%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : GEO181+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 : n028.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 06:30:44 EDT 2022 % Result : Theorem 6.02s 6.22s % Output : Proof 6.19s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.11 % Problem : GEO181+3 : TPTP v8.1.0. Released v4.0.0. % 0.00/0.12 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 0.12/0.32 % Computer : n028.cluster.edu % 0.12/0.32 % Model : x86_64 x86_64 % 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.32 % Memory : 8042.1875MB % 0.12/0.32 % 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 17:58:29 EDT 2022 % 0.12/0.33 % CPUTime : % 6.02/6.22 % SZS status Theorem % 6.02/6.22 (* PROOF-FOUND *) % 6.02/6.22 (* BEGIN-PROOF *) % 6.02/6.22 % SZS output start Proof % 6.02/6.22 1. (distinct_points T_0 T_1) (-. (distinct_points T_0 T_1)) ### Axiom % 6.02/6.22 2. (distinct_points T_0 T_1) (-. (distinct_points T_0 T_1)) ### Axiom % 6.02/6.22 3. (distinct_points T_0 T_1) (-. (distinct_points T_0 T_1)) ### Axiom % 6.02/6.22 4. (-. (distinct_points T_0 T_0)) (distinct_points T_0 T_0) ### Axiom % 6.02/6.22 5. (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 % 6.02/6.22 6. (-. (distinct_points T_2 T_0)) (distinct_points T_2 T_0) ### Axiom % 6.02/6.22 7. (-. (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 % 6.02/6.22 8. ((apart_point_and_line T_2 (line_connecting T_0 T_1)) => ((distinct_points T_2 T_0) \/ (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_2 T_0)) (apart_point_and_line T_2 (line_connecting T_0 T_1)) ### DisjTree 5 6 7 % 6.02/6.22 9. (All Z, ((apart_point_and_line T_2 (line_connecting T_0 T_1)) => ((distinct_points T_2 Z) \/ (apart_point_and_line Z (line_connecting T_0 T_1))))) (apart_point_and_line T_2 (line_connecting T_0 T_1)) (-. (distinct_points T_2 T_0)) (-. (apart_point_and_line T_0 (line_connecting T_0 T_1))) ### All 8 % 6.02/6.22 10. (All Y, (All Z, ((apart_point_and_line T_2 Y) => ((distinct_points T_2 Z) \/ (apart_point_and_line Z Y))))) (-. (apart_point_and_line T_0 (line_connecting T_0 T_1))) (-. (distinct_points T_2 T_0)) (apart_point_and_line T_2 (line_connecting T_0 T_1)) ### All 9 % 6.02/6.22 11. (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_2 (line_connecting T_0 T_1)) (-. (distinct_points T_2 T_0)) (-. (apart_point_and_line T_0 (line_connecting T_0 T_1))) ### All 10 % 6.02/6.22 12. (distinct_points T_2 T_0) (-. (distinct_points T_2 T_0)) ### Axiom % 6.02/6.22 13. (distinct_points T_2 T_2) (-. (distinct_points T_2 T_2)) ### Axiom % 6.02/6.22 14. (All X, (-. (distinct_points X X))) (distinct_points T_2 T_2) ### All 13 % 6.02/6.22 15. (-. (distinct_points T_0 T_2)) (distinct_points T_0 T_2) ### Axiom % 6.02/6.22 16. ((distinct_points T_2 T_0) => ((distinct_points T_2 T_2) \/ (distinct_points T_0 T_2))) (-. (distinct_points T_0 T_2)) (All X, (-. (distinct_points X X))) (distinct_points T_2 T_0) ### DisjTree 12 14 15 % 6.02/6.22 17. (All Z, ((distinct_points T_2 T_0) => ((distinct_points T_2 Z) \/ (distinct_points T_0 Z)))) (distinct_points T_2 T_0) (All X, (-. (distinct_points X X))) (-. (distinct_points T_0 T_2)) ### All 16 % 6.02/6.22 18. (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 % 6.02/6.22 19. (distinct_points T_1 T_0) (-. (distinct_points T_1 T_0)) ### Axiom % 6.02/6.22 20. (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 % 6.02/6.22 21. (-. (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 % 6.02/6.22 22. (-. (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 % 6.02/6.23 23. (-. (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 % 6.02/6.23 24. (-. (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 % 6.02/6.23 25. (((distinct_points T_1 T_0) /\ (distinct_lines (line_connecting T_0 T_1) (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)) \/ ((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_0 (line_connecting T_0 T_2))) (-. (apart_point_and_line T_0 (line_connecting T_0 T_1))) (-. (apart_point_and_line T_1 (line_connecting T_0 T_2))) (-. (apart_point_and_line T_1 (line_connecting T_0 T_1))) (distinct_lines (line_connecting T_0 T_1) (line_connecting T_0 T_2)) (distinct_points T_1 T_0) ### DisjTree 19 20 21 22 23 24 % 6.02/6.23 26. (All V, (((distinct_points T_1 T_0) /\ (distinct_lines (line_connecting T_0 T_1) V)) => ((apart_point_and_line T_1 (line_connecting T_0 T_1)) \/ ((apart_point_and_line T_1 V) \/ ((apart_point_and_line T_0 (line_connecting T_0 T_1)) \/ (apart_point_and_line T_0 V)))))) (distinct_points T_1 T_0) (distinct_lines (line_connecting T_0 T_1) (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))) (-. (apart_point_and_line T_0 (line_connecting T_0 T_1))) (-. (apart_point_and_line T_0 (line_connecting T_0 T_2))) ### All 25 % 6.02/6.23 27. (All U, (All V, (((distinct_points T_1 T_0) /\ (distinct_lines U V)) => ((apart_point_and_line T_1 U) \/ ((apart_point_and_line T_1 V) \/ ((apart_point_and_line T_0 U) \/ (apart_point_and_line T_0 V))))))) (-. (apart_point_and_line T_0 (line_connecting T_0 T_2))) (-. (apart_point_and_line T_0 (line_connecting T_0 T_1))) (-. (apart_point_and_line T_1 (line_connecting T_0 T_2))) (-. (apart_point_and_line T_1 (line_connecting T_0 T_1))) (distinct_lines (line_connecting T_0 T_1) (line_connecting T_0 T_2)) (distinct_points T_1 T_0) ### All 26 % 6.02/6.23 28. (-. (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 % 6.02/6.23 29. ((apart_point_and_line T_2 (line_connecting T_0 T_1)) => ((distinct_lines (line_connecting T_0 T_1) (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_2))) (distinct_points T_1 T_0) (-. (apart_point_and_line T_1 (line_connecting T_0 T_1))) (-. (apart_point_and_line 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))) (All U, (All V, (((distinct_points T_1 T_0) /\ (distinct_lines U V)) => ((apart_point_and_line T_1 U) \/ ((apart_point_and_line T_1 V) \/ ((apart_point_and_line T_0 U) \/ (apart_point_and_line T_0 V))))))) (apart_point_and_line T_2 (line_connecting T_0 T_1)) ### DisjTree 18 27 28 % 6.02/6.23 30. (All Z, ((apart_point_and_line T_2 (line_connecting T_0 T_1)) => ((distinct_lines (line_connecting T_0 T_1) Z) \/ (apart_point_and_line T_2 Z)))) (apart_point_and_line T_2 (line_connecting T_0 T_1)) (All U, (All V, (((distinct_points T_1 T_0) /\ (distinct_lines U V)) => ((apart_point_and_line T_1 U) \/ ((apart_point_and_line T_1 V) \/ ((apart_point_and_line T_0 U) \/ (apart_point_and_line T_0 V))))))) (-. (apart_point_and_line T_0 (line_connecting T_0 T_2))) (-. (apart_point_and_line T_0 (line_connecting T_0 T_1))) (-. (apart_point_and_line T_1 (line_connecting T_0 T_2))) (-. (apart_point_and_line T_1 (line_connecting T_0 T_1))) (distinct_points T_1 T_0) (-. (apart_point_and_line T_2 (line_connecting T_0 T_2))) ### All 29 % 6.02/6.23 31. ((distinct_points T_0 T_2) => (-. (apart_point_and_line T_0 (line_connecting T_0 T_2)))) (-. (apart_point_and_line T_2 (line_connecting T_0 T_2))) (distinct_points T_1 T_0) (-. (apart_point_and_line T_1 (line_connecting T_0 T_1))) (-. (apart_point_and_line 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_1 T_0) /\ (distinct_lines U V)) => ((apart_point_and_line T_1 U) \/ ((apart_point_and_line T_1 V) \/ ((apart_point_and_line T_0 U) \/ (apart_point_and_line T_0 V))))))) (apart_point_and_line T_2 (line_connecting T_0 T_1)) (All Z, ((apart_point_and_line T_2 (line_connecting T_0 T_1)) => ((distinct_lines (line_connecting T_0 T_1) Z) \/ (apart_point_and_line T_2 Z)))) (All X, (-. (distinct_points X X))) (distinct_points T_2 T_0) (All Z, ((distinct_points T_2 T_0) => ((distinct_points T_2 Z) \/ (distinct_points T_0 Z)))) ### Imply 17 30 % 6.02/6.23 32. (All Y, ((distinct_points T_0 Y) => (-. (apart_point_and_line T_0 (line_connecting T_0 Y))))) (All Z, ((distinct_points T_2 T_0) => ((distinct_points T_2 Z) \/ (distinct_points T_0 Z)))) (distinct_points T_2 T_0) (All X, (-. (distinct_points X X))) (All Z, ((apart_point_and_line T_2 (line_connecting T_0 T_1)) => ((distinct_lines (line_connecting T_0 T_1) Z) \/ (apart_point_and_line T_2 Z)))) (apart_point_and_line T_2 (line_connecting T_0 T_1)) (All U, (All V, (((distinct_points T_1 T_0) /\ (distinct_lines U V)) => ((apart_point_and_line T_1 U) \/ ((apart_point_and_line T_1 V) \/ ((apart_point_and_line T_0 U) \/ (apart_point_and_line T_0 V))))))) (-. (apart_point_and_line T_0 (line_connecting T_0 T_1))) (-. (apart_point_and_line T_1 (line_connecting T_0 T_2))) (-. (apart_point_and_line T_1 (line_connecting T_0 T_1))) (distinct_points T_1 T_0) (-. (apart_point_and_line T_2 (line_connecting T_0 T_2))) ### All 31 % 6.19/6.44 33. ((distinct_points T_0 T_2) => (-. (apart_point_and_line T_2 (line_connecting T_0 T_2)))) (distinct_points T_1 T_0) (-. (apart_point_and_line T_1 (line_connecting T_0 T_1))) (-. (apart_point_and_line 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_1 T_0) /\ (distinct_lines U V)) => ((apart_point_and_line T_1 U) \/ ((apart_point_and_line T_1 V) \/ ((apart_point_and_line T_0 U) \/ (apart_point_and_line T_0 V))))))) (apart_point_and_line T_2 (line_connecting T_0 T_1)) (All Z, ((apart_point_and_line T_2 (line_connecting T_0 T_1)) => ((distinct_lines (line_connecting T_0 T_1) Z) \/ (apart_point_and_line T_2 Z)))) (All Y, ((distinct_points T_0 Y) => (-. (apart_point_and_line T_0 (line_connecting T_0 Y))))) (All X, (-. (distinct_points X X))) (distinct_points T_2 T_0) (All Z, ((distinct_points T_2 T_0) => ((distinct_points T_2 Z) \/ (distinct_points T_0 Z)))) ### Imply 17 32 % 6.19/6.44 34. (All Y, ((distinct_points T_0 Y) => (-. (apart_point_and_line Y (line_connecting T_0 Y))))) (All Z, ((distinct_points T_2 T_0) => ((distinct_points T_2 Z) \/ (distinct_points T_0 Z)))) (distinct_points T_2 T_0) (All X, (-. (distinct_points X X))) (All Y, ((distinct_points T_0 Y) => (-. (apart_point_and_line T_0 (line_connecting T_0 Y))))) (All Z, ((apart_point_and_line T_2 (line_connecting T_0 T_1)) => ((distinct_lines (line_connecting T_0 T_1) Z) \/ (apart_point_and_line T_2 Z)))) (apart_point_and_line T_2 (line_connecting T_0 T_1)) (All U, (All V, (((distinct_points T_1 T_0) /\ (distinct_lines U V)) => ((apart_point_and_line T_1 U) \/ ((apart_point_and_line T_1 V) \/ ((apart_point_and_line T_0 U) \/ (apart_point_and_line T_0 V))))))) (-. (apart_point_and_line T_0 (line_connecting T_0 T_1))) (-. (apart_point_and_line T_1 (line_connecting T_0 T_2))) (-. (apart_point_and_line T_1 (line_connecting T_0 T_1))) (distinct_points T_1 T_0) ### All 33 % 6.19/6.44 35. (-. (distinct_points T_0 T_0)) (distinct_points T_0 T_0) ### Axiom % 6.19/6.44 36. ((distinct_points T_2 T_0) => ((distinct_points T_2 T_0) \/ (distinct_points T_0 T_0))) (-. (distinct_points T_0 T_0)) (distinct_points T_1 T_0) (-. (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 U, (All V, (((distinct_points T_1 T_0) /\ (distinct_lines U V)) => ((apart_point_and_line T_1 U) \/ ((apart_point_and_line T_1 V) \/ ((apart_point_and_line T_0 U) \/ (apart_point_and_line T_0 V))))))) (All Z, ((apart_point_and_line T_2 (line_connecting T_0 T_1)) => ((distinct_lines (line_connecting T_0 T_1) Z) \/ (apart_point_and_line T_2 Z)))) (All Y, ((distinct_points T_0 Y) => (-. (apart_point_and_line T_0 (line_connecting T_0 Y))))) (All X, (-. (distinct_points X X))) (All Z, ((distinct_points T_2 T_0) => ((distinct_points T_2 Z) \/ (distinct_points T_0 Z)))) (All Y, ((distinct_points T_0 Y) => (-. (apart_point_and_line Y (line_connecting T_0 Y))))) (-. (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 X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_points X Z) \/ (apart_point_and_line Z Y)))))) ### DisjTree 11 34 35 % 6.19/6.44 37. (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_2 (line_connecting T_0 T_1)) (-. (apart_point_and_line T_0 (line_connecting T_0 T_1))) (All Y, ((distinct_points T_0 Y) => (-. (apart_point_and_line Y (line_connecting T_0 Y))))) (All Z, ((distinct_points T_2 T_0) => ((distinct_points T_2 Z) \/ (distinct_points T_0 Z)))) (All X, (-. (distinct_points X X))) (All Y, ((distinct_points T_0 Y) => (-. (apart_point_and_line T_0 (line_connecting T_0 Y))))) (All Z, ((apart_point_and_line T_2 (line_connecting T_0 T_1)) => ((distinct_lines (line_connecting T_0 T_1) Z) \/ (apart_point_and_line T_2 Z)))) (All U, (All V, (((distinct_points T_1 T_0) /\ (distinct_lines U V)) => ((apart_point_and_line T_1 U) \/ ((apart_point_and_line T_1 V) \/ ((apart_point_and_line T_0 U) \/ (apart_point_and_line T_0 V))))))) (-. (apart_point_and_line T_1 (line_connecting T_0 T_2))) (-. (apart_point_and_line T_1 (line_connecting T_0 T_1))) (distinct_points T_1 T_0) (-. (distinct_points T_0 T_0)) ### All 36 % 6.19/6.44 38. (All Y, (All Z, ((distinct_points T_2 Y) => ((distinct_points T_2 Z) \/ (distinct_points Y Z))))) (-. (distinct_points T_0 T_0)) (distinct_points T_1 T_0) (-. (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 U, (All V, (((distinct_points T_1 T_0) /\ (distinct_lines U V)) => ((apart_point_and_line T_1 U) \/ ((apart_point_and_line T_1 V) \/ ((apart_point_and_line T_0 U) \/ (apart_point_and_line T_0 V))))))) (All Z, ((apart_point_and_line T_2 (line_connecting T_0 T_1)) => ((distinct_lines (line_connecting T_0 T_1) Z) \/ (apart_point_and_line T_2 Z)))) (All Y, ((distinct_points T_0 Y) => (-. (apart_point_and_line T_0 (line_connecting T_0 Y))))) (All X, (-. (distinct_points X X))) (All Y, ((distinct_points T_0 Y) => (-. (apart_point_and_line Y (line_connecting T_0 Y))))) (-. (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 X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_points X Z) \/ (apart_point_and_line Z Y)))))) ### All 37 % 6.19/6.44 39. (All X, (All Y, (All Z, ((distinct_points X Y) => ((distinct_points X Z) \/ (distinct_points Y Z)))))) (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_2 (line_connecting T_0 T_1)) (-. (apart_point_and_line T_0 (line_connecting T_0 T_1))) (All Y, ((distinct_points T_0 Y) => (-. (apart_point_and_line Y (line_connecting T_0 Y))))) (All X, (-. (distinct_points X X))) (All Y, ((distinct_points T_0 Y) => (-. (apart_point_and_line T_0 (line_connecting T_0 Y))))) (All Z, ((apart_point_and_line T_2 (line_connecting T_0 T_1)) => ((distinct_lines (line_connecting T_0 T_1) Z) \/ (apart_point_and_line T_2 Z)))) (All U, (All V, (((distinct_points T_1 T_0) /\ (distinct_lines U V)) => ((apart_point_and_line T_1 U) \/ ((apart_point_and_line T_1 V) \/ ((apart_point_and_line T_0 U) \/ (apart_point_and_line T_0 V))))))) (-. (apart_point_and_line T_1 (line_connecting T_0 T_2))) (-. (apart_point_and_line T_1 (line_connecting T_0 T_1))) (distinct_points T_1 T_0) (-. (distinct_points T_0 T_0)) ### All 38 % 6.19/6.44 40. (All Y, (All Z, ((apart_point_and_line T_2 Y) => ((distinct_lines Y Z) \/ (apart_point_and_line T_2 Z))))) (-. (distinct_points T_0 T_0)) (distinct_points T_1 T_0) (-. (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 U, (All V, (((distinct_points T_1 T_0) /\ (distinct_lines U V)) => ((apart_point_and_line T_1 U) \/ ((apart_point_and_line T_1 V) \/ ((apart_point_and_line T_0 U) \/ (apart_point_and_line T_0 V))))))) (All Y, ((distinct_points T_0 Y) => (-. (apart_point_and_line T_0 (line_connecting T_0 Y))))) (All X, (-. (distinct_points X X))) (All Y, ((distinct_points T_0 Y) => (-. (apart_point_and_line Y (line_connecting T_0 Y))))) (-. (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 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) => ((distinct_points X Z) \/ (distinct_points Y Z)))))) ### All 39 % 6.19/6.44 41. (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, ((distinct_points X Y) => ((distinct_points X Z) \/ (distinct_points Y Z)))))) (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_2 (line_connecting T_0 T_1)) (-. (apart_point_and_line T_0 (line_connecting T_0 T_1))) (All Y, ((distinct_points T_0 Y) => (-. (apart_point_and_line Y (line_connecting T_0 Y))))) (All X, (-. (distinct_points X X))) (All Y, ((distinct_points T_0 Y) => (-. (apart_point_and_line T_0 (line_connecting T_0 Y))))) (All U, (All V, (((distinct_points T_1 T_0) /\ (distinct_lines U V)) => ((apart_point_and_line T_1 U) \/ ((apart_point_and_line T_1 V) \/ ((apart_point_and_line T_0 U) \/ (apart_point_and_line T_0 V))))))) (-. (apart_point_and_line T_1 (line_connecting T_0 T_2))) (-. (apart_point_and_line T_1 (line_connecting T_0 T_1))) (distinct_points T_1 T_0) (-. (distinct_points T_0 T_0)) ### All 40 % 6.19/6.45 42. (All Y, (All U, (All V, (((distinct_points T_1 Y) /\ (distinct_lines U V)) => ((apart_point_and_line T_1 U) \/ ((apart_point_and_line T_1 V) \/ ((apart_point_and_line Y U) \/ (apart_point_and_line Y V)))))))) (-. (distinct_points T_0 T_0)) (distinct_points T_1 T_0) (-. (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 Y, ((distinct_points T_0 Y) => (-. (apart_point_and_line T_0 (line_connecting T_0 Y))))) (All X, (-. (distinct_points X X))) (All Y, ((distinct_points T_0 Y) => (-. (apart_point_and_line Y (line_connecting T_0 Y))))) (-. (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 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) => ((distinct_points X Z) \/ (distinct_points Y Z)))))) (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_lines Y Z) \/ (apart_point_and_line X Z)))))) ### All 41 % 6.19/6.45 43. (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, ((apart_point_and_line X Y) => ((distinct_lines Y Z) \/ (apart_point_and_line X Z)))))) (All X, (All Y, (All Z, ((distinct_points X Y) => ((distinct_points X Z) \/ (distinct_points Y Z)))))) (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_2 (line_connecting T_0 T_1)) (-. (apart_point_and_line T_0 (line_connecting T_0 T_1))) (All Y, ((distinct_points T_0 Y) => (-. (apart_point_and_line Y (line_connecting T_0 Y))))) (All X, (-. (distinct_points X X))) (All Y, ((distinct_points T_0 Y) => (-. (apart_point_and_line T_0 (line_connecting T_0 Y))))) (-. (apart_point_and_line T_1 (line_connecting T_0 T_2))) (-. (apart_point_and_line T_1 (line_connecting T_0 T_1))) (distinct_points T_1 T_0) (-. (distinct_points T_0 T_0)) ### All 42 % 6.19/6.45 44. ((distinct_points T_0 T_1) => ((distinct_points T_0 T_0) \/ (distinct_points T_1 T_0))) (-. (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 Y, ((distinct_points T_0 Y) => (-. (apart_point_and_line T_0 (line_connecting T_0 Y))))) (All X, (-. (distinct_points X X))) (All Y, ((distinct_points T_0 Y) => (-. (apart_point_and_line Y (line_connecting T_0 Y))))) (-. (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 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) => ((distinct_points X Z) \/ (distinct_points Y Z)))))) (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 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_0 T_0)) (distinct_points T_0 T_1) ### DisjTree 3 4 43 % 6.19/6.45 45. (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_0)) (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, ((apart_point_and_line X Y) => ((distinct_lines Y Z) \/ (apart_point_and_line X Z)))))) (All X, (All Y, (All Z, ((distinct_points X Y) => ((distinct_points X Z) \/ (distinct_points Y Z)))))) (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_2 (line_connecting T_0 T_1)) (-. (apart_point_and_line T_0 (line_connecting T_0 T_1))) (All Y, ((distinct_points T_0 Y) => (-. (apart_point_and_line Y (line_connecting T_0 Y))))) (All X, (-. (distinct_points X X))) (All Y, ((distinct_points T_0 Y) => (-. (apart_point_and_line T_0 (line_connecting T_0 Y))))) (-. (apart_point_and_line T_1 (line_connecting T_0 T_2))) (-. (apart_point_and_line T_1 (line_connecting T_0 T_1))) ### All 44 % 6.19/6.45 46. (-. (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 Y, ((distinct_points T_0 Y) => (-. (apart_point_and_line T_0 (line_connecting T_0 Y))))) (All X, (-. (distinct_points X X))) (All Y, ((distinct_points T_0 Y) => (-. (apart_point_and_line Y (line_connecting T_0 Y))))) (-. (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 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) => ((distinct_points X Z) \/ (distinct_points Y Z)))))) (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 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_0 T_1) (All Z, ((distinct_points T_0 T_1) => ((distinct_points T_0 Z) \/ (distinct_points T_1 Z)))) ### All 45 % 6.19/6.45 47. ((distinct_points T_0 T_1) => (-. (apart_point_and_line T_1 (line_connecting T_0 T_1)))) (All Z, ((distinct_points T_0 T_1) => ((distinct_points T_0 Z) \/ (distinct_points T_1 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, ((apart_point_and_line X Y) => ((distinct_lines Y Z) \/ (apart_point_and_line X Z)))))) (All X, (All Y, (All Z, ((distinct_points X Y) => ((distinct_points X Z) \/ (distinct_points Y Z)))))) (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_2 (line_connecting T_0 T_1)) (-. (apart_point_and_line T_0 (line_connecting T_0 T_1))) (All Y, ((distinct_points T_0 Y) => (-. (apart_point_and_line Y (line_connecting T_0 Y))))) (All X, (-. (distinct_points X X))) (All Y, ((distinct_points T_0 Y) => (-. (apart_point_and_line T_0 (line_connecting T_0 Y))))) (-. (apart_point_and_line T_1 (line_connecting T_0 T_2))) (distinct_points T_0 T_1) ### Imply 2 46 % 6.19/6.45 48. (distinct_points T_0 T_1) (-. (apart_point_and_line T_1 (line_connecting T_0 T_2))) (All Y, ((distinct_points T_0 Y) => (-. (apart_point_and_line T_0 (line_connecting T_0 Y))))) (All X, (-. (distinct_points X X))) (All Y, ((distinct_points T_0 Y) => (-. (apart_point_and_line Y (line_connecting T_0 Y))))) (-. (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 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) => ((distinct_points X Z) \/ (distinct_points Y Z)))))) (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 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 Z, ((distinct_points T_0 T_1) => ((distinct_points T_0 Z) \/ (distinct_points T_1 Z)))) ### All 47 % 6.19/6.45 49. ((distinct_points T_0 T_1) => (-. (apart_point_and_line T_0 (line_connecting T_0 T_1)))) (All Z, ((distinct_points T_0 T_1) => ((distinct_points T_0 Z) \/ (distinct_points T_1 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, ((apart_point_and_line X Y) => ((distinct_lines Y Z) \/ (apart_point_and_line X Z)))))) (All X, (All Y, (All Z, ((distinct_points X Y) => ((distinct_points X Z) \/ (distinct_points Y Z)))))) (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_2 (line_connecting T_0 T_1)) (All Y, ((distinct_points T_0 Y) => (-. (apart_point_and_line Y (line_connecting T_0 Y))))) (All X, (-. (distinct_points X X))) (All Y, ((distinct_points T_0 Y) => (-. (apart_point_and_line T_0 (line_connecting T_0 Y))))) (-. (apart_point_and_line T_1 (line_connecting T_0 T_2))) (distinct_points T_0 T_1) ### Imply 1 48 % 6.19/6.45 50. (distinct_points T_0 T_1) (-. (apart_point_and_line T_1 (line_connecting T_0 T_2))) (All Y, ((distinct_points T_0 Y) => (-. (apart_point_and_line T_0 (line_connecting T_0 Y))))) (All X, (-. (distinct_points X X))) (All Y, ((distinct_points T_0 Y) => (-. (apart_point_and_line Y (line_connecting T_0 Y))))) (apart_point_and_line T_2 (line_connecting 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)))))) (All X, (All Y, (All Z, ((distinct_points X Y) => ((distinct_points X Z) \/ (distinct_points Y Z)))))) (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 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 Z, ((distinct_points T_0 T_1) => ((distinct_points T_0 Z) \/ (distinct_points T_1 Z)))) ### All 49 % 6.19/6.45 51. (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line Y (line_connecting X Y)))))) (All Z, ((distinct_points T_0 T_1) => ((distinct_points T_0 Z) \/ (distinct_points T_1 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, ((apart_point_and_line X Y) => ((distinct_lines Y Z) \/ (apart_point_and_line X Z)))))) (All X, (All Y, (All Z, ((distinct_points X Y) => ((distinct_points X Z) \/ (distinct_points Y Z)))))) (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_2 (line_connecting T_0 T_1)) (All X, (-. (distinct_points X X))) (All Y, ((distinct_points T_0 Y) => (-. (apart_point_and_line T_0 (line_connecting T_0 Y))))) (-. (apart_point_and_line T_1 (line_connecting T_0 T_2))) (distinct_points T_0 T_1) ### All 50 % 6.19/6.45 52. (All Y, (All Z, ((distinct_points T_0 Y) => ((distinct_points T_0 Z) \/ (distinct_points Y Z))))) (distinct_points T_0 T_1) (-. (apart_point_and_line T_1 (line_connecting T_0 T_2))) (All Y, ((distinct_points T_0 Y) => (-. (apart_point_and_line T_0 (line_connecting T_0 Y))))) (All X, (-. (distinct_points X X))) (apart_point_and_line T_2 (line_connecting 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)))))) (All X, (All Y, (All Z, ((distinct_points X Y) => ((distinct_points X Z) \/ (distinct_points Y Z)))))) (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 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 Y (line_connecting X Y)))))) ### All 51 % 6.19/6.45 53. (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 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, ((apart_point_and_line X Y) => ((distinct_lines Y Z) \/ (apart_point_and_line X Z)))))) (All X, (All Y, (All Z, ((distinct_points X Y) => ((distinct_points X Z) \/ (distinct_points Y Z)))))) (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_2 (line_connecting T_0 T_1)) (All X, (-. (distinct_points X X))) (-. (apart_point_and_line T_1 (line_connecting T_0 T_2))) (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 52 % 6.19/6.45 54. (distinct_points T_0 T_1) (-. (apart_point_and_line T_1 (line_connecting T_0 T_2))) (All X, (-. (distinct_points X X))) (apart_point_and_line T_2 (line_connecting 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)))))) (All X, (All Y, (All Z, ((distinct_points X Y) => ((distinct_points X Z) \/ (distinct_points Y Z)))))) (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 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 Y (line_connecting X Y)))))) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line X (line_connecting X Y)))))) ### All 53 % 6.19/6.45 55. (-. ((distinct_points T_0 T_1) => ((apart_point_and_line T_2 (line_connecting T_0 T_1)) => (apart_point_and_line 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)))))) (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, ((apart_point_and_line X Y) => ((distinct_lines Y Z) \/ (apart_point_and_line X Z)))))) (All X, (All Y, (All Z, ((distinct_points X Y) => ((distinct_points X Z) \/ (distinct_points Y 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, (-. (distinct_points X X))) ### ConjTree 54 % 6.19/6.45 56. (-. (All Z, ((distinct_points T_0 T_1) => ((apart_point_and_line Z (line_connecting T_0 T_1)) => (apart_point_and_line T_1 (line_connecting T_0 Z)))))) (All X, (-. (distinct_points X X))) (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) => ((distinct_points X Z) \/ (distinct_points Y Z)))))) (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 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 Y (line_connecting X Y)))))) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line X (line_connecting X Y)))))) ### NotAllEx 55 % 6.19/6.46 57. (-. (All Y, (All Z, ((distinct_points T_0 Y) => ((apart_point_and_line Z (line_connecting T_0 Y)) => (apart_point_and_line Y (line_connecting T_0 Z))))))) (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 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, ((apart_point_and_line X Y) => ((distinct_lines Y Z) \/ (apart_point_and_line X Z)))))) (All X, (All Y, (All Z, ((distinct_points X Y) => ((distinct_points X Z) \/ (distinct_points Y 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, (-. (distinct_points X X))) ### NotAllEx 56 % 6.19/6.46 58. (-. (All X, (All Y, (All Z, ((distinct_points X Y) => ((apart_point_and_line Z (line_connecting X Y)) => (apart_point_and_line Y (line_connecting X Z)))))))) (All X, (-. (distinct_points X X))) (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) => ((distinct_points X Z) \/ (distinct_points Y Z)))))) (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 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 Y (line_connecting X Y)))))) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line X (line_connecting X Y)))))) ### NotAllEx 57 % 6.19/6.46 % SZS output end Proof % 6.19/6.46 (* END-PROOF *) %------------------------------------------------------------------------------