%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : COM003+1 : TPTP v8.1.0. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % Computer : n018.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 01:45:46 EDT 2022 % Result : Theorem 0.20s 0.43s % Output : Proof 0.20s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : COM003+1 : TPTP v8.1.0. Released v2.0.0. % 0.11/0.12 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 0.13/0.33 % Computer : n018.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 600 % 0.13/0.33 % DateTime : Thu Jun 16 18:54:46 EDT 2022 % 0.13/0.33 % CPUTime : % 0.20/0.43 % SZS status Theorem % 0.20/0.43 (* PROOF-FOUND *) % 0.20/0.43 (* BEGIN-PROOF *) % 0.20/0.43 % SZS output start Proof % 0.20/0.43 1. (Ex X, ((algorithm X) /\ (All Y, ((program Y) => (All Z, (decides X Y Z)))))) (-. (Ex X, ((algorithm X) /\ (All Y, ((program Y) => (All Z, (decides X Y Z))))))) ### Axiom % 0.20/0.43 2. (program T_0) (-. (program T_0)) ### Axiom % 0.20/0.43 3. (All Y, ((program Y) => (All Z, (decides T_0 Y Z)))) (-. (All Y, ((program Y) => (All Z, (decides T_0 Y Z))))) ### Axiom % 0.20/0.43 4. (program T_0) (-. (program T_0)) ### Axiom % 0.20/0.43 5. (-. (((program T_1) /\ (halts2 T_1 T_1)) => ((halts3 T_0 T_1 T_1) /\ (outputs T_0 (good))))) (((program T_1) /\ (halts2 T_1 T_1)) => ((halts3 T_0 T_1 T_1) /\ (outputs T_0 (good)))) ### Axiom % 0.20/0.43 6. ((((program T_1) /\ (halts2 T_1 T_1)) => ((halts3 T_0 T_1 T_1) /\ (outputs T_0 (good)))) /\ (((program T_1) /\ (-. (halts2 T_1 T_1))) => ((halts3 T_0 T_1 T_1) /\ (outputs T_0 (bad))))) (-. (((program T_1) /\ (halts2 T_1 T_1)) => ((halts3 T_0 T_1 T_1) /\ (outputs T_0 (good))))) ### And 5 % 0.20/0.43 7. (All Z, ((((program T_1) /\ (halts2 T_1 Z)) => ((halts3 T_0 T_1 Z) /\ (outputs T_0 (good)))) /\ (((program T_1) /\ (-. (halts2 T_1 Z))) => ((halts3 T_0 T_1 Z) /\ (outputs T_0 (bad)))))) (-. (((program T_1) /\ (halts2 T_1 T_1)) => ((halts3 T_0 T_1 T_1) /\ (outputs T_0 (good))))) ### All 6 % 0.20/0.43 8. (All Y, (All Z, ((((program Y) /\ (halts2 Y Z)) => ((halts3 T_0 Y Z) /\ (outputs T_0 (good)))) /\ (((program Y) /\ (-. (halts2 Y Z))) => ((halts3 T_0 Y Z) /\ (outputs T_0 (bad))))))) (-. (((program T_1) /\ (halts2 T_1 T_1)) => ((halts3 T_0 T_1 T_1) /\ (outputs T_0 (good))))) ### All 7 % 0.20/0.43 9. (-. (((program T_1) /\ (-. (halts2 T_1 T_1))) => ((halts3 T_0 T_1 T_1) /\ (outputs T_0 (bad))))) (((program T_1) /\ (-. (halts2 T_1 T_1))) => ((halts3 T_0 T_1 T_1) /\ (outputs T_0 (bad)))) ### Axiom % 0.20/0.43 10. ((((program T_1) /\ (halts2 T_1 T_1)) => ((halts3 T_0 T_1 T_1) /\ (outputs T_0 (good)))) /\ (((program T_1) /\ (-. (halts2 T_1 T_1))) => ((halts3 T_0 T_1 T_1) /\ (outputs T_0 (bad))))) (-. (((program T_1) /\ (-. (halts2 T_1 T_1))) => ((halts3 T_0 T_1 T_1) /\ (outputs T_0 (bad))))) ### And 9 % 0.20/0.43 11. (All Z, ((((program T_1) /\ (halts2 T_1 Z)) => ((halts3 T_0 T_1 Z) /\ (outputs T_0 (good)))) /\ (((program T_1) /\ (-. (halts2 T_1 Z))) => ((halts3 T_0 T_1 Z) /\ (outputs T_0 (bad)))))) (-. (((program T_1) /\ (-. (halts2 T_1 T_1))) => ((halts3 T_0 T_1 T_1) /\ (outputs T_0 (bad))))) ### All 10 % 0.20/0.43 12. (All Y, (All Z, ((((program Y) /\ (halts2 Y Z)) => ((halts3 T_0 Y Z) /\ (outputs T_0 (good)))) /\ (((program Y) /\ (-. (halts2 Y Z))) => ((halts3 T_0 Y Z) /\ (outputs T_0 (bad))))))) (-. (((program T_1) /\ (-. (halts2 T_1 T_1))) => ((halts3 T_0 T_1 T_1) /\ (outputs T_0 (bad))))) ### All 11 % 0.20/0.43 13. (-. ((((program T_1) /\ (halts2 T_1 T_1)) => ((halts3 T_0 T_1 T_1) /\ (outputs T_0 (good)))) /\ (((program T_1) /\ (-. (halts2 T_1 T_1))) => ((halts3 T_0 T_1 T_1) /\ (outputs T_0 (bad)))))) (All Y, (All Z, ((((program Y) /\ (halts2 Y Z)) => ((halts3 T_0 Y Z) /\ (outputs T_0 (good)))) /\ (((program Y) /\ (-. (halts2 Y Z))) => ((halts3 T_0 Y Z) /\ (outputs T_0 (bad))))))) ### NotAnd 8 12 % 0.20/0.43 14. (-. (All Y, ((((program Y) /\ (halts2 Y Y)) => ((halts3 T_0 Y Y) /\ (outputs T_0 (good)))) /\ (((program Y) /\ (-. (halts2 Y Y))) => ((halts3 T_0 Y Y) /\ (outputs T_0 (bad))))))) (All Y, (All Z, ((((program Y) /\ (halts2 Y Z)) => ((halts3 T_0 Y Z) /\ (outputs T_0 (good)))) /\ (((program Y) /\ (-. (halts2 Y Z))) => ((halts3 T_0 Y Z) /\ (outputs T_0 (bad))))))) ### NotAllEx 13 % 0.20/0.43 15. (-. ((program T_0) /\ (All Y, ((((program Y) /\ (halts2 Y Y)) => ((halts3 T_0 Y Y) /\ (outputs T_0 (good)))) /\ (((program Y) /\ (-. (halts2 Y Y))) => ((halts3 T_0 Y Y) /\ (outputs T_0 (bad)))))))) (All Y, (All Z, ((((program Y) /\ (halts2 Y Z)) => ((halts3 T_0 Y Z) /\ (outputs T_0 (good)))) /\ (((program Y) /\ (-. (halts2 Y Z))) => ((halts3 T_0 Y Z) /\ (outputs T_0 (bad))))))) (program T_0) ### NotAnd 4 14 % 0.20/0.43 16. (-. (Ex W, ((program W) /\ (All Y, ((((program Y) /\ (halts2 Y Y)) => ((halts3 W Y Y) /\ (outputs W (good)))) /\ (((program Y) /\ (-. (halts2 Y Y))) => ((halts3 W Y Y) /\ (outputs W (bad))))))))) (program T_0) (All Y, (All Z, ((((program Y) /\ (halts2 Y Z)) => ((halts3 T_0 Y Z) /\ (outputs T_0 (good)))) /\ (((program Y) /\ (-. (halts2 Y Z))) => ((halts3 T_0 Y Z) /\ (outputs T_0 (bad))))))) ### NotExists 15 % 0.20/0.43 17. (((program T_0) /\ (All Y, ((program Y) => (All Z, (decides T_0 Y Z))))) => (All Y, (All Z, ((((program Y) /\ (halts2 Y Z)) => ((halts3 T_0 Y Z) /\ (outputs T_0 (good)))) /\ (((program Y) /\ (-. (halts2 Y Z))) => ((halts3 T_0 Y Z) /\ (outputs T_0 (bad)))))))) (-. (Ex W, ((program W) /\ (All Y, ((((program Y) /\ (halts2 Y Y)) => ((halts3 W Y Y) /\ (outputs W (good)))) /\ (((program Y) /\ (-. (halts2 Y Y))) => ((halts3 W Y Y) /\ (outputs W (bad))))))))) (All Y, ((program Y) => (All Z, (decides T_0 Y Z)))) (program T_0) ### DisjTree 2 3 16 % 0.20/0.43 18. (All W, (((program W) /\ (All Y, ((program Y) => (All Z, (decides W Y Z))))) => (All Y, (All Z, ((((program Y) /\ (halts2 Y Z)) => ((halts3 W Y Z) /\ (outputs W (good)))) /\ (((program Y) /\ (-. (halts2 Y Z))) => ((halts3 W Y Z) /\ (outputs W (bad))))))))) (program T_0) (All Y, ((program Y) => (All Z, (decides T_0 Y Z)))) (-. (Ex W, ((program W) /\ (All Y, ((((program Y) /\ (halts2 Y Y)) => ((halts3 W Y Y) /\ (outputs W (good)))) /\ (((program Y) /\ (-. (halts2 Y Y))) => ((halts3 W Y Y) /\ (outputs W (bad))))))))) ### All 17 % 0.20/0.43 19. (Ex V, ((program V) /\ (All Y, ((((program Y) /\ (halts2 Y Y)) => ((halts2 V Y) /\ (outputs V (good)))) /\ (((program Y) /\ (-. (halts2 Y Y))) => ((halts2 V Y) /\ (outputs V (bad)))))))) (-. (Ex V, ((program V) /\ (All Y, ((((program Y) /\ (halts2 Y Y)) => ((halts2 V Y) /\ (outputs V (good)))) /\ (((program Y) /\ (-. (halts2 Y Y))) => ((halts2 V Y) /\ (outputs V (bad))))))))) ### Axiom % 0.20/0.43 20. (program T_2) (-. (program T_2)) ### Axiom % 0.20/0.43 21. (program T_2) (-. (program T_2)) ### Axiom % 0.20/0.43 22. (-. (halts2 T_2 T_2)) (halts2 T_2 T_2) ### Axiom % 0.20/0.43 23. (-. (halts2 T_2 T_2)) (halts2 T_2 T_2) ### Axiom % 0.20/0.43 24. ((halts2 T_2 T_2) /\ (outputs T_2 (bad))) (-. (halts2 T_2 T_2)) ### And 23 % 0.20/0.43 25. (((program T_2) /\ (-. (halts2 T_2 T_2))) => ((halts2 T_2 T_2) /\ (outputs T_2 (bad)))) (-. (halts2 T_2 T_2)) (program T_2) ### DisjTree 21 22 24 % 0.20/0.43 26. (((program T_2) /\ (halts2 T_2 T_2)) => (-. (halts2 T_2 T_2))) (((program T_2) /\ (-. (halts2 T_2 T_2))) => ((halts2 T_2 T_2) /\ (outputs T_2 (bad)))) (program T_2) ### DisjTree 20 25 25 % 0.20/0.43 27. ((((program T_2) /\ (halts2 T_2 T_2)) => (-. (halts2 T_2 T_2))) /\ (((program T_2) /\ (-. (halts2 T_2 T_2))) => ((halts2 T_2 T_2) /\ (outputs T_2 (bad))))) (program T_2) ### And 26 % 0.20/0.43 28. (All Y, ((((program Y) /\ (halts2 Y Y)) => (-. (halts2 T_2 Y))) /\ (((program Y) /\ (-. (halts2 Y Y))) => ((halts2 T_2 Y) /\ (outputs T_2 (bad)))))) (program T_2) ### All 27 % 0.20/0.43 29. ((program T_2) /\ (All Y, ((((program Y) /\ (halts2 Y Y)) => (-. (halts2 T_2 Y))) /\ (((program Y) /\ (-. (halts2 Y Y))) => ((halts2 T_2 Y) /\ (outputs T_2 (bad))))))) ### And 28 % 0.20/0.43 30. (Ex U, ((program U) /\ (All Y, ((((program Y) /\ (halts2 Y Y)) => (-. (halts2 U Y))) /\ (((program Y) /\ (-. (halts2 Y Y))) => ((halts2 U Y) /\ (outputs U (bad)))))))) ### Exists 29 % 0.20/0.43 31. ((Ex V, ((program V) /\ (All Y, ((((program Y) /\ (halts2 Y Y)) => ((halts2 V Y) /\ (outputs V (good)))) /\ (((program Y) /\ (-. (halts2 Y Y))) => ((halts2 V Y) /\ (outputs V (bad)))))))) => (Ex U, ((program U) /\ (All Y, ((((program Y) /\ (halts2 Y Y)) => (-. (halts2 U Y))) /\ (((program Y) /\ (-. (halts2 Y Y))) => ((halts2 U Y) /\ (outputs U (bad))))))))) (Ex V, ((program V) /\ (All Y, ((((program Y) /\ (halts2 Y Y)) => ((halts2 V Y) /\ (outputs V (good)))) /\ (((program Y) /\ (-. (halts2 Y Y))) => ((halts2 V Y) /\ (outputs V (bad)))))))) ### Imply 19 30 % 0.20/0.43 32. ((Ex W, ((program W) /\ (All Y, ((((program Y) /\ (halts2 Y Y)) => ((halts3 W Y Y) /\ (outputs W (good)))) /\ (((program Y) /\ (-. (halts2 Y Y))) => ((halts3 W Y Y) /\ (outputs W (bad)))))))) => (Ex V, ((program V) /\ (All Y, ((((program Y) /\ (halts2 Y Y)) => ((halts2 V Y) /\ (outputs V (good)))) /\ (((program Y) /\ (-. (halts2 Y Y))) => ((halts2 V Y) /\ (outputs V (bad))))))))) ((Ex V, ((program V) /\ (All Y, ((((program Y) /\ (halts2 Y Y)) => ((halts2 V Y) /\ (outputs V (good)))) /\ (((program Y) /\ (-. (halts2 Y Y))) => ((halts2 V Y) /\ (outputs V (bad)))))))) => (Ex U, ((program U) /\ (All Y, ((((program Y) /\ (halts2 Y Y)) => (-. (halts2 U Y))) /\ (((program Y) /\ (-. (halts2 Y Y))) => ((halts2 U Y) /\ (outputs U (bad))))))))) (All Y, ((program Y) => (All Z, (decides T_0 Y Z)))) (program T_0) (All W, (((program W) /\ (All Y, ((program Y) => (All Z, (decides W Y Z))))) => (All Y, (All Z, ((((program Y) /\ (halts2 Y Z)) => ((halts3 W Y Z) /\ (outputs W (good)))) /\ (((program Y) /\ (-. (halts2 Y Z))) => ((halts3 W Y Z) /\ (outputs W (bad))))))))) ### Imply 18 31 % 0.20/0.44 33. ((program T_0) /\ (All Y, ((program Y) => (All Z, (decides T_0 Y Z))))) (All W, (((program W) /\ (All Y, ((program Y) => (All Z, (decides W Y Z))))) => (All Y, (All Z, ((((program Y) /\ (halts2 Y Z)) => ((halts3 W Y Z) /\ (outputs W (good)))) /\ (((program Y) /\ (-. (halts2 Y Z))) => ((halts3 W Y Z) /\ (outputs W (bad))))))))) ((Ex V, ((program V) /\ (All Y, ((((program Y) /\ (halts2 Y Y)) => ((halts2 V Y) /\ (outputs V (good)))) /\ (((program Y) /\ (-. (halts2 Y Y))) => ((halts2 V Y) /\ (outputs V (bad)))))))) => (Ex U, ((program U) /\ (All Y, ((((program Y) /\ (halts2 Y Y)) => (-. (halts2 U Y))) /\ (((program Y) /\ (-. (halts2 Y Y))) => ((halts2 U Y) /\ (outputs U (bad))))))))) ((Ex W, ((program W) /\ (All Y, ((((program Y) /\ (halts2 Y Y)) => ((halts3 W Y Y) /\ (outputs W (good)))) /\ (((program Y) /\ (-. (halts2 Y Y))) => ((halts3 W Y Y) /\ (outputs W (bad)))))))) => (Ex V, ((program V) /\ (All Y, ((((program Y) /\ (halts2 Y Y)) => ((halts2 V Y) /\ (outputs V (good)))) /\ (((program Y) /\ (-. (halts2 Y Y))) => ((halts2 V Y) /\ (outputs V (bad))))))))) ### And 32 % 0.20/0.44 34. (Ex W, ((program W) /\ (All Y, ((program Y) => (All Z, (decides W Y Z)))))) ((Ex W, ((program W) /\ (All Y, ((((program Y) /\ (halts2 Y Y)) => ((halts3 W Y Y) /\ (outputs W (good)))) /\ (((program Y) /\ (-. (halts2 Y Y))) => ((halts3 W Y Y) /\ (outputs W (bad)))))))) => (Ex V, ((program V) /\ (All Y, ((((program Y) /\ (halts2 Y Y)) => ((halts2 V Y) /\ (outputs V (good)))) /\ (((program Y) /\ (-. (halts2 Y Y))) => ((halts2 V Y) /\ (outputs V (bad))))))))) ((Ex V, ((program V) /\ (All Y, ((((program Y) /\ (halts2 Y Y)) => ((halts2 V Y) /\ (outputs V (good)))) /\ (((program Y) /\ (-. (halts2 Y Y))) => ((halts2 V Y) /\ (outputs V (bad)))))))) => (Ex U, ((program U) /\ (All Y, ((((program Y) /\ (halts2 Y Y)) => (-. (halts2 U Y))) /\ (((program Y) /\ (-. (halts2 Y Y))) => ((halts2 U Y) /\ (outputs U (bad))))))))) (All W, (((program W) /\ (All Y, ((program Y) => (All Z, (decides W Y Z))))) => (All Y, (All Z, ((((program Y) /\ (halts2 Y Z)) => ((halts3 W Y Z) /\ (outputs W (good)))) /\ (((program Y) /\ (-. (halts2 Y Z))) => ((halts3 W Y Z) /\ (outputs W (bad))))))))) ### Exists 33 % 0.20/0.44 35. ((Ex X, ((algorithm X) /\ (All Y, ((program Y) => (All Z, (decides X Y Z)))))) => (Ex W, ((program W) /\ (All Y, ((program Y) => (All Z, (decides W Y Z))))))) (All W, (((program W) /\ (All Y, ((program Y) => (All Z, (decides W Y Z))))) => (All Y, (All Z, ((((program Y) /\ (halts2 Y Z)) => ((halts3 W Y Z) /\ (outputs W (good)))) /\ (((program Y) /\ (-. (halts2 Y Z))) => ((halts3 W Y Z) /\ (outputs W (bad))))))))) ((Ex V, ((program V) /\ (All Y, ((((program Y) /\ (halts2 Y Y)) => ((halts2 V Y) /\ (outputs V (good)))) /\ (((program Y) /\ (-. (halts2 Y Y))) => ((halts2 V Y) /\ (outputs V (bad)))))))) => (Ex U, ((program U) /\ (All Y, ((((program Y) /\ (halts2 Y Y)) => (-. (halts2 U Y))) /\ (((program Y) /\ (-. (halts2 Y Y))) => ((halts2 U Y) /\ (outputs U (bad))))))))) ((Ex W, ((program W) /\ (All Y, ((((program Y) /\ (halts2 Y Y)) => ((halts3 W Y Y) /\ (outputs W (good)))) /\ (((program Y) /\ (-. (halts2 Y Y))) => ((halts3 W Y Y) /\ (outputs W (bad)))))))) => (Ex V, ((program V) /\ (All Y, ((((program Y) /\ (halts2 Y Y)) => ((halts2 V Y) /\ (outputs V (good)))) /\ (((program Y) /\ (-. (halts2 Y Y))) => ((halts2 V Y) /\ (outputs V (bad))))))))) (Ex X, ((algorithm X) /\ (All Y, ((program Y) => (All Z, (decides X Y Z)))))) ### Imply 1 34 % 0.20/0.44 36. (-. (-. (Ex X, ((algorithm X) /\ (All Y, ((program Y) => (All Z, (decides X Y Z)))))))) ((Ex W, ((program W) /\ (All Y, ((((program Y) /\ (halts2 Y Y)) => ((halts3 W Y Y) /\ (outputs W (good)))) /\ (((program Y) /\ (-. (halts2 Y Y))) => ((halts3 W Y Y) /\ (outputs W (bad)))))))) => (Ex V, ((program V) /\ (All Y, ((((program Y) /\ (halts2 Y Y)) => ((halts2 V Y) /\ (outputs V (good)))) /\ (((program Y) /\ (-. (halts2 Y Y))) => ((halts2 V Y) /\ (outputs V (bad))))))))) ((Ex V, ((program V) /\ (All Y, ((((program Y) /\ (halts2 Y Y)) => ((halts2 V Y) /\ (outputs V (good)))) /\ (((program Y) /\ (-. (halts2 Y Y))) => ((halts2 V Y) /\ (outputs V (bad)))))))) => (Ex U, ((program U) /\ (All Y, ((((program Y) /\ (halts2 Y Y)) => (-. (halts2 U Y))) /\ (((program Y) /\ (-. (halts2 Y Y))) => ((halts2 U Y) /\ (outputs U (bad))))))))) (All W, (((program W) /\ (All Y, ((program Y) => (All Z, (decides W Y Z))))) => (All Y, (All Z, ((((program Y) /\ (halts2 Y Z)) => ((halts3 W Y Z) /\ (outputs W (good)))) /\ (((program Y) /\ (-. (halts2 Y Z))) => ((halts3 W Y Z) /\ (outputs W (bad))))))))) ((Ex X, ((algorithm X) /\ (All Y, ((program Y) => (All Z, (decides X Y Z)))))) => (Ex W, ((program W) /\ (All Y, ((program Y) => (All Z, (decides W Y Z))))))) ### NotNot 35 % 0.20/0.44 % SZS output end Proof % 0.20/0.44 (* END-PROOF *) %------------------------------------------------------------------------------