%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SET643+3 : TPTP v8.1.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n004.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 06:37:41 EDT 2022 % Result : Theorem 0.39s 0.56s % Output : Proof 0.39s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SET643+3 : TPTP v8.1.0. Released v2.2.0. % 0.03/0.12 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n004.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 04:07:52 EDT 2022 % 0.12/0.33 % CPUTime : % 0.39/0.56 (* PROOF-FOUND *) % 0.39/0.56 % SZS status Theorem % 0.39/0.56 (* BEGIN-PROOF *) % 0.39/0.56 % SZS output start Proof % 0.39/0.56 Theorem prove_relset_1_5 : (forall B : zenon_U, ((ilf_type B (set_type))->(forall C : zenon_U, ((ilf_type C (set_type))->(ilf_type (cross_product B C) (relation_type B C)))))). % 0.39/0.56 Proof. % 0.39/0.56 assert (zenon_L1_ : forall (zenon_TC_x : zenon_U) (zenon_TB_y : zenon_U), (ilf_type zenon_TB_y (set_type)) -> (ilf_type zenon_TC_x (set_type)) -> (~(ilf_type (cross_product zenon_TB_y zenon_TC_x) (set_type))) -> False). % 0.39/0.56 do 2 intro. intros zenon_H14 zenon_H15 zenon_H16. % 0.39/0.56 generalize (p3 zenon_TB_y). zenon_intro zenon_H19. % 0.39/0.56 apply (zenon_imply_s _ _ zenon_H19); [ zenon_intro zenon_H1b | zenon_intro zenon_H1a ]. % 0.39/0.56 exact (zenon_H1b zenon_H14). % 0.39/0.56 generalize (zenon_H1a zenon_TC_x). zenon_intro zenon_H1c. % 0.39/0.56 apply (zenon_imply_s _ _ zenon_H1c); [ zenon_intro zenon_H1e | zenon_intro zenon_H1d ]. % 0.39/0.56 exact (zenon_H1e zenon_H15). % 0.39/0.56 exact (zenon_H16 zenon_H1d). % 0.39/0.56 (* end of lemma zenon_L1_ *) % 0.39/0.56 apply NNPP. intro zenon_G. % 0.39/0.56 apply (zenon_notallex_s (fun B : zenon_U => ((ilf_type B (set_type))->(forall C : zenon_U, ((ilf_type C (set_type))->(ilf_type (cross_product B C) (relation_type B C)))))) zenon_G); [ zenon_intro zenon_H1f; idtac ]. % 0.39/0.56 elim zenon_H1f. zenon_intro zenon_TB_y. zenon_intro zenon_H20. % 0.39/0.56 apply (zenon_notimply_s _ _ zenon_H20). zenon_intro zenon_H14. zenon_intro zenon_H21. % 0.39/0.56 apply (zenon_notallex_s (fun C : zenon_U => ((ilf_type C (set_type))->(ilf_type (cross_product zenon_TB_y C) (relation_type zenon_TB_y C)))) zenon_H21); [ zenon_intro zenon_H22; idtac ]. % 0.39/0.56 elim zenon_H22. zenon_intro zenon_TC_x. zenon_intro zenon_H23. % 0.39/0.56 apply (zenon_notimply_s _ _ zenon_H23). zenon_intro zenon_H15. zenon_intro zenon_H24. % 0.39/0.56 generalize (p1 (cross_product zenon_TB_y zenon_TC_x)). zenon_intro zenon_H25. % 0.39/0.56 apply (zenon_imply_s _ _ zenon_H25); [ zenon_intro zenon_H16 | zenon_intro zenon_H26 ]. % 0.39/0.56 apply (zenon_L1_ zenon_TC_x zenon_TB_y); trivial. % 0.39/0.56 generalize (zenon_H26 zenon_TB_y). zenon_intro zenon_H27. % 0.39/0.56 apply (zenon_imply_s _ _ zenon_H27); [ zenon_intro zenon_H1b | zenon_intro zenon_H28 ]. % 0.39/0.56 exact (zenon_H1b zenon_H14). % 0.39/0.56 generalize (zenon_H28 zenon_TC_x). zenon_intro zenon_H29. % 0.39/0.56 apply (zenon_imply_s _ _ zenon_H29); [ zenon_intro zenon_H1e | zenon_intro zenon_H2a ]. % 0.39/0.56 exact (zenon_H1e zenon_H15). % 0.39/0.56 apply (zenon_imply_s _ _ zenon_H2a); [ zenon_intro zenon_H2c | zenon_intro zenon_H2b ]. % 0.39/0.56 generalize (p9 (cross_product zenon_TB_y zenon_TC_x)). zenon_intro zenon_H2d. % 0.39/0.56 apply (zenon_imply_s _ _ zenon_H2d); [ zenon_intro zenon_H16 | zenon_intro zenon_H2e ]. % 0.39/0.56 apply (zenon_L1_ zenon_TC_x zenon_TB_y); trivial. % 0.39/0.56 generalize (zenon_H2e (cross_product zenon_TB_y zenon_TC_x)). zenon_intro zenon_H2f. % 0.39/0.56 apply (zenon_imply_s _ _ zenon_H2f); [ zenon_intro zenon_H16 | zenon_intro zenon_H30 ]. % 0.39/0.56 apply (zenon_L1_ zenon_TC_x zenon_TB_y); trivial. % 0.39/0.56 apply (zenon_equiv_s _ _ zenon_H30); [ zenon_intro zenon_H2c; zenon_intro zenon_H33 | zenon_intro zenon_H32; zenon_intro zenon_H31 ]. % 0.39/0.56 apply (zenon_notallex_s (fun D : zenon_U => ((ilf_type D (set_type))->((member D (cross_product zenon_TB_y zenon_TC_x))->(member D (cross_product zenon_TB_y zenon_TC_x))))) zenon_H33); [ zenon_intro zenon_H34; idtac ]. % 0.39/0.56 elim zenon_H34. zenon_intro zenon_TD_cb. zenon_intro zenon_H36. % 0.39/0.56 apply (zenon_notimply_s _ _ zenon_H36). zenon_intro zenon_H38. zenon_intro zenon_H37. % 0.39/0.56 apply (zenon_notimply_s _ _ zenon_H37). zenon_intro zenon_H3a. zenon_intro zenon_H39. % 0.39/0.56 exact (zenon_H39 zenon_H3a). % 0.39/0.56 exact (zenon_H2c zenon_H32). % 0.39/0.56 exact (zenon_H24 zenon_H2b). % 0.39/0.56 Qed. % 0.39/0.56 % SZS output end Proof % 0.39/0.56 (* END-PROOF *) % 0.39/0.56 nodes searched: 2140 % 0.39/0.56 max branch formulas: 1191 % 0.39/0.56 proof nodes created: 149 % 0.39/0.56 formulas created: 12295 % 0.39/0.56 %------------------------------------------------------------------------------