%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : GEO219+3 : TPTP v8.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % Computer : n022.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 06:31:16 EDT 2022 % Result : Theorem 14.49s 14.68s % Output : Proof 14.49s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.12 % Problem : GEO219+3 : TPTP v8.1.0. Released v4.0.0. % 0.10/0.12 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 0.12/0.33 % Computer : n022.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 : Sat Jun 18 10:08:02 EDT 2022 % 0.12/0.33 % CPUTime : % 14.49/14.68 % SZS status Theorem % 14.49/14.68 (* PROOF-FOUND *) % 14.49/14.68 (* BEGIN-PROOF *) % 14.49/14.68 % SZS output start Proof % 14.49/14.68 1. (convergent_lines T_0 T_1) (-. (convergent_lines T_0 T_1)) ### Axiom % 14.49/14.68 2. (-. (convergent_lines T_0 T_2)) (convergent_lines T_0 T_2) ### Axiom % 14.49/14.68 3. (-. (convergent_lines T_1 T_2)) (convergent_lines T_1 T_2) ### Axiom % 14.49/14.68 4. ((convergent_lines T_0 T_1) => ((convergent_lines T_0 T_2) \/ (convergent_lines T_1 T_2))) (-. (convergent_lines T_1 T_2)) (-. (convergent_lines T_0 T_2)) (convergent_lines T_0 T_1) ### DisjTree 1 2 3 % 14.49/14.68 5. (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_2)) (-. (convergent_lines T_1 T_2)) ### All 4 % 14.49/14.68 6. (All Y, (All Z, ((convergent_lines T_0 Y) => ((convergent_lines T_0 Z) \/ (convergent_lines Y Z))))) (-. (convergent_lines T_1 T_2)) (-. (convergent_lines T_0 T_2)) (convergent_lines T_0 T_1) ### All 5 % 14.49/14.68 7. (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (convergent_lines T_0 T_1) (-. (convergent_lines T_0 T_2)) (-. (convergent_lines T_1 T_2)) ### All 6 % 14.49/14.68 8. (unorthogonal_lines T_1 T_2) (-. (unorthogonal_lines T_1 T_2)) ### Axiom % 14.49/14.68 9. (-. (unorthogonal_lines T_0 T_1)) (unorthogonal_lines T_0 T_1) ### Axiom % 14.49/14.68 10. (-. (-. (unorthogonal_lines T_0 T_1))) (-. (unorthogonal_lines T_0 T_1)) ### NotNot 9 % 14.49/14.68 11. (-. ((-. (convergent_lines T_0 T_1)) \/ (-. (unorthogonal_lines T_0 T_1)))) (-. (unorthogonal_lines T_0 T_1)) ### NotOr 10 % 14.49/14.68 12. (-. (convergent_lines T_0 T_2)) (convergent_lines T_0 T_2) ### Axiom % 14.49/14.68 13. (-. (-. (convergent_lines T_0 T_2))) (-. (convergent_lines T_0 T_2)) ### NotNot 12 % 14.49/14.68 14. (-. ((-. (convergent_lines T_0 T_2)) \/ (-. (unorthogonal_lines T_0 T_2)))) (-. (convergent_lines T_0 T_2)) ### NotOr 13 % 14.49/14.68 15. (convergent_lines T_1 T_2) (-. (convergent_lines T_1 T_2)) ### Axiom % 14.49/14.68 16. (unorthogonal_lines T_1 T_2) (-. (unorthogonal_lines T_1 T_2)) ### Axiom % 14.49/14.68 17. ((((-. (convergent_lines T_0 T_1)) \/ (-. (unorthogonal_lines T_0 T_1))) /\ ((-. (convergent_lines T_0 T_2)) \/ (-. (unorthogonal_lines T_0 T_2)))) => ((-. (convergent_lines T_1 T_2)) \/ (-. (unorthogonal_lines T_1 T_2)))) (unorthogonal_lines T_1 T_2) (convergent_lines T_1 T_2) (-. (convergent_lines T_0 T_2)) (-. (unorthogonal_lines T_0 T_1)) ### DisjTree 11 14 15 16 % 14.49/14.68 18. (All N, ((((-. (convergent_lines T_0 T_1)) \/ (-. (unorthogonal_lines T_0 T_1))) /\ ((-. (convergent_lines T_0 N)) \/ (-. (unorthogonal_lines T_0 N)))) => ((-. (convergent_lines T_1 N)) \/ (-. (unorthogonal_lines T_1 N))))) (-. (unorthogonal_lines T_0 T_1)) (-. (convergent_lines T_0 T_2)) (convergent_lines T_1 T_2) (unorthogonal_lines T_1 T_2) ### All 17 % 14.49/14.68 19. (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_1 T_2) (convergent_lines T_1 T_2) (-. (convergent_lines T_0 T_2)) (-. (unorthogonal_lines T_0 T_1)) ### All 18 % 14.49/14.68 20. ((convergent_lines T_1 T_2) /\ (unorthogonal_lines T_1 T_2)) (-. (unorthogonal_lines T_0 T_1)) (-. (convergent_lines T_0 T_2)) (unorthogonal_lines T_1 T_2) (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)))))) ### And 19 % 14.49/14.68 21. (-. (convergent_lines T_2 T_2)) (convergent_lines T_2 T_2) ### Axiom % 14.49/14.68 22. ((convergent_lines T_2 T_2) /\ (unorthogonal_lines T_2 T_2)) (-. (convergent_lines T_2 T_2)) ### And 21 % 14.49/14.68 23. (((convergent_lines T_1 T_2) /\ (unorthogonal_lines T_1 T_2)) => (((convergent_lines T_1 T_2) /\ (unorthogonal_lines T_1 T_2)) \/ ((convergent_lines T_2 T_2) /\ (unorthogonal_lines T_2 T_2)))) (-. (convergent_lines T_2 T_2)) (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_1 T_2) (-. (convergent_lines T_0 T_2)) (convergent_lines T_0 T_1) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) ### DisjTree 7 8 20 22 % 14.49/14.68 24. (All N, (((convergent_lines T_1 T_2) /\ (unorthogonal_lines T_1 T_2)) => (((convergent_lines T_1 N) /\ (unorthogonal_lines T_1 N)) \/ ((convergent_lines T_2 N) /\ (unorthogonal_lines T_2 N))))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (convergent_lines T_0 T_1) (-. (convergent_lines T_0 T_2)) (unorthogonal_lines T_1 T_2) (-. (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)))))) (-. (convergent_lines T_2 T_2)) ### All 23 % 14.49/14.68 25. (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))))))) (-. (convergent_lines T_2 T_2)) (-. (unorthogonal_lines T_0 T_1)) (unorthogonal_lines T_1 T_2) (-. (convergent_lines T_0 T_2)) (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 N, (((convergent_lines T_1 T_2) /\ (unorthogonal_lines T_1 T_2)) => (((convergent_lines T_1 N) /\ (unorthogonal_lines T_1 N)) \/ ((convergent_lines T_2 N) /\ (unorthogonal_lines T_2 N))))) ### All 24 % 14.49/14.68 26. (All M, (All N, (((convergent_lines T_1 M) /\ (unorthogonal_lines T_1 M)) => (((convergent_lines T_1 N) /\ (unorthogonal_lines T_1 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)))))) (convergent_lines T_0 T_1) (-. (convergent_lines T_0 T_2)) (unorthogonal_lines T_1 T_2) (-. (unorthogonal_lines T_0 T_1)) (-. (convergent_lines T_2 T_2)) (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 25 % 14.49/14.68 27. (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, (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))))))) (-. (convergent_lines T_2 T_2)) (-. (unorthogonal_lines T_0 T_1)) (unorthogonal_lines T_1 T_2) (-. (convergent_lines T_0 T_2)) (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 26 % 14.49/14.68 28. (-. (unorthogonal_lines T_0 T_1)) (unorthogonal_lines T_0 T_1) ### Axiom % 14.49/14.68 29. ((convergent_lines T_0 T_1) \/ (unorthogonal_lines T_0 T_1)) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (-. (convergent_lines T_0 T_2)) (unorthogonal_lines T_1 T_2) (-. (unorthogonal_lines T_0 T_1)) (-. (convergent_lines T_2 T_2)) (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, (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 27 28 % 14.49/14.68 30. (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 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))))))) (-. (convergent_lines T_2 T_2)) (-. (unorthogonal_lines T_0 T_1)) (unorthogonal_lines T_1 T_2) (-. (convergent_lines T_0 T_2)) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) ### All 29 % 14.49/14.69 31. (All L, (All M, ((convergent_lines L M) \/ (unorthogonal_lines L M)))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (-. (convergent_lines T_0 T_2)) (unorthogonal_lines T_1 T_2) (-. (unorthogonal_lines T_0 T_1)) (-. (convergent_lines T_2 T_2)) (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, (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 30 % 14.49/14.69 32. (All X, (-. (convergent_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 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_1 T_2) (-. (convergent_lines T_0 T_2)) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (All L, (All M, ((convergent_lines L M) \/ (unorthogonal_lines L M)))) ### All 31 % 14.49/14.69 33. (-. (-. (unorthogonal_lines T_1 T_2))) (All L, (All M, ((convergent_lines L M) \/ (unorthogonal_lines L M)))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (-. (convergent_lines T_0 T_2)) (-. (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, (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, (-. (convergent_lines X X))) ### NotNot 32 % 14.49/14.69 34. (-. (orthogonal_lines T_1 T_2)) (All X, (-. (convergent_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 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_2)) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (All L, (All M, ((convergent_lines L M) \/ (unorthogonal_lines L M)))) ### Definition-Pseudo(orthogonal_lines) 33 % 14.49/14.69 35. (parallel_lines T_0 T_2) (All L, (All M, ((convergent_lines L M) \/ (unorthogonal_lines L M)))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (-. (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, (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, (-. (convergent_lines X X))) (-. (orthogonal_lines T_1 T_2)) ### Definition-Pseudo(parallel_lines) 34 % 14.49/14.69 36. (orthogonal_lines T_0 T_1) (-. (orthogonal_lines T_1 T_2)) (All X, (-. (convergent_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 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 L, (All M, ((convergent_lines L M) \/ (unorthogonal_lines L M)))) (parallel_lines T_0 T_2) ### Definition-Pseudo(orthogonal_lines) 35 % 14.49/14.69 37. (-. (((orthogonal_lines T_0 T_1) /\ (parallel_lines T_0 T_2)) => (orthogonal_lines T_1 T_2))) (All L, (All M, ((convergent_lines L M) \/ (unorthogonal_lines L M)))) (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, (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, (-. (convergent_lines X X))) ### ConjTree 36 % 14.49/14.69 38. (-. (All N, (((orthogonal_lines T_0 T_1) /\ (parallel_lines T_0 N)) => (orthogonal_lines T_1 N)))) (All X, (-. (convergent_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 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 L, (All M, ((convergent_lines L M) \/ (unorthogonal_lines L M)))) ### NotAllEx 37 % 14.49/14.69 39. (-. (All M, (All N, (((orthogonal_lines T_0 M) /\ (parallel_lines T_0 N)) => (orthogonal_lines M N))))) (All L, (All M, ((convergent_lines L M) \/ (unorthogonal_lines L M)))) (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, (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, (-. (convergent_lines X X))) ### NotAllEx 38 % 14.49/14.69 40. (-. (All L, (All M, (All N, (((orthogonal_lines L M) /\ (parallel_lines L N)) => (orthogonal_lines M N)))))) (All X, (-. (convergent_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 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 L, (All M, ((convergent_lines L M) \/ (unorthogonal_lines L M)))) ### NotAllEx 39 % 14.49/14.69 % SZS output end Proof % 14.49/14.69 (* END-PROOF *) %------------------------------------------------------------------------------