%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : KRS104+1 : TPTP v8.1.0. Released v3.1.0. % Transfm : none % Format : tptp:raw % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % Computer : n021.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 : Sun Jul 17 03:31:55 EDT 2022 % Result : Unsatisfiable 0.18s 0.42s % Output : Proof 0.18s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.11 % Problem : KRS104+1 : TPTP v8.1.0. Released v3.1.0. % 0.10/0.12 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 0.12/0.33 % Computer : n021.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 : Tue Jun 7 09:07:51 EDT 2022 % 0.12/0.33 % CPUTime : % 0.18/0.42 % SZS status Theorem % 0.18/0.42 (* PROOF-FOUND *) % 0.18/0.42 (* BEGIN-PROOF *) % 0.18/0.42 % SZS output start Proof % 0.18/0.42 1. (-. (Ex Y0, (ra_Px7 (i2003_11_14_17_20_50869) Y0))) (Ex Y0, (ra_Px7 (i2003_11_14_17_20_50869) Y0)) ### Axiom % 0.18/0.42 2. (-. (-. (Ex Y0, (ra_Px7 (i2003_11_14_17_20_50869) Y0)))) (-. (Ex Y0, (ra_Px7 (i2003_11_14_17_20_50869) Y0))) ### NotNot 1 % 0.18/0.42 3. (-. (ca_Cx7xcomp (i2003_11_14_17_20_50869))) (ca_Cx7xcomp (i2003_11_14_17_20_50869)) ### Axiom % 0.18/0.42 4. ((ca_Cx7xcomp (i2003_11_14_17_20_50869)) <=> (-. (Ex Y0, (ra_Px7 (i2003_11_14_17_20_50869) Y0)))) (-. (ca_Cx7xcomp (i2003_11_14_17_20_50869))) (-. (Ex Y0, (ra_Px7 (i2003_11_14_17_20_50869) Y0))) ### Equiv 2 3 % 0.18/0.42 5. (All X, ((ca_Cx7xcomp X) <=> (-. (Ex Y0, (ra_Px7 X Y0))))) (-. (Ex Y0, (ra_Px7 (i2003_11_14_17_20_50869) Y0))) (-. (ca_Cx7xcomp (i2003_11_14_17_20_50869))) ### All 4 % 0.18/0.42 6. (ca (i2003_11_14_17_20_50869)) (-. (ca (i2003_11_14_17_20_50869))) ### Axiom % 0.18/0.42 7. (-. (ca_Cx1 (i2003_11_14_17_20_50869))) (ca_Cx1 (i2003_11_14_17_20_50869)) ### Axiom % 0.18/0.42 8. ((ca (i2003_11_14_17_20_50869)) => (ca_Cx1 (i2003_11_14_17_20_50869))) (-. (ca_Cx1 (i2003_11_14_17_20_50869))) (ca (i2003_11_14_17_20_50869)) ### Imply 6 7 % 0.18/0.42 9. (All X, ((ca X) => (ca_Cx1 X))) (ca (i2003_11_14_17_20_50869)) (-. (ca_Cx1 (i2003_11_14_17_20_50869))) ### All 8 % 0.18/0.42 10. (Ex Y0, (ra_Px2 (i2003_11_14_17_20_50869) Y0)) (-. (Ex Y0, (ra_Px2 (i2003_11_14_17_20_50869) Y0))) ### Axiom % 0.18/0.42 11. (ccxcomp (i2003_11_14_17_20_50869)) (Ex Y0, (ra_Px2 (i2003_11_14_17_20_50869) Y0)) ### Definition-Pseudo(ccxcomp) 10 % 0.18/0.42 12. ((cbxcomp (i2003_11_14_17_20_50869)) /\ (ccxcomp (i2003_11_14_17_20_50869))) (Ex Y0, (ra_Px2 (i2003_11_14_17_20_50869) Y0)) ### And 11 % 0.18/0.42 13. ((ca_Cx1 (i2003_11_14_17_20_50869)) <=> ((cbxcomp (i2003_11_14_17_20_50869)) /\ (ccxcomp (i2003_11_14_17_20_50869)))) (Ex Y0, (ra_Px2 (i2003_11_14_17_20_50869) Y0)) (ca (i2003_11_14_17_20_50869)) (All X, ((ca X) => (ca_Cx1 X))) ### Equiv 9 12 % 0.18/0.42 14. (All X, ((ca_Cx1 X) <=> ((cbxcomp X) /\ (ccxcomp X)))) (All X, ((ca X) => (ca_Cx1 X))) (ca (i2003_11_14_17_20_50869)) (Ex Y0, (ra_Px2 (i2003_11_14_17_20_50869) Y0)) ### All 13 % 0.18/0.42 15. (cc (i2003_11_14_17_20_50869)) (ca (i2003_11_14_17_20_50869)) (All X, ((ca X) => (ca_Cx1 X))) (All X, ((ca_Cx1 X) <=> ((cbxcomp X) /\ (ccxcomp X)))) ### Definition-Pseudo(cc) 14 % 0.18/0.42 16. ((cc (i2003_11_14_17_20_50869)) /\ (ca (i2003_11_14_17_20_50869))) (All X, ((ca_Cx1 X) <=> ((cbxcomp X) /\ (ccxcomp X)))) (All X, ((ca X) => (ca_Cx1 X))) ### And 15 % 0.18/0.42 17. ((ca_Cx7xcomp (i2003_11_14_17_20_50869)) <=> ((cc (i2003_11_14_17_20_50869)) /\ (ca (i2003_11_14_17_20_50869)))) (All X, ((ca X) => (ca_Cx1 X))) (All X, ((ca_Cx1 X) <=> ((cbxcomp X) /\ (ccxcomp X)))) (-. (Ex Y0, (ra_Px7 (i2003_11_14_17_20_50869) Y0))) (All X, ((ca_Cx7xcomp X) <=> (-. (Ex Y0, (ra_Px7 X Y0))))) ### Equiv 5 16 % 0.18/0.42 18. (All X, ((ca_Cx7xcomp X) <=> ((cc X) /\ (ca X)))) (All X, ((ca_Cx7xcomp X) <=> (-. (Ex Y0, (ra_Px7 X Y0))))) (-. (Ex Y0, (ra_Px7 (i2003_11_14_17_20_50869) Y0))) (All X, ((ca_Cx1 X) <=> ((cbxcomp X) /\ (ccxcomp X)))) (All X, ((ca X) => (ca_Cx1 X))) ### All 17 % 0.18/0.42 19. (-. (ca_Cx7 (i2003_11_14_17_20_50869))) (All X, ((ca X) => (ca_Cx1 X))) (All X, ((ca_Cx1 X) <=> ((cbxcomp X) /\ (ccxcomp X)))) (All X, ((ca_Cx7xcomp X) <=> (-. (Ex Y0, (ra_Px7 X Y0))))) (All X, ((ca_Cx7xcomp X) <=> ((cc X) /\ (ca X)))) ### Definition-Pseudo(ca_Cx7) 18 % 0.18/0.42 20. (Ex Y, (ra_Px8 (i2003_11_14_17_20_50869) Y)) (-. (Ex Y, (ra_Px8 (i2003_11_14_17_20_50869) Y))) ### Axiom % 0.18/0.42 21. (ca_Cx8xcomp (i2003_11_14_17_20_50869)) (-. (ca_Cx8xcomp (i2003_11_14_17_20_50869))) ### Axiom % 0.18/0.42 22. (Ex Y0, (ra_Px3 (i2003_11_14_17_20_50869) Y0)) (-. (Ex Y0, (ra_Px3 (i2003_11_14_17_20_50869) Y0))) ### Axiom % 0.18/0.42 23. (-. (cb (i2003_11_14_17_20_50869))) (Ex Y0, (ra_Px3 (i2003_11_14_17_20_50869) Y0)) ### Definition-Pseudo(cb) 22 % 0.18/0.42 24. ((cb (i2003_11_14_17_20_50869)) => (ccxcomp (i2003_11_14_17_20_50869))) (Ex Y0, (ra_Px2 (i2003_11_14_17_20_50869) Y0)) (Ex Y0, (ra_Px3 (i2003_11_14_17_20_50869) Y0)) ### Imply 23 11 % 0.18/0.42 25. (All X, ((cb X) => (ccxcomp X))) (Ex Y0, (ra_Px3 (i2003_11_14_17_20_50869) Y0)) (Ex Y0, (ra_Px2 (i2003_11_14_17_20_50869) Y0)) ### All 24 % 0.18/0.42 26. (cb (i2003_11_14_17_20_50869)) (Ex Y0, (ra_Px2 (i2003_11_14_17_20_50869) Y0)) (All X, ((cb X) => (ccxcomp X))) ### Definition-Pseudo(cb) 25 % 0.18/0.42 27. (cc (i2003_11_14_17_20_50869)) (All X, ((cb X) => (ccxcomp X))) (cb (i2003_11_14_17_20_50869)) ### Definition-Pseudo(cc) 26 % 0.18/0.42 28. ((cc (i2003_11_14_17_20_50869)) /\ (cb (i2003_11_14_17_20_50869))) (All X, ((cb X) => (ccxcomp X))) ### And 27 % 0.18/0.42 29. ((ca_Cx8xcomp (i2003_11_14_17_20_50869)) <=> ((cc (i2003_11_14_17_20_50869)) /\ (cb (i2003_11_14_17_20_50869)))) (All X, ((cb X) => (ccxcomp X))) (ca_Cx8xcomp (i2003_11_14_17_20_50869)) ### Equiv 21 28 % 0.18/0.42 30. (All X, ((ca_Cx8xcomp X) <=> ((cc X) /\ (cb X)))) (ca_Cx8xcomp (i2003_11_14_17_20_50869)) (All X, ((cb X) => (ccxcomp X))) ### All 29 % 0.18/0.42 31. ((ca_Cx8xcomp (i2003_11_14_17_20_50869)) <=> (Ex Y, (ra_Px8 (i2003_11_14_17_20_50869) Y))) (All X, ((cb X) => (ccxcomp X))) (All X, ((ca_Cx8xcomp X) <=> ((cc X) /\ (cb X)))) (Ex Y, (ra_Px8 (i2003_11_14_17_20_50869) Y)) ### Equiv 20 30 % 0.18/0.42 32. (All X, ((ca_Cx8xcomp X) <=> (Ex Y, (ra_Px8 X Y)))) (Ex Y, (ra_Px8 (i2003_11_14_17_20_50869) Y)) (All X, ((ca_Cx8xcomp X) <=> ((cc X) /\ (cb X)))) (All X, ((cb X) => (ccxcomp X))) ### All 31 % 0.18/0.42 33. (-. (-. (Ex Y, (ra_Px8 (i2003_11_14_17_20_50869) Y)))) (All X, ((cb X) => (ccxcomp X))) (All X, ((ca_Cx8xcomp X) <=> ((cc X) /\ (cb X)))) (All X, ((ca_Cx8xcomp X) <=> (Ex Y, (ra_Px8 X Y)))) ### NotNot 32 % 0.18/0.42 34. (-. (ca_Cx8 (i2003_11_14_17_20_50869))) (All X, ((ca_Cx8xcomp X) <=> (Ex Y, (ra_Px8 X Y)))) (All X, ((ca_Cx8xcomp X) <=> ((cc X) /\ (cb X)))) (All X, ((cb X) => (ccxcomp X))) ### Definition-Pseudo(ca_Cx8) 33 % 0.18/0.42 35. (Ex Y, (ra_Px6 (i2003_11_14_17_20_50869) Y)) (-. (Ex Y, (ra_Px6 (i2003_11_14_17_20_50869) Y))) ### Axiom % 0.18/0.42 36. (-. (ca_Cx6xcomp (i2003_11_14_17_20_50869))) (ca_Cx6xcomp (i2003_11_14_17_20_50869)) ### Axiom % 0.18/0.42 37. ((ca_Cx6xcomp (i2003_11_14_17_20_50869)) <=> (Ex Y, (ra_Px6 (i2003_11_14_17_20_50869) Y))) (-. (ca_Cx6xcomp (i2003_11_14_17_20_50869))) (Ex Y, (ra_Px6 (i2003_11_14_17_20_50869) Y)) ### Equiv 35 36 % 0.18/0.42 38. (All X, ((ca_Cx6xcomp X) <=> (Ex Y, (ra_Px6 X Y)))) (Ex Y, (ra_Px6 (i2003_11_14_17_20_50869) Y)) (-. (ca_Cx6xcomp (i2003_11_14_17_20_50869))) ### All 37 % 0.18/0.42 39. (Ex Y0, (ra_Px3 (i2003_11_14_17_20_50869) Y0)) (-. (Ex Y0, (ra_Px3 (i2003_11_14_17_20_50869) Y0))) ### Axiom % 0.18/0.42 40. (cbxcomp (i2003_11_14_17_20_50869)) (Ex Y0, (ra_Px3 (i2003_11_14_17_20_50869) Y0)) ### Definition-Pseudo(cbxcomp) 39 % 0.18/0.42 41. ((cbxcomp (i2003_11_14_17_20_50869)) /\ (ccxcomp (i2003_11_14_17_20_50869))) (Ex Y0, (ra_Px3 (i2003_11_14_17_20_50869) Y0)) ### And 40 % 0.18/0.42 42. ((ca_Cx1 (i2003_11_14_17_20_50869)) <=> ((cbxcomp (i2003_11_14_17_20_50869)) /\ (ccxcomp (i2003_11_14_17_20_50869)))) (Ex Y0, (ra_Px3 (i2003_11_14_17_20_50869) Y0)) (ca (i2003_11_14_17_20_50869)) (All X, ((ca X) => (ca_Cx1 X))) ### Equiv 9 41 % 0.18/0.42 43. (All X, ((ca_Cx1 X) <=> ((cbxcomp X) /\ (ccxcomp X)))) (All X, ((ca X) => (ca_Cx1 X))) (ca (i2003_11_14_17_20_50869)) (Ex Y0, (ra_Px3 (i2003_11_14_17_20_50869) Y0)) ### All 42 % 0.18/0.42 44. (cb (i2003_11_14_17_20_50869)) (ca (i2003_11_14_17_20_50869)) (All X, ((ca X) => (ca_Cx1 X))) (All X, ((ca_Cx1 X) <=> ((cbxcomp X) /\ (ccxcomp X)))) ### Definition-Pseudo(cb) 43 % 0.18/0.42 45. ((ca (i2003_11_14_17_20_50869)) /\ (cb (i2003_11_14_17_20_50869))) (All X, ((ca_Cx1 X) <=> ((cbxcomp X) /\ (ccxcomp X)))) (All X, ((ca X) => (ca_Cx1 X))) ### And 44 % 0.18/0.42 46. ((ca_Cx6xcomp (i2003_11_14_17_20_50869)) <=> ((ca (i2003_11_14_17_20_50869)) /\ (cb (i2003_11_14_17_20_50869)))) (All X, ((ca X) => (ca_Cx1 X))) (All X, ((ca_Cx1 X) <=> ((cbxcomp X) /\ (ccxcomp X)))) (Ex Y, (ra_Px6 (i2003_11_14_17_20_50869) Y)) (All X, ((ca_Cx6xcomp X) <=> (Ex Y, (ra_Px6 X Y)))) ### Equiv 38 45 % 0.18/0.42 47. (All X, ((ca_Cx6xcomp X) <=> ((ca X) /\ (cb X)))) (All X, ((ca_Cx6xcomp X) <=> (Ex Y, (ra_Px6 X Y)))) (Ex Y, (ra_Px6 (i2003_11_14_17_20_50869) Y)) (All X, ((ca_Cx1 X) <=> ((cbxcomp X) /\ (ccxcomp X)))) (All X, ((ca X) => (ca_Cx1 X))) ### All 46 % 0.18/0.42 48. (-. (-. (Ex Y, (ra_Px6 (i2003_11_14_17_20_50869) Y)))) (All X, ((ca X) => (ca_Cx1 X))) (All X, ((ca_Cx1 X) <=> ((cbxcomp X) /\ (ccxcomp X)))) (All X, ((ca_Cx6xcomp X) <=> (Ex Y, (ra_Px6 X Y)))) (All X, ((ca_Cx6xcomp X) <=> ((ca X) /\ (cb X)))) ### NotNot 47 % 0.18/0.42 49. (-. (ca_Cx6 (i2003_11_14_17_20_50869))) (All X, ((ca_Cx6xcomp X) <=> ((ca X) /\ (cb X)))) (All X, ((ca_Cx6xcomp X) <=> (Ex Y, (ra_Px6 X Y)))) (All X, ((ca_Cx1 X) <=> ((cbxcomp X) /\ (ccxcomp X)))) (All X, ((ca X) => (ca_Cx1 X))) ### Definition-Pseudo(ca_Cx6) 48 % 0.18/0.42 50. (-. ((ca_Cx7 (i2003_11_14_17_20_50869)) /\ ((ca_Cx8 (i2003_11_14_17_20_50869)) /\ (ca_Cx6 (i2003_11_14_17_20_50869))))) (All X, ((ca_Cx6xcomp X) <=> (Ex Y, (ra_Px6 X Y)))) (All X, ((ca_Cx6xcomp X) <=> ((ca X) /\ (cb X)))) (All X, ((cb X) => (ccxcomp X))) (All X, ((ca_Cx8xcomp X) <=> ((cc X) /\ (cb X)))) (All X, ((ca_Cx8xcomp X) <=> (Ex Y, (ra_Px8 X Y)))) (All X, ((ca_Cx7xcomp X) <=> ((cc X) /\ (ca X)))) (All X, ((ca_Cx7xcomp X) <=> (-. (Ex Y0, (ra_Px7 X Y0))))) (All X, ((ca_Cx1 X) <=> ((cbxcomp X) /\ (ccxcomp X)))) (All X, ((ca X) => (ca_Cx1 X))) ### DisjTree 19 34 49 % 0.18/0.42 51. (-. (cUnsatisfiablexcomp (i2003_11_14_17_20_50869))) (cUnsatisfiablexcomp (i2003_11_14_17_20_50869)) ### Axiom % 0.18/0.42 52. ((cUnsatisfiablexcomp (i2003_11_14_17_20_50869)) <=> ((ca_Cx7 (i2003_11_14_17_20_50869)) /\ ((ca_Cx8 (i2003_11_14_17_20_50869)) /\ (ca_Cx6 (i2003_11_14_17_20_50869))))) (-. (cUnsatisfiablexcomp (i2003_11_14_17_20_50869))) (All X, ((ca X) => (ca_Cx1 X))) (All X, ((ca_Cx1 X) <=> ((cbxcomp X) /\ (ccxcomp X)))) (All X, ((ca_Cx7xcomp X) <=> (-. (Ex Y0, (ra_Px7 X Y0))))) (All X, ((ca_Cx7xcomp X) <=> ((cc X) /\ (ca X)))) (All X, ((ca_Cx8xcomp X) <=> (Ex Y, (ra_Px8 X Y)))) (All X, ((ca_Cx8xcomp X) <=> ((cc X) /\ (cb X)))) (All X, ((cb X) => (ccxcomp X))) (All X, ((ca_Cx6xcomp X) <=> ((ca X) /\ (cb X)))) (All X, ((ca_Cx6xcomp X) <=> (Ex Y, (ra_Px6 X Y)))) ### Equiv 50 51 % 0.18/0.42 53. (All X, ((cUnsatisfiablexcomp X) <=> ((ca_Cx7 X) /\ ((ca_Cx8 X) /\ (ca_Cx6 X))))) (All X, ((ca_Cx6xcomp X) <=> (Ex Y, (ra_Px6 X Y)))) (All X, ((ca_Cx6xcomp X) <=> ((ca X) /\ (cb X)))) (All X, ((cb X) => (ccxcomp X))) (All X, ((ca_Cx8xcomp X) <=> ((cc X) /\ (cb X)))) (All X, ((ca_Cx8xcomp X) <=> (Ex Y, (ra_Px8 X Y)))) (All X, ((ca_Cx7xcomp X) <=> ((cc X) /\ (ca X)))) (All X, ((ca_Cx7xcomp X) <=> (-. (Ex Y0, (ra_Px7 X Y0))))) (All X, ((ca_Cx1 X) <=> ((cbxcomp X) /\ (ccxcomp X)))) (All X, ((ca X) => (ca_Cx1 X))) (-. (cUnsatisfiablexcomp (i2003_11_14_17_20_50869))) ### All 52 % 0.18/0.42 54. (-. (Ex Y, (ra_Px5 (i2003_11_14_17_20_50869) Y))) (Ex Y, (ra_Px5 (i2003_11_14_17_20_50869) Y)) ### Axiom % 0.18/0.42 55. ((cUnsatisfiablexcomp (i2003_11_14_17_20_50869)) <=> (Ex Y, (ra_Px5 (i2003_11_14_17_20_50869) Y))) (-. (Ex Y, (ra_Px5 (i2003_11_14_17_20_50869) Y))) (All X, ((ca X) => (ca_Cx1 X))) (All X, ((ca_Cx1 X) <=> ((cbxcomp X) /\ (ccxcomp X)))) (All X, ((ca_Cx7xcomp X) <=> (-. (Ex Y0, (ra_Px7 X Y0))))) (All X, ((ca_Cx7xcomp X) <=> ((cc X) /\ (ca X)))) (All X, ((ca_Cx8xcomp X) <=> (Ex Y, (ra_Px8 X Y)))) (All X, ((ca_Cx8xcomp X) <=> ((cc X) /\ (cb X)))) (All X, ((cb X) => (ccxcomp X))) (All X, ((ca_Cx6xcomp X) <=> ((ca X) /\ (cb X)))) (All X, ((ca_Cx6xcomp X) <=> (Ex Y, (ra_Px6 X Y)))) (All X, ((cUnsatisfiablexcomp X) <=> ((ca_Cx7 X) /\ ((ca_Cx8 X) /\ (ca_Cx6 X))))) ### Equiv 53 54 % 0.18/0.42 56. (All X, ((cUnsatisfiablexcomp X) <=> (Ex Y, (ra_Px5 X Y)))) (All X, ((cUnsatisfiablexcomp X) <=> ((ca_Cx7 X) /\ ((ca_Cx8 X) /\ (ca_Cx6 X))))) (All X, ((ca_Cx6xcomp X) <=> (Ex Y, (ra_Px6 X Y)))) (All X, ((ca_Cx6xcomp X) <=> ((ca X) /\ (cb X)))) (All X, ((cb X) => (ccxcomp X))) (All X, ((ca_Cx8xcomp X) <=> ((cc X) /\ (cb X)))) (All X, ((ca_Cx8xcomp X) <=> (Ex Y, (ra_Px8 X Y)))) (All X, ((ca_Cx7xcomp X) <=> ((cc X) /\ (ca X)))) (All X, ((ca_Cx7xcomp X) <=> (-. (Ex Y0, (ra_Px7 X Y0))))) (All X, ((ca_Cx1 X) <=> ((cbxcomp X) /\ (ccxcomp X)))) (All X, ((ca X) => (ca_Cx1 X))) (-. (Ex Y, (ra_Px5 (i2003_11_14_17_20_50869) Y))) ### All 55 % 0.18/0.42 57. (cUnsatisfiable (i2003_11_14_17_20_50869)) (All X, ((ca X) => (ca_Cx1 X))) (All X, ((ca_Cx1 X) <=> ((cbxcomp X) /\ (ccxcomp X)))) (All X, ((ca_Cx7xcomp X) <=> (-. (Ex Y0, (ra_Px7 X Y0))))) (All X, ((ca_Cx7xcomp X) <=> ((cc X) /\ (ca X)))) (All X, ((ca_Cx8xcomp X) <=> (Ex Y, (ra_Px8 X Y)))) (All X, ((ca_Cx8xcomp X) <=> ((cc X) /\ (cb X)))) (All X, ((cb X) => (ccxcomp X))) (All X, ((ca_Cx6xcomp X) <=> ((ca X) /\ (cb X)))) (All X, ((ca_Cx6xcomp X) <=> (Ex Y, (ra_Px6 X Y)))) (All X, ((cUnsatisfiablexcomp X) <=> ((ca_Cx7 X) /\ ((ca_Cx8 X) /\ (ca_Cx6 X))))) (All X, ((cUnsatisfiablexcomp X) <=> (Ex Y, (ra_Px5 X Y)))) ### Definition-Pseudo(cUnsatisfiable) 56 % 0.18/0.42 % SZS output end Proof % 0.18/0.42 (* END-PROOF *) %------------------------------------------------------------------------------