%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : GEO213+1 : 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 : n012.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 6.64s 6.87s % Output : Proof 6.94s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.13 % Problem : GEO213+1 : TPTP v8.1.0. Released v3.3.0. % 0.08/0.13 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 0.13/0.35 % Computer : n012.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 600 % 0.13/0.35 % DateTime : Sat Jun 18 00:18:23 EDT 2022 % 0.13/0.35 % CPUTime : % 6.64/6.87 % SZS status Theorem % 6.64/6.87 (* PROOF-FOUND *) % 6.64/6.87 (* BEGIN-PROOF *) % 6.64/6.87 % SZS output start Proof % 6.64/6.87 1. (convergent_lines T_0 T_1) (-. (convergent_lines T_0 T_1)) ### Axiom % 6.64/6.87 2. (-. (convergent_lines T_0 T_0)) (convergent_lines T_0 T_0) ### Axiom % 6.64/6.87 3. (convergent_lines T_1 T_0) (-. (convergent_lines T_1 T_0)) ### Axiom % 6.64/6.87 4. (convergent_lines T_1 T_2) (-. (convergent_lines T_1 T_2)) ### Axiom % 6.64/6.87 5. (-. (distinct_lines T_2 T_1)) (distinct_lines T_2 T_1) ### Axiom % 6.64/6.87 6. (-. (convergent_lines T_1 T_1)) (convergent_lines T_1 T_1) ### Axiom % 6.64/6.87 7. ((convergent_lines T_1 T_2) => ((distinct_lines T_2 T_1) \/ (convergent_lines T_1 T_1))) (-. (convergent_lines T_1 T_1)) (-. (distinct_lines T_2 T_1)) (convergent_lines T_1 T_2) ### DisjTree 4 5 6 % 6.64/6.87 8. (All Z, ((convergent_lines T_1 T_2) => ((distinct_lines T_2 Z) \/ (convergent_lines T_1 Z)))) (convergent_lines T_1 T_2) (-. (distinct_lines T_2 T_1)) (-. (convergent_lines T_1 T_1)) ### All 7 % 6.64/6.87 9. (All Y, (All Z, ((convergent_lines T_1 Y) => ((distinct_lines Y Z) \/ (convergent_lines T_1 Z))))) (-. (convergent_lines T_1 T_1)) (-. (distinct_lines T_2 T_1)) (convergent_lines T_1 T_2) ### All 8 % 6.64/6.87 10. (convergent_lines T_0 T_2) (-. (convergent_lines T_0 T_2)) ### Axiom % 6.64/6.87 11. (-. (convergent_lines T_0 T_0)) (convergent_lines T_0 T_0) ### Axiom % 6.64/6.87 12. (-. (convergent_lines T_2 T_0)) (convergent_lines T_2 T_0) ### Axiom % 6.64/6.87 13. ((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 10 11 12 % 6.64/6.87 14. (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 13 % 6.64/6.87 15. (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 14 % 6.64/6.87 16. ((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))))) (-. (distinct_lines T_2 T_1)) (-. (convergent_lines T_1 T_1)) (All Y, (All Z, ((convergent_lines T_1 Y) => ((distinct_lines Y Z) \/ (convergent_lines T_1 Z))))) (convergent_lines T_1 T_0) ### DisjTree 3 9 15 % 6.64/6.87 17. (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) => ((distinct_lines Y Z) \/ (convergent_lines T_1 Z))))) (-. (convergent_lines T_1 T_1)) (-. (distinct_lines T_2 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 16 % 6.64/6.87 18. (All Y, (All Z, ((convergent_lines T_1 Y) => ((convergent_lines T_1 Z) \/ (convergent_lines Y Z))))) (-. (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))))) (-. (distinct_lines T_2 T_1)) (-. (convergent_lines T_1 T_1)) (All Y, (All Z, ((convergent_lines T_1 Y) => ((distinct_lines Y Z) \/ (convergent_lines T_1 Z))))) (convergent_lines T_1 T_0) ### All 17 % 6.64/6.87 19. (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (convergent_lines T_1 T_0) (All Y, (All Z, ((convergent_lines T_1 Y) => ((distinct_lines Y Z) \/ (convergent_lines T_1 Z))))) (-. (convergent_lines T_1 T_1)) (-. (distinct_lines T_2 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 % 6.64/6.87 20. (All X, (All Y, (All Z, ((convergent_lines X Y) => ((distinct_lines Y Z) \/ (convergent_lines X Z)))))) (-. (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))))) (-. (distinct_lines T_2 T_1)) (-. (convergent_lines T_1 T_1)) (convergent_lines T_1 T_0) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) ### All 19 % 6.64/6.87 21. ((convergent_lines T_0 T_1) => ((convergent_lines T_0 T_0) \/ (convergent_lines T_1 T_0))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (-. (convergent_lines T_1 T_1)) (-. (distinct_lines T_2 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)) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((distinct_lines Y Z) \/ (convergent_lines X Z)))))) (-. (convergent_lines T_0 T_0)) (convergent_lines T_0 T_1) ### DisjTree 1 2 20 % 6.64/6.87 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)) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((distinct_lines Y Z) \/ (convergent_lines X Z)))))) (-. (convergent_lines T_2 T_0)) (All Y, (All Z, ((convergent_lines T_0 Y) => ((convergent_lines T_0 Z) \/ (convergent_lines Y Z))))) (-. (distinct_lines T_2 T_1)) (-. (convergent_lines T_1 T_1)) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) ### All 21 % 6.64/6.87 23. (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (-. (convergent_lines T_1 T_1)) (-. (distinct_lines T_2 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)) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((distinct_lines Y Z) \/ (convergent_lines X Z)))))) (-. (convergent_lines T_0 T_0)) (convergent_lines T_0 T_1) ### All 22 % 6.64/6.87 24. (All X, (-. (convergent_lines X X))) (convergent_lines T_0 T_1) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((distinct_lines Y Z) \/ (convergent_lines X Z)))))) (-. (convergent_lines T_2 T_0)) (All Y, (All Z, ((convergent_lines T_0 Y) => ((convergent_lines T_0 Z) \/ (convergent_lines Y Z))))) (-. (distinct_lines T_2 T_1)) (-. (convergent_lines T_1 T_1)) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) ### All 23 % 6.64/6.87 25. (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (-. (convergent_lines T_1 T_1)) (-. (distinct_lines T_2 T_1)) (-. (convergent_lines T_2 T_0)) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((distinct_lines Y Z) \/ (convergent_lines X Z)))))) (convergent_lines T_0 T_1) (All X, (-. (convergent_lines X X))) ### All 24 % 6.64/6.87 26. (unorthogonal_lines T_2 T_0) (-. (unorthogonal_lines T_2 T_0)) ### Axiom % 6.64/6.87 27. (-. (convergent_lines T_2 T_1)) (convergent_lines T_2 T_1) ### Axiom % 6.64/6.87 28. ((convergent_lines T_2 T_1) /\ (unorthogonal_lines T_2 T_1)) (-. (convergent_lines T_2 T_1)) ### And 27 % 6.64/6.87 29. (-. (unorthogonal_lines T_0 T_1)) (unorthogonal_lines T_0 T_1) ### Axiom % 6.64/6.87 30. ((convergent_lines T_0 T_1) /\ (unorthogonal_lines T_0 T_1)) (-. (unorthogonal_lines T_0 T_1)) ### And 29 % 6.64/6.87 31. (((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) (All X, (-. (convergent_lines X X))) (convergent_lines T_0 T_1) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((distinct_lines Y Z) \/ (convergent_lines X Z)))))) (-. (distinct_lines T_2 T_1)) (-. (convergent_lines T_1 T_1)) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) ### DisjTree 25 26 28 30 % 6.64/6.87 32. (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 X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (-. (convergent_lines T_1 T_1)) (-. (distinct_lines T_2 T_1)) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((distinct_lines Y Z) \/ (convergent_lines X Z)))))) (convergent_lines T_0 T_1) (All X, (-. (convergent_lines X X))) (unorthogonal_lines T_2 T_0) (-. (convergent_lines T_2 T_1)) (-. (unorthogonal_lines T_0 T_1)) ### All 31 % 6.94/7.18 33. (convergent_lines T_2 T_1) (-. (convergent_lines T_2 T_1)) ### Axiom % 6.94/7.18 34. (convergent_lines T_2 T_2) (-. (convergent_lines T_2 T_2)) ### Axiom % 6.94/7.18 35. (All X, (-. (convergent_lines X X))) (convergent_lines T_2 T_2) ### All 34 % 6.94/7.18 36. ((convergent_lines T_2 T_1) => ((convergent_lines T_2 T_2) \/ (convergent_lines T_1 T_2))) (-. (distinct_lines T_2 T_1)) (-. (convergent_lines T_1 T_1)) (All Y, (All Z, ((convergent_lines T_1 Y) => ((distinct_lines Y Z) \/ (convergent_lines T_1 Z))))) (All X, (-. (convergent_lines X X))) (convergent_lines T_2 T_1) ### DisjTree 33 35 9 % 6.94/7.18 37. (All Z, ((convergent_lines T_2 T_1) => ((convergent_lines T_2 Z) \/ (convergent_lines T_1 Z)))) (convergent_lines T_2 T_1) (All X, (-. (convergent_lines X X))) (All Y, (All Z, ((convergent_lines T_1 Y) => ((distinct_lines Y Z) \/ (convergent_lines T_1 Z))))) (-. (convergent_lines T_1 T_1)) (-. (distinct_lines T_2 T_1)) ### All 36 % 6.94/7.18 38. (All Y, (All Z, ((convergent_lines T_2 Y) => ((convergent_lines T_2 Z) \/ (convergent_lines Y Z))))) (-. (distinct_lines T_2 T_1)) (-. (convergent_lines T_1 T_1)) (All Y, (All Z, ((convergent_lines T_1 Y) => ((distinct_lines Y Z) \/ (convergent_lines T_1 Z))))) (All X, (-. (convergent_lines X X))) (convergent_lines T_2 T_1) ### All 37 % 6.94/7.18 39. (All X, (All Y, (All Z, ((convergent_lines X Y) => ((distinct_lines Y Z) \/ (convergent_lines X Z)))))) (convergent_lines T_2 T_1) (All X, (-. (convergent_lines X X))) (-. (convergent_lines T_1 T_1)) (-. (distinct_lines T_2 T_1)) (All Y, (All Z, ((convergent_lines T_2 Y) => ((convergent_lines T_2 Z) \/ (convergent_lines Y Z))))) ### All 38 % 6.94/7.18 40. (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (-. (distinct_lines T_2 T_1)) (-. (convergent_lines T_1 T_1)) (All X, (-. (convergent_lines X X))) (convergent_lines T_2 T_1) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((distinct_lines Y Z) \/ (convergent_lines X Z)))))) ### All 39 % 6.94/7.18 41. (-. (unorthogonal_lines T_2 T_1)) (unorthogonal_lines T_2 T_1) ### Axiom % 6.94/7.18 42. ((convergent_lines T_2 T_1) \/ (unorthogonal_lines T_2 T_1)) (-. (unorthogonal_lines T_2 T_1)) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((distinct_lines Y Z) \/ (convergent_lines X Z)))))) (All X, (-. (convergent_lines X X))) (-. (convergent_lines T_1 T_1)) (-. (distinct_lines T_2 T_1)) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) ### Or 40 41 % 6.94/7.18 43. (All M, ((convergent_lines T_2 M) \/ (unorthogonal_lines T_2 M))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (-. (distinct_lines T_2 T_1)) (-. (convergent_lines T_1 T_1)) (All X, (-. (convergent_lines X X))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((distinct_lines Y Z) \/ (convergent_lines X Z)))))) (-. (unorthogonal_lines T_2 T_1)) ### All 42 % 6.94/7.18 44. (All L, (All M, ((convergent_lines L M) \/ (unorthogonal_lines L M)))) (-. (unorthogonal_lines T_2 T_1)) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((distinct_lines Y Z) \/ (convergent_lines X Z)))))) (All X, (-. (convergent_lines X X))) (-. (convergent_lines T_1 T_1)) (-. (distinct_lines T_2 T_1)) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) ### All 43 % 6.94/7.18 45. ((convergent_lines T_2 T_1) /\ (unorthogonal_lines T_2 T_1)) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((distinct_lines Y Z) \/ (convergent_lines X Z)))))) (All X, (-. (convergent_lines X X))) (-. (convergent_lines T_1 T_1)) (-. (distinct_lines T_2 T_1)) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) ### And 40 % 6.94/7.18 46. (-. (convergent_lines T_1 T_1)) (convergent_lines T_1 T_1) ### Axiom % 6.94/7.18 47. ((convergent_lines T_1 T_1) /\ (unorthogonal_lines T_1 T_1)) (-. (convergent_lines T_1 T_1)) ### And 46 % 6.94/7.18 48. (((convergent_lines T_2 T_1) /\ (unorthogonal_lines T_2 T_1)) => (((convergent_lines T_2 T_1) /\ (unorthogonal_lines T_2 T_1)) \/ ((convergent_lines T_1 T_1) /\ (unorthogonal_lines T_1 T_1)))) (All L, (All M, ((convergent_lines L M) \/ (unorthogonal_lines L M)))) (-. (unorthogonal_lines T_0 T_1)) (unorthogonal_lines T_2 T_0) (All X, (-. (convergent_lines X X))) (convergent_lines T_0 T_1) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((distinct_lines Y Z) \/ (convergent_lines X Z)))))) (-. (distinct_lines T_2 T_1)) (-. (convergent_lines T_1 T_1)) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (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))))) ### DisjTree 32 44 45 47 % 6.94/7.18 49. (All N, (((convergent_lines T_2 T_1) /\ (unorthogonal_lines T_2 T_1)) => (((convergent_lines T_2 N) /\ (unorthogonal_lines T_2 N)) \/ ((convergent_lines T_1 N) /\ (unorthogonal_lines T_1 N))))) (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 X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (-. (convergent_lines T_1 T_1)) (-. (distinct_lines T_2 T_1)) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((distinct_lines Y Z) \/ (convergent_lines X Z)))))) (convergent_lines T_0 T_1) (All X, (-. (convergent_lines X X))) (unorthogonal_lines T_2 T_0) (-. (unorthogonal_lines T_0 T_1)) (All L, (All M, ((convergent_lines L M) \/ (unorthogonal_lines L M)))) ### All 48 % 6.94/7.18 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)))))) (All L, (All M, ((convergent_lines L M) \/ (unorthogonal_lines L M)))) (-. (unorthogonal_lines T_0 T_1)) (unorthogonal_lines T_2 T_0) (All X, (-. (convergent_lines X X))) (convergent_lines T_0 T_1) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((distinct_lines Y Z) \/ (convergent_lines X Z)))))) (-. (distinct_lines T_2 T_1)) (-. (convergent_lines T_1 T_1)) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (All N, (((convergent_lines T_2 T_1) /\ (unorthogonal_lines T_2 T_1)) => (((convergent_lines T_2 N) /\ (unorthogonal_lines T_2 N)) \/ ((convergent_lines T_1 N) /\ (unorthogonal_lines T_1 N))))) ### All 49 % 6.94/7.18 51. (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (-. (convergent_lines T_1 T_1)) (-. (distinct_lines T_2 T_1)) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((distinct_lines Y Z) \/ (convergent_lines X Z)))))) (convergent_lines T_0 T_1) (All X, (-. (convergent_lines X X))) (unorthogonal_lines T_2 T_0) (-. (unorthogonal_lines T_0 T_1)) (All L, (All M, ((convergent_lines L M) \/ (unorthogonal_lines L M)))) (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 % 6.94/7.18 52. (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 L, (All M, ((convergent_lines L M) \/ (unorthogonal_lines L M)))) (-. (unorthogonal_lines T_0 T_1)) (unorthogonal_lines T_2 T_0) (All X, (-. (convergent_lines X X))) (convergent_lines T_0 T_1) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((distinct_lines Y Z) \/ (convergent_lines X Z)))))) (-. (distinct_lines T_2 T_1)) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) ### All 51 % 6.94/7.19 53. (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)))))) (-. (distinct_lines T_2 T_1)) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((distinct_lines Y Z) \/ (convergent_lines X Z)))))) (convergent_lines T_0 T_1) (All X, (-. (convergent_lines X X))) (unorthogonal_lines T_2 T_0) (-. (unorthogonal_lines T_0 T_1)) (All L, (All M, ((convergent_lines L M) \/ (unorthogonal_lines L M)))) ### All 52 % 6.94/7.19 54. (-. (unorthogonal_lines T_0 T_1)) (unorthogonal_lines T_0 T_1) ### Axiom % 6.94/7.19 55. ((convergent_lines T_0 T_1) \/ (unorthogonal_lines T_0 T_1)) (All L, (All M, ((convergent_lines L M) \/ (unorthogonal_lines L M)))) (-. (unorthogonal_lines T_0 T_1)) (unorthogonal_lines T_2 T_0) (All X, (-. (convergent_lines X X))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((distinct_lines Y Z) \/ (convergent_lines X Z)))))) (-. (distinct_lines T_2 T_1)) (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))))))) ### Or 53 54 % 6.94/7.19 56. (All M, ((convergent_lines T_0 M) \/ (unorthogonal_lines T_0 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)))))) (-. (distinct_lines T_2 T_1)) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((distinct_lines Y Z) \/ (convergent_lines X Z)))))) (All X, (-. (convergent_lines X X))) (unorthogonal_lines T_2 T_0) (-. (unorthogonal_lines T_0 T_1)) (All L, (All M, ((convergent_lines L M) \/ (unorthogonal_lines L M)))) ### All 55 % 6.94/7.19 57. (All L, (All M, ((convergent_lines L M) \/ (unorthogonal_lines L M)))) (-. (unorthogonal_lines T_0 T_1)) (unorthogonal_lines T_2 T_0) (All X, (-. (convergent_lines X X))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((distinct_lines Y Z) \/ (convergent_lines X Z)))))) (-. (distinct_lines T_2 T_1)) (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 56 % 6.94/7.19 58. (-. ((unorthogonal_lines T_2 T_0) => ((distinct_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 X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((distinct_lines Y Z) \/ (convergent_lines X Z)))))) (All X, (-. (convergent_lines X X))) (All L, (All M, ((convergent_lines L M) \/ (unorthogonal_lines L M)))) ### ConjTree 57 % 6.94/7.19 59. (-. (All N, ((unorthogonal_lines T_2 T_0) => ((distinct_lines T_2 N) \/ (unorthogonal_lines T_0 N))))) (All L, (All M, ((convergent_lines L M) \/ (unorthogonal_lines L M)))) (All X, (-. (convergent_lines X X))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((distinct_lines Y Z) \/ (convergent_lines X Z)))))) (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))))))) ### NotAllEx 58 % 6.94/7.19 60. (-. (All M, (All N, ((unorthogonal_lines T_2 M) => ((distinct_lines T_2 N) \/ (unorthogonal_lines M N)))))) (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, (All Y, (All Z, ((convergent_lines X Y) => ((distinct_lines Y Z) \/ (convergent_lines X Z)))))) (All X, (-. (convergent_lines X X))) (All L, (All M, ((convergent_lines L M) \/ (unorthogonal_lines L M)))) ### NotAllEx 59 % 6.94/7.19 61. (-. (All L, (All M, (All N, ((unorthogonal_lines L M) => ((distinct_lines L N) \/ (unorthogonal_lines M N))))))) (All L, (All M, ((convergent_lines L M) \/ (unorthogonal_lines L M)))) (All X, (-. (convergent_lines X X))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((distinct_lines Y Z) \/ (convergent_lines X Z)))))) (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))))))) ### NotAllEx 60 % 6.94/7.19 % SZS output end Proof % 6.94/7.19 (* END-PROOF *) %------------------------------------------------------------------------------