%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : NUM578+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 : n003.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 14:43:48 EDT 2022 % Result : Theorem 2.56s 2.72s % Output : Proof 2.56s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.11 % Problem : NUM578+3 : TPTP v8.1.0. Released v4.0.0. % 0.11/0.12 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 0.11/0.32 % Computer : n003.cluster.edu % 0.11/0.32 % Model : x86_64 x86_64 % 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.32 % Memory : 8042.1875MB % 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.32 % CPULimit : 300 % 0.11/0.32 % WCLimit : 600 % 0.11/0.32 % DateTime : Thu Jul 7 18:50:12 EDT 2022 % 0.11/0.33 % CPUTime : % 2.56/2.72 % SZS status Theorem % 2.56/2.72 (* PROOF-FOUND *) % 2.56/2.72 (* BEGIN-PROOF *) % 2.56/2.72 % SZS output start Proof % 2.56/2.72 1. ((xi) != (xj)) ((xi) = (xj)) ### Axiom % 2.56/2.72 2. (aElementOf0 (xj) (szNzAzT0)) (-. (aElementOf0 (xj) (szNzAzT0))) ### Axiom % 2.56/2.72 3. (aElementOf0 (xi) (szNzAzT0)) (-. (aElementOf0 (xi) (szNzAzT0))) ### Axiom % 2.56/2.72 4. (sdtlseqdt0 (szszuzczcdt0 (xj)) (xi)) (-. (sdtlseqdt0 (szszuzczcdt0 (xj)) (xi))) ### Axiom % 2.56/2.72 5. ((szmzizndt0 (sdtlpdtrp0 (xN) (xi))) = (szmzizndt0 (sdtlpdtrp0 (xN) (xj)))) ((szmzizndt0 (sdtlpdtrp0 (xN) (xi))) != (szmzizndt0 (sdtlpdtrp0 (xN) (xj)))) ### Axiom % 2.56/2.72 6. ((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) (xj))) (sdtlpdtrp0 (xN) (xj))) /\ ((All W1, ((aElementOf0 W1 (sdtlpdtrp0 (xN) (xj))) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) (xj))) W1))) /\ ((aSet0 (sdtmndt0 (sdtlpdtrp0 (xN) (xj)) (szmzizndt0 (sdtlpdtrp0 (xN) (xj))))) /\ ((All W1, ((aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xj)) (szmzizndt0 (sdtlpdtrp0 (xN) (xj))))) <=> ((aElement0 W1) /\ ((aElementOf0 W1 (sdtlpdtrp0 (xN) (xj))) /\ (W1 != (szmzizndt0 (sdtlpdtrp0 (xN) (xj)))))))) /\ ((All W2, ((aElementOf0 W2 (sdtlpdtrp0 (xN) (xi))) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) (xj)) (szmzizndt0 (sdtlpdtrp0 (xN) (xj))))))) /\ ((aSubsetOf0 (sdtlpdtrp0 (xN) (xi)) (sdtmndt0 (sdtlpdtrp0 (xN) (xj)) (szmzizndt0 (sdtlpdtrp0 (xN) (xj))))) /\ (-. (((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) (xi))) (sdtlpdtrp0 (xN) (xi))) /\ (All W0, ((aElementOf0 W0 (sdtlpdtrp0 (xN) (xi))) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) (xi))) W0)))) => (((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) (xi))) (sdtlpdtrp0 (xN) (xj))) /\ (All W0, ((aElementOf0 W0 (sdtlpdtrp0 (xN) (xj))) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) (xi))) W0)))) \/ ((szmzizndt0 (sdtlpdtrp0 (xN) (xi))) = (szmzizndt0 (sdtlpdtrp0 (xN) (xj))))))))))))) ((szmzizndt0 (sdtlpdtrp0 (xN) (xi))) = (szmzizndt0 (sdtlpdtrp0 (xN) (xj)))) ### ConjTree 5 % 2.56/2.72 7. (((aElementOf0 (xj) (szNzAzT0)) /\ (aElementOf0 (xi) (szNzAzT0))) => ((sdtlseqdt0 (szszuzczcdt0 (xj)) (xi)) => ((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) (xj))) (sdtlpdtrp0 (xN) (xj))) /\ ((All W1, ((aElementOf0 W1 (sdtlpdtrp0 (xN) (xj))) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) (xj))) W1))) /\ ((aSet0 (sdtmndt0 (sdtlpdtrp0 (xN) (xj)) (szmzizndt0 (sdtlpdtrp0 (xN) (xj))))) /\ ((All W1, ((aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xj)) (szmzizndt0 (sdtlpdtrp0 (xN) (xj))))) <=> ((aElement0 W1) /\ ((aElementOf0 W1 (sdtlpdtrp0 (xN) (xj))) /\ (W1 != (szmzizndt0 (sdtlpdtrp0 (xN) (xj)))))))) /\ ((All W2, ((aElementOf0 W2 (sdtlpdtrp0 (xN) (xi))) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) (xj)) (szmzizndt0 (sdtlpdtrp0 (xN) (xj))))))) /\ ((aSubsetOf0 (sdtlpdtrp0 (xN) (xi)) (sdtmndt0 (sdtlpdtrp0 (xN) (xj)) (szmzizndt0 (sdtlpdtrp0 (xN) (xj))))) /\ (-. (((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) (xi))) (sdtlpdtrp0 (xN) (xi))) /\ (All W0, ((aElementOf0 W0 (sdtlpdtrp0 (xN) (xi))) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) (xi))) W0)))) => (((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) (xi))) (sdtlpdtrp0 (xN) (xj))) /\ (All W0, ((aElementOf0 W0 (sdtlpdtrp0 (xN) (xj))) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) (xi))) W0)))) \/ ((szmzizndt0 (sdtlpdtrp0 (xN) (xi))) = (szmzizndt0 (sdtlpdtrp0 (xN) (xj))))))))))))))) ((szmzizndt0 (sdtlpdtrp0 (xN) (xi))) = (szmzizndt0 (sdtlpdtrp0 (xN) (xj)))) (sdtlseqdt0 (szszuzczcdt0 (xj)) (xi)) (aElementOf0 (xi) (szNzAzT0)) (aElementOf0 (xj) (szNzAzT0)) ### DisjTree 2 3 4 6 % 2.56/2.72 8. (All W1, (((aElementOf0 (xj) (szNzAzT0)) /\ (aElementOf0 W1 (szNzAzT0))) => ((sdtlseqdt0 (szszuzczcdt0 (xj)) W1) => ((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) (xj))) (sdtlpdtrp0 (xN) (xj))) /\ ((All W1, ((aElementOf0 W1 (sdtlpdtrp0 (xN) (xj))) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) (xj))) W1))) /\ ((aSet0 (sdtmndt0 (sdtlpdtrp0 (xN) (xj)) (szmzizndt0 (sdtlpdtrp0 (xN) (xj))))) /\ ((All W1, ((aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xj)) (szmzizndt0 (sdtlpdtrp0 (xN) (xj))))) <=> ((aElement0 W1) /\ ((aElementOf0 W1 (sdtlpdtrp0 (xN) (xj))) /\ (W1 != (szmzizndt0 (sdtlpdtrp0 (xN) (xj)))))))) /\ ((All W2, ((aElementOf0 W2 (sdtlpdtrp0 (xN) W1)) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) (xj)) (szmzizndt0 (sdtlpdtrp0 (xN) (xj))))))) /\ ((aSubsetOf0 (sdtlpdtrp0 (xN) W1) (sdtmndt0 (sdtlpdtrp0 (xN) (xj)) (szmzizndt0 (sdtlpdtrp0 (xN) (xj))))) /\ (-. (((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) W1)) (sdtlpdtrp0 (xN) W1)) /\ (All W2, ((aElementOf0 W2 (sdtlpdtrp0 (xN) W1)) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) W1)) W2)))) => (((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) W1)) (sdtlpdtrp0 (xN) (xj))) /\ (All W2, ((aElementOf0 W2 (sdtlpdtrp0 (xN) (xj))) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) W1)) W2)))) \/ ((szmzizndt0 (sdtlpdtrp0 (xN) W1)) = (szmzizndt0 (sdtlpdtrp0 (xN) (xj)))))))))))))))) (aElementOf0 (xj) (szNzAzT0)) (aElementOf0 (xi) (szNzAzT0)) (sdtlseqdt0 (szszuzczcdt0 (xj)) (xi)) ((szmzizndt0 (sdtlpdtrp0 (xN) (xi))) = (szmzizndt0 (sdtlpdtrp0 (xN) (xj)))) ### All 7 % 2.56/2.72 9. (All W0, (All W1, (((aElementOf0 W0 (szNzAzT0)) /\ (aElementOf0 W1 (szNzAzT0))) => ((sdtlseqdt0 (szszuzczcdt0 W0) 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))))))) /\ ((All W2, ((aElementOf0 W2 (sdtlpdtrp0 (xN) W1)) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))))) /\ ((aSubsetOf0 (sdtlpdtrp0 (xN) W1) (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) /\ (-. (((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) W1)) (sdtlpdtrp0 (xN) W1)) /\ (All W2, ((aElementOf0 W2 (sdtlpdtrp0 (xN) W1)) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) W1)) W2)))) => (((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) W1)) (sdtlpdtrp0 (xN) W0)) /\ (All W2, ((aElementOf0 W2 (sdtlpdtrp0 (xN) W0)) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) W1)) W2)))) \/ ((szmzizndt0 (sdtlpdtrp0 (xN) W1)) = (szmzizndt0 (sdtlpdtrp0 (xN) W0)))))))))))))))) ((szmzizndt0 (sdtlpdtrp0 (xN) (xi))) = (szmzizndt0 (sdtlpdtrp0 (xN) (xj)))) (sdtlseqdt0 (szszuzczcdt0 (xj)) (xi)) (aElementOf0 (xi) (szNzAzT0)) (aElementOf0 (xj) (szNzAzT0)) ### All 8 % 2.56/2.72 10. (aElementOf0 (xi) (szNzAzT0)) (-. (aElementOf0 (xi) (szNzAzT0))) ### Axiom % 2.56/2.72 11. (aElementOf0 (xj) (szNzAzT0)) (-. (aElementOf0 (xj) (szNzAzT0))) ### Axiom % 2.56/2.72 12. (sdtlseqdt0 (szszuzczcdt0 (xi)) (xj)) (-. (sdtlseqdt0 (szszuzczcdt0 (xi)) (xj))) ### Axiom % 2.56/2.72 13. ((szmzizndt0 (sdtlpdtrp0 (xN) (xi))) = (szmzizndt0 (sdtlpdtrp0 (xN) (xj)))) ((szmzizndt0 (sdtlpdtrp0 (xN) (xj))) != (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))) ### Sym(=) % 2.56/2.72 14. ((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) (xi))) (sdtlpdtrp0 (xN) (xi))) /\ ((All W0, ((aElementOf0 W0 (sdtlpdtrp0 (xN) (xi))) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) (xi))) W0))) /\ ((aSet0 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))) /\ ((All W1, ((aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))) <=> ((aElement0 W1) /\ ((aElementOf0 W1 (sdtlpdtrp0 (xN) (xi))) /\ (W1 != (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))))))) /\ ((All W2, ((aElementOf0 W2 (sdtlpdtrp0 (xN) (xj))) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))))) /\ ((aSubsetOf0 (sdtlpdtrp0 (xN) (xj)) (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))) /\ (-. (((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) (xj))) (sdtlpdtrp0 (xN) (xj))) /\ (All W1, ((aElementOf0 W1 (sdtlpdtrp0 (xN) (xj))) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) (xj))) W1)))) => (((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) (xj))) (sdtlpdtrp0 (xN) (xi))) /\ (All W2, ((aElementOf0 W2 (sdtlpdtrp0 (xN) (xi))) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) (xj))) W2)))) \/ ((szmzizndt0 (sdtlpdtrp0 (xN) (xj))) = (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))))))))))) ((szmzizndt0 (sdtlpdtrp0 (xN) (xi))) = (szmzizndt0 (sdtlpdtrp0 (xN) (xj)))) ### ConjTree 13 % 2.56/2.72 15. (((aElementOf0 (xi) (szNzAzT0)) /\ (aElementOf0 (xj) (szNzAzT0))) => ((sdtlseqdt0 (szszuzczcdt0 (xi)) (xj)) => ((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) (xi))) (sdtlpdtrp0 (xN) (xi))) /\ ((All W0, ((aElementOf0 W0 (sdtlpdtrp0 (xN) (xi))) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) (xi))) W0))) /\ ((aSet0 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))) /\ ((All W1, ((aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))) <=> ((aElement0 W1) /\ ((aElementOf0 W1 (sdtlpdtrp0 (xN) (xi))) /\ (W1 != (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))))))) /\ ((All W2, ((aElementOf0 W2 (sdtlpdtrp0 (xN) (xj))) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))))) /\ ((aSubsetOf0 (sdtlpdtrp0 (xN) (xj)) (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))) /\ (-. (((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) (xj))) (sdtlpdtrp0 (xN) (xj))) /\ (All W1, ((aElementOf0 W1 (sdtlpdtrp0 (xN) (xj))) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) (xj))) W1)))) => (((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) (xj))) (sdtlpdtrp0 (xN) (xi))) /\ (All W2, ((aElementOf0 W2 (sdtlpdtrp0 (xN) (xi))) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) (xj))) W2)))) \/ ((szmzizndt0 (sdtlpdtrp0 (xN) (xj))) = (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))))))))))))) ((szmzizndt0 (sdtlpdtrp0 (xN) (xi))) = (szmzizndt0 (sdtlpdtrp0 (xN) (xj)))) (sdtlseqdt0 (szszuzczcdt0 (xi)) (xj)) (aElementOf0 (xj) (szNzAzT0)) (aElementOf0 (xi) (szNzAzT0)) ### DisjTree 10 11 12 14 % 2.56/2.72 16. (All W1, (((aElementOf0 (xi) (szNzAzT0)) /\ (aElementOf0 W1 (szNzAzT0))) => ((sdtlseqdt0 (szszuzczcdt0 (xi)) W1) => ((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) (xi))) (sdtlpdtrp0 (xN) (xi))) /\ ((All W0, ((aElementOf0 W0 (sdtlpdtrp0 (xN) (xi))) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) (xi))) W0))) /\ ((aSet0 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))) /\ ((All W1, ((aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))) <=> ((aElement0 W1) /\ ((aElementOf0 W1 (sdtlpdtrp0 (xN) (xi))) /\ (W1 != (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))))))) /\ ((All W2, ((aElementOf0 W2 (sdtlpdtrp0 (xN) W1)) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))))) /\ ((aSubsetOf0 (sdtlpdtrp0 (xN) W1) (sdtmndt0 (sdtlpdtrp0 (xN) (xi)) (szmzizndt0 (sdtlpdtrp0 (xN) (xi))))) /\ (-. (((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) W1)) (sdtlpdtrp0 (xN) W1)) /\ (All W2, ((aElementOf0 W2 (sdtlpdtrp0 (xN) W1)) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) W1)) W2)))) => (((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) W1)) (sdtlpdtrp0 (xN) (xi))) /\ (All W2, ((aElementOf0 W2 (sdtlpdtrp0 (xN) (xi))) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) W1)) W2)))) \/ ((szmzizndt0 (sdtlpdtrp0 (xN) W1)) = (szmzizndt0 (sdtlpdtrp0 (xN) (xi)))))))))))))))) (aElementOf0 (xi) (szNzAzT0)) (aElementOf0 (xj) (szNzAzT0)) (sdtlseqdt0 (szszuzczcdt0 (xi)) (xj)) ((szmzizndt0 (sdtlpdtrp0 (xN) (xi))) = (szmzizndt0 (sdtlpdtrp0 (xN) (xj)))) ### All 15 % 2.56/2.72 17. (All W0, (All W1, (((aElementOf0 W0 (szNzAzT0)) /\ (aElementOf0 W1 (szNzAzT0))) => ((sdtlseqdt0 (szszuzczcdt0 W0) 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))))))) /\ ((All W2, ((aElementOf0 W2 (sdtlpdtrp0 (xN) W1)) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))))) /\ ((aSubsetOf0 (sdtlpdtrp0 (xN) W1) (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) /\ (-. (((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) W1)) (sdtlpdtrp0 (xN) W1)) /\ (All W2, ((aElementOf0 W2 (sdtlpdtrp0 (xN) W1)) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) W1)) W2)))) => (((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) W1)) (sdtlpdtrp0 (xN) W0)) /\ (All W2, ((aElementOf0 W2 (sdtlpdtrp0 (xN) W0)) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) W1)) W2)))) \/ ((szmzizndt0 (sdtlpdtrp0 (xN) W1)) = (szmzizndt0 (sdtlpdtrp0 (xN) W0)))))))))))))))) ((szmzizndt0 (sdtlpdtrp0 (xN) (xi))) = (szmzizndt0 (sdtlpdtrp0 (xN) (xj)))) (sdtlseqdt0 (szszuzczcdt0 (xi)) (xj)) (aElementOf0 (xj) (szNzAzT0)) (aElementOf0 (xi) (szNzAzT0)) ### All 16 % 2.56/2.72 18. (((xi) != (xj)) => ((sdtlseqdt0 (szszuzczcdt0 (xj)) (xi)) \/ (sdtlseqdt0 (szszuzczcdt0 (xi)) (xj)))) (aElementOf0 (xj) (szNzAzT0)) (aElementOf0 (xi) (szNzAzT0)) ((szmzizndt0 (sdtlpdtrp0 (xN) (xi))) = (szmzizndt0 (sdtlpdtrp0 (xN) (xj)))) (All W0, (All W1, (((aElementOf0 W0 (szNzAzT0)) /\ (aElementOf0 W1 (szNzAzT0))) => ((sdtlseqdt0 (szszuzczcdt0 W0) 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))))))) /\ ((All W2, ((aElementOf0 W2 (sdtlpdtrp0 (xN) W1)) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))))) /\ ((aSubsetOf0 (sdtlpdtrp0 (xN) W1) (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) /\ (-. (((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) W1)) (sdtlpdtrp0 (xN) W1)) /\ (All W2, ((aElementOf0 W2 (sdtlpdtrp0 (xN) W1)) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) W1)) W2)))) => (((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) W1)) (sdtlpdtrp0 (xN) W0)) /\ (All W2, ((aElementOf0 W2 (sdtlpdtrp0 (xN) W0)) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) W1)) W2)))) \/ ((szmzizndt0 (sdtlpdtrp0 (xN) W1)) = (szmzizndt0 (sdtlpdtrp0 (xN) W0)))))))))))))))) ((xi) != (xj)) ### DisjTree 1 9 17 % 2.56/2.72 19. ((aElementOf0 (xi) (szNzAzT0)) /\ (aElementOf0 (xj) (szNzAzT0))) ((xi) != (xj)) (All W0, (All W1, (((aElementOf0 W0 (szNzAzT0)) /\ (aElementOf0 W1 (szNzAzT0))) => ((sdtlseqdt0 (szszuzczcdt0 W0) 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))))))) /\ ((All W2, ((aElementOf0 W2 (sdtlpdtrp0 (xN) W1)) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))))) /\ ((aSubsetOf0 (sdtlpdtrp0 (xN) W1) (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) /\ (-. (((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) W1)) (sdtlpdtrp0 (xN) W1)) /\ (All W2, ((aElementOf0 W2 (sdtlpdtrp0 (xN) W1)) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) W1)) W2)))) => (((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) W1)) (sdtlpdtrp0 (xN) W0)) /\ (All W2, ((aElementOf0 W2 (sdtlpdtrp0 (xN) W0)) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) W1)) W2)))) \/ ((szmzizndt0 (sdtlpdtrp0 (xN) W1)) = (szmzizndt0 (sdtlpdtrp0 (xN) W0)))))))))))))))) ((szmzizndt0 (sdtlpdtrp0 (xN) (xi))) = (szmzizndt0 (sdtlpdtrp0 (xN) (xj)))) (((xi) != (xj)) => ((sdtlseqdt0 (szszuzczcdt0 (xj)) (xi)) \/ (sdtlseqdt0 (szszuzczcdt0 (xi)) (xj)))) ### And 18 % 2.56/2.72 20. (-. ((All W0, (All W1, (((aElementOf0 W0 (szNzAzT0)) /\ (aElementOf0 W1 (szNzAzT0))) => ((sdtlseqdt0 (szszuzczcdt0 W0) 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))))))) /\ ((All W2, ((aElementOf0 W2 (sdtlpdtrp0 (xN) W1)) => (aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))))) /\ ((aSubsetOf0 (sdtlpdtrp0 (xN) W1) (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0)))) /\ (-. (((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) W1)) (sdtlpdtrp0 (xN) W1)) /\ (All W2, ((aElementOf0 W2 (sdtlpdtrp0 (xN) W1)) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) W1)) W2)))) => (((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) W1)) (sdtlpdtrp0 (xN) W0)) /\ (All W2, ((aElementOf0 W2 (sdtlpdtrp0 (xN) W0)) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) W1)) W2)))) \/ ((szmzizndt0 (sdtlpdtrp0 (xN) W1)) = (szmzizndt0 (sdtlpdtrp0 (xN) W0)))))))))))))))) => (((xi) != (xj)) => (-. ((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) (xi))) (sdtlpdtrp0 (xN) (xi))) /\ ((All W0, ((aElementOf0 W0 (sdtlpdtrp0 (xN) (xi))) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) (xi))) W0))) /\ ((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) (xi))) (sdtlpdtrp0 (xN) (xj))) /\ ((All W0, ((aElementOf0 W0 (sdtlpdtrp0 (xN) (xj))) => (sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) (xi))) W0))) /\ ((szmzizndt0 (sdtlpdtrp0 (xN) (xi))) = (szmzizndt0 (sdtlpdtrp0 (xN) (xj)))))))))))) (((xi) != (xj)) => ((sdtlseqdt0 (szszuzczcdt0 (xj)) (xi)) \/ (sdtlseqdt0 (szszuzczcdt0 (xi)) (xj)))) ((aElementOf0 (xi) (szNzAzT0)) /\ (aElementOf0 (xj) (szNzAzT0))) ### ConjTree 19 % 2.56/2.73 % SZS output end Proof % 2.56/2.73 (* END-PROOF *) %------------------------------------------------------------------------------