%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : NUM423+1 : 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 : n008.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 14:42:18 EDT 2022 % Result : Theorem 260.78s 260.95s % Output : Proof 260.78s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : NUM423+1 : TPTP v8.1.0. Released v4.0.0. % 0.07/0.13 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 0.13/0.34 % Computer : n008.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Tue Jul 5 11:56:23 EDT 2022 % 0.13/0.34 % CPUTime : % 260.78/260.95 % SZS status Theorem % 260.78/260.95 (* PROOF-FOUND *) % 260.78/260.95 (* BEGIN-PROOF *) % 260.78/260.95 % SZS output start Proof % 260.78/260.95 1. (aInteger0 (xa)) (-. (aInteger0 (xa))) ### Axiom % 260.78/260.95 2. (aInteger0 (xa)) (-. (aInteger0 (xa))) ### Axiom % 260.78/260.95 3. (aInteger0 (xq)) (-. (aInteger0 (xq))) ### Axiom % 260.78/260.95 4. ((xq) != (sz00)) ((xq) = (sz00)) ### Axiom % 260.78/260.95 5. (aInteger0 (xa)) (-. (aInteger0 (xa))) ### Axiom % 260.78/260.95 6. (aInteger0 (xa)) (-. (aInteger0 (xa))) ### Axiom % 260.78/260.95 7. (-. (aInteger0 (smndt0 (xa)))) (aInteger0 (smndt0 (xa))) ### Axiom % 260.78/260.95 8. ((aInteger0 (xa)) => (aInteger0 (smndt0 (xa)))) (-. (aInteger0 (smndt0 (xa)))) (aInteger0 (xa)) ### Imply 6 7 % 260.78/260.95 9. (All W0, ((aInteger0 W0) => (aInteger0 (smndt0 W0)))) (aInteger0 (xa)) (-. (aInteger0 (smndt0 (xa)))) ### All 8 % 260.78/260.95 10. (-. (aInteger0 (sdtpldt0 (xa) (smndt0 (xa))))) (aInteger0 (sdtpldt0 (xa) (smndt0 (xa)))) ### Axiom % 260.78/260.95 11. (((aInteger0 (xa)) /\ (aInteger0 (smndt0 (xa)))) => (aInteger0 (sdtpldt0 (xa) (smndt0 (xa))))) (-. (aInteger0 (sdtpldt0 (xa) (smndt0 (xa))))) (All W0, ((aInteger0 W0) => (aInteger0 (smndt0 W0)))) (aInteger0 (xa)) ### DisjTree 5 9 10 % 260.78/260.95 12. (All W1, (((aInteger0 (xa)) /\ (aInteger0 W1)) => (aInteger0 (sdtpldt0 (xa) W1)))) (aInteger0 (xa)) (All W0, ((aInteger0 W0) => (aInteger0 (smndt0 W0)))) (-. (aInteger0 (sdtpldt0 (xa) (smndt0 (xa))))) ### All 11 % 260.78/260.95 13. (All W0, (All W1, (((aInteger0 W0) /\ (aInteger0 W1)) => (aInteger0 (sdtpldt0 W0 W1))))) (-. (aInteger0 (sdtpldt0 (xa) (smndt0 (xa))))) (All W0, ((aInteger0 W0) => (aInteger0 (smndt0 W0)))) (aInteger0 (xa)) ### All 12 % 260.78/260.95 14. (aInteger0 (xq)) (-. (aInteger0 (xq))) ### Axiom % 260.78/260.95 15. ((xq) != (sz00)) ((xq) = (sz00)) ### Axiom % 260.78/260.95 16. (aInteger0 (sz00)) (-. (aInteger0 (sz00))) ### Axiom % 260.78/260.95 17. (aInteger0 (xq)) (-. (aInteger0 (xq))) ### Axiom % 260.78/260.95 18. (aInteger0 (xa)) (-. (aInteger0 (xa))) ### Axiom % 260.78/260.95 19. ((sdtpldt0 (xa) (smndt0 (xa))) != (sdtpldt0 (xa) (smndt0 (xa)))) ### Refl(=) % 260.78/260.95 20. ((sdtasdt0 (xq) (sz00)) = (sz00)) ((sz00) != (sdtasdt0 (xq) (sz00))) ### Sym(=) % 260.78/260.95 21. ((sdtasdt0 (xq) (sz00)) != (sdtpldt0 (xa) (smndt0 (xa)))) ((sdtpldt0 (xa) (smndt0 (xa))) = (sz00)) ((sdtasdt0 (xq) (sz00)) = (sz00)) ### Trans-sym 19 20 % 260.78/260.95 22. (((sdtpldt0 (xa) (smndt0 (xa))) = (sz00)) /\ ((sz00) = (sdtpldt0 (smndt0 (xa)) (xa)))) ((sdtasdt0 (xq) (sz00)) = (sz00)) ((sdtasdt0 (xq) (sz00)) != (sdtpldt0 (xa) (smndt0 (xa)))) ### And 21 % 260.78/260.95 23. ((aInteger0 (xa)) => (((sdtpldt0 (xa) (smndt0 (xa))) = (sz00)) /\ ((sz00) = (sdtpldt0 (smndt0 (xa)) (xa))))) ((sdtasdt0 (xq) (sz00)) != (sdtpldt0 (xa) (smndt0 (xa)))) ((sdtasdt0 (xq) (sz00)) = (sz00)) (aInteger0 (xa)) ### Imply 18 22 % 260.78/260.95 24. (All W0, ((aInteger0 W0) => (((sdtpldt0 W0 (smndt0 W0)) = (sz00)) /\ ((sz00) = (sdtpldt0 (smndt0 W0) W0))))) (aInteger0 (xa)) ((sdtasdt0 (xq) (sz00)) = (sz00)) ((sdtasdt0 (xq) (sz00)) != (sdtpldt0 (xa) (smndt0 (xa)))) ### All 23 % 260.78/260.95 25. (((sdtasdt0 (xq) (sz00)) = (sz00)) /\ ((sz00) = (sdtasdt0 (sz00) (xq)))) ((sdtasdt0 (xq) (sz00)) != (sdtpldt0 (xa) (smndt0 (xa)))) (aInteger0 (xa)) (All W0, ((aInteger0 W0) => (((sdtpldt0 W0 (smndt0 W0)) = (sz00)) /\ ((sz00) = (sdtpldt0 (smndt0 W0) W0))))) ### And 24 % 260.78/260.95 26. ((aInteger0 (xq)) => (((sdtasdt0 (xq) (sz00)) = (sz00)) /\ ((sz00) = (sdtasdt0 (sz00) (xq))))) (All W0, ((aInteger0 W0) => (((sdtpldt0 W0 (smndt0 W0)) = (sz00)) /\ ((sz00) = (sdtpldt0 (smndt0 W0) W0))))) (aInteger0 (xa)) ((sdtasdt0 (xq) (sz00)) != (sdtpldt0 (xa) (smndt0 (xa)))) (aInteger0 (xq)) ### Imply 17 25 % 260.78/260.95 27. (All W0, ((aInteger0 W0) => (((sdtasdt0 W0 (sz00)) = (sz00)) /\ ((sz00) = (sdtasdt0 (sz00) W0))))) (aInteger0 (xq)) ((sdtasdt0 (xq) (sz00)) != (sdtpldt0 (xa) (smndt0 (xa)))) (aInteger0 (xa)) (All W0, ((aInteger0 W0) => (((sdtpldt0 W0 (smndt0 W0)) = (sz00)) /\ ((sz00) = (sdtpldt0 (smndt0 W0) W0))))) ### All 26 % 260.78/260.95 28. (-. ((aInteger0 (sz00)) /\ ((sdtasdt0 (xq) (sz00)) = (sdtpldt0 (xa) (smndt0 (xa)))))) (All W0, ((aInteger0 W0) => (((sdtpldt0 W0 (smndt0 W0)) = (sz00)) /\ ((sz00) = (sdtpldt0 (smndt0 W0) W0))))) (aInteger0 (xa)) (aInteger0 (xq)) (All W0, ((aInteger0 W0) => (((sdtasdt0 W0 (sz00)) = (sz00)) /\ ((sz00) = (sdtasdt0 (sz00) W0))))) (aInteger0 (sz00)) ### NotAnd 16 27 % 260.78/260.95 29. (-. (Ex W2, ((aInteger0 W2) /\ ((sdtasdt0 (xq) W2) = (sdtpldt0 (xa) (smndt0 (xa))))))) (aInteger0 (sz00)) (All W0, ((aInteger0 W0) => (((sdtasdt0 W0 (sz00)) = (sz00)) /\ ((sz00) = (sdtasdt0 (sz00) W0))))) (aInteger0 (xq)) (aInteger0 (xa)) (All W0, ((aInteger0 W0) => (((sdtpldt0 W0 (smndt0 W0)) = (sz00)) /\ ((sz00) = (sdtpldt0 (smndt0 W0) W0))))) ### NotExists 28 % 260.78/260.95 30. (-. ((aInteger0 (xq)) /\ (((xq) != (sz00)) /\ (Ex W2, ((aInteger0 W2) /\ ((sdtasdt0 (xq) W2) = (sdtpldt0 (xa) (smndt0 (xa))))))))) (All W0, ((aInteger0 W0) => (((sdtpldt0 W0 (smndt0 W0)) = (sz00)) /\ ((sz00) = (sdtpldt0 (smndt0 W0) W0))))) (aInteger0 (xa)) (All W0, ((aInteger0 W0) => (((sdtasdt0 W0 (sz00)) = (sz00)) /\ ((sz00) = (sdtasdt0 (sz00) W0))))) (aInteger0 (sz00)) ((xq) != (sz00)) (aInteger0 (xq)) ### DisjTree 14 15 29 % 260.78/260.95 31. (-. (aDivisorOf0 (xq) (sdtpldt0 (xa) (smndt0 (xa))))) (aDivisorOf0 (xq) (sdtpldt0 (xa) (smndt0 (xa)))) ### Axiom % 260.78/260.95 32. ((aDivisorOf0 (xq) (sdtpldt0 (xa) (smndt0 (xa)))) <=> ((aInteger0 (xq)) /\ (((xq) != (sz00)) /\ (Ex W2, ((aInteger0 W2) /\ ((sdtasdt0 (xq) W2) = (sdtpldt0 (xa) (smndt0 (xa))))))))) (-. (aDivisorOf0 (xq) (sdtpldt0 (xa) (smndt0 (xa))))) (aInteger0 (xq)) ((xq) != (sz00)) (aInteger0 (sz00)) (All W0, ((aInteger0 W0) => (((sdtasdt0 W0 (sz00)) = (sz00)) /\ ((sz00) = (sdtasdt0 (sz00) W0))))) (aInteger0 (xa)) (All W0, ((aInteger0 W0) => (((sdtpldt0 W0 (smndt0 W0)) = (sz00)) /\ ((sz00) = (sdtpldt0 (smndt0 W0) W0))))) ### Equiv 30 31 % 260.78/260.95 33. (All W1, ((aDivisorOf0 W1 (sdtpldt0 (xa) (smndt0 (xa)))) <=> ((aInteger0 W1) /\ ((W1 != (sz00)) /\ (Ex W2, ((aInteger0 W2) /\ ((sdtasdt0 W1 W2) = (sdtpldt0 (xa) (smndt0 (xa)))))))))) (All W0, ((aInteger0 W0) => (((sdtpldt0 W0 (smndt0 W0)) = (sz00)) /\ ((sz00) = (sdtpldt0 (smndt0 W0) W0))))) (aInteger0 (xa)) (All W0, ((aInteger0 W0) => (((sdtasdt0 W0 (sz00)) = (sz00)) /\ ((sz00) = (sdtasdt0 (sz00) W0))))) (aInteger0 (sz00)) ((xq) != (sz00)) (aInteger0 (xq)) (-. (aDivisorOf0 (xq) (sdtpldt0 (xa) (smndt0 (xa))))) ### All 32 % 260.78/260.95 34. ((aInteger0 (sdtpldt0 (xa) (smndt0 (xa)))) => (All W1, ((aDivisorOf0 W1 (sdtpldt0 (xa) (smndt0 (xa)))) <=> ((aInteger0 W1) /\ ((W1 != (sz00)) /\ (Ex W2, ((aInteger0 W2) /\ ((sdtasdt0 W1 W2) = (sdtpldt0 (xa) (smndt0 (xa))))))))))) (-. (aDivisorOf0 (xq) (sdtpldt0 (xa) (smndt0 (xa))))) (aInteger0 (xq)) ((xq) != (sz00)) (aInteger0 (sz00)) (All W0, ((aInteger0 W0) => (((sdtasdt0 W0 (sz00)) = (sz00)) /\ ((sz00) = (sdtasdt0 (sz00) W0))))) (All W0, ((aInteger0 W0) => (((sdtpldt0 W0 (smndt0 W0)) = (sz00)) /\ ((sz00) = (sdtpldt0 (smndt0 W0) W0))))) (aInteger0 (xa)) (All W0, ((aInteger0 W0) => (aInteger0 (smndt0 W0)))) (All W0, (All W1, (((aInteger0 W0) /\ (aInteger0 W1)) => (aInteger0 (sdtpldt0 W0 W1))))) ### Imply 13 33 % 260.78/260.95 35. (All W0, ((aInteger0 W0) => (All W1, ((aDivisorOf0 W1 W0) <=> ((aInteger0 W1) /\ ((W1 != (sz00)) /\ (Ex W2, ((aInteger0 W2) /\ ((sdtasdt0 W1 W2) = W0))))))))) (All W0, (All W1, (((aInteger0 W0) /\ (aInteger0 W1)) => (aInteger0 (sdtpldt0 W0 W1))))) (All W0, ((aInteger0 W0) => (aInteger0 (smndt0 W0)))) (aInteger0 (xa)) (All W0, ((aInteger0 W0) => (((sdtpldt0 W0 (smndt0 W0)) = (sz00)) /\ ((sz00) = (sdtpldt0 (smndt0 W0) W0))))) (All W0, ((aInteger0 W0) => (((sdtasdt0 W0 (sz00)) = (sz00)) /\ ((sz00) = (sdtasdt0 (sz00) W0))))) (aInteger0 (sz00)) ((xq) != (sz00)) (aInteger0 (xq)) (-. (aDivisorOf0 (xq) (sdtpldt0 (xa) (smndt0 (xa))))) ### All 34 % 260.78/260.95 36. (-. (sdteqdtlpzmzozddtrp0 (xa) (xa) (xq))) (sdteqdtlpzmzozddtrp0 (xa) (xa) (xq)) ### Axiom % 260.78/260.95 37. ((sdteqdtlpzmzozddtrp0 (xa) (xa) (xq)) <=> (aDivisorOf0 (xq) (sdtpldt0 (xa) (smndt0 (xa))))) (-. (sdteqdtlpzmzozddtrp0 (xa) (xa) (xq))) (aInteger0 (xq)) ((xq) != (sz00)) (aInteger0 (sz00)) (All W0, ((aInteger0 W0) => (((sdtasdt0 W0 (sz00)) = (sz00)) /\ ((sz00) = (sdtasdt0 (sz00) W0))))) (All W0, ((aInteger0 W0) => (((sdtpldt0 W0 (smndt0 W0)) = (sz00)) /\ ((sz00) = (sdtpldt0 (smndt0 W0) W0))))) (aInteger0 (xa)) (All W0, ((aInteger0 W0) => (aInteger0 (smndt0 W0)))) (All W0, (All W1, (((aInteger0 W0) /\ (aInteger0 W1)) => (aInteger0 (sdtpldt0 W0 W1))))) (All W0, ((aInteger0 W0) => (All W1, ((aDivisorOf0 W1 W0) <=> ((aInteger0 W1) /\ ((W1 != (sz00)) /\ (Ex W2, ((aInteger0 W2) /\ ((sdtasdt0 W1 W2) = W0))))))))) ### Equiv 35 36 % 260.78/260.96 38. (((aInteger0 (xa)) /\ ((aInteger0 (xa)) /\ ((aInteger0 (xq)) /\ ((xq) != (sz00))))) => ((sdteqdtlpzmzozddtrp0 (xa) (xa) (xq)) <=> (aDivisorOf0 (xq) (sdtpldt0 (xa) (smndt0 (xa)))))) (All W0, ((aInteger0 W0) => (All W1, ((aDivisorOf0 W1 W0) <=> ((aInteger0 W1) /\ ((W1 != (sz00)) /\ (Ex W2, ((aInteger0 W2) /\ ((sdtasdt0 W1 W2) = W0))))))))) (All W0, (All W1, (((aInteger0 W0) /\ (aInteger0 W1)) => (aInteger0 (sdtpldt0 W0 W1))))) (All W0, ((aInteger0 W0) => (aInteger0 (smndt0 W0)))) (All W0, ((aInteger0 W0) => (((sdtpldt0 W0 (smndt0 W0)) = (sz00)) /\ ((sz00) = (sdtpldt0 (smndt0 W0) W0))))) (All W0, ((aInteger0 W0) => (((sdtasdt0 W0 (sz00)) = (sz00)) /\ ((sz00) = (sdtasdt0 (sz00) W0))))) (aInteger0 (sz00)) (-. (sdteqdtlpzmzozddtrp0 (xa) (xa) (xq))) ((xq) != (sz00)) (aInteger0 (xq)) (aInteger0 (xa)) ### DisjTree 1 2 3 4 37 % 260.78/260.96 39. (All W2, (((aInteger0 (xa)) /\ ((aInteger0 (xa)) /\ ((aInteger0 W2) /\ (W2 != (sz00))))) => ((sdteqdtlpzmzozddtrp0 (xa) (xa) W2) <=> (aDivisorOf0 W2 (sdtpldt0 (xa) (smndt0 (xa))))))) (aInteger0 (xa)) (aInteger0 (xq)) ((xq) != (sz00)) (-. (sdteqdtlpzmzozddtrp0 (xa) (xa) (xq))) (aInteger0 (sz00)) (All W0, ((aInteger0 W0) => (((sdtasdt0 W0 (sz00)) = (sz00)) /\ ((sz00) = (sdtasdt0 (sz00) W0))))) (All W0, ((aInteger0 W0) => (((sdtpldt0 W0 (smndt0 W0)) = (sz00)) /\ ((sz00) = (sdtpldt0 (smndt0 W0) W0))))) (All W0, ((aInteger0 W0) => (aInteger0 (smndt0 W0)))) (All W0, (All W1, (((aInteger0 W0) /\ (aInteger0 W1)) => (aInteger0 (sdtpldt0 W0 W1))))) (All W0, ((aInteger0 W0) => (All W1, ((aDivisorOf0 W1 W0) <=> ((aInteger0 W1) /\ ((W1 != (sz00)) /\ (Ex W2, ((aInteger0 W2) /\ ((sdtasdt0 W1 W2) = W0))))))))) ### All 38 % 260.78/260.96 40. (All W1, (All W2, (((aInteger0 (xa)) /\ ((aInteger0 W1) /\ ((aInteger0 W2) /\ (W2 != (sz00))))) => ((sdteqdtlpzmzozddtrp0 (xa) W1 W2) <=> (aDivisorOf0 W2 (sdtpldt0 (xa) (smndt0 W1))))))) (All W0, ((aInteger0 W0) => (All W1, ((aDivisorOf0 W1 W0) <=> ((aInteger0 W1) /\ ((W1 != (sz00)) /\ (Ex W2, ((aInteger0 W2) /\ ((sdtasdt0 W1 W2) = W0))))))))) (All W0, (All W1, (((aInteger0 W0) /\ (aInteger0 W1)) => (aInteger0 (sdtpldt0 W0 W1))))) (All W0, ((aInteger0 W0) => (aInteger0 (smndt0 W0)))) (All W0, ((aInteger0 W0) => (((sdtpldt0 W0 (smndt0 W0)) = (sz00)) /\ ((sz00) = (sdtpldt0 (smndt0 W0) W0))))) (All W0, ((aInteger0 W0) => (((sdtasdt0 W0 (sz00)) = (sz00)) /\ ((sz00) = (sdtasdt0 (sz00) W0))))) (aInteger0 (sz00)) (-. (sdteqdtlpzmzozddtrp0 (xa) (xa) (xq))) ((xq) != (sz00)) (aInteger0 (xq)) (aInteger0 (xa)) ### All 39 % 260.78/260.96 41. (All W0, (All W1, (All W2, (((aInteger0 W0) /\ ((aInteger0 W1) /\ ((aInteger0 W2) /\ (W2 != (sz00))))) => ((sdteqdtlpzmzozddtrp0 W0 W1 W2) <=> (aDivisorOf0 W2 (sdtpldt0 W0 (smndt0 W1)))))))) (aInteger0 (xa)) (aInteger0 (xq)) ((xq) != (sz00)) (-. (sdteqdtlpzmzozddtrp0 (xa) (xa) (xq))) (aInteger0 (sz00)) (All W0, ((aInteger0 W0) => (((sdtasdt0 W0 (sz00)) = (sz00)) /\ ((sz00) = (sdtasdt0 (sz00) W0))))) (All W0, ((aInteger0 W0) => (((sdtpldt0 W0 (smndt0 W0)) = (sz00)) /\ ((sz00) = (sdtpldt0 (smndt0 W0) W0))))) (All W0, ((aInteger0 W0) => (aInteger0 (smndt0 W0)))) (All W0, (All W1, (((aInteger0 W0) /\ (aInteger0 W1)) => (aInteger0 (sdtpldt0 W0 W1))))) (All W0, ((aInteger0 W0) => (All W1, ((aDivisorOf0 W1 W0) <=> ((aInteger0 W1) /\ ((W1 != (sz00)) /\ (Ex W2, ((aInteger0 W2) /\ ((sdtasdt0 W1 W2) = W0))))))))) ### All 40 % 260.78/260.96 42. ((aInteger0 (xa)) /\ ((aInteger0 (xq)) /\ ((xq) != (sz00)))) (All W0, ((aInteger0 W0) => (All W1, ((aDivisorOf0 W1 W0) <=> ((aInteger0 W1) /\ ((W1 != (sz00)) /\ (Ex W2, ((aInteger0 W2) /\ ((sdtasdt0 W1 W2) = W0))))))))) (All W0, (All W1, (((aInteger0 W0) /\ (aInteger0 W1)) => (aInteger0 (sdtpldt0 W0 W1))))) (All W0, ((aInteger0 W0) => (aInteger0 (smndt0 W0)))) (All W0, ((aInteger0 W0) => (((sdtpldt0 W0 (smndt0 W0)) = (sz00)) /\ ((sz00) = (sdtpldt0 (smndt0 W0) W0))))) (All W0, ((aInteger0 W0) => (((sdtasdt0 W0 (sz00)) = (sz00)) /\ ((sz00) = (sdtasdt0 (sz00) W0))))) (aInteger0 (sz00)) (-. (sdteqdtlpzmzozddtrp0 (xa) (xa) (xq))) (All W0, (All W1, (All W2, (((aInteger0 W0) /\ ((aInteger0 W1) /\ ((aInteger0 W2) /\ (W2 != (sz00))))) => ((sdteqdtlpzmzozddtrp0 W0 W1 W2) <=> (aDivisorOf0 W2 (sdtpldt0 W0 (smndt0 W1)))))))) ### ConjTree 41 % 260.78/260.96 % SZS output end Proof % 260.78/260.96 (* END-PROOF *) %------------------------------------------------------------------------------