TSTP Solution File: RNG123+1 by SuperZenon---0.0.1
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%------------------------------------------------------------------------------
% 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 :
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%----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 *)
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