%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SET954+1 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n025.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 06:39:52 EDT 2022 % Result : Theorem 9.33s 9.52s % Output : Proof 9.33s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.13 % Problem : SET954+1 : TPTP v8.1.0. Released v3.2.0. % 0.08/0.14 % Command : run_zenon %s %d % 0.14/0.35 % Computer : n025.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 600 % 0.14/0.35 % DateTime : Sat Jul 9 17:45:16 EDT 2022 % 0.14/0.35 % CPUTime : % 9.33/9.52 (* PROOF-FOUND *) % 9.33/9.52 % SZS status Theorem % 9.33/9.52 (* BEGIN-PROOF *) % 9.33/9.52 % SZS output start Proof % 9.33/9.52 Theorem t107_zfmisc_1 : (forall A : zenon_U, (forall B : zenon_U, (forall C : zenon_U, (forall D : zenon_U, ((in (ordered_pair A B) (cartesian_product2 C D))->(in (ordered_pair B A) (cartesian_product2 D C))))))). % 9.33/9.52 Proof. % 9.33/9.52 assert (zenon_L1_ : forall (zenon_TD_l : zenon_U) (zenon_TC_m : zenon_U) (zenon_TB_n : zenon_U) (zenon_TA_o : zenon_U), (forall C : zenon_U, (forall D : zenon_U, ((in (ordered_pair zenon_TA_o zenon_TB_n) (cartesian_product2 C D))<->((in zenon_TA_o C)/\(in zenon_TB_n D))))) -> (~(in zenon_TA_o zenon_TC_m)) -> (in (ordered_pair zenon_TA_o zenon_TB_n) (cartesian_product2 zenon_TC_m zenon_TD_l)) -> False). % 9.33/9.52 do 4 intro. intros zenon_H8 zenon_H9 zenon_Ha. % 9.33/9.52 generalize (zenon_H8 zenon_TC_m). zenon_intro zenon_Hf. % 9.33/9.52 generalize (zenon_Hf zenon_TD_l). zenon_intro zenon_H10. % 9.33/9.52 apply (zenon_equiv_s _ _ zenon_H10); [ zenon_intro zenon_H13; zenon_intro zenon_H12 | zenon_intro zenon_Ha; zenon_intro zenon_H11 ]. % 9.33/9.52 exact (zenon_H13 zenon_Ha). % 9.33/9.52 apply (zenon_and_s _ _ zenon_H11). zenon_intro zenon_H15. zenon_intro zenon_H14. % 9.33/9.52 exact (zenon_H9 zenon_H15). % 9.33/9.52 (* end of lemma zenon_L1_ *) % 9.33/9.52 assert (zenon_L2_ : forall (zenon_TD_l : zenon_U) (zenon_TC_m : zenon_U) (zenon_TB_n : zenon_U) (zenon_TA_o : zenon_U), (forall B : zenon_U, (forall C : zenon_U, (forall D : zenon_U, ((in (ordered_pair zenon_TA_o B) (cartesian_product2 C D))<->((in zenon_TA_o C)/\(in B D)))))) -> (in (ordered_pair zenon_TA_o zenon_TB_n) (cartesian_product2 zenon_TC_m zenon_TD_l)) -> (~(in zenon_TA_o zenon_TC_m)) -> False). % 9.33/9.52 do 4 intro. intros zenon_H16 zenon_Ha zenon_H9. % 9.33/9.52 generalize (zenon_H16 zenon_TB_n). zenon_intro zenon_H8. % 9.33/9.52 apply (zenon_L1_ zenon_TD_l zenon_TC_m zenon_TB_n zenon_TA_o); trivial. % 9.33/9.52 (* end of lemma zenon_L2_ *) % 9.33/9.52 assert (zenon_L3_ : forall (zenon_TC_m : zenon_U) (zenon_TD_l : zenon_U) (zenon_TB_n : zenon_U) (zenon_TA_o : zenon_U), (forall C : zenon_U, (forall D : zenon_U, ((in (ordered_pair zenon_TA_o zenon_TB_n) (cartesian_product2 C D))<->((in zenon_TA_o C)/\(in zenon_TB_n D))))) -> (~(in zenon_TB_n zenon_TD_l)) -> (in (ordered_pair zenon_TA_o zenon_TB_n) (cartesian_product2 zenon_TC_m zenon_TD_l)) -> False). % 9.33/9.52 do 4 intro. intros zenon_H8 zenon_H17 zenon_Ha. % 9.33/9.52 generalize (zenon_H8 zenon_TC_m). zenon_intro zenon_Hf. % 9.33/9.52 generalize (zenon_Hf zenon_TD_l). zenon_intro zenon_H10. % 9.33/9.52 apply (zenon_equiv_s _ _ zenon_H10); [ zenon_intro zenon_H13; zenon_intro zenon_H12 | zenon_intro zenon_Ha; zenon_intro zenon_H11 ]. % 9.33/9.52 exact (zenon_H13 zenon_Ha). % 9.33/9.52 apply (zenon_and_s _ _ zenon_H11). zenon_intro zenon_H15. zenon_intro zenon_H14. % 9.33/9.52 exact (zenon_H17 zenon_H14). % 9.33/9.52 (* end of lemma zenon_L3_ *) % 9.33/9.52 assert (zenon_L4_ : forall (zenon_TD_l : zenon_U) (zenon_TC_m : zenon_U) (zenon_TA_o : zenon_U) (zenon_TB_n : zenon_U), (forall C : zenon_U, (forall D : zenon_U, ((in (ordered_pair zenon_TB_n zenon_TA_o) (cartesian_product2 C D))<->((in zenon_TB_n C)/\(in zenon_TA_o D))))) -> (in zenon_TA_o zenon_TC_m) -> (in (ordered_pair zenon_TA_o zenon_TB_n) (cartesian_product2 zenon_TC_m zenon_TD_l)) -> (~(in (ordered_pair zenon_TB_n zenon_TA_o) (cartesian_product2 zenon_TD_l zenon_TC_m))) -> (forall B : zenon_U, (forall C : zenon_U, (forall D : zenon_U, ((in (ordered_pair zenon_TA_o B) (cartesian_product2 C D))<->((in zenon_TA_o C)/\(in B D)))))) -> False). % 9.33/9.52 do 4 intro. intros zenon_H18 zenon_H15 zenon_Ha zenon_H19 zenon_H16. % 9.33/9.52 generalize (zenon_H18 zenon_TD_l). zenon_intro zenon_H1a. % 9.33/9.52 generalize (zenon_H16 zenon_TB_n). zenon_intro zenon_H8. % 9.33/9.52 generalize (zenon_H1a zenon_TC_m). zenon_intro zenon_H1b. % 9.33/9.52 apply (zenon_equiv_s _ _ zenon_H1b); [ zenon_intro zenon_H19; zenon_intro zenon_H1e | zenon_intro zenon_H1d; zenon_intro zenon_H1c ]. % 9.33/9.52 apply (zenon_notand_s _ _ zenon_H1e); [ zenon_intro zenon_H17 | zenon_intro zenon_H9 ]. % 9.33/9.52 apply (zenon_L3_ zenon_TC_m zenon_TD_l zenon_TB_n zenon_TA_o); trivial. % 9.33/9.52 exact (zenon_H9 zenon_H15). % 9.33/9.52 exact (zenon_H19 zenon_H1d). % 9.33/9.52 (* end of lemma zenon_L4_ *) % 9.33/9.52 assert (zenon_L5_ : forall (zenon_TC_m : zenon_U) (zenon_TD_l : zenon_U) (zenon_TA_o : zenon_U) (zenon_TB_n : zenon_U), (forall B : zenon_U, (forall C : zenon_U, (forall D : zenon_U, ((in (ordered_pair zenon_TB_n B) (cartesian_product2 C D))<->((in zenon_TB_n C)/\(in B D)))))) -> (forall B : zenon_U, (forall C : zenon_U, (forall D : zenon_U, ((in (ordered_pair zenon_TA_o B) (cartesian_product2 C D))<->((in zenon_TA_o C)/\(in B D)))))) -> (~(in (ordered_pair zenon_TB_n zenon_TA_o) (cartesian_product2 zenon_TD_l zenon_TC_m))) -> (in (ordered_pair zenon_TA_o zenon_TB_n) (cartesian_product2 zenon_TC_m zenon_TD_l)) -> (in zenon_TA_o zenon_TC_m) -> False). % 9.33/9.52 do 4 intro. intros zenon_H1f zenon_H16 zenon_H19 zenon_Ha zenon_H15. % 9.33/9.52 generalize (zenon_H1f zenon_TA_o). zenon_intro zenon_H18. % 9.33/9.52 apply (zenon_L4_ zenon_TD_l zenon_TC_m zenon_TA_o zenon_TB_n); trivial. % 9.33/9.52 (* end of lemma zenon_L5_ *) % 9.33/9.52 apply NNPP. intro zenon_G. % 9.33/9.52 apply (zenon_notallex_s (fun A : zenon_U => (forall B : zenon_U, (forall C : zenon_U, (forall D : zenon_U, ((in (ordered_pair A B) (cartesian_product2 C D))->(in (ordered_pair B A) (cartesian_product2 D C))))))) zenon_G); [ zenon_intro zenon_H20; idtac ]. % 9.33/9.52 elim zenon_H20. zenon_intro zenon_TA_o. zenon_intro zenon_H21. % 9.33/9.52 apply (zenon_notallex_s (fun B : zenon_U => (forall C : zenon_U, (forall D : zenon_U, ((in (ordered_pair zenon_TA_o B) (cartesian_product2 C D))->(in (ordered_pair B zenon_TA_o) (cartesian_product2 D C)))))) zenon_H21); [ zenon_intro zenon_H22; idtac ]. % 9.33/9.52 elim zenon_H22. zenon_intro zenon_TB_n. zenon_intro zenon_H23. % 9.33/9.52 apply (zenon_notallex_s (fun C : zenon_U => (forall D : zenon_U, ((in (ordered_pair zenon_TA_o zenon_TB_n) (cartesian_product2 C D))->(in (ordered_pair zenon_TB_n zenon_TA_o) (cartesian_product2 D C))))) zenon_H23); [ zenon_intro zenon_H24; idtac ]. % 9.33/9.52 elim zenon_H24. zenon_intro zenon_TC_m. zenon_intro zenon_H25. % 9.33/9.52 apply (zenon_notallex_s (fun D : zenon_U => ((in (ordered_pair zenon_TA_o zenon_TB_n) (cartesian_product2 zenon_TC_m D))->(in (ordered_pair zenon_TB_n zenon_TA_o) (cartesian_product2 D zenon_TC_m)))) zenon_H25); [ zenon_intro zenon_H26; idtac ]. % 9.33/9.52 elim zenon_H26. zenon_intro zenon_TD_l. zenon_intro zenon_H27. % 9.33/9.52 apply (zenon_notimply_s _ _ zenon_H27). zenon_intro zenon_Ha. zenon_intro zenon_H19. % 9.33/9.52 generalize (l55_zfmisc_1 zenon_TB_n). zenon_intro zenon_H1f. % 9.33/9.52 generalize (l55_zfmisc_1 zenon_TA_o). zenon_intro zenon_H16. % 9.33/9.52 generalize (zenon_H16 zenon_TA_o). zenon_intro zenon_H28. % 9.33/9.52 generalize (zenon_H28 zenon_TC_m). zenon_intro zenon_H29. % 9.33/9.52 generalize (zenon_H29 zenon_TC_m). zenon_intro zenon_H2a. % 9.33/9.52 apply (zenon_equiv_s _ _ zenon_H2a); [ zenon_intro zenon_H2e; zenon_intro zenon_H2d | zenon_intro zenon_H2c; zenon_intro zenon_H2b ]. % 9.33/9.52 apply (zenon_notand_s _ _ zenon_H2d); [ zenon_intro zenon_H9 | zenon_intro zenon_H9 ]. % 9.33/9.52 apply (zenon_L2_ zenon_TD_l zenon_TC_m zenon_TB_n zenon_TA_o); trivial. % 9.33/9.52 apply (zenon_L2_ zenon_TD_l zenon_TC_m zenon_TB_n zenon_TA_o); trivial. % 9.33/9.52 apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H15. zenon_intro zenon_H15. % 9.33/9.52 apply (zenon_L5_ zenon_TC_m zenon_TD_l zenon_TA_o zenon_TB_n); trivial. % 9.33/9.52 Qed. % 9.33/9.52 % SZS output end Proof % 9.33/9.52 (* END-PROOF *) % 9.33/9.52 nodes searched: 703215 % 9.33/9.52 max branch formulas: 41474 % 9.33/9.52 proof nodes created: 7429 % 9.33/9.52 formulas created: 1611651 % 9.33/9.52 %------------------------------------------------------------------------------