TSTP Solution File: RNG125+1 by SuperZenon---0.0.1
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%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : RNG125+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 : n032.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 2.56s 2.76s
% Output : Proof 2.56s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : RNG125+1 : TPTP v8.1.0. Released v4.0.0.
% 0.05/0.10 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.10/0.29 % Computer : n032.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 600
% 0.10/0.29 % DateTime : Mon May 30 04:51:27 EDT 2022
% 0.10/0.29 % CPUTime :
% 2.56/2.76 % SZS status Theorem
% 2.56/2.76 (* PROOF-FOUND *)
% 2.56/2.76 (* BEGIN-PROOF *)
% 2.56/2.76 % SZS output start Proof
% 2.56/2.76 1. (aElement0 (xa)) (-. (aElement0 (xa))) ### Axiom
% 2.56/2.76 2. (aSet0 (xI)) (-. (aSet0 (xI))) ### Axiom
% 2.56/2.76 3. (aElementOf0 (xu) (xI)) (-. (aElementOf0 (xu) (xI))) ### Axiom
% 2.56/2.76 4. (-. (aElement0 (xu))) (aElement0 (xu)) ### Axiom
% 2.56/2.76 5. ((aElementOf0 (xu) (xI)) => (aElement0 (xu))) (-. (aElement0 (xu))) (aElementOf0 (xu) (xI)) ### Imply 3 4
% 2.56/2.76 6. (All W1, ((aElementOf0 W1 (xI)) => (aElement0 W1))) (aElementOf0 (xu) (xI)) (-. (aElement0 (xu))) ### All 5
% 2.56/2.76 7. ((aSet0 (xI)) => (All W1, ((aElementOf0 W1 (xI)) => (aElement0 W1)))) (-. (aElement0 (xu))) (aElementOf0 (xu) (xI)) (aSet0 (xI)) ### Imply 2 6
% 2.56/2.76 8. (All W0, ((aSet0 W0) => (All W1, ((aElementOf0 W1 W0) => (aElement0 W1))))) (aSet0 (xI)) (aElementOf0 (xu) (xI)) (-. (aElement0 (xu))) ### All 7
% 2.56/2.76 9. (doDivides0 (xu) (xa)) (-. (doDivides0 (xu) (xa))) ### Axiom
% 2.56/2.76 10. (-. ((aElement0 (xu)) /\ (doDivides0 (xu) (xa)))) (doDivides0 (xu) (xa)) (aElementOf0 (xu) (xI)) (aSet0 (xI)) (All W0, ((aSet0 W0) => (All W1, ((aElementOf0 W1 W0) => (aElement0 W1))))) ### NotAnd 8 9
% 2.56/2.76 11. (-. (aDivisorOf0 (xu) (xa))) (aDivisorOf0 (xu) (xa)) ### Axiom
% 2.56/2.76 12. ((aDivisorOf0 (xu) (xa)) <=> ((aElement0 (xu)) /\ (doDivides0 (xu) (xa)))) (-. (aDivisorOf0 (xu) (xa))) (All W0, ((aSet0 W0) => (All W1, ((aElementOf0 W1 W0) => (aElement0 W1))))) (aSet0 (xI)) (aElementOf0 (xu) (xI)) (doDivides0 (xu) (xa)) ### Equiv 10 11
% 2.56/2.76 13. (All W1, ((aDivisorOf0 W1 (xa)) <=> ((aElement0 W1) /\ (doDivides0 W1 (xa))))) (doDivides0 (xu) (xa)) (aElementOf0 (xu) (xI)) (aSet0 (xI)) (All W0, ((aSet0 W0) => (All W1, ((aElementOf0 W1 W0) => (aElement0 W1))))) (-. (aDivisorOf0 (xu) (xa))) ### All 12
% 2.56/2.76 14. ((aElement0 (xa)) => (All W1, ((aDivisorOf0 W1 (xa)) <=> ((aElement0 W1) /\ (doDivides0 W1 (xa)))))) (-. (aDivisorOf0 (xu) (xa))) (All W0, ((aSet0 W0) => (All W1, ((aElementOf0 W1 W0) => (aElement0 W1))))) (aSet0 (xI)) (aElementOf0 (xu) (xI)) (doDivides0 (xu) (xa)) (aElement0 (xa)) ### Imply 1 13
% 2.56/2.76 15. (All W0, ((aElement0 W0) => (All W1, ((aDivisorOf0 W1 W0) <=> ((aElement0 W1) /\ (doDivides0 W1 W0)))))) (aElement0 (xa)) (doDivides0 (xu) (xa)) (aElementOf0 (xu) (xI)) (aSet0 (xI)) (All W0, ((aSet0 W0) => (All W1, ((aElementOf0 W1 W0) => (aElement0 W1))))) (-. (aDivisorOf0 (xu) (xa))) ### All 14
% 2.56/2.76 16. (aElement0 (xb)) (-. (aElement0 (xb))) ### Axiom
% 2.56/2.76 17. (doDivides0 (xu) (xb)) (-. (doDivides0 (xu) (xb))) ### Axiom
% 2.56/2.76 18. (-. ((aElement0 (xu)) /\ (doDivides0 (xu) (xb)))) (doDivides0 (xu) (xb)) (aElementOf0 (xu) (xI)) (aSet0 (xI)) (All W0, ((aSet0 W0) => (All W1, ((aElementOf0 W1 W0) => (aElement0 W1))))) ### NotAnd 8 17
% 2.56/2.76 19. (-. (aDivisorOf0 (xu) (xb))) (aDivisorOf0 (xu) (xb)) ### Axiom
% 2.56/2.76 20. ((aDivisorOf0 (xu) (xb)) <=> ((aElement0 (xu)) /\ (doDivides0 (xu) (xb)))) (-. (aDivisorOf0 (xu) (xb))) (All W0, ((aSet0 W0) => (All W1, ((aElementOf0 W1 W0) => (aElement0 W1))))) (aSet0 (xI)) (aElementOf0 (xu) (xI)) (doDivides0 (xu) (xb)) ### Equiv 18 19
% 2.56/2.76 21. (All W1, ((aDivisorOf0 W1 (xb)) <=> ((aElement0 W1) /\ (doDivides0 W1 (xb))))) (doDivides0 (xu) (xb)) (aElementOf0 (xu) (xI)) (aSet0 (xI)) (All W0, ((aSet0 W0) => (All W1, ((aElementOf0 W1 W0) => (aElement0 W1))))) (-. (aDivisorOf0 (xu) (xb))) ### All 20
% 2.56/2.76 22. ((aElement0 (xb)) => (All W1, ((aDivisorOf0 W1 (xb)) <=> ((aElement0 W1) /\ (doDivides0 W1 (xb)))))) (-. (aDivisorOf0 (xu) (xb))) (All W0, ((aSet0 W0) => (All W1, ((aElementOf0 W1 W0) => (aElement0 W1))))) (aSet0 (xI)) (aElementOf0 (xu) (xI)) (doDivides0 (xu) (xb)) (aElement0 (xb)) ### Imply 16 21
% 2.56/2.76 23. (All W0, ((aElement0 W0) => (All W1, ((aDivisorOf0 W1 W0) <=> ((aElement0 W1) /\ (doDivides0 W1 W0)))))) (aElement0 (xb)) (doDivides0 (xu) (xb)) (aElementOf0 (xu) (xI)) (aSet0 (xI)) (All W0, ((aSet0 W0) => (All W1, ((aElementOf0 W1 W0) => (aElement0 W1))))) (-. (aDivisorOf0 (xu) (xb))) ### All 22
% 2.56/2.76 24. (-. ((aDivisorOf0 (xu) (xa)) /\ (aDivisorOf0 (xu) (xb)))) (doDivides0 (xu) (xb)) (aElement0 (xb)) (All W0, ((aSet0 W0) => (All W1, ((aElementOf0 W1 W0) => (aElement0 W1))))) (aSet0 (xI)) (aElementOf0 (xu) (xI)) (doDivides0 (xu) (xa)) (aElement0 (xa)) (All W0, ((aElement0 W0) => (All W1, ((aDivisorOf0 W1 W0) <=> ((aElement0 W1) /\ (doDivides0 W1 W0)))))) ### NotAnd 15 23
% 2.56/2.76 25. ((aElement0 (xa)) /\ (aElement0 (xb))) (All W0, ((aElement0 W0) => (All W1, ((aDivisorOf0 W1 W0) <=> ((aElement0 W1) /\ (doDivides0 W1 W0)))))) (doDivides0 (xu) (xa)) (aElementOf0 (xu) (xI)) (aSet0 (xI)) (All W0, ((aSet0 W0) => (All W1, ((aElementOf0 W1 W0) => (aElement0 W1))))) (doDivides0 (xu) (xb)) (-. ((aDivisorOf0 (xu) (xa)) /\ (aDivisorOf0 (xu) (xb)))) ### And 24
% 2.56/2.76 26. ((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)))))))) (-. ((aDivisorOf0 (xu) (xa)) /\ (aDivisorOf0 (xu) (xb)))) (doDivides0 (xu) (xb)) (All W0, ((aSet0 W0) => (All W1, ((aElementOf0 W1 W0) => (aElement0 W1))))) (aElementOf0 (xu) (xI)) (doDivides0 (xu) (xa)) (All W0, ((aElement0 W0) => (All W1, ((aDivisorOf0 W1 W0) <=> ((aElement0 W1) /\ (doDivides0 W1 W0)))))) ((aElement0 (xa)) /\ (aElement0 (xb))) ### And 25
% 2.56/2.76 27. (aIdeal0 (xI)) ((aElement0 (xa)) /\ (aElement0 (xb))) (All W0, ((aElement0 W0) => (All W1, ((aDivisorOf0 W1 W0) <=> ((aElement0 W1) /\ (doDivides0 W1 W0)))))) (doDivides0 (xu) (xa)) (aElementOf0 (xu) (xI)) (All W0, ((aSet0 W0) => (All W1, ((aElementOf0 W1 W0) => (aElement0 W1))))) (doDivides0 (xu) (xb)) (-. ((aDivisorOf0 (xu) (xa)) /\ (aDivisorOf0 (xu) (xb)))) ### Definition-Pseudo(aIdeal0) 26
% 2.56/2.76 28. ((aIdeal0 (xI)) /\ ((xI) = (sdtpldt1 (slsdtgt0 (xa)) (slsdtgt0 (xb))))) (-. ((aDivisorOf0 (xu) (xa)) /\ (aDivisorOf0 (xu) (xb)))) (doDivides0 (xu) (xb)) (All W0, ((aSet0 W0) => (All W1, ((aElementOf0 W1 W0) => (aElement0 W1))))) (aElementOf0 (xu) (xI)) (doDivides0 (xu) (xa)) (All W0, ((aElement0 W0) => (All W1, ((aDivisorOf0 W1 W0) <=> ((aElement0 W1) /\ (doDivides0 W1 W0)))))) ((aElement0 (xa)) /\ (aElement0 (xb))) ### And 27
% 2.56/2.76 29. ((aElementOf0 (xu) (xI)) /\ (((xu) != (sz00)) /\ (All W0, (((aElementOf0 W0 (xI)) /\ (W0 != (sz00))) => (-. (iLess0 (sbrdtbr0 W0) (sbrdtbr0 (xu)))))))) ((aElement0 (xa)) /\ (aElement0 (xb))) (All W0, ((aElement0 W0) => (All W1, ((aDivisorOf0 W1 W0) <=> ((aElement0 W1) /\ (doDivides0 W1 W0)))))) (doDivides0 (xu) (xa)) (All W0, ((aSet0 W0) => (All W1, ((aElementOf0 W1 W0) => (aElement0 W1))))) (doDivides0 (xu) (xb)) (-. ((aDivisorOf0 (xu) (xa)) /\ (aDivisorOf0 (xu) (xb)))) ((aIdeal0 (xI)) /\ ((xI) = (sdtpldt1 (slsdtgt0 (xa)) (slsdtgt0 (xb))))) ### ConjTree 28
% 2.56/2.76 30. (-. (-. (doDivides0 (xu) (xa)))) ((aIdeal0 (xI)) /\ ((xI) = (sdtpldt1 (slsdtgt0 (xa)) (slsdtgt0 (xb))))) (-. ((aDivisorOf0 (xu) (xa)) /\ (aDivisorOf0 (xu) (xb)))) (doDivides0 (xu) (xb)) (All W0, ((aSet0 W0) => (All W1, ((aElementOf0 W1 W0) => (aElement0 W1))))) (All W0, ((aElement0 W0) => (All W1, ((aDivisorOf0 W1 W0) <=> ((aElement0 W1) /\ (doDivides0 W1 W0)))))) ((aElement0 (xa)) /\ (aElement0 (xb))) ((aElementOf0 (xu) (xI)) /\ (((xu) != (sz00)) /\ (All W0, (((aElementOf0 W0 (xI)) /\ (W0 != (sz00))) => (-. (iLess0 (sbrdtbr0 W0) (sbrdtbr0 (xu)))))))) ### NotNot 29
% 2.56/2.76 31. (-. (-. (doDivides0 (xu) (xb)))) ((aElementOf0 (xu) (xI)) /\ (((xu) != (sz00)) /\ (All W0, (((aElementOf0 W0 (xI)) /\ (W0 != (sz00))) => (-. (iLess0 (sbrdtbr0 W0) (sbrdtbr0 (xu)))))))) ((aElement0 (xa)) /\ (aElement0 (xb))) (All W0, ((aElement0 W0) => (All W1, ((aDivisorOf0 W1 W0) <=> ((aElement0 W1) /\ (doDivides0 W1 W0)))))) (All W0, ((aSet0 W0) => (All W1, ((aElementOf0 W1 W0) => (aElement0 W1))))) (-. ((aDivisorOf0 (xu) (xa)) /\ (aDivisorOf0 (xu) (xb)))) ((aIdeal0 (xI)) /\ ((xI) = (sdtpldt1 (slsdtgt0 (xa)) (slsdtgt0 (xb))))) (-. (-. (doDivides0 (xu) (xa)))) ### NotNot 30
% 2.56/2.76 % SZS output end Proof
% 2.56/2.76 (* END-PROOF *)
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