%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : NUM432+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 : n013.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 14:42:24 EDT 2022 % Result : Theorem 242.24s 242.50s % Output : Proof 242.24s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.13 % Problem : NUM432+1 : TPTP v8.1.0. Released v4.0.0. % 0.12/0.13 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 0.13/0.35 % Computer : n013.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 600 % 0.13/0.35 % DateTime : Thu Jul 7 22:09:29 EDT 2022 % 0.19/0.35 % CPUTime : % 242.24/242.50 % SZS status Theorem % 242.24/242.50 (* PROOF-FOUND *) % 242.24/242.50 (* BEGIN-PROOF *) % 242.24/242.50 % SZS output start Proof % 242.24/242.50 1. (aInteger0 (xa)) (-. (aInteger0 (xa))) ### Axiom % 242.24/242.50 2. (aInteger0 (xc)) (-. (aInteger0 (xc))) ### Axiom % 242.24/242.50 3. (aInteger0 (xq)) (-. (aInteger0 (xq))) ### Axiom % 242.24/242.50 4. ((xq) != (sz00)) ((xq) = (sz00)) ### Axiom % 242.24/242.50 5. (aInteger0 (xa)) (-. (aInteger0 (xa))) ### Axiom % 242.24/242.50 6. (aInteger0 (xc)) (-. (aInteger0 (xc))) ### Axiom % 242.24/242.50 7. (-. (aInteger0 (smndt0 (xc)))) (aInteger0 (smndt0 (xc))) ### Axiom % 242.24/242.50 8. ((aInteger0 (xc)) => (aInteger0 (smndt0 (xc)))) (-. (aInteger0 (smndt0 (xc)))) (aInteger0 (xc)) ### Imply 6 7 % 242.24/242.50 9. (All W0, ((aInteger0 W0) => (aInteger0 (smndt0 W0)))) (aInteger0 (xc)) (-. (aInteger0 (smndt0 (xc)))) ### All 8 % 242.24/242.50 10. (-. (aInteger0 (sdtpldt0 (xa) (smndt0 (xc))))) (aInteger0 (sdtpldt0 (xa) (smndt0 (xc)))) ### Axiom % 242.24/242.50 11. (((aInteger0 (xa)) /\ (aInteger0 (smndt0 (xc)))) => (aInteger0 (sdtpldt0 (xa) (smndt0 (xc))))) (-. (aInteger0 (sdtpldt0 (xa) (smndt0 (xc))))) (aInteger0 (xc)) (All W0, ((aInteger0 W0) => (aInteger0 (smndt0 W0)))) (aInteger0 (xa)) ### DisjTree 5 9 10 % 242.24/242.50 12. (All W1, (((aInteger0 (xa)) /\ (aInteger0 W1)) => (aInteger0 (sdtpldt0 (xa) W1)))) (aInteger0 (xa)) (All W0, ((aInteger0 W0) => (aInteger0 (smndt0 W0)))) (aInteger0 (xc)) (-. (aInteger0 (sdtpldt0 (xa) (smndt0 (xc))))) ### All 11 % 242.24/242.50 13. (All W0, (All W1, (((aInteger0 W0) /\ (aInteger0 W1)) => (aInteger0 (sdtpldt0 W0 W1))))) (-. (aInteger0 (sdtpldt0 (xa) (smndt0 (xc))))) (aInteger0 (xc)) (All W0, ((aInteger0 W0) => (aInteger0 (smndt0 W0)))) (aInteger0 (xa)) ### All 12 % 242.24/242.50 14. (aInteger0 (xq)) (-. (aInteger0 (xq))) ### Axiom % 242.24/242.50 15. ((xq) != (sz00)) ((xq) = (sz00)) ### Axiom % 242.24/242.50 16. (aInteger0 (xn)) (-. (aInteger0 (xn))) ### Axiom % 242.24/242.50 17. (aInteger0 (xm)) (-. (aInteger0 (xm))) ### Axiom % 242.24/242.50 18. (-. (aInteger0 (sdtpldt0 (xn) (xm)))) (aInteger0 (sdtpldt0 (xn) (xm))) ### Axiom % 242.24/242.50 19. (((aInteger0 (xn)) /\ (aInteger0 (xm))) => (aInteger0 (sdtpldt0 (xn) (xm)))) (-. (aInteger0 (sdtpldt0 (xn) (xm)))) (aInteger0 (xm)) (aInteger0 (xn)) ### DisjTree 16 17 18 % 242.24/242.50 20. (All W1, (((aInteger0 (xn)) /\ (aInteger0 W1)) => (aInteger0 (sdtpldt0 (xn) W1)))) (aInteger0 (xn)) (aInteger0 (xm)) (-. (aInteger0 (sdtpldt0 (xn) (xm)))) ### All 19 % 242.24/242.50 21. (All W0, (All W1, (((aInteger0 W0) /\ (aInteger0 W1)) => (aInteger0 (sdtpldt0 W0 W1))))) (-. (aInteger0 (sdtpldt0 (xn) (xm)))) (aInteger0 (xm)) (aInteger0 (xn)) ### All 20 % 242.24/242.50 22. ((sdtasdt0 (xq) (sdtpldt0 (xn) (xm))) = (sdtpldt0 (xa) (smndt0 (xc)))) ((sdtasdt0 (xq) (sdtpldt0 (xn) (xm))) != (sdtpldt0 (xa) (smndt0 (xc)))) ### Axiom % 242.24/242.50 23. (-. ((aInteger0 (sdtpldt0 (xn) (xm))) /\ ((sdtasdt0 (xq) (sdtpldt0 (xn) (xm))) = (sdtpldt0 (xa) (smndt0 (xc)))))) ((sdtasdt0 (xq) (sdtpldt0 (xn) (xm))) = (sdtpldt0 (xa) (smndt0 (xc)))) (aInteger0 (xn)) (aInteger0 (xm)) (All W0, (All W1, (((aInteger0 W0) /\ (aInteger0 W1)) => (aInteger0 (sdtpldt0 W0 W1))))) ### NotAnd 21 22 % 242.24/242.50 24. (-. (Ex W2, ((aInteger0 W2) /\ ((sdtasdt0 (xq) W2) = (sdtpldt0 (xa) (smndt0 (xc))))))) (All W0, (All W1, (((aInteger0 W0) /\ (aInteger0 W1)) => (aInteger0 (sdtpldt0 W0 W1))))) (aInteger0 (xm)) (aInteger0 (xn)) ((sdtasdt0 (xq) (sdtpldt0 (xn) (xm))) = (sdtpldt0 (xa) (smndt0 (xc)))) ### NotExists 23 % 242.24/242.50 25. (-. ((aInteger0 (xq)) /\ (((xq) != (sz00)) /\ (Ex W2, ((aInteger0 W2) /\ ((sdtasdt0 (xq) W2) = (sdtpldt0 (xa) (smndt0 (xc))))))))) ((sdtasdt0 (xq) (sdtpldt0 (xn) (xm))) = (sdtpldt0 (xa) (smndt0 (xc)))) (aInteger0 (xn)) (aInteger0 (xm)) (All W0, (All W1, (((aInteger0 W0) /\ (aInteger0 W1)) => (aInteger0 (sdtpldt0 W0 W1))))) ((xq) != (sz00)) (aInteger0 (xq)) ### DisjTree 14 15 24 % 242.24/242.50 26. (-. (aDivisorOf0 (xq) (sdtpldt0 (xa) (smndt0 (xc))))) (aDivisorOf0 (xq) (sdtpldt0 (xa) (smndt0 (xc)))) ### Axiom % 242.24/242.50 27. ((aDivisorOf0 (xq) (sdtpldt0 (xa) (smndt0 (xc)))) <=> ((aInteger0 (xq)) /\ (((xq) != (sz00)) /\ (Ex W2, ((aInteger0 W2) /\ ((sdtasdt0 (xq) W2) = (sdtpldt0 (xa) (smndt0 (xc))))))))) (-. (aDivisorOf0 (xq) (sdtpldt0 (xa) (smndt0 (xc))))) (aInteger0 (xq)) ((xq) != (sz00)) (All W0, (All W1, (((aInteger0 W0) /\ (aInteger0 W1)) => (aInteger0 (sdtpldt0 W0 W1))))) (aInteger0 (xm)) (aInteger0 (xn)) ((sdtasdt0 (xq) (sdtpldt0 (xn) (xm))) = (sdtpldt0 (xa) (smndt0 (xc)))) ### Equiv 25 26 % 242.24/242.50 28. (All W1, ((aDivisorOf0 W1 (sdtpldt0 (xa) (smndt0 (xc)))) <=> ((aInteger0 W1) /\ ((W1 != (sz00)) /\ (Ex W2, ((aInteger0 W2) /\ ((sdtasdt0 W1 W2) = (sdtpldt0 (xa) (smndt0 (xc)))))))))) ((sdtasdt0 (xq) (sdtpldt0 (xn) (xm))) = (sdtpldt0 (xa) (smndt0 (xc)))) (aInteger0 (xn)) (aInteger0 (xm)) (All W0, (All W1, (((aInteger0 W0) /\ (aInteger0 W1)) => (aInteger0 (sdtpldt0 W0 W1))))) ((xq) != (sz00)) (aInteger0 (xq)) (-. (aDivisorOf0 (xq) (sdtpldt0 (xa) (smndt0 (xc))))) ### All 27 % 242.24/242.50 29. ((aInteger0 (sdtpldt0 (xa) (smndt0 (xc)))) => (All W1, ((aDivisorOf0 W1 (sdtpldt0 (xa) (smndt0 (xc)))) <=> ((aInteger0 W1) /\ ((W1 != (sz00)) /\ (Ex W2, ((aInteger0 W2) /\ ((sdtasdt0 W1 W2) = (sdtpldt0 (xa) (smndt0 (xc))))))))))) (-. (aDivisorOf0 (xq) (sdtpldt0 (xa) (smndt0 (xc))))) (aInteger0 (xq)) ((xq) != (sz00)) (aInteger0 (xm)) (aInteger0 (xn)) ((sdtasdt0 (xq) (sdtpldt0 (xn) (xm))) = (sdtpldt0 (xa) (smndt0 (xc)))) (aInteger0 (xa)) (All W0, ((aInteger0 W0) => (aInteger0 (smndt0 W0)))) (aInteger0 (xc)) (All W0, (All W1, (((aInteger0 W0) /\ (aInteger0 W1)) => (aInteger0 (sdtpldt0 W0 W1))))) ### Imply 13 28 % 242.24/242.50 30. (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))))) (aInteger0 (xc)) (All W0, ((aInteger0 W0) => (aInteger0 (smndt0 W0)))) (aInteger0 (xa)) ((sdtasdt0 (xq) (sdtpldt0 (xn) (xm))) = (sdtpldt0 (xa) (smndt0 (xc)))) (aInteger0 (xn)) (aInteger0 (xm)) ((xq) != (sz00)) (aInteger0 (xq)) (-. (aDivisorOf0 (xq) (sdtpldt0 (xa) (smndt0 (xc))))) ### All 29 % 242.24/242.50 31. (-. (sdteqdtlpzmzozddtrp0 (xa) (xc) (xq))) (sdteqdtlpzmzozddtrp0 (xa) (xc) (xq)) ### Axiom % 242.24/242.50 32. ((sdteqdtlpzmzozddtrp0 (xa) (xc) (xq)) <=> (aDivisorOf0 (xq) (sdtpldt0 (xa) (smndt0 (xc))))) (-. (sdteqdtlpzmzozddtrp0 (xa) (xc) (xq))) (aInteger0 (xq)) ((xq) != (sz00)) (aInteger0 (xm)) (aInteger0 (xn)) ((sdtasdt0 (xq) (sdtpldt0 (xn) (xm))) = (sdtpldt0 (xa) (smndt0 (xc)))) (aInteger0 (xa)) (All W0, ((aInteger0 W0) => (aInteger0 (smndt0 W0)))) (aInteger0 (xc)) (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 30 31 % 242.24/242.50 33. (((aInteger0 (xa)) /\ ((aInteger0 (xc)) /\ ((aInteger0 (xq)) /\ ((xq) != (sz00))))) => ((sdteqdtlpzmzozddtrp0 (xa) (xc) (xq)) <=> (aDivisorOf0 (xq) (sdtpldt0 (xa) (smndt0 (xc)))))) (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)))) ((sdtasdt0 (xq) (sdtpldt0 (xn) (xm))) = (sdtpldt0 (xa) (smndt0 (xc)))) (aInteger0 (xn)) (aInteger0 (xm)) (-. (sdteqdtlpzmzozddtrp0 (xa) (xc) (xq))) ((xq) != (sz00)) (aInteger0 (xq)) (aInteger0 (xc)) (aInteger0 (xa)) ### DisjTree 1 2 3 4 32 % 242.24/242.50 34. (All W2, (((aInteger0 (xa)) /\ ((aInteger0 (xc)) /\ ((aInteger0 W2) /\ (W2 != (sz00))))) => ((sdteqdtlpzmzozddtrp0 (xa) (xc) W2) <=> (aDivisorOf0 W2 (sdtpldt0 (xa) (smndt0 (xc))))))) (aInteger0 (xa)) (aInteger0 (xc)) (aInteger0 (xq)) ((xq) != (sz00)) (-. (sdteqdtlpzmzozddtrp0 (xa) (xc) (xq))) (aInteger0 (xm)) (aInteger0 (xn)) ((sdtasdt0 (xq) (sdtpldt0 (xn) (xm))) = (sdtpldt0 (xa) (smndt0 (xc)))) (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 33 % 242.24/242.50 35. (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)))) ((sdtasdt0 (xq) (sdtpldt0 (xn) (xm))) = (sdtpldt0 (xa) (smndt0 (xc)))) (aInteger0 (xn)) (aInteger0 (xm)) (-. (sdteqdtlpzmzozddtrp0 (xa) (xc) (xq))) ((xq) != (sz00)) (aInteger0 (xq)) (aInteger0 (xc)) (aInteger0 (xa)) ### All 34 % 242.24/242.50 36. (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 (xc)) (aInteger0 (xq)) ((xq) != (sz00)) (-. (sdteqdtlpzmzozddtrp0 (xa) (xc) (xq))) (aInteger0 (xm)) (aInteger0 (xn)) ((sdtasdt0 (xq) (sdtpldt0 (xn) (xm))) = (sdtpldt0 (xa) (smndt0 (xc)))) (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 35 % 242.24/242.50 37. ((aInteger0 (xa)) /\ ((aInteger0 (xb)) /\ ((aInteger0 (xq)) /\ (((xq) != (sz00)) /\ (aInteger0 (xc)))))) (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)))) ((sdtasdt0 (xq) (sdtpldt0 (xn) (xm))) = (sdtpldt0 (xa) (smndt0 (xc)))) (aInteger0 (xn)) (aInteger0 (xm)) (-. (sdteqdtlpzmzozddtrp0 (xa) (xc) (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 36 % 242.24/242.50 38. ((aInteger0 (xn)) /\ ((sdtasdt0 (xq) (xn)) = (sdtpldt0 (xa) (smndt0 (xb))))) (All W0, (All W1, (All W2, (((aInteger0 W0) /\ ((aInteger0 W1) /\ ((aInteger0 W2) /\ (W2 != (sz00))))) => ((sdteqdtlpzmzozddtrp0 W0 W1 W2) <=> (aDivisorOf0 W2 (sdtpldt0 W0 (smndt0 W1)))))))) (-. (sdteqdtlpzmzozddtrp0 (xa) (xc) (xq))) (aInteger0 (xm)) ((sdtasdt0 (xq) (sdtpldt0 (xn) (xm))) = (sdtpldt0 (xa) (smndt0 (xc)))) (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))))))))) ((aInteger0 (xa)) /\ ((aInteger0 (xb)) /\ ((aInteger0 (xq)) /\ (((xq) != (sz00)) /\ (aInteger0 (xc)))))) ### And 37 % 242.24/242.50 39. ((aInteger0 (xm)) /\ ((sdtasdt0 (xq) (xm)) = (sdtpldt0 (xb) (smndt0 (xc))))) ((aInteger0 (xa)) /\ ((aInteger0 (xb)) /\ ((aInteger0 (xq)) /\ (((xq) != (sz00)) /\ (aInteger0 (xc)))))) (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)))) ((sdtasdt0 (xq) (sdtpldt0 (xn) (xm))) = (sdtpldt0 (xa) (smndt0 (xc)))) (-. (sdteqdtlpzmzozddtrp0 (xa) (xc) (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)))))))) ((aInteger0 (xn)) /\ ((sdtasdt0 (xq) (xn)) = (sdtpldt0 (xa) (smndt0 (xb))))) ### And 38 % 242.24/242.50 % SZS output end Proof % 242.24/242.50 (* END-PROOF *) %------------------------------------------------------------------------------