%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : NUM500+3 : TPTP v8.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % Computer : n019.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 : Mon Jul 18 14:43:02 EDT 2022 % Result : Theorem 9.62s 9.81s % Output : Proof 9.62s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : NUM500+3 : TPTP v8.1.0. Released v4.0.0. % 0.11/0.13 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 0.12/0.34 % Computer : n019.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 600 % 0.12/0.34 % DateTime : Thu Jul 7 02:01:08 EDT 2022 % 0.12/0.34 % CPUTime : % 9.62/9.81 % SZS status Theorem % 9.62/9.81 (* PROOF-FOUND *) % 9.62/9.81 (* BEGIN-PROOF *) % 9.62/9.81 % SZS output start Proof % 9.62/9.81 1. (aNaturalNumber0 (xk)) (-. (aNaturalNumber0 (xk))) ### Axiom % 9.62/9.81 2. ((xk) != (sz00)) ((xk) = (sz00)) ### Axiom % 9.62/9.81 3. ((xk) != (sz10)) ((xk) = (sz10)) ### Axiom % 9.62/9.81 4. (aNaturalNumber0 T_0) (-. (aNaturalNumber0 T_0)) ### Axiom % 9.62/9.81 5. (doDivides0 T_0 (xk)) (-. (doDivides0 T_0 (xk))) ### Axiom % 9.62/9.81 6. (-. ((Ex W1, ((aNaturalNumber0 W1) /\ ((xk) = (sdtasdt0 T_0 W1)))) \/ (doDivides0 T_0 (xk)))) (doDivides0 T_0 (xk)) ### NotOr 5 % 9.62/9.81 7. (isPrime0 T_0) (-. (isPrime0 T_0)) ### Axiom % 9.62/9.81 8. (-. (((T_0 != (sz00)) /\ ((T_0 != (sz10)) /\ (All W1, (((aNaturalNumber0 W1) /\ ((Ex W2, ((aNaturalNumber0 W2) /\ (T_0 = (sdtasdt0 W1 W2)))) /\ (doDivides0 W1 T_0))) => ((W1 = (sz10)) \/ (W1 = T_0)))))) \/ (isPrime0 T_0))) (isPrime0 T_0) ### NotOr 7 % 9.62/9.81 9. (-. ((aNaturalNumber0 T_0) /\ (((Ex W1, ((aNaturalNumber0 W1) /\ ((xk) = (sdtasdt0 T_0 W1)))) \/ (doDivides0 T_0 (xk))) /\ (((T_0 != (sz00)) /\ ((T_0 != (sz10)) /\ (All W1, (((aNaturalNumber0 W1) /\ ((Ex W2, ((aNaturalNumber0 W2) /\ (T_0 = (sdtasdt0 W1 W2)))) /\ (doDivides0 W1 T_0))) => ((W1 = (sz10)) \/ (W1 = T_0)))))) \/ (isPrime0 T_0))))) (isPrime0 T_0) (doDivides0 T_0 (xk)) (aNaturalNumber0 T_0) ### DisjTree 4 6 8 % 9.62/9.81 10. (-. (Ex W0, ((aNaturalNumber0 W0) /\ (((Ex W1, ((aNaturalNumber0 W1) /\ ((xk) = (sdtasdt0 W0 W1)))) \/ (doDivides0 W0 (xk))) /\ (((W0 != (sz00)) /\ ((W0 != (sz10)) /\ (All W1, (((aNaturalNumber0 W1) /\ ((Ex W2, ((aNaturalNumber0 W2) /\ (W0 = (sdtasdt0 W1 W2)))) /\ (doDivides0 W1 W0))) => ((W1 = (sz10)) \/ (W1 = W0)))))) \/ (isPrime0 W0)))))) (aNaturalNumber0 T_0) (doDivides0 T_0 (xk)) (isPrime0 T_0) ### NotExists 9 % 9.62/9.81 11. ((aNaturalNumber0 T_0) /\ ((doDivides0 T_0 (xk)) /\ (isPrime0 T_0))) (-. (Ex W0, ((aNaturalNumber0 W0) /\ (((Ex W1, ((aNaturalNumber0 W1) /\ ((xk) = (sdtasdt0 W0 W1)))) \/ (doDivides0 W0 (xk))) /\ (((W0 != (sz00)) /\ ((W0 != (sz10)) /\ (All W1, (((aNaturalNumber0 W1) /\ ((Ex W2, ((aNaturalNumber0 W2) /\ (W0 = (sdtasdt0 W1 W2)))) /\ (doDivides0 W1 W0))) => ((W1 = (sz10)) \/ (W1 = W0)))))) \/ (isPrime0 W0)))))) ### ConjTree 10 % 9.62/9.81 12. (Ex W1, ((aNaturalNumber0 W1) /\ ((doDivides0 W1 (xk)) /\ (isPrime0 W1)))) (-. (Ex W0, ((aNaturalNumber0 W0) /\ (((Ex W1, ((aNaturalNumber0 W1) /\ ((xk) = (sdtasdt0 W0 W1)))) \/ (doDivides0 W0 (xk))) /\ (((W0 != (sz00)) /\ ((W0 != (sz10)) /\ (All W1, (((aNaturalNumber0 W1) /\ ((Ex W2, ((aNaturalNumber0 W2) /\ (W0 = (sdtasdt0 W1 W2)))) /\ (doDivides0 W1 W0))) => ((W1 = (sz10)) \/ (W1 = W0)))))) \/ (isPrime0 W0)))))) ### Exists 11 % 9.62/9.81 13. (((aNaturalNumber0 (xk)) /\ (((xk) != (sz00)) /\ ((xk) != (sz10)))) => (Ex W1, ((aNaturalNumber0 W1) /\ ((doDivides0 W1 (xk)) /\ (isPrime0 W1))))) (-. (Ex W0, ((aNaturalNumber0 W0) /\ (((Ex W1, ((aNaturalNumber0 W1) /\ ((xk) = (sdtasdt0 W0 W1)))) \/ (doDivides0 W0 (xk))) /\ (((W0 != (sz00)) /\ ((W0 != (sz10)) /\ (All W1, (((aNaturalNumber0 W1) /\ ((Ex W2, ((aNaturalNumber0 W2) /\ (W0 = (sdtasdt0 W1 W2)))) /\ (doDivides0 W1 W0))) => ((W1 = (sz10)) \/ (W1 = W0)))))) \/ (isPrime0 W0)))))) ((xk) != (sz10)) ((xk) != (sz00)) (aNaturalNumber0 (xk)) ### DisjTree 1 2 3 12 % 9.62/9.81 14. (All W0, (((aNaturalNumber0 W0) /\ ((W0 != (sz00)) /\ (W0 != (sz10)))) => (Ex W1, ((aNaturalNumber0 W1) /\ ((doDivides0 W1 W0) /\ (isPrime0 W1)))))) (aNaturalNumber0 (xk)) ((xk) != (sz00)) ((xk) != (sz10)) (-. (Ex W0, ((aNaturalNumber0 W0) /\ (((Ex W1, ((aNaturalNumber0 W1) /\ ((xk) = (sdtasdt0 W0 W1)))) \/ (doDivides0 W0 (xk))) /\ (((W0 != (sz00)) /\ ((W0 != (sz10)) /\ (All W1, (((aNaturalNumber0 W1) /\ ((Ex W2, ((aNaturalNumber0 W2) /\ (W0 = (sdtasdt0 W1 W2)))) /\ (doDivides0 W1 W0))) => ((W1 = (sz10)) \/ (W1 = W0)))))) \/ (isPrime0 W0)))))) ### All 13 % 9.62/9.81 15. ((aNaturalNumber0 (xk)) /\ (((sdtasdt0 (xn) (xm)) = (sdtasdt0 (xp) (xk))) /\ ((xk) = (sdtsldt0 (sdtasdt0 (xn) (xm)) (xp))))) (-. (Ex W0, ((aNaturalNumber0 W0) /\ (((Ex W1, ((aNaturalNumber0 W1) /\ ((xk) = (sdtasdt0 W0 W1)))) \/ (doDivides0 W0 (xk))) /\ (((W0 != (sz00)) /\ ((W0 != (sz10)) /\ (All W1, (((aNaturalNumber0 W1) /\ ((Ex W2, ((aNaturalNumber0 W2) /\ (W0 = (sdtasdt0 W1 W2)))) /\ (doDivides0 W1 W0))) => ((W1 = (sz10)) \/ (W1 = W0)))))) \/ (isPrime0 W0)))))) ((xk) != (sz10)) ((xk) != (sz00)) (All W0, (((aNaturalNumber0 W0) /\ ((W0 != (sz00)) /\ (W0 != (sz10)))) => (Ex W1, ((aNaturalNumber0 W1) /\ ((doDivides0 W1 W0) /\ (isPrime0 W1)))))) ### ConjTree 14 % 9.62/9.81 16. (((xk) != (sz00)) /\ ((xk) != (sz10))) (All W0, (((aNaturalNumber0 W0) /\ ((W0 != (sz00)) /\ (W0 != (sz10)))) => (Ex W1, ((aNaturalNumber0 W1) /\ ((doDivides0 W1 W0) /\ (isPrime0 W1)))))) (-. (Ex W0, ((aNaturalNumber0 W0) /\ (((Ex W1, ((aNaturalNumber0 W1) /\ ((xk) = (sdtasdt0 W0 W1)))) \/ (doDivides0 W0 (xk))) /\ (((W0 != (sz00)) /\ ((W0 != (sz10)) /\ (All W1, (((aNaturalNumber0 W1) /\ ((Ex W2, ((aNaturalNumber0 W2) /\ (W0 = (sdtasdt0 W1 W2)))) /\ (doDivides0 W1 W0))) => ((W1 = (sz10)) \/ (W1 = W0)))))) \/ (isPrime0 W0)))))) ((aNaturalNumber0 (xk)) /\ (((sdtasdt0 (xn) (xm)) = (sdtasdt0 (xp) (xk))) /\ ((xk) = (sdtsldt0 (sdtasdt0 (xn) (xm)) (xp))))) ### And 15 % 9.62/9.81 % SZS output end Proof % 9.62/9.81 (* END-PROOF *) %------------------------------------------------------------------------------