%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : GEO204+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 : n006.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 31.30s 31.46s % Output : Proof 31.70s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.05/0.13 % Problem : GEO204+2 : TPTP v8.1.0. Released v3.3.0. % 0.05/0.14 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 0.13/0.35 % Computer : n006.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 05:30:55 EDT 2022 % 0.13/0.35 % CPUTime : % 31.30/31.46 % SZS status Theorem % 31.30/31.46 (* PROOF-FOUND *) % 31.30/31.46 (* BEGIN-PROOF *) % 31.30/31.46 % SZS output start Proof % 31.30/31.46 1. (distinct_points T_0 T_1) (-. (distinct_points T_0 T_1)) ### Axiom % 31.30/31.46 2. (-. (distinct_points T_0 T_2)) (distinct_points T_0 T_2) ### Axiom % 31.30/31.46 3. (-. (distinct_points T_1 T_2)) (distinct_points T_1 T_2) ### Axiom % 31.30/31.46 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 % 31.30/31.46 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 % 31.30/31.46 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 % 31.30/31.46 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 % 31.30/31.46 8. (distinct_points T_0 T_1) (-. (distinct_points T_0 T_1)) ### Axiom % 31.30/31.46 9. (distinct_points T_0 T_1) (-. (distinct_points T_0 T_1)) ### Axiom % 31.30/31.46 10. (distinct_points T_0 T_1) (-. (distinct_points T_0 T_1)) ### Axiom % 31.30/31.46 11. (distinct_points T_0 T_2) (-. (distinct_points T_0 T_2)) ### Axiom % 31.30/31.46 12. (distinct_points T_0 T_2) (-. (distinct_points T_0 T_2)) ### Axiom % 31.30/31.46 13. (distinct_points T_0 T_2) (-. (distinct_points T_0 T_2)) ### Axiom % 31.30/31.46 14. (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 % 31.30/31.46 15. (-. (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 % 31.30/31.46 16. (-. (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 % 31.30/31.46 17. (-. (apart_point_and_line T_2 (line_connecting T_0 T_1))) (apart_point_and_line T_2 (line_connecting T_0 T_1)) ### Axiom % 31.30/31.46 18. (-. (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 % 31.30/31.46 19. (((distinct_points T_0 T_2) /\ (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_2 (line_connecting T_0 T_1)) \/ (apart_point_and_line T_2 (line_connecting T_0 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_1))) (-. (apart_point_and_line T_0 (line_connecting T_0 T_2))) (-. (apart_point_and_line T_0 (line_connecting T_0 T_1))) (distinct_lines (line_connecting T_0 T_1) (line_connecting T_0 T_2)) (distinct_points T_0 T_2) ### DisjTree 13 14 15 16 17 18 % 31.30/31.46 20. (All V, (((distinct_points T_0 T_2) /\ (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_2 (line_connecting T_0 T_1)) \/ (apart_point_and_line T_2 V)))))) (distinct_points T_0 T_2) (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_2 (line_connecting T_0 T_1))) (-. (apart_point_and_line T_2 (line_connecting T_0 T_2))) ### All 19 % 31.30/31.46 21. (All U, (All V, (((distinct_points T_0 T_2) /\ (distinct_lines U V)) => ((apart_point_and_line T_0 U) \/ ((apart_point_and_line T_0 V) \/ ((apart_point_and_line T_2 U) \/ (apart_point_and_line T_2 V))))))) (-. (apart_point_and_line T_2 (line_connecting T_0 T_2))) (-. (apart_point_and_line T_2 (line_connecting T_0 T_1))) (-. (apart_point_and_line T_0 (line_connecting T_0 T_2))) (-. (apart_point_and_line T_0 (line_connecting T_0 T_1))) (distinct_lines (line_connecting T_0 T_1) (line_connecting T_0 T_2)) (distinct_points T_0 T_2) ### All 20 % 31.30/31.46 22. (-. (distinct_points T_0 T_0)) (distinct_points T_0 T_0) ### Axiom % 31.30/31.46 23. ((distinct_points T_0 T_0) /\ (distinct_points T_0 T_2)) (-. (distinct_points T_0 T_0)) ### And 22 % 31.30/31.46 24. ((distinct_points T_0 T_2) => ((apart_point_and_line T_0 (line_connecting T_0 T_2)) => ((distinct_points T_0 T_0) /\ (distinct_points T_0 T_2)))) (-. (distinct_points T_0 T_0)) (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_2 (line_connecting T_0 T_1))) (-. (apart_point_and_line T_2 (line_connecting T_0 T_2))) (All U, (All V, (((distinct_points T_0 T_2) /\ (distinct_lines U V)) => ((apart_point_and_line T_0 U) \/ ((apart_point_and_line T_0 V) \/ ((apart_point_and_line T_2 U) \/ (apart_point_and_line T_2 V))))))) (distinct_points T_0 T_2) ### DisjTree 12 21 23 % 31.30/31.46 25. (All Z, ((distinct_points T_0 T_2) => ((apart_point_and_line Z (line_connecting T_0 T_2)) => ((distinct_points Z T_0) /\ (distinct_points Z T_2))))) (distinct_points T_0 T_2) (All U, (All V, (((distinct_points T_0 T_2) /\ (distinct_lines U V)) => ((apart_point_and_line T_0 U) \/ ((apart_point_and_line T_0 V) \/ ((apart_point_and_line T_2 U) \/ (apart_point_and_line T_2 V))))))) (-. (apart_point_and_line T_2 (line_connecting T_0 T_2))) (-. (apart_point_and_line T_2 (line_connecting T_0 T_1))) (-. (apart_point_and_line T_0 (line_connecting T_0 T_1))) (distinct_lines (line_connecting T_0 T_1) (line_connecting T_0 T_2)) (-. (distinct_points T_0 T_0)) ### All 24 % 31.30/31.46 26. (-. (distinct_points T_2 T_2)) (distinct_points T_2 T_2) ### Axiom % 31.30/31.46 27. ((distinct_points T_2 T_0) /\ (distinct_points T_2 T_2)) (-. (distinct_points T_2 T_2)) ### And 26 % 31.30/31.46 28. ((distinct_points T_0 T_2) => ((apart_point_and_line T_2 (line_connecting T_0 T_2)) => ((distinct_points T_2 T_0) /\ (distinct_points T_2 T_2)))) (-. (distinct_points T_2 T_2)) (-. (distinct_points T_0 T_0)) (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_2 (line_connecting T_0 T_1))) (All U, (All V, (((distinct_points T_0 T_2) /\ (distinct_lines U V)) => ((apart_point_and_line T_0 U) \/ ((apart_point_and_line T_0 V) \/ ((apart_point_and_line T_2 U) \/ (apart_point_and_line T_2 V))))))) (All Z, ((distinct_points T_0 T_2) => ((apart_point_and_line Z (line_connecting T_0 T_2)) => ((distinct_points Z T_0) /\ (distinct_points Z T_2))))) (distinct_points T_0 T_2) ### DisjTree 11 25 27 % 31.30/31.46 29. (distinct_points T_0 T_2) (All Z, ((distinct_points T_0 T_2) => ((apart_point_and_line Z (line_connecting T_0 T_2)) => ((distinct_points Z T_0) /\ (distinct_points Z T_2))))) (All U, (All V, (((distinct_points T_0 T_2) /\ (distinct_lines U V)) => ((apart_point_and_line T_0 U) \/ ((apart_point_and_line T_0 V) \/ ((apart_point_and_line T_2 U) \/ (apart_point_and_line T_2 V))))))) (-. (apart_point_and_line T_2 (line_connecting T_0 T_1))) (-. (apart_point_and_line T_0 (line_connecting T_0 T_1))) (distinct_lines (line_connecting T_0 T_1) (line_connecting T_0 T_2)) (-. (distinct_points T_0 T_0)) (-. (distinct_points T_2 T_2)) ### All 28 % 31.30/31.46 30. (-. (distinct_points T_2 T_1)) (distinct_points T_2 T_1) ### Axiom % 31.30/31.46 31. ((distinct_points T_2 T_0) /\ (distinct_points T_2 T_1)) (-. (distinct_points T_2 T_1)) ### And 30 % 31.30/31.46 32. ((distinct_points T_0 T_1) => ((apart_point_and_line T_2 (line_connecting T_0 T_1)) => ((distinct_points T_2 T_0) /\ (distinct_points T_2 T_1)))) (-. (distinct_points T_2 T_1)) (-. (distinct_points T_2 T_2)) (-. (distinct_points T_0 T_0)) (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))) (All U, (All V, (((distinct_points T_0 T_2) /\ (distinct_lines U V)) => ((apart_point_and_line T_0 U) \/ ((apart_point_and_line T_0 V) \/ ((apart_point_and_line T_2 U) \/ (apart_point_and_line T_2 V))))))) (All Z, ((distinct_points T_0 T_2) => ((apart_point_and_line Z (line_connecting T_0 T_2)) => ((distinct_points Z T_0) /\ (distinct_points Z T_2))))) (distinct_points T_0 T_2) (distinct_points T_0 T_1) ### DisjTree 10 29 31 % 31.65/31.86 33. (All Z, ((distinct_points T_0 T_1) => ((apart_point_and_line Z (line_connecting T_0 T_1)) => ((distinct_points Z T_0) /\ (distinct_points Z T_1))))) (distinct_points T_0 T_1) (distinct_points T_0 T_2) (All Z, ((distinct_points T_0 T_2) => ((apart_point_and_line Z (line_connecting T_0 T_2)) => ((distinct_points Z T_0) /\ (distinct_points Z T_2))))) (All U, (All V, (((distinct_points T_0 T_2) /\ (distinct_lines U V)) => ((apart_point_and_line T_0 U) \/ ((apart_point_and_line T_0 V) \/ ((apart_point_and_line T_2 U) \/ (apart_point_and_line T_2 V))))))) (-. (apart_point_and_line T_0 (line_connecting T_0 T_1))) (distinct_lines (line_connecting T_0 T_1) (line_connecting T_0 T_2)) (-. (distinct_points T_0 T_0)) (-. (distinct_points T_2 T_2)) (-. (distinct_points T_2 T_1)) ### All 32 % 31.65/31.86 34. (distinct_points T_2 T_1) (-. (distinct_points T_2 T_1)) ### Axiom % 31.65/31.86 35. (-. (distinct_points T_2 T_2)) (distinct_points T_2 T_2) ### Axiom % 31.65/31.86 36. (-. (distinct_points T_1 T_2)) (distinct_points T_1 T_2) ### Axiom % 31.65/31.86 37. ((distinct_points T_2 T_1) => ((distinct_points T_2 T_2) \/ (distinct_points T_1 T_2))) (-. (distinct_points T_1 T_2)) (-. (distinct_points T_2 T_2)) (distinct_points T_2 T_1) ### DisjTree 34 35 36 % 31.65/31.86 38. (All Z, ((distinct_points T_2 T_1) => ((distinct_points T_2 Z) \/ (distinct_points T_1 Z)))) (distinct_points T_2 T_1) (-. (distinct_points T_2 T_2)) (-. (distinct_points T_1 T_2)) ### All 37 % 31.65/31.86 39. (-. (distinct_points T_1 T_1)) (distinct_points T_1 T_1) ### Axiom % 31.65/31.86 40. ((distinct_points T_2 T_1) => ((distinct_points T_2 T_1) \/ (distinct_points T_1 T_1))) (-. (distinct_points T_1 T_1)) (-. (distinct_points T_1 T_2)) (All Z, ((distinct_points T_2 T_1) => ((distinct_points T_2 Z) \/ (distinct_points T_1 Z)))) (-. (distinct_points T_2 T_2)) (-. (distinct_points T_0 T_0)) (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))) (All U, (All V, (((distinct_points T_0 T_2) /\ (distinct_lines U V)) => ((apart_point_and_line T_0 U) \/ ((apart_point_and_line T_0 V) \/ ((apart_point_and_line T_2 U) \/ (apart_point_and_line T_2 V))))))) (All Z, ((distinct_points T_0 T_2) => ((apart_point_and_line Z (line_connecting T_0 T_2)) => ((distinct_points Z T_0) /\ (distinct_points Z T_2))))) (distinct_points T_0 T_2) (distinct_points T_0 T_1) (All Z, ((distinct_points T_0 T_1) => ((apart_point_and_line Z (line_connecting T_0 T_1)) => ((distinct_points Z T_0) /\ (distinct_points Z T_1))))) ### DisjTree 33 38 39 % 31.65/31.86 41. (All Z, ((distinct_points T_0 T_1) => ((apart_point_and_line Z (line_connecting T_0 T_1)) => ((distinct_points Z T_0) /\ (distinct_points Z T_1))))) (distinct_points T_0 T_1) (distinct_points T_0 T_2) (All Z, ((distinct_points T_0 T_2) => ((apart_point_and_line Z (line_connecting T_0 T_2)) => ((distinct_points Z T_0) /\ (distinct_points Z T_2))))) (All U, (All V, (((distinct_points T_0 T_2) /\ (distinct_lines U V)) => ((apart_point_and_line T_0 U) \/ ((apart_point_and_line T_0 V) \/ ((apart_point_and_line T_2 U) \/ (apart_point_and_line T_2 V))))))) (-. (apart_point_and_line T_0 (line_connecting T_0 T_1))) (distinct_lines (line_connecting T_0 T_1) (line_connecting T_0 T_2)) (-. (distinct_points T_0 T_0)) (-. (distinct_points T_2 T_2)) (All Z, ((distinct_points T_2 T_1) => ((distinct_points T_2 Z) \/ (distinct_points T_1 Z)))) (-. (distinct_points T_1 T_2)) (-. (distinct_points T_1 T_1)) ### All 40 % 31.65/31.86 42. (All Y, (All Z, ((distinct_points T_2 Y) => ((distinct_points T_2 Z) \/ (distinct_points Y Z))))) (-. (distinct_points T_1 T_1)) (-. (distinct_points T_1 T_2)) (-. (distinct_points T_2 T_2)) (-. (distinct_points T_0 T_0)) (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))) (All U, (All V, (((distinct_points T_0 T_2) /\ (distinct_lines U V)) => ((apart_point_and_line T_0 U) \/ ((apart_point_and_line T_0 V) \/ ((apart_point_and_line T_2 U) \/ (apart_point_and_line T_2 V))))))) (All Z, ((distinct_points T_0 T_2) => ((apart_point_and_line Z (line_connecting T_0 T_2)) => ((distinct_points Z T_0) /\ (distinct_points Z T_2))))) (distinct_points T_0 T_2) (distinct_points T_0 T_1) (All Z, ((distinct_points T_0 T_1) => ((apart_point_and_line Z (line_connecting T_0 T_1)) => ((distinct_points Z T_0) /\ (distinct_points Z T_1))))) ### All 41 % 31.65/31.86 43. (All X, (All Y, (All Z, ((distinct_points X Y) => ((distinct_points X Z) \/ (distinct_points Y Z)))))) (All Z, ((distinct_points T_0 T_1) => ((apart_point_and_line Z (line_connecting T_0 T_1)) => ((distinct_points Z T_0) /\ (distinct_points Z T_1))))) (distinct_points T_0 T_1) (distinct_points T_0 T_2) (All Z, ((distinct_points T_0 T_2) => ((apart_point_and_line Z (line_connecting T_0 T_2)) => ((distinct_points Z T_0) /\ (distinct_points Z T_2))))) (All U, (All V, (((distinct_points T_0 T_2) /\ (distinct_lines U V)) => ((apart_point_and_line T_0 U) \/ ((apart_point_and_line T_0 V) \/ ((apart_point_and_line T_2 U) \/ (apart_point_and_line T_2 V))))))) (-. (apart_point_and_line T_0 (line_connecting T_0 T_1))) (distinct_lines (line_connecting T_0 T_1) (line_connecting T_0 T_2)) (-. (distinct_points T_0 T_0)) (-. (distinct_points T_2 T_2)) (-. (distinct_points T_1 T_2)) (-. (distinct_points T_1 T_1)) ### All 42 % 31.65/31.86 44. (-. (distinct_points T_0 T_0)) (distinct_points T_0 T_0) ### Axiom % 31.65/31.86 45. ((distinct_points T_0 T_0) /\ (distinct_points T_0 T_1)) (-. (distinct_points T_0 T_0)) ### And 44 % 31.65/31.86 46. ((distinct_points T_0 T_1) => ((apart_point_and_line T_0 (line_connecting T_0 T_1)) => ((distinct_points T_0 T_0) /\ (distinct_points T_0 T_1)))) (-. (distinct_points T_1 T_1)) (-. (distinct_points T_1 T_2)) (-. (distinct_points T_2 T_2)) (-. (distinct_points T_0 T_0)) (distinct_lines (line_connecting T_0 T_1) (line_connecting T_0 T_2)) (All U, (All V, (((distinct_points T_0 T_2) /\ (distinct_lines U V)) => ((apart_point_and_line T_0 U) \/ ((apart_point_and_line T_0 V) \/ ((apart_point_and_line T_2 U) \/ (apart_point_and_line T_2 V))))))) (All Z, ((distinct_points T_0 T_2) => ((apart_point_and_line Z (line_connecting T_0 T_2)) => ((distinct_points Z T_0) /\ (distinct_points Z T_2))))) (distinct_points T_0 T_2) (All Z, ((distinct_points T_0 T_1) => ((apart_point_and_line Z (line_connecting T_0 T_1)) => ((distinct_points Z T_0) /\ (distinct_points Z T_1))))) (All X, (All Y, (All Z, ((distinct_points X Y) => ((distinct_points X Z) \/ (distinct_points Y Z)))))) (distinct_points T_0 T_1) ### DisjTree 9 43 45 % 31.65/31.86 47. (distinct_points T_0 T_1) (All X, (All Y, (All Z, ((distinct_points X Y) => ((distinct_points X Z) \/ (distinct_points Y Z)))))) (All Z, ((distinct_points T_0 T_1) => ((apart_point_and_line Z (line_connecting T_0 T_1)) => ((distinct_points Z T_0) /\ (distinct_points Z T_1))))) (distinct_points T_0 T_2) (All Z, ((distinct_points T_0 T_2) => ((apart_point_and_line Z (line_connecting T_0 T_2)) => ((distinct_points Z T_0) /\ (distinct_points Z T_2))))) (All U, (All V, (((distinct_points T_0 T_2) /\ (distinct_lines U V)) => ((apart_point_and_line T_0 U) \/ ((apart_point_and_line T_0 V) \/ ((apart_point_and_line T_2 U) \/ (apart_point_and_line T_2 V))))))) (distinct_lines (line_connecting T_0 T_1) (line_connecting T_0 T_2)) (-. (distinct_points T_0 T_0)) (-. (distinct_points T_2 T_2)) (-. (distinct_points T_1 T_2)) (-. (distinct_points T_1 T_1)) ### All 46 % 31.65/31.86 48. (All Y, (All Z, ((distinct_points T_0 Y) => ((apart_point_and_line Z (line_connecting T_0 Y)) => ((distinct_points Z T_0) /\ (distinct_points Z Y)))))) (-. (distinct_points T_1 T_1)) (-. (distinct_points T_1 T_2)) (-. (distinct_points T_2 T_2)) (-. (distinct_points T_0 T_0)) (distinct_lines (line_connecting T_0 T_1) (line_connecting T_0 T_2)) (All U, (All V, (((distinct_points T_0 T_2) /\ (distinct_lines U V)) => ((apart_point_and_line T_0 U) \/ ((apart_point_and_line T_0 V) \/ ((apart_point_and_line T_2 U) \/ (apart_point_and_line T_2 V))))))) (distinct_points T_0 T_2) (All Z, ((distinct_points T_0 T_1) => ((apart_point_and_line Z (line_connecting T_0 T_1)) => ((distinct_points Z T_0) /\ (distinct_points Z T_1))))) (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 47 % 31.70/31.88 49. (distinct_points T_0 T_1) (All X, (All Y, (All Z, ((distinct_points X Y) => ((distinct_points X Z) \/ (distinct_points Y Z)))))) (distinct_points T_0 T_2) (All U, (All V, (((distinct_points T_0 T_2) /\ (distinct_lines U V)) => ((apart_point_and_line T_0 U) \/ ((apart_point_and_line T_0 V) \/ ((apart_point_and_line T_2 U) \/ (apart_point_and_line T_2 V))))))) (distinct_lines (line_connecting T_0 T_1) (line_connecting T_0 T_2)) (-. (distinct_points T_0 T_0)) (-. (distinct_points T_2 T_2)) (-. (distinct_points T_1 T_2)) (-. (distinct_points T_1 T_1)) (All Y, (All Z, ((distinct_points T_0 Y) => ((apart_point_and_line Z (line_connecting T_0 Y)) => ((distinct_points Z T_0) /\ (distinct_points Z Y)))))) ### All 48 % 31.70/31.88 50. (All X, (-. (distinct_points X X))) (All Y, (All Z, ((distinct_points T_0 Y) => ((apart_point_and_line Z (line_connecting T_0 Y)) => ((distinct_points Z T_0) /\ (distinct_points Z Y)))))) (-. (distinct_points T_1 T_1)) (-. (distinct_points T_1 T_2)) (-. (distinct_points T_2 T_2)) (distinct_lines (line_connecting T_0 T_1) (line_connecting T_0 T_2)) (All U, (All V, (((distinct_points T_0 T_2) /\ (distinct_lines U V)) => ((apart_point_and_line T_0 U) \/ ((apart_point_and_line T_0 V) \/ ((apart_point_and_line T_2 U) \/ (apart_point_and_line T_2 V))))))) (distinct_points T_0 T_2) (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 49 % 31.70/31.88 51. (-. (distinct_points T_1 T_2)) (distinct_points T_1 T_2) ### Axiom % 31.70/31.88 52. ((distinct_points T_0 T_1) => ((distinct_points T_0 T_2) \/ (distinct_points T_1 T_2))) (All X, (All Y, (All Z, ((distinct_points X Y) => ((distinct_points X Z) \/ (distinct_points Y Z)))))) (All U, (All V, (((distinct_points T_0 T_2) /\ (distinct_lines U V)) => ((apart_point_and_line T_0 U) \/ ((apart_point_and_line T_0 V) \/ ((apart_point_and_line T_2 U) \/ (apart_point_and_line T_2 V))))))) (distinct_lines (line_connecting T_0 T_1) (line_connecting T_0 T_2)) (-. (distinct_points T_2 T_2)) (-. (distinct_points T_1 T_2)) (-. (distinct_points T_1 T_1)) (All Y, (All Z, ((distinct_points T_0 Y) => ((apart_point_and_line Z (line_connecting T_0 Y)) => ((distinct_points Z T_0) /\ (distinct_points Z Y)))))) (All X, (-. (distinct_points X X))) (distinct_points T_0 T_1) ### DisjTree 8 50 51 % 31.70/31.88 53. (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 X, (-. (distinct_points X X))) (All Y, (All Z, ((distinct_points T_0 Y) => ((apart_point_and_line Z (line_connecting T_0 Y)) => ((distinct_points Z T_0) /\ (distinct_points Z Y)))))) (-. (distinct_points T_1 T_1)) (-. (distinct_points T_1 T_2)) (-. (distinct_points T_2 T_2)) (distinct_lines (line_connecting T_0 T_1) (line_connecting T_0 T_2)) (All U, (All V, (((distinct_points T_0 T_2) /\ (distinct_lines U V)) => ((apart_point_and_line T_0 U) \/ ((apart_point_and_line T_0 V) \/ ((apart_point_and_line T_2 U) \/ (apart_point_and_line T_2 V))))))) (All X, (All Y, (All Z, ((distinct_points X Y) => ((distinct_points X Z) \/ (distinct_points Y Z)))))) ### All 52 % 31.70/31.88 54. (All X, (All Y, (All Z, ((distinct_points X Y) => ((apart_point_and_line Z (line_connecting X Y)) => ((distinct_points Z X) /\ (distinct_points Z Y))))))) (All X, (All Y, (All Z, ((distinct_points X Y) => ((distinct_points X Z) \/ (distinct_points Y Z)))))) (All U, (All V, (((distinct_points T_0 T_2) /\ (distinct_lines U V)) => ((apart_point_and_line T_0 U) \/ ((apart_point_and_line T_0 V) \/ ((apart_point_and_line T_2 U) \/ (apart_point_and_line T_2 V))))))) (distinct_lines (line_connecting T_0 T_1) (line_connecting T_0 T_2)) (-. (distinct_points T_2 T_2)) (-. (distinct_points T_1 T_2)) (-. (distinct_points T_1 T_1)) (All X, (-. (distinct_points X X))) (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 53 % 31.70/31.88 55. (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 Z, ((distinct_points T_0 T_1) => ((distinct_points T_0 Z) \/ (distinct_points T_1 Z)))) (distinct_points T_0 T_1) (All X, (-. (distinct_points X X))) (-. (distinct_points T_1 T_1)) (-. (distinct_points T_1 T_2)) (-. (distinct_points T_2 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 Z, ((distinct_points X Y) => ((apart_point_and_line Z (line_connecting X Y)) => ((distinct_points Z X) /\ (distinct_points Z Y))))))) ### All 54 % 31.70/31.88 56. (All X, (All Y, (All Z, ((distinct_points X Y) => ((apart_point_and_line Z (line_connecting X Y)) => ((distinct_points Z X) /\ (distinct_points Z Y))))))) (All X, (All Y, (All Z, ((distinct_points X Y) => ((distinct_points X Z) \/ (distinct_points Y Z)))))) (distinct_lines (line_connecting T_0 T_1) (line_connecting T_0 T_2)) (-. (distinct_points T_1 T_2)) (-. (distinct_points T_1 T_1)) (All X, (-. (distinct_points X X))) (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 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 55 % 31.70/31.88 57. (All Y, (All Z, ((distinct_points T_0 Y) => ((distinct_points T_0 Z) \/ (distinct_points Y Z))))) (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_points T_0 T_1) (All X, (-. (distinct_points X X))) (-. (distinct_points T_1 T_1)) (-. (distinct_points T_1 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 Z, ((distinct_points X Y) => ((apart_point_and_line Z (line_connecting X Y)) => ((distinct_points Z X) /\ (distinct_points Z Y))))))) ### All 56 % 31.70/31.88 58. (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) => ((apart_point_and_line Z (line_connecting X Y)) => ((distinct_points Z X) /\ (distinct_points Z Y))))))) (All X, (All Y, (All Z, ((distinct_points X Y) => ((distinct_points X Z) \/ (distinct_points Y Z)))))) (distinct_lines (line_connecting T_0 T_1) (line_connecting T_0 T_2)) (-. (distinct_points T_1 T_2)) (-. (distinct_points T_1 T_1)) (All X, (-. (distinct_points X X))) (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 57 % 31.70/31.88 59. (distinct_points T_0 T_1) (All X, (-. (distinct_points X X))) (-. (distinct_points T_1 T_1)) (-. (distinct_points T_1 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 Z, ((distinct_points X Y) => ((apart_point_and_line Z (line_connecting X Y)) => ((distinct_points Z X) /\ (distinct_points Z 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 58 % 31.70/31.88 60. (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) => ((apart_point_and_line Z (line_connecting X Y)) => ((distinct_points Z X) /\ (distinct_points Z Y))))))) (All X, (All Y, (All Z, ((distinct_points X Y) => ((distinct_points X Z) \/ (distinct_points Y Z)))))) (distinct_lines (line_connecting T_0 T_1) (line_connecting T_0 T_2)) (-. (distinct_points T_1 T_2)) (All X, (-. (distinct_points X X))) (distinct_points T_0 T_1) ### All 59 % 31.70/31.89 61. (-. (-. (distinct_lines (line_connecting T_0 T_1) (line_connecting T_0 T_2)))) (distinct_points T_0 T_1) (All X, (-. (distinct_points X X))) (-. (distinct_points T_1 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 Z, ((distinct_points X Y) => ((apart_point_and_line Z (line_connecting X Y)) => ((distinct_points Z X) /\ (distinct_points Z 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))))))))) ### NotNot 60 % 31.70/31.89 62. (-. ((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 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) => ((apart_point_and_line Z (line_connecting X Y)) => ((distinct_points Z X) /\ (distinct_points Z Y))))))) (All X, (-. (distinct_points X X))) (-. (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 61 % 31.70/31.89 63. (-. (((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, (-. (distinct_points X X))) (All X, (All Y, (All Z, ((distinct_points X Y) => ((apart_point_and_line Z (line_connecting X Y)) => ((distinct_points Z X) /\ (distinct_points Z 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))))))))) ### ConjTree 62 % 31.70/31.89 64. (-. (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 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) => ((apart_point_and_line Z (line_connecting X Y)) => ((distinct_points Z X) /\ (distinct_points Z Y))))))) (All X, (-. (distinct_points X X))) (All X, (All Y, (All Z, ((distinct_points X Y) => ((distinct_points X Z) \/ (distinct_points Y Z)))))) ### NotAllEx 63 % 31.70/31.89 65. (-. (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, (-. (distinct_points X X))) (All X, (All Y, (All Z, ((distinct_points X Y) => ((apart_point_and_line Z (line_connecting X Y)) => ((distinct_points Z X) /\ (distinct_points Z 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))))))))) ### NotAllEx 64 % 31.70/31.89 66. (-. (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 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) => ((apart_point_and_line Z (line_connecting X Y)) => ((distinct_points Z X) /\ (distinct_points Z Y))))))) (All X, (-. (distinct_points X X))) (All X, (All Y, (All Z, ((distinct_points X Y) => ((distinct_points X Z) \/ (distinct_points Y Z)))))) ### NotAllEx 65 % 31.70/31.89 % SZS output end Proof % 31.70/31.89 (* END-PROOF *) %------------------------------------------------------------------------------