_intro zenon_TX1_l. zenon_intro zenon_Hc. % 0.14/0.40 apply (zenon_notimply_s _ _ zenon_Hc). zenon_intro zenon_He. zenon_intro zenon_Hd. % 0.14/0.40 apply (zenon_and_s _ _ zenon_He). zenon_intro zenon_H10. zenon_intro zenon_Hf. % 0.14/0.40 apply (zenon_and_s _ _ zenon_Hf). zenon_intro zenon_H12. zenon_intro zenon_H11. % 0.14/0.40 generalize (isomorphic_groups_defn (first_homotop_grp zenon_TX_f zenon_TX0_i)). zenon_intro zenon_H13. % 0.14/0.40 generalize (zenon_H13 (first_homotop_grp zenon_TX_f zenon_TX1_l)). zenon_intro zenon_H14. % 0.14/0.40 apply (zenon_equiv_s _ _ zenon_H14); [ zenon_intro zenon_Hd; zenon_intro zenon_H17 | zenon_intro zenon_H16; zenon_intro zenon_H15 ]. % 0.14/0.40 generalize (path_connected_defn zenon_TX_f). zenon_intro zenon_H18. % 0.14/0.40 generalize (zenon_H18 zenon_TX0_i). zenon_intro zenon_H19. % 0.14/0.40 generalize (zenon_H19 zenon_TX1_l). zenon_intro zenon_H1a. % 0.14/0.40 apply (zenon_equiv_s _ _ zenon_H1a); [ zenon_intro zenon_H1d; zenon_intro zenon_H1c | zenon_intro zenon_H10; zenon_intro zenon_H1b ]. % 0.14/0.40 exact (zenon_H1d zenon_H10). % 0.14/0.40 apply (zenon_imply_s _ _ zenon_H1b); [ zenon_intro zenon_H1f | zenon_intro zenon_H1e ]. % 0.14/0.40 apply (zenon_notand_s _ _ zenon_H1f); [ zenon_intro zenon_H21 | zenon_intro zenon_H20 ]. % 0.14/0.40 exact (zenon_H21 zenon_H12). % 0.14/0.40 exact (zenon_H20 zenon_H11). % 0.14/0.40 elim zenon_H1e. zenon_intro zenon_TP_bi. zenon_intro zenon_H23. % 0.14/0.40 generalize (m_8_2_1 zenon_TP_bi). zenon_intro zenon_H24. % 0.14/0.40 generalize (zenon_H24 zenon_TX0_i). zenon_intro zenon_H25. % 0.14/0.40 generalize (zenon_H25 zenon_TX1_l). zenon_intro zenon_H26. % 0.14/0.40 generalize (zenon_H26 zenon_TX_f). zenon_intro zenon_H27. % 0.14/0.40 apply (zenon_imply_s _ _ zenon_H27); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 0.14/0.40 exact (zenon_H29 zenon_H23). % 0.14/0.40 apply zenon_H17. exists (alpha_hat zenon_TP_bi). apply NNPP. zenon_intro zenon_H2a. % 0.14/0.40 exact (zenon_H2a zenon_H28). % 0.14/0.40 exact (zenon_Hd zenon_H16). % 0.14/0.40 Qed. % 0.14/0.40 % SZS output end Proof % 0.14/0.40 (* END-PROOF *) % 0.14/0.40 nodes searched: 201 % 0.14/0.40 max branch formulas: 161 % 0.14/0.40 proof nodes created: 59 % 0.14/0.40 formulas created: 1073 % 0.14/0.40 %------------------------------------------------------------------------------