%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : NUM434+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 14:42:25 EDT 2022 % Result : Theorem 245.24s 245.41s % Output : Proof 245.24s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : NUM434+1 : TPTP v8.1.0. Released v4.0.0. % 0.03/0.13 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 0.12/0.34 % Computer : n013.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 : Wed Jul 6 08:05:29 EDT 2022 % 0.12/0.34 % CPUTime : % 245.24/245.41 % SZS status Theorem % 245.24/245.41 (* PROOF-FOUND *) % 245.24/245.41 (* BEGIN-PROOF *) % 245.24/245.41 % SZS output start Proof % 245.24/245.41 1. (aInteger0 (xa)) (-. (aInteger0 (xa))) ### Axiom % 245.24/245.41 2. (aInteger0 (xb)) (-. (aInteger0 (xb))) ### Axiom % 245.24/245.41 3. (-. (aInteger0 (smndt0 (xb)))) (aInteger0 (smndt0 (xb))) ### Axiom % 245.24/245.41 4. ((aInteger0 (xb)) => (aInteger0 (smndt0 (xb)))) (-. (aInteger0 (smndt0 (xb)))) (aInteger0 (xb)) ### Imply 2 3 % 245.24/245.41 5. (All W0, ((aInteger0 W0) => (aInteger0 (smndt0 W0)))) (aInteger0 (xb)) (-. (aInteger0 (smndt0 (xb)))) ### All 4 % 245.24/245.41 6. (-. (aInteger0 (sdtpldt0 (xa) (smndt0 (xb))))) (aInteger0 (sdtpldt0 (xa) (smndt0 (xb)))) ### Axiom % 245.24/245.41 7. (((aInteger0 (xa)) /\ (aInteger0 (smndt0 (xb)))) => (aInteger0 (sdtpldt0 (xa) (smndt0 (xb))))) (-. (aInteger0 (sdtpldt0 (xa) (smndt0 (xb))))) (aInteger0 (xb)) (All W0, ((aInteger0 W0) => (aInteger0 (smndt0 W0)))) (aInteger0 (xa)) ### DisjTree 1 5 6 % 245.24/245.41 8. (All W1, (((aInteger0 (xa)) /\ (aInteger0 W1)) => (aInteger0 (sdtpldt0 (xa) W1)))) (aInteger0 (xa)) (All W0, ((aInteger0 W0) => (aInteger0 (smndt0 W0)))) (aInteger0 (xb)) (-. (aInteger0 (sdtpldt0 (xa) (smndt0 (xb))))) ### All 7 % 245.24/245.41 9. (All W0, (All W1, (((aInteger0 W0) /\ (aInteger0 W1)) => (aInteger0 (sdtpldt0 W0 W1))))) (-. (aInteger0 (sdtpldt0 (xa) (smndt0 (xb))))) (aInteger0 (xb)) (All W0, ((aInteger0 W0) => (aInteger0 (smndt0 W0)))) (aInteger0 (xa)) ### All 8 % 245.24/245.41 10. (aInteger0 (xp)) (-. (aInteger0 (xp))) ### Axiom % 245.24/245.41 11. (aInteger0 (xq)) (-. (aInteger0 (xq))) ### Axiom % 245.24/245.41 12. (aInteger0 (xa)) (-. (aInteger0 (xa))) ### Axiom % 245.24/245.41 13. (aInteger0 (xb)) (-. (aInteger0 (xb))) ### Axiom % 245.24/245.41 14. (aInteger0 (xp)) (-. (aInteger0 (xp))) ### Axiom % 245.24/245.41 15. (aInteger0 (xq)) (-. (aInteger0 (xq))) ### Axiom % 245.24/245.41 16. (-. (aInteger0 (sdtasdt0 (xp) (xq)))) (aInteger0 (sdtasdt0 (xp) (xq))) ### Axiom % 245.24/245.41 17. (((aInteger0 (xp)) /\ (aInteger0 (xq))) => (aInteger0 (sdtasdt0 (xp) (xq)))) (-. (aInteger0 (sdtasdt0 (xp) (xq)))) (aInteger0 (xq)) (aInteger0 (xp)) ### DisjTree 14 15 16 % 245.24/245.41 18. (All W1, (((aInteger0 (xp)) /\ (aInteger0 W1)) => (aInteger0 (sdtasdt0 (xp) W1)))) (aInteger0 (xp)) (aInteger0 (xq)) (-. (aInteger0 (sdtasdt0 (xp) (xq)))) ### All 17 % 245.24/245.41 19. (All W0, (All W1, (((aInteger0 W0) /\ (aInteger0 W1)) => (aInteger0 (sdtasdt0 W0 W1))))) (-. (aInteger0 (sdtasdt0 (xp) (xq)))) (aInteger0 (xq)) (aInteger0 (xp)) ### All 18 % 245.24/245.41 20. ((sdtasdt0 (xp) (xq)) != (sz00)) ((sdtasdt0 (xp) (xq)) = (sz00)) ### Axiom % 245.24/245.41 21. (sdteqdtlpzmzozddtrp0 (xa) (xb) (sdtasdt0 (xp) (xq))) (-. (sdteqdtlpzmzozddtrp0 (xa) (xb) (sdtasdt0 (xp) (xq)))) ### Axiom % 245.24/245.41 22. (-. (aDivisorOf0 (sdtasdt0 (xp) (xq)) (sdtpldt0 (xa) (smndt0 (xb))))) (aDivisorOf0 (sdtasdt0 (xp) (xq)) (sdtpldt0 (xa) (smndt0 (xb)))) ### Axiom % 245.24/245.41 23. ((sdteqdtlpzmzozddtrp0 (xa) (xb) (sdtasdt0 (xp) (xq))) <=> (aDivisorOf0 (sdtasdt0 (xp) (xq)) (sdtpldt0 (xa) (smndt0 (xb))))) (-. (aDivisorOf0 (sdtasdt0 (xp) (xq)) (sdtpldt0 (xa) (smndt0 (xb))))) (sdteqdtlpzmzozddtrp0 (xa) (xb) (sdtasdt0 (xp) (xq))) ### Equiv 21 22 % 245.24/245.41 24. (((aInteger0 (xa)) /\ ((aInteger0 (xb)) /\ ((aInteger0 (sdtasdt0 (xp) (xq))) /\ ((sdtasdt0 (xp) (xq)) != (sz00))))) => ((sdteqdtlpzmzozddtrp0 (xa) (xb) (sdtasdt0 (xp) (xq))) <=> (aDivisorOf0 (sdtasdt0 (xp) (xq)) (sdtpldt0 (xa) (smndt0 (xb)))))) (sdteqdtlpzmzozddtrp0 (xa) (xb) (sdtasdt0 (xp) (xq))) (-. (aDivisorOf0 (sdtasdt0 (xp) (xq)) (sdtpldt0 (xa) (smndt0 (xb))))) ((sdtasdt0 (xp) (xq)) != (sz00)) (aInteger0 (xp)) (aInteger0 (xq)) (All W0, (All W1, (((aInteger0 W0) /\ (aInteger0 W1)) => (aInteger0 (sdtasdt0 W0 W1))))) (aInteger0 (xb)) (aInteger0 (xa)) ### DisjTree 12 13 19 20 23 % 245.24/245.41 25. (All W2, (((aInteger0 (xa)) /\ ((aInteger0 (xb)) /\ ((aInteger0 W2) /\ (W2 != (sz00))))) => ((sdteqdtlpzmzozddtrp0 (xa) (xb) W2) <=> (aDivisorOf0 W2 (sdtpldt0 (xa) (smndt0 (xb))))))) (aInteger0 (xa)) (aInteger0 (xb)) (All W0, (All W1, (((aInteger0 W0) /\ (aInteger0 W1)) => (aInteger0 (sdtasdt0 W0 W1))))) (aInteger0 (xq)) (aInteger0 (xp)) ((sdtasdt0 (xp) (xq)) != (sz00)) (-. (aDivisorOf0 (sdtasdt0 (xp) (xq)) (sdtpldt0 (xa) (smndt0 (xb))))) (sdteqdtlpzmzozddtrp0 (xa) (xb) (sdtasdt0 (xp) (xq))) ### All 24 % 245.24/245.41 26. (-. (Ex W0, ((aInteger0 W0) /\ ((sdtasdt0 (sdtasdt0 (xp) (xq)) W0) = (sdtpldt0 (xa) (smndt0 (xb))))))) (Ex W0, ((aInteger0 W0) /\ ((sdtasdt0 (sdtasdt0 (xp) (xq)) W0) = (sdtpldt0 (xa) (smndt0 (xb)))))) ### Axiom % 245.24/245.41 27. ((aInteger0 (sdtasdt0 (xp) (xq))) /\ (((sdtasdt0 (xp) (xq)) != (sz00)) /\ (Ex W0, ((aInteger0 W0) /\ ((sdtasdt0 (sdtasdt0 (xp) (xq)) W0) = (sdtpldt0 (xa) (smndt0 (xb)))))))) (-. (Ex W0, ((aInteger0 W0) /\ ((sdtasdt0 (sdtasdt0 (xp) (xq)) W0) = (sdtpldt0 (xa) (smndt0 (xb))))))) ### ConjTree 26 % 245.24/245.41 28. ((aDivisorOf0 (sdtasdt0 (xp) (xq)) (sdtpldt0 (xa) (smndt0 (xb)))) <=> ((aInteger0 (sdtasdt0 (xp) (xq))) /\ (((sdtasdt0 (xp) (xq)) != (sz00)) /\ (Ex W0, ((aInteger0 W0) /\ ((sdtasdt0 (sdtasdt0 (xp) (xq)) W0) = (sdtpldt0 (xa) (smndt0 (xb))))))))) (-. (Ex W0, ((aInteger0 W0) /\ ((sdtasdt0 (sdtasdt0 (xp) (xq)) W0) = (sdtpldt0 (xa) (smndt0 (xb))))))) (sdteqdtlpzmzozddtrp0 (xa) (xb) (sdtasdt0 (xp) (xq))) ((sdtasdt0 (xp) (xq)) != (sz00)) (aInteger0 (xp)) (aInteger0 (xq)) (All W0, (All W1, (((aInteger0 W0) /\ (aInteger0 W1)) => (aInteger0 (sdtasdt0 W0 W1))))) (aInteger0 (xb)) (aInteger0 (xa)) (All W2, (((aInteger0 (xa)) /\ ((aInteger0 (xb)) /\ ((aInteger0 W2) /\ (W2 != (sz00))))) => ((sdteqdtlpzmzozddtrp0 (xa) (xb) W2) <=> (aDivisorOf0 W2 (sdtpldt0 (xa) (smndt0 (xb))))))) ### Equiv 25 27 % 245.24/245.41 29. (All W1, ((aDivisorOf0 W1 (sdtpldt0 (xa) (smndt0 (xb)))) <=> ((aInteger0 W1) /\ ((W1 != (sz00)) /\ (Ex W2, ((aInteger0 W2) /\ ((sdtasdt0 W1 W2) = (sdtpldt0 (xa) (smndt0 (xb)))))))))) (All W2, (((aInteger0 (xa)) /\ ((aInteger0 (xb)) /\ ((aInteger0 W2) /\ (W2 != (sz00))))) => ((sdteqdtlpzmzozddtrp0 (xa) (xb) W2) <=> (aDivisorOf0 W2 (sdtpldt0 (xa) (smndt0 (xb))))))) (aInteger0 (xa)) (aInteger0 (xb)) (All W0, (All W1, (((aInteger0 W0) /\ (aInteger0 W1)) => (aInteger0 (sdtasdt0 W0 W1))))) (aInteger0 (xq)) (aInteger0 (xp)) ((sdtasdt0 (xp) (xq)) != (sz00)) (sdteqdtlpzmzozddtrp0 (xa) (xb) (sdtasdt0 (xp) (xq))) (-. (Ex W0, ((aInteger0 W0) /\ ((sdtasdt0 (sdtasdt0 (xp) (xq)) W0) = (sdtpldt0 (xa) (smndt0 (xb))))))) ### All 28 % 245.24/245.41 30. ((xp) != (sz00)) ((xp) = (sz00)) ### Axiom % 245.24/245.41 31. ((xq) != (sz00)) ((xq) = (sz00)) ### Axiom % 245.24/245.41 32. (((aInteger0 (xp)) /\ (aInteger0 (xq))) => (((sdtasdt0 (xp) (xq)) = (sz00)) => (((xp) = (sz00)) \/ ((xq) = (sz00))))) ((xq) != (sz00)) ((xp) != (sz00)) (-. (Ex W0, ((aInteger0 W0) /\ ((sdtasdt0 (sdtasdt0 (xp) (xq)) W0) = (sdtpldt0 (xa) (smndt0 (xb))))))) (sdteqdtlpzmzozddtrp0 (xa) (xb) (sdtasdt0 (xp) (xq))) (All W0, (All W1, (((aInteger0 W0) /\ (aInteger0 W1)) => (aInteger0 (sdtasdt0 W0 W1))))) (aInteger0 (xb)) (aInteger0 (xa)) (All W2, (((aInteger0 (xa)) /\ ((aInteger0 (xb)) /\ ((aInteger0 W2) /\ (W2 != (sz00))))) => ((sdteqdtlpzmzozddtrp0 (xa) (xb) W2) <=> (aDivisorOf0 W2 (sdtpldt0 (xa) (smndt0 (xb))))))) (All W1, ((aDivisorOf0 W1 (sdtpldt0 (xa) (smndt0 (xb)))) <=> ((aInteger0 W1) /\ ((W1 != (sz00)) /\ (Ex W2, ((aInteger0 W2) /\ ((sdtasdt0 W1 W2) = (sdtpldt0 (xa) (smndt0 (xb)))))))))) (aInteger0 (xq)) (aInteger0 (xp)) ### DisjTree 10 11 29 30 31 % 245.24/245.41 33. (All W1, (((aInteger0 (xp)) /\ (aInteger0 W1)) => (((sdtasdt0 (xp) W1) = (sz00)) => (((xp) = (sz00)) \/ (W1 = (sz00)))))) (aInteger0 (xp)) (aInteger0 (xq)) (All W1, ((aDivisorOf0 W1 (sdtpldt0 (xa) (smndt0 (xb)))) <=> ((aInteger0 W1) /\ ((W1 != (sz00)) /\ (Ex W2, ((aInteger0 W2) /\ ((sdtasdt0 W1 W2) = (sdtpldt0 (xa) (smndt0 (xb)))))))))) (All W2, (((aInteger0 (xa)) /\ ((aInteger0 (xb)) /\ ((aInteger0 W2) /\ (W2 != (sz00))))) => ((sdteqdtlpzmzozddtrp0 (xa) (xb) W2) <=> (aDivisorOf0 W2 (sdtpldt0 (xa) (smndt0 (xb))))))) (aInteger0 (xa)) (aInteger0 (xb)) (All W0, (All W1, (((aInteger0 W0) /\ (aInteger0 W1)) => (aInteger0 (sdtasdt0 W0 W1))))) (sdteqdtlpzmzozddtrp0 (xa) (xb) (sdtasdt0 (xp) (xq))) (-. (Ex W0, ((aInteger0 W0) /\ ((sdtasdt0 (sdtasdt0 (xp) (xq)) W0) = (sdtpldt0 (xa) (smndt0 (xb))))))) ((xp) != (sz00)) ((xq) != (sz00)) ### All 32 % 245.24/245.41 34. (All W1, (All W2, (((aInteger0 (xa)) /\ ((aInteger0 W1) /\ ((aInteger0 W2) /\ (W2 != (sz00))))) => ((sdteqdtlpzmzozddtrp0 (xa) W1 W2) <=> (aDivisorOf0 W2 (sdtpldt0 (xa) (smndt0 W1))))))) ((xq) != (sz00)) ((xp) != (sz00)) (-. (Ex W0, ((aInteger0 W0) /\ ((sdtasdt0 (sdtasdt0 (xp) (xq)) W0) = (sdtpldt0 (xa) (smndt0 (xb))))))) (sdteqdtlpzmzozddtrp0 (xa) (xb) (sdtasdt0 (xp) (xq))) (All W0, (All W1, (((aInteger0 W0) /\ (aInteger0 W1)) => (aInteger0 (sdtasdt0 W0 W1))))) (aInteger0 (xb)) (aInteger0 (xa)) (All W1, ((aDivisorOf0 W1 (sdtpldt0 (xa) (smndt0 (xb)))) <=> ((aInteger0 W1) /\ ((W1 != (sz00)) /\ (Ex W2, ((aInteger0 W2) /\ ((sdtasdt0 W1 W2) = (sdtpldt0 (xa) (smndt0 (xb)))))))))) (aInteger0 (xq)) (aInteger0 (xp)) (All W1, (((aInteger0 (xp)) /\ (aInteger0 W1)) => (((sdtasdt0 (xp) W1) = (sz00)) => (((xp) = (sz00)) \/ (W1 = (sz00)))))) ### All 33 % 245.24/245.41 35. (All W0, (All W1, (All W2, (((aInteger0 W0) /\ ((aInteger0 W1) /\ ((aInteger0 W2) /\ (W2 != (sz00))))) => ((sdteqdtlpzmzozddtrp0 W0 W1 W2) <=> (aDivisorOf0 W2 (sdtpldt0 W0 (smndt0 W1)))))))) (All W1, (((aInteger0 (xp)) /\ (aInteger0 W1)) => (((sdtasdt0 (xp) W1) = (sz00)) => (((xp) = (sz00)) \/ (W1 = (sz00)))))) (aInteger0 (xp)) (aInteger0 (xq)) (All W1, ((aDivisorOf0 W1 (sdtpldt0 (xa) (smndt0 (xb)))) <=> ((aInteger0 W1) /\ ((W1 != (sz00)) /\ (Ex W2, ((aInteger0 W2) /\ ((sdtasdt0 W1 W2) = (sdtpldt0 (xa) (smndt0 (xb)))))))))) (aInteger0 (xa)) (aInteger0 (xb)) (All W0, (All W1, (((aInteger0 W0) /\ (aInteger0 W1)) => (aInteger0 (sdtasdt0 W0 W1))))) (sdteqdtlpzmzozddtrp0 (xa) (xb) (sdtasdt0 (xp) (xq))) (-. (Ex W0, ((aInteger0 W0) /\ ((sdtasdt0 (sdtasdt0 (xp) (xq)) W0) = (sdtpldt0 (xa) (smndt0 (xb))))))) ((xp) != (sz00)) ((xq) != (sz00)) ### All 34 % 245.24/245.41 36. ((aInteger0 (sdtpldt0 (xa) (smndt0 (xb)))) => (All W1, ((aDivisorOf0 W1 (sdtpldt0 (xa) (smndt0 (xb)))) <=> ((aInteger0 W1) /\ ((W1 != (sz00)) /\ (Ex W2, ((aInteger0 W2) /\ ((sdtasdt0 W1 W2) = (sdtpldt0 (xa) (smndt0 (xb))))))))))) ((xq) != (sz00)) ((xp) != (sz00)) (-. (Ex W0, ((aInteger0 W0) /\ ((sdtasdt0 (sdtasdt0 (xp) (xq)) W0) = (sdtpldt0 (xa) (smndt0 (xb))))))) (sdteqdtlpzmzozddtrp0 (xa) (xb) (sdtasdt0 (xp) (xq))) (All W0, (All W1, (((aInteger0 W0) /\ (aInteger0 W1)) => (aInteger0 (sdtasdt0 W0 W1))))) (aInteger0 (xq)) (aInteger0 (xp)) (All W1, (((aInteger0 (xp)) /\ (aInteger0 W1)) => (((sdtasdt0 (xp) W1) = (sz00)) => (((xp) = (sz00)) \/ (W1 = (sz00)))))) (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)) (All W0, ((aInteger0 W0) => (aInteger0 (smndt0 W0)))) (aInteger0 (xb)) (All W0, (All W1, (((aInteger0 W0) /\ (aInteger0 W1)) => (aInteger0 (sdtpldt0 W0 W1))))) ### Imply 9 35 % 245.24/245.41 37. (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 (xb)) (All W0, ((aInteger0 W0) => (aInteger0 (smndt0 W0)))) (aInteger0 (xa)) (All W0, (All W1, (All W2, (((aInteger0 W0) /\ ((aInteger0 W1) /\ ((aInteger0 W2) /\ (W2 != (sz00))))) => ((sdteqdtlpzmzozddtrp0 W0 W1 W2) <=> (aDivisorOf0 W2 (sdtpldt0 W0 (smndt0 W1)))))))) (All W1, (((aInteger0 (xp)) /\ (aInteger0 W1)) => (((sdtasdt0 (xp) W1) = (sz00)) => (((xp) = (sz00)) \/ (W1 = (sz00)))))) (aInteger0 (xp)) (aInteger0 (xq)) (All W0, (All W1, (((aInteger0 W0) /\ (aInteger0 W1)) => (aInteger0 (sdtasdt0 W0 W1))))) (sdteqdtlpzmzozddtrp0 (xa) (xb) (sdtasdt0 (xp) (xq))) (-. (Ex W0, ((aInteger0 W0) /\ ((sdtasdt0 (sdtasdt0 (xp) (xq)) W0) = (sdtpldt0 (xa) (smndt0 (xb))))))) ((xp) != (sz00)) ((xq) != (sz00)) ### All 36 % 245.24/245.41 38. (All W0, (All W1, (((aInteger0 W0) /\ (aInteger0 W1)) => (((sdtasdt0 W0 W1) = (sz00)) => ((W0 = (sz00)) \/ (W1 = (sz00))))))) ((xq) != (sz00)) ((xp) != (sz00)) (-. (Ex W0, ((aInteger0 W0) /\ ((sdtasdt0 (sdtasdt0 (xp) (xq)) W0) = (sdtpldt0 (xa) (smndt0 (xb))))))) (sdteqdtlpzmzozddtrp0 (xa) (xb) (sdtasdt0 (xp) (xq))) (All W0, (All W1, (((aInteger0 W0) /\ (aInteger0 W1)) => (aInteger0 (sdtasdt0 W0 W1))))) (aInteger0 (xq)) (aInteger0 (xp)) (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)) (All W0, ((aInteger0 W0) => (aInteger0 (smndt0 W0)))) (aInteger0 (xb)) (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 37 % 245.24/245.41 39. ((aInteger0 (xa)) /\ ((aInteger0 (xb)) /\ ((aInteger0 (xp)) /\ (((xp) != (sz00)) /\ ((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, (All W1, (All W2, (((aInteger0 W0) /\ ((aInteger0 W1) /\ ((aInteger0 W2) /\ (W2 != (sz00))))) => ((sdteqdtlpzmzozddtrp0 W0 W1 W2) <=> (aDivisorOf0 W2 (sdtpldt0 W0 (smndt0 W1)))))))) (All W0, (All W1, (((aInteger0 W0) /\ (aInteger0 W1)) => (aInteger0 (sdtasdt0 W0 W1))))) (sdteqdtlpzmzozddtrp0 (xa) (xb) (sdtasdt0 (xp) (xq))) (-. (Ex W0, ((aInteger0 W0) /\ ((sdtasdt0 (sdtasdt0 (xp) (xq)) W0) = (sdtpldt0 (xa) (smndt0 (xb))))))) (All W0, (All W1, (((aInteger0 W0) /\ (aInteger0 W1)) => (((sdtasdt0 W0 W1) = (sz00)) => ((W0 = (sz00)) \/ (W1 = (sz00))))))) ### ConjTree 38 % 245.24/245.41 % SZS output end Proof % 245.24/245.41 (* END-PROOF *) %------------------------------------------------------------------------------