%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : GEO212+2 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % Computer : n024.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 : Sat Jul 16 06:31:10 EDT 2022 % Result : Theorem 23.44s 23.67s % Output : Proof 23.74s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.11 % Problem : GEO212+2 : TPTP v8.1.0. Released v3.3.0. % 0.00/0.12 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 0.11/0.33 % Computer : n024.cluster.edu % 0.11/0.33 % Model : x86_64 x86_64 % 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.33 % Memory : 8042.1875MB % 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.33 % CPULimit : 300 % 0.11/0.33 % WCLimit : 600 % 0.11/0.33 % DateTime : Sat Jun 18 01:49:02 EDT 2022 % 0.11/0.33 % CPUTime : % 23.44/23.67 % SZS status Theorem % 23.44/23.67 (* PROOF-FOUND *) % 23.44/23.67 (* BEGIN-PROOF *) % 23.44/23.67 % SZS output start Proof % 23.44/23.67 1. (convergent_lines T_0 T_0) (-. (convergent_lines T_0 T_0)) ### Axiom % 23.44/23.67 2. (All X, (-. (convergent_lines X X))) (convergent_lines T_0 T_0) ### All 1 % 23.44/23.67 3. (convergent_lines T_0 T_1) (-. (convergent_lines T_0 T_1)) ### Axiom % 23.44/23.67 4. (-. (convergent_lines T_0 T_0)) (convergent_lines T_0 T_0) ### Axiom % 23.44/23.67 5. (convergent_lines T_1 T_0) (-. (convergent_lines T_1 T_0)) ### Axiom % 23.44/23.67 6. (convergent_lines T_1 T_2) (-. (convergent_lines T_1 T_2)) ### Axiom % 23.44/23.67 7. (-. (convergent_lines T_1 T_1)) (convergent_lines T_1 T_1) ### Axiom % 23.44/23.67 8. (-. (convergent_lines T_2 T_1)) (convergent_lines T_2 T_1) ### Axiom % 23.44/23.67 9. ((convergent_lines T_1 T_2) => ((convergent_lines T_1 T_1) \/ (convergent_lines T_2 T_1))) (-. (convergent_lines T_2 T_1)) (-. (convergent_lines T_1 T_1)) (convergent_lines T_1 T_2) ### DisjTree 6 7 8 % 23.44/23.67 10. (All Z, ((convergent_lines T_1 T_2) => ((convergent_lines T_1 Z) \/ (convergent_lines T_2 Z)))) (convergent_lines T_1 T_2) (-. (convergent_lines T_1 T_1)) (-. (convergent_lines T_2 T_1)) ### All 9 % 23.44/23.67 11. (All Y, (All Z, ((convergent_lines T_1 Y) => ((convergent_lines T_1 Z) \/ (convergent_lines Y Z))))) (-. (convergent_lines T_2 T_1)) (-. (convergent_lines T_1 T_1)) (convergent_lines T_1 T_2) ### All 10 % 23.44/23.67 12. (convergent_lines T_0 T_2) (-. (convergent_lines T_0 T_2)) ### Axiom % 23.44/23.67 13. (-. (convergent_lines T_0 T_0)) (convergent_lines T_0 T_0) ### Axiom % 23.44/23.67 14. (-. (convergent_lines T_2 T_0)) (convergent_lines T_2 T_0) ### Axiom % 23.44/23.67 15. ((convergent_lines T_0 T_2) => ((convergent_lines T_0 T_0) \/ (convergent_lines T_2 T_0))) (-. (convergent_lines T_2 T_0)) (-. (convergent_lines T_0 T_0)) (convergent_lines T_0 T_2) ### DisjTree 12 13 14 % 23.44/23.67 16. (All Z, ((convergent_lines T_0 T_2) => ((convergent_lines T_0 Z) \/ (convergent_lines T_2 Z)))) (convergent_lines T_0 T_2) (-. (convergent_lines T_0 T_0)) (-. (convergent_lines T_2 T_0)) ### All 15 % 23.44/23.67 17. (All Y, (All Z, ((convergent_lines T_0 Y) => ((convergent_lines T_0 Z) \/ (convergent_lines Y Z))))) (-. (convergent_lines T_2 T_0)) (-. (convergent_lines T_0 T_0)) (convergent_lines T_0 T_2) ### All 16 % 23.44/23.67 18. ((convergent_lines T_1 T_0) => ((convergent_lines T_1 T_2) \/ (convergent_lines T_0 T_2))) (-. (convergent_lines T_0 T_0)) (-. (convergent_lines T_2 T_0)) (All Y, (All Z, ((convergent_lines T_0 Y) => ((convergent_lines T_0 Z) \/ (convergent_lines Y Z))))) (-. (convergent_lines T_1 T_1)) (-. (convergent_lines T_2 T_1)) (All Y, (All Z, ((convergent_lines T_1 Y) => ((convergent_lines T_1 Z) \/ (convergent_lines Y Z))))) (convergent_lines T_1 T_0) ### DisjTree 5 11 17 % 23.44/23.67 19. (All Z, ((convergent_lines T_1 T_0) => ((convergent_lines T_1 Z) \/ (convergent_lines T_0 Z)))) (convergent_lines T_1 T_0) (All Y, (All Z, ((convergent_lines T_1 Y) => ((convergent_lines T_1 Z) \/ (convergent_lines Y Z))))) (-. (convergent_lines T_2 T_1)) (-. (convergent_lines T_1 T_1)) (All Y, (All Z, ((convergent_lines T_0 Y) => ((convergent_lines T_0 Z) \/ (convergent_lines Y Z))))) (-. (convergent_lines T_2 T_0)) (-. (convergent_lines T_0 T_0)) ### All 18 % 23.44/23.67 20. (-. (convergent_lines T_0 T_0)) (-. (convergent_lines T_2 T_0)) (All Y, (All Z, ((convergent_lines T_0 Y) => ((convergent_lines T_0 Z) \/ (convergent_lines Y Z))))) (-. (convergent_lines T_1 T_1)) (-. (convergent_lines T_2 T_1)) (All Y, (All Z, ((convergent_lines T_1 Y) => ((convergent_lines T_1 Z) \/ (convergent_lines Y Z))))) (convergent_lines T_1 T_0) ### All 19 % 23.44/23.67 21. ((convergent_lines T_0 T_1) => ((convergent_lines T_0 T_0) \/ (convergent_lines T_1 T_0))) (All Y, (All Z, ((convergent_lines T_1 Y) => ((convergent_lines T_1 Z) \/ (convergent_lines Y Z))))) (-. (convergent_lines T_2 T_1)) (-. (convergent_lines T_1 T_1)) (All Y, (All Z, ((convergent_lines T_0 Y) => ((convergent_lines T_0 Z) \/ (convergent_lines Y Z))))) (-. (convergent_lines T_2 T_0)) (-. (convergent_lines T_0 T_0)) (convergent_lines T_0 T_1) ### DisjTree 3 4 20 % 23.44/23.67 22. (All Z, ((convergent_lines T_0 T_1) => ((convergent_lines T_0 Z) \/ (convergent_lines T_1 Z)))) (convergent_lines T_0 T_1) (-. (convergent_lines T_0 T_0)) (-. (convergent_lines T_2 T_0)) (All Y, (All Z, ((convergent_lines T_0 Y) => ((convergent_lines T_0 Z) \/ (convergent_lines Y Z))))) (-. (convergent_lines T_1 T_1)) (-. (convergent_lines T_2 T_1)) (All Y, (All Z, ((convergent_lines T_1 Y) => ((convergent_lines T_1 Z) \/ (convergent_lines Y Z))))) ### All 21 % 23.44/23.67 23. (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (-. (convergent_lines T_2 T_1)) (-. (convergent_lines T_1 T_1)) (All Y, (All Z, ((convergent_lines T_0 Y) => ((convergent_lines T_0 Z) \/ (convergent_lines Y Z))))) (-. (convergent_lines T_2 T_0)) (-. (convergent_lines T_0 T_0)) (convergent_lines T_0 T_1) (All Z, ((convergent_lines T_0 T_1) => ((convergent_lines T_0 Z) \/ (convergent_lines T_1 Z)))) ### All 22 % 23.44/23.67 24. (unorthogonal_lines T_0 T_0) (-. (unorthogonal_lines T_0 T_0)) ### Axiom % 23.44/23.67 25. (-. (unorthogonal_lines T_0 T_1)) (unorthogonal_lines T_0 T_1) ### Axiom % 23.44/23.67 26. ((convergent_lines T_0 T_1) /\ (unorthogonal_lines T_0 T_1)) (-. (unorthogonal_lines T_0 T_1)) ### And 25 % 23.44/23.68 27. (((convergent_lines T_0 T_0) /\ (unorthogonal_lines T_0 T_0)) => (((convergent_lines T_0 T_1) /\ (unorthogonal_lines T_0 T_1)) \/ ((convergent_lines T_0 T_1) /\ (unorthogonal_lines T_0 T_1)))) (-. (unorthogonal_lines T_0 T_1)) (unorthogonal_lines T_0 T_0) (All Z, ((convergent_lines T_0 T_1) => ((convergent_lines T_0 Z) \/ (convergent_lines T_1 Z)))) (convergent_lines T_0 T_1) (-. (convergent_lines T_2 T_0)) (All Y, (All Z, ((convergent_lines T_0 Y) => ((convergent_lines T_0 Z) \/ (convergent_lines Y Z))))) (-. (convergent_lines T_1 T_1)) (-. (convergent_lines T_2 T_1)) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) ### DisjTree 23 24 26 26 % 23.44/23.68 28. (All N, (((convergent_lines T_0 T_0) /\ (unorthogonal_lines T_0 T_0)) => (((convergent_lines T_0 N) /\ (unorthogonal_lines T_0 N)) \/ ((convergent_lines T_0 N) /\ (unorthogonal_lines T_0 N))))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (-. (convergent_lines T_2 T_1)) (-. (convergent_lines T_1 T_1)) (All Y, (All Z, ((convergent_lines T_0 Y) => ((convergent_lines T_0 Z) \/ (convergent_lines Y Z))))) (-. (convergent_lines T_2 T_0)) (convergent_lines T_0 T_1) (All Z, ((convergent_lines T_0 T_1) => ((convergent_lines T_0 Z) \/ (convergent_lines T_1 Z)))) (unorthogonal_lines T_0 T_0) (-. (unorthogonal_lines T_0 T_1)) ### All 27 % 23.44/23.68 29. (All M, (All N, (((convergent_lines T_0 M) /\ (unorthogonal_lines T_0 M)) => (((convergent_lines T_0 N) /\ (unorthogonal_lines T_0 N)) \/ ((convergent_lines M N) /\ (unorthogonal_lines M N)))))) (-. (unorthogonal_lines T_0 T_1)) (unorthogonal_lines T_0 T_0) (All Z, ((convergent_lines T_0 T_1) => ((convergent_lines T_0 Z) \/ (convergent_lines T_1 Z)))) (convergent_lines T_0 T_1) (-. (convergent_lines T_2 T_0)) (All Y, (All Z, ((convergent_lines T_0 Y) => ((convergent_lines T_0 Z) \/ (convergent_lines Y Z))))) (-. (convergent_lines T_1 T_1)) (-. (convergent_lines T_2 T_1)) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) ### All 28 % 23.44/23.68 30. (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (-. (convergent_lines T_2 T_1)) (-. (convergent_lines T_1 T_1)) (All Y, (All Z, ((convergent_lines T_0 Y) => ((convergent_lines T_0 Z) \/ (convergent_lines Y Z))))) (-. (convergent_lines T_2 T_0)) (convergent_lines T_0 T_1) (unorthogonal_lines T_0 T_0) (-. (unorthogonal_lines T_0 T_1)) (All M, (All N, (((convergent_lines T_0 M) /\ (unorthogonal_lines T_0 M)) => (((convergent_lines T_0 N) /\ (unorthogonal_lines T_0 N)) \/ ((convergent_lines M N) /\ (unorthogonal_lines M N)))))) ### All 29 % 23.44/23.68 31. (All L, (All M, (All N, (((convergent_lines L M) /\ (unorthogonal_lines L M)) => (((convergent_lines L N) /\ (unorthogonal_lines L N)) \/ ((convergent_lines M N) /\ (unorthogonal_lines M N))))))) (-. (unorthogonal_lines T_0 T_1)) (unorthogonal_lines T_0 T_0) (convergent_lines T_0 T_1) (-. (convergent_lines T_2 T_0)) (All Y, (All Z, ((convergent_lines T_0 Y) => ((convergent_lines T_0 Z) \/ (convergent_lines Y Z))))) (-. (convergent_lines T_1 T_1)) (-. (convergent_lines T_2 T_1)) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) ### All 30 % 23.55/23.73 32. (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (-. (convergent_lines T_2 T_1)) (-. (convergent_lines T_1 T_1)) (-. (convergent_lines T_2 T_0)) (convergent_lines T_0 T_1) (unorthogonal_lines T_0 T_0) (-. (unorthogonal_lines T_0 T_1)) (All L, (All M, (All N, (((convergent_lines L M) /\ (unorthogonal_lines L M)) => (((convergent_lines L N) /\ (unorthogonal_lines L N)) \/ ((convergent_lines M N) /\ (unorthogonal_lines M N))))))) ### All 31 % 23.55/23.73 33. ((convergent_lines T_0 T_0) \/ (unorthogonal_lines T_0 T_0)) (All L, (All M, (All N, (((convergent_lines L M) /\ (unorthogonal_lines L M)) => (((convergent_lines L N) /\ (unorthogonal_lines L N)) \/ ((convergent_lines M N) /\ (unorthogonal_lines M N))))))) (-. (unorthogonal_lines T_0 T_1)) (convergent_lines T_0 T_1) (-. (convergent_lines T_2 T_0)) (-. (convergent_lines T_1 T_1)) (-. (convergent_lines T_2 T_1)) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (All X, (-. (convergent_lines X X))) ### Or 2 32 % 23.55/23.73 34. (All M, ((convergent_lines T_0 M) \/ (unorthogonal_lines T_0 M))) (All X, (-. (convergent_lines X X))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (-. (convergent_lines T_2 T_1)) (-. (convergent_lines T_1 T_1)) (-. (convergent_lines T_2 T_0)) (convergent_lines T_0 T_1) (-. (unorthogonal_lines T_0 T_1)) (All L, (All M, (All N, (((convergent_lines L M) /\ (unorthogonal_lines L M)) => (((convergent_lines L N) /\ (unorthogonal_lines L N)) \/ ((convergent_lines M N) /\ (unorthogonal_lines M N))))))) ### All 33 % 23.55/23.73 35. (-. (unorthogonal_lines T_0 T_1)) (unorthogonal_lines T_0 T_1) ### Axiom % 23.55/23.73 36. ((convergent_lines T_0 T_1) \/ (unorthogonal_lines T_0 T_1)) (All L, (All M, (All N, (((convergent_lines L M) /\ (unorthogonal_lines L M)) => (((convergent_lines L N) /\ (unorthogonal_lines L N)) \/ ((convergent_lines M N) /\ (unorthogonal_lines M N))))))) (-. (unorthogonal_lines T_0 T_1)) (-. (convergent_lines T_2 T_0)) (-. (convergent_lines T_1 T_1)) (-. (convergent_lines T_2 T_1)) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (All X, (-. (convergent_lines X X))) (All M, ((convergent_lines T_0 M) \/ (unorthogonal_lines T_0 M))) ### Or 34 35 % 23.55/23.73 37. (All M, ((convergent_lines T_0 M) \/ (unorthogonal_lines T_0 M))) (All X, (-. (convergent_lines X X))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (-. (convergent_lines T_2 T_1)) (-. (convergent_lines T_1 T_1)) (-. (convergent_lines T_2 T_0)) (-. (unorthogonal_lines T_0 T_1)) (All L, (All M, (All N, (((convergent_lines L M) /\ (unorthogonal_lines L M)) => (((convergent_lines L N) /\ (unorthogonal_lines L N)) \/ ((convergent_lines M N) /\ (unorthogonal_lines M N))))))) ### All 36 % 23.55/23.73 38. (All L, (All M, ((convergent_lines L M) \/ (unorthogonal_lines L M)))) (All L, (All M, (All N, (((convergent_lines L M) /\ (unorthogonal_lines L M)) => (((convergent_lines L N) /\ (unorthogonal_lines L N)) \/ ((convergent_lines M N) /\ (unorthogonal_lines M N))))))) (-. (unorthogonal_lines T_0 T_1)) (-. (convergent_lines T_2 T_0)) (-. (convergent_lines T_1 T_1)) (-. (convergent_lines T_2 T_1)) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (All X, (-. (convergent_lines X X))) ### All 37 % 23.55/23.73 39. (unorthogonal_lines T_2 T_0) (-. (unorthogonal_lines T_2 T_0)) ### Axiom % 23.55/23.73 40. (convergent_lines T_2 T_0) (-. (convergent_lines T_2 T_0)) ### Axiom % 23.55/23.73 41. (unorthogonal_lines T_2 T_0) (-. (unorthogonal_lines T_2 T_0)) ### Axiom % 23.55/23.73 42. (-. (convergent_lines T_2 T_1)) (convergent_lines T_2 T_1) ### Axiom % 23.55/23.73 43. ((convergent_lines T_2 T_1) /\ (unorthogonal_lines T_2 T_1)) (-. (convergent_lines T_2 T_1)) ### And 42 % 23.55/23.73 44. (((convergent_lines T_2 T_0) /\ (unorthogonal_lines T_2 T_0)) => (((convergent_lines T_2 T_1) /\ (unorthogonal_lines T_2 T_1)) \/ ((convergent_lines T_0 T_1) /\ (unorthogonal_lines T_0 T_1)))) (-. (unorthogonal_lines T_0 T_1)) (-. (convergent_lines T_2 T_1)) (unorthogonal_lines T_2 T_0) (convergent_lines T_2 T_0) ### DisjTree 40 41 43 26 % 23.55/23.73 45. (All N, (((convergent_lines T_2 T_0) /\ (unorthogonal_lines T_2 T_0)) => (((convergent_lines T_2 N) /\ (unorthogonal_lines T_2 N)) \/ ((convergent_lines T_0 N) /\ (unorthogonal_lines T_0 N))))) (convergent_lines T_2 T_0) (unorthogonal_lines T_2 T_0) (-. (convergent_lines T_2 T_1)) (-. (unorthogonal_lines T_0 T_1)) ### All 44 % 23.55/23.73 46. ((convergent_lines T_2 T_0) /\ (unorthogonal_lines T_2 T_0)) (-. (unorthogonal_lines T_0 T_1)) (-. (convergent_lines T_2 T_1)) (unorthogonal_lines T_2 T_0) (All N, (((convergent_lines T_2 T_0) /\ (unorthogonal_lines T_2 T_0)) => (((convergent_lines T_2 N) /\ (unorthogonal_lines T_2 N)) \/ ((convergent_lines T_0 N) /\ (unorthogonal_lines T_0 N))))) ### And 45 % 23.55/23.73 47. ((convergent_lines T_0 T_0) /\ (unorthogonal_lines T_0 T_0)) (All X, (-. (convergent_lines X X))) ### And 2 % 23.55/23.73 48. (((convergent_lines T_2 T_0) /\ (unorthogonal_lines T_2 T_0)) => (((convergent_lines T_2 T_0) /\ (unorthogonal_lines T_2 T_0)) \/ ((convergent_lines T_0 T_0) /\ (unorthogonal_lines T_0 T_0)))) (All N, (((convergent_lines T_2 T_0) /\ (unorthogonal_lines T_2 T_0)) => (((convergent_lines T_2 N) /\ (unorthogonal_lines T_2 N)) \/ ((convergent_lines T_0 N) /\ (unorthogonal_lines T_0 N))))) (unorthogonal_lines T_2 T_0) (All X, (-. (convergent_lines X X))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (-. (convergent_lines T_2 T_1)) (-. (convergent_lines T_1 T_1)) (-. (unorthogonal_lines T_0 T_1)) (All L, (All M, (All N, (((convergent_lines L M) /\ (unorthogonal_lines L M)) => (((convergent_lines L N) /\ (unorthogonal_lines L N)) \/ ((convergent_lines M N) /\ (unorthogonal_lines M N))))))) (All L, (All M, ((convergent_lines L M) \/ (unorthogonal_lines L M)))) ### DisjTree 38 39 46 47 % 23.55/23.73 49. (All L, (All M, ((convergent_lines L M) \/ (unorthogonal_lines L M)))) (All L, (All M, (All N, (((convergent_lines L M) /\ (unorthogonal_lines L M)) => (((convergent_lines L N) /\ (unorthogonal_lines L N)) \/ ((convergent_lines M N) /\ (unorthogonal_lines M N))))))) (-. (unorthogonal_lines T_0 T_1)) (-. (convergent_lines T_1 T_1)) (-. (convergent_lines T_2 T_1)) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (All X, (-. (convergent_lines X X))) (unorthogonal_lines T_2 T_0) (All N, (((convergent_lines T_2 T_0) /\ (unorthogonal_lines T_2 T_0)) => (((convergent_lines T_2 N) /\ (unorthogonal_lines T_2 N)) \/ ((convergent_lines T_0 N) /\ (unorthogonal_lines T_0 N))))) ### All 48 % 23.55/23.73 50. (All M, (All N, (((convergent_lines T_2 M) /\ (unorthogonal_lines T_2 M)) => (((convergent_lines T_2 N) /\ (unorthogonal_lines T_2 N)) \/ ((convergent_lines M N) /\ (unorthogonal_lines M N)))))) (unorthogonal_lines T_2 T_0) (All X, (-. (convergent_lines X X))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (-. (convergent_lines T_2 T_1)) (-. (convergent_lines T_1 T_1)) (-. (unorthogonal_lines T_0 T_1)) (All L, (All M, (All N, (((convergent_lines L M) /\ (unorthogonal_lines L M)) => (((convergent_lines L N) /\ (unorthogonal_lines L N)) \/ ((convergent_lines M N) /\ (unorthogonal_lines M N))))))) (All L, (All M, ((convergent_lines L M) \/ (unorthogonal_lines L M)))) ### All 49 % 23.55/23.73 51. (All L, (All M, ((convergent_lines L M) \/ (unorthogonal_lines L M)))) (All L, (All M, (All N, (((convergent_lines L M) /\ (unorthogonal_lines L M)) => (((convergent_lines L N) /\ (unorthogonal_lines L N)) \/ ((convergent_lines M N) /\ (unorthogonal_lines M N))))))) (-. (unorthogonal_lines T_0 T_1)) (-. (convergent_lines T_2 T_1)) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (All X, (-. (convergent_lines X X))) (unorthogonal_lines T_2 T_0) (All M, (All N, (((convergent_lines T_2 M) /\ (unorthogonal_lines T_2 M)) => (((convergent_lines T_2 N) /\ (unorthogonal_lines T_2 N)) \/ ((convergent_lines M N) /\ (unorthogonal_lines M N)))))) ### All 50 % 23.74/23.92 52. (unorthogonal_lines T_2 T_0) (All X, (-. (convergent_lines X X))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (-. (convergent_lines T_2 T_1)) (-. (unorthogonal_lines T_0 T_1)) (All L, (All M, (All N, (((convergent_lines L M) /\ (unorthogonal_lines L M)) => (((convergent_lines L N) /\ (unorthogonal_lines L N)) \/ ((convergent_lines M N) /\ (unorthogonal_lines M N))))))) (All L, (All M, ((convergent_lines L M) \/ (unorthogonal_lines L M)))) ### All 51 % 23.74/23.92 53. (-. ((unorthogonal_lines T_2 T_0) => ((convergent_lines T_2 T_1) \/ (unorthogonal_lines T_0 T_1)))) (All L, (All M, ((convergent_lines L M) \/ (unorthogonal_lines L M)))) (All L, (All M, (All N, (((convergent_lines L M) /\ (unorthogonal_lines L M)) => (((convergent_lines L N) /\ (unorthogonal_lines L N)) \/ ((convergent_lines M N) /\ (unorthogonal_lines M N))))))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (All X, (-. (convergent_lines X X))) ### ConjTree 52 % 23.74/23.92 54. (-. (All N, ((unorthogonal_lines T_2 T_0) => ((convergent_lines T_2 N) \/ (unorthogonal_lines T_0 N))))) (All X, (-. (convergent_lines X X))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (All L, (All M, (All N, (((convergent_lines L M) /\ (unorthogonal_lines L M)) => (((convergent_lines L N) /\ (unorthogonal_lines L N)) \/ ((convergent_lines M N) /\ (unorthogonal_lines M N))))))) (All L, (All M, ((convergent_lines L M) \/ (unorthogonal_lines L M)))) ### NotAllEx 53 % 23.74/23.92 55. (-. (All M, (All N, ((unorthogonal_lines T_2 M) => ((convergent_lines T_2 N) \/ (unorthogonal_lines M N)))))) (All L, (All M, ((convergent_lines L M) \/ (unorthogonal_lines L M)))) (All L, (All M, (All N, (((convergent_lines L M) /\ (unorthogonal_lines L M)) => (((convergent_lines L N) /\ (unorthogonal_lines L N)) \/ ((convergent_lines M N) /\ (unorthogonal_lines M N))))))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (All X, (-. (convergent_lines X X))) ### NotAllEx 54 % 23.74/23.92 56. (-. (All L, (All M, (All N, ((unorthogonal_lines L M) => ((convergent_lines L N) \/ (unorthogonal_lines M N))))))) (All X, (-. (convergent_lines X X))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (All L, (All M, (All N, (((convergent_lines L M) /\ (unorthogonal_lines L M)) => (((convergent_lines L N) /\ (unorthogonal_lines L N)) \/ ((convergent_lines M N) /\ (unorthogonal_lines M N))))))) (All L, (All M, ((convergent_lines L M) \/ (unorthogonal_lines L M)))) ### NotAllEx 55 % 23.74/23.92 % SZS output end Proof % 23.74/23.92 (* END-PROOF *) %------------------------------------------------------------------------------