%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : NUM533+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 : n029.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 14:43:21 EDT 2022 % Result : Theorem 0.12s 0.40s % Output : Proof 0.12s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : NUM533+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 : n029.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 15:36:58 EDT 2022 % 0.12/0.33 % CPUTime : % 0.12/0.40 % SZS status Theorem % 0.12/0.40 (* PROOF-FOUND *) % 0.12/0.40 (* BEGIN-PROOF *) % 0.12/0.40 % SZS output start Proof % 0.12/0.40 1. (aSet0 (xC)) (-. (aSet0 (xC))) ### Axiom % 0.12/0.40 2. (aSet0 (xA)) (-. (aSet0 (xA))) ### Axiom % 0.12/0.40 3. (aSet0 (xB)) (-. (aSet0 (xB))) ### Axiom % 0.12/0.40 4. (aSubsetOf0 (xB) (xC)) (-. (aSubsetOf0 (xB) (xC))) ### Axiom % 0.12/0.40 5. (aSubsetOf0 (xA) (xB)) (-. (aSubsetOf0 (xA) (xB))) ### Axiom % 0.12/0.40 6. (aElementOf0 T_0 (xA)) (-. (aElementOf0 T_0 (xA))) ### Axiom % 0.12/0.40 7. (-. (aElementOf0 T_0 (xB))) (aElementOf0 T_0 (xB)) ### Axiom % 0.12/0.40 8. ((aElementOf0 T_0 (xA)) => (aElementOf0 T_0 (xB))) (-. (aElementOf0 T_0 (xB))) (aElementOf0 T_0 (xA)) ### Imply 6 7 % 0.12/0.40 9. (All W2, ((aElementOf0 W2 (xA)) => (aElementOf0 W2 (xB)))) (aElementOf0 T_0 (xA)) (-. (aElementOf0 T_0 (xB))) ### All 8 % 0.12/0.40 10. ((aSet0 (xA)) /\ (All W2, ((aElementOf0 W2 (xA)) => (aElementOf0 W2 (xB))))) (-. (aElementOf0 T_0 (xB))) (aElementOf0 T_0 (xA)) ### And 9 % 0.12/0.40 11. ((aSubsetOf0 (xA) (xB)) <=> ((aSet0 (xA)) /\ (All W2, ((aElementOf0 W2 (xA)) => (aElementOf0 W2 (xB)))))) (aElementOf0 T_0 (xA)) (-. (aElementOf0 T_0 (xB))) (aSubsetOf0 (xA) (xB)) ### Equiv 5 10 % 0.12/0.40 12. (All W1, ((aSubsetOf0 W1 (xB)) <=> ((aSet0 W1) /\ (All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (xB))))))) (aSubsetOf0 (xA) (xB)) (-. (aElementOf0 T_0 (xB))) (aElementOf0 T_0 (xA)) ### All 11 % 0.12/0.40 13. (-. (aElementOf0 T_0 (xC))) (aElementOf0 T_0 (xC)) ### Axiom % 0.12/0.40 14. ((aElementOf0 T_0 (xB)) => (aElementOf0 T_0 (xC))) (-. (aElementOf0 T_0 (xC))) (aElementOf0 T_0 (xA)) (aSubsetOf0 (xA) (xB)) (All W1, ((aSubsetOf0 W1 (xB)) <=> ((aSet0 W1) /\ (All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (xB))))))) ### Imply 12 13 % 0.12/0.40 15. (All W2, ((aElementOf0 W2 (xB)) => (aElementOf0 W2 (xC)))) (All W1, ((aSubsetOf0 W1 (xB)) <=> ((aSet0 W1) /\ (All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (xB))))))) (aSubsetOf0 (xA) (xB)) (aElementOf0 T_0 (xA)) (-. (aElementOf0 T_0 (xC))) ### All 14 % 0.12/0.40 16. ((aSet0 (xB)) /\ (All W2, ((aElementOf0 W2 (xB)) => (aElementOf0 W2 (xC))))) (-. (aElementOf0 T_0 (xC))) (aElementOf0 T_0 (xA)) (aSubsetOf0 (xA) (xB)) (All W1, ((aSubsetOf0 W1 (xB)) <=> ((aSet0 W1) /\ (All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (xB))))))) ### And 15 % 0.12/0.40 17. ((aSubsetOf0 (xB) (xC)) <=> ((aSet0 (xB)) /\ (All W2, ((aElementOf0 W2 (xB)) => (aElementOf0 W2 (xC)))))) (All W1, ((aSubsetOf0 W1 (xB)) <=> ((aSet0 W1) /\ (All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (xB))))))) (aSubsetOf0 (xA) (xB)) (aElementOf0 T_0 (xA)) (-. (aElementOf0 T_0 (xC))) (aSubsetOf0 (xB) (xC)) ### Equiv 4 16 % 0.12/0.40 18. (All W1, ((aSubsetOf0 W1 (xC)) <=> ((aSet0 W1) /\ (All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (xC))))))) (aSubsetOf0 (xB) (xC)) (-. (aElementOf0 T_0 (xC))) (aElementOf0 T_0 (xA)) (aSubsetOf0 (xA) (xB)) (All W1, ((aSubsetOf0 W1 (xB)) <=> ((aSet0 W1) /\ (All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (xB))))))) ### All 17 % 0.12/0.40 19. ((aSet0 (xB)) => (All W1, ((aSubsetOf0 W1 (xB)) <=> ((aSet0 W1) /\ (All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (xB)))))))) (aSubsetOf0 (xA) (xB)) (aElementOf0 T_0 (xA)) (-. (aElementOf0 T_0 (xC))) (aSubsetOf0 (xB) (xC)) (All W1, ((aSubsetOf0 W1 (xC)) <=> ((aSet0 W1) /\ (All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (xC))))))) (aSet0 (xB)) ### Imply 3 18 % 0.12/0.40 20. (All W0, ((aSet0 W0) => (All W1, ((aSubsetOf0 W1 W0) <=> ((aSet0 W1) /\ (All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 W0)))))))) (aSet0 (xB)) (All W1, ((aSubsetOf0 W1 (xC)) <=> ((aSet0 W1) /\ (All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (xC))))))) (aSubsetOf0 (xB) (xC)) (-. (aElementOf0 T_0 (xC))) (aElementOf0 T_0 (xA)) (aSubsetOf0 (xA) (xB)) ### All 19 % 0.12/0.40 21. (-. ((aElementOf0 T_0 (xA)) => (aElementOf0 T_0 (xC)))) (aSubsetOf0 (xA) (xB)) (aSubsetOf0 (xB) (xC)) (All W1, ((aSubsetOf0 W1 (xC)) <=> ((aSet0 W1) /\ (All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (xC))))))) (aSet0 (xB)) (All W0, ((aSet0 W0) => (All W1, ((aSubsetOf0 W1 W0) <=> ((aSet0 W1) /\ (All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 W0)))))))) ### NotImply 20 % 0.12/0.40 22. (-. (All W2, ((aElementOf0 W2 (xA)) => (aElementOf0 W2 (xC))))) (All W0, ((aSet0 W0) => (All W1, ((aSubsetOf0 W1 W0) <=> ((aSet0 W1) /\ (All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 W0)))))))) (aSet0 (xB)) (All W1, ((aSubsetOf0 W1 (xC)) <=> ((aSet0 W1) /\ (All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (xC))))))) (aSubsetOf0 (xB) (xC)) (aSubsetOf0 (xA) (xB)) ### NotAllEx 21 % 0.12/0.40 23. (-. ((aSet0 (xA)) /\ (All W2, ((aElementOf0 W2 (xA)) => (aElementOf0 W2 (xC)))))) (aSubsetOf0 (xA) (xB)) (aSubsetOf0 (xB) (xC)) (All W1, ((aSubsetOf0 W1 (xC)) <=> ((aSet0 W1) /\ (All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (xC))))))) (aSet0 (xB)) (All W0, ((aSet0 W0) => (All W1, ((aSubsetOf0 W1 W0) <=> ((aSet0 W1) /\ (All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 W0)))))))) (aSet0 (xA)) ### NotAnd 2 22 % 0.12/0.40 24. (-. (aSubsetOf0 (xA) (xC))) (aSubsetOf0 (xA) (xC)) ### Axiom % 0.12/0.40 25. ((aSubsetOf0 (xA) (xC)) <=> ((aSet0 (xA)) /\ (All W2, ((aElementOf0 W2 (xA)) => (aElementOf0 W2 (xC)))))) (-. (aSubsetOf0 (xA) (xC))) (aSet0 (xA)) (All W0, ((aSet0 W0) => (All W1, ((aSubsetOf0 W1 W0) <=> ((aSet0 W1) /\ (All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 W0)))))))) (aSet0 (xB)) (All W1, ((aSubsetOf0 W1 (xC)) <=> ((aSet0 W1) /\ (All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (xC))))))) (aSubsetOf0 (xB) (xC)) (aSubsetOf0 (xA) (xB)) ### Equiv 23 24 % 0.12/0.40 26. (aSubsetOf0 (xA) (xB)) (aSubsetOf0 (xB) (xC)) (All W1, ((aSubsetOf0 W1 (xC)) <=> ((aSet0 W1) /\ (All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (xC))))))) (aSet0 (xB)) (All W0, ((aSet0 W0) => (All W1, ((aSubsetOf0 W1 W0) <=> ((aSet0 W1) /\ (All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 W0)))))))) (aSet0 (xA)) (-. (aSubsetOf0 (xA) (xC))) ### All 25 % 0.12/0.40 27. ((aSet0 (xC)) => (All W1, ((aSubsetOf0 W1 (xC)) <=> ((aSet0 W1) /\ (All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 (xC)))))))) (-. (aSubsetOf0 (xA) (xC))) (aSet0 (xA)) (All W0, ((aSet0 W0) => (All W1, ((aSubsetOf0 W1 W0) <=> ((aSet0 W1) /\ (All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 W0)))))))) (aSet0 (xB)) (aSubsetOf0 (xB) (xC)) (aSubsetOf0 (xA) (xB)) (aSet0 (xC)) ### Imply 1 26 % 0.12/0.40 28. (aSet0 (xC)) (aSubsetOf0 (xA) (xB)) (aSubsetOf0 (xB) (xC)) (aSet0 (xB)) (All W0, ((aSet0 W0) => (All W1, ((aSubsetOf0 W1 W0) <=> ((aSet0 W1) /\ (All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 W0)))))))) (aSet0 (xA)) (-. (aSubsetOf0 (xA) (xC))) ### All 27 % 0.12/0.40 29. (-. (((aSubsetOf0 (xA) (xB)) /\ (aSubsetOf0 (xB) (xC))) => (aSubsetOf0 (xA) (xC)))) (aSet0 (xA)) (All W0, ((aSet0 W0) => (All W1, ((aSubsetOf0 W1 W0) <=> ((aSet0 W1) /\ (All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 W0)))))))) (aSet0 (xB)) (aSet0 (xC)) ### ConjTree 28 % 0.12/0.40 30. ((aSet0 (xA)) /\ ((aSet0 (xB)) /\ (aSet0 (xC)))) (All W0, ((aSet0 W0) => (All W1, ((aSubsetOf0 W1 W0) <=> ((aSet0 W1) /\ (All W2, ((aElementOf0 W2 W1) => (aElementOf0 W2 W0)))))))) (-. (((aSubsetOf0 (xA) (xB)) /\ (aSubsetOf0 (xB) (xC))) => (aSubsetOf0 (xA) (xC)))) ### ConjTree 29 % 0.12/0.40 % SZS output end Proof % 0.12/0.40 (* END-PROOF *) %------------------------------------------------------------------------------