%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SET978+1 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n012.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 06:40:00 EDT 2022 % Result : Theorem 0.19s 0.52s % Output : Proof 0.19s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : SET978+1 : TPTP v8.1.0. Released v3.2.0. % 0.07/0.13 % Command : run_zenon %s %d % 0.13/0.35 % Computer : n012.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 600 % 0.13/0.35 % DateTime : Sat Jul 9 16:00:14 EDT 2022 % 0.13/0.35 % CPUTime : % 0.19/0.52 (* PROOF-FOUND *) % 0.19/0.52 % SZS status Theorem % 0.19/0.52 (* BEGIN-PROOF *) % 0.19/0.52 % SZS output start Proof % 0.19/0.52 Theorem t131_zfmisc_1 : (forall A : zenon_U, (forall B : zenon_U, (forall C : zenon_U, (forall D : zenon_U, ((~(A = B))->((disjoint (cartesian_product2 (singleton A) C) (cartesian_product2 (singleton B) D))/\(disjoint (cartesian_product2 C (singleton A)) (cartesian_product2 D (singleton B))))))))). % 0.19/0.52 Proof. % 0.19/0.52 assert (zenon_L1_ : forall (zenon_TA_i : zenon_U) (zenon_TB_j : zenon_U), (~(disjoint (singleton zenon_TB_j) (singleton zenon_TA_i))) -> (~(zenon_TA_i = zenon_TB_j)) -> False). % 0.19/0.52 do 2 intro. intros zenon_H6 zenon_H7. % 0.19/0.52 generalize (t17_zfmisc_1 zenon_TA_i). zenon_intro zenon_Ha. % 0.19/0.52 generalize (zenon_Ha zenon_TB_j). zenon_intro zenon_Hb. % 0.19/0.52 apply (zenon_imply_s _ _ zenon_Hb); [ zenon_intro zenon_Hd | zenon_intro zenon_Hc ]. % 0.19/0.52 exact (zenon_Hd zenon_H7). % 0.19/0.52 generalize (symmetry_r1_xboole_0 (singleton zenon_TA_i)). zenon_intro zenon_He. % 0.19/0.52 generalize (zenon_He (singleton zenon_TB_j)). zenon_intro zenon_Hf. % 0.19/0.52 apply (zenon_imply_s _ _ zenon_Hf); [ zenon_intro zenon_H11 | zenon_intro zenon_H10 ]. % 0.19/0.52 exact (zenon_H11 zenon_Hc). % 0.19/0.52 exact (zenon_H6 zenon_H10). % 0.19/0.52 (* end of lemma zenon_L1_ *) % 0.19/0.52 apply NNPP. intro zenon_G. % 0.19/0.52 apply (zenon_notallex_s (fun A : zenon_U => (forall B : zenon_U, (forall C : zenon_U, (forall D : zenon_U, ((~(A = B))->((disjoint (cartesian_product2 (singleton A) C) (cartesian_product2 (singleton B) D))/\(disjoint (cartesian_product2 C (singleton A)) (cartesian_product2 D (singleton B))))))))) zenon_G); [ zenon_intro zenon_H12; idtac ]. % 0.19/0.52 elim zenon_H12. zenon_intro zenon_TA_i. zenon_intro zenon_H13. % 0.19/0.52 apply (zenon_notallex_s (fun B : zenon_U => (forall C : zenon_U, (forall D : zenon_U, ((~(zenon_TA_i = B))->((disjoint (cartesian_product2 (singleton zenon_TA_i) C) (cartesian_product2 (singleton B) D))/\(disjoint (cartesian_product2 C (singleton zenon_TA_i)) (cartesian_product2 D (singleton B)))))))) zenon_H13); [ zenon_intro zenon_H14; idtac ]. % 0.19/0.52 elim zenon_H14. zenon_intro zenon_TB_j. zenon_intro zenon_H15. % 0.19/0.52 apply (zenon_notallex_s (fun C : zenon_U => (forall D : zenon_U, ((~(zenon_TA_i = zenon_TB_j))->((disjoint (cartesian_product2 (singleton zenon_TA_i) C) (cartesian_product2 (singleton zenon_TB_j) D))/\(disjoint (cartesian_product2 C (singleton zenon_TA_i)) (cartesian_product2 D (singleton zenon_TB_j))))))) zenon_H15); [ zenon_intro zenon_H16; idtac ]. % 0.19/0.52 elim zenon_H16. zenon_intro zenon_TC_x. zenon_intro zenon_H18. % 0.19/0.52 apply (zenon_notallex_s (fun D : zenon_U => ((~(zenon_TA_i = zenon_TB_j))->((disjoint (cartesian_product2 (singleton zenon_TA_i) zenon_TC_x) (cartesian_product2 (singleton zenon_TB_j) D))/\(disjoint (cartesian_product2 zenon_TC_x (singleton zenon_TA_i)) (cartesian_product2 D (singleton zenon_TB_j)))))) zenon_H18); [ zenon_intro zenon_H19; idtac ]. % 0.19/0.52 elim zenon_H19. zenon_intro zenon_TD_ba. zenon_intro zenon_H1b. % 0.19/0.52 apply (zenon_notimply_s _ _ zenon_H1b). zenon_intro zenon_H7. zenon_intro zenon_H1c. % 0.19/0.52 apply (zenon_notand_s _ _ zenon_H1c); [ zenon_intro zenon_H1e | zenon_intro zenon_H1d ]. % 0.19/0.52 generalize (t127_zfmisc_1 (singleton zenon_TB_j)). zenon_intro zenon_H1f. % 0.19/0.52 generalize (zenon_H1f (singleton zenon_TA_i)). zenon_intro zenon_H20. % 0.19/0.52 generalize (zenon_H20 zenon_TD_ba). zenon_intro zenon_H21. % 0.19/0.52 generalize (zenon_H21 zenon_TC_x). zenon_intro zenon_H22. % 0.19/0.52 apply (zenon_imply_s _ _ zenon_H22); [ zenon_intro zenon_H24 | zenon_intro zenon_H23 ]. % 0.19/0.52 apply (zenon_notor_s _ _ zenon_H24). zenon_intro zenon_H6. zenon_intro zenon_H25. % 0.19/0.52 apply (zenon_L1_ zenon_TA_i zenon_TB_j); trivial. % 0.19/0.52 generalize (symmetry_r1_xboole_0 (cartesian_product2 (singleton zenon_TB_j) zenon_TD_ba)). zenon_intro zenon_H26. % 0.19/0.52 generalize (zenon_H26 (cartesian_product2 (singleton zenon_TA_i) zenon_TC_x)). zenon_intro zenon_H27. % 0.19/0.52 apply (zenon_imply_s _ _ zenon_H27); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 0.19/0.52 exact (zenon_H29 zenon_H23). % 0.19/0.52 exact (zenon_H1e zenon_H28). % 0.19/0.52 generalize (t127_zfmisc_1 zenon_TD_ba). zenon_intro zenon_H2a. % 0.19/0.52 generalize (zenon_H2a zenon_TC_x). zenon_intro zenon_H2b. % 0.19/0.52 generalize (zenon_H2b (singleton zenon_TB_j)). zenon_intro zenon_H2c. % 0.19/0.52 generalize (zenon_H2c (singleton zenon_TA_i)). zenon_intro zenon_H2d. % 0.19/0.52 apply (zenon_imply_s _ _ zenon_H2d); [ zenon_intro zenon_H2f | zenon_intro zenon_H2e ]. % 0.19/0.52 apply (zenon_notor_s _ _ zenon_H2f). zenon_intro zenon_H25. zenon_intro zenon_H6. % 0.19/0.52 apply (zenon_L1_ zenon_TA_i zenon_TB_j); trivial. % 0.19/0.52 generalize (symmetry_r1_xboole_0 (cartesian_product2 zenon_TD_ba (singleton zenon_TB_j))). zenon_intro zenon_H30. % 0.19/0.52 generalize (zenon_H30 (cartesian_product2 zenon_TC_x (singleton zenon_TA_i))). zenon_intro zenon_H31. % 0.19/0.52 apply (zenon_imply_s _ _ zenon_H31); [ zenon_intro zenon_H33 | zenon_intro zenon_H32 ]. % 0.19/0.52 exact (zenon_H33 zenon_H2e). % 0.19/0.52 exact (zenon_H1d zenon_H32). % 0.19/0.52 Qed. % 0.19/0.52 % SZS output end Proof % 0.19/0.52 (* END-PROOF *) % 0.19/0.52 nodes searched: 363 % 0.19/0.52 max branch formulas: 169 % 0.19/0.52 proof nodes created: 58 % 0.19/0.52 formulas created: 2305 % 0.19/0.52 %------------------------------------------------------------------------------