%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : GEO179+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 : n008.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 06:30:42 EDT 2022 % Result : Theorem 2.34s 2.51s % Output : Proof 2.44s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : GEO179+2 : TPTP v8.1.0. Released v3.3.0. % 0.07/0.12 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 0.13/0.33 % Computer : n008.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 600 % 0.13/0.33 % DateTime : Sat Jun 18 01:02:37 EDT 2022 % 0.13/0.33 % CPUTime : % 2.34/2.51 % SZS status Theorem % 2.34/2.51 (* PROOF-FOUND *) % 2.34/2.51 (* BEGIN-PROOF *) % 2.34/2.51 % SZS output start Proof % 2.34/2.51 1. (apart_point_and_line T_0 (line_connecting T_1 T_2)) (-. (apart_point_and_line T_0 (line_connecting T_1 T_2))) ### Axiom % 2.34/2.51 2. (-. (distinct_lines (line_connecting T_1 T_2) (line_connecting T_0 T_1))) (distinct_lines (line_connecting T_1 T_2) (line_connecting T_0 T_1)) ### Axiom % 2.34/2.51 3. (apart_point_and_line T_0 (line_connecting T_1 T_2)) (-. (apart_point_and_line T_0 (line_connecting T_1 T_2))) ### Axiom % 2.34/2.51 4. (distinct_points T_0 T_1) (-. (distinct_points T_0 T_1)) ### Axiom % 2.34/2.51 5. (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 % 2.34/2.51 6. (distinct_points T_0 T_0) ### Extension/test/apart1 % 2.34/2.51 7. ((distinct_points T_0 T_0) /\ (distinct_points T_0 T_1)) ### And 6 % 2.34/2.51 8. ((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)))) (apart_point_and_line T_0 (line_connecting T_0 T_1)) (distinct_points T_0 T_1) ### DisjTree 4 5 7 % 2.34/2.52 9. (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) (apart_point_and_line T_0 (line_connecting T_0 T_1)) ### All 8 % 2.34/2.52 10. (distinct_points T_1 T_2) (-. (distinct_points T_1 T_2)) ### Axiom % 2.34/2.52 11. (apart_point_and_line T_1 (line_connecting T_1 T_2)) (-. (apart_point_and_line T_1 (line_connecting T_1 T_2))) ### Axiom % 2.34/2.52 12. (distinct_points T_1 T_1) ### Extension/test/apart1 % 2.34/2.52 13. ((distinct_points T_1 T_1) /\ (distinct_points T_1 T_2)) ### And 12 % 2.34/2.52 14. ((distinct_points T_1 T_2) => ((apart_point_and_line T_1 (line_connecting T_1 T_2)) => ((distinct_points T_1 T_1) /\ (distinct_points T_1 T_2)))) (apart_point_and_line T_1 (line_connecting T_1 T_2)) (distinct_points T_1 T_2) ### DisjTree 10 11 13 % 2.34/2.52 15. (All Z, ((distinct_points T_1 T_2) => ((apart_point_and_line Z (line_connecting T_1 T_2)) => ((distinct_points Z T_1) /\ (distinct_points Z T_2))))) (distinct_points T_1 T_2) (apart_point_and_line T_1 (line_connecting T_1 T_2)) ### All 14 % 2.34/2.52 16. ((apart_point_and_line T_0 (line_connecting T_1 T_2)) => ((distinct_points T_0 T_1) \/ (apart_point_and_line T_1 (line_connecting T_1 T_2)))) (distinct_points T_1 T_2) (All Z, ((distinct_points T_1 T_2) => ((apart_point_and_line Z (line_connecting T_1 T_2)) => ((distinct_points Z T_1) /\ (distinct_points Z T_2))))) (apart_point_and_line T_0 (line_connecting 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))))) (apart_point_and_line T_0 (line_connecting T_1 T_2)) ### DisjTree 3 9 15 % 2.34/2.52 17. (All Z, ((apart_point_and_line T_0 (line_connecting T_1 T_2)) => ((distinct_points T_0 Z) \/ (apart_point_and_line Z (line_connecting T_1 T_2))))) (apart_point_and_line T_0 (line_connecting T_1 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))))) (apart_point_and_line T_0 (line_connecting T_0 T_1)) (All Z, ((distinct_points T_1 T_2) => ((apart_point_and_line Z (line_connecting T_1 T_2)) => ((distinct_points Z T_1) /\ (distinct_points Z T_2))))) (distinct_points T_1 T_2) ### All 16 % 2.34/2.52 18. ((apart_point_and_line T_0 (line_connecting T_1 T_2)) => ((distinct_lines (line_connecting T_1 T_2) (line_connecting T_0 T_1)) \/ (apart_point_and_line T_0 (line_connecting T_0 T_1)))) (distinct_points T_1 T_2) (All Z, ((distinct_points T_1 T_2) => ((apart_point_and_line Z (line_connecting T_1 T_2)) => ((distinct_points Z T_1) /\ (distinct_points Z 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 Z, ((apart_point_and_line T_0 (line_connecting T_1 T_2)) => ((distinct_points T_0 Z) \/ (apart_point_and_line Z (line_connecting T_1 T_2))))) (-. (distinct_lines (line_connecting T_1 T_2) (line_connecting T_0 T_1))) (apart_point_and_line T_0 (line_connecting T_1 T_2)) ### DisjTree 1 2 17 % 2.34/2.52 19. (All Z, ((apart_point_and_line T_0 (line_connecting T_1 T_2)) => ((distinct_lines (line_connecting T_1 T_2) Z) \/ (apart_point_and_line T_0 Z)))) (apart_point_and_line T_0 (line_connecting T_1 T_2)) (-. (distinct_lines (line_connecting T_1 T_2) (line_connecting T_0 T_1))) (All Z, ((apart_point_and_line T_0 (line_connecting T_1 T_2)) => ((distinct_points T_0 Z) \/ (apart_point_and_line Z (line_connecting T_1 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 Z, ((distinct_points T_1 T_2) => ((apart_point_and_line Z (line_connecting T_1 T_2)) => ((distinct_points Z T_1) /\ (distinct_points Z T_2))))) (distinct_points T_1 T_2) ### All 18 % 2.34/2.52 20. (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_2) (All Z, ((distinct_points T_1 T_2) => ((apart_point_and_line Z (line_connecting T_1 T_2)) => ((distinct_points Z T_1) /\ (distinct_points Z T_2))))) (All Z, ((apart_point_and_line T_0 (line_connecting T_1 T_2)) => ((distinct_points T_0 Z) \/ (apart_point_and_line Z (line_connecting T_1 T_2))))) (-. (distinct_lines (line_connecting T_1 T_2) (line_connecting T_0 T_1))) (apart_point_and_line T_0 (line_connecting T_1 T_2)) (All Z, ((apart_point_and_line T_0 (line_connecting T_1 T_2)) => ((distinct_lines (line_connecting T_1 T_2) Z) \/ (apart_point_and_line T_0 Z)))) ### All 19 % 2.34/2.52 21. (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 Z, ((apart_point_and_line T_0 (line_connecting T_1 T_2)) => ((distinct_lines (line_connecting T_1 T_2) Z) \/ (apart_point_and_line T_0 Z)))) (apart_point_and_line T_0 (line_connecting T_1 T_2)) (-. (distinct_lines (line_connecting T_1 T_2) (line_connecting T_0 T_1))) (All Z, ((apart_point_and_line T_0 (line_connecting T_1 T_2)) => ((distinct_points T_0 Z) \/ (apart_point_and_line Z (line_connecting T_1 T_2))))) (All Z, ((distinct_points T_1 T_2) => ((apart_point_and_line Z (line_connecting T_1 T_2)) => ((distinct_points Z T_1) /\ (distinct_points Z T_2))))) (distinct_points T_1 T_2) ### All 20 % 2.34/2.52 22. (All Y, (All Z, ((apart_point_and_line T_0 Y) => ((distinct_points T_0 Z) \/ (apart_point_and_line Z Y))))) (distinct_points T_1 T_2) (All Z, ((distinct_points T_1 T_2) => ((apart_point_and_line Z (line_connecting T_1 T_2)) => ((distinct_points Z T_1) /\ (distinct_points Z T_2))))) (-. (distinct_lines (line_connecting T_1 T_2) (line_connecting T_0 T_1))) (apart_point_and_line T_0 (line_connecting T_1 T_2)) (All Z, ((apart_point_and_line T_0 (line_connecting T_1 T_2)) => ((distinct_lines (line_connecting T_1 T_2) Z) \/ (apart_point_and_line T_0 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 21 % 2.34/2.52 23. (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, (All Z, ((distinct_points X Y) => ((apart_point_and_line Z (line_connecting X Y)) => ((distinct_points Z X) /\ (distinct_points Z Y))))))) (All Z, ((apart_point_and_line T_0 (line_connecting T_1 T_2)) => ((distinct_lines (line_connecting T_1 T_2) Z) \/ (apart_point_and_line T_0 Z)))) (apart_point_and_line T_0 (line_connecting T_1 T_2)) (-. (distinct_lines (line_connecting T_1 T_2) (line_connecting T_0 T_1))) (All Z, ((distinct_points T_1 T_2) => ((apart_point_and_line Z (line_connecting T_1 T_2)) => ((distinct_points Z T_1) /\ (distinct_points Z T_2))))) (distinct_points T_1 T_2) ### All 22 % 2.34/2.52 24. (All Y, (All Z, ((distinct_points T_1 Y) => ((apart_point_and_line Z (line_connecting T_1 Y)) => ((distinct_points Z T_1) /\ (distinct_points Z Y)))))) (distinct_points T_1 T_2) (-. (distinct_lines (line_connecting T_1 T_2) (line_connecting T_0 T_1))) (apart_point_and_line T_0 (line_connecting T_1 T_2)) (All Z, ((apart_point_and_line T_0 (line_connecting T_1 T_2)) => ((distinct_lines (line_connecting T_1 T_2) Z) \/ (apart_point_and_line T_0 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 Z, ((apart_point_and_line X Y) => ((distinct_points X Z) \/ (apart_point_and_line Z Y)))))) ### All 23 % 2.34/2.54 25. (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, (All Z, ((distinct_points X Y) => ((apart_point_and_line Z (line_connecting X Y)) => ((distinct_points Z X) /\ (distinct_points Z Y))))))) (All Z, ((apart_point_and_line T_0 (line_connecting T_1 T_2)) => ((distinct_lines (line_connecting T_1 T_2) Z) \/ (apart_point_and_line T_0 Z)))) (apart_point_and_line T_0 (line_connecting T_1 T_2)) (-. (distinct_lines (line_connecting T_1 T_2) (line_connecting T_0 T_1))) (distinct_points T_1 T_2) ### All 24 % 2.34/2.54 26. (All Y, (All Z, ((apart_point_and_line T_0 Y) => ((distinct_lines Y Z) \/ (apart_point_and_line T_0 Z))))) (distinct_points T_1 T_2) (-. (distinct_lines (line_connecting T_1 T_2) (line_connecting T_0 T_1))) (apart_point_and_line T_0 (line_connecting T_1 T_2)) (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, ((apart_point_and_line X Y) => ((distinct_points X Z) \/ (apart_point_and_line Z Y)))))) ### All 25 % 2.34/2.54 27. (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_lines Y Z) \/ (apart_point_and_line 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, (All Z, ((distinct_points X Y) => ((apart_point_and_line Z (line_connecting X Y)) => ((distinct_points Z X) /\ (distinct_points Z Y))))))) (apart_point_and_line T_0 (line_connecting T_1 T_2)) (-. (distinct_lines (line_connecting T_1 T_2) (line_connecting T_0 T_1))) (distinct_points T_1 T_2) ### All 26 % 2.34/2.54 28. (distinct_points T_1 T_2) (-. (distinct_points T_1 T_2)) ### Axiom % 2.34/2.54 29. (apart_point_and_line T_0 (line_connecting T_1 T_2)) (-. (apart_point_and_line T_0 (line_connecting T_1 T_2))) ### Axiom % 2.34/2.54 30. (apart_point_and_line T_0 (line_connecting T_1 T_2)) (-. (apart_point_and_line T_0 (line_connecting T_1 T_2))) ### Axiom % 2.34/2.54 31. (-. (distinct_lines (line_connecting T_1 T_2) (line_connecting T_0 T_2))) (distinct_lines (line_connecting T_1 T_2) (line_connecting T_0 T_2)) ### Axiom % 2.34/2.54 32. (distinct_points T_0 T_2) (-. (distinct_points T_0 T_2)) ### Axiom % 2.34/2.54 33. (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 % 2.34/2.54 34. ((distinct_points T_0 T_0) /\ (distinct_points T_0 T_2)) ### And 6 % 2.34/2.54 35. ((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)))) (apart_point_and_line T_0 (line_connecting T_0 T_2)) (distinct_points T_0 T_2) ### DisjTree 32 33 34 % 2.34/2.54 36. (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) (apart_point_and_line T_0 (line_connecting T_0 T_2)) ### All 35 % 2.34/2.54 37. ((apart_point_and_line T_0 (line_connecting T_1 T_2)) => ((distinct_lines (line_connecting T_1 T_2) (line_connecting T_0 T_2)) \/ (apart_point_and_line T_0 (line_connecting T_0 T_2)))) (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))))) (-. (distinct_lines (line_connecting T_1 T_2) (line_connecting T_0 T_2))) (apart_point_and_line T_0 (line_connecting T_1 T_2)) ### DisjTree 30 31 36 % 2.34/2.54 38. (All Z, ((apart_point_and_line T_0 (line_connecting T_1 T_2)) => ((distinct_lines (line_connecting T_1 T_2) Z) \/ (apart_point_and_line T_0 Z)))) (apart_point_and_line T_0 (line_connecting T_1 T_2)) (-. (distinct_lines (line_connecting T_1 T_2) (line_connecting 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))))) (distinct_points T_0 T_2) ### All 37 % 2.34/2.54 39. (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_0 T_2) (-. (distinct_lines (line_connecting T_1 T_2) (line_connecting T_0 T_2))) (apart_point_and_line T_0 (line_connecting T_1 T_2)) (All Z, ((apart_point_and_line T_0 (line_connecting T_1 T_2)) => ((distinct_lines (line_connecting T_1 T_2) Z) \/ (apart_point_and_line T_0 Z)))) ### All 38 % 2.34/2.54 40. (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 Z, ((apart_point_and_line T_0 (line_connecting T_1 T_2)) => ((distinct_lines (line_connecting T_1 T_2) Z) \/ (apart_point_and_line T_0 Z)))) (apart_point_and_line T_0 (line_connecting T_1 T_2)) (-. (distinct_lines (line_connecting T_1 T_2) (line_connecting T_0 T_2))) (distinct_points T_0 T_2) ### All 39 % 2.34/2.54 41. (-. (apart_point_and_line T_2 (line_connecting T_1 T_2))) (apart_point_and_line T_2 (line_connecting T_1 T_2)) ### Axiom % 2.34/2.54 42. ((apart_point_and_line T_0 (line_connecting T_1 T_2)) => ((distinct_points T_0 T_2) \/ (apart_point_and_line T_2 (line_connecting T_1 T_2)))) (-. (apart_point_and_line T_2 (line_connecting T_1 T_2))) (-. (distinct_lines (line_connecting T_1 T_2) (line_connecting T_0 T_2))) (All Z, ((apart_point_and_line T_0 (line_connecting T_1 T_2)) => ((distinct_lines (line_connecting T_1 T_2) Z) \/ (apart_point_and_line T_0 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))))))) (apart_point_and_line T_0 (line_connecting T_1 T_2)) ### DisjTree 29 40 41 % 2.34/2.54 43. (All Z, ((apart_point_and_line T_0 (line_connecting T_1 T_2)) => ((distinct_points T_0 Z) \/ (apart_point_and_line Z (line_connecting T_1 T_2))))) (apart_point_and_line T_0 (line_connecting T_1 T_2)) (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 Z, ((apart_point_and_line T_0 (line_connecting T_1 T_2)) => ((distinct_lines (line_connecting T_1 T_2) Z) \/ (apart_point_and_line T_0 Z)))) (-. (distinct_lines (line_connecting T_1 T_2) (line_connecting T_0 T_2))) (-. (apart_point_and_line T_2 (line_connecting T_1 T_2))) ### All 42 % 2.34/2.54 44. (distinct_points T_2 T_2) ### Extension/test/apart1 % 2.34/2.54 45. ((distinct_points T_2 T_1) /\ (distinct_points T_2 T_2)) ### And 44 % 2.34/2.54 46. ((distinct_points T_1 T_2) => ((apart_point_and_line T_2 (line_connecting T_1 T_2)) => ((distinct_points T_2 T_1) /\ (distinct_points T_2 T_2)))) (-. (distinct_lines (line_connecting T_1 T_2) (line_connecting T_0 T_2))) (All Z, ((apart_point_and_line T_0 (line_connecting T_1 T_2)) => ((distinct_lines (line_connecting T_1 T_2) Z) \/ (apart_point_and_line T_0 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))))))) (apart_point_and_line T_0 (line_connecting T_1 T_2)) (All Z, ((apart_point_and_line T_0 (line_connecting T_1 T_2)) => ((distinct_points T_0 Z) \/ (apart_point_and_line Z (line_connecting T_1 T_2))))) (distinct_points T_1 T_2) ### DisjTree 28 43 45 % 2.34/2.54 47. (All Z, ((distinct_points T_1 T_2) => ((apart_point_and_line Z (line_connecting T_1 T_2)) => ((distinct_points Z T_1) /\ (distinct_points Z T_2))))) (distinct_points T_1 T_2) (All Z, ((apart_point_and_line T_0 (line_connecting T_1 T_2)) => ((distinct_points T_0 Z) \/ (apart_point_and_line Z (line_connecting T_1 T_2))))) (apart_point_and_line T_0 (line_connecting T_1 T_2)) (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 Z, ((apart_point_and_line T_0 (line_connecting T_1 T_2)) => ((distinct_lines (line_connecting T_1 T_2) Z) \/ (apart_point_and_line T_0 Z)))) (-. (distinct_lines (line_connecting T_1 T_2) (line_connecting T_0 T_2))) ### All 46 % 2.44/2.63 48. (All Y, (All Z, ((apart_point_and_line T_0 Y) => ((distinct_points T_0 Z) \/ (apart_point_and_line Z Y))))) (-. (distinct_lines (line_connecting T_1 T_2) (line_connecting T_0 T_2))) (All Z, ((apart_point_and_line T_0 (line_connecting T_1 T_2)) => ((distinct_lines (line_connecting T_1 T_2) Z) \/ (apart_point_and_line T_0 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))))))) (apart_point_and_line T_0 (line_connecting T_1 T_2)) (distinct_points T_1 T_2) (All Z, ((distinct_points T_1 T_2) => ((apart_point_and_line Z (line_connecting T_1 T_2)) => ((distinct_points Z T_1) /\ (distinct_points Z T_2))))) ### All 47 % 2.44/2.63 49. (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_points X Z) \/ (apart_point_and_line Z Y)))))) (All Z, ((distinct_points T_1 T_2) => ((apart_point_and_line Z (line_connecting T_1 T_2)) => ((distinct_points Z T_1) /\ (distinct_points Z T_2))))) (distinct_points T_1 T_2) (apart_point_and_line T_0 (line_connecting T_1 T_2)) (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 Z, ((apart_point_and_line T_0 (line_connecting T_1 T_2)) => ((distinct_lines (line_connecting T_1 T_2) Z) \/ (apart_point_and_line T_0 Z)))) (-. (distinct_lines (line_connecting T_1 T_2) (line_connecting T_0 T_2))) ### All 48 % 2.44/2.63 50. (All Y, (All Z, ((distinct_points T_1 Y) => ((apart_point_and_line Z (line_connecting T_1 Y)) => ((distinct_points Z T_1) /\ (distinct_points Z Y)))))) (-. (distinct_lines (line_connecting T_1 T_2) (line_connecting T_0 T_2))) (All Z, ((apart_point_and_line T_0 (line_connecting T_1 T_2)) => ((distinct_lines (line_connecting T_1 T_2) Z) \/ (apart_point_and_line T_0 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))))))) (apart_point_and_line T_0 (line_connecting T_1 T_2)) (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 49 % 2.44/2.63 51. (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) (apart_point_and_line T_0 (line_connecting T_1 T_2)) (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 Z, ((apart_point_and_line T_0 (line_connecting T_1 T_2)) => ((distinct_lines (line_connecting T_1 T_2) Z) \/ (apart_point_and_line T_0 Z)))) (-. (distinct_lines (line_connecting T_1 T_2) (line_connecting T_0 T_2))) ### All 50 % 2.44/2.63 52. (All Y, (All Z, ((apart_point_and_line T_0 Y) => ((distinct_lines Y Z) \/ (apart_point_and_line T_0 Z))))) (-. (distinct_lines (line_connecting T_1 T_2) (line_connecting T_0 T_2))) (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))))))) (apart_point_and_line T_0 (line_connecting T_1 T_2)) (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 51 % 2.44/2.63 53. (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_lines Y Z) \/ (apart_point_and_line X Z)))))) (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) (apart_point_and_line T_0 (line_connecting T_1 T_2)) (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))))))) (-. (distinct_lines (line_connecting T_1 T_2) (line_connecting T_0 T_2))) ### All 52 % 2.44/2.63 54. (-. ((distinct_lines (line_connecting T_1 T_2) (line_connecting T_0 T_1)) /\ (distinct_lines (line_connecting T_1 T_2) (line_connecting T_0 T_2)))) (distinct_points T_1 T_2) (apart_point_and_line T_0 (line_connecting T_1 T_2)) (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, ((apart_point_and_line X Y) => ((distinct_points X Z) \/ (apart_point_and_line Z Y)))))) (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_lines Y Z) \/ (apart_point_and_line X Z)))))) ### NotAnd 27 53 % 2.44/2.63 55. (-. (((distinct_points T_1 T_2) /\ (apart_point_and_line T_0 (line_connecting T_1 T_2))) => ((distinct_lines (line_connecting T_1 T_2) (line_connecting T_0 T_1)) /\ (distinct_lines (line_connecting T_1 T_2) (line_connecting T_0 T_2))))) (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_lines Y Z) \/ (apart_point_and_line 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, (All Z, ((distinct_points X Y) => ((apart_point_and_line Z (line_connecting X Y)) => ((distinct_points Z X) /\ (distinct_points Z Y))))))) ### ConjTree 54 % 2.44/2.63 56. (-. (All Z, (((distinct_points T_1 T_2) /\ (apart_point_and_line Z (line_connecting T_1 T_2))) => ((distinct_lines (line_connecting T_1 T_2) (line_connecting Z T_1)) /\ (distinct_lines (line_connecting T_1 T_2) (line_connecting Z T_2)))))) (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, ((apart_point_and_line X Y) => ((distinct_points X Z) \/ (apart_point_and_line Z Y)))))) (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_lines Y Z) \/ (apart_point_and_line X Z)))))) ### NotAllEx 55 % 2.44/2.63 57. (-. (All Y, (All Z, (((distinct_points T_1 Y) /\ (apart_point_and_line Z (line_connecting T_1 Y))) => ((distinct_lines (line_connecting T_1 Y) (line_connecting Z T_1)) /\ (distinct_lines (line_connecting T_1 Y) (line_connecting Z Y))))))) (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_lines Y Z) \/ (apart_point_and_line 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, (All Z, ((distinct_points X Y) => ((apart_point_and_line Z (line_connecting X Y)) => ((distinct_points Z X) /\ (distinct_points Z Y))))))) ### NotAllEx 56 % 2.44/2.63 58. (-. (All X, (All Y, (All Z, (((distinct_points X Y) /\ (apart_point_and_line Z (line_connecting X Y))) => ((distinct_lines (line_connecting X Y) (line_connecting Z X)) /\ (distinct_lines (line_connecting X Y) (line_connecting Z Y)))))))) (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, ((apart_point_and_line X Y) => ((distinct_points X Z) \/ (apart_point_and_line Z Y)))))) (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_lines Y Z) \/ (apart_point_and_line X Z)))))) ### NotAllEx 57 % 2.44/2.63 % SZS output end Proof % 2.44/2.63 (* END-PROOF *) %------------------------------------------------------------------------------