%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : NUM571+3 : 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 : n004.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 14:43:44 EDT 2022 % Result : Theorem 2.84s 3.06s % Output : Proof 2.84s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.14 % Problem : NUM571+3 : TPTP v8.1.0. Released v4.0.0. % 0.08/0.14 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 0.14/0.36 % Computer : n004.cluster.edu % 0.14/0.36 % Model : x86_64 x86_64 % 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.36 % Memory : 8042.1875MB % 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.36 % CPULimit : 300 % 0.14/0.36 % WCLimit : 600 % 0.14/0.36 % DateTime : Wed Jul 6 06:11:52 EDT 2022 % 0.14/0.36 % CPUTime : % 2.84/3.06 % SZS status Theorem % 2.84/3.06 (* PROOF-FOUND *) % 2.84/3.06 (* BEGIN-PROOF *) % 2.84/3.06 % SZS output start Proof % 2.84/3.06 1. ((xN) != (xN)) ### NotEqual % 2.84/3.06 2. ((xi) = (sz00)) ((xi) != (sz00)) ### Axiom % 2.84/3.06 3. ((sdtlpdtrp0 (xN) (xi)) != (sdtlpdtrp0 (xN) (sz00))) ((xi) = (sz00)) ### NotEqual 1 2 % 2.84/3.06 4. ((xS) != (xS)) ### NotEqual % 2.84/3.06 5. ((xS) != (sdtlpdtrp0 (xN) (xi))) ((sdtlpdtrp0 (xN) (sz00)) = (xS)) ((xi) = (sz00)) ### Trans-sym 3 4 % 2.84/3.06 6. ((szNzAzT0) != (szNzAzT0)) ### NotEqual % 2.84/3.06 7. (-. (aSubsetOf0 (sdtlpdtrp0 (xN) (xi)) (szNzAzT0))) (aSubsetOf0 (xS) (szNzAzT0)) ((xi) = (sz00)) ((sdtlpdtrp0 (xN) (sz00)) = (xS)) ### P-NotP 5 6 % 2.84/3.06 8. (-. ((xi) != (sz00))) ((sdtlpdtrp0 (xN) (sz00)) = (xS)) (aSubsetOf0 (xS) (szNzAzT0)) (-. (aSubsetOf0 (sdtlpdtrp0 (xN) (xi)) (szNzAzT0))) ### NotNot 7 % 2.84/3.06 9. (-. (aSet0 (sdtlpdtrp0 (xN) (xi)))) (aSet0 (sdtlpdtrp0 (xN) (xi))) ### Axiom % 2.84/3.06 10. ((Ex W0, ((aElementOf0 W0 (szNzAzT0)) /\ ((szszuzczcdt0 W0) = (xi)))) /\ ((aSet0 (sdtlpdtrp0 (xN) (xi))) /\ ((All W0, ((aElementOf0 W0 (sdtlpdtrp0 (xN) (xi))) => (aElementOf0 W0 (szNzAzT0)))) /\ ((aSubsetOf0 (sdtlpdtrp0 (xN) (xi)) (szNzAzT0)) /\ (isCountable0 (sdtlpdtrp0 (xN) (xi))))))) (-. (aSet0 (sdtlpdtrp0 (xN) (xi)))) ### ConjTree 9 % 2.84/3.06 11. (((xi) != (sz00)) => ((Ex W0, ((aElementOf0 W0 (szNzAzT0)) /\ ((szszuzczcdt0 W0) = (xi)))) /\ ((aSet0 (sdtlpdtrp0 (xN) (xi))) /\ ((All W0, ((aElementOf0 W0 (sdtlpdtrp0 (xN) (xi))) => (aElementOf0 W0 (szNzAzT0)))) /\ ((aSubsetOf0 (sdtlpdtrp0 (xN) (xi)) (szNzAzT0)) /\ (isCountable0 (sdtlpdtrp0 (xN) (xi)))))))) (-. (aSet0 (sdtlpdtrp0 (xN) (xi)))) (-. (aSubsetOf0 (sdtlpdtrp0 (xN) (xi)) (szNzAzT0))) (aSubsetOf0 (xS) (szNzAzT0)) ((sdtlpdtrp0 (xN) (sz00)) = (xS)) ### Imply 8 10 % 2.84/3.06 12. (-. (All W0, ((aElementOf0 W0 (sdtlpdtrp0 (xN) (xi))) => (aElementOf0 W0 (szNzAzT0))))) (All W0, ((aElementOf0 W0 (sdtlpdtrp0 (xN) (xi))) => (aElementOf0 W0 (szNzAzT0)))) ### Axiom % 2.84/3.06 13. ((Ex W0, ((aElementOf0 W0 (szNzAzT0)) /\ ((szszuzczcdt0 W0) = (xi)))) /\ ((aSet0 (sdtlpdtrp0 (xN) (xi))) /\ ((All W0, ((aElementOf0 W0 (sdtlpdtrp0 (xN) (xi))) => (aElementOf0 W0 (szNzAzT0)))) /\ ((aSubsetOf0 (sdtlpdtrp0 (xN) (xi)) (szNzAzT0)) /\ (isCountable0 (sdtlpdtrp0 (xN) (xi))))))) (-. (All W0, ((aElementOf0 W0 (sdtlpdtrp0 (xN) (xi))) => (aElementOf0 W0 (szNzAzT0))))) ### ConjTree 12 % 2.84/3.06 14. (((xi) != (sz00)) => ((Ex W0, ((aElementOf0 W0 (szNzAzT0)) /\ ((szszuzczcdt0 W0) = (xi)))) /\ ((aSet0 (sdtlpdtrp0 (xN) (xi))) /\ ((All W0, ((aElementOf0 W0 (sdtlpdtrp0 (xN) (xi))) => (aElementOf0 W0 (szNzAzT0)))) /\ ((aSubsetOf0 (sdtlpdtrp0 (xN) (xi)) (szNzAzT0)) /\ (isCountable0 (sdtlpdtrp0 (xN) (xi)))))))) (-. (All W0, ((aElementOf0 W0 (sdtlpdtrp0 (xN) (xi))) => (aElementOf0 W0 (szNzAzT0))))) (-. (aSubsetOf0 (sdtlpdtrp0 (xN) (xi)) (szNzAzT0))) (aSubsetOf0 (xS) (szNzAzT0)) ((sdtlpdtrp0 (xN) (sz00)) = (xS)) ### Imply 8 13 % 2.84/3.06 15. (-. ((aSet0 (sdtlpdtrp0 (xN) (xi))) /\ (All W0, ((aElementOf0 W0 (sdtlpdtrp0 (xN) (xi))) => (aElementOf0 W0 (szNzAzT0)))))) ((sdtlpdtrp0 (xN) (sz00)) = (xS)) (aSubsetOf0 (xS) (szNzAzT0)) (-. (aSubsetOf0 (sdtlpdtrp0 (xN) (xi)) (szNzAzT0))) (((xi) != (sz00)) => ((Ex W0, ((aElementOf0 W0 (szNzAzT0)) /\ ((szszuzczcdt0 W0) = (xi)))) /\ ((aSet0 (sdtlpdtrp0 (xN) (xi))) /\ ((All W0, ((aElementOf0 W0 (sdtlpdtrp0 (xN) (xi))) => (aElementOf0 W0 (szNzAzT0)))) /\ ((aSubsetOf0 (sdtlpdtrp0 (xN) (xi)) (szNzAzT0)) /\ (isCountable0 (sdtlpdtrp0 (xN) (xi)))))))) ### NotAnd 11 14 % 2.84/3.06 16. (-. (((aSet0 (sdtlpdtrp0 (xN) (xi))) /\ (All W0, ((aElementOf0 W0 (sdtlpdtrp0 (xN) (xi))) => (aElementOf0 W0 (szNzAzT0))))) \/ (aSubsetOf0 (sdtlpdtrp0 (xN) (xi)) (szNzAzT0)))) (((xi) != (sz00)) => ((Ex W0, ((aElementOf0 W0 (szNzAzT0)) /\ ((szszuzczcdt0 W0) = (xi)))) /\ ((aSet0 (sdtlpdtrp0 (xN) (xi))) /\ ((All W0, ((aElementOf0 W0 (sdtlpdtrp0 (xN) (xi))) => (aElementOf0 W0 (szNzAzT0)))) /\ ((aSubsetOf0 (sdtlpdtrp0 (xN) (xi)) (szNzAzT0)) /\ (isCountable0 (sdtlpdtrp0 (xN) (xi)))))))) (aSubsetOf0 (xS) (szNzAzT0)) ((sdtlpdtrp0 (xN) (sz00)) = (xS)) ### NotOr 15 % 2.84/3.06 17. (-. (isCountable0 (sdtlpdtrp0 (xN) (xi)))) (isCountable0 (xS)) ((xi) = (sz00)) ((sdtlpdtrp0 (xN) (sz00)) = (xS)) ### P-NotP 5 % 2.84/3.06 18. (-. ((xi) != (sz00))) ((sdtlpdtrp0 (xN) (sz00)) = (xS)) (isCountable0 (xS)) (-. (isCountable0 (sdtlpdtrp0 (xN) (xi)))) ### NotNot 17 % 2.84/3.06 19. (-. (isCountable0 (sdtlpdtrp0 (xN) (xi)))) (isCountable0 (sdtlpdtrp0 (xN) (xi))) ### Axiom % 2.84/3.06 20. ((Ex W0, ((aElementOf0 W0 (szNzAzT0)) /\ ((szszuzczcdt0 W0) = (xi)))) /\ ((aSet0 (sdtlpdtrp0 (xN) (xi))) /\ ((All W0, ((aElementOf0 W0 (sdtlpdtrp0 (xN) (xi))) => (aElementOf0 W0 (szNzAzT0)))) /\ ((aSubsetOf0 (sdtlpdtrp0 (xN) (xi)) (szNzAzT0)) /\ (isCountable0 (sdtlpdtrp0 (xN) (xi))))))) (-. (isCountable0 (sdtlpdtrp0 (xN) (xi)))) ### ConjTree 19 % 2.84/3.06 21. (((xi) != (sz00)) => ((Ex W0, ((aElementOf0 W0 (szNzAzT0)) /\ ((szszuzczcdt0 W0) = (xi)))) /\ ((aSet0 (sdtlpdtrp0 (xN) (xi))) /\ ((All W0, ((aElementOf0 W0 (sdtlpdtrp0 (xN) (xi))) => (aElementOf0 W0 (szNzAzT0)))) /\ ((aSubsetOf0 (sdtlpdtrp0 (xN) (xi)) (szNzAzT0)) /\ (isCountable0 (sdtlpdtrp0 (xN) (xi)))))))) (-. (isCountable0 (sdtlpdtrp0 (xN) (xi)))) (isCountable0 (xS)) ((sdtlpdtrp0 (xN) (sz00)) = (xS)) ### Imply 18 20 % 2.84/3.06 22. (-. ((((aSet0 (sdtlpdtrp0 (xN) (xi))) /\ (All W0, ((aElementOf0 W0 (sdtlpdtrp0 (xN) (xi))) => (aElementOf0 W0 (szNzAzT0))))) \/ (aSubsetOf0 (sdtlpdtrp0 (xN) (xi)) (szNzAzT0))) /\ (isCountable0 (sdtlpdtrp0 (xN) (xi))))) (isCountable0 (xS)) ((sdtlpdtrp0 (xN) (sz00)) = (xS)) (aSubsetOf0 (xS) (szNzAzT0)) (((xi) != (sz00)) => ((Ex W0, ((aElementOf0 W0 (szNzAzT0)) /\ ((szszuzczcdt0 W0) = (xi)))) /\ ((aSet0 (sdtlpdtrp0 (xN) (xi))) /\ ((All W0, ((aElementOf0 W0 (sdtlpdtrp0 (xN) (xi))) => (aElementOf0 W0 (szNzAzT0)))) /\ ((aSubsetOf0 (sdtlpdtrp0 (xN) (xi)) (szNzAzT0)) /\ (isCountable0 (sdtlpdtrp0 (xN) (xi)))))))) ### NotAnd 16 21 % 2.84/3.06 23. ((aSet0 (xS)) /\ ((All W0, ((aElementOf0 W0 (xS)) => (aElementOf0 W0 (szNzAzT0)))) /\ ((aSubsetOf0 (xS) (szNzAzT0)) /\ (isCountable0 (xS))))) (((xi) != (sz00)) => ((Ex W0, ((aElementOf0 W0 (szNzAzT0)) /\ ((szszuzczcdt0 W0) = (xi)))) /\ ((aSet0 (sdtlpdtrp0 (xN) (xi))) /\ ((All W0, ((aElementOf0 W0 (sdtlpdtrp0 (xN) (xi))) => (aElementOf0 W0 (szNzAzT0)))) /\ ((aSubsetOf0 (sdtlpdtrp0 (xN) (xi)) (szNzAzT0)) /\ (isCountable0 (sdtlpdtrp0 (xN) (xi)))))))) ((sdtlpdtrp0 (xN) (sz00)) = (xS)) (-. ((((aSet0 (sdtlpdtrp0 (xN) (xi))) /\ (All W0, ((aElementOf0 W0 (sdtlpdtrp0 (xN) (xi))) => (aElementOf0 W0 (szNzAzT0))))) \/ (aSubsetOf0 (sdtlpdtrp0 (xN) (xi)) (szNzAzT0))) /\ (isCountable0 (sdtlpdtrp0 (xN) (xi))))) ### ConjTree 22 % 2.84/3.06 24. ((aFunction0 (xN)) /\ (((szDzozmdt0 (xN)) = (szNzAzT0)) /\ (((sdtlpdtrp0 (xN) (sz00)) = (xS)) /\ (All W0, ((aElementOf0 W0 (szNzAzT0)) => (((((aSet0 (sdtlpdtrp0 (xN) W0)) /\ (All W1, ((aElementOf0 W1 (sdtlpdtrp0 (xN) W0)) => (aElementOf0 W1 (szNzAzT0))))) \/ (aSubsetOf0 (sdtlpdtrp0 (xN) W0) (szNzAzT0))) /\ (isCountable0 (sdtlpdtrp0 (xN) W0))) => ((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) (sdtlpdtrp0 (xN) W0)) /\ ((All W1, ((aElementOf0 W1 (sdtlpdtrp0 (xN) W0)) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) W1))) /\ ((aSet0 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) /\ ((All W1, ((aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) <=> ((aElement0 W1) /\ ((aElementOf0 W1 (sdtlpdtrp0 (xN) W0)) /\ (W1 != (szmzizndt0 (sdtlpdtrp0 (xN) W0))))))) /\ ((aSet0 (sdtlpdtrp0 (xN) (szszuzczcdt0 W0))) /\ ((All W1, ((aElementOf0 W1 (sdtlpdtrp0 (xN) (szszuzczcdt0 W0))) => (aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))))) /\ ((aSubsetOf0 (sdtlpdtrp0 (xN) (szszuzczcdt0 W0)) (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) /\ (isCountable0 (sdtlpdtrp0 (xN) (szszuzczcdt0 W0)))))))))))))))) (-. ((((aSet0 (sdtlpdtrp0 (xN) (xi))) /\ (All W0, ((aElementOf0 W0 (sdtlpdtrp0 (xN) (xi))) => (aElementOf0 W0 (szNzAzT0))))) \/ (aSubsetOf0 (sdtlpdtrp0 (xN) (xi)) (szNzAzT0))) /\ (isCountable0 (sdtlpdtrp0 (xN) (xi))))) (((xi) != (sz00)) => ((Ex W0, ((aElementOf0 W0 (szNzAzT0)) /\ ((szszuzczcdt0 W0) = (xi)))) /\ ((aSet0 (sdtlpdtrp0 (xN) (xi))) /\ ((All W0, ((aElementOf0 W0 (sdtlpdtrp0 (xN) (xi))) => (aElementOf0 W0 (szNzAzT0)))) /\ ((aSubsetOf0 (sdtlpdtrp0 (xN) (xi)) (szNzAzT0)) /\ (isCountable0 (sdtlpdtrp0 (xN) (xi)))))))) ((aSet0 (xS)) /\ ((All W0, ((aElementOf0 W0 (xS)) => (aElementOf0 W0 (szNzAzT0)))) /\ ((aSubsetOf0 (xS) (szNzAzT0)) /\ (isCountable0 (xS))))) ### ConjTree 23 % 2.84/3.06 % SZS output end Proof % 2.84/3.06 (* END-PROOF *) %------------------------------------------------------------------------------