%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SET616+3 : TPTP v8.1.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n015.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 06:37:24 EDT 2022 % Result : Theorem 0.18s 0.60s % Output : Proof 0.18s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SET616+3 : TPTP v8.1.0. Released v2.2.0. % 0.07/0.12 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n015.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 : Mon Jul 11 04:36:09 EDT 2022 % 0.12/0.33 % CPUTime : % 0.18/0.60 (* PROOF-FOUND *) % 0.18/0.60 % SZS status Theorem % 0.18/0.60 (* BEGIN-PROOF *) % 0.18/0.60 % SZS output start Proof % 0.18/0.60 Theorem prove_th90 : (forall B : zenon_U, (forall C : zenon_U, (((difference B C) = (difference C B))->(B = C)))). % 0.18/0.60 Proof. % 0.18/0.60 apply NNPP. intro zenon_G. % 0.18/0.60 apply (zenon_notallex_s (fun B : zenon_U => (forall C : zenon_U, (((difference B C) = (difference C B))->(B = C)))) zenon_G); [ zenon_intro zenon_H7; idtac ]. % 0.18/0.60 elim zenon_H7. zenon_intro zenon_TB_i. zenon_intro zenon_H9. % 0.18/0.60 apply (zenon_notallex_s (fun C : zenon_U => (((difference zenon_TB_i C) = (difference C zenon_TB_i))->(zenon_TB_i = C))) zenon_H9); [ zenon_intro zenon_Ha; idtac ]. % 0.18/0.60 elim zenon_Ha. zenon_intro zenon_TC_l. zenon_intro zenon_Hc. % 0.18/0.60 apply (zenon_notimply_s _ _ zenon_Hc). zenon_intro zenon_He. zenon_intro zenon_Hd. % 0.18/0.60 generalize (member_equal zenon_TB_i). zenon_intro zenon_Hf. % 0.18/0.60 generalize (difference_defn zenon_TC_l). zenon_intro zenon_H10. % 0.18/0.60 generalize (difference_defn zenon_TB_i). zenon_intro zenon_H11. % 0.18/0.60 generalize (zenon_Hf zenon_TC_l). zenon_intro zenon_H12. % 0.18/0.60 apply (zenon_imply_s _ _ zenon_H12); [ zenon_intro zenon_H14 | zenon_intro zenon_H13 ]. % 0.18/0.60 apply (zenon_notallex_s (fun D : zenon_U => ((member D zenon_TB_i)<->(member D zenon_TC_l))) zenon_H14); [ zenon_intro zenon_H15; idtac ]. % 0.18/0.60 elim zenon_H15. zenon_intro zenon_TD_w. zenon_intro zenon_H17. % 0.18/0.60 apply (zenon_notequiv_s _ _ zenon_H17); [ zenon_intro zenon_H1b; zenon_intro zenon_H1a | zenon_intro zenon_H19; zenon_intro zenon_H18 ]. % 0.18/0.60 generalize (zenon_H10 zenon_TB_i). zenon_intro zenon_H1c. % 0.18/0.60 generalize (zenon_H11 zenon_TC_l). zenon_intro zenon_H1d. % 0.18/0.60 generalize (zenon_H1d zenon_TD_w). zenon_intro zenon_H1e. % 0.18/0.60 apply (zenon_equiv_s _ _ zenon_H1e); [ zenon_intro zenon_H22; zenon_intro zenon_H21 | zenon_intro zenon_H20; zenon_intro zenon_H1f ]. % 0.18/0.60 generalize (zenon_H1c zenon_TD_w). zenon_intro zenon_H23. % 0.18/0.60 apply (zenon_equiv_s _ _ zenon_H23); [ zenon_intro zenon_H27; zenon_intro zenon_H26 | zenon_intro zenon_H25; zenon_intro zenon_H24 ]. % 0.18/0.60 apply (zenon_notand_s _ _ zenon_H26); [ zenon_intro zenon_H18 | zenon_intro zenon_H28 ]. % 0.18/0.60 exact (zenon_H18 zenon_H1a). % 0.18/0.60 exact (zenon_H28 zenon_H1b). % 0.18/0.60 cut ((member zenon_TD_w (difference zenon_TC_l zenon_TB_i)) = (member zenon_TD_w (difference zenon_TB_i zenon_TC_l))). % 0.18/0.60 intro zenon_D_pnotp. % 0.18/0.60 apply zenon_H22. % 0.18/0.60 rewrite <- zenon_D_pnotp. % 0.18/0.60 exact zenon_H25. % 0.18/0.60 cut (((difference zenon_TC_l zenon_TB_i) = (difference zenon_TB_i zenon_TC_l))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 0.18/0.60 cut ((zenon_TD_w = zenon_TD_w)); [idtac | apply NNPP; zenon_intro zenon_H2a]. % 0.18/0.60 congruence. % 0.18/0.60 apply zenon_H2a. apply refl_equal. % 0.18/0.60 apply zenon_H29. apply sym_equal. exact zenon_He. % 0.18/0.60 apply (zenon_and_s _ _ zenon_H1f). zenon_intro zenon_H19. zenon_intro zenon_H18. % 0.18/0.60 exact (zenon_H1b zenon_H19). % 0.18/0.60 generalize (zenon_H10 zenon_TB_i). zenon_intro zenon_H1c. % 0.18/0.60 generalize (zenon_H11 zenon_TC_l). zenon_intro zenon_H1d. % 0.18/0.60 generalize (zenon_H1c zenon_TD_w). zenon_intro zenon_H23. % 0.18/0.60 apply (zenon_equiv_s _ _ zenon_H23); [ zenon_intro zenon_H27; zenon_intro zenon_H26 | zenon_intro zenon_H25; zenon_intro zenon_H24 ]. % 0.18/0.60 generalize (zenon_H1d zenon_TD_w). zenon_intro zenon_H1e. % 0.18/0.60 apply (zenon_equiv_s _ _ zenon_H1e); [ zenon_intro zenon_H22; zenon_intro zenon_H21 | zenon_intro zenon_H20; zenon_intro zenon_H1f ]. % 0.18/0.60 apply (zenon_notand_s _ _ zenon_H21); [ zenon_intro zenon_H1b | zenon_intro zenon_H2b ]. % 0.18/0.60 exact (zenon_H1b zenon_H19). % 0.18/0.60 exact (zenon_H2b zenon_H18). % 0.18/0.60 cut ((member zenon_TD_w (difference zenon_TB_i zenon_TC_l)) = (member zenon_TD_w (difference zenon_TC_l zenon_TB_i))). % 0.18/0.60 intro zenon_D_pnotp. % 0.18/0.60 apply zenon_H27. % 0.18/0.60 rewrite <- zenon_D_pnotp. % 0.18/0.60 exact zenon_H20. % 0.18/0.60 cut (((difference zenon_TB_i zenon_TC_l) = (difference zenon_TC_l zenon_TB_i))); [idtac | apply NNPP; zenon_intro zenon_H2c]. % 0.18/0.60 cut ((zenon_TD_w = zenon_TD_w)); [idtac | apply NNPP; zenon_intro zenon_H2a]. % 0.18/0.60 congruence. % 0.18/0.60 apply zenon_H2a. apply refl_equal. % 0.18/0.60 exact (zenon_H2c zenon_He). % 0.18/0.60 apply (zenon_and_s _ _ zenon_H24). zenon_intro zenon_H1a. zenon_intro zenon_H1b. % 0.18/0.60 exact (zenon_H18 zenon_H1a). % 0.18/0.60 exact (zenon_Hd zenon_H13). % 0.18/0.60 Qed. % 0.18/0.60 % SZS output end Proof % 0.18/0.60 (* END-PROOF *) % 0.18/0.60 nodes searched: 5400 % 0.18/0.60 max branch formulas: 951 % 0.18/0.60 proof nodes created: 490 % 0.18/0.60 formulas created: 14848 % 0.18/0.60 %------------------------------------------------------------------------------