%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SET928+1 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n011.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 06:39:43 EDT 2022 % Result : Theorem 3.70s 3.93s % Output : Proof 3.76s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SET928+1 : TPTP v8.1.0. Released v3.2.0. % 0.03/0.12 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n011.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 : Sun Jul 10 18:44:11 EDT 2022 % 0.12/0.34 % CPUTime : % 3.70/3.93 (* PROOF-FOUND *) % 3.70/3.93 % SZS status Theorem % 3.70/3.93 (* BEGIN-PROOF *) % 3.70/3.93 % SZS output start Proof % 3.70/3.93 Theorem t72_zfmisc_1 : (forall A : zenon_U, (forall B : zenon_U, (forall C : zenon_U, (((set_difference (unordered_pair A B) C) = (unordered_pair A B))<->((~(in A C))/\(~(in B C))))))). % 3.70/3.93 Proof. % 3.70/3.93 apply NNPP. intro zenon_G. % 3.70/3.93 apply (zenon_notallex_s (fun A : zenon_U => (forall B : zenon_U, (forall C : zenon_U, (((set_difference (unordered_pair A B) C) = (unordered_pair A B))<->((~(in A C))/\(~(in B C))))))) zenon_G); [ zenon_intro zenon_H9; idtac ]. % 3.70/3.93 elim zenon_H9. zenon_intro zenon_TA_k. zenon_intro zenon_Hb. % 3.70/3.93 apply (zenon_notallex_s (fun B : zenon_U => (forall C : zenon_U, (((set_difference (unordered_pair zenon_TA_k B) C) = (unordered_pair zenon_TA_k B))<->((~(in zenon_TA_k C))/\(~(in B C)))))) zenon_Hb); [ zenon_intro zenon_Hc; idtac ]. % 3.70/3.93 elim zenon_Hc. zenon_intro zenon_TB_n. zenon_intro zenon_He. % 3.70/3.93 apply (zenon_notallex_s (fun C : zenon_U => (((set_difference (unordered_pair zenon_TA_k zenon_TB_n) C) = (unordered_pair zenon_TA_k zenon_TB_n))<->((~(in zenon_TA_k C))/\(~(in zenon_TB_n C))))) zenon_He); [ zenon_intro zenon_Hf; idtac ]. % 3.70/3.93 elim zenon_Hf. zenon_intro zenon_TC_q. zenon_intro zenon_H11. % 3.70/3.93 apply (zenon_notequiv_s _ _ zenon_H11); [ zenon_intro zenon_H15; zenon_intro zenon_H14 | zenon_intro zenon_H13; zenon_intro zenon_H12 ]. % 3.70/3.93 apply (zenon_and_s _ _ zenon_H14). zenon_intro zenon_H17. zenon_intro zenon_H16. % 3.70/3.93 generalize (t57_zfmisc_1 zenon_TA_k). zenon_intro zenon_H18. % 3.70/3.93 generalize (zenon_H18 zenon_TC_q). zenon_intro zenon_H19. % 3.70/3.93 generalize (zenon_H19 zenon_TB_n). zenon_intro zenon_H1a. % 3.70/3.93 apply (zenon_notand_s _ _ zenon_H1a); [ zenon_intro zenon_H1c | zenon_intro zenon_H1b ]. % 3.70/3.93 exact (zenon_H1c zenon_H17). % 3.70/3.93 apply (zenon_notand_s _ _ zenon_H1b); [ zenon_intro zenon_H1e | zenon_intro zenon_H1d ]. % 3.70/3.93 exact (zenon_H1e zenon_H16). % 3.70/3.93 apply zenon_H1d. zenon_intro zenon_H1f. % 3.70/3.93 generalize (t83_xboole_1 (unordered_pair zenon_TA_k zenon_TB_n)). zenon_intro zenon_H20. % 3.70/3.93 generalize (zenon_H20 zenon_TC_q). zenon_intro zenon_H21. % 3.70/3.93 apply (zenon_equiv_s _ _ zenon_H21); [ zenon_intro zenon_H22; zenon_intro zenon_H15 | zenon_intro zenon_H1f; zenon_intro zenon_H13 ]. % 3.70/3.93 exact (zenon_H22 zenon_H1f). % 3.70/3.93 exact (zenon_H15 zenon_H13). % 3.70/3.93 apply (zenon_notand_s _ _ zenon_H12); [ zenon_intro zenon_H1c | zenon_intro zenon_H1e ]. % 3.70/3.93 apply zenon_H1c. zenon_intro zenon_H23. % 3.70/3.93 generalize (t55_zfmisc_1 zenon_TA_k). zenon_intro zenon_H24. % 3.70/3.93 generalize (zenon_H24 zenon_TB_n). zenon_intro zenon_H25. % 3.70/3.93 generalize (zenon_H25 zenon_TC_q). zenon_intro zenon_H26. % 3.70/3.93 apply (zenon_notand_s _ _ zenon_H26); [ zenon_intro zenon_H22 | zenon_intro zenon_H17 ]. % 3.70/3.93 generalize (t83_xboole_1 (unordered_pair zenon_TA_k zenon_TB_n)). zenon_intro zenon_H20. % 3.70/3.93 generalize (zenon_H20 zenon_TC_q). zenon_intro zenon_H21. % 3.70/3.93 apply (zenon_equiv_s _ _ zenon_H21); [ zenon_intro zenon_H22; zenon_intro zenon_H15 | zenon_intro zenon_H1f; zenon_intro zenon_H13 ]. % 3.70/3.93 exact (zenon_H15 zenon_H13). % 3.70/3.93 exact (zenon_H22 zenon_H1f). % 3.70/3.93 exact (zenon_H17 zenon_H23). % 3.70/3.93 apply zenon_H1e. zenon_intro zenon_H27. % 3.70/3.93 generalize (t55_zfmisc_1 zenon_TB_n). zenon_intro zenon_H28. % 3.70/3.93 generalize (commutativity_k2_tarski zenon_TB_n). zenon_intro zenon_H29. % 3.70/3.93 generalize (zenon_H29 zenon_TA_k). zenon_intro zenon_H2a. % 3.70/3.93 generalize (zenon_H28 zenon_TA_k). zenon_intro zenon_H2b. % 3.70/3.93 generalize (zenon_H2b zenon_TC_q). zenon_intro zenon_H2c. % 3.70/3.93 apply (zenon_notand_s _ _ zenon_H2c); [ zenon_intro zenon_H2d | zenon_intro zenon_H16 ]. % 3.70/3.93 generalize (t83_xboole_1 (unordered_pair zenon_TB_n zenon_TA_k)). zenon_intro zenon_H2e. % 3.70/3.93 generalize (zenon_H2e zenon_TC_q). zenon_intro zenon_H2f. % 3.70/3.93 apply (zenon_equiv_s _ _ zenon_H2f); [ zenon_intro zenon_H2d; zenon_intro zenon_H32 | zenon_intro zenon_H31; zenon_intro zenon_H30 ]. % 3.70/3.93 cut (((set_difference (unordered_pair zenon_TA_k zenon_TB_n) zenon_TC_q) = (unordered_pair zenon_TA_k zenon_TB_n)) = ((set_difference (unordered_pair zenon_TB_n zenon_TA_k) zenon_TC_q) = (unordered_pair zenon_TB_n zenon_TA_k))). % 3.70/3.93 intro zenon_D_pnotp. % 3.70/3.93 apply zenon_H32. % 3.70/3.93 rewrite <- zenon_D_pnotp. % 3.70/3.93 exact zenon_H13. % 3.70/3.93 cut (((unordered_pair zenon_TA_k zenon_TB_n) = (unordered_pair zenon_TB_n zenon_TA_k))); [idtac | apply NNPP; zenon_intro zenon_H33]. % 3.76/3.93 cut (((set_difference (unordered_pair zenon_TA_k zenon_TB_n) zenon_TC_q) = (set_difference (unordered_pair zenon_TB_n zenon_TA_k) zenon_TC_q))); [idtac | apply NNPP; zenon_intro zenon_H34]. % 3.76/3.93 congruence. % 3.76/3.93 elim (classic ((set_difference (unordered_pair zenon_TB_n zenon_TA_k) zenon_TC_q) = (set_difference (unordered_pair zenon_TB_n zenon_TA_k) zenon_TC_q))); [ zenon_intro zenon_H35 | zenon_intro zenon_H36 ]. % 3.76/3.93 cut (((set_difference (unordered_pair zenon_TB_n zenon_TA_k) zenon_TC_q) = (set_difference (unordered_pair zenon_TB_n zenon_TA_k) zenon_TC_q)) = ((set_difference (unordered_pair zenon_TA_k zenon_TB_n) zenon_TC_q) = (set_difference (unordered_pair zenon_TB_n zenon_TA_k) zenon_TC_q))). % 3.76/3.93 intro zenon_D_pnotp. % 3.76/3.93 apply zenon_H34. % 3.76/3.93 rewrite <- zenon_D_pnotp. % 3.76/3.93 exact zenon_H35. % 3.76/3.93 cut (((set_difference (unordered_pair zenon_TB_n zenon_TA_k) zenon_TC_q) = (set_difference (unordered_pair zenon_TB_n zenon_TA_k) zenon_TC_q))); [idtac | apply NNPP; zenon_intro zenon_H36]. % 3.76/3.93 cut (((set_difference (unordered_pair zenon_TB_n zenon_TA_k) zenon_TC_q) = (set_difference (unordered_pair zenon_TA_k zenon_TB_n) zenon_TC_q))); [idtac | apply NNPP; zenon_intro zenon_H37]. % 3.76/3.93 congruence. % 3.76/3.93 cut ((zenon_TC_q = zenon_TC_q)); [idtac | apply NNPP; zenon_intro zenon_H38]. % 3.76/3.93 cut (((unordered_pair zenon_TB_n zenon_TA_k) = (unordered_pair zenon_TA_k zenon_TB_n))); [idtac | apply NNPP; zenon_intro zenon_H39]. % 3.76/3.93 congruence. % 3.76/3.93 exact (zenon_H39 zenon_H2a). % 3.76/3.93 apply zenon_H38. apply refl_equal. % 3.76/3.93 apply zenon_H36. apply refl_equal. % 3.76/3.93 apply zenon_H36. apply refl_equal. % 3.76/3.93 apply zenon_H33. apply sym_equal. exact zenon_H2a. % 3.76/3.93 exact (zenon_H2d zenon_H31). % 3.76/3.93 exact (zenon_H16 zenon_H27). % 3.76/3.93 Qed. % 3.76/3.93 % SZS output end Proof % 3.76/3.93 (* END-PROOF *) % 3.76/3.93 nodes searched: 129296 % 3.76/3.93 max branch formulas: 8283 % 3.76/3.93 proof nodes created: 2108 % 3.76/3.93 formulas created: 286993 % 3.76/3.93 %------------------------------------------------------------------------------