%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : GEO204+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 : n014.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 06:31:03 EDT 2022 % Result : Theorem 0.20s 0.44s % Output : Proof 0.20s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : GEO204+1 : TPTP v8.1.0. Released v3.3.0. % 0.13/0.13 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 0.14/0.34 % Computer : n014.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 600 % 0.14/0.34 % DateTime : Sat Jun 18 08:39:49 EDT 2022 % 0.14/0.34 % CPUTime : % 0.20/0.44 % SZS status Theorem % 0.20/0.44 (* PROOF-FOUND *) % 0.20/0.44 (* BEGIN-PROOF *) % 0.20/0.44 % SZS output start Proof % 0.20/0.44 1. (distinct_points T_0 T_1) (-. (distinct_points T_0 T_1)) ### Axiom % 0.20/0.44 2. (-. (distinct_points T_0 T_2)) (distinct_points T_0 T_2) ### Axiom % 0.20/0.44 3. (-. (distinct_points T_1 T_2)) (distinct_points T_1 T_2) ### Axiom % 0.20/0.44 4. ((distinct_points T_0 T_1) => ((distinct_points T_0 T_2) \/ (distinct_points T_1 T_2))) (-. (distinct_points T_1 T_2)) (-. (distinct_points T_0 T_2)) (distinct_points T_0 T_1) ### DisjTree 1 2 3 % 0.20/0.44 5. (All Z, ((distinct_points T_0 T_1) => ((distinct_points T_0 Z) \/ (distinct_points T_1 Z)))) (distinct_points T_0 T_1) (-. (distinct_points T_0 T_2)) (-. (distinct_points T_1 T_2)) ### All 4 % 0.20/0.44 6. (All Y, (All Z, ((distinct_points T_0 Y) => ((distinct_points T_0 Z) \/ (distinct_points Y Z))))) (-. (distinct_points T_1 T_2)) (-. (distinct_points T_0 T_2)) (distinct_points T_0 T_1) ### All 5 % 0.20/0.44 7. (All X, (All Y, (All Z, ((distinct_points X Y) => ((distinct_points X Z) \/ (distinct_points Y Z)))))) (distinct_points T_0 T_1) (-. (distinct_points T_0 T_2)) (-. (distinct_points T_1 T_2)) ### All 6 % 0.20/0.44 8. (distinct_points T_0 T_1) (-. (distinct_points T_0 T_1)) ### Axiom % 0.20/0.44 9. (distinct_points T_0 T_1) (-. (distinct_points T_0 T_1)) ### Axiom % 0.20/0.44 10. (distinct_lines (line_connecting T_0 T_1) (line_connecting T_0 T_2)) (-. (distinct_lines (line_connecting T_0 T_1) (line_connecting T_0 T_2))) ### Axiom % 0.20/0.44 11. (distinct_points T_0 T_1) (-. (distinct_points T_0 T_1)) ### Axiom % 0.20/0.44 12. (apart_point_and_line T_0 (line_connecting T_0 T_1)) (-. (apart_point_and_line T_0 (line_connecting T_0 T_1))) ### Axiom % 0.20/0.44 13. ((distinct_points T_0 T_1) => (-. (apart_point_and_line T_0 (line_connecting T_0 T_1)))) (apart_point_and_line T_0 (line_connecting T_0 T_1)) (distinct_points T_0 T_1) ### Imply 11 12 % 0.20/0.44 14. (All Y, ((distinct_points T_0 Y) => (-. (apart_point_and_line T_0 (line_connecting T_0 Y))))) (distinct_points T_0 T_1) (apart_point_and_line T_0 (line_connecting T_0 T_1)) ### All 13 % 0.20/0.44 15. (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line X (line_connecting X Y)))))) (apart_point_and_line T_0 (line_connecting T_0 T_1)) (distinct_points T_0 T_1) ### All 14 % 0.20/0.44 16. (distinct_points T_0 T_2) (-. (distinct_points T_0 T_2)) ### Axiom % 0.20/0.44 17. (apart_point_and_line T_0 (line_connecting T_0 T_2)) (-. (apart_point_and_line T_0 (line_connecting T_0 T_2))) ### Axiom % 0.20/0.44 18. ((distinct_points T_0 T_2) => (-. (apart_point_and_line T_0 (line_connecting T_0 T_2)))) (apart_point_and_line T_0 (line_connecting T_0 T_2)) (distinct_points T_0 T_2) ### Imply 16 17 % 0.20/0.44 19. (All Y, ((distinct_points T_0 Y) => (-. (apart_point_and_line T_0 (line_connecting T_0 Y))))) (distinct_points T_0 T_2) (apart_point_and_line T_0 (line_connecting T_0 T_2)) ### All 18 % 0.20/0.44 20. (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line X (line_connecting X Y)))))) (apart_point_and_line T_0 (line_connecting T_0 T_2)) (distinct_points T_0 T_2) ### All 19 % 0.20/0.44 21. (distinct_points T_0 T_1) (-. (distinct_points T_0 T_1)) ### Axiom % 0.20/0.44 22. (apart_point_and_line T_1 (line_connecting T_0 T_1)) (-. (apart_point_and_line T_1 (line_connecting T_0 T_1))) ### Axiom % 0.20/0.44 23. ((distinct_points T_0 T_1) => (-. (apart_point_and_line T_1 (line_connecting T_0 T_1)))) (apart_point_and_line T_1 (line_connecting T_0 T_1)) (distinct_points T_0 T_1) ### Imply 21 22 % 0.20/0.44 24. (All Y, ((distinct_points T_0 Y) => (-. (apart_point_and_line Y (line_connecting T_0 Y))))) (distinct_points T_0 T_1) (apart_point_and_line T_1 (line_connecting T_0 T_1)) ### All 23 % 0.20/0.44 25. (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line Y (line_connecting X Y)))))) (apart_point_and_line T_1 (line_connecting T_0 T_1)) (distinct_points T_0 T_1) ### All 24 % 0.20/0.44 26. (distinct_points T_0 T_2) (-. (distinct_points T_0 T_2)) ### Axiom % 0.20/0.44 27. (apart_point_and_line T_1 (line_connecting T_0 T_2)) (-. (apart_point_and_line T_1 (line_connecting T_0 T_2))) ### Axiom % 0.20/0.44 28. (-. (distinct_points T_1 T_2)) (distinct_points T_1 T_2) ### Axiom % 0.20/0.44 29. (-. (apart_point_and_line T_2 (line_connecting T_0 T_2))) (apart_point_and_line T_2 (line_connecting T_0 T_2)) ### Axiom % 0.20/0.44 30. ((apart_point_and_line T_1 (line_connecting T_0 T_2)) => ((distinct_points T_1 T_2) \/ (apart_point_and_line T_2 (line_connecting T_0 T_2)))) (-. (apart_point_and_line T_2 (line_connecting T_0 T_2))) (-. (distinct_points T_1 T_2)) (apart_point_and_line T_1 (line_connecting T_0 T_2)) ### DisjTree 27 28 29 % 0.20/0.44 31. (All Z, ((apart_point_and_line T_1 (line_connecting T_0 T_2)) => ((distinct_points T_1 Z) \/ (apart_point_and_line Z (line_connecting T_0 T_2))))) (apart_point_and_line T_1 (line_connecting T_0 T_2)) (-. (distinct_points T_1 T_2)) (-. (apart_point_and_line T_2 (line_connecting T_0 T_2))) ### All 30 % 0.20/0.44 32. (All Y, (All Z, ((apart_point_and_line T_1 Y) => ((distinct_points T_1 Z) \/ (apart_point_and_line Z Y))))) (-. (apart_point_and_line T_2 (line_connecting T_0 T_2))) (-. (distinct_points T_1 T_2)) (apart_point_and_line T_1 (line_connecting T_0 T_2)) ### All 31 % 0.20/0.44 33. (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_points X Z) \/ (apart_point_and_line Z Y)))))) (apart_point_and_line T_1 (line_connecting T_0 T_2)) (-. (distinct_points T_1 T_2)) (-. (apart_point_and_line T_2 (line_connecting T_0 T_2))) ### All 32 % 0.20/0.44 34. ((distinct_points T_0 T_2) => (-. (apart_point_and_line T_2 (line_connecting T_0 T_2)))) (-. (distinct_points T_1 T_2)) (apart_point_and_line T_1 (line_connecting T_0 T_2)) (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_points X Z) \/ (apart_point_and_line Z Y)))))) (distinct_points T_0 T_2) ### Imply 26 33 % 0.20/0.44 35. (All Y, ((distinct_points T_0 Y) => (-. (apart_point_and_line Y (line_connecting T_0 Y))))) (distinct_points T_0 T_2) (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_points X Z) \/ (apart_point_and_line Z Y)))))) (apart_point_and_line T_1 (line_connecting T_0 T_2)) (-. (distinct_points T_1 T_2)) ### All 34 % 0.20/0.44 36. (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line Y (line_connecting X Y)))))) (-. (distinct_points T_1 T_2)) (apart_point_and_line T_1 (line_connecting T_0 T_2)) (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_points X Z) \/ (apart_point_and_line Z Y)))))) (distinct_points T_0 T_2) ### All 35 % 0.20/0.44 37. (((distinct_points T_0 T_1) /\ (distinct_lines (line_connecting T_0 T_1) (line_connecting T_0 T_2))) => ((apart_point_and_line T_0 (line_connecting T_0 T_1)) \/ ((apart_point_and_line T_0 (line_connecting T_0 T_2)) \/ ((apart_point_and_line T_1 (line_connecting T_0 T_1)) \/ (apart_point_and_line T_1 (line_connecting T_0 T_2)))))) (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_points X Z) \/ (apart_point_and_line Z Y)))))) (-. (distinct_points T_1 T_2)) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line Y (line_connecting X Y)))))) (distinct_points T_0 T_2) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line X (line_connecting X Y)))))) (distinct_lines (line_connecting T_0 T_1) (line_connecting T_0 T_2)) (distinct_points T_0 T_1) ### DisjTree 9 10 15 20 25 36 % 0.20/0.44 38. (All V, (((distinct_points T_0 T_1) /\ (distinct_lines (line_connecting T_0 T_1) V)) => ((apart_point_and_line T_0 (line_connecting T_0 T_1)) \/ ((apart_point_and_line T_0 V) \/ ((apart_point_and_line T_1 (line_connecting T_0 T_1)) \/ (apart_point_and_line T_1 V)))))) (distinct_points T_0 T_1) (distinct_lines (line_connecting T_0 T_1) (line_connecting T_0 T_2)) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line X (line_connecting X Y)))))) (distinct_points T_0 T_2) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line Y (line_connecting X Y)))))) (-. (distinct_points T_1 T_2)) (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_points X Z) \/ (apart_point_and_line Z Y)))))) ### All 37 % 0.20/0.44 39. (All U, (All V, (((distinct_points T_0 T_1) /\ (distinct_lines U V)) => ((apart_point_and_line T_0 U) \/ ((apart_point_and_line T_0 V) \/ ((apart_point_and_line T_1 U) \/ (apart_point_and_line T_1 V))))))) (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_points X Z) \/ (apart_point_and_line Z Y)))))) (-. (distinct_points T_1 T_2)) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line Y (line_connecting X Y)))))) (distinct_points T_0 T_2) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line X (line_connecting X Y)))))) (distinct_lines (line_connecting T_0 T_1) (line_connecting T_0 T_2)) (distinct_points T_0 T_1) ### All 38 % 0.20/0.44 40. (-. (distinct_points T_1 T_2)) (distinct_points T_1 T_2) ### Axiom % 0.20/0.44 41. ((distinct_points T_0 T_1) => ((distinct_points T_0 T_2) \/ (distinct_points T_1 T_2))) (distinct_lines (line_connecting T_0 T_1) (line_connecting T_0 T_2)) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line X (line_connecting X Y)))))) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line Y (line_connecting X Y)))))) (-. (distinct_points T_1 T_2)) (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_points X Z) \/ (apart_point_and_line Z Y)))))) (All U, (All V, (((distinct_points T_0 T_1) /\ (distinct_lines U V)) => ((apart_point_and_line T_0 U) \/ ((apart_point_and_line T_0 V) \/ ((apart_point_and_line T_1 U) \/ (apart_point_and_line T_1 V))))))) (distinct_points T_0 T_1) ### DisjTree 8 39 40 % 0.20/0.44 42. (All Z, ((distinct_points T_0 T_1) => ((distinct_points T_0 Z) \/ (distinct_points T_1 Z)))) (distinct_points T_0 T_1) (All U, (All V, (((distinct_points T_0 T_1) /\ (distinct_lines U V)) => ((apart_point_and_line T_0 U) \/ ((apart_point_and_line T_0 V) \/ ((apart_point_and_line T_1 U) \/ (apart_point_and_line T_1 V))))))) (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_points X Z) \/ (apart_point_and_line Z Y)))))) (-. (distinct_points T_1 T_2)) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line Y (line_connecting X Y)))))) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line X (line_connecting X Y)))))) (distinct_lines (line_connecting T_0 T_1) (line_connecting T_0 T_2)) ### All 41 % 0.20/0.44 43. (All Y, (All U, (All V, (((distinct_points T_0 Y) /\ (distinct_lines U V)) => ((apart_point_and_line T_0 U) \/ ((apart_point_and_line T_0 V) \/ ((apart_point_and_line Y U) \/ (apart_point_and_line Y V)))))))) (distinct_lines (line_connecting T_0 T_1) (line_connecting T_0 T_2)) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line X (line_connecting X Y)))))) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line Y (line_connecting X Y)))))) (-. (distinct_points T_1 T_2)) (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_points X Z) \/ (apart_point_and_line Z Y)))))) (distinct_points T_0 T_1) (All Z, ((distinct_points T_0 T_1) => ((distinct_points T_0 Z) \/ (distinct_points T_1 Z)))) ### All 42 % 0.20/0.44 44. (All Y, (All Z, ((distinct_points T_0 Y) => ((distinct_points T_0 Z) \/ (distinct_points Y Z))))) (distinct_points T_0 T_1) (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_points X Z) \/ (apart_point_and_line Z Y)))))) (-. (distinct_points T_1 T_2)) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line Y (line_connecting X Y)))))) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line X (line_connecting X Y)))))) (distinct_lines (line_connecting T_0 T_1) (line_connecting T_0 T_2)) (All Y, (All U, (All V, (((distinct_points T_0 Y) /\ (distinct_lines U V)) => ((apart_point_and_line T_0 U) \/ ((apart_point_and_line T_0 V) \/ ((apart_point_and_line Y U) \/ (apart_point_and_line Y V)))))))) ### All 43 % 0.20/0.44 45. (All X, (All Y, (All U, (All V, (((distinct_points X Y) /\ (distinct_lines U V)) => ((apart_point_and_line X U) \/ ((apart_point_and_line X V) \/ ((apart_point_and_line Y U) \/ (apart_point_and_line Y V))))))))) (distinct_lines (line_connecting T_0 T_1) (line_connecting T_0 T_2)) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line X (line_connecting X Y)))))) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line Y (line_connecting X Y)))))) (-. (distinct_points T_1 T_2)) (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_points X Z) \/ (apart_point_and_line Z Y)))))) (distinct_points T_0 T_1) (All Y, (All Z, ((distinct_points T_0 Y) => ((distinct_points T_0 Z) \/ (distinct_points Y Z))))) ### All 44 % 0.20/0.44 46. (All X, (All Y, (All Z, ((distinct_points X Y) => ((distinct_points X Z) \/ (distinct_points Y Z)))))) (distinct_points T_0 T_1) (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_points X Z) \/ (apart_point_and_line Z Y)))))) (-. (distinct_points T_1 T_2)) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line Y (line_connecting X Y)))))) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line X (line_connecting X Y)))))) (distinct_lines (line_connecting T_0 T_1) (line_connecting T_0 T_2)) (All X, (All Y, (All U, (All V, (((distinct_points X Y) /\ (distinct_lines U V)) => ((apart_point_and_line X U) \/ ((apart_point_and_line X V) \/ ((apart_point_and_line Y U) \/ (apart_point_and_line Y V))))))))) ### All 45 % 0.20/0.44 47. (-. (-. (distinct_lines (line_connecting T_0 T_1) (line_connecting T_0 T_2)))) (All X, (All Y, (All U, (All V, (((distinct_points X Y) /\ (distinct_lines U V)) => ((apart_point_and_line X U) \/ ((apart_point_and_line X V) \/ ((apart_point_and_line Y U) \/ (apart_point_and_line Y V))))))))) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line X (line_connecting X Y)))))) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line Y (line_connecting X Y)))))) (-. (distinct_points T_1 T_2)) (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_points X Z) \/ (apart_point_and_line Z Y)))))) (distinct_points T_0 T_1) (All X, (All Y, (All Z, ((distinct_points X Y) => ((distinct_points X Z) \/ (distinct_points Y Z)))))) ### NotNot 46 % 0.20/0.44 48. (-. ((distinct_points T_0 T_2) /\ (-. (distinct_lines (line_connecting T_0 T_1) (line_connecting T_0 T_2))))) (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_points X Z) \/ (apart_point_and_line Z Y)))))) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line Y (line_connecting X Y)))))) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line X (line_connecting X Y)))))) (All X, (All Y, (All U, (All V, (((distinct_points X Y) /\ (distinct_lines U V)) => ((apart_point_and_line X U) \/ ((apart_point_and_line X V) \/ ((apart_point_and_line Y U) \/ (apart_point_and_line Y V))))))))) (-. (distinct_points T_1 T_2)) (distinct_points T_0 T_1) (All X, (All Y, (All Z, ((distinct_points X Y) => ((distinct_points X Z) \/ (distinct_points Y Z)))))) ### NotAnd 7 47 % 0.20/0.44 49. (-. (((distinct_points T_0 T_1) /\ (-. (distinct_points T_1 T_2))) => ((distinct_points T_0 T_2) /\ (-. (distinct_lines (line_connecting T_0 T_1) (line_connecting T_0 T_2)))))) (All X, (All Y, (All Z, ((distinct_points X Y) => ((distinct_points X Z) \/ (distinct_points Y Z)))))) (All X, (All Y, (All U, (All V, (((distinct_points X Y) /\ (distinct_lines U V)) => ((apart_point_and_line X U) \/ ((apart_point_and_line X V) \/ ((apart_point_and_line Y U) \/ (apart_point_and_line Y V))))))))) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line X (line_connecting X Y)))))) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line Y (line_connecting X Y)))))) (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_points X Z) \/ (apart_point_and_line Z Y)))))) ### ConjTree 48 % 0.20/0.44 50. (-. (All Z, (((distinct_points T_0 T_1) /\ (-. (distinct_points T_1 Z))) => ((distinct_points T_0 Z) /\ (-. (distinct_lines (line_connecting T_0 T_1) (line_connecting T_0 Z))))))) (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_points X Z) \/ (apart_point_and_line Z Y)))))) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line Y (line_connecting X Y)))))) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line X (line_connecting X Y)))))) (All X, (All Y, (All U, (All V, (((distinct_points X Y) /\ (distinct_lines U V)) => ((apart_point_and_line X U) \/ ((apart_point_and_line X V) \/ ((apart_point_and_line Y U) \/ (apart_point_and_line Y V))))))))) (All X, (All Y, (All Z, ((distinct_points X Y) => ((distinct_points X Z) \/ (distinct_points Y Z)))))) ### NotAllEx 49 % 0.20/0.44 51. (-. (All Y, (All Z, (((distinct_points T_0 Y) /\ (-. (distinct_points Y Z))) => ((distinct_points T_0 Z) /\ (-. (distinct_lines (line_connecting T_0 Y) (line_connecting T_0 Z)))))))) (All X, (All Y, (All Z, ((distinct_points X Y) => ((distinct_points X Z) \/ (distinct_points Y Z)))))) (All X, (All Y, (All U, (All V, (((distinct_points X Y) /\ (distinct_lines U V)) => ((apart_point_and_line X U) \/ ((apart_point_and_line X V) \/ ((apart_point_and_line Y U) \/ (apart_point_and_line Y V))))))))) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line X (line_connecting X Y)))))) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line Y (line_connecting X Y)))))) (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_points X Z) \/ (apart_point_and_line Z Y)))))) ### NotAllEx 50 % 0.20/0.44 52. (-. (All X, (All Y, (All Z, (((distinct_points X Y) /\ (-. (distinct_points Y Z))) => ((distinct_points X Z) /\ (-. (distinct_lines (line_connecting X Y) (line_connecting X Z))))))))) (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_points X Z) \/ (apart_point_and_line Z Y)))))) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line Y (line_connecting X Y)))))) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line X (line_connecting X Y)))))) (All X, (All Y, (All U, (All V, (((distinct_points X Y) /\ (distinct_lines U V)) => ((apart_point_and_line X U) \/ ((apart_point_and_line X V) \/ ((apart_point_and_line Y U) \/ (apart_point_and_line Y V))))))))) (All X, (All Y, (All Z, ((distinct_points X Y) => ((distinct_points X Z) \/ (distinct_points Y Z)))))) ### NotAllEx 51 % 0.20/0.44 % SZS output end Proof % 0.20/0.44 (* END-PROOF *) %------------------------------------------------------------------------------