%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : NUM429+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 : n024.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 14:42:22 EDT 2022 % Result : Theorem 245.11s 245.32s % Output : Proof 245.11s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM429+1 : TPTP v8.1.0. Released v4.0.0. % 0.12/0.13 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 0.12/0.34 % Computer : n024.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 00:09:14 EDT 2022 % 0.12/0.34 % CPUTime : % 245.11/245.32 % SZS status Theorem % 245.11/245.32 (* PROOF-FOUND *) % 245.11/245.32 (* BEGIN-PROOF *) % 245.11/245.32 % SZS output start Proof % 245.11/245.32 1. (aInteger0 (xa)) (-. (aInteger0 (xa))) ### Axiom % 245.11/245.32 2. (aInteger0 (xb)) (-. (aInteger0 (xb))) ### Axiom % 245.11/245.32 3. (-. (aInteger0 (smndt0 (xb)))) (aInteger0 (smndt0 (xb))) ### Axiom % 245.11/245.32 4. ((aInteger0 (xb)) => (aInteger0 (smndt0 (xb)))) (-. (aInteger0 (smndt0 (xb)))) (aInteger0 (xb)) ### Imply 2 3 % 245.11/245.32 5. (All W0, ((aInteger0 W0) => (aInteger0 (smndt0 W0)))) (aInteger0 (xb)) (-. (aInteger0 (smndt0 (xb)))) ### All 4 % 245.11/245.32 6. (-. (aInteger0 (sdtpldt0 (xa) (smndt0 (xb))))) (aInteger0 (sdtpldt0 (xa) (smndt0 (xb)))) ### Axiom % 245.11/245.32 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 % 245.11/245.32 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 % 245.11/245.32 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 % 245.11/245.32 10. (aInteger0 (xa)) (-. (aInteger0 (xa))) ### Axiom % 245.11/245.32 11. (aInteger0 (xb)) (-. (aInteger0 (xb))) ### Axiom % 245.11/245.32 12. (aInteger0 (xq)) (-. (aInteger0 (xq))) ### Axiom % 245.11/245.32 13. ((xq) != (sz00)) ((xq) = (sz00)) ### Axiom % 245.11/245.32 14. (sdteqdtlpzmzozddtrp0 (xa) (xb) (xq)) (-. (sdteqdtlpzmzozddtrp0 (xa) (xb) (xq))) ### Axiom % 245.11/245.32 15. (aDivisorOf0 (xq) (sdtpldt0 (xa) (smndt0 (xb)))) (-. (aDivisorOf0 (xq) (sdtpldt0 (xa) (smndt0 (xb))))) ### Axiom % 245.11/245.32 16. (-. (Ex W0, ((aInteger0 W0) /\ ((sdtasdt0 (xq) W0) = (sdtpldt0 (xa) (smndt0 (xb))))))) (Ex W0, ((aInteger0 W0) /\ ((sdtasdt0 (xq) W0) = (sdtpldt0 (xa) (smndt0 (xb)))))) ### Axiom % 245.11/245.32 17. ((aInteger0 (xq)) /\ (((xq) != (sz00)) /\ (Ex W0, ((aInteger0 W0) /\ ((sdtasdt0 (xq) W0) = (sdtpldt0 (xa) (smndt0 (xb)))))))) (-. (Ex W0, ((aInteger0 W0) /\ ((sdtasdt0 (xq) W0) = (sdtpldt0 (xa) (smndt0 (xb))))))) ### ConjTree 16 % 245.11/245.32 18. ((aDivisorOf0 (xq) (sdtpldt0 (xa) (smndt0 (xb)))) <=> ((aInteger0 (xq)) /\ (((xq) != (sz00)) /\ (Ex W0, ((aInteger0 W0) /\ ((sdtasdt0 (xq) W0) = (sdtpldt0 (xa) (smndt0 (xb))))))))) (-. (Ex W0, ((aInteger0 W0) /\ ((sdtasdt0 (xq) W0) = (sdtpldt0 (xa) (smndt0 (xb))))))) (aDivisorOf0 (xq) (sdtpldt0 (xa) (smndt0 (xb)))) ### Equiv 15 17 % 245.11/245.32 19. (All W1, ((aDivisorOf0 W1 (sdtpldt0 (xa) (smndt0 (xb)))) <=> ((aInteger0 W1) /\ ((W1 != (sz00)) /\ (Ex W2, ((aInteger0 W2) /\ ((sdtasdt0 W1 W2) = (sdtpldt0 (xa) (smndt0 (xb)))))))))) (aDivisorOf0 (xq) (sdtpldt0 (xa) (smndt0 (xb)))) (-. (Ex W0, ((aInteger0 W0) /\ ((sdtasdt0 (xq) W0) = (sdtpldt0 (xa) (smndt0 (xb))))))) ### All 18 % 245.11/245.32 20. ((sdteqdtlpzmzozddtrp0 (xa) (xb) (xq)) <=> (aDivisorOf0 (xq) (sdtpldt0 (xa) (smndt0 (xb))))) (-. (Ex W0, ((aInteger0 W0) /\ ((sdtasdt0 (xq) W0) = (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)))))))))) (sdteqdtlpzmzozddtrp0 (xa) (xb) (xq)) ### Equiv 14 19 % 245.11/245.32 21. (((aInteger0 (xa)) /\ ((aInteger0 (xb)) /\ ((aInteger0 (xq)) /\ ((xq) != (sz00))))) => ((sdteqdtlpzmzozddtrp0 (xa) (xb) (xq)) <=> (aDivisorOf0 (xq) (sdtpldt0 (xa) (smndt0 (xb)))))) (sdteqdtlpzmzozddtrp0 (xa) (xb) (xq)) (All W1, ((aDivisorOf0 W1 (sdtpldt0 (xa) (smndt0 (xb)))) <=> ((aInteger0 W1) /\ ((W1 != (sz00)) /\ (Ex W2, ((aInteger0 W2) /\ ((sdtasdt0 W1 W2) = (sdtpldt0 (xa) (smndt0 (xb)))))))))) (-. (Ex W0, ((aInteger0 W0) /\ ((sdtasdt0 (xq) W0) = (sdtpldt0 (xa) (smndt0 (xb))))))) ((xq) != (sz00)) (aInteger0 (xq)) (aInteger0 (xb)) (aInteger0 (xa)) ### DisjTree 10 11 12 13 20 % 245.11/245.32 22. (All W2, (((aInteger0 (xa)) /\ ((aInteger0 (xb)) /\ ((aInteger0 W2) /\ (W2 != (sz00))))) => ((sdteqdtlpzmzozddtrp0 (xa) (xb) W2) <=> (aDivisorOf0 W2 (sdtpldt0 (xa) (smndt0 (xb))))))) (aInteger0 (xa)) (aInteger0 (xb)) (aInteger0 (xq)) ((xq) != (sz00)) (-. (Ex W0, ((aInteger0 W0) /\ ((sdtasdt0 (xq) W0) = (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)))))))))) (sdteqdtlpzmzozddtrp0 (xa) (xb) (xq)) ### All 21 % 245.11/245.32 23. (All W1, (All W2, (((aInteger0 (xa)) /\ ((aInteger0 W1) /\ ((aInteger0 W2) /\ (W2 != (sz00))))) => ((sdteqdtlpzmzozddtrp0 (xa) W1 W2) <=> (aDivisorOf0 W2 (sdtpldt0 (xa) (smndt0 W1))))))) (sdteqdtlpzmzozddtrp0 (xa) (xb) (xq)) (All W1, ((aDivisorOf0 W1 (sdtpldt0 (xa) (smndt0 (xb)))) <=> ((aInteger0 W1) /\ ((W1 != (sz00)) /\ (Ex W2, ((aInteger0 W2) /\ ((sdtasdt0 W1 W2) = (sdtpldt0 (xa) (smndt0 (xb)))))))))) (-. (Ex W0, ((aInteger0 W0) /\ ((sdtasdt0 (xq) W0) = (sdtpldt0 (xa) (smndt0 (xb))))))) ((xq) != (sz00)) (aInteger0 (xq)) (aInteger0 (xb)) (aInteger0 (xa)) ### All 22 % 245.11/245.32 24. (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 (xb)) (aInteger0 (xq)) ((xq) != (sz00)) (-. (Ex W0, ((aInteger0 W0) /\ ((sdtasdt0 (xq) W0) = (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)))))))))) (sdteqdtlpzmzozddtrp0 (xa) (xb) (xq)) ### All 23 % 245.11/245.32 25. ((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))))))))))) (sdteqdtlpzmzozddtrp0 (xa) (xb) (xq)) (-. (Ex W0, ((aInteger0 W0) /\ ((sdtasdt0 (xq) W0) = (sdtpldt0 (xa) (smndt0 (xb))))))) ((xq) != (sz00)) (aInteger0 (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 (xa)) (All W0, ((aInteger0 W0) => (aInteger0 (smndt0 W0)))) (aInteger0 (xb)) (All W0, (All W1, (((aInteger0 W0) /\ (aInteger0 W1)) => (aInteger0 (sdtpldt0 W0 W1))))) ### Imply 9 24 % 245.11/245.32 26. (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)))))))) (aInteger0 (xq)) ((xq) != (sz00)) (-. (Ex W0, ((aInteger0 W0) /\ ((sdtasdt0 (xq) W0) = (sdtpldt0 (xa) (smndt0 (xb))))))) (sdteqdtlpzmzozddtrp0 (xa) (xb) (xq)) ### All 25 % 245.11/245.32 27. ((aInteger0 (xa)) /\ ((aInteger0 (xb)) /\ ((aInteger0 (xq)) /\ (((xq) != (sz00)) /\ (aInteger0 (xc)))))) (sdteqdtlpzmzozddtrp0 (xa) (xb) (xq)) (-. (Ex W0, ((aInteger0 W0) /\ ((sdtasdt0 (xq) W0) = (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)))))))) (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))))))))) ### ConjTree 26 % 245.11/245.32 28. ((sdteqdtlpzmzozddtrp0 (xa) (xb) (xq)) /\ (sdteqdtlpzmzozddtrp0 (xb) (xc) (xq))) (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)))))))) (-. (Ex W0, ((aInteger0 W0) /\ ((sdtasdt0 (xq) W0) = (sdtpldt0 (xa) (smndt0 (xb))))))) ((aInteger0 (xa)) /\ ((aInteger0 (xb)) /\ ((aInteger0 (xq)) /\ (((xq) != (sz00)) /\ (aInteger0 (xc)))))) ### And 27 % 245.11/245.32 % SZS output end Proof % 245.11/245.32 (* END-PROOF *) %------------------------------------------------------------------------------