%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SYN417+1 : TPTP v8.1.0. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n026.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 : Thu Jul 21 13:51:58 EDT 2022 % Result : Theorem 0.21s 0.55s % Output : Proof 0.21s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.13 % Problem : SYN417+1 : TPTP v8.1.0. Released v2.0.0. % 0.08/0.14 % Command : run_zenon %s %d % 0.14/0.35 % Computer : n026.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 : Tue Jul 12 02:55:42 EDT 2022 % 0.14/0.36 % CPUTime : % 0.21/0.55 (* PROOF-FOUND *) % 0.21/0.55 % SZS status Theorem % 0.21/0.55 (* BEGIN-PROOF *) % 0.21/0.55 % SZS output start Proof % 0.21/0.55 Theorem cute : ((exists X : zenon_U, ((X = (f (g X)))/\(forall Y : zenon_U, ((Y = (f (g Y)))->(X = Y)))))<->(exists X : zenon_U, ((X = (g (f X)))/\(forall Y : zenon_U, ((Y = (g (f Y)))->(X = Y)))))). % 0.21/0.55 Proof. % 0.21/0.55 apply NNPP. intro zenon_G. % 0.21/0.55 apply (zenon_notequiv_s _ _ zenon_G); [ zenon_intro zenon_H4; zenon_intro zenon_H3 | zenon_intro zenon_H2; zenon_intro zenon_H1 ]. % 0.21/0.55 elim zenon_H3. zenon_intro zenon_TX_f. zenon_intro zenon_H6. % 0.21/0.55 apply (zenon_and_s _ _ zenon_H6). zenon_intro zenon_H8. zenon_intro zenon_H7. % 0.21/0.55 apply zenon_H4. exists (f zenon_TX_f). apply NNPP. zenon_intro zenon_H9. % 0.21/0.55 apply (zenon_notand_s _ _ zenon_H9); [ zenon_intro zenon_Hb | zenon_intro zenon_Ha ]. % 0.21/0.55 cut ((zenon_TX_f = (g (f zenon_TX_f)))); [idtac | apply NNPP; zenon_intro zenon_Hc]. % 0.21/0.55 congruence. % 0.21/0.55 exact (zenon_Hc zenon_H8). % 0.21/0.55 apply (zenon_notallex_s (fun Y : zenon_U => ((Y = (f (g Y)))->((f zenon_TX_f) = Y))) zenon_Ha); [ zenon_intro zenon_Hd; idtac ]. % 0.21/0.55 elim zenon_Hd. zenon_intro zenon_TY_o. zenon_intro zenon_Hf. % 0.21/0.55 apply (zenon_notimply_s _ _ zenon_Hf). zenon_intro zenon_H11. zenon_intro zenon_H10. % 0.21/0.55 elim (classic (zenon_TY_o = zenon_TY_o)); [ zenon_intro zenon_H12 | zenon_intro zenon_H13 ]. % 0.21/0.55 cut ((zenon_TY_o = zenon_TY_o) = ((f zenon_TX_f) = zenon_TY_o)). % 0.21/0.55 intro zenon_D_pnotp. % 0.21/0.55 apply zenon_H10. % 0.21/0.55 rewrite <- zenon_D_pnotp. % 0.21/0.55 exact zenon_H12. % 0.21/0.55 cut ((zenon_TY_o = zenon_TY_o)); [idtac | apply NNPP; zenon_intro zenon_H13]. % 0.21/0.55 cut ((zenon_TY_o = (f zenon_TX_f))); [idtac | apply NNPP; zenon_intro zenon_H14]. % 0.21/0.55 congruence. % 0.21/0.55 cut ((zenon_TY_o = (f (g zenon_TY_o))) = (zenon_TY_o = (f zenon_TX_f))). % 0.21/0.55 intro zenon_D_pnotp. % 0.21/0.55 apply zenon_H14. % 0.21/0.55 rewrite <- zenon_D_pnotp. % 0.21/0.55 exact zenon_H11. % 0.21/0.55 cut (((f (g zenon_TY_o)) = (f zenon_TX_f))); [idtac | apply NNPP; zenon_intro zenon_H15]. % 0.21/0.55 cut ((zenon_TY_o = zenon_TY_o)); [idtac | apply NNPP; zenon_intro zenon_H13]. % 0.21/0.55 congruence. % 0.21/0.55 apply zenon_H13. apply refl_equal. % 0.21/0.55 cut (((g zenon_TY_o) = zenon_TX_f)); [idtac | apply NNPP; zenon_intro zenon_H16]. % 0.21/0.55 congruence. % 0.21/0.55 generalize (zenon_H7 (g zenon_TY_o)). zenon_intro zenon_H17. % 0.21/0.55 apply (zenon_imply_s _ _ zenon_H17); [ zenon_intro zenon_H19 | zenon_intro zenon_H18 ]. % 0.21/0.55 cut ((zenon_TY_o = (f (g zenon_TY_o)))); [idtac | apply NNPP; zenon_intro zenon_H1a]. % 0.21/0.55 congruence. % 0.21/0.55 exact (zenon_H1a zenon_H11). % 0.21/0.55 apply zenon_H16. apply sym_equal. exact zenon_H18. % 0.21/0.55 apply zenon_H13. apply refl_equal. % 0.21/0.55 apply zenon_H13. apply refl_equal. % 0.21/0.55 elim zenon_H2. zenon_intro zenon_TX_bb. zenon_intro zenon_H1c. % 0.21/0.55 apply (zenon_and_s _ _ zenon_H1c). zenon_intro zenon_H1e. zenon_intro zenon_H1d. % 0.21/0.55 apply zenon_H1. exists (g zenon_TX_bb). apply NNPP. zenon_intro zenon_H1f. % 0.21/0.55 apply (zenon_notand_s _ _ zenon_H1f); [ zenon_intro zenon_H21 | zenon_intro zenon_H20 ]. % 0.21/0.55 cut ((zenon_TX_bb = (f (g zenon_TX_bb)))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 0.21/0.55 congruence. % 0.21/0.55 exact (zenon_H22 zenon_H1e). % 0.21/0.55 apply (zenon_notallex_s (fun Y : zenon_U => ((Y = (g (f Y)))->((g zenon_TX_bb) = Y))) zenon_H20); [ zenon_intro zenon_H23; idtac ]. % 0.21/0.55 elim zenon_H23. zenon_intro zenon_TY_bk. zenon_intro zenon_H25. % 0.21/0.55 apply (zenon_notimply_s _ _ zenon_H25). zenon_intro zenon_H27. zenon_intro zenon_H26. % 0.21/0.55 elim (classic (zenon_TY_bk = zenon_TY_bk)); [ zenon_intro zenon_H28 | zenon_intro zenon_H29 ]. % 0.21/0.55 cut ((zenon_TY_bk = zenon_TY_bk) = ((g zenon_TX_bb) = zenon_TY_bk)). % 0.21/0.55 intro zenon_D_pnotp. % 0.21/0.55 apply zenon_H26. % 0.21/0.55 rewrite <- zenon_D_pnotp. % 0.21/0.55 exact zenon_H28. % 0.21/0.55 cut ((zenon_TY_bk = zenon_TY_bk)); [idtac | apply NNPP; zenon_intro zenon_H29]. % 0.21/0.55 cut ((zenon_TY_bk = (g zenon_TX_bb))); [idtac | apply NNPP; zenon_intro zenon_H2a]. % 0.21/0.55 congruence. % 0.21/0.55 cut ((zenon_TY_bk = (g (f zenon_TY_bk))) = (zenon_TY_bk = (g zenon_TX_bb))). % 0.21/0.55 intro zenon_D_pnotp. % 0.21/0.55 apply zenon_H2a. % 0.21/0.55 rewrite <- zenon_D_pnotp. % 0.21/0.55 exact zenon_H27. % 0.21/0.55 cut (((g (f zenon_TY_bk)) = (g zenon_TX_bb))); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 0.21/0.55 cut ((zenon_TY_bk = zenon_TY_bk)); [idtac | apply NNPP; zenon_intro zenon_H29]. % 0.21/0.55 congruence. % 0.21/0.55 apply zenon_H29. apply refl_equal. % 0.21/0.55 cut (((f zenon_TY_bk) = zenon_TX_bb)); [idtac | apply NNPP; zenon_intro zenon_H2c]. % 0.21/0.55 congruence. % 0.21/0.55 generalize (zenon_H1d (f zenon_TY_bk)). zenon_intro zenon_H2d. % 0.21/0.55 apply (zenon_imply_s _ _ zenon_H2d); [ zenon_intro zenon_H2f | zenon_intro zenon_H2e ]. % 0.21/0.55 cut ((zenon_TY_bk = (g (f zenon_TY_bk)))); [idtac | apply NNPP; zenon_intro zenon_H30]. % 0.21/0.55 congruence. % 0.21/0.55 exact (zenon_H30 zenon_H27). % 0.21/0.55 apply zenon_H2c. apply sym_equal. exact zenon_H2e. % 0.21/0.55 apply zenon_H29. apply refl_equal. % 0.21/0.55 apply zenon_H29. apply refl_equal. % 0.21/0.55 Qed. % 0.21/0.55 % SZS output end Proof % 0.21/0.55 (* END-PROOF *) % 0.21/0.55 nodes searched: 545 % 0.21/0.55 max branch formulas: 59 % 0.21/0.55 proof nodes created: 109 % 0.21/0.55 formulas created: 1420 % 0.21/0.55 %------------------------------------------------------------------------------