%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : COM003+1 : TPTP v8.1.0. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n017.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 : Fri Jul 15 01:52:54 EDT 2022 % Result : Theorem 0.38s 0.55s % Output : Proof 0.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.14 % Problem : COM003+1 : TPTP v8.1.0. Released v2.0.0. % 0.14/0.14 % Command : run_zenon %s %d % 0.14/0.35 % Computer : n017.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 % 0.14/0.36 % DateTime : Thu Jun 16 18:15:26 EDT 2022 % 0.14/0.36 % CPUTime : % 0.38/0.55 (* PROOF-FOUND *) % 0.38/0.55 % SZS status Theorem % 0.38/0.55 (* BEGIN-PROOF *) % 0.38/0.55 % SZS output start Proof % 0.38/0.55 Theorem prove_this : (~(exists X : zenon_U, ((algorithm X)/\(forall Y : zenon_U, ((program Y)->(forall Z : zenon_U, (decides X Y Z))))))). % 0.38/0.55 Proof. % 0.38/0.55 assert (zenon_L1_ : forall (zenon_TU_i : zenon_U), (((program zenon_TU_i)/\(~(halts2 zenon_TU_i zenon_TU_i)))->((halts2 zenon_TU_i zenon_TU_i)/\(outputs zenon_TU_i (bad)))) -> (program zenon_TU_i) -> (~(halts2 zenon_TU_i zenon_TU_i)) -> False). % 0.38/0.55 do 1 intro. intros zenon_H5 zenon_H6 zenon_H7. % 0.38/0.55 apply (zenon_imply_s _ _ zenon_H5); [ zenon_intro zenon_Ha | zenon_intro zenon_H9 ]. % 0.38/0.55 apply (zenon_notand_s _ _ zenon_Ha); [ zenon_intro zenon_Hc | zenon_intro zenon_Hb ]. % 0.38/0.55 exact (zenon_Hc zenon_H6). % 0.38/0.55 exact (zenon_Hb zenon_H7). % 0.38/0.55 apply (zenon_and_s _ _ zenon_H9). zenon_intro zenon_He. zenon_intro zenon_Hd. % 0.38/0.55 exact (zenon_H7 zenon_He). % 0.38/0.55 (* end of lemma zenon_L1_ *) % 0.38/0.55 assert (zenon_L2_ : (exists U : zenon_U, ((program U)/\(forall Y : zenon_U, ((((program Y)/\(halts2 Y Y))->(~(halts2 U Y)))/\(((program Y)/\(~(halts2 Y Y)))->((halts2 U Y)/\(outputs U (bad)))))))) -> False). % 0.38/0.55 do 0 intro. intros zenon_Hf. % 0.38/0.55 elim zenon_Hf. zenon_intro zenon_TU_i. zenon_intro zenon_H10. % 0.38/0.55 apply (zenon_and_s _ _ zenon_H10). zenon_intro zenon_H6. zenon_intro zenon_H11. % 0.38/0.55 generalize (zenon_H11 zenon_TU_i). zenon_intro zenon_H12. % 0.38/0.55 apply (zenon_and_s _ _ zenon_H12). zenon_intro zenon_H13. zenon_intro zenon_H5. % 0.38/0.55 apply (zenon_imply_s _ _ zenon_H13); [ zenon_intro zenon_H14 | zenon_intro zenon_H7 ]. % 0.38/0.55 apply (zenon_notand_s _ _ zenon_H14); [ zenon_intro zenon_Hc | zenon_intro zenon_H7 ]. % 0.38/0.55 exact (zenon_Hc zenon_H6). % 0.38/0.55 apply (zenon_L1_ zenon_TU_i); trivial. % 0.38/0.55 apply (zenon_L1_ zenon_TU_i); trivial. % 0.38/0.55 (* end of lemma zenon_L2_ *) % 0.38/0.55 apply NNPP. intro zenon_G. % 0.38/0.55 apply zenon_G. zenon_intro zenon_H15. % 0.38/0.55 apply (zenon_imply_s _ _ p1); [ zenon_intro zenon_H17 | zenon_intro zenon_H16 ]. % 0.38/0.55 exact (zenon_H17 zenon_H15). % 0.38/0.55 elim zenon_H16. zenon_intro zenon_TW_y. zenon_intro zenon_H19. % 0.38/0.55 apply (zenon_and_s _ _ zenon_H19). zenon_intro zenon_H1b. zenon_intro zenon_H1a. % 0.38/0.55 apply (zenon_imply_s _ _ p3); [ zenon_intro zenon_H1d | zenon_intro zenon_H1c ]. % 0.38/0.55 generalize (p2 zenon_TW_y). zenon_intro zenon_H1e. % 0.38/0.55 apply (zenon_imply_s _ _ zenon_H1e); [ zenon_intro zenon_H20 | zenon_intro zenon_H1f ]. % 0.38/0.55 apply (zenon_notand_s _ _ zenon_H20); [ zenon_intro zenon_H22 | zenon_intro zenon_H21 ]. % 0.38/0.55 exact (zenon_H22 zenon_H1b). % 0.38/0.55 exact (zenon_H21 zenon_H1a). % 0.38/0.55 apply zenon_H1d. exists zenon_TW_y. apply NNPP. zenon_intro zenon_H23. % 0.38/0.55 apply (zenon_notand_s _ _ zenon_H23); [ zenon_intro zenon_H22 | zenon_intro zenon_H24 ]. % 0.38/0.55 exact (zenon_H22 zenon_H1b). % 0.38/0.55 apply (zenon_notallex_s (fun Y : zenon_U => ((((program Y)/\(halts2 Y Y))->((halts3 zenon_TW_y Y Y)/\(outputs zenon_TW_y (good))))/\(((program Y)/\(~(halts2 Y Y)))->((halts3 zenon_TW_y Y Y)/\(outputs zenon_TW_y (bad)))))) zenon_H24); [ zenon_intro zenon_H25; idtac ]. % 0.38/0.55 elim zenon_H25. zenon_intro zenon_TY_bm. zenon_intro zenon_H27. % 0.38/0.55 apply (zenon_notand_s _ _ zenon_H27); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 0.38/0.55 generalize (zenon_H1f zenon_TY_bm). zenon_intro zenon_H2a. % 0.38/0.55 generalize (zenon_H2a zenon_TY_bm). zenon_intro zenon_H2b. % 0.38/0.55 apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H2d. zenon_intro zenon_H2c. % 0.38/0.55 exact (zenon_H29 zenon_H2d). % 0.38/0.55 generalize (zenon_H1f zenon_TY_bm). zenon_intro zenon_H2a. % 0.38/0.55 generalize (zenon_H2a zenon_TY_bm). zenon_intro zenon_H2b. % 0.38/0.55 apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H2d. zenon_intro zenon_H2c. % 0.38/0.55 exact (zenon_H28 zenon_H2c). % 0.38/0.55 apply (zenon_imply_s _ _ p4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hf ]. % 0.38/0.55 exact (zenon_H2e zenon_H1c). % 0.38/0.55 apply (zenon_L2_); trivial. % 0.38/0.55 Qed. % 0.38/0.55 % SZS output end Proof % 0.38/0.55 (* END-PROOF *) % 0.38/0.55 nodes searched: 1189 % 0.38/0.55 max branch formulas: 441 % 0.38/0.55 proof nodes created: 212 % 0.38/0.55 formulas created: 4542 % 0.38/0.55 %------------------------------------------------------------------------------