%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : GEO213+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 : n004.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 06:31:11 EDT 2022 % Result : Theorem 21.90s 22.14s % Output : Proof 22.27s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : GEO213+2 : TPTP v8.1.0. Released v3.3.0. % 0.04/0.12 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 0.14/0.33 % Computer : n004.cluster.edu % 0.14/0.33 % Model : x86_64 x86_64 % 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.33 % Memory : 8042.1875MB % 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.33 % CPULimit : 300 % 0.14/0.33 % WCLimit : 600 % 0.14/0.33 % DateTime : Sat Jun 18 13:49:08 EDT 2022 % 0.14/0.33 % CPUTime : % 21.90/22.14 % SZS status Theorem % 21.90/22.14 (* PROOF-FOUND *) % 21.90/22.14 (* BEGIN-PROOF *) % 21.90/22.14 % SZS output start Proof % 21.90/22.14 1. (convergent_lines T_0 T_0) (-. (convergent_lines T_0 T_0)) ### Axiom % 21.90/22.14 2. (All X, (-. (convergent_lines X X))) (convergent_lines T_0 T_0) ### All 1 % 21.90/22.14 3. (convergent_lines T_0 T_1) (-. (convergent_lines T_0 T_1)) ### Axiom % 21.90/22.14 4. (-. (convergent_lines T_0 T_0)) (convergent_lines T_0 T_0) ### Axiom % 21.90/22.14 5. (convergent_lines T_0 T_2) (-. (convergent_lines T_0 T_2)) ### Axiom % 21.90/22.14 6. (-. (convergent_lines T_0 T_0)) (convergent_lines T_0 T_0) ### Axiom % 21.90/22.14 7. (-. (convergent_lines T_2 T_0)) (convergent_lines T_2 T_0) ### Axiom % 21.90/22.14 8. ((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 5 6 7 % 21.90/22.14 9. (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 8 % 21.90/22.14 10. (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 9 % 21.90/22.14 11. (convergent_lines T_1 T_0) (-. (convergent_lines T_1 T_0)) ### Axiom % 21.90/22.14 12. (-. (convergent_lines T_1 T_2)) (convergent_lines T_1 T_2) ### Axiom % 21.90/22.14 13. (-. (convergent_lines T_0 T_2)) (convergent_lines T_0 T_2) ### Axiom % 21.90/22.14 14. ((convergent_lines T_1 T_0) => ((convergent_lines T_1 T_2) \/ (convergent_lines T_0 T_2))) (-. (convergent_lines T_0 T_2)) (-. (convergent_lines T_1 T_2)) (convergent_lines T_1 T_0) ### DisjTree 11 12 13 % 21.90/22.14 15. (All Z, ((convergent_lines T_1 T_0) => ((convergent_lines T_1 Z) \/ (convergent_lines T_0 Z)))) (convergent_lines T_1 T_0) (-. (convergent_lines T_1 T_2)) (-. (convergent_lines T_0 T_2)) ### All 14 % 21.90/22.14 16. (distinct_lines T_1 T_2) (-. (distinct_lines T_1 T_2)) ### Axiom % 21.90/22.14 17. (-. (distinct_lines T_1 T_1)) (distinct_lines T_1 T_1) ### Axiom % 21.90/22.14 18. (-. (distinct_lines T_2 T_1)) (distinct_lines T_2 T_1) ### Axiom % 21.90/22.14 19. ((distinct_lines T_1 T_2) => ((distinct_lines T_1 T_1) \/ (distinct_lines T_2 T_1))) (-. (distinct_lines T_2 T_1)) (-. (distinct_lines T_1 T_1)) (distinct_lines T_1 T_2) ### DisjTree 16 17 18 % 21.90/22.14 20. (All Z, ((distinct_lines T_1 T_2) => ((distinct_lines T_1 Z) \/ (distinct_lines T_2 Z)))) (distinct_lines T_1 T_2) (-. (distinct_lines T_1 T_1)) (-. (distinct_lines T_2 T_1)) ### All 19 % 21.90/22.14 21. (All Y, (All Z, ((distinct_lines T_1 Y) => ((distinct_lines T_1 Z) \/ (distinct_lines Y Z))))) (-. (distinct_lines T_2 T_1)) (-. (distinct_lines T_1 T_1)) (distinct_lines T_1 T_2) ### All 20 % 21.90/22.14 22. ((convergent_lines T_1 T_2) => (distinct_lines T_1 T_2)) (-. (distinct_lines T_1 T_1)) (-. (distinct_lines T_2 T_1)) (All Y, (All Z, ((distinct_lines T_1 Y) => ((distinct_lines T_1 Z) \/ (distinct_lines Y Z))))) (-. (convergent_lines T_0 T_2)) (convergent_lines T_1 T_0) (All Z, ((convergent_lines T_1 T_0) => ((convergent_lines T_1 Z) \/ (convergent_lines T_0 Z)))) ### Imply 15 21 % 21.90/22.14 23. (All Y, ((convergent_lines T_1 Y) => (distinct_lines T_1 Y))) (All Z, ((convergent_lines T_1 T_0) => ((convergent_lines T_1 Z) \/ (convergent_lines T_0 Z)))) (convergent_lines T_1 T_0) (-. (convergent_lines T_0 T_2)) (All Y, (All Z, ((distinct_lines T_1 Y) => ((distinct_lines T_1 Z) \/ (distinct_lines Y Z))))) (-. (distinct_lines T_2 T_1)) (-. (distinct_lines T_1 T_1)) ### All 22 % 21.90/22.14 24. (unorthogonal_lines T_0 T_2) (-. (unorthogonal_lines T_0 T_2)) ### Axiom % 21.90/22.14 25. (-. (unorthogonal_lines T_0 T_1)) (unorthogonal_lines T_0 T_1) ### Axiom % 21.90/22.14 26. ((convergent_lines T_0 T_1) /\ (unorthogonal_lines T_0 T_1)) (-. (unorthogonal_lines T_0 T_1)) ### And 25 % 21.90/22.14 27. (-. (convergent_lines T_2 T_1)) (convergent_lines T_2 T_1) ### Axiom % 21.90/22.14 28. ((convergent_lines T_2 T_1) /\ (unorthogonal_lines T_2 T_1)) (-. (convergent_lines T_2 T_1)) ### And 27 % 21.90/22.14 29. (((convergent_lines T_0 T_2) /\ (unorthogonal_lines T_0 T_2)) => (((convergent_lines T_0 T_1) /\ (unorthogonal_lines T_0 T_1)) \/ ((convergent_lines T_2 T_1) /\ (unorthogonal_lines T_2 T_1)))) (-. (convergent_lines T_2 T_1)) (-. (unorthogonal_lines T_0 T_1)) (unorthogonal_lines T_0 T_2) (-. (distinct_lines T_1 T_1)) (-. (distinct_lines T_2 T_1)) (All Y, (All Z, ((distinct_lines T_1 Y) => ((distinct_lines T_1 Z) \/ (distinct_lines Y Z))))) (convergent_lines T_1 T_0) (All Z, ((convergent_lines T_1 T_0) => ((convergent_lines T_1 Z) \/ (convergent_lines T_0 Z)))) (All Y, ((convergent_lines T_1 Y) => (distinct_lines T_1 Y))) ### DisjTree 23 24 26 28 % 21.90/22.14 30. (All N, (((convergent_lines T_0 T_2) /\ (unorthogonal_lines T_0 T_2)) => (((convergent_lines T_0 N) /\ (unorthogonal_lines T_0 N)) \/ ((convergent_lines T_2 N) /\ (unorthogonal_lines T_2 N))))) (All Y, ((convergent_lines T_1 Y) => (distinct_lines T_1 Y))) (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, ((distinct_lines T_1 Y) => ((distinct_lines T_1 Z) \/ (distinct_lines Y Z))))) (-. (distinct_lines T_2 T_1)) (-. (distinct_lines T_1 T_1)) (unorthogonal_lines T_0 T_2) (-. (unorthogonal_lines T_0 T_1)) (-. (convergent_lines T_2 T_1)) ### All 29 % 21.90/22.14 31. (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)))))) (-. (convergent_lines T_2 T_1)) (-. (unorthogonal_lines T_0 T_1)) (unorthogonal_lines T_0 T_2) (-. (distinct_lines T_1 T_1)) (-. (distinct_lines T_2 T_1)) (All Y, (All Z, ((distinct_lines T_1 Y) => ((distinct_lines T_1 Z) \/ (distinct_lines Y Z))))) (convergent_lines T_1 T_0) (All Z, ((convergent_lines T_1 T_0) => ((convergent_lines T_1 Z) \/ (convergent_lines T_0 Z)))) (All Y, ((convergent_lines T_1 Y) => (distinct_lines T_1 Y))) ### All 30 % 21.90/22.14 32. ((convergent_lines T_0 T_2) \/ (unorthogonal_lines T_0 T_2)) (All Y, ((convergent_lines T_1 Y) => (distinct_lines T_1 Y))) (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, ((distinct_lines T_1 Y) => ((distinct_lines T_1 Z) \/ (distinct_lines Y Z))))) (-. (distinct_lines T_2 T_1)) (-. (distinct_lines T_1 T_1)) (-. (unorthogonal_lines T_0 T_1)) (-. (convergent_lines T_2 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)))))) (-. (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))))) ### Or 10 31 % 21.90/22.14 33. (All M, ((convergent_lines T_0 M) \/ (unorthogonal_lines T_0 M))) (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 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)))))) (-. (convergent_lines T_2 T_1)) (-. (unorthogonal_lines T_0 T_1)) (-. (distinct_lines T_1 T_1)) (-. (distinct_lines T_2 T_1)) (All Y, (All Z, ((distinct_lines T_1 Y) => ((distinct_lines T_1 Z) \/ (distinct_lines Y Z))))) (convergent_lines T_1 T_0) (All Z, ((convergent_lines T_1 T_0) => ((convergent_lines T_1 Z) \/ (convergent_lines T_0 Z)))) (All Y, ((convergent_lines T_1 Y) => (distinct_lines T_1 Y))) ### All 32 % 21.90/22.14 34. (All Y, (All Z, ((convergent_lines T_1 Y) => ((convergent_lines T_1 Z) \/ (convergent_lines Y Z))))) (All Y, ((convergent_lines T_1 Y) => (distinct_lines T_1 Y))) (convergent_lines T_1 T_0) (All Y, (All Z, ((distinct_lines T_1 Y) => ((distinct_lines T_1 Z) \/ (distinct_lines Y Z))))) (-. (distinct_lines T_2 T_1)) (-. (distinct_lines T_1 T_1)) (-. (unorthogonal_lines T_0 T_1)) (-. (convergent_lines T_2 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)))))) (-. (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))))) (All M, ((convergent_lines T_0 M) \/ (unorthogonal_lines T_0 M))) ### All 33 % 22.03/22.21 35. (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (All M, ((convergent_lines T_0 M) \/ (unorthogonal_lines T_0 M))) (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 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)))))) (-. (convergent_lines T_2 T_1)) (-. (unorthogonal_lines T_0 T_1)) (-. (distinct_lines T_1 T_1)) (-. (distinct_lines T_2 T_1)) (All Y, (All Z, ((distinct_lines T_1 Y) => ((distinct_lines T_1 Z) \/ (distinct_lines Y Z))))) (convergent_lines T_1 T_0) (All Y, ((convergent_lines T_1 Y) => (distinct_lines T_1 Y))) ### All 34 % 22.03/22.21 36. ((convergent_lines T_0 T_1) => ((convergent_lines T_0 T_0) \/ (convergent_lines T_1 T_0))) (All Y, ((convergent_lines T_1 Y) => (distinct_lines T_1 Y))) (All Y, (All Z, ((distinct_lines T_1 Y) => ((distinct_lines T_1 Z) \/ (distinct_lines Y Z))))) (-. (distinct_lines T_2 T_1)) (-. (distinct_lines T_1 T_1)) (-. (unorthogonal_lines T_0 T_1)) (-. (convergent_lines T_2 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)))))) (-. (convergent_lines T_2 T_0)) (All Y, (All Z, ((convergent_lines T_0 Y) => ((convergent_lines T_0 Z) \/ (convergent_lines Y Z))))) (All M, ((convergent_lines T_0 M) \/ (unorthogonal_lines T_0 M))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (-. (convergent_lines T_0 T_0)) (convergent_lines T_0 T_1) ### DisjTree 3 4 35 % 22.03/22.21 37. (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) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (All M, ((convergent_lines T_0 M) \/ (unorthogonal_lines T_0 M))) (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 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)))))) (-. (convergent_lines T_2 T_1)) (-. (unorthogonal_lines T_0 T_1)) (-. (distinct_lines T_1 T_1)) (-. (distinct_lines T_2 T_1)) (All Y, (All Z, ((distinct_lines T_1 Y) => ((distinct_lines T_1 Z) \/ (distinct_lines Y Z))))) (All Y, ((convergent_lines T_1 Y) => (distinct_lines T_1 Y))) ### All 36 % 22.03/22.21 38. (All X, (All Y, (All Z, ((distinct_lines X Y) => ((distinct_lines X Z) \/ (distinct_lines Y Z)))))) (All Y, ((convergent_lines T_1 Y) => (distinct_lines T_1 Y))) (-. (distinct_lines T_2 T_1)) (-. (distinct_lines T_1 T_1)) (-. (unorthogonal_lines T_0 T_1)) (-. (convergent_lines T_2 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)))))) (-. (convergent_lines T_2 T_0)) (All Y, (All Z, ((convergent_lines T_0 Y) => ((convergent_lines T_0 Z) \/ (convergent_lines Y Z))))) (All M, ((convergent_lines T_0 M) \/ (unorthogonal_lines T_0 M))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (-. (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 37 % 22.03/22.21 39. (convergent_lines T_0 T_1) (-. (convergent_lines T_0 T_0)) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (All M, ((convergent_lines T_0 M) \/ (unorthogonal_lines T_0 M))) (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 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)))))) (-. (convergent_lines T_2 T_1)) (-. (unorthogonal_lines T_0 T_1)) (-. (distinct_lines T_1 T_1)) (-. (distinct_lines T_2 T_1)) (All Y, ((convergent_lines T_1 Y) => (distinct_lines T_1 Y))) (All X, (All Y, (All Z, ((distinct_lines X Y) => ((distinct_lines X Z) \/ (distinct_lines Y Z)))))) ### All 38 % 22.03/22.21 40. (All X, (All Y, (All Z, ((distinct_lines X Y) => ((distinct_lines X Z) \/ (distinct_lines Y Z)))))) (All Y, ((convergent_lines T_1 Y) => (distinct_lines T_1 Y))) (-. (distinct_lines T_2 T_1)) (-. (distinct_lines T_1 T_1)) (-. (unorthogonal_lines T_0 T_1)) (-. (convergent_lines T_2 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)))))) (-. (convergent_lines T_2 T_0)) (All M, ((convergent_lines T_0 M) \/ (unorthogonal_lines T_0 M))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (-. (convergent_lines T_0 T_0)) (convergent_lines T_0 T_1) ### All 39 % 22.03/22.21 41. (All X, (All Y, ((convergent_lines X Y) => (distinct_lines X Y)))) (convergent_lines T_0 T_1) (-. (convergent_lines T_0 T_0)) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (All M, ((convergent_lines T_0 M) \/ (unorthogonal_lines T_0 M))) (-. (convergent_lines T_2 T_0)) (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)))))) (-. (convergent_lines T_2 T_1)) (-. (unorthogonal_lines T_0 T_1)) (-. (distinct_lines T_1 T_1)) (-. (distinct_lines T_2 T_1)) (All X, (All Y, (All Z, ((distinct_lines X Y) => ((distinct_lines X Z) \/ (distinct_lines Y Z)))))) ### All 40 % 22.03/22.21 42. (unorthogonal_lines T_2 T_0) (-. (unorthogonal_lines T_2 T_0)) ### Axiom % 22.03/22.21 43. (convergent_lines T_2 T_0) (-. (convergent_lines T_2 T_0)) ### Axiom % 22.03/22.21 44. (unorthogonal_lines T_2 T_0) (-. (unorthogonal_lines T_2 T_0)) ### Axiom % 22.03/22.21 45. (((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 43 44 28 26 % 22.03/22.21 46. (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 45 % 22.03/22.21 47. ((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 46 % 22.03/22.21 48. (-. (convergent_lines T_0 T_0)) (convergent_lines T_0 T_0) ### Axiom % 22.03/22.21 49. ((convergent_lines T_0 T_0) /\ (unorthogonal_lines T_0 T_0)) (-. (convergent_lines T_0 T_0)) ### And 48 % 22.03/22.21 50. (((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, (All Y, (All Z, ((distinct_lines X Y) => ((distinct_lines X Z) \/ (distinct_lines Y Z)))))) (-. (distinct_lines T_2 T_1)) (-. (distinct_lines T_1 T_1)) (-. (unorthogonal_lines T_0 T_1)) (-. (convergent_lines T_2 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 M, ((convergent_lines T_0 M) \/ (unorthogonal_lines T_0 M))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (-. (convergent_lines T_0 T_0)) (convergent_lines T_0 T_1) (All X, (All Y, ((convergent_lines X Y) => (distinct_lines X Y)))) ### DisjTree 41 42 47 49 % 22.27/22.46 51. (All X, (All Y, ((convergent_lines X Y) => (distinct_lines X Y)))) (convergent_lines T_0 T_1) (-. (convergent_lines T_0 T_0)) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (All M, ((convergent_lines T_0 M) \/ (unorthogonal_lines T_0 M))) (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)))))) (-. (convergent_lines T_2 T_1)) (-. (unorthogonal_lines T_0 T_1)) (-. (distinct_lines T_1 T_1)) (-. (distinct_lines T_2 T_1)) (All X, (All Y, (All Z, ((distinct_lines X Y) => ((distinct_lines X Z) \/ (distinct_lines Y Z)))))) (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 50 % 22.27/22.46 52. (unorthogonal_lines T_0 T_0) (-. (unorthogonal_lines T_0 T_0)) ### Axiom % 22.27/22.46 53. (((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_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, (All Y, (All Z, ((distinct_lines X Y) => ((distinct_lines X Z) \/ (distinct_lines Y Z)))))) (-. (distinct_lines T_2 T_1)) (-. (distinct_lines T_1 T_1)) (-. (unorthogonal_lines T_0 T_1)) (-. (convergent_lines T_2 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 M, ((convergent_lines T_0 M) \/ (unorthogonal_lines T_0 M))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (convergent_lines T_0 T_1) (All X, (All Y, ((convergent_lines X Y) => (distinct_lines X Y)))) ### DisjTree 51 52 26 26 % 22.27/22.46 54. (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, ((convergent_lines X Y) => (distinct_lines X Y)))) (convergent_lines T_0 T_1) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (All M, ((convergent_lines T_0 M) \/ (unorthogonal_lines T_0 M))) (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)))))) (-. (convergent_lines T_2 T_1)) (-. (unorthogonal_lines T_0 T_1)) (-. (distinct_lines T_1 T_1)) (-. (distinct_lines T_2 T_1)) (All X, (All Y, (All Z, ((distinct_lines X Y) => ((distinct_lines X Z) \/ (distinct_lines Y Z)))))) (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))))) (unorthogonal_lines T_0 T_0) ### All 53 % 22.27/22.46 55. (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, (All Y, (All Z, ((distinct_lines X Y) => ((distinct_lines X Z) \/ (distinct_lines Y Z)))))) (-. (distinct_lines T_2 T_1)) (-. (distinct_lines T_1 T_1)) (-. (unorthogonal_lines T_0 T_1)) (-. (convergent_lines T_2 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 M, ((convergent_lines T_0 M) \/ (unorthogonal_lines T_0 M))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (convergent_lines T_0 T_1) (All X, (All Y, ((convergent_lines X Y) => (distinct_lines X Y)))) ### All 54 % 22.27/22.46 56. (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 X, (All Y, ((convergent_lines X Y) => (distinct_lines X Y)))) (convergent_lines T_0 T_1) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (All M, ((convergent_lines T_0 M) \/ (unorthogonal_lines T_0 M))) (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)))))) (-. (convergent_lines T_2 T_1)) (-. (unorthogonal_lines T_0 T_1)) (-. (distinct_lines T_1 T_1)) (-. (distinct_lines T_2 T_1)) (All X, (All Y, (All Z, ((distinct_lines X Y) => ((distinct_lines X Z) \/ (distinct_lines Y Z)))))) (unorthogonal_lines T_2 T_0) (unorthogonal_lines T_0 T_0) ### All 55 % 22.27/22.46 57. (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_0) (unorthogonal_lines T_2 T_0) (All X, (All Y, (All Z, ((distinct_lines X Y) => ((distinct_lines X Z) \/ (distinct_lines Y Z)))))) (-. (distinct_lines T_2 T_1)) (-. (distinct_lines T_1 T_1)) (-. (unorthogonal_lines T_0 T_1)) (-. (convergent_lines T_2 T_1)) (All M, ((convergent_lines T_0 M) \/ (unorthogonal_lines T_0 M))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (convergent_lines T_0 T_1) (All X, (All Y, ((convergent_lines X Y) => (distinct_lines X Y)))) (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 56 % 22.27/22.46 58. (-. (convergent_lines T_2 T_1)) (convergent_lines T_2 T_1) ### Axiom % 22.27/22.46 59. (-. (unorthogonal_lines T_2 T_1)) (unorthogonal_lines T_2 T_1) ### Axiom % 22.27/22.46 60. ((convergent_lines T_2 T_1) \/ (unorthogonal_lines T_2 T_1)) (-. (unorthogonal_lines T_2 T_1)) (-. (convergent_lines T_2 T_1)) ### Or 58 59 % 22.27/22.46 61. (All M, ((convergent_lines T_2 M) \/ (unorthogonal_lines T_2 M))) (-. (convergent_lines T_2 T_1)) (-. (unorthogonal_lines T_2 T_1)) ### All 60 % 22.27/22.46 62. (All L, (All M, ((convergent_lines L M) \/ (unorthogonal_lines L M)))) (-. (unorthogonal_lines T_2 T_1)) (-. (convergent_lines T_2 T_1)) ### All 61 % 22.27/22.46 63. (-. (distinct_lines T_2 T_1)) (distinct_lines T_2 T_1) ### Axiom % 22.27/22.46 64. ((convergent_lines T_2 T_1) => (distinct_lines T_2 T_1)) (-. (distinct_lines T_2 T_1)) (-. (unorthogonal_lines T_2 T_1)) (All L, (All M, ((convergent_lines L M) \/ (unorthogonal_lines L M)))) ### Imply 62 63 % 22.27/22.46 65. (All Y, ((convergent_lines T_2 Y) => (distinct_lines T_2 Y))) (All L, (All M, ((convergent_lines L M) \/ (unorthogonal_lines L M)))) (-. (unorthogonal_lines T_2 T_1)) (-. (distinct_lines T_2 T_1)) ### All 64 % 22.27/22.46 66. (All X, (All Y, ((convergent_lines X Y) => (distinct_lines X Y)))) (-. (distinct_lines T_2 T_1)) (-. (unorthogonal_lines T_2 T_1)) (All L, (All M, ((convergent_lines L M) \/ (unorthogonal_lines L M)))) ### All 65 % 22.27/22.47 67. (convergent_lines T_2 T_1) (-. (convergent_lines T_2 T_1)) ### Axiom % 22.27/22.47 68. (-. (distinct_lines T_2 T_1)) (distinct_lines T_2 T_1) ### Axiom % 22.27/22.47 69. ((convergent_lines T_2 T_1) => (distinct_lines T_2 T_1)) (-. (distinct_lines T_2 T_1)) (convergent_lines T_2 T_1) ### Imply 67 68 % 22.27/22.47 70. (All Y, ((convergent_lines T_2 Y) => (distinct_lines T_2 Y))) (convergent_lines T_2 T_1) (-. (distinct_lines T_2 T_1)) ### All 69 % 22.27/22.47 71. (All X, (All Y, ((convergent_lines X Y) => (distinct_lines X Y)))) (-. (distinct_lines T_2 T_1)) (convergent_lines T_2 T_1) ### All 70 % 22.27/22.47 72. ((convergent_lines T_2 T_1) /\ (unorthogonal_lines T_2 T_1)) (-. (distinct_lines T_2 T_1)) (All X, (All Y, ((convergent_lines X Y) => (distinct_lines X Y)))) ### And 71 % 22.27/22.47 73. (-. (convergent_lines T_1 T_1)) (convergent_lines T_1 T_1) ### Axiom % 22.27/22.47 74. ((convergent_lines T_1 T_1) /\ (unorthogonal_lines T_1 T_1)) (-. (convergent_lines T_1 T_1)) ### And 73 % 22.27/22.47 75. (((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)))) (-. (convergent_lines T_1 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 X, (All Y, ((convergent_lines X Y) => (distinct_lines X Y)))) (convergent_lines T_0 T_1) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (All M, ((convergent_lines T_0 M) \/ (unorthogonal_lines T_0 M))) (-. (unorthogonal_lines T_0 T_1)) (-. (distinct_lines T_1 T_1)) (-. (distinct_lines T_2 T_1)) (All X, (All Y, (All Z, ((distinct_lines X Y) => ((distinct_lines X Z) \/ (distinct_lines Y Z)))))) (unorthogonal_lines T_2 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))))))) ### DisjTree 57 66 72 74 % 22.27/22.47 76. (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 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_0) (unorthogonal_lines T_2 T_0) (All X, (All Y, (All Z, ((distinct_lines X Y) => ((distinct_lines X Z) \/ (distinct_lines Y Z)))))) (-. (distinct_lines T_2 T_1)) (-. (distinct_lines T_1 T_1)) (-. (unorthogonal_lines T_0 T_1)) (All M, ((convergent_lines T_0 M) \/ (unorthogonal_lines T_0 M))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (convergent_lines T_0 T_1) (All X, (All Y, ((convergent_lines X Y) => (distinct_lines X Y)))) (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)))) (-. (convergent_lines T_1 T_1)) ### All 75 % 22.27/22.47 77. (-. (convergent_lines T_1 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 X, (All Y, ((convergent_lines X Y) => (distinct_lines X Y)))) (convergent_lines T_0 T_1) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (All M, ((convergent_lines T_0 M) \/ (unorthogonal_lines T_0 M))) (-. (unorthogonal_lines T_0 T_1)) (-. (distinct_lines T_1 T_1)) (-. (distinct_lines T_2 T_1)) (All X, (All Y, (All Z, ((distinct_lines X Y) => ((distinct_lines X Z) \/ (distinct_lines Y Z)))))) (unorthogonal_lines T_2 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))))))) ### All 76 % 22.27/22.47 78. (All X, (-. (distinct_lines X X))) (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_0) (unorthogonal_lines T_2 T_0) (All X, (All Y, (All Z, ((distinct_lines X Y) => ((distinct_lines X Z) \/ (distinct_lines Y Z)))))) (-. (distinct_lines T_2 T_1)) (-. (unorthogonal_lines T_0 T_1)) (All M, ((convergent_lines T_0 M) \/ (unorthogonal_lines T_0 M))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (convergent_lines T_0 T_1) (All X, (All Y, ((convergent_lines X Y) => (distinct_lines X Y)))) (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)))) (-. (convergent_lines T_1 T_1)) ### All 77 % 22.27/22.47 79. ((convergent_lines T_0 T_0) \/ (unorthogonal_lines T_0 T_0)) (-. (convergent_lines T_1 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 X, (All Y, ((convergent_lines X Y) => (distinct_lines X Y)))) (convergent_lines T_0 T_1) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (All M, ((convergent_lines T_0 M) \/ (unorthogonal_lines T_0 M))) (-. (unorthogonal_lines T_0 T_1)) (-. (distinct_lines T_2 T_1)) (All X, (All Y, (All Z, ((distinct_lines X Y) => ((distinct_lines X Z) \/ (distinct_lines Y Z)))))) (unorthogonal_lines T_2 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))))))) (All X, (-. (distinct_lines X X))) (All X, (-. (convergent_lines X X))) ### Or 2 78 % 22.27/22.47 80. (All X, (-. (convergent_lines X X))) (All X, (-. (distinct_lines X X))) (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_2 T_0) (All X, (All Y, (All Z, ((distinct_lines X Y) => ((distinct_lines X Z) \/ (distinct_lines Y Z)))))) (-. (distinct_lines T_2 T_1)) (-. (unorthogonal_lines T_0 T_1)) (All M, ((convergent_lines T_0 M) \/ (unorthogonal_lines T_0 M))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (convergent_lines T_0 T_1) (All X, (All Y, ((convergent_lines X Y) => (distinct_lines X Y)))) (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)))) (-. (convergent_lines T_1 T_1)) ### All 79 % 22.27/22.47 81. (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 X, (All Y, ((convergent_lines X Y) => (distinct_lines X Y)))) (convergent_lines T_0 T_1) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (All M, ((convergent_lines T_0 M) \/ (unorthogonal_lines T_0 M))) (-. (unorthogonal_lines T_0 T_1)) (-. (distinct_lines T_2 T_1)) (All X, (All Y, (All Z, ((distinct_lines X Y) => ((distinct_lines X Z) \/ (distinct_lines Y Z)))))) (unorthogonal_lines T_2 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))))))) (All X, (-. (distinct_lines X X))) (All X, (-. (convergent_lines X X))) ### All 80 % 22.27/22.47 82. (All X, (-. (convergent_lines X X))) (All X, (-. (distinct_lines X X))) (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_2 T_0) (All X, (All Y, (All Z, ((distinct_lines X Y) => ((distinct_lines X Z) \/ (distinct_lines Y Z)))))) (-. (distinct_lines T_2 T_1)) (-. (unorthogonal_lines T_0 T_1)) (All M, ((convergent_lines T_0 M) \/ (unorthogonal_lines T_0 M))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (convergent_lines T_0 T_1) (All X, (All Y, ((convergent_lines X Y) => (distinct_lines X Y)))) (All L, (All M, ((convergent_lines L M) \/ (unorthogonal_lines L M)))) ### All 81 % 22.27/22.47 83. (-. (unorthogonal_lines T_0 T_1)) (unorthogonal_lines T_0 T_1) ### Axiom % 22.27/22.47 84. ((convergent_lines T_0 T_1) \/ (unorthogonal_lines T_0 T_1)) (All L, (All M, ((convergent_lines L M) \/ (unorthogonal_lines L M)))) (All X, (All Y, ((convergent_lines X Y) => (distinct_lines X Y)))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (All M, ((convergent_lines T_0 M) \/ (unorthogonal_lines T_0 M))) (-. (unorthogonal_lines T_0 T_1)) (-. (distinct_lines T_2 T_1)) (All X, (All Y, (All Z, ((distinct_lines X Y) => ((distinct_lines X Z) \/ (distinct_lines Y Z)))))) (unorthogonal_lines T_2 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))))))) (All X, (-. (distinct_lines X X))) (All X, (-. (convergent_lines X X))) ### Or 82 83 % 22.27/22.47 85. (All X, (-. (convergent_lines X X))) (All X, (-. (distinct_lines X X))) (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_2 T_0) (All X, (All Y, (All Z, ((distinct_lines X Y) => ((distinct_lines X Z) \/ (distinct_lines Y Z)))))) (-. (distinct_lines T_2 T_1)) (-. (unorthogonal_lines T_0 T_1)) (All M, ((convergent_lines T_0 M) \/ (unorthogonal_lines T_0 M))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (All X, (All Y, ((convergent_lines X Y) => (distinct_lines X Y)))) (All L, (All M, ((convergent_lines L M) \/ (unorthogonal_lines L M)))) ### All 84 % 22.27/22.47 86. (All L, (All M, ((convergent_lines L M) \/ (unorthogonal_lines L M)))) (All X, (All Y, ((convergent_lines X Y) => (distinct_lines X Y)))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (-. (unorthogonal_lines T_0 T_1)) (-. (distinct_lines T_2 T_1)) (All X, (All Y, (All Z, ((distinct_lines X Y) => ((distinct_lines X Z) \/ (distinct_lines Y Z)))))) (unorthogonal_lines T_2 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))))))) (All X, (-. (distinct_lines X X))) (All X, (-. (convergent_lines X X))) ### All 85 % 22.27/22.47 87. (-. ((unorthogonal_lines T_2 T_0) => ((distinct_lines T_2 T_1) \/ (unorthogonal_lines T_0 T_1)))) (All X, (-. (convergent_lines X X))) (All X, (-. (distinct_lines X X))) (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, ((distinct_lines X Y) => ((distinct_lines X Z) \/ (distinct_lines Y Z)))))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (All X, (All Y, ((convergent_lines X Y) => (distinct_lines X Y)))) (All L, (All M, ((convergent_lines L M) \/ (unorthogonal_lines L M)))) ### ConjTree 86 % 22.27/22.47 88. (-. (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, (All Y, ((convergent_lines X Y) => (distinct_lines X Y)))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (All X, (All Y, (All Z, ((distinct_lines X Y) => ((distinct_lines X Z) \/ (distinct_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 X, (-. (distinct_lines X X))) (All X, (-. (convergent_lines X X))) ### NotAllEx 87 % 22.27/22.47 89. (-. (All M, (All N, ((unorthogonal_lines T_2 M) => ((distinct_lines T_2 N) \/ (unorthogonal_lines M N)))))) (All X, (-. (convergent_lines X X))) (All X, (-. (distinct_lines X X))) (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, ((distinct_lines X Y) => ((distinct_lines X Z) \/ (distinct_lines Y Z)))))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (All X, (All Y, ((convergent_lines X Y) => (distinct_lines X Y)))) (All L, (All M, ((convergent_lines L M) \/ (unorthogonal_lines L M)))) ### NotAllEx 88 % 22.27/22.47 90. (-. (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, (All Y, ((convergent_lines X Y) => (distinct_lines X Y)))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (All X, (All Y, (All Z, ((distinct_lines X Y) => ((distinct_lines X Z) \/ (distinct_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 X, (-. (distinct_lines X X))) (All X, (-. (convergent_lines X X))) ### NotAllEx 89 % 22.27/22.47 % SZS output end Proof % 22.27/22.47 (* END-PROOF *) %------------------------------------------------------------------------------