%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : NUM588+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 : n006.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 14:43:54 EDT 2022 % Result : Theorem 0.61s 0.79s % Output : Proof 0.61s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.11 % Problem : NUM588+3 : TPTP v8.1.0. Released v4.0.0. % 0.06/0.12 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 0.12/0.33 % Computer : n006.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 : Wed Jul 6 21:26:21 EDT 2022 % 0.12/0.33 % CPUTime : % 0.61/0.79 % SZS status Theorem % 0.61/0.79 (* PROOF-FOUND *) % 0.61/0.79 (* BEGIN-PROOF *) % 0.61/0.79 % SZS output start Proof % 0.61/0.79 1. (aElementOf0 T_0 T_1) (-. (aElementOf0 T_0 T_1)) ### Axiom % 0.61/0.79 2. (-. (aElementOf0 T_0 T_2)) (aElementOf0 T_0 T_2) ### Axiom % 0.61/0.79 3. ((aElementOf0 T_0 T_1) => (aElementOf0 T_0 T_2)) (-. (aElementOf0 T_0 T_2)) (aElementOf0 T_0 T_1) ### Imply 1 2 % 0.61/0.79 4. (All W3, ((aElementOf0 W3 T_1) => (aElementOf0 W3 T_2))) (aElementOf0 T_0 T_1) (-. (aElementOf0 T_0 T_2)) ### All 3 % 0.61/0.79 5. (-. (aElementOf0 T_0 (sdtmndt0 (sdtlpdtrp0 (xN) T_3) (szmzizndt0 (sdtlpdtrp0 (xN) T_3))))) (aElementOf0 T_0 (sdtmndt0 (sdtlpdtrp0 (xN) T_3) (szmzizndt0 (sdtlpdtrp0 (xN) T_3)))) ### Axiom % 0.61/0.79 6. ((aElementOf0 T_0 T_2) => (aElementOf0 T_0 (sdtmndt0 (sdtlpdtrp0 (xN) T_3) (szmzizndt0 (sdtlpdtrp0 (xN) T_3))))) (-. (aElementOf0 T_0 (sdtmndt0 (sdtlpdtrp0 (xN) T_3) (szmzizndt0 (sdtlpdtrp0 (xN) T_3))))) (aElementOf0 T_0 T_1) (All W3, ((aElementOf0 W3 T_1) => (aElementOf0 W3 T_2))) ### Imply 4 5 % 0.61/0.79 7. (All W2, ((aElementOf0 W2 T_2) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) T_3) (szmzizndt0 (sdtlpdtrp0 (xN) T_3)))))) (All W3, ((aElementOf0 W3 T_1) => (aElementOf0 W3 T_2))) (aElementOf0 T_0 T_1) (-. (aElementOf0 T_0 (sdtmndt0 (sdtlpdtrp0 (xN) T_3) (szmzizndt0 (sdtlpdtrp0 (xN) T_3))))) ### All 6 % 0.61/0.79 8. (-. ((aElementOf0 T_0 T_1) => (aElementOf0 T_0 (sdtmndt0 (sdtlpdtrp0 (xN) T_3) (szmzizndt0 (sdtlpdtrp0 (xN) T_3)))))) (All W3, ((aElementOf0 W3 T_1) => (aElementOf0 W3 T_2))) (All W2, ((aElementOf0 W2 T_2) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) T_3) (szmzizndt0 (sdtlpdtrp0 (xN) T_3)))))) ### NotImply 7 % 0.61/0.79 9. (-. (All W3, ((aElementOf0 W3 T_1) => (aElementOf0 W3 (sdtmndt0 (sdtlpdtrp0 (xN) T_3) (szmzizndt0 (sdtlpdtrp0 (xN) T_3))))))) (All W2, ((aElementOf0 W2 T_2) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) T_3) (szmzizndt0 (sdtlpdtrp0 (xN) T_3)))))) (All W3, ((aElementOf0 W3 T_1) => (aElementOf0 W3 T_2))) ### NotAllEx 8 % 0.61/0.79 10. (-. (((aSet0 T_1) /\ ((All W3, ((aElementOf0 W3 T_1) => (aElementOf0 W3 T_2))) /\ ((aSubsetOf0 T_1 T_2) /\ (((sbrdtbr0 T_1) = (xk)) /\ (aElementOf0 T_1 (slbdtsldtrb0 T_2 (xk))))))) => (((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) T_3)) (sdtlpdtrp0 (xN) T_3)) /\ (All W1, ((aElementOf0 W1 (sdtlpdtrp0 (xN) T_3)) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) T_3)) W1)))) => (((aSet0 (sdtmndt0 (sdtlpdtrp0 (xN) T_3) (szmzizndt0 (sdtlpdtrp0 (xN) T_3)))) /\ (All W1, ((aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) T_3) (szmzizndt0 (sdtlpdtrp0 (xN) T_3)))) <=> ((aElement0 W1) /\ ((aElementOf0 W1 (sdtlpdtrp0 (xN) T_3)) /\ (W1 != (szmzizndt0 (sdtlpdtrp0 (xN) T_3)))))))) => ((All W3, ((aElementOf0 W3 T_1) => (aElementOf0 W3 (sdtmndt0 (sdtlpdtrp0 (xN) T_3) (szmzizndt0 (sdtlpdtrp0 (xN) T_3)))))) \/ ((aSubsetOf0 T_1 (sdtmndt0 (sdtlpdtrp0 (xN) T_3) (szmzizndt0 (sdtlpdtrp0 (xN) T_3)))) \/ (aElementOf0 T_1 (slbdtsldtrb0 (sdtmndt0 (sdtlpdtrp0 (xN) T_3) (szmzizndt0 (sdtlpdtrp0 (xN) T_3))) (xk))))))))) (All W2, ((aElementOf0 W2 T_2) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) T_3) (szmzizndt0 (sdtlpdtrp0 (xN) T_3)))))) ### ConjTree 9 % 0.61/0.79 11. (-. (All W2, (((aSet0 W2) /\ ((All W3, ((aElementOf0 W3 W2) => (aElementOf0 W3 T_2))) /\ ((aSubsetOf0 W2 T_2) /\ (((sbrdtbr0 W2) = (xk)) /\ (aElementOf0 W2 (slbdtsldtrb0 T_2 (xk))))))) => (((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) T_3)) (sdtlpdtrp0 (xN) T_3)) /\ (All W1, ((aElementOf0 W1 (sdtlpdtrp0 (xN) T_3)) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) T_3)) W1)))) => (((aSet0 (sdtmndt0 (sdtlpdtrp0 (xN) T_3) (szmzizndt0 (sdtlpdtrp0 (xN) T_3)))) /\ (All W1, ((aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) T_3) (szmzizndt0 (sdtlpdtrp0 (xN) T_3)))) <=> ((aElement0 W1) /\ ((aElementOf0 W1 (sdtlpdtrp0 (xN) T_3)) /\ (W1 != (szmzizndt0 (sdtlpdtrp0 (xN) T_3)))))))) => ((All W3, ((aElementOf0 W3 W2) => (aElementOf0 W3 (sdtmndt0 (sdtlpdtrp0 (xN) T_3) (szmzizndt0 (sdtlpdtrp0 (xN) T_3)))))) \/ ((aSubsetOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) T_3) (szmzizndt0 (sdtlpdtrp0 (xN) T_3)))) \/ (aElementOf0 W2 (slbdtsldtrb0 (sdtmndt0 (sdtlpdtrp0 (xN) T_3) (szmzizndt0 (sdtlpdtrp0 (xN) T_3))) (xk)))))))))) (All W2, ((aElementOf0 W2 T_2) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) T_3) (szmzizndt0 (sdtlpdtrp0 (xN) T_3)))))) ### NotAllEx 10 % 0.61/0.79 12. (-. (((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) T_3)) (sdtlpdtrp0 (xN) T_3)) /\ ((All W1, ((aElementOf0 W1 (sdtlpdtrp0 (xN) T_3)) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) T_3)) W1))) /\ ((aSet0 (sdtmndt0 (sdtlpdtrp0 (xN) T_3) (szmzizndt0 (sdtlpdtrp0 (xN) T_3)))) /\ ((All W1, ((aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) T_3) (szmzizndt0 (sdtlpdtrp0 (xN) T_3)))) <=> ((aElement0 W1) /\ ((aElementOf0 W1 (sdtlpdtrp0 (xN) T_3)) /\ (W1 != (szmzizndt0 (sdtlpdtrp0 (xN) T_3))))))) /\ ((aSet0 T_2) /\ ((All W2, ((aElementOf0 W2 T_2) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) T_3) (szmzizndt0 (sdtlpdtrp0 (xN) T_3)))))) /\ ((aSubsetOf0 T_2 (sdtmndt0 (sdtlpdtrp0 (xN) T_3) (szmzizndt0 (sdtlpdtrp0 (xN) T_3)))) /\ (isCountable0 T_2)))))))) => (All W2, (((aSet0 W2) /\ ((All W3, ((aElementOf0 W3 W2) => (aElementOf0 W3 T_2))) /\ ((aSubsetOf0 W2 T_2) /\ (((sbrdtbr0 W2) = (xk)) /\ (aElementOf0 W2 (slbdtsldtrb0 T_2 (xk))))))) => (((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) T_3)) (sdtlpdtrp0 (xN) T_3)) /\ (All W1, ((aElementOf0 W1 (sdtlpdtrp0 (xN) T_3)) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) T_3)) W1)))) => (((aSet0 (sdtmndt0 (sdtlpdtrp0 (xN) T_3) (szmzizndt0 (sdtlpdtrp0 (xN) T_3)))) /\ (All W1, ((aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) T_3) (szmzizndt0 (sdtlpdtrp0 (xN) T_3)))) <=> ((aElement0 W1) /\ ((aElementOf0 W1 (sdtlpdtrp0 (xN) T_3)) /\ (W1 != (szmzizndt0 (sdtlpdtrp0 (xN) T_3)))))))) => ((All W3, ((aElementOf0 W3 W2) => (aElementOf0 W3 (sdtmndt0 (sdtlpdtrp0 (xN) T_3) (szmzizndt0 (sdtlpdtrp0 (xN) T_3)))))) \/ ((aSubsetOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) T_3) (szmzizndt0 (sdtlpdtrp0 (xN) T_3)))) \/ (aElementOf0 W2 (slbdtsldtrb0 (sdtmndt0 (sdtlpdtrp0 (xN) T_3) (szmzizndt0 (sdtlpdtrp0 (xN) T_3))) (xk))))))))))) ### ConjTree 11 % 0.61/0.79 13. (-. (All W1, (((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) T_3)) (sdtlpdtrp0 (xN) T_3)) /\ ((All W1, ((aElementOf0 W1 (sdtlpdtrp0 (xN) T_3)) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) T_3)) W1))) /\ ((aSet0 (sdtmndt0 (sdtlpdtrp0 (xN) T_3) (szmzizndt0 (sdtlpdtrp0 (xN) T_3)))) /\ ((All W1, ((aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) T_3) (szmzizndt0 (sdtlpdtrp0 (xN) T_3)))) <=> ((aElement0 W1) /\ ((aElementOf0 W1 (sdtlpdtrp0 (xN) T_3)) /\ (W1 != (szmzizndt0 (sdtlpdtrp0 (xN) T_3))))))) /\ ((aSet0 W1) /\ ((All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) T_3) (szmzizndt0 (sdtlpdtrp0 (xN) T_3)))))) /\ ((aSubsetOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) T_3) (szmzizndt0 (sdtlpdtrp0 (xN) T_3)))) /\ (isCountable0 W1)))))))) => (All W2, (((aSet0 W2) /\ ((All W3, ((aElementOf0 W3 W2) => (aElementOf0 W3 W1))) /\ ((aSubsetOf0 W2 W1) /\ (((sbrdtbr0 W2) = (xk)) /\ (aElementOf0 W2 (slbdtsldtrb0 W1 (xk))))))) => (((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) T_3)) (sdtlpdtrp0 (xN) T_3)) /\ (All W1, ((aElementOf0 W1 (sdtlpdtrp0 (xN) T_3)) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) T_3)) W1)))) => (((aSet0 (sdtmndt0 (sdtlpdtrp0 (xN) T_3) (szmzizndt0 (sdtlpdtrp0 (xN) T_3)))) /\ (All W1, ((aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) T_3) (szmzizndt0 (sdtlpdtrp0 (xN) T_3)))) <=> ((aElement0 W1) /\ ((aElementOf0 W1 (sdtlpdtrp0 (xN) T_3)) /\ (W1 != (szmzizndt0 (sdtlpdtrp0 (xN) T_3)))))))) => ((All W3, ((aElementOf0 W3 W2) => (aElementOf0 W3 (sdtmndt0 (sdtlpdtrp0 (xN) T_3) (szmzizndt0 (sdtlpdtrp0 (xN) T_3)))))) \/ ((aSubsetOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) T_3) (szmzizndt0 (sdtlpdtrp0 (xN) T_3)))) \/ (aElementOf0 W2 (slbdtsldtrb0 (sdtmndt0 (sdtlpdtrp0 (xN) T_3) (szmzizndt0 (sdtlpdtrp0 (xN) T_3))) (xk)))))))))))) ### NotAllEx 12 % 0.61/0.79 14. (-. ((aElementOf0 T_3 (szNzAzT0)) => (All W1, (((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) T_3)) (sdtlpdtrp0 (xN) T_3)) /\ ((All W1, ((aElementOf0 W1 (sdtlpdtrp0 (xN) T_3)) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) T_3)) W1))) /\ ((aSet0 (sdtmndt0 (sdtlpdtrp0 (xN) T_3) (szmzizndt0 (sdtlpdtrp0 (xN) T_3)))) /\ ((All W1, ((aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) T_3) (szmzizndt0 (sdtlpdtrp0 (xN) T_3)))) <=> ((aElement0 W1) /\ ((aElementOf0 W1 (sdtlpdtrp0 (xN) T_3)) /\ (W1 != (szmzizndt0 (sdtlpdtrp0 (xN) T_3))))))) /\ ((aSet0 W1) /\ ((All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) T_3) (szmzizndt0 (sdtlpdtrp0 (xN) T_3)))))) /\ ((aSubsetOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) T_3) (szmzizndt0 (sdtlpdtrp0 (xN) T_3)))) /\ (isCountable0 W1)))))))) => (All W2, (((aSet0 W2) /\ ((All W3, ((aElementOf0 W3 W2) => (aElementOf0 W3 W1))) /\ ((aSubsetOf0 W2 W1) /\ (((sbrdtbr0 W2) = (xk)) /\ (aElementOf0 W2 (slbdtsldtrb0 W1 (xk))))))) => (((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) T_3)) (sdtlpdtrp0 (xN) T_3)) /\ (All W1, ((aElementOf0 W1 (sdtlpdtrp0 (xN) T_3)) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) T_3)) W1)))) => (((aSet0 (sdtmndt0 (sdtlpdtrp0 (xN) T_3) (szmzizndt0 (sdtlpdtrp0 (xN) T_3)))) /\ (All W1, ((aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) T_3) (szmzizndt0 (sdtlpdtrp0 (xN) T_3)))) <=> ((aElement0 W1) /\ ((aElementOf0 W1 (sdtlpdtrp0 (xN) T_3)) /\ (W1 != (szmzizndt0 (sdtlpdtrp0 (xN) T_3)))))))) => ((All W3, ((aElementOf0 W3 W2) => (aElementOf0 W3 (sdtmndt0 (sdtlpdtrp0 (xN) T_3) (szmzizndt0 (sdtlpdtrp0 (xN) T_3)))))) \/ ((aSubsetOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) T_3) (szmzizndt0 (sdtlpdtrp0 (xN) T_3)))) \/ (aElementOf0 W2 (slbdtsldtrb0 (sdtmndt0 (sdtlpdtrp0 (xN) T_3) (szmzizndt0 (sdtlpdtrp0 (xN) T_3))) (xk))))))))))))) ### NotImply 13 % 0.61/0.79 15. (-. (All W0, ((aElementOf0 W0 (szNzAzT0)) => (All W1, (((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 W1) /\ ((All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))))) /\ ((aSubsetOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) /\ (isCountable0 W1)))))))) => (All W2, (((aSet0 W2) /\ ((All W3, ((aElementOf0 W3 W2) => (aElementOf0 W3 W1))) /\ ((aSubsetOf0 W2 W1) /\ (((sbrdtbr0 W2) = (xk)) /\ (aElementOf0 W2 (slbdtsldtrb0 W1 (xk))))))) => (((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)))))))) => ((All W3, ((aElementOf0 W3 W2) => (aElementOf0 W3 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))))) \/ ((aSubsetOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) \/ (aElementOf0 W2 (slbdtsldtrb0 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0))) (xk)))))))))))))) ### NotAllEx 14 % 0.61/0.79 % SZS output end Proof % 0.61/0.79 (* END-PROOF *) %------------------------------------------------------------------------------