%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : RNG123+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 : n023.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 20:42:02 EDT 2022 % Result : Theorem 159.19s 159.41s % Output : Proof 159.19s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : RNG123+1 : TPTP v8.1.0. Released v4.0.0. % 0.11/0.12 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 0.12/0.33 % Computer : n023.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Mon May 30 14:03:57 EDT 2022 % 0.12/0.33 % CPUTime : % 159.19/159.41 % SZS status Theorem % 159.19/159.41 (* PROOF-FOUND *) % 159.19/159.41 (* BEGIN-PROOF *) % 159.19/159.41 % SZS output start Proof % 159.19/159.41 1. ((sdtpldt0 (smndt0 (sdtasdt0 (xq) (xu))) (xb)) != (sz00)) ((sdtpldt0 (smndt0 (sdtasdt0 (xq) (xu))) (xb)) = (sz00)) ### Axiom % 159.19/159.41 2. ((xr) = (sz00)) ((sdtpldt0 (smndt0 (sdtasdt0 (xq) (xu))) (xb)) != (sz00)) ### Definition-Pseudo(xr) 1 % 159.19/159.41 3. (aElementOf0 (smndt0 (sdtasdt0 (xq) (xu))) (xI)) (-. (aElementOf0 (smndt0 (sdtasdt0 (xq) (xu))) (xI))) ### Axiom % 159.19/159.41 4. (aElementOf0 (xb) (xI)) (-. (aElementOf0 (xb) (xI))) ### Axiom % 159.19/159.41 5. (aElementOf0 (sdtpldt0 (smndt0 (sdtasdt0 (xq) (xu))) (xb)) (xI)) (-. (aElementOf0 (sdtpldt0 (smndt0 (sdtasdt0 (xq) (xu))) (xb)) (xI))) ### Axiom % 159.19/159.41 6. ((sdtpldt0 (smndt0 (sdtasdt0 (xq) (xu))) (xb)) != (sz00)) ((sdtpldt0 (smndt0 (sdtasdt0 (xq) (xu))) (xb)) = (sz00)) ### Axiom % 159.19/159.41 7. ((sdtpldt0 (smndt0 (sdtasdt0 (xq) (xu))) (xb)) != (sdtpldt0 (smndt0 (sdtasdt0 (xq) (xu))) (xb))) ### Refl(=) % 159.19/159.41 8. ((xr) != (sdtpldt0 (smndt0 (sdtasdt0 (xq) (xu))) (xb))) ### Definition-Pseudo(xr) 7 % 159.19/159.41 9. ((sbrdtbr0 (xr)) != (sbrdtbr0 (sdtpldt0 (smndt0 (sdtasdt0 (xq) (xu))) (xb)))) ### NotEqual 8 % 159.19/159.41 10. ((sbrdtbr0 (xu)) != (sbrdtbr0 (xu))) ### Refl(=) % 159.19/159.41 11. (-. (iLess0 (sbrdtbr0 (sdtpldt0 (smndt0 (sdtasdt0 (xq) (xu))) (xb))) (sbrdtbr0 (xu)))) (iLess0 (sbrdtbr0 (xr)) (sbrdtbr0 (xu))) ### P-NotP 9 10 % 159.19/159.41 12. (((aElementOf0 (sdtpldt0 (smndt0 (sdtasdt0 (xq) (xu))) (xb)) (xI)) /\ ((sdtpldt0 (smndt0 (sdtasdt0 (xq) (xu))) (xb)) != (sz00))) => (-. (iLess0 (sbrdtbr0 (sdtpldt0 (smndt0 (sdtasdt0 (xq) (xu))) (xb))) (sbrdtbr0 (xu))))) (iLess0 (sbrdtbr0 (xr)) (sbrdtbr0 (xu))) ((sdtpldt0 (smndt0 (sdtasdt0 (xq) (xu))) (xb)) != (sz00)) (aElementOf0 (sdtpldt0 (smndt0 (sdtasdt0 (xq) (xu))) (xb)) (xI)) ### DisjTree 5 6 11 % 159.19/159.41 13. (All W0, (((aElementOf0 W0 (xI)) /\ (W0 != (sz00))) => (-. (iLess0 (sbrdtbr0 W0) (sbrdtbr0 (xu)))))) (aElementOf0 (sdtpldt0 (smndt0 (sdtasdt0 (xq) (xu))) (xb)) (xI)) ((sdtpldt0 (smndt0 (sdtasdt0 (xq) (xu))) (xb)) != (sz00)) (iLess0 (sbrdtbr0 (xr)) (sbrdtbr0 (xu))) ### All 12 % 159.19/159.41 14. ((aElementOf0 (xb) (xI)) => (aElementOf0 (sdtpldt0 (smndt0 (sdtasdt0 (xq) (xu))) (xb)) (xI))) (iLess0 (sbrdtbr0 (xr)) (sbrdtbr0 (xu))) ((sdtpldt0 (smndt0 (sdtasdt0 (xq) (xu))) (xb)) != (sz00)) (All W0, (((aElementOf0 W0 (xI)) /\ (W0 != (sz00))) => (-. (iLess0 (sbrdtbr0 W0) (sbrdtbr0 (xu)))))) (aElementOf0 (xb) (xI)) ### Imply 4 13 % 159.19/159.41 15. (All W2, ((aElementOf0 W2 (xI)) => (aElementOf0 (sdtpldt0 (smndt0 (sdtasdt0 (xq) (xu))) W2) (xI)))) (aElementOf0 (xb) (xI)) (All W0, (((aElementOf0 W0 (xI)) /\ (W0 != (sz00))) => (-. (iLess0 (sbrdtbr0 W0) (sbrdtbr0 (xu)))))) ((sdtpldt0 (smndt0 (sdtasdt0 (xq) (xu))) (xb)) != (sz00)) (iLess0 (sbrdtbr0 (xr)) (sbrdtbr0 (xu))) ### All 14 % 159.19/159.41 16. ((All W2, ((aElementOf0 W2 (xI)) => (aElementOf0 (sdtpldt0 (smndt0 (sdtasdt0 (xq) (xu))) W2) (xI)))) /\ (All W2, ((aElement0 W2) => (aElementOf0 (sdtasdt0 W2 (smndt0 (sdtasdt0 (xq) (xu)))) (xI))))) (iLess0 (sbrdtbr0 (xr)) (sbrdtbr0 (xu))) ((sdtpldt0 (smndt0 (sdtasdt0 (xq) (xu))) (xb)) != (sz00)) (All W0, (((aElementOf0 W0 (xI)) /\ (W0 != (sz00))) => (-. (iLess0 (sbrdtbr0 W0) (sbrdtbr0 (xu)))))) (aElementOf0 (xb) (xI)) ### And 15 % 159.19/159.41 17. ((aElementOf0 (smndt0 (sdtasdt0 (xq) (xu))) (xI)) => ((All W2, ((aElementOf0 W2 (xI)) => (aElementOf0 (sdtpldt0 (smndt0 (sdtasdt0 (xq) (xu))) W2) (xI)))) /\ (All W2, ((aElement0 W2) => (aElementOf0 (sdtasdt0 W2 (smndt0 (sdtasdt0 (xq) (xu)))) (xI)))))) (aElementOf0 (xb) (xI)) (All W0, (((aElementOf0 W0 (xI)) /\ (W0 != (sz00))) => (-. (iLess0 (sbrdtbr0 W0) (sbrdtbr0 (xu)))))) ((sdtpldt0 (smndt0 (sdtasdt0 (xq) (xu))) (xb)) != (sz00)) (iLess0 (sbrdtbr0 (xr)) (sbrdtbr0 (xu))) (aElementOf0 (smndt0 (sdtasdt0 (xq) (xu))) (xI)) ### Imply 3 16 % 159.19/159.41 18. (All W1, ((aElementOf0 W1 (xI)) => ((All W2, ((aElementOf0 W2 (xI)) => (aElementOf0 (sdtpldt0 W1 W2) (xI)))) /\ (All W2, ((aElement0 W2) => (aElementOf0 (sdtasdt0 W2 W1) (xI))))))) (aElementOf0 (smndt0 (sdtasdt0 (xq) (xu))) (xI)) (iLess0 (sbrdtbr0 (xr)) (sbrdtbr0 (xu))) ((sdtpldt0 (smndt0 (sdtasdt0 (xq) (xu))) (xb)) != (sz00)) (All W0, (((aElementOf0 W0 (xI)) /\ (W0 != (sz00))) => (-. (iLess0 (sbrdtbr0 W0) (sbrdtbr0 (xu)))))) (aElementOf0 (xb) (xI)) ### All 17 % 159.19/159.41 19. (((xr) = (sz00)) \/ (iLess0 (sbrdtbr0 (xr)) (sbrdtbr0 (xu)))) (aElementOf0 (xb) (xI)) (All W0, (((aElementOf0 W0 (xI)) /\ (W0 != (sz00))) => (-. (iLess0 (sbrdtbr0 W0) (sbrdtbr0 (xu)))))) (aElementOf0 (smndt0 (sdtasdt0 (xq) (xu))) (xI)) (All W1, ((aElementOf0 W1 (xI)) => ((All W2, ((aElementOf0 W2 (xI)) => (aElementOf0 (sdtpldt0 W1 W2) (xI)))) /\ (All W2, ((aElement0 W2) => (aElementOf0 (sdtasdt0 W2 W1) (xI))))))) ((sdtpldt0 (smndt0 (sdtasdt0 (xq) (xu))) (xb)) != (sz00)) ### Or 2 18 % 159.19/159.41 20. ((aSet0 (xI)) /\ (All W1, ((aElementOf0 W1 (xI)) => ((All W2, ((aElementOf0 W2 (xI)) => (aElementOf0 (sdtpldt0 W1 W2) (xI)))) /\ (All W2, ((aElement0 W2) => (aElementOf0 (sdtasdt0 W2 W1) (xI)))))))) ((sdtpldt0 (smndt0 (sdtasdt0 (xq) (xu))) (xb)) != (sz00)) (aElementOf0 (smndt0 (sdtasdt0 (xq) (xu))) (xI)) (All W0, (((aElementOf0 W0 (xI)) /\ (W0 != (sz00))) => (-. (iLess0 (sbrdtbr0 W0) (sbrdtbr0 (xu)))))) (aElementOf0 (xb) (xI)) (((xr) = (sz00)) \/ (iLess0 (sbrdtbr0 (xr)) (sbrdtbr0 (xu)))) ### And 19 % 159.19/159.41 21. (aIdeal0 (xI)) (((xr) = (sz00)) \/ (iLess0 (sbrdtbr0 (xr)) (sbrdtbr0 (xu)))) (aElementOf0 (xb) (xI)) (All W0, (((aElementOf0 W0 (xI)) /\ (W0 != (sz00))) => (-. (iLess0 (sbrdtbr0 W0) (sbrdtbr0 (xu)))))) (aElementOf0 (smndt0 (sdtasdt0 (xq) (xu))) (xI)) ((sdtpldt0 (smndt0 (sdtasdt0 (xq) (xu))) (xb)) != (sz00)) ### Definition-Pseudo(aIdeal0) 20 % 159.19/159.41 22. ((aIdeal0 (xI)) /\ ((xI) = (sdtpldt1 (slsdtgt0 (xa)) (slsdtgt0 (xb))))) ((sdtpldt0 (smndt0 (sdtasdt0 (xq) (xu))) (xb)) != (sz00)) (aElementOf0 (smndt0 (sdtasdt0 (xq) (xu))) (xI)) (All W0, (((aElementOf0 W0 (xI)) /\ (W0 != (sz00))) => (-. (iLess0 (sbrdtbr0 W0) (sbrdtbr0 (xu)))))) (aElementOf0 (xb) (xI)) (((xr) = (sz00)) \/ (iLess0 (sbrdtbr0 (xr)) (sbrdtbr0 (xu)))) ### And 21 % 159.19/159.41 23. ((aElementOf0 (xu) (xI)) /\ (((xu) != (sz00)) /\ (All W0, (((aElementOf0 W0 (xI)) /\ (W0 != (sz00))) => (-. (iLess0 (sbrdtbr0 W0) (sbrdtbr0 (xu)))))))) (((xr) = (sz00)) \/ (iLess0 (sbrdtbr0 (xr)) (sbrdtbr0 (xu)))) (aElementOf0 (xb) (xI)) (aElementOf0 (smndt0 (sdtasdt0 (xq) (xu))) (xI)) ((sdtpldt0 (smndt0 (sdtasdt0 (xq) (xu))) (xb)) != (sz00)) ((aIdeal0 (xI)) /\ ((xI) = (sdtpldt1 (slsdtgt0 (xa)) (slsdtgt0 (xb))))) ### ConjTree 22 % 159.19/159.41 24. ((aElement0 (xq)) /\ ((aElement0 (xr)) /\ (((xb) = (sdtpldt0 (sdtasdt0 (xq) (xu)) (xr))) /\ (((xr) = (sz00)) \/ (iLess0 (sbrdtbr0 (xr)) (sbrdtbr0 (xu))))))) ((aIdeal0 (xI)) /\ ((xI) = (sdtpldt1 (slsdtgt0 (xa)) (slsdtgt0 (xb))))) ((sdtpldt0 (smndt0 (sdtasdt0 (xq) (xu))) (xb)) != (sz00)) (aElementOf0 (smndt0 (sdtasdt0 (xq) (xu))) (xI)) (aElementOf0 (xb) (xI)) ((aElementOf0 (xu) (xI)) /\ (((xu) != (sz00)) /\ (All W0, (((aElementOf0 W0 (xI)) /\ (W0 != (sz00))) => (-. (iLess0 (sbrdtbr0 W0) (sbrdtbr0 (xu)))))))) ### ConjTree 23 % 159.19/159.41 25. ((xr) != (sz00)) ((aElementOf0 (xu) (xI)) /\ (((xu) != (sz00)) /\ (All W0, (((aElementOf0 W0 (xI)) /\ (W0 != (sz00))) => (-. (iLess0 (sbrdtbr0 W0) (sbrdtbr0 (xu)))))))) (aElementOf0 (xb) (xI)) (aElementOf0 (smndt0 (sdtasdt0 (xq) (xu))) (xI)) ((aIdeal0 (xI)) /\ ((xI) = (sdtpldt1 (slsdtgt0 (xa)) (slsdtgt0 (xb))))) ((aElement0 (xq)) /\ ((aElement0 (xr)) /\ (((xb) = (sdtpldt0 (sdtasdt0 (xq) (xu)) (xr))) /\ (((xr) = (sz00)) \/ (iLess0 (sbrdtbr0 (xr)) (sbrdtbr0 (xu))))))) ### Definition-Pseudo(xr) 24 % 159.19/159.41 % SZS output end Proof % 159.19/159.41 (* END-PROOF *) %------------------------------------------------------------------------------